Subgroups — #72341430

Order 2048.

At least 12254 conjugacy classes of subgroups; only the 4044 normal subgroups are shown.

The subgroup lattice has 1174 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341411	C₂	1	8	yes	maximal, complemented
2	#72341408	C₂	1	4	yes	maximal, complemented
3	#72341405	C₂	1	2	yes	maximal, complemented
4	#72341403	C₂	1	2	yes	maximal, complemented
5	#72341401	C₂	1	2	yes	maximal, complemented
6	#72341394	C₂	1	4	yes	maximal, complemented
7	#72341388	C₂	1	2	yes	maximal, complemented
8	#72341381	C₂	1	2	yes	maximal, complemented
9	#72318522	C₂	1	2	yes	maximal, complemented
10	#72318494	C₂	1	2	yes	maximal, complemented
11	#72318026	C₂	1	8	yes	maximal, complemented
12	#72312346	C₂	1	4	yes	maximal, complemented
13	#72312153	C₂	1	1	yes	maximal, characteristic, complemented
14	#72311315	C₂	1	2	yes	maximal, complemented
15	#72311246	C₂	1	2	yes	maximal, complemented
16	#72311231	C₂	1	2	yes	maximal, complemented
17	#72306899	C₂	1	1	yes	maximal, characteristic, complemented
18	#72303059	C₂	1	1	yes	maximal, characteristic, complemented
19	#72285500	C₂	1	2	yes	maximal, complemented
20	#72262180	C₂	1	2	yes	maximal, complemented
21	#72249425	C₂	1	4	yes	maximal, complemented
22	#72236706	C₂	1	1	yes	maximal, characteristic, complemented
23	#72236657	C₂	1	1	yes	maximal, characteristic, complemented
24	#72234146	C₂	1	1	yes	maximal, characteristic, complemented
25	#72215857	C₂	1	1	yes	maximal, characteristic, complemented
26	#10586097	C₂²	1	1	yes	characteristic, complemented
27	C₂×#60388	C₂²	1	1	yes	characteristic
28	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
29	#9910000	C₂²	1	4	yes	complemented
30	#9909812	C₂²	1	4	yes	complemented
31	#8926850	C₂²	1	2	yes	complemented
32	#8926849	C₂²	1	2	yes	complemented
33	#8757069	C₂²	1	2	yes	complemented
34	#7989737	C₂²	1	2	yes	complemented
35	#7989726	C₂²	1	2	yes	complemented
36	#7985329	C₂²	1	2	yes	complemented
37	#7985088	C₂²	1	2	yes	complemented
38	#7743195	C₂²	1	2	yes	—
39	#7737652	C₂²	1	1	yes	characteristic, complemented
40	#7737412	C₂²	1	2	yes	complemented
41	#7737411	C₂²	1	1	yes	characteristic, complemented
42	#7711121	C₂²	1	2	yes	complemented
43	#7672751	C₂²	1	1	yes	characteristic
44	C₂×#33557	C₂²	1	4	yes	complemented
45	C₂²×#2198	C₂²	1	2	yes	complemented
46	C₂²×#2196	C₂²	1	2	yes	complemented
47	#6629397	C₂²	1	4	yes	complemented
48	#6628970	C₂²	1	1	yes	characteristic, complemented
49	#6628900	C₂²	1	4	yes	complemented
50	#6628897	C₂²	1	2	yes	complemented
51	#6628896	C₂²	1	2	yes	complemented
52	#6628872	C₂²	1	1	yes	characteristic, complemented
53	#6628872	C₂²	1	1	yes	characteristic, complemented
54	#6591510	C₂²	1	8	yes	complemented
55	#6591506	C₂²	1	8	yes	complemented
56	#6573719	C₂²	1	8	yes	complemented
57	#6573715	C₂²	1	8	yes	complemented
58	#6573693	C₂²	1	4	yes	complemented
59	#6573693	C₂²	1	4	yes	complemented
60	D₄×#453	C₂²	1	4	yes	—
61	D₄×#453	C₂²	1	4	yes	complemented
62	#6487655	C₂²	1	4	yes	complemented
63	#6470246	C₂²	1	4	yes	complemented
64	#6470235	C₂²	1	2	yes	complemented
65	#6470234	C₂²	1	2	yes	complemented
66	#6443331	C₂²	1	1	yes	characteristic, complemented
67	#6442555	C₂²	1	1	yes	characteristic, complemented
68	#6437969	C₂²	1	1	yes	characteristic, complemented
69	#6437969	C₂²	1	1	yes	characteristic, complemented
70	#6437452	C₂²	1	1	yes	characteristic
71	#6437452	C₂²	1	1	yes	characteristic, complemented
72	#6385980	C₂²	1	2	yes	complemented
73	#6379033	C₂²	1	1	yes	characteristic, complemented
74	C₄×#3018	C₂²	1	1	yes	characteristic, complemented
75	#512122	C₂²	1	2	yes	complemented
76	#512122	C₂²	1	2	yes	complemented
77	#512116	C₂²	1	4	yes	complemented
78	#511916	C₂²	1	4	yes	complemented
79	#511914	C₂²	1	4	yes	complemented
80	#511785	C₂²	1	4	yes	complemented
81	#511773	C₂²	1	2	yes	complemented
82	#511771	C₂²	1	2	yes	complemented
83	#508200	C₂²	1	8	yes	complemented
84	#508099	C₂²	1	8	yes	complemented
85	#508096	C₂²	1	4	yes	complemented
86	#508095	C₂²	1	4	yes	complemented
87	#503582	C₂²	1	4	yes	complemented
88	#503243	C₂²	1	8	yes	complemented
89	#503237	C₂²	1	8	yes	complemented
90	#503198	C₂²	1	4	yes	complemented
91	#502832	C₂²	1	8	yes	complemented
92	#502830	C₂²	1	8	yes	complemented
93	#502785	C₂²	1	8	yes	complemented
94	#502731	C₂²	1	8	yes	complemented
95	#502725	C₂²	1	8	yes	complemented
96	#502723	C₂²	1	8	yes	complemented
97	#502717	C₂²	1	8	yes	complemented
98	#501176	C₂²	1	8	yes	complemented
99	#501175	C₂²	1	8	yes	complemented
100	#501169	C₂²	1	8	yes	complemented
101	#501166	C₂²	1	8	yes	complemented
102	#501103	C₂²	1	8	yes	complemented
103	#501099	C₂²	1	4	yes	complemented
104	#501097	C₂²	1	4	yes	complemented
105	#501086	C₂²	1	4	yes	complemented
106	#501086	C₂²	1	4	yes	complemented
107	#501084	C₂²	1	4	yes	complemented
108	#501084	C₂²	1	4	yes	complemented
109	#500958	C₂²	1	4	yes	complemented
110	#500828	C₂²	1	8	yes	complemented
111	#500822	C₂²	1	8	yes	complemented
112	#500773	C₂²	1	4	yes	complemented
113	#500541	C₂²	1	8	yes	complemented
114	#500539	C₂²	1	8	yes	complemented
115	#500494	C₂²	1	8	yes	complemented
116	#500368	C₂²	1	4	yes	complemented
117	#500191	C₂²	1	4	yes	complemented
118	#500180	C₂²	1	2	yes	complemented
119	#500179	C₂²	1	2	yes	complemented
120	#500175	C₂²	1	2	yes	complemented
121	#500174	C₂²	1	2	yes	complemented
122	#500079	C₂²	1	8	yes	complemented
123	#500073	C₂²	1	8	yes	complemented
124	#500071	C₂²	1	8	yes	complemented
125	#500065	C₂²	1	8	yes	complemented
126	#500020	C₂²	1	4	yes	complemented
127	#500020	C₂²	1	4	yes	complemented
128	#500020	C₂²	1	4	yes	complemented
129	#499846	C₂²	1	2	yes	complemented
130	#499846	C₂²	1	2	yes	complemented
131	#499846	C₂²	1	2	yes	complemented
132	#499845	C₂²	1	4	yes	complemented
133	#499845	C₂²	1	4	yes	complemented
134	#499844	C₂²	1	2	yes	—
135	#499844	C₂²	1	2	yes	complemented
136	#499844	C₂²	1	2	yes	complemented
137	#499843	C₂²	1	4	yes	complemented
138	#499843	C₂²	1	4	yes	complemented
139	#499838	C₂²	1	8	yes	complemented
140	#499837	C₂²	1	4	yes	complemented
141	#499837	C₂²	1	4	yes	complemented
142	#499837	C₂²	1	4	yes	complemented
143	#499834	C₂²	1	4	yes	complemented
144	#499833	C₂²	1	2	yes	complemented
145	#499833	C₂²	1	2	yes	complemented
146	#499833	C₂²	1	2	yes	complemented
147	#499832	C₂²	1	4	yes	complemented
148	#499831	C₂²	1	2	yes	complemented
149	#499831	C₂²	1	2	yes	complemented
150	#499831	C₂²	1	2	yes	complemented
151	#499809	C₂²	1	8	yes	complemented
152	#499804	C₂²	1	8	yes	complemented
153	#499800	C₂²	1	8	yes	complemented
154	#499797	C₂²	1	8	yes	complemented
155	#499289	C₂²	1	8	yes	complemented
156	#498931	C₂²	1	8	yes	complemented
157	#498928	C₂²	1	4	yes	complemented
158	#498927	C₂²	1	4	yes	complemented
159	#497516	C₂²	1	8	yes	complemented
160	#497514	C₂²	1	8	yes	complemented
161	#497355	C₂²	1	8	yes	complemented
162	#497353	C₂²	1	8	yes	complemented
163	#497307	C₂²	1	4	yes	complemented
164	#497307	C₂²	1	4	yes	complemented
165	D₄×#353	C₂²	1	4	yes	complemented
166	D₄×#353	C₂²	1	4	yes	complemented
167	#496515	C₂²	1	4	yes	complemented
168	#496311	C₂²	1	2	yes	complemented
169	#496246	C₂²	1	4	yes	complemented
170	#496241	C₂²	1	2	yes	complemented
171	#496240	C₂²	1	2	yes	complemented
172	#496203	C₂²	1	2	yes	complemented
173	#496203	C₂²	1	2	yes	complemented
