Subgroups — #72341145

Order 2048.

At least 7629 conjugacy classes of subgroups; only the 4044 normal subgroups are shown.

The subgroup lattice has 906 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341119	C₂	1	2	yes	maximal, complemented
2	#72341112	C₂	1	2	yes	maximal, complemented
3	#72341109	C₂	1	2	yes	maximal, complemented
4	#72341102	C₂	1	1	yes	maximal, characteristic, complemented
5	#72341094	C₂	1	2	yes	maximal, complemented
6	#72341090	C₂	1	2	yes	maximal, complemented
7	#72341086	C₂	1	8	yes	maximal, complemented
8	#72341078	C₂	1	2	yes	maximal, complemented
9	#72341064	C₂	1	2	yes	maximal, complemented
10	#72341023	C₂	1	8	yes	maximal, complemented
11	#72341021	C₂	1	2	yes	maximal, complemented
12	#72340990	C₂	1	1	yes	maximal, characteristic, complemented
13	#72338954	C₂	1	1	yes	maximal, characteristic, complemented
14	#72338740	C₂	1	1	yes	maximal, characteristic, complemented
15	#72338475	C₂	1	1	yes	maximal, characteristic, complemented
16	#72337646	C₂	1	2	yes	maximal, complemented
17	#72337626	C₂	1	1	yes	maximal, characteristic, complemented
18	#72265972	C₂	1	2	yes	maximal, complemented
19	#72265948	C₂	1	2	yes	maximal, complemented
20	#72251351	C₂	1	8	yes	maximal, complemented
21	#72240626	C₂	1	8	yes	maximal, complemented
22	#72236108	C₂	1	2	yes	maximal, complemented
23	#72213228	C₂	1	1	yes	maximal, characteristic, complemented
24	#10586066	C₂²	1	1	yes	characteristic, complemented
25	#8934620	C₂²	1	1	yes	characteristic, complemented
26	#8933802	C₂²	1	2	yes	complemented
27	#8933802	C₂²	1	1	yes	characteristic, complemented
28	#8926210	C₂²	1	2	yes	complemented
29	#8926210	C₂²	1	4	yes	complemented
30	#8925308	C₂²	1	2	yes	complemented
31	#8925308	C₂²	1	4	yes	complemented
32	#7806601	C₂²	1	2	yes	complemented
33	#7806601	C₂²	1	4	yes	complemented
34	#7739460	C₂²	1	4	yes	—
35	#7739460	C₂²	1	2	yes	—
36	#7739460	C₂²	1	4	yes	complemented
37	#7643002	C₂²	1	1	yes	characteristic
38	#7643002	C₂²	1	1	yes	characteristic
39	#7643002	C₂²	1	2	yes	complemented
40	C₂×#35527	C₂²	1	1	yes	characteristic
41	#6629398	C₂²	1	4	yes	complemented
42	#6629267	C₂²	1	1	yes	characteristic
43	#6629267	C₂²	1	1	yes	characteristic, complemented
44	#6628901	C₂²	1	1	yes	characteristic
45	#6628901	C₂²	1	1	yes	characteristic, complemented
46	#6628901	C₂²	1	2	yes	complemented
47	#6628897	C₂²	1	2	yes	complemented
48	#6628892	C₂²	1	4	yes	complemented
49	#6487656	C₂²	1	8	yes	complemented
50	#6487656	C₂²	1	4	yes	complemented
51	#6470244	C₂²	1	8	yes	complemented
52	#6470244	C₂²	1	2	yes	complemented
53	#6470244	C₂²	1	4	yes	complemented
54	#6470237	C₂²	1	8	yes	complemented
55	#6470237	C₂²	1	4	yes	complemented
56	#6470237	C₂²	1	4	yes	complemented
57	#6470232	C₂²	1	2	yes	complemented
58	#6470232	C₂²	1	4	yes	complemented
59	#6470225	C₂²	1	8	yes	complemented
60	#6470225	C₂²	1	4	yes	complemented
61	#6432958	C₂²	1	1	yes	characteristic
62	#6432958	C₂²	1	1	yes	characteristic
63	#6432958	C₂²	1	1	yes	characteristic, complemented
64	#6432958	C₂²	1	1	yes	characteristic, complemented
65	#6385975	C₂²	1	2	yes	complemented
66	#6385975	C₂²	1	4	yes	complemented
67	#6374211	C₂²	1	1	yes	characteristic, complemented
68	#6374211	C₂²	1	1	yes	characteristic, complemented
69	#6370693	C₂²	1	1	yes	characteristic, complemented
70	#251929	C₂²	1	8	yes	complemented
71	#251929	C₂²	1	8	yes	complemented
72	#251924	C₂²	1	8	yes	complemented
73	#251914	C₂²	1	8	yes	complemented
74	#251914	C₂²	1	8	yes	complemented
75	#251908	C₂²	1	8	yes	complemented
76	#251903	C₂²	1	4	yes	complemented
77	#251899	C₂²	1	8	yes	complemented
78	#251893	C₂²	1	8	yes	complemented
79	#251883	C₂²	1	8	yes	complemented
80	#251883	C₂²	1	4	yes	complemented
81	#251877	C₂²	1	8	yes	complemented
82	#251877	C₂²	1	8	yes	complemented
83	#251874	C₂²	1	4	yes	complemented
84	#251872	C₂²	1	4	yes	complemented
85	#251872	C₂²	1	8	yes	complemented
86	#251872	C₂²	1	4	yes	complemented
87	#251872	C₂²	1	4	yes	complemented
88	#251864	C₂²	1	8	yes	complemented
89	#251864	C₂²	1	8	yes	complemented
90	#251857	C₂²	1	2	yes	complemented
91	#251855	C₂²	1	2	yes	complemented
92	#251855	C₂²	1	2	yes	complemented
93	#251855	C₂²	1	2	yes	complemented
94	#251855	C₂²	1	8	yes	complemented
95	#251849	C₂²	1	4	yes	complemented
96	#251847	C₂²	1	8	yes	complemented
97	#251841	C₂²	1	8	yes	complemented
98	#251835	C₂²	1	2	yes	complemented
99	#251833	C₂²	1	2	yes	complemented
100	#251833	C₂²	1	2	yes	complemented
101	#251833	C₂²	1	2	yes	complemented
102	#251827	C₂²	1	8	yes	complemented
103	#251827	C₂²	1	4	yes	complemented
104	#245293	C₂²	1	8	yes	complemented
105	#245290	C₂²	1	8	yes	complemented
106	#245290	C₂²	1	8	yes	complemented
107	#245283	C₂²	1	8	yes	complemented
108	#245283	C₂²	1	8	yes	complemented
109	#245281	C₂²	1	8	yes	complemented
110	#245281	C₂²	1	8	yes	complemented
111	#245270	C₂²	1	8	yes	complemented
112	#245270	C₂²	1	8	yes	complemented
113	#245267	C₂²	1	4	yes	complemented
114	#245267	C₂²	1	4	yes	complemented
115	#245255	C₂²	1	4	yes	complemented
116	#245255	C₂²	1	8	yes	complemented
117	#245255	C₂²	1	8	yes	complemented