174	#495746	C₂²	1	4	yes	complemented
175	#495744	C₂²	1	4	yes	complemented
176	#495586	C₂²	1	4	yes	complemented
177	#494685	C₂²	1	4	yes	complemented
178	#494682	C₂²	1	2	yes	complemented
179	#494681	C₂²	1	2	yes	complemented
180	#494596	C₂²	1	2	yes	complemented
181	#494596	C₂²	1	2	yes	complemented
182	C₂×#13047	C₂²	1	4	yes	complemented
183	#493957	C₂²	1	2	yes	complemented
184	#493430	C₂²	1	1	yes	characteristic, complemented
185	#493430	C₂²	1	1	yes	characteristic, complemented
186	#493430	C₂²	1	2	yes	complemented
187	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
188	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
189	D₄×H(5,𝔽₂)	C₂³	1	4	yes	—
190	D₄×H(5,𝔽₂)	C₂³	1	4	yes	complemented
191	#62852	C₂³	1	1	yes	characteristic
192	#62852	C₂³	1	1	yes	characteristic, complemented
193	#62812	C₂³	1	1	yes	characteristic, complemented
194	C₂×#3498	D₄	1	1	yes	characteristic, complemented
195	C₂×#3498	C₂³	1	1	yes	characteristic
196	C₂×#3498	C₂³	1	1	yes	characteristic
197	C₂×#3498	C₂³	1	1	yes	characteristic
198	C₂×#3543	C₂³	1	2	yes	complemented
199	C₂²×#559	C₂³	1	1	yes	characteristic, complemented
200	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
201	C₂²×#560	D₄	1	2	yes	complemented
202	C₄×#585	C₂³	1	1	yes	characteristic, complemented
203	C₂×#3026	C₂³	1	8	yes	—
204	C₂²×#458	C₂³	1	4	yes	complemented
205	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
206	C₂×#3021	C₂³	1	1	yes	characteristic
207	C₂×#3021	C₂³	1	1	yes	characteristic
208	C₂×#3021	C₂³	1	1	yes	characteristic
209	C₂×#3021	C₂³	1	1	yes	characteristic, complemented
210	C₂×#3021	C₂³	1	1	yes	characteristic, complemented
211	C₂×#3021	C₂³	1	1	yes	characteristic, complemented
212	C₂×#3019	C₂³	1	2	yes	—
213	C₂×#3019	C₂³	1	2	yes	—
214	C₂×#3019	C₂³	1	4	yes	complemented
215	C₂×#3018	C₂³	1	1	yes	characteristic
216	C₂×#3018	C₂³	1	1	yes	characteristic
217	C₂×#3018	C₂³	1	1	yes	characteristic
218	C₂²×#453	C₂³	1	2	yes	—
219	C₂²×#453	C₂³	1	2	yes	—
220	C₂²×#453	C₂³	1	4	yes	—
221	C₂×#2888	C₂³	1	1	yes	characteristic
222	C₂×#2888	C₂³	1	1	yes	characteristic, complemented
223	#59466	C₂³	1	2	yes	complemented
224	#59420	C₂³	1	2	yes	complemented
225	#59143	C₂³	1	2	yes	complemented
226	#59143	C₂³	1	2	yes	complemented
227	#59126	C₂³	1	2	yes	complemented
228	#59126	C₂³	1	2	yes	complemented
229	#59070	C₂³	1	2	yes	—
230	#59041	C₂³	1	2	yes	—
231	#52054	C₂³	1	2	yes	—
232	#52054	C₂³	1	2	yes	complemented
233	#52013	C₂³	1	4	yes	—
234	#52012	C₂³	1	4	yes	complemented
235	#52004	C₂³	1	2	yes	—
236	#52004	C₂³	1	2	yes	complemented
237	#50684	C₂³	1	4	yes	complemented
238	#50635	C₂³	1	4	yes	complemented
239	#49793	C₂³	1	4	yes	complemented
240	#48184	C₂³	1	4	yes	complemented
241	#48143	C₂³	1	4	yes	complemented
242	#48058	C₂³	1	4	yes	complemented
243	#47932	C₂³	1	4	yes	complemented
244	#47827	C₂³	1	4	yes	complemented
245	#46302	C₂³	1	4	yes	complemented
246	#46271	C₂³	1	4	yes	—
247	#45727	C₂³	1	4	yes	complemented
248	#45537	C₂³	1	4	yes	complemented
249	#45455	C₂³	1	4	yes	complemented
250	#45438	C₂³	1	4	yes	complemented
251	#39361	D₄	1	2	yes	complemented
252	#39361	D₄	1	2	yes	complemented
253	#39361	C₂³	1	2	yes	—
254	#39361	C₂³	1	2	yes	—
255	#38022	D₄	1	4	yes	complemented
256	#38022	C₂³	1	4	yes	—
257	#38020	D₄	1	4	yes	complemented
258	#38020	C₂³	1	4	yes	—
259	#37646	D₄	1	4	yes	complemented
260	#37646	C₂³	1	4	yes	—
261	#37644	D₄	1	4	yes	complemented
262	#37644	C₂³	1	4	yes	—
263	#37547	D₄	1	4	yes	complemented
264	#37175	C₂³	1	4	yes	complemented
265	#36955	D₄	1	2	yes	complemented
266	#36955	C₂³	1	2	yes	complemented
267	#36737	C₂³	1	4	yes	complemented
268	#36704	D₄	1	4	yes	complemented
269	#36702	D₄	1	2	yes	complemented
270	#36702	C₂³	1	2	yes	complemented
271	C₂×#2867	D₄	1	1	yes	characteristic, complemented
272	#36128	D₄	1	2	yes	complemented
273	#36128	D₄	1	2	yes	complemented
274	D₄×#127	C₂³	1	2	yes	—
275	D₄×#127	C₂³	1	2	yes	—
276	#35527	D₄	1	1	yes	characteristic, complemented
277	#35527	D₄	1	1	yes	characteristic, complemented
278	#35527	C₂³	1	1	yes	characteristic
279	#35527	C₂³	1	1	yes	characteristic
280	#35446	C₂³	1	2	yes	—
281	#35347	C₂³	1	4	yes	—
282	#35346	C₂³	1	2	yes	—
283	#35272	D₄	1	1	yes	characteristic, complemented
284	#35272	D₄	1	1	yes	characteristic, complemented
285	#35272	D₄	1	1	yes	characteristic, complemented
286	#35272	C₂³	1	1	yes	characteristic
287	#35143	C₂³	1	4	yes	—
288	#34498	C₂³	1	2	yes	complemented
289	#34493	C₂³	1	2	yes	complemented
290	#34364	D₄	1	2	yes	complemented
291	#34364	C₂³	1	1	yes	characteristic, complemented
292	#34364	C₂³	1	1	yes	characteristic, complemented
293	C₂×#2366	C₂³	1	2	yes	complemented
294	C₄×#532	D₄	1	1	yes	characteristic, complemented
295	C₄×#532	C₂³	1	1	yes	characteristic
296	C₂×#2200	C₂³	1	8	yes	—
297	C₂×#2200	C₂³	1	8	yes	complemented
298	C₂×#2200	C₂³	1	8	yes	complemented
299	C₂×#2198	C₂³	1	4	yes	—
300	C₂×#2198	C₂³	1	4	yes	complemented
301	C₂×#2198	C₂³	1	4	yes	complemented
302	C₂×#2198	C₂³	1	4	yes	complemented
303	C₂×#2198	C₂³	1	4	yes	complemented
304	C₂×#2198	C₂³	1	4	yes	complemented
305	C₂×#2196	C₂³	1	4	yes	—
306	C₂×#2196	C₂³	1	4	yes	—
307	C₂×#2196	C₂³	1	4	yes	complemented
308	C₂×#2196	C₂³	1	4	yes	complemented
309	C₂×#2196	C₂³	1	4	yes	complemented
310	C₂×#2196	C₂³	1	4	yes	complemented
311	C₂×#2127	C₂³	1	2	yes	complemented
312	C₂×#2127	C₂³	1	2	yes	complemented
313	C₂×#2127	C₂³	1	4	yes	complemented
314	C₂²×#353	C₂³	1	2	yes	complemented
315	C₂²×#353	C₂³	1	2	yes	complemented
316	C₂²×#353	C₂³	1	4	yes	complemented
317	C₂×#2121	C₂³	1	8	yes	complemented
318	C₂²×#352	C₂³	1	4	yes	complemented
319	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
320	#33023	C₂³	1	4	yes	complemented
321	#33021	C₂³	1	4	yes	—
322	#32977	C₂³	1	8	yes	complemented
323	#32928	C₂³	1	8	yes	—
324	#32920	C₂³	1	4	yes	—
325	#32920	C₂³	1	4	yes	complemented
326	#32901	C₂³	1	4	yes	complemented
327	#32901	C₂³	1	4	yes	complemented
328	#32901	C₂³	1	4	yes	complemented
329	#32900	C₂³	1	8	yes	—
330	#32900	C₂³	1	8	yes	complemented
331	#32899	C₂³	1	4	yes	—
332	#32899	C₂³	1	4	yes	—
333	#32899	C₂³	1	4	yes	—
334	#32898	C₂³	1	8	yes	—
335	#32898	C₂³	1	8	yes	—
336	#32888	C₂³	1	4	yes	—
337	#32888	C₂³	1	4	yes	—
338	#32888	C₂³	1	4	yes	complemented
339	#32888	C₂³	1	4	yes	complemented
340	#25901	C₂³	1	8	yes	complemented
341	#25773	C₂³	1	8	yes	—
342	#25739	C₂³	1	4	yes	—
343	#25739	C₂³	1	4	yes	complemented
344	#24412	C₂³	1	4	yes	—
345	#24412	C₂³	1	4	yes	—
346	#24412	C₂³	1	4	yes	complemented
347	#24412	C₂³	1	4	yes	complemented
348	#24405	C₂³	1	8	yes	—
349	#24405	C₂³	1	8	yes	complemented
350	#24404	C₂³	1	8	yes	—
351	#24404	C₂³	1	8	yes	—
352	#24263	C₂³	1	8	yes	complemented
353	#24262	C₂³	1	8	yes	—
354	#24224	C₂³	1	4	yes	complemented
355	#24222	C₂³	1	4	yes	—
356	#24058	C₂³	1	4	yes	—
357	#24058	C₂³	1	4	yes	complemented
358	#24056	C₂³	1	8	yes	complemented
359	#23912	C₂³	1	2	yes	—
360	#23912	C₂³	1	2	yes	—
361	#23912	C₂³	1	4	yes	complemented
362	#23906	C₂³	1	2	yes	—
363	#23906	C₂³	1	2	yes	—
364	#23906	C₂³	1	4	yes	—
365	#23903	C₂³	1	8	yes	—
366	#23901	C₂³	1	4	yes	complemented
367	#23900	C₂³	1	4	yes	—
368	D₄×#100	C₂³	1	4	yes	—
369	D₄×#100	C₂³	1	4	yes	complemented
370	D₄×#99	C₂³	1	8	yes	—
371	D₄×#99	C₂³	1	8	yes	complemented
372	#21482	C₂³	1	8	yes	—
373	#21481	C₂³	1	8	yes	complemented
374	C₄×#455	C₂³	1	4	yes	complemented
375	C₄×#453	C₂³	1	4	yes	—
376	#20956	C₂³	1	1	yes	characteristic
377	#20956	C₂³	1	1	yes	characteristic, complemented
378	#20952	C₂³	1	1	yes	characteristic
379	#20855	C₂³	1	1	yes	characteristic, complemented
380	#20723	C₂³	1	4	yes	complemented
381	#20637	C₂³	1	1	yes	characteristic, complemented
382	#20615	C₂³	1	1	yes	characteristic, complemented
383	#20615	C₂³	1	1	yes	characteristic, complemented
384	#20615	C₂³	1	1	yes	characteristic, complemented
385	#20609	C₂³	1	4	yes	—
386	#20609	C₂³	1	4	yes	complemented
387	C₂×#1790	C₂³	1	8	yes	complemented
388	#20592	C₂³	1	1	yes	characteristic
389	#20592	C₂³	1	1	yes	characteristic, complemented
390	#20585	C₂³	1	2	yes	—
391	#20585	C₂³	1	2	yes	—
392	#20585	C₂³	1	4	yes	complemented
393	C₄×#413	C₂³	1	1	yes	characteristic, complemented
394	#13462	C₂³	1	8	yes	complemented
395	#13425	C₂³	1	8	yes	complemented
396	#13424	C₂³	1	8	yes	complemented
397	#13423	C₂³	1	8	yes	complemented
398	#13423	C₂³	1	8	yes	complemented
399	#13422	C₂³	1	8	yes	complemented
400	#13422	C₂³	1	8	yes	complemented
401	#13420	C₂³	1	8	yes	complemented
402	#13376	C₂³	1	8	yes	complemented
403	#13376	C₂³	1	8	yes	complemented
404	#13376	C₂³	1	8	yes	complemented
405	#13349	C₂³	1	8	yes	complemented
406	#13349	C₂³	1	8	yes	complemented
407	#13349	C₂³	1	8	yes	complemented
408	#13348	C₂³	1	8	yes	—
409	#13348	C₂³	1	8	yes	complemented
410	#13348	C₂³	1	8	yes	complemented
411	#13347	C₂³	1	8	yes	—
412	#13347	C₂³	1	8	yes	complemented
413	#13347	C₂³	1	8	yes	complemented
414	#13347	C₂³	1	8	yes	complemented
415	#13347	C₂³	1	8	yes	complemented
416	#13347	C₂³	1	8	yes	complemented
417	#13346	C₂³	1	8	yes	—
418	#13346	C₂³	1	8	yes	—
419	#13346	C₂³	1	8	yes	complemented
420	#13346	C₂³	1	8	yes	complemented
421	#13346	C₂³	1	8	yes	complemented
422	#13346	C₂³	1	8	yes	complemented
423	#13344	C₂³	1	8	yes	—
424	#13344	C₂³	1	8	yes	complemented
425	#13344	C₂³	1	8	yes	complemented
426	#13297	C₂³	1	8	yes	complemented
427	#13294	C₂³	1	8	yes	complemented
428	#13223	C₂³	1	8	yes	complemented
429	#13223	C₂³	1	8	yes	complemented
430	#13222	C₂³	1	8	yes	complemented
431	#13219	C₂³	1	8	yes	complemented
432	#13088	C₂³	1	8	yes	complemented
433	#13088	C₂³	1	8	yes	complemented
434	#13088	C₂³	1	8	yes	complemented
435	#13088	C₂³	1	8	yes	complemented
436	#13086	C₂³	1	8	yes	complemented
437	#13086	C₂³	1	8	yes	complemented
438	#13084	C₂³	1	8	yes	complemented
439	#13084	C₂³	1	8	yes	complemented
440	#13083	C₂³	1	4	yes	—
441	#13083	C₂³	1	4	yes	—
442	#13083	C₂³	1	4	yes	—
443	#13083	C₂³	1	4	yes	—
444	#13082	C₂³	1	8	yes	complemented
445	#13082	C₂³	1	8	yes	complemented
446	#13081	C₂³	1	4	yes	complemented
447	#13081	C₂³	1	4	yes	complemented
448	#13081	C₂³	1	4	yes	complemented
449	#13081	C₂³	1	4	yes	complemented
450	#13080	C₂³	1	8	yes	complemented
451	#13080	C₂³	1	8	yes	complemented
452	#13049	C₂³	1	4	yes	—
453	#13049	C₂³	1	4	yes	complemented
454	#13049	C₂³	1	4	yes	complemented
455	#13049	C₂³	1	4	yes	complemented
456	#13049	C₂³	1	4	yes	complemented
457	#13049	C₂³	1	4	yes	complemented
458	#13047	C₂³	1	4	yes	—
459	#13047	C₂³	1	4	yes	—
460	#13047	C₂³	1	4	yes	complemented
461	#13047	C₂³	1	4	yes	complemented
462	#13047	C₂³	1	4	yes	complemented
463	#13047	C₂³	1	4	yes	complemented
464	#13047	C₂³	1	8	yes	complemented
465	#13047	C₂³	1	8	yes	complemented
466	#13047	C₂³	1	8	yes	complemented
467	#13044	C₂³	1	8	yes	complemented
468	#13044	C₂³	1	8	yes	complemented
469	#13044	C₂³	1	8	yes	complemented
470	#13043	C₂³	1	8	yes	—
471	#13043	C₂³	1	8	yes	complemented
472	#13043	C₂³	1	8	yes	complemented
473	#12966	C₂³	1	4	yes	complemented
474	#12966	C₂³	1	4	yes	complemented
475	#12964	C₂³	1	8	yes	complemented
476	#12964	C₂³	1	4	yes	complemented
477	#12964	C₂³	1	4	yes	complemented
478	#12961	C₂³	1	8	yes	complemented
479	#12960	C₂³	1	8	yes	complemented
480	#12857	C₂³	1	4	yes	complemented
481	#12854	C₂³	1	4	yes	complemented
482	#12854	C₂³	1	4	yes	complemented
483	#12852	C₂³	1	8	yes	complemented
484	#12798	C₂³	1	4	yes	complemented
485	#12797	C₂³	1	4	yes	complemented
486	#12796	C₂³	1	8	yes	complemented
487	#12795	C₂³	1	8	yes	complemented
488	#12762	C₂³	1	8	yes	complemented
489	#12760	C₂³	1	4	yes	complemented
490	#12760	C₂³	1	4	yes	complemented
491	#12759	C₂³	1	4	yes	complemented
492	#12759	C₂³	1	4	yes	complemented
493	#12697	C₂³	1	2	yes	—
494	#12697	C₂³	1	2	yes	—
495	#12697	C₂³	1	4	yes	complemented
496	#12696	C₂³	1	2	yes	complemented
497	#12696	C₂³	1	2	yes	complemented
498	#12696	C₂³	1	4	yes	complemented
499	#12695	C₂³	1	2	yes	—
500	#12695	C₂³	1	2	yes	—
501	#12693	C₂³	1	2	yes	complemented
502	#12693	C₂³	1	2	yes	complemented
503	#12693	C₂³	1	4	yes	complemented
504	#12690	C₂³	1	8	yes	complemented
505	#12688	C₂³	1	4	yes	complemented
506	#12687	C₂³	1	4	yes	complemented
507	C₄×#354	C₂³	1	4	yes	complemented
508	C₄×#353	C₂³	1	4	yes	complemented
509	#12622	C₂³	1	8	yes	complemented
510	#12621	C₂³	1	8	yes	complemented
511	#12574	C₂³	1	4	yes	complemented
512	#12574	C₂³	1	4	yes	complemented
513	C₂×#1390	C₂³	1	8	yes	complemented
514	C₂×#585	C₂⁴	1	1	yes	characteristic
515	C₂×#585	C₂⁴	1	1	yes	characteristic
516	C₂×#585	C₂⁴	1	1	yes	characteristic
517	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
518	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
519	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
520	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
521	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
522	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
523	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
524	C₂×#560	C₂⁴	1	4	yes	—
525	#3496	C₂⁴	1	4	yes	—
526	#3484	C₂⁴	1	2	yes	—
527	#3484	C₂⁴	1	4	yes	—
528	#3484	C₂⁴	1	2	yes	—
529	C₂×#559	C₂⁴	1	2	yes	—
530	C₂×#559	C₂⁴	1	2	yes	—
531	C₂×#550	C₂×D₄	1	2	yes	—
532	C₂×#550	C₂×D₄	1	2	yes	—
533	C₂×#550	C₂×D₄	1	2	yes	—
534	C₂×#550	C₂×D₄	1	2	yes	complemented
535	C₂×D₄²	C₂×D₄	1	4	yes	—
536	C₂×D₄²	C₂×D₄	1	4	yes	—
537	C₂×D₄²	C₂×D₄	1	2	yes	—
538	C₂×D₄²	C₂×D₄	1	2	yes	complemented
539	C₂×D₄²	C₂⁴	1	2	yes	—
540	C₂×D₄²	C₂⁴	1	2	yes	—
541	C₂×D₄²	C₂⁴	1	2	yes	—
542	C₂×D₄²	C₂⁴	1	2	yes	—
543	C₂×#535	C₂×D₄	1	1	yes	characteristic
544	C₂×#535	C₂×D₄	1	1	yes	characteristic
545	C₂×#535	C₂×D₄	1	1	yes	characteristic
546	C₂×#535	C₂×D₄	1	1	yes	characteristic
547	C₂×#535	C₂×D₄	1	1	yes	characteristic
548	C₂×#535	C₂×D₄	1	1	yes	characteristic
549	C₂×#535	C₂×D₄	1	2	yes	—
550	C₂×#535	C₂×D₄	1	2	yes	—
551	C₂×#535	C₂×D₄	1	2	yes	complemented
552	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
553	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
554	C₂×#535	C₂⁴	1	1	yes	characteristic
555	C₂×#535	C₂⁴	1	1	yes	characteristic
556	C₂×#535	C₂⁴	1	1	yes	characteristic
557	C₂×#535	C₂⁴	1	2	yes	—
558	C₂×#535	C₂⁴	1	1	yes	characteristic
559	C₂×#534	C₂×D₄	1	4	yes	complemented
560	C₂×#534	C₂⁴	1	4	yes	—
561	C₂×#532	C₂×D₄	1	1	yes	characteristic
562	C₂×#532	C₂×D₄	1	1	yes	characteristic
563	C₂×#532	C₂×D₄	1	2	yes	—
564	C₂×#532	C₂×D₄	1	1	yes	characteristic
565	C₂×#532	C₂×D₄	1	2	yes	complemented
566	C₂×#532	C₂⁴	1	1	yes	characteristic
567	C₂²×#127	C₂×D₄	1	2	yes	—
568	C₂²×#127	C₂×D₄	1	1	yes	characteristic
569	C₂²×#127	C₂×D₄	1	1	yes	characteristic
570	C₂²×#127	C₂×D₄	1	1	yes	characteristic