118	#245255	C₂²	1	4	yes	complemented
119	#245255	C₂²	1	4	yes	complemented
120	#245255	C₂²	1	8	yes	complemented
121	#245255	C₂²	1	4	yes	complemented
122	#245247	C₂²	1	8	yes	complemented
123	#245247	C₂²	1	8	yes	complemented
124	#245243	C₂²	1	8	yes	complemented
125	#245241	C₂²	1	2	yes	complemented
126	#245234	C₂²	1	2	yes	—
127	#245234	C₂²	1	2	yes	complemented
128	#245234	C₂²	1	4	yes	complemented
129	#245234	C₂²	1	2	yes	complemented
130	#245234	C₂²	1	2	yes	complemented
131	#245233	C₂²	1	2	yes	—
132	#245233	C₂²	1	2	yes	complemented
133	#245233	C₂²	1	2	yes	complemented
134	#245233	C₂²	1	8	yes	complemented
135	#245233	C₂²	1	4	yes	complemented
136	#245227	C₂²	1	8	yes	complemented
137	#245227	C₂²	1	8	yes	complemented
138	#238077	C₂²	1	4	yes	complemented
139	C₂×#10390	C₂²	1	4	yes	complemented
140	#233559	C₂²	1	4	yes	complemented
141	#233549	C₂²	1	8	yes	complemented
142	#233549	C₂²	1	4	yes	complemented
143	#233541	C₂²	1	8	yes	complemented
144	#213882	C₂²	1	8	yes	complemented
145	#213880	C₂²	1	8	yes	complemented
146	#213880	C₂²	1	4	yes	complemented
147	#213877	C₂²	1	4	yes	complemented
148	#213873	C₂²	1	4	yes	complemented
149	#213865	C₂²	1	2	yes	complemented
150	#213861	C₂²	1	2	yes	complemented
151	#213861	C₂²	1	1	yes	characteristic, complemented
152	#213860	C₂²	1	1	yes	characteristic, complemented
153	#213855	C₂²	1	2	yes	complemented
154	#213845	C₂²	1	4	yes	complemented
155	#213842	C₂²	1	2	yes	complemented
156	#213838	C₂²	1	2	yes	complemented
157	#213838	C₂²	1	2	yes	complemented
158	#213831	C₂²	1	2	yes	complemented
159	#201717	C₂²	1	8	yes	complemented
160	#201717	C₂²	1	8	yes	complemented
161	#201701	C₂²	1	4	yes	complemented
162	#201701	C₂²	1	4	yes	complemented
163	#201690	C₂²	1	4	yes	complemented
164	#201678	C₂²	1	8	yes	complemented
165	#201678	C₂²	1	8	yes	complemented
166	#201664	C₂²	1	4	yes	complemented
167	#190124	C₂²	1	4	yes	complemented
168	#190107	C₂²	1	2	yes	complemented
169	#188064	C₂²	1	4	yes	complemented
170	C₂×#8546	C₂²	1	2	yes	complemented
171	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
172	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
173	#62842	C₂³	1	1	yes	characteristic
174	#62842	C₂³	1	1	yes	characteristic
175	#62842	C₂³	1	4	yes	—
176	C₂×#3484	C₂³	1	4	yes	—
177	C₂×#3484	C₂³	1	1	yes	characteristic
178	C₂×#3484	C₂³	1	1	yes	characteristic
179	C₂×#3484	C₂³	1	2	yes	complemented
180	C₂²×#560	C₂³	1	2	yes	—
181	C₂³×#127	C₂³	1	1	yes	characteristic
182	#62652	C₂³	1	1	yes	characteristic
183	#47563	C₂³	1	2	yes	—
184	#47563	C₂³	1	4	yes	complemented
185	#46998	C₂³	1	2	yes	—
186	#46998	C₂³	1	4	yes	complemented
187	#46996	C₂³	1	2	yes	complemented
188	#46996	C₂³	1	4	yes	complemented
189	#46837	C₂³	1	4	yes	complemented
190	#46837	C₂³	1	2	yes	complemented
191	#46385	C₂³	1	4	yes	—
192	#46385	C₂³	1	4	yes	complemented
193	#46385	C₂³	1	4	yes	complemented
194	#46385	C₂³	1	4	yes	complemented
195	#46385	C₂³	1	4	yes	complemented
196	#46385	C₂³	1	4	yes	complemented
197	#39332	D₄	1	8	yes	complemented
198	#38904	D₄	1	8	yes	complemented
199	#38030	D₄	1	8	yes	complemented
200	#37646	D₄	1	8	yes	complemented
201	#37436	C₂³	1	8	yes	—
202	#37436	C₂³	1	4	yes	—
203	#37436	C₂³	1	2	yes	complemented
204	#37232	D₄	1	4	yes	complemented
205	#37232	C₂³	1	4	yes	—
206	#37232	C₂³	1	4	yes	—
207	#37232	C₂³	1	4	yes	—
208	#37232	C₂³	1	4	yes	—
209	#37232	C₂³	1	2	yes	—
210	#37232	C₂³	1	4	yes	complemented
211	#37232	C₂³	1	4	yes	complemented
212	#36965	C₂³	1	4	yes	—
213	#36965	C₂³	1	2	yes	—
214	#36965	C₂³	1	4	yes	complemented
215	#36721	C₂³	1	8	yes	—
216	#36721	C₂³	1	4	yes	—
217	#36721	C₂³	1	4	yes	complemented
218	#36721	C₂³	1	4	yes	complemented
219	C₂×#2840	C₂³	1	2	yes	complemented
220	#36626	D₄	1	2	yes	complemented
221	#35554	C₂³	1	2	yes	—
222	#35554	C₂³	1	1	yes	characteristic
223	#35554	C₂³	1	1	yes	characteristic
224	#35554	C₂³	1	1	yes	characteristic
225	#35554	C₂³	1	1	yes	characteristic
226	#35554	C₂³	1	2	yes	complemented
227	#35528	D₄	1	2	yes	complemented
228	#35528	D₄	1	2	yes	complemented
229	#35527	C₂³	1	2	yes	—
230	#35527	C₂³	1	1	yes	characteristic
231	#35527	C₂³	1	1	yes	characteristic
232	#35527	C₂³	1	1	yes	characteristic
233	#35527	C₂³	1	4	yes	—
234	#35527	C₂³	1	4	yes	—
235	#35527	C₂³	1	1	yes	characteristic
236	#35527	C₂³	1	1	yes	characteristic
237	#35527	C₂³	1	1	yes	characteristic
238	#35527	C₂³	1	1	yes	characteristic
239	#35527	C₂³	1	1	yes	characteristic
240	#35527	C₂³	1	2	yes	—
241	#35527	C₂³	1	2	yes	complemented
242	#35527	C₂³	1	4	yes	complemented
243	#35446	C₂³	1	4	yes	—
244	#35446	C₂³	1	2	yes	—
245	#35446	C₂³	1	4	yes	complemented
246	#35354	C₂³	1	8	yes	—
247	#35354	C₂³	1	4	yes	—
248	#35354	C₂³	1	4	yes	complemented
249	#35354	C₂³	1	4	yes	complemented
250	#35222	D₄	1	2	yes	complemented
251	#34980	D₄	1	4	yes	complemented
252	#34980	C₂³	1	8	yes	—
253	#34980	C₂³	1	4	yes	—
254	#34980	C₂³	1	4	yes	—
255	#34980	C₂³	1	4	yes	—
256	#34980	C₂³	1	4	yes	complemented
257	C₂×#2403	C₂³	1	4	yes	—
258	#34356	C₂³	1	2	yes	—
259	#34356	C₂³	1	4	yes	—
260	#34356	C₂³	1	4	yes	complemented
261	#34171	C₂³	1	1	yes	characteristic
262	#34171	C₂³	1	1	yes	characteristic
263	#34171	C₂³	1	2	yes	complemented
264	C₂×#2309	C₂³	1	1	yes	characteristic
265	#33022	C₂³	1	4	yes	—
266	#33022	C₂³	1	8	yes	—
267	#33022	C₂³	1	4	yes	complemented
268	#33020	C₂³	1	4	yes	—
269	#33020	C₂³	1	8	yes	—
270	#33020	C₂³	1	8	yes	—
271	#33020	C₂³	1	8	yes	—
272	#33020	C₂³	1	4	yes	—
273	#33020	C₂³	1	4	yes	complemented
274	#33020	C₂³	1	4	yes	complemented
275	#32900	C₂³	1	4	yes	—
276	#32900	C₂³	1	4	yes	—
277	#32900	C₂³	1	8	yes	—
278	#32900	C₂³	1	4	yes	—
279	#32900	C₂³	1	8	yes	—
280	#32900	C₂³	1	4	yes	complemented
281	#32898	C₂³	1	4	yes	—
282	#32898	C₂³	1	8	yes	—
283	#32898	C₂³	1	4	yes	—
284	#32898	C₂³	1	8	yes	—
285	#32898	C₂³	1	4	yes	—
286	#32898	C₂³	1	8	yes	—
287	#32898	C₂³	1	8	yes	—
288	#32898	C₂³	1	4	yes	—
289	#32898	C₂³	1	4	yes	complemented
290	#32898	C₂³	1	4	yes	complemented
291	#29635	C₂³	1	8	yes	—
292	#29635	C₂³	1	8	yes	—
293	#29635	C₂³	1	8	yes	—
294	#29635	C₂³	1	8	yes	complemented
295	#29634	C₂³	1	8	yes	—
296	#29634	C₂³	1	8	yes	—
297	#29634	C₂³	1	8	yes	—
298	#29634	C₂³	1	8	yes	—
299	#29634	C₂³	1	8	yes	—
300	#29634	C₂³	1	8	yes	—
301	#29634	C₂³	1	8	yes	—
302	#29634	C₂³	1	8	yes	—
303	#29634	C₂³	1	8	yes	complemented
304	#29634	C₂³	1	8	yes	complemented
305	#21795	C₂³	1	8	yes	—
306	#21795	C₂³	1	4	yes	—
307	#21749	C₂³	1	4	yes	—
308	#21749	C₂³	1	4	yes	—
309	#21749	C₂³	1	4	yes	—
310	#21749	C₂³	1	4	yes	—
311	#21749	C₂³	1	4	yes	—
312	#21746	C₂³	1	8	yes	—
313	#21746	C₂³	1	4	yes	—
314	#21746	C₂³	1	4	yes	—
315	#21746	C₂³	1	4	yes	—
316	#21746	C₂³	1	8	yes	complemented
317	#21746	C₂³	1	8	yes	complemented
318	#20724	C₂³	1	4	yes	—
319	#20724	C₂³	1	8	yes	—
320	#20690	C₂³	1	1	yes	characteristic
321	#20690	C₂³	1	1	yes	characteristic
322	#20690	C₂³	1	1	yes	characteristic
323	#20690	C₂³	1	1	yes	characteristic
324	#20586	C₂³	1	1	yes	characteristic
325	#20586	C₂³	1	1	yes	characteristic
326	#20586	C₂³	1	1	yes	characteristic
327	#20586	C₂³	1	2	yes	—
328	#20586	C₂³	1	4	yes	—
329	#20586	C₂³	1	1	yes	characteristic
330	#20586	C₂³	1	1	yes	characteristic
331	#20586	C₂³	1	1	yes	characteristic
332	#20586	C₂³	1	1	yes	characteristic
333	#20586	C₂³	1	1	yes	characteristic
334	#20585	C₂³	1	2	yes	—
335	#20585	C₂³	1	4	yes	—
336	#20585	C₂³	1	4	yes	—
337	C₂×#1781	C₂³	1	8	yes	—
338	C₂×#1781	C₂³	1	4	yes	—
339	C₂×#1781	C₂³	1	4	yes	—
340	C₂×#1781	C₂³	1	4	yes	complemented
341	C₂×#1781	C₂³	1	4	yes	complemented
342	#10391	C₂³	1	4	yes	complemented
343	#10391	C₂³	1	8	yes	complemented
344	#10391	C₂³	1	4	yes	complemented
345	#10390	C₂³	1	4	yes	—
346	#10390	C₂³	1	8	yes	—
347	#10390	C₂³	1	4	yes	—
348	#10390	C₂³	1	4	yes	complemented
349	#10390	C₂³	1	4	yes	complemented
350	#10390	C₂³	1	4	yes	complemented
351	#10390	C₂³	1	8	yes	complemented
352	#10390	C₂³	1	8	yes	complemented
353	#10390	C₂³	1	4	yes	complemented
354	#10339	C₂³	1	4	yes	complemented
355	#10338	C₂³	1	4	yes	—
356	#10338	C₂³	1	8	yes	complemented
357	#10338	C₂³	1	8	yes	complemented
358	#10338	C₂³	1	8	yes	complemented
359	#10338	C₂³	1	4	yes	complemented
360	#10338	C₂³	1	4	yes	complemented
361	#10337	C₂³	1	8	yes	—
362	#10337	C₂³	1	8	yes	—
363	#10337	C₂³	1	8	yes	—
364	#10337	C₂³	1	8	yes	complemented
365	#10337	C₂³	1	4	yes	complemented
366	#10337	C₂³	1	8	yes	complemented
367	#10337	C₂³	1	8	yes	complemented
368	#10337	C₂³	1	8	yes	complemented
369	#10337	C₂³	1	8	yes	complemented
370	#10337	C₂³	1	8	yes	complemented
371	#10337	C₂³	1	8	yes	complemented
372	#10337	C₂³	1	8	yes	complemented
373	#10336	C₂³	1	8	yes	—
374	#10336	C₂³	1	8	yes	—
375	#10336	C₂³	1	4	yes	—
376	#10336	C₂³	1	8	yes	complemented
377	#10336	C₂³	1	8	yes	complemented
378	#10336	C₂³	1	4	yes	complemented
379	#10336	C₂³	1	8	yes	complemented
380	#10336	C₂³	1	8	yes	complemented
381	#10336	C₂³	1	4	yes	complemented
382	#9502	C₂³	1	8	yes	complemented
383	#9502	C₂³	1	8	yes	complemented
384	#9501	C₂³	1	4	yes	—
385	#9501	C₂³	1	4	yes	—
386	#9501	C₂³	1	4	yes	—
387	#9501	C₂³	1	4	yes	—
388	#9501	C₂³	1	4	yes	complemented
389	#9501	C₂³	1	8	yes	complemented
390	#9501	C₂³	1	4	yes	complemented
391	#9501	C₂³	1	8	yes	complemented
392	#9501	C₂³	1	8	yes	complemented
393	#9500	C₂³	1	8	yes	complemented
394	#9500	C₂³	1	8	yes	complemented
395	#9499	C₂³	1	8	yes	complemented
396	#9499	C₂³	1	8	yes	complemented
397	#9499	C₂³	1	8	yes	complemented
398	#9499	C₂³	1	8	yes	complemented
399	#9498	C₂³	1	8	yes	—
400	#9498	C₂³	1	8	yes	complemented
401	#9498	C₂³	1	8	yes	complemented
402	#9498	C₂³	1	8	yes	complemented
403	#9498	C₂³	1	8	yes	complemented
404	#9498	C₂³	1	8	yes	complemented
405	#9497	C₂³	1	4	yes	—
406	#9497	C₂³	1	4	yes	—
407	#9497	C₂³	1	4	yes	—
408	#9497	C₂³	1	4	yes	—
409	#9497	C₂³	1	8	yes	—
410	#9497	C₂³	1	4	yes	—
411	#9497	C₂³	1	4	yes	—
412	#9497	C₂³	1	4	yes	complemented
413	#9497	C₂³	1	8	yes	complemented
414	#9497	C₂³	1	4	yes	complemented
415	#9497	C₂³	1	8	yes	complemented
416	#9497	C₂³	1	8	yes	complemented
417	#9497	C₂³	1	4	yes	complemented
418	#9497	C₂³	1	8	yes	complemented
419	#9497	C₂³	1	4	yes	complemented
420	#9497	C₂³	1	8	yes	complemented
421	#9497	C₂³	1	8	yes	complemented