571	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
572	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
573	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
574	C₂²×#127	C₂⁴	1	1	yes	characteristic
575	C₂²×#127	C₂⁴	1	2	yes	—
576	C₂²×#127	C₂⁴	1	1	yes	characteristic
577	C₂²×#126	C₂×D₄	1	4	yes	complemented
578	C₂²×#123	C₂×D₄	1	2	yes	—
579	C₂²×#123	C₂×D₄	1	2	yes	—
580	C₂²×#123	C₂×D₄	1	4	yes	—
581	C₂²×#123	C₂⁴	1	2	yes	—
582	C₂²×#121	C₂×D₄	1	4	yes	complemented
583	C₂²×#121	C₂×D₄	1	4	yes	complemented
584	C₂²×#121	C₂×D₄	1	4	yes	complemented
585	C₂²×#120	C₂×D₄	1	2	yes	—
586	C₂²×#120	C₂×D₄	1	4	yes	—
587	C₂²×#120	C₂×D₄	1	2	yes	—
588	C₂²×#120	C₂⁴	1	2	yes	—
589	C₄×H(5,𝔽₂)	C₂⁴	1	4	yes	—
590	#3428	C₂⁴	1	1	yes	characteristic
591	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
592	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
593	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
594	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
595	C₂×#458	C₂⁴	1	8	yes	—
596	C₂×#458	C₂⁴	1	8	yes	—
597	C₂×#458	C₂⁴	1	8	yes	—
598	C₂×B(4,𝔽₂)	C₂⁴	1	8	yes	—
599	C₂×B(4,𝔽₂)	C₂⁴	1	8	yes	—
600	C₂×B(4,𝔽₂)	C₂⁴	1	8	yes	—
601	C₂×#455	C₂⁴	1	2	yes	—
602	C₂×#455	C₂⁴	1	2	yes	—
603	C₂×#455	C₂⁴	1	2	yes	—
604	C₂×#453	C₂⁴	1	2	yes	—
605	C₂×#453	C₂⁴	1	2	yes	—
606	C₂×#453	C₂⁴	1	2	yes	—
607	C₂×#453	C₂⁴	1	2	yes	—
608	C₂×#453	C₂⁴	1	2	yes	—
609	C₂×#453	C₂⁴	1	2	yes	—
610	C₂×#453	C₂⁴	1	4	yes	—
611	C₂×#453	C₂⁴	1	4	yes	—
612	C₂×#453	C₂⁴	1	2	yes	—
613	C₂×#453	C₂⁴	1	2	yes	—
614	C₂×#453	C₂⁴	1	2	yes	—
615	C₂×#453	C₂⁴	1	4	yes	—
616	C₂×#413	C₂⁴	1	1	yes	characteristic
617	C₂×#413	C₂⁴	1	1	yes	characteristic
618	C₂×#413	C₂⁴	1	1	yes	characteristic
619	C₂×#413	C₂⁴	1	1	yes	characteristic
620	C₂²×#100	C₂⁴	1	2	yes	—
621	C₂²×#100	C₂⁴	1	4	yes	—
622	C₂²×#100	C₂⁴	1	2	yes	—
623	C₂²×#99	C₂⁴	1	8	yes	—
624	C₂²×#99	C₂⁴	1	4	yes	—
625	C₂²×#99	C₂⁴	1	4	yes	—
626	#2867	C₂×D₄	1	2	yes	—
627	#2867	C₂×D₄	1	2	yes	—
628	#2867	C₂×D₄	1	2	yes	complemented
629	#2867	C₂×D₄	1	2	yes	complemented
630	#2856	C₂×D₄	1	2	yes	—
631	#2856	C₂×D₄	1	2	yes	—
632	#2856	C₂×D₄	1	2	yes	complemented
633	#2856	C₂×D₄	1	2	yes	complemented
634	#2849	C₂×D₄	1	4	yes	—
635	#2849	C₂×D₄	1	4	yes	complemented
636	#2849	C₂×D₄	1	4	yes	complemented
637	#2846	C₂×D₄	1	4	yes	—
638	#2748	C₂⁴	1	4	yes	—
639	#2717	C₂⁴	1	4	yes	—
640	#2709	C₂⁴	1	4	yes	—
641	#2709	C₂⁴	1	4	yes	—
642	#2697	C₂⁴	1	4	yes	—
643	#2684	C₂⁴	1	4	yes	—
644	#2669	C₂⁴	1	4	yes	—
645	#2669	C₂⁴	1	4	yes	—
646	#2622	C₂×D₄	1	4	yes	—
647	#2622	C₂×D₄	1	4	yes	complemented
648	#2619	C₂×D₄	1	2	yes	—
649	#2619	C₂×D₄	1	2	yes	—
650	#2619	C₂×D₄	1	2	yes	complemented
651	#2619	C₂×D₄	1	2	yes	complemented
652	#2618	C₂×D₄	1	4	yes	—
653	#2618	C₂×D₄	1	4	yes	complemented
654	#2617	C₂×D₄	1	4	yes	—
655	#2617	C₂×D₄	1	4	yes	complemented
656	#2613	C₂×D₄	1	4	yes	—
657	#2613	C₂×D₄	1	4	yes	complemented
658	#2591	C₂×D₄	1	4	yes	—
659	#2591	C₂×D₄	1	4	yes	complemented
660	#2579	C₂×D₄	1	4	yes	complemented
661	#2579	C₂⁴	1	4	yes	—
662	#2548	C₂×D₄	1	2	yes	—
663	#2548	C₂×D₄	1	2	yes	complemented
664	#2548	C₂×D₄	1	2	yes	complemented
665	#2548	C₂×D₄	1	2	yes	complemented
666	#2541	C₂×D₄	1	2	yes	—
667	#2541	C₂×D₄	1	2	yes	complemented
668	#2541	C₂⁴	1	2	yes	—
669	#2541	C₂⁴	1	2	yes	—
670	#2539	C₂×D₄	1	4	yes	—
671	#2539	C₂×D₄	1	4	yes	complemented
672	#2534	C₂×D₄	1	4	yes	complemented
673	#2534	C₂⁴	1	4	yes	—
674	#2484	C₂×D₄	1	4	yes	complemented
675	#2482	C₂×D₄	1	4	yes	complemented
676	#2433	C₂×D₄	1	2	yes	—
677	#2433	C₂×D₄	1	2	yes	—
678	#2433	C₂×D₄	1	2	yes	complemented
679	#2433	C₂×D₄	1	2	yes	complemented
680	#2433	C₂⁴	1	2	yes	—
681	#2433	C₂⁴	1	2	yes	—
682	#2433	C₂⁴	1	2	yes	—
683	#2433	C₂⁴	1	2	yes	—
684	#2431	C₂×D₄	1	2	yes	—
685	#2431	C₂×D₄	1	2	yes	—
686	#2431	C₂×D₄	1	2	yes	—
687	#2431	C₂×D₄	1	2	yes	—
688	#2431	C₂×D₄	1	2	yes	complemented
689	#2431	C₂×D₄	1	2	yes	complemented
690	#2431	C₂×D₄	1	2	yes	complemented
691	#2431	C₂×D₄	1	2	yes	complemented
692	#2412	C₂×D₄	1	4	yes	—
693	#2412	C₂×D₄	1	4	yes	—
694	#2412	C₂×D₄	1	4	yes	—
695	#2412	C₂×D₄	1	4	yes	complemented
696	#2410	C₂×D₄	1	4	yes	—
697	#2410	C₂×D₄	1	4	yes	complemented
698	#2410	C₂×D₄	1	4	yes	complemented
699	#2410	C₂×D₄	1	4	yes	complemented
700	#2406	C₂×D₄	1	4	yes	—
701	#2406	C₂×D₄	1	4	yes	complemented
702	#2406	C₂⁴	1	4	yes	—
703	#2405	C₂×D₄	1	4	yes	—
704	#2405	C₂×D₄	1	4	yes	complemented
705	#2405	C₂⁴	1	4	yes	—
706	#2405	C₂⁴	1	4	yes	—
707	#2404	C₂×D₄	1	4	yes	—
708	#2404	C₂×D₄	1	4	yes	complemented
709	#2404	C₂⁴	1	4	yes	—
710	#2403	C₂×D₄	1	4	yes	—
711	#2403	C₂×D₄	1	4	yes	complemented
712	#2403	C₂⁴	1	4	yes	—
713	#2403	C₂⁴	1	4	yes	—
714	#2380	C₂⁴	1	2	yes	—
715	#2380	C₂⁴	1	2	yes	—
716	#2376	C₂⁴	1	4	yes	—
717	#2375	C₂⁴	1	4	yes	—
718	#2366	C₂⁴	1	2	yes	—
719	#2366	C₂⁴	1	2	yes	—
720	#2366	C₂⁴	1	4	yes	—
721	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
722	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
723	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
724	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
725	#2322	C₂×D₄	1	4	yes	complemented
726	#2322	C₂⁴	1	4	yes	—
727	#2321	C₂×D₄	1	4	yes	complemented
728	#2321	C₂⁴	1	4	yes	—
729	#2309	C₂×D₄	1	1	yes	characteristic
730	#2309	C₂×D₄	1	1	yes	characteristic, complemented
731	#2309	C₂×D₄	1	1	yes	characteristic, complemented
732	#2309	C₂×D₄	1	1	yes	characteristic, complemented
733	#2308	C₂×D₄	1	2	yes	—
734	#2308	C₂×D₄	1	2	yes	—
735	#2308	C₂×D₄	1	2	yes	—
736	#2308	C₂×D₄	1	2	yes	—
737	#2308	C₂×D₄	1	4	yes	complemented
738	#2308	C₂⁴	1	2	yes	—
739	#2308	C₂⁴	1	2	yes	—
740	C₄×C₄⋊Q₈	C₂×D₄	1	2	yes	complemented
741	C₄×#127	C₂⁴	1	2	yes	—
742	C₄×#124	C₂×D₄	1	2	yes	complemented
743	C₄×#124	C₂⁴	1	2	yes	—
744	#2297	C₂×D₄	1	1	yes	characteristic
745	#2297	C₂×D₄	1	1	yes	characteristic, complemented
746	#2297	C₂×D₄	1	1	yes	characteristic, complemented
747	#2297	C₂⁴	1	1	yes	characteristic
748	#2293	C₂×D₄	1	2	yes	—
749	#2293	C₂×D₄	1	2	yes	complemented
750	C₂×#386	C₂×D₄	1	4	yes	complemented
751	C₂×#386	C₂⁴	1	4	yes	—
752	#2285	C₂×D₄	1	1	yes	characteristic, complemented
753	#2285	C₂×D₄	1	1	yes	characteristic, complemented
754	#2283	C₂×D₄	1	4	yes	complemented
755	C₄²×D₄	C₂×D₄	1	2	yes	—
756	C₄²×D₄	C₂×D₄	1	2	yes	complemented
757	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
758	C₂×#354	C₂⁴	1	4	yes	—
759	C₂×#354	C₂⁴	1	4	yes	—
760	C₂×#353	C₂⁴	1	4	yes	—
761	C₂×#353	C₂⁴	1	4	yes	—
762	C₂×#353	C₂⁴	1	4	yes	—
763	C₂×#353	C₂⁴	1	4	yes	—
764	C₂×#353	C₂⁴	1	4	yes	—
765	C₂×#353	C₂⁴	1	4	yes	—
766	C₂×#353	C₂⁴	1	8	yes	—
767	C₂×#353	C₂⁴	1	8	yes	—
768	C₂×#352	C₂⁴	1	8	yes	—
769	C₂×#352	C₂⁴	1	8	yes	—
770	C₂×#352	C₂⁴	1	8	yes	—
771	C₂×#352	C₂⁴	1	8	yes	—
772	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
773	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
774	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
775	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	8	yes	—
776	#1890	C₂⁴	1	8	yes	—
777	#1889	C₂⁴	1	8	yes	—
778	#1887	C₂⁴	1	2	yes	—
779	#1887	C₂⁴	1	4	yes	—
780	#1887	C₂⁴	1	2	yes	—
781	#1887	C₂⁴	1	2	yes	—
782	#1885	C₂⁴	1	2	yes	—
783	#1867	C₂⁴	1	8	yes	—
784	#1867	C₂⁴	1	8	yes	—
785	#1856	C₂⁴	1	4	yes	—
786	#1800	C₂⁴	1	4	yes	—
787	#1799	C₂⁴	1	8	yes	—
788	#1792	C₂⁴	1	4	yes	—
789	#1792	C₂⁴	1	4	yes	—
790	#1792	C₂⁴	1	4	yes	—
791	#1790	C₂⁴	1	8	yes	—