422	#9496	C₂³	1	8	yes	—
423	#9496	C₂³	1	8	yes	complemented
424	#9496	C₂³	1	8	yes	complemented
425	#9496	C₂³	1	8	yes	complemented
426	#9496	C₂³	1	8	yes	complemented
427	#9496	C₂³	1	8	yes	complemented
428	#9495	C₂³	1	8	yes	—
429	#9495	C₂³	1	8	yes	—
430	#9495	C₂³	1	8	yes	complemented
431	#9495	C₂³	1	8	yes	complemented
432	#9495	C₂³	1	8	yes	complemented
433	#9495	C₂³	1	8	yes	complemented
434	#9495	C₂³	1	8	yes	complemented
435	#9495	C₂³	1	8	yes	complemented
436	#9495	C₂³	1	8	yes	complemented
437	#9495	C₂³	1	8	yes	complemented
438	#8750	C₂³	1	8	yes	complemented
439	#8750	C₂³	1	8	yes	complemented
440	#8749	C₂³	1	4	yes	—
441	#8749	C₂³	1	4	yes	complemented
442	#8748	C₂³	1	2	yes	—
443	#8748	C₂³	1	2	yes	—
444	#8748	C₂³	1	4	yes	complemented
445	#8747	C₂³	1	4	yes	complemented
446	#8747	C₂³	1	4	yes	complemented
447	#8746	C₂³	1	4	yes	complemented
448	#8746	C₂³	1	4	yes	complemented
449	#8546	C₂³	1	4	yes	—
450	#8546	C₂³	1	2	yes	—
451	#8546	C₂³	1	2	yes	—
452	#8546	C₂³	1	4	yes	complemented
453	#8546	C₂³	1	4	yes	complemented
454	#8546	C₂³	1	4	yes	complemented
455	#8546	C₂³	1	4	yes	complemented
456	#8543	C₂³	1	8	yes	complemented
457	#8543	C₂³	1	4	yes	complemented
458	#8543	C₂³	1	4	yes	complemented
459	#8543	C₂³	1	8	yes	complemented
460	#8101	C₂³	1	8	yes	complemented
461	#8101	C₂³	1	4	yes	complemented
462	C₂×#1304	C₂³	1	4	yes	complemented
463	C₂×#1304	C₂³	1	8	yes	complemented
464	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
465	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
466	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
467	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
468	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
469	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
470	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
471	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
472	C₂⁴×D₄	C₂×D₄	1	2	yes	—
473	C₂⁴×D₄	C₂⁴	1	2	yes	—
474	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
475	C₂⁴×D₄	C₂⁴	1	2	yes	—
476	C₂×#546	C₂×D₄	1	8	yes	—
477	C₂×D₄²	C₂×D₄	1	8	yes	—
478	C₂×#535	C₂×D₄	1	2	yes	—
479	C₂×#535	C₂×D₄	1	2	yes	—
480	C₂×#535	C₂×D₄	1	2	yes	—
481	C₂×#535	C₂×D₄	1	4	yes	complemented
482	C₂×#534	C₂×D₄	1	8	yes	—
483	C₂×#534	C₂×D₄	1	2	yes	—
484	C₂×#534	C₂⁴	1	4	yes	—
485	C₂×#534	C₂⁴	1	4	yes	—
486	C₂×#534	C₂⁴	1	2	yes	—
487	C₂×#534	C₂⁴	1	4	yes	—
488	C₂×#534	C₂⁴	1	2	yes	—
489	C₂²×#127	C₂×D₄	1	2	yes	—
490	C₂²×#127	C₂×D₄	1	1	yes	characteristic
491	C₂²×#127	C₂×D₄	1	1	yes	characteristic
492	C₂²×#127	C₂⁴	1	1	yes	characteristic
493	C₂²×#127	C₂⁴	1	1	yes	characteristic
494	C₂²×#127	C₂⁴	1	2	yes	—
495	C₂²×#127	C₂⁴	1	2	yes	—
496	C₂²×#126	C₂×D₄	1	4	yes	—
497	C₂×#525	C₂×D₄	1	2	yes	—
498	C₂²×#123	C₂×D₄	1	4	yes	complemented
499	C₂²×#123	C₂⁴	1	4	yes	—
500	C₂²×#123	C₂⁴	1	2	yes	—
501	C₂²×#121	C₂×D₄	1	4	yes	—
502	C₂²×#121	C₂×D₄	1	4	yes	—
503	C₂²×#121	C₂×D₄	1	4	yes	—
504	C₂²×#120	C₂×D₄	1	2	yes	—
505	C₂²×#120	C₂⁴	1	4	yes	—
506	C₂²×#120	C₂⁴	1	2	yes	—
507	C₂²×#120	C₂⁴	1	2	yes	—
508	C₂×#518	C₂×D₄	1	2	yes	—
509	C₂×#518	C₂⁴	1	4	yes	—
510	C₂×#518	C₂⁴	1	1	yes	characteristic
511	C₂×#518	C₂⁴	1	2	yes	—
512	C₂×#518	C₂⁴	1	1	yes	characteristic
513	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
514	#2853	C₂×D₄	1	8	yes	—
515	#2853	C₂×D₄	1	4	yes	complemented
516	#2849	C₂×D₄	1	8	yes	—
517	#2849	C₂×D₄	1	4	yes	complemented
518	#2847	C₂×D₄	1	8	yes	complemented
519	#2846	C₂×D₄	1	8	yes	—
520	#2840	C₂⁴	1	4	yes	—
521	#2840	C₂⁴	1	2	yes	—
522	#2840	C₂⁴	1	2	yes	—
523	#2622	C₂×D₄	1	8	yes	—
524	#2622	C₂×D₄	1	4	yes	complemented
525	#2618	C₂×D₄	1	8	yes	complemented
526	#2613	C₂×D₄	1	8	yes	—
527	#2613	C₂×D₄	1	8	yes	—
528	#2613	C₂×D₄	1	4	yes	complemented
529	#2539	C₂×D₄	1	8	yes	complemented
530	#2534	C₂×D₄	1	8	yes	complemented
531	#2504	C₂×D₄	1	8	yes	complemented
532	#2487	C₂×D₄	1	8	yes	complemented
533	#2483	C₂⁴	1	2	yes	—
534	#2483	C₂⁴	1	8	yes	—
535	#2483	C₂⁴	1	4	yes	—
536	#2413	C₂×D₄	1	8	yes	complemented
537	#2412	C₂×D₄	1	8	yes	—
538	#2410	C₂×D₄	1	8	yes	—
539	#2410	C₂×D₄	1	8	yes	—
540	#2410	C₂×D₄	1	8	yes	—
541	#2410	C₂×D₄	1	8	yes	—
542	#2410	C₂×D₄	1	8	yes	—
543	#2410	C₂×D₄	1	8	yes	complemented
544	#2406	C₂×D₄	1	8	yes	complemented
545	#2405	C₂×D₄	1	4	yes	—
546	#2405	C₂×D₄	1	4	yes	—
547	#2405	C₂×D₄	1	8	yes	—
548	#2405	C₂⁴	1	4	yes	—
549	#2405	C₂⁴	1	4	yes	—
550	#2405	C₂⁴	1	4	yes	—
551	#2405	C₂⁴	1	8	yes	—
552	#2405	C₂⁴	1	8	yes	—
553	#2405	C₂⁴	1	8	yes	—
554	#2405	C₂⁴	1	8	yes	—
555	#2405	C₂⁴	1	4	yes	—
556	#2405	C₂⁴	1	4	yes	—
557	#2405	C₂⁴	1	4	yes	—
558	#2405	C₂⁴	1	4	yes	—
559	#2405	C₂⁴	1	4	yes	—
560	#2405	C₂⁴	1	4	yes	—
561	#2405	C₂⁴	1	4	yes	—
562	#2405	C₂⁴	1	4	yes	—
563	#2403	C₂×D₄	1	4	yes	—
564	#2403	C₂×D₄	1	8	yes	—
565	#2403	C₂×D₄	1	4	yes	—
566	#2403	C₂×D₄	1	8	yes	complemented
567	#2403	C₂⁴	1	4	yes	—
568	#2403	C₂⁴	1	4	yes	—
569	#2403	C₂⁴	1	2	yes	—
570	#2403	C₂⁴	1	4	yes	—
571	#2403	C₂⁴	1	8	yes	—
572	#2403	C₂⁴	1	4	yes	—
573	#2403	C₂⁴	1	4	yes	—
574	#2403	C₂⁴	1	8	yes	—
575	#2403	C₂⁴	1	8	yes	—
576	#2403	C₂⁴	1	4	yes	—
577	#2403	C₂⁴	1	4	yes	—
578	#2403	C₂⁴	1	4	yes	—
579	#2403	C₂⁴	1	4	yes	—
580	#2403	C₂⁴	1	4	yes	—