792	#1790	C₂⁴	1	8	yes	—
793	#1790	C₂⁴	1	8	yes	—
794	#1790	C₂⁴	1	8	yes	—
795	#1790	C₂⁴	1	8	yes	—
796	#1790	C₂⁴	1	8	yes	—
797	#1783	C₂⁴	1	2	yes	—
798	#1783	C₂⁴	1	4	yes	—
799	#1783	C₂⁴	1	2	yes	—
800	#1782	C₂⁴	1	4	yes	—
801	#1782	C₂⁴	1	4	yes	—
802	#1781	C₂⁴	1	4	yes	—
803	#1781	C₂⁴	1	8	yes	—
804	#1781	C₂⁴	1	4	yes	—
805	C₄×#100	C₂⁴	1	4	yes	—
806	C₄×#99	C₂⁴	1	8	yes	—
807	#1393	C₂⁴	1	8	yes	—
808	#1393	C₂⁴	1	8	yes	—
809	#1390	C₂⁴	1	8	yes	—
810	#1390	C₂⁴	1	8	yes	—
811	#1390	C₂⁴	1	8	yes	—
812	#1390	C₂⁴	1	8	yes	—
813	#1390	C₂⁴	1	8	yes	—
814	#1390	C₂⁴	1	8	yes	—
815	#1390	C₂⁴	1	8	yes	—
816	#1390	C₂⁴	1	8	yes	—
817	C₂⁶	C₂²×D₄	1	2	yes	—
818	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
819	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
820	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
821	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
822	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
823	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
824	C₂²×#41	C₂²×D₄	1	2	yes	—
825	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
826	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
827	C₂²×#41	C₂²×D₄	1	2	yes	—
828	C₂²×#41	C₂²×D₄	1	2	yes	—
829	C₂²×#41	C₂²×D₄	1	2	yes	—
830	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
831	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
832	C₂²×#41	C₂⁵	1	1	yes	characteristic
833	C₂³×D₄	#120	1	4	yes	—
834	C₂³×D₄	C₂²×D₄	1	2	yes	—
835	C₂³×D₄	C₂²×D₄	1	2	yes	—
836	C₂³×D₄	C₂²×D₄	1	4	yes	—
837	C₂³×D₄	C₂²×D₄	1	2	yes	—
838	C₂³×D₄	C₂²×D₄	1	2	yes	—
839	C₂³×D₄	C₂²×D₄	1	4	yes	—
840	C₂³×D₄	C₂²×D₄	1	4	yes	—
841	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
842	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
843	C₂³×D₄	C₂²×D₄	1	2	yes	—
844	C₂³×D₄	C₂²×D₄	1	4	yes	—
845	C₂³×D₄	C₂²×D₄	1	4	yes	—
846	C₂³×D₄	C₂²×D₄	1	4	yes	—
847	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
848	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
849	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
850	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
851	C₂³×D₄	C₂⁵	1	1	yes	characteristic
852	C₂³×D₄	C₂⁵	1	1	yes	characteristic
853	C₂³×D₄	C₂⁵	1	2	yes	—
854	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
855	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
856	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
857	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
858	C₂×#127	#120	1	2	yes	—
859	C₂×#127	#120	1	4	yes	—
860	C₂×#127	#120	1	4	yes	—
861	C₂×#127	#120	1	2	yes	—
862	C₂×#127	#120	1	2	yes	—
863	C₂×#127	#120	1	2	yes	—
864	C₂×#127	#120	1	1	yes	characteristic
865	C₂×#127	C₂²×D₄	1	1	yes	characteristic
866	C₂×#127	C₂²×D₄	1	2	yes	—
867	C₂×#127	C₂²×D₄	1	1	yes	characteristic
868	C₂×#127	C₂²×D₄	1	2	yes	—
869	C₂×#127	C₂²×D₄	1	1	yes	characteristic
870	C₂×#127	C₂²×D₄	1	1	yes	characteristic
871	C₂×#127	C₂²×D₄	1	1	yes	characteristic
872	C₂×#127	C₂²×D₄	1	2	yes	—
873	C₂×#127	C₂²×D₄	1	2	yes	—
874	C₂×#127	C₂²×D₄	1	2	yes	—
875	C₂×#127	C₂²×D₄	1	1	yes	characteristic
876	C₂×#127	C₂²×D₄	1	2	yes	—
877	C₂×#127	C₂²×D₄	1	2	yes	—
878	C₂×#127	C₂²×D₄	1	2	yes	—
879	C₂×#127	C₂²×D₄	1	2	yes	—
880	C₂×#127	C₂²×D₄	1	2	yes	—
881	C₂×#127	C₂²×D₄	1	2	yes	—
882	C₂×#127	C₂⁵	1	2	yes	—
883	C₂×#127	C₂⁵	1	1	yes	characteristic
884	C₂×#127	C₂⁵	1	1	yes	characteristic
885	C₂×#127	C₂⁵	1	1	yes	characteristic
886	C₂×#124	#120	1	1	yes	characteristic
887	C₂×#124	#120	1	1	yes	characteristic
888	C₂×#124	#120	1	2	yes	—
889	C₂×#124	#120	1	2	yes	—
890	C₂×#124	C₂²×D₄	1	1	yes	characteristic
891	C₂×#124	C₂²×D₄	1	1	yes	characteristic
892	C₂×#124	C₂²×D₄	1	1	yes	characteristic
893	C₂×#124	C₂²×D₄	1	1	yes	characteristic
894	C₂×#124	C₂²×D₄	1	1	yes	characteristic
895	C₂×#124	C₂²×D₄	1	2	yes	—
896	C₂×#124	C₂²×D₄	1	2	yes	—
897	C₂×#124	C₂⁵	1	1	yes	characteristic
898	C₂×#123	C₂²×D₄	1	4	yes	—
899	C₂×#123	C₂²×D₄	1	4	yes	—
900	C₂×#123	C₂²×D₄	1	4	yes	—
901	C₂×#123	C₂²×D₄	1	4	yes	—
902	C₂×#123	C₂²×D₄	1	4	yes	—
903	C₂×#123	C₂⁵	1	4	yes	—
904	C₂×#121	#120	1	2	yes	—
905	C₂×#121	#120	1	2	yes	—
906	C₂×#121	#120	1	4	yes	—
907	C₂×#121	#120	1	4	yes	—
908	C₂×#121	#120	1	4	yes	—
909	C₂×#121	#120	1	4	yes	—
910	C₂×#121	C₂²×D₄	1	2	yes	—
911	C₂×#121	C₂²×D₄	1	2	yes	—
912	C₂×#121	C₂²×D₄	1	2	yes	—
913	C₂×#121	C₂²×D₄	1	2	yes	—
914	C₂×#121	C₂²×D₄	1	4	yes	—
915	C₂×#121	C₂²×D₄	1	4	yes	—
916	C₂×#121	C₂²×D₄	1	2	yes	—
917	C₂×#121	C₂²×D₄	1	2	yes	—
918	C₂×#121	C₂²×D₄	1	2	yes	—
919	C₂×#121	C₂²×D₄	1	2	yes	—
920	C₂×#120	#120	1	4	yes	—
921	C₂×#120	#120	1	2	yes	—
922	C₂×#120	#120	1	2	yes	—
923	C₂×#120	C₂²×D₄	1	4	yes	—
924	C₂×#120	C₂²×D₄	1	4	yes	—
925	C₂×#120	C₂²×D₄	1	4	yes	—
926	C₂×#120	C₂²×D₄	1	4	yes	—
927	C₂×#120	C₂²×D₄	1	4	yes	—
928	C₂×#120	C₂²×D₄	1	4	yes	—
929	C₂×#120	C₂²×D₄	1	4	yes	—
930	C₂×#120	C₂²×D₄	1	4	yes	—
931	C₂×#120	C₂²×D₄	1	4	yes	—
932	C₂×#120	C₂⁵	1	4	yes	—
933	#518	C₂⁵	1	2	yes	—
934	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
935	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
936	C₂×C₄×D₄	#120	1	4	yes	—
937	C₂×C₄×D₄	#120	1	4	yes	—
938	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
939	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
940	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
941	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
942	C₂×C₄×D₄	C₂⁵	1	2	yes	—
943	C₂×#117	C₂²×D₄	1	1	yes	characteristic
944	C₂×#117	C₂²×D₄	1	1	yes	characteristic
945	C₂×#117	C₂²×D₄	1	2	yes	—
946	C₂×#117	C₂²×D₄	1	1	yes	characteristic
947	C₂×#117	C₂²×D₄	1	1	yes	characteristic
948	C₂×#117	C₂²×D₄	1	1	yes	characteristic
949	C₂×#117	C₂²×D₄	1	1	yes	characteristic
950	C₂×#117	C₂²×D₄	1	2	yes	—
951	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
952	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
953	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
954	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
955	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
956	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
957	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
958	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
959	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
960	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
961	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
962	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
963	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
964	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
965	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
966	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
967	C₂²×C₄²	C₂²×D₄	1	2	yes	—
968	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
969	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
970	C₂²×C₄²	C₂²×D₄	1	2	yes	—
971	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
972	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
973	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
974	#453	H(5,𝔽₂)	1	8	yes	—
975	C₂×#100	C₂⁵	1	2	yes	—
976	C₂×#100	C₂⁵	1	2	yes	—
977	C₂×#100	C₂⁵	1	2	yes	—
978	C₂×#100	C₂⁵	1	2	yes	—
979	C₂×#99	C₂⁵	1	8	yes	—
980	C₂×#99	C₂⁵	1	8	yes	—
981	#391	C₂²×D₄	1	2	yes	—
982	#391	C₂²×D₄	1	2	yes	—
983	#390	C₂²×D₄	1	2	yes	—
984	#390	C₂²×D₄	1	2	yes	—
985	#390	C₂²×D₄	1	2	yes	—
986	#390	C₂²×D₄	1	2	yes	—
987	#390	C₂²×D₄	1	2	yes	—
988	#390	C₂²×D₄	1	2	yes	—
989	#390	C₂²×D₄	1	2	yes	—
990	#390	C₂²×D₄	1	2	yes	—
991	#390	C₂²×D₄	1	2	yes	—
992	#390	C₂⁵	1	2	yes	—
993	#386	C₂²×D₄	1	4	yes	—
994	#386	C₂²×D₄	1	4	yes	—
995	#386	C₂²×D₄	1	4	yes	—
996	#386	C₂²×D₄	1	4	yes	—
997	#386	C₂²×D₄	1	4	yes	—
998	#386	C₂²×D₄	1	4	yes	—
999	#386	C₂²×D₄	1	4	yes	—
1000	#386	C₂²×D₄	1	4	yes	—
1001	#386	C₂²×D₄	1	4	yes	—
1002	#386	C₂²×D₄	1	4	yes	—
1003	#386	C₂⁵	1	4	yes	—
1004	#386	C₂⁵	1	4	yes	—
1005	#385	C₂²×D₄	1	4	yes	—
1006	#385	C₂²×D₄	1	4	yes	—
1007	#385	C₂²×D₄	1	4	yes	—
1008	#385	C₂²×D₄	1	4	yes	—
1009	#384	C₂²×D₄	1	2	yes	—
1010	#382	C₂²×D₄	1	2	yes	—
1011	#381	C₂²×D₄	1	4	yes	—
1012	#381	C₂²×D₄	1	4	yes	—
1013	#381	C₂²×D₄	1	4	yes	—
1014	#381	C₂²×D₄	1	4	yes	—
1015	#380	C₂²×D₄	1	4	yes	—
1016	#380	C₂²×D₄	1	4	yes	—
1017	#379	C₂²×D₄	1	4	yes	—
1018	#379	C₂²×D₄	1	4	yes	—
1019	#379	C₂²×D₄	1	4	yes	—
1020	#379	C₂²×D₄	1	4	yes	—
1021	#379	C₂²×D₄	1	4	yes	—
1022	#379	C₂²×D₄	1	4	yes	—
1023	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
1024	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
1025	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
1026	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
1027	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
1028	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
1029	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
1030	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
1031	C₄³	C₂²×D₄	1	2	yes	—
1032	C₄³	C₂²×D₄	1	2	yes	—
1033	C₂⁵	C₂×#120	1	2	yes	—
1034	C₂⁵	C₂×#120	1	2	yes	—
1035	C₂⁵	C₂³×D₄	1	2	yes	—
1036	C₂⁵	C₂³×D₄	1	4	yes	—
1037	C₂⁵	C₂³×D₄	1	2	yes	—
1038	C₂⁵	C₂³×D₄	1	4	yes	—
1039	H(5,𝔽₂)	C₂×H(5,𝔽₂)	1	4	yes	—
1040	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
1041	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
1042	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
1043	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
1044	C₂²×D₄	C₂×#120	1	1	yes	characteristic
1045	C₂²×D₄	C₂×#120	1	2	yes	—
1046	C₂²×D₄	C₂×#120	1	1	yes	characteristic
1047	C₂²×D₄	C₂×#120	1	2	yes	—
1048	C₂²×D₄	C₂×#120	1	2	yes	—
1049	C₂²×D₄	C₂×#120	1	4	yes	—
1050	C₂²×D₄	C₂×#120	1	2	yes	—
1051	C₂²×D₄	C₂×#120	1	2	yes	—
1052	C₂²×D₄	C₂×#120	1	4	yes	—
1053	C₂²×D₄	C₂×#120	1	4	yes	—
1054	C₂²×D₄	C₂×#120	1	4	yes	—
1055	C₂²×D₄	C₂×#120	1	4	yes	—
1056	C₂²×D₄	C₂×#120	1	4	yes	—
1057	C₂²×D₄	C₂×#120	1	4	yes	—
1058	C₂²×D₄	C₂×#120	1	1	yes	characteristic
1059	C₂²×D₄	C₂×#120	1	1	yes	characteristic
1060	C₂²×D₄	C₂×#120	1	4	yes	—
1061	C₂²×D₄	C₂×#120	1	4	yes	—
1062	C₂²×D₄	C₂×#120	1	2	yes	—
1063	C₂²×D₄	C₂×#120	1	2	yes	—
1064	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
1065	C₂²×D₄	C₂³×D₄	1	2	yes	—
1066	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
1067	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
1068	C₂²×D₄	C₂³×D₄	1	2	yes	—
1069	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
1070	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
1071	C₂²×D₄	C₂³×D₄	1	2	yes	—
1072	C₂²×D₄	C₂³×D₄	1	2	yes	—
1073	C₂²×D₄	C₂³×D₄	1	4	yes	—
1074	C₂²×D₄	C₂³×D₄	1	2	yes	—
1075	C₂²×D₄	C₂⁶	1	1	yes	characteristic
1076	C₂³×C₄	C₂×#120	1	2	yes	—
1077	C₂³×C₄	C₂×#120	1	2	yes	—
1078	C₂³×C₄	C₂×#120	1	2	yes	—
1079	C₂³×C₄	C₂×#120	1	4	yes	—
1080	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
1081	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
1082	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
1083	C₂³×C₄	C₂³×D₄	1	2	yes	—
1084	C₂³×C₄	C₂³×D₄	1	2	yes	—
1085	C₂³×C₄	C₂³×D₄	1	4	yes	—
1086	C₂³×C₄	C₂³×D₄	1	4	yes	—
1087	C₂³×C₄	C₂³×D₄	1	4	yes	—
1088	C₂³×C₄	C₂³×D₄	1	4	yes	—
1089	#127	B(4,𝔽₂)	1	2	yes	—
1090	#127	B(4,𝔽₂)	1	2	yes	—
1091	#127	B(4,𝔽₂)	1	4	yes	—
1092	#127	C₂×H(5,𝔽₂)	1	4	yes	—
1093	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
1094	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
1095	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
1096	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
1097	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
1098	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
1099	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
1100	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
1101	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
1102	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
1103	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
1104	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
1105	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
1106	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
1107	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
1108	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
1109	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
1110	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
1111	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
1112	C₂×C₄²	C₂×#120	1	1	yes	characteristic
1113	C₂×C₄²	C₂×#120	1	2	yes	—
1114	C₂×C₄²	C₂×#120	1	4	yes	—
1115	C₂×C₄²	C₂×#120	1	1	yes	characteristic
1116	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
1117	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
1118	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
1119	C₂×C₄²	C₂³×D₄	1	2	yes	—
1120	C₂×C₄²	C₂³×D₄	1	2	yes	—
1121	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
1122	C₂×C₄²	C₂³×D₄	1	2	yes	—
1123	#100	C₂×H(5,𝔽₂)	1	4	yes	—
1124	C₂⁴	C₂²×#120	1	2	yes	—
1125	C₂⁴	C₂²×#120	1	4	yes	—
1126	C₂⁴	C₂²×#120	1	2	yes	—
1127	C₂⁴	C₂²×#120	1	1	yes	characteristic
1128	C₂⁴	C₂²×#120	1	1	yes	characteristic
1129	C₂⁴	C₂²×#120	1	2	yes	—
1130	C₂⁴	C₂²×#120	1	1	yes	characteristic
1131	C₂⁴	C₂⁴×D₄	1	2	yes	—
1132	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
1133	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
1134	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
1135	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
1136	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
1137	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
1138	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
1139	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
1140	C₂×D₄	#3484	1	2	yes	—
1141	C₂×D₄	C₂²×H(5,𝔽₂)	1	2	yes	—
1142	C₂×D₄	H(7,𝔽₂)	1	2	yes	—
1143	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1144	C₂²×C₄	C₂²×#120	1	2	yes	—
1145	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1146	C₂²×C₄	C₂²×#120	1	2	yes	—
1147	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1148	C₂²×C₄	C₂²×#120	1	2	yes	—
1149	C₂²×C₄	C₂²×#120	1	4	yes	—
1150	C₂²×C₄	C₂²×#120	1	2	yes	—
1151	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
1152	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1153	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1154	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
1155	C₄²	#3484	1	2	yes	—
1156	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
1157	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
1158	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
1159	C₂³	#60399	1	2	yes	—
1160	C₂³	C₂³×#120	1	1	yes	characteristic
1161	C₂³	D₄×H(5,𝔽₂)	1	4	yes	—
1162	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
1163	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1164	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