581	#2403	C₂⁴	1	4	yes	—
582	#2403	C₂⁴	1	4	yes	—
583	#2403	C₂⁴	1	4	yes	—
584	#2342	C₂×D₄	1	8	yes	—
585	D₄×C₂²⋊C₄	C₂×D₄	1	8	yes	—
586	#2322	C₂×D₄	1	8	yes	complemented
587	#2312	C₂⁴	1	4	yes	—
588	#2312	C₂⁴	1	4	yes	—
589	#2312	C₂⁴	1	8	yes	—
590	#2312	C₂⁴	1	4	yes	—
591	#2309	C₂×D₄	1	2	yes	—
592	#2309	C₂×D₄	1	2	yes	—
593	#2309	C₂⁴	1	2	yes	—
594	#2309	C₂⁴	1	4	yes	—
595	#2309	C₂⁴	1	2	yes	—
596	#2309	C₂⁴	1	1	yes	characteristic
597	#2309	C₂⁴	1	1	yes	characteristic
598	#2309	C₂⁴	1	1	yes	characteristic
599	#2309	C₂⁴	1	1	yes	characteristic
600	#2309	C₂⁴	1	4	yes	—
601	#2309	C₂⁴	1	2	yes	—
602	#2309	C₂⁴	1	1	yes	characteristic
603	#2309	C₂⁴	1	2	yes	—
604	#2309	C₂⁴	1	1	yes	characteristic
605	#2308	C₂×D₄	1	8	yes	—
606	#2308	C₂×D₄	1	2	yes	—
607	#2308	C₂×D₄	1	4	yes	complemented
608	#2308	C₂⁴	1	4	yes	—
609	#2308	C₂⁴	1	4	yes	—
610	#2308	C₂⁴	1	4	yes	—
611	#2308	C₂⁴	1	2	yes	—
612	#2308	C₂⁴	1	2	yes	—
613	#2308	C₂⁴	1	2	yes	—
614	C₄×#120	C₂×D₄	1	8	yes	complemented
615	#2297	C₂×D₄	1	2	yes	—
616	#2297	C₂×D₄	1	2	yes	—
617	#2297	C₂×D₄	1	4	yes	complemented
618	#2296	C₂×D₄	1	2	yes	—
619	#2296	C₂×D₄	1	2	yes	—
620	#2280	C₂×D₄	1	2	yes	—
621	C₂×#379	C₂×D₄	1	2	yes	—
622	C₂×#379	C₂⁴	1	8	yes	—
623	C₂×#379	C₂⁴	1	2	yes	—
624	C₂×#379	C₂⁴	1	2	yes	—
625	C₂×#379	C₂⁴	1	4	yes	—
626	C₂×#379	C₂⁴	1	2	yes	—
627	#1819	C₂⁴	1	8	yes	—
628	#1819	C₂⁴	1	4	yes	—
629	#1819	C₂⁴	1	4	yes	—
630	#1819	C₂⁴	1	8	yes	—
631	#1819	C₂⁴	1	4	yes	—
632	#1819	C₂⁴	1	8	yes	—
633	#1819	C₂⁴	1	4	yes	—
634	#1819	C₂⁴	1	8	yes	—
635	#1819	C₂⁴	1	8	yes	—
636	#1819	C₂⁴	1	8	yes	—
637	#1819	C₂⁴	1	8	yes	—
638	#1781	C₂⁴	1	8	yes	—
639	#1781	C₂⁴	1	4	yes	—
640	#1781	C₂⁴	1	8	yes	—
641	#1781	C₂⁴	1	8	yes	—
642	#1781	C₂⁴	1	8	yes	—
643	#1781	C₂⁴	1	4	yes	—
644	#1781	C₂⁴	1	4	yes	—
645	#1781	C₂⁴	1	4	yes	—
646	#1781	C₂⁴	1	4	yes	—
647	#1781	C₂⁴	1	4	yes	—
648	#1781	C₂⁴	1	8	yes	—
649	#1781	C₂⁴	1	8	yes	—
650	#1781	C₂⁴	1	8	yes	—
651	#1781	C₂⁴	1	4	yes	—
652	#1781	C₂⁴	1	4	yes	—
653	#1781	C₂⁴	1	4	yes	—
654	#1781	C₂⁴	1	4	yes	—
655	#1781	C₂⁴	1	4	yes	—
656	#1781	C₂⁴	1	4	yes	—
657	#1781	C₂⁴	1	8	yes	—
658	#1781	C₂⁴	1	8	yes	—
659	#1781	C₂⁴	1	4	yes	—
660	#1781	C₂⁴	1	8	yes	—
661	#1781	C₂⁴	1	8	yes	—
662	#1781	C₂⁴	1	4	yes	—
663	#1781	C₂⁴	1	8	yes	—
664	#1781	C₂⁴	1	4	yes	—
665	#1781	C₂⁴	1	8	yes	—
666	#1781	C₂⁴	1	4	yes	—
667	#1304	C₂⁴	1	8	yes	—
668	#1304	C₂⁴	1	8	yes	—
669	#1304	C₂⁴	1	8	yes	—
670	#1304	C₂⁴	1	8	yes	—
671	#1304	C₂⁴	1	4	yes	—
672	#1304	C₂⁴	1	8	yes	—
673	#1304	C₂⁴	1	4	yes	—
674	#1304	C₂⁴	1	8	yes	—
675	#1304	C₂⁴	1	8	yes	—
676	#1304	C₂⁴	1	8	yes	—
677	#1304	C₂⁴	1	8	yes	—
678	#1304	C₂⁴	1	4	yes	—
679	#1304	C₂⁴	1	8	yes	—
680	#1304	C₂⁴	1	4	yes	—
681	C₂⁶	C₂²×D₄	1	2	yes	—
682	C₂⁶	C₂²×D₄	1	1	yes	characteristic
683	C₂⁶	H(5,𝔽₂)	1	2	yes	—
684	C₂⁶	C₂⁵	1	1	yes	characteristic
685	C₂²×#41	C₂²×D₄	1	2	yes	—
686	C₂²×#41	C₂²×D₄	1	4	yes	—
687	C₂³×D₄	#120	1	4	yes	—
688	C₂³×D₄	C₂²×D₄	1	8	yes	—
689	C₂³×D₄	C₂²×D₄	1	4	yes	—
690	C₂³×D₄	C₂²×D₄	1	2	yes	—
691	C₂³×D₄	C₂²×D₄	1	2	yes	—
692	C₂³×D₄	C₂²×D₄	1	4	yes	—
693	C₂³×D₄	C₂²×D₄	1	2	yes	—
694	C₂³×D₄	C₂²×D₄	1	4	yes	—
695	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
696	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
697	C₂³×D₄	C₂²×D₄	1	4	yes	—
698	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
699	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
700	C₂³×D₄	C₂²×D₄	1	2	yes	—
701	C₂³×D₄	C₂²×D₄	1	2	yes	—
702	C₂³×D₄	C₂²×D₄	1	2	yes	—
703	C₂³×D₄	C₂²×D₄	1	2	yes	—
704	C₂³×D₄	C₂²×D₄	1	2	yes	—
705	C₂³×D₄	C₂²×D₄	1	2	yes	—
706	C₂³×D₄	C₂²×D₄	1	4	yes	—
707	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
708	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
709	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
710	C₂³×D₄	C₂⁵	1	2	yes	—
711	C₂³×D₄	C₂⁵	1	2	yes	—
712	C₂³×D₄	C₂⁵	1	4	yes	—
713	C₂³×D₄	C₂⁵	1	1	yes	characteristic
714	C₂³×D₄	C₂⁵	1	1	yes	characteristic
715	C₂³×D₄	C₂⁵	1	2	yes	—
716	C₂³×D₄	C₂⁵	1	2	yes	—
717	C₂³×D₄	C₂⁵	1	2	yes	—
718	C₂³×D₄	C₂⁵	1	2	yes	—
719	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
720	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
721	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
722	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
723	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
724	C₂×#127	#120	1	4	yes	—
725	C₂×#124	#120	1	4	yes	—
726	C₂×#123	#120	1	4	yes	—
727	C₂×#123	C₂²×D₄	1	8	yes	—
728	C₂×#123	C₂²×D₄	1	8	yes	—
729	C₂×#123	C₂²×D₄	1	8	yes	—
730	C₂×#123	C₂²×D₄	1	4	yes	—
731	C₂×#123	C₂²×D₄	1	4	yes	—
732	C₂×C₂²⋊Q₈	#120	1	4	yes	—
733	C₂×#121	#120	1	4	yes	—
734	C₂×#121	#120	1	8	yes	—
735	C₂×#121	#120	1	8	yes	—
736	C₂×#121	C₂²×D₄	1	8	yes	—
737	C₂×#120	#120	1	8	yes	—
738	C₂×#120	#120	1	4	yes	—
739	C₂×#120	C₂²×D₄	1	8	yes	—
740	C₂×#120	C₂²×D₄	1	8	yes	—
741	C₂×#120	C₂²×D₄	1	8	yes	—
742	C₂×#120	C₂²×D₄	1	8	yes	—
743	C₂×#120	C₂²×D₄	1	8	yes	—
744	C₂×#120	C₂²×D₄	1	8	yes	—
745	C₂×#120	C₂²×D₄	1	4	yes	—
746	C₂×#120	C₂²×D₄	1	4	yes	—
747	C₂×#120	C₂²×D₄	1	4	yes	—
748	C₂×#120	C₂²×D₄	1	4	yes	—
749	C₂×C₄×D₄	#120	1	8	yes	—
750	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
751	C₂×#117	C₂²×D₄	1	2	yes	—
752	C₂×#117	C₂²×D₄	1	2	yes	—
753	C₂×#117	C₂²×D₄	1	4	yes	—
754	C₂×#117	C₂²×D₄	1	2	yes	—
755	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
756	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
757	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
758	C₂²×C₂²⋊C₄	#120	1	4	yes	—
759	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
760	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
761	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
762	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
763	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
764	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
765	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
766	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
767	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
768	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
769	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
770	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
771	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
772	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
773	C₂²×C₄²	C₂²×D₄	1	2	yes	—
774	C₂²×C₄²	C₂²×D₄	1	2	yes	—
775	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
776	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
777	#386	C₂²×D₄	1	8	yes	—
778	#386	C₂²×D₄	1	8	yes	—
779	#386	C₂²×D₄	1	8	yes	—
780	#386	C₂²×D₄	1	8	yes	—
781	#386	C₂²×D₄	1	8	yes	—
782	#386	C₂²×D₄	1	8	yes	—
783	#386	C₂²×D₄	1	8	yes	—
784	#386	C₂²×D₄	1	8	yes	—
785	#385	C₂²×D₄	1	8	yes	—
786	#385	C₂²×D₄	1	8	yes	—
787	#385	C₂²×D₄	1	8	yes	—
788	#385	C₂²×D₄	1	8	yes	—
789	#381	C₂²×D₄	1	4	yes	—
790	#381	C₂²×D₄	1	4	yes	—
791	#381	C₂²×D₄	1	8	yes	—
792	#380	C₂²×D₄	1	8	yes	—
793	#379	C₂²×D₄	1	8	yes	—
794	#379	C₂²×D₄	1	2	yes	—
795	#379	C₂²×D₄	1	2	yes	—
796	#379	C₂²×D₄	1	8	yes	—
797	#379	C₂²×D₄	1	4	yes	—
798	#379	C₂²×D₄	1	8	yes	—
799	#379	C₂²×D₄	1	4	yes	—
800	#379	C₂²×D₄	1	8	yes	—
801	#379	C₂⁵	1	2	yes	—
802	#379	C₂⁵	1	2	yes	—
803	#379	C₂⁵	1	8	yes	—
804	#379	C₂⁵	1	2	yes	—
805	#379	C₂⁵	1	2	yes	—
806	#379	C₂⁵	1	8	yes	—
807	#379	C₂⁵	1	4	yes	—
808	#379	C₂⁵	1	2	yes	—
809	#379	C₂⁵	1	4	yes	—
810	#379	C₂⁵	1	2	yes	—
811	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
812	C₂⁵	C₂×#120	1	4	yes	—
813	C₂⁵	C₂×#120	1	2	yes	—
814	C₂⁵	C₂³×D₄	1	2	yes	—
815	C₂⁵	C₂³×D₄	1	4	yes	—
816	C₂⁵	C₂³×D₄	1	2	yes	—
817	C₂⁵	C₂³×D₄	1	1	yes	characteristic
818	C₂⁵	C₂³×D₄	1	2	yes	—
819	C₂⁵	C₂³×D₄	1	1	yes	characteristic
820	C₂⁵	C₂³×D₄	1	1	yes	characteristic
821	C₂⁵	C₂³×D₄	1	4	yes	—
822	C₂⁵	C₂³×D₄	1	1	yes	characteristic
823	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
824	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
825	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
826	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
827	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
828	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
829	C₂⁵	C₂⁶	1	1	yes	characteristic
830	C₂²×Q₈	C₂×#120	1	2	yes	—
831	C₂²×D₄	C₂×#120	1	4	yes	—
832	C₂²×D₄	C₂×#120	1	4	yes	—
833	C₂²×D₄	C₂×#120	1	2	yes	—
834	C₂²×D₄	C₂×#120	1	8	yes	—
835	C₂²×D₄	C₂×#120	1	8	yes	—
836	C₂²×D₄	C₂×#120	1	4	yes	—
837	C₂²×D₄	C₂×#120	1	8	yes	—
838	C₂²×D₄	C₂³×D₄	1	4	yes	—
839	C₂²×D₄	C₂³×D₄	1	4	yes	—
840	C₂²×D₄	C₂³×D₄	1	4	yes	—
841	C₂²×D₄	C₂³×D₄	1	4	yes	—
842	C₂³×C₄	C₂×#120	1	4	yes	—
843	C₂³×C₄	C₂×#120	1	4	yes	—
844	C₂³×C₄	C₂×#120	1	2	yes	—
845	C₂³×C₄	C₂×#120	1	4	yes	—
846	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
847	C₂³×C₄	C₂³×D₄	1	4	yes	—
848	C₂³×C₄	C₂³×D₄	1	2	yes	—
849	C₂³×C₄	C₂³×D₄	1	4	yes	—
850	C₂³×C₄	C₂³×D₄	1	4	yes	—
851	C₂³×C₄	C₂³×D₄	1	2	yes	—
852	C₂³×C₄	C₂³×D₄	1	2	yes	—
853	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
854	C₂³×C₄	C₂³×D₄	1	4	yes	—
855	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
856	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
857	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
858	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
859	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
860	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
861	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
862	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
863	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
864	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
865	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
866	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
867	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
868	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
869	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
870	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
871	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
872	C₂×C₄²	C₂×#120	1	4	yes	—
873	C₂⁴	C₂²×#120	1	2	yes	—
874	C₂⁴	C₂²×#120	1	2	yes	—
875	C₂⁴	C₂²×#120	1	4	yes	—
876	C₂⁴	C₂²×#120	1	2	yes	—
877	C₂⁴	C₂²×#120	1	2	yes	—
878	C₂⁴	#3484	1	8	yes	—
879	C₂⁴	#3484	1	8	yes	—
880	C₂⁴	#3484	1	2	yes	—
881	C₂⁴	#3484	1	2	yes	—
882	C₂⁴	#3484	1	1	yes	characteristic