1165	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1166	C₂×C₄	C₂×#3484	1	1	yes	characteristic
1167	C₂×C₄	#62842	1	1	yes	characteristic
1168	C₂²	#7631286	1	1	yes	characteristic
1169	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
1170	C₂²	C₂×#60399	1	1	yes	characteristic
1171	C₂	#72216616	1	1	yes	characteristic
1172	C₂	#72249654	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂³×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#127 ◁ C₂×#3498 ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72341411	C₂	semidirect
2. #72341408	C₂	semidirect
3. #72341405	C₂	semidirect
4. #72341403	C₂	semidirect
5. #72341401	C₂	semidirect
6. #72341394	C₂	semidirect
7. #72341388	C₂	semidirect
8. #72341381	C₂	semidirect
9. #72318522	C₂	semidirect
10. #72318494	C₂	semidirect
11. #72318026	C₂	semidirect
12. #72312346	C₂	semidirect
13. #72312153	C₂	semidirect
14. #72311315	C₂	semidirect
15. #72311246	C₂	semidirect
16. #72311231	C₂	semidirect
17. #72306899	C₂	semidirect
18. #72303059	C₂	semidirect
19. #72285500	C₂	semidirect
20. #72262180	C₂	semidirect
21. #72249425	C₂	semidirect
22. #72236706	C₂	semidirect
23. #72236657	C₂	semidirect
24. #72234146	C₂	semidirect
25. #72215857	C₂	semidirect
26. #10586097	C₂²	semidirect
28. C₂×#60388	C₂²	semidirect
29. #9910000	C₂²	semidirect
30. #9909812	C₂²	semidirect
31. #8926850	C₂²	semidirect
32. #8926849	C₂²	semidirect
33. #8757069	C₂²	semidirect
34. #7989737	C₂²	semidirect
35. #7989726	C₂²	semidirect
36. #7985329	C₂²	semidirect
37. #7985088	C₂²	semidirect
39. #7737652	C₂²	semidirect
40. #7737412	C₂²	semidirect
41. #7737411	C₂²	semidirect
42. #7711121	C₂²	semidirect
44. C₂×#33557	C₂²	semidirect
45. C₂²×#2198	C₂²	semidirect
46. C₂²×#2196	C₂²	semidirect
47. #6629397	C₂²	semidirect
48. #6628970	C₂²	semidirect
49. #6628900	C₂²	semidirect
50. #6628897	C₂²	semidirect
51. #6628896	C₂²	semidirect
52. #6628872	C₂²	semidirect
53. #6628872	C₂²	semidirect
54. #6591510	C₂²	semidirect
55. #6591506	C₂²	semidirect
56. #6573719	C₂²	semidirect
57. #6573715	C₂²	semidirect
58. #6573693	C₂²	semidirect
59. #6573693	C₂²	semidirect
61. D₄×#453	C₂²	semidirect
62. #6487655	C₂²	semidirect
63. #6470246	C₂²	semidirect
64. #6470235	C₂²	semidirect
65. #6470234	C₂²	semidirect
66. #6443331	C₂²	semidirect
67. #6442555	C₂²	semidirect
68. #6437969	C₂²	semidirect
69. #6437969	C₂²	semidirect
71. #6437452	C₂²	semidirect
72. #6385980	C₂²	semidirect
73. #6379033	C₂²	semidirect
74. C₄×#3018	C₂²	semidirect
75. #512122	C₂²	semidirect
76. #512122	C₂²	semidirect
77. #512116	C₂²	semidirect
78. #511916	C₂²	semidirect
79. #511914	C₂²	semidirect
80. #511785	C₂²	semidirect
81. #511773	C₂²	semidirect
82. #511771	C₂²	semidirect
83. #508200	C₂²	semidirect
84. #508099	C₂²	semidirect
85. #508096	C₂²	semidirect
86. #508095	C₂²	semidirect
87. #503582	C₂²	semidirect
88. #503243	C₂²	semidirect
89. #503237	C₂²	semidirect
90. #503198	C₂²	semidirect
91. #502832	C₂²	semidirect
92. #502830	C₂²	semidirect
93. #502785	C₂²	semidirect
94. #502731	C₂²	semidirect
95. #502725	C₂²	semidirect
96. #502723	C₂²	semidirect
97. #502717	C₂²	semidirect
98. #501176	C₂²	semidirect
99. #501175	C₂²	semidirect
100. #501169	C₂²	semidirect
101. #501166	C₂²	semidirect
102. #501103	C₂²	semidirect
103. #501099	C₂²	semidirect
104. #501097	C₂²	semidirect
105. #501086	C₂²	semidirect
106. #501086	C₂²	semidirect
107. #501084	C₂²	semidirect
108. #501084	C₂²	semidirect
109. #500958	C₂²	semidirect
110. #500828	C₂²	semidirect
111. #500822	C₂²	semidirect
112. #500773	C₂²	semidirect
113. #500541	C₂²	semidirect
114. #500539	C₂²	semidirect
115. #500494	C₂²	semidirect
116. #500368	C₂²	semidirect
117. #500191	C₂²	semidirect
118. #500180	C₂²	semidirect
119. #500179	C₂²	semidirect
120. #500175	C₂²	semidirect
121. #500174	C₂²	semidirect
122. #500079	C₂²	semidirect
123. #500073	C₂²	semidirect
124. #500071	C₂²	semidirect
125. #500065	C₂²	semidirect
126. #500020	C₂²	semidirect
127. #500020	C₂²	semidirect
128. #500020	C₂²	semidirect
129. #499846	C₂²	semidirect
130. #499846	C₂²	semidirect
131. #499846	C₂²	semidirect
132. #499845	C₂²	semidirect
133. #499845	C₂²	semidirect
135. #499844	C₂²	semidirect
136. #499844	C₂²	semidirect
137. #499843	C₂²	semidirect
138. #499843	C₂²	semidirect
139. #499838	C₂²	semidirect
140. #499837	C₂²	semidirect
141. #499837	C₂²	semidirect
142. #499837	C₂²	semidirect
143. #499834	C₂²	semidirect
144. #499833	C₂²	semidirect
145. #499833	C₂²	semidirect
146. #499833	C₂²	semidirect
147. #499832	C₂²	semidirect
148. #499831	C₂²	semidirect
149. #499831	C₂²	semidirect
150. #499831	C₂²	semidirect
151. #499809	C₂²	semidirect
152. #499804	C₂²	semidirect
153. #499800	C₂²	semidirect
154. #499797	C₂²	semidirect
155. #499289	C₂²	semidirect
156. #498931	C₂²	semidirect
157. #498928	C₂²	semidirect
158. #498927	C₂²	semidirect
159. #497516	C₂²	semidirect
160. #497514	C₂²	semidirect
161. #497355	C₂²	semidirect
162. #497353	C₂²	semidirect
163. #497307	C₂²	semidirect
164. #497307	C₂²	semidirect
165. D₄×#353	C₂²	semidirect
166. D₄×#353	C₂²	semidirect
167. #496515	C₂²	semidirect
168. #496311	C₂²	semidirect
169. #496246	C₂²	semidirect
170. #496241	C₂²	semidirect
171. #496240	C₂²	semidirect
172. #496203	C₂²	semidirect
173. #496203	C₂²	semidirect
174. #495746	C₂²	semidirect
175. #495744	C₂²	semidirect
176. #495586	C₂²	semidirect
177. #494685	C₂²	semidirect
178. #494682	C₂²	semidirect
179. #494681	C₂²	semidirect
180. #494596	C₂²	semidirect
181. #494596	C₂²	semidirect
182. C₂×#13047	C₂²	semidirect
183. #493957	C₂²	semidirect
184. #493430	C₂²	semidirect
185. #493430	C₂²	semidirect
186. #493430	C₂²	semidirect
188. C₂×H(7,𝔽₂)	C₂³	semidirect
190. D₄×H(5,𝔽₂)	C₂³	semidirect
192. #62852	C₂³	semidirect
193. #62812	C₂³	semidirect
194. C₂×#3498	D₄	semidirect
198. C₂×#3543	C₂³	semidirect
199. C₂²×#559	C₂³	semidirect
200. C₂²×D₄²	C₂³	semidirect
201. C₂²×#560	D₄	semidirect
202. C₄×#585	C₂³	semidirect
204. C₂²×#458	C₂³	semidirect
209. C₂×#3021	C₂³	semidirect
210. C₂×#3021	C₂³	semidirect
211. C₂×#3021	C₂³	semidirect
214. C₂×#3019	C₂³	semidirect
222. C₂×#2888	C₂³	semidirect
223. #59466	C₂³	semidirect
224. #59420	C₂³	semidirect
225. #59143	C₂³	semidirect
226. #59143	C₂³	semidirect
227. #59126	C₂³	semidirect
228. #59126	C₂³	semidirect
232. #52054	C₂³	semidirect
234. #52012	C₂³	semidirect
236. #52004	C₂³	semidirect
237. #50684	C₂³	semidirect
238. #50635	C₂³	semidirect
239. #49793	C₂³	semidirect
240. #48184	C₂³	semidirect
241. #48143	C₂³	semidirect
242. #48058	C₂³	semidirect
243. #47932	C₂³	semidirect
244. #47827	C₂³	semidirect
245. #46302	C₂³	semidirect
247. #45727	C₂³	semidirect
248. #45537	C₂³	semidirect
249. #45455	C₂³	semidirect
250. #45438	C₂³	semidirect
251. #39361	D₄	semidirect
252. #39361	D₄	semidirect
255. #38022	D₄	semidirect
257. #38020	D₄	semidirect
259. #37646	D₄	semidirect
261. #37644	D₄	semidirect
263. #37547	D₄	semidirect
264. #37175	C₂³	semidirect
265. #36955	D₄	semidirect
266. #36955	C₂³	semidirect
267. #36737	C₂³	semidirect
268. #36704	D₄	semidirect
269. #36702	D₄	semidirect
270. #36702	C₂³	semidirect
271. C₂×#2867	D₄	semidirect
272. #36128	D₄	semidirect
273. #36128	D₄	semidirect
276. #35527	D₄	semidirect