883	C₂⁴	#3484	1	2	yes	—
884	C₂⁴	#3484	1	1	yes	characteristic
885	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
886	C₂⁴	C₂⁴×D₄	1	2	yes	—
887	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
888	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
889	C₂²×C₄	C₂²×#120	1	2	yes	—
890	C₂²×C₄	C₂²×#120	1	4	yes	—
891	C₂²×C₄	C₂²×#120	1	2	yes	—
892	C₂²×C₄	C₂²×#120	1	8	yes	—
893	C₂³	#35346	1	2	yes	—
894	C₂³	#35346	1	2	yes	—
895	C₂³	#35346	1	4	yes	—
896	C₂³	C₂³×#120	1	1	yes	characteristic
897	C₂³	C₂×#3484	1	1	yes	characteristic
898	C₂³	C₂×#3484	1	1	yes	characteristic
899	C₂³	C₂×#3484	1	4	yes	—
900	C₂×C₄	#60399	1	4	yes	—
901	C₂²	C₂×#35346	1	1	yes	characteristic
902	C₂²	C₂×#60399	1	2	yes	—
903	C₂	#72224136	1	1	yes	characteristic
904	C₂	#72234693	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#35346
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341119	C₂	semidirect
2. #72341112	C₂	semidirect
3. #72341109	C₂	semidirect
4. #72341102	C₂	semidirect
5. #72341094	C₂	semidirect
6. #72341090	C₂	semidirect
7. #72341086	C₂	semidirect
8. #72341078	C₂	semidirect
9. #72341064	C₂	semidirect
10. #72341023	C₂	semidirect
11. #72341021	C₂	semidirect
12. #72340990	C₂	semidirect
13. #72338954	C₂	semidirect
14. #72338740	C₂	semidirect
15. #72338475	C₂	semidirect
16. #72337646	C₂	semidirect
17. #72337626	C₂	semidirect
18. #72265972	C₂	semidirect
19. #72265948	C₂	semidirect
20. #72251351	C₂	semidirect
21. #72240626	C₂	semidirect
22. #72236108	C₂	semidirect
23. #72213228	C₂	semidirect
24. #10586066	C₂²	semidirect
25. #8934620	C₂²	semidirect
26. #8933802	C₂²	semidirect
27. #8933802	C₂²	semidirect
28. #8926210	C₂²	semidirect
29. #8926210	C₂²	semidirect
30. #8925308	C₂²	semidirect
31. #8925308	C₂²	semidirect
32. #7806601	C₂²	semidirect
33. #7806601	C₂²	semidirect
36. #7739460	C₂²	semidirect
39. #7643002	C₂²	semidirect
41. #6629398	C₂²	semidirect
43. #6629267	C₂²	semidirect
45. #6628901	C₂²	semidirect
46. #6628901	C₂²	semidirect
47. #6628897	C₂²	semidirect
48. #6628892	C₂²	semidirect
49. #6487656	C₂²	semidirect
50. #6487656	C₂²	semidirect
51. #6470244	C₂²	semidirect
52. #6470244	C₂²	semidirect
53. #6470244	C₂²	semidirect
54. #6470237	C₂²	semidirect
55. #6470237	C₂²	semidirect
56. #6470237	C₂²	semidirect
57. #6470232	C₂²	semidirect
58. #6470232	C₂²	semidirect
59. #6470225	C₂²	semidirect
60. #6470225	C₂²	semidirect
63. #6432958	C₂²	semidirect
64. #6432958	C₂²	semidirect
65. #6385975	C₂²	semidirect
66. #6385975	C₂²	semidirect
67. #6374211	C₂²	semidirect
68. #6374211	C₂²	semidirect
69. #6370693	C₂²	semidirect
70. #251929	C₂²	semidirect
71. #251929	C₂²	semidirect
72. #251924	C₂²	semidirect
73. #251914	C₂²	semidirect
74. #251914	C₂²	semidirect
75. #251908	C₂²	semidirect
76. #251903	C₂²	semidirect
77. #251899	C₂²	semidirect
78. #251893	C₂²	semidirect
79. #251883	C₂²	semidirect
80. #251883	C₂²	semidirect
81. #251877	C₂²	semidirect
82. #251877	C₂²	semidirect
83. #251874	C₂²	semidirect
84. #251872	C₂²	semidirect
85. #251872	C₂²	semidirect
86. #251872	C₂²	semidirect
87. #251872	C₂²	semidirect
88. #251864	C₂²	semidirect
89. #251864	C₂²	semidirect
90. #251857	C₂²	semidirect
91. #251855	C₂²	semidirect
92. #251855	C₂²	semidirect
93. #251855	C₂²	semidirect
94. #251855	C₂²	semidirect
95. #251849	C₂²	semidirect
96. #251847	C₂²	semidirect
97. #251841	C₂²	semidirect
98. #251835	C₂²	semidirect
99. #251833	C₂²	semidirect
100. #251833	C₂²	semidirect
101. #251833	C₂²	semidirect
102. #251827	C₂²	semidirect
103. #251827	C₂²	semidirect
104. #245293	C₂²	semidirect
105. #245290	C₂²	semidirect
106. #245290	C₂²	semidirect
107. #245283	C₂²	semidirect
108. #245283	C₂²	semidirect
109. #245281	C₂²	semidirect
110. #245281	C₂²	semidirect
111. #245270	C₂²	semidirect
112. #245270	C₂²	semidirect
113. #245267	C₂²	semidirect
114. #245267	C₂²	semidirect
115. #245255	C₂²	semidirect
116. #245255	C₂²	semidirect
117. #245255	C₂²	semidirect
118. #245255	C₂²	semidirect
119. #245255	C₂²	semidirect
120. #245255	C₂²	semidirect
121. #245255	C₂²	semidirect
122. #245247	C₂²	semidirect
123. #245247	C₂²	semidirect
124. #245243	C₂²	semidirect
125. #245241	C₂²	semidirect
127. #245234	C₂²	semidirect
128. #245234	C₂²	semidirect
129. #245234	C₂²	semidirect
130. #245234	C₂²	semidirect
132. #245233	C₂²	semidirect
133. #245233	C₂²	semidirect
134. #245233	C₂²	semidirect
135. #245233	C₂²	semidirect
136. #245227	C₂²	semidirect
137. #245227	C₂²	semidirect
138. #238077	C₂²	semidirect
139. C₂×#10390	C₂²	semidirect
140. #233559	C₂²	semidirect
141. #233549	C₂²	semidirect
142. #233549	C₂²	semidirect
143. #233541	C₂²	semidirect
144. #213882	C₂²	semidirect
145. #213880	C₂²	semidirect
146. #213880	C₂²	semidirect
147. #213877	C₂²	semidirect
148. #213873	C₂²	semidirect
149. #213865	C₂²	semidirect
150. #213861	C₂²	semidirect
151. #213861	C₂²	semidirect
152. #213860	C₂²	semidirect
153. #213855	C₂²	semidirect
154. #213845	C₂²	semidirect
155. #213842	C₂²	semidirect
156. #213838	C₂²	semidirect
157. #213838	C₂²	semidirect
158. #213831	C₂²	semidirect
159. #201717	C₂²	semidirect