277. #35527	D₄	semidirect
283. #35272	D₄	semidirect
284. #35272	D₄	semidirect
285. #35272	D₄	semidirect
288. #34498	C₂³	semidirect
289. #34493	C₂³	semidirect
290. #34364	D₄	semidirect
291. #34364	C₂³	semidirect
292. #34364	C₂³	semidirect
293. C₂×#2366	C₂³	semidirect
294. C₄×#532	D₄	semidirect
297. C₂×#2200	C₂³	semidirect
298. C₂×#2200	C₂³	semidirect
300. C₂×#2198	C₂³	semidirect
301. C₂×#2198	C₂³	semidirect
302. C₂×#2198	C₂³	semidirect
303. C₂×#2198	C₂³	semidirect
304. C₂×#2198	C₂³	semidirect
307. C₂×#2196	C₂³	semidirect
308. C₂×#2196	C₂³	semidirect
309. C₂×#2196	C₂³	semidirect
310. C₂×#2196	C₂³	semidirect
311. C₂×#2127	C₂³	semidirect
312. C₂×#2127	C₂³	semidirect
313. C₂×#2127	C₂³	semidirect
314. C₂²×#353	C₂³	semidirect
315. C₂²×#353	C₂³	semidirect
316. C₂²×#353	C₂³	semidirect
317. C₂×#2121	C₂³	semidirect
318. C₂²×#352	C₂³	semidirect
319. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
320. #33023	C₂³	semidirect
322. #32977	C₂³	semidirect
325. #32920	C₂³	semidirect
326. #32901	C₂³	semidirect
327. #32901	C₂³	semidirect
328. #32901	C₂³	semidirect
330. #32900	C₂³	semidirect
338. #32888	C₂³	semidirect
339. #32888	C₂³	semidirect
340. #25901	C₂³	semidirect
343. #25739	C₂³	semidirect
346. #24412	C₂³	semidirect
347. #24412	C₂³	semidirect
349. #24405	C₂³	semidirect
352. #24263	C₂³	semidirect
354. #24224	C₂³	semidirect
357. #24058	C₂³	semidirect
358. #24056	C₂³	semidirect
361. #23912	C₂³	semidirect
366. #23901	C₂³	semidirect
369. D₄×#100	C₂³	semidirect
371. D₄×#99	C₂³	semidirect
373. #21481	C₂³	semidirect
374. C₄×#455	C₂³	semidirect
377. #20956	C₂³	semidirect
379. #20855	C₂³	semidirect
380. #20723	C₂³	semidirect
381. #20637	C₂³	semidirect
382. #20615	C₂³	semidirect
383. #20615	C₂³	semidirect
384. #20615	C₂³	semidirect
386. #20609	C₂³	semidirect
387. C₂×#1790	C₂³	semidirect
389. #20592	C₂³	semidirect
392. #20585	C₂³	semidirect
393. C₄×#413	C₂³	semidirect
394. #13462	C₂³	semidirect
395. #13425	C₂³	semidirect
396. #13424	C₂³	semidirect
397. #13423	C₂³	semidirect
398. #13423	C₂³	semidirect
399. #13422	C₂³	semidirect
400. #13422	C₂³	semidirect
401. #13420	C₂³	semidirect
402. #13376	C₂³	semidirect
403. #13376	C₂³	semidirect
404. #13376	C₂³	semidirect
405. #13349	C₂³	semidirect
406. #13349	C₂³	semidirect
407. #13349	C₂³	semidirect
409. #13348	C₂³	semidirect
410. #13348	C₂³	semidirect
412. #13347	C₂³	semidirect
413. #13347	C₂³	semidirect
414. #13347	C₂³	semidirect
415. #13347	C₂³	semidirect
416. #13347	C₂³	semidirect
419. #13346	C₂³	semidirect
420. #13346	C₂³	semidirect
421. #13346	C₂³	semidirect
422. #13346	C₂³	semidirect
424. #13344	C₂³	semidirect
425. #13344	C₂³	semidirect
426. #13297	C₂³	semidirect
427. #13294	C₂³	semidirect
428. #13223	C₂³	semidirect
429. #13223	C₂³	semidirect
430. #13222	C₂³	semidirect
431. #13219	C₂³	semidirect
432. #13088	C₂³	semidirect
433. #13088	C₂³	semidirect
434. #13088	C₂³	semidirect
435. #13088	C₂³	semidirect
436. #13086	C₂³	semidirect
437. #13086	C₂³	semidirect
438. #13084	C₂³	semidirect
439. #13084	C₂³	semidirect
444. #13082	C₂³	semidirect
445. #13082	C₂³	semidirect
446. #13081	C₂³	semidirect
447. #13081	C₂³	semidirect
448. #13081	C₂³	semidirect
449. #13081	C₂³	semidirect
450. #13080	C₂³	semidirect
451. #13080	C₂³	semidirect
453. #13049	C₂³	semidirect
454. #13049	C₂³	semidirect
455. #13049	C₂³	semidirect
456. #13049	C₂³	semidirect
457. #13049	C₂³	semidirect
460. #13047	C₂³	semidirect
461. #13047	C₂³	semidirect
462. #13047	C₂³	semidirect
463. #13047	C₂³	semidirect
464. #13047	C₂³	semidirect
465. #13047	C₂³	semidirect
466. #13047	C₂³	semidirect
467. #13044	C₂³	semidirect
468. #13044	C₂³	semidirect
469. #13044	C₂³	semidirect
471. #13043	C₂³	semidirect
472. #13043	C₂³	semidirect
473. #12966	C₂³	semidirect
474. #12966	C₂³	semidirect
475. #12964	C₂³	semidirect
476. #12964	C₂³	semidirect
477. #12964	C₂³	semidirect
478. #12961	C₂³	semidirect
479. #12960	C₂³	semidirect
480. #12857	C₂³	semidirect
481. #12854	C₂³	semidirect
482. #12854	C₂³	semidirect
483. #12852	C₂³	semidirect
484. #12798	C₂³	semidirect
485. #12797	C₂³	semidirect
486. #12796	C₂³	semidirect
487. #12795	C₂³	semidirect
488. #12762	C₂³	semidirect
489. #12760	C₂³	semidirect
490. #12760	C₂³	semidirect
491. #12759	C₂³	semidirect
492. #12759	C₂³	semidirect
495. #12697	C₂³	semidirect
496. #12696	C₂³	semidirect
497. #12696	C₂³	semidirect
498. #12696	C₂³	semidirect
501. #12693	C₂³	semidirect
502. #12693	C₂³	semidirect
503. #12693	C₂³	semidirect
504. #12690	C₂³	semidirect
505. #12688	C₂³	semidirect
506. #12687	C₂³	semidirect
507. C₄×#354	C₂³	semidirect
508. C₄×#353	C₂³	semidirect
509. #12622	C₂³	semidirect
510. #12621	C₂³	semidirect
511. #12574	C₂³	semidirect
512. #12574	C₂³	semidirect
513. C₂×#1390	C₂³	semidirect
518. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
534. C₂×#550	C₂×D₄	semidirect
538. C₂×D₄²	C₂×D₄	semidirect
551. C₂×#535	C₂×D₄	semidirect
552. C₂×#535	C₂×D₄	semidirect
553. C₂×#535	C₂×D₄	semidirect
559. C₂×#534	C₂×D₄	semidirect
565. C₂×#532	C₂×D₄	semidirect
571. C₂²×#127	C₂×D₄	semidirect
572. C₂²×#127	C₂×D₄	semidirect
573. C₂²×#127	C₂×D₄	semidirect
577. C₂²×#126	C₂×D₄	semidirect
582. C₂²×#121	C₂×D₄	semidirect
583. C₂²×#121	C₂×D₄	semidirect
584. C₂²×#121	C₂×D₄	semidirect
592. C₂×C₄×#41	C₂×D₄	semidirect
593. C₂×C₄×#41	C₂×D₄	semidirect
628. #2867	C₂×D₄	semidirect
629. #2867	C₂×D₄	semidirect
632. #2856	C₂×D₄	semidirect
633. #2856	C₂×D₄	semidirect
635. #2849	C₂×D₄	semidirect
636. #2849	C₂×D₄	semidirect
647. #2622	C₂×D₄	semidirect
650. #2619	C₂×D₄	semidirect
651. #2619	C₂×D₄	semidirect
653. #2618	C₂×D₄	semidirect
655. #2617	C₂×D₄	semidirect
657. #2613	C₂×D₄	semidirect
659. #2591	C₂×D₄	semidirect
660. #2579	C₂×D₄	semidirect
663. #2548	C₂×D₄	semidirect
664. #2548	C₂×D₄	semidirect
665. #2548	C₂×D₄	semidirect
667. #2541	C₂×D₄	semidirect
671. #2539	C₂×D₄	semidirect
672. #2534	C₂×D₄	semidirect
674. #2484	C₂×D₄	semidirect
675. #2482	C₂×D₄	semidirect
678. #2433	C₂×D₄	semidirect
679. #2433	C₂×D₄	semidirect
688. #2431	C₂×D₄	semidirect
689. #2431	C₂×D₄	semidirect
690. #2431	C₂×D₄	semidirect
691. #2431	C₂×D₄	semidirect
695. #2412	C₂×D₄	semidirect
697. #2410	C₂×D₄	semidirect
698. #2410	C₂×D₄	semidirect
699. #2410	C₂×D₄	semidirect
701. #2406	C₂×D₄	semidirect
704. #2405	C₂×D₄	semidirect
708. #2404	C₂×D₄	semidirect
711. #2403	C₂×D₄	semidirect
723. D₄×C₂²⋊C₄	C₂×D₄	semidirect
724. D₄×C₂²⋊C₄	C₂×D₄	semidirect
725. #2322	C₂×D₄	semidirect
727. #2321	C₂×D₄	semidirect
730. #2309	C₂×D₄	semidirect
731. #2309	C₂×D₄	semidirect
732. #2309	C₂×D₄	semidirect
737. #2308	C₂×D₄	semidirect
740. C₄×C₄⋊Q₈	C₂×D₄	semidirect
742. C₄×#124	C₂×D₄	semidirect
745. #2297	C₂×D₄	semidirect
746. #2297	C₂×D₄	semidirect
749. #2293	C₂×D₄	semidirect
750. C₂×#386	C₂×D₄	semidirect
752. #2285	C₂×D₄	semidirect
753. #2285	C₂×D₄	semidirect
754. #2283	C₂×D₄	semidirect
756. C₄²×D₄	C₂×D₄	semidirect
757. C₂×C₄³	C₂×D₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72341411	2
#72341408	2
#72341405	2
#72341403	2
#72341401	2
#72341394	2
#72341388	2
#72341381	2
#72318522	2
#72318494	2
#72318026	2
#72312346	2
#72312153	2
#72311315	2
#72311246	2
#72311231	2
#72306899	2
#72303059	2
#72285500	2
#72262180	2
#72249425	2
#72236706	2
#72236657	2
#72234146	2
#72215857	2