160. #201717	C₂²	semidirect
161. #201701	C₂²	semidirect
162. #201701	C₂²	semidirect
163. #201690	C₂²	semidirect
164. #201678	C₂²	semidirect
165. #201678	C₂²	semidirect
166. #201664	C₂²	semidirect
167. #190124	C₂²	semidirect
168. #190107	C₂²	semidirect
169. #188064	C₂²	semidirect
170. C₂×#8546	C₂²	semidirect
179. C₂×#3484	C₂³	semidirect
184. #47563	C₂³	semidirect
186. #46998	C₂³	semidirect
187. #46996	C₂³	semidirect
188. #46996	C₂³	semidirect
189. #46837	C₂³	semidirect
190. #46837	C₂³	semidirect
192. #46385	C₂³	semidirect
193. #46385	C₂³	semidirect
194. #46385	C₂³	semidirect
195. #46385	C₂³	semidirect
196. #46385	C₂³	semidirect
197. #39332	D₄	semidirect
198. #38904	D₄	semidirect
199. #38030	D₄	semidirect
200. #37646	D₄	semidirect
203. #37436	C₂³	semidirect
204. #37232	D₄	semidirect
210. #37232	C₂³	semidirect
211. #37232	C₂³	semidirect
214. #36965	C₂³	semidirect
217. #36721	C₂³	semidirect
218. #36721	C₂³	semidirect
219. C₂×#2840	C₂³	semidirect
220. #36626	D₄	semidirect
226. #35554	C₂³	semidirect
227. #35528	D₄	semidirect
228. #35528	D₄	semidirect
241. #35527	C₂³	semidirect
242. #35527	C₂³	semidirect
245. #35446	C₂³	semidirect
248. #35354	C₂³	semidirect
249. #35354	C₂³	semidirect
250. #35222	D₄	semidirect
251. #34980	D₄	semidirect
256. #34980	C₂³	semidirect
260. #34356	C₂³	semidirect
263. #34171	C₂³	semidirect
267. #33022	C₂³	semidirect
273. #33020	C₂³	semidirect
274. #33020	C₂³	semidirect
280. #32900	C₂³	semidirect
289. #32898	C₂³	semidirect
290. #32898	C₂³	semidirect
294. #29635	C₂³	semidirect
303. #29634	C₂³	semidirect
304. #29634	C₂³	semidirect
316. #21746	C₂³	semidirect
317. #21746	C₂³	semidirect
340. C₂×#1781	C₂³	semidirect
341. C₂×#1781	C₂³	semidirect
342. #10391	C₂³	semidirect
343. #10391	C₂³	semidirect
344. #10391	C₂³	semidirect
348. #10390	C₂³	semidirect
349. #10390	C₂³	semidirect
350. #10390	C₂³	semidirect
351. #10390	C₂³	semidirect
352. #10390	C₂³	semidirect
353. #10390	C₂³	semidirect
354. #10339	C₂³	semidirect
356. #10338	C₂³	semidirect
357. #10338	C₂³	semidirect
358. #10338	C₂³	semidirect
359. #10338	C₂³	semidirect
360. #10338	C₂³	semidirect
364. #10337	C₂³	semidirect
365. #10337	C₂³	semidirect
366. #10337	C₂³	semidirect
367. #10337	C₂³	semidirect
368. #10337	C₂³	semidirect
369. #10337	C₂³	semidirect
370. #10337	C₂³	semidirect
371. #10337	C₂³	semidirect
372. #10337	C₂³	semidirect
376. #10336	C₂³	semidirect
377. #10336	C₂³	semidirect
378. #10336	C₂³	semidirect
379. #10336	C₂³	semidirect
380. #10336	C₂³	semidirect
381. #10336	C₂³	semidirect
382. #9502	C₂³	semidirect
383. #9502	C₂³	semidirect
388. #9501	C₂³	semidirect
389. #9501	C₂³	semidirect
390. #9501	C₂³	semidirect
391. #9501	C₂³	semidirect
392. #9501	C₂³	semidirect
393. #9500	C₂³	semidirect
394. #9500	C₂³	semidirect
395. #9499	C₂³	semidirect
396. #9499	C₂³	semidirect
397. #9499	C₂³	semidirect
398. #9499	C₂³	semidirect
400. #9498	C₂³	semidirect
401. #9498	C₂³	semidirect
402. #9498	C₂³	semidirect
403. #9498	C₂³	semidirect
404. #9498	C₂³	semidirect
412. #9497	C₂³	semidirect
413. #9497	C₂³	semidirect
414. #9497	C₂³	semidirect
415. #9497	C₂³	semidirect
416. #9497	C₂³	semidirect
417. #9497	C₂³	semidirect
418. #9497	C₂³	semidirect
419. #9497	C₂³	semidirect
420. #9497	C₂³	semidirect
421. #9497	C₂³	semidirect
423. #9496	C₂³	semidirect
424. #9496	C₂³	semidirect
425. #9496	C₂³	semidirect
426. #9496	C₂³	semidirect
427. #9496	C₂³	semidirect
430. #9495	C₂³	semidirect
431. #9495	C₂³	semidirect
432. #9495	C₂³	semidirect
433. #9495	C₂³	semidirect
434. #9495	C₂³	semidirect
435. #9495	C₂³	semidirect
436. #9495	C₂³	semidirect
437. #9495	C₂³	semidirect
438. #8750	C₂³	semidirect
439. #8750	C₂³	semidirect
441. #8749	C₂³	semidirect
444. #8748	C₂³	semidirect
445. #8747	C₂³	semidirect
446. #8747	C₂³	semidirect
447. #8746	C₂³	semidirect
448. #8746	C₂³	semidirect
452. #8546	C₂³	semidirect
453. #8546	C₂³	semidirect
454. #8546	C₂³	semidirect
455. #8546	C₂³	semidirect
456. #8543	C₂³	semidirect
457. #8543	C₂³	semidirect
458. #8543	C₂³	semidirect
459. #8543	C₂³	semidirect
460. #8101	C₂³	semidirect
461. #8101	C₂³	semidirect
462. C₂×#1304	C₂³	semidirect
463. C₂×#1304	C₂³	semidirect
481. C₂×#535	C₂×D₄	semidirect
498. C₂²×#123	C₂×D₄	semidirect
515. #2853	C₂×D₄	semidirect
517. #2849	C₂×D₄	semidirect
518. #2847	C₂×D₄	semidirect
524. #2622	C₂×D₄	semidirect
525. #2618	C₂×D₄	semidirect
528. #2613	C₂×D₄	semidirect
529. #2539	C₂×D₄	semidirect
530. #2534	C₂×D₄	semidirect
531. #2504	C₂×D₄	semidirect
532. #2487	C₂×D₄	semidirect
536. #2413	C₂×D₄	semidirect
543. #2410	C₂×D₄	semidirect
544. #2406	C₂×D₄	semidirect
566. #2403	C₂×D₄	semidirect
586. #2322	C₂×D₄	semidirect
607. #2308	C₂×D₄	semidirect
614. C₄×#120	C₂×D₄	semidirect
617. #2297	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72341119	2
#72341112	2
#72341109	2
#72341102	2
#72341094	2
#72341090	2
#72341086	2
#72341078	2
#72341064	2
#72341023	2
#72341021	2
#72340990	2
#72338954	2
#72338740	2
#72338475	2
#72337646	2
#72337626	2
#72265972	2
#72265948	2
#72251351	2
#72240626	2
#72236108	2
#72213228	2