Subgroups — #72309341

Order 2048.

At least 7742 conjugacy classes of subgroups; only the 8140 normal subgroups are shown.

The subgroup lattice has 1115 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72309339	C₂	1	4	yes	maximal, complemented
2	#72309335	C₂	1	4	yes	maximal, complemented
3	#72309329	C₂	1	4	yes	maximal, complemented
4	#72309325	C₂	1	2	yes	maximal, complemented
5	#72309324	C₂	1	2	yes	maximal, complemented
6	#72309322	C₂	1	8	yes	maximal, complemented
7	#72309321	C₂	1	8	yes	maximal, complemented
8	#72237627	C₂	1	2	yes	maximal, complemented
9	#72234591	C₂	1	2	yes	maximal, complemented
10	#72225698	C₂	1	8	yes	maximal, complemented
11	#72225631	C₂	1	8	yes	maximal, complemented
12	#72225617	C₂	1	4	yes	maximal, complemented
13	C₂×#359428	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#364410	C₂	1	2	yes	maximal, complemented
15	#72217818	C₂	1	2	yes	maximal, complemented
16	#72217789	C₂	1	1	yes	maximal, characteristic, complemented
17	#72217511	C₂	1	1	yes	maximal, characteristic
18	C₂×#62817	C₂²	1	1	yes	characteristic
19	C₂⁴×#120	C₂²	1	1	yes	characteristic
20	#7708349	C₄	1	16	yes	complemented
21	#7670206	C₂²	1	8	yes	—
22	#7670203	C₂²	1	8	yes	—
23	#7642273	C₄	1	4	yes	complemented
24	#7642273	C₂²	1	2	yes	—
25	#7642244	C₄	1	4	yes	complemented
26	#7642244	C₂²	1	2	yes	—
27	#7641845	C₂²	1	2	yes	—
28	C₂²×#2846	C₂²	1	2	yes	—
29	#7630944	C₄	1	4	yes	complemented
30	#7630944	C₂²	1	2	yes	—
31	#7630939	C₄	1	4	yes	complemented
32	#7630939	C₂²	1	2	yes	—
33	#7626202	C₂²	1	1	yes	characteristic
34	#7626202	C₂²	1	2	yes	complemented
35	C₂×#34198	C₂²	1	2	yes	complemented
36	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
37	#6379246	C₂²	1	8	yes	complemented
38	#6379246	C₂²	1	8	yes	complemented
39	#6379010	C₂²	1	8	yes	complemented
40	#6379010	C₂²	1	8	yes	complemented
41	#6374548	C₂²	1	4	yes	complemented
42	#6374210	C₂²	1	4	yes	complemented
43	C₂×#21776	C₂²	1	4	yes	complemented
44	C₂×#21746	C₂²	1	2	yes	—
45	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
46	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
47	C₂×#21746	C₂²	1	2	yes	complemented
48	#6372488	C₂²	1	4	yes	complemented
49	#6371504	C₂²	1	4	yes	complemented
50	C₂²×#1898	C₂²	1	2	yes	—
51	C₂²×#1898	C₂²	1	2	yes	complemented
52	C₂²×#1898	C₂²	1	2	yes	complemented
53	C₂²×#1889	C₂²	1	4	yes	complemented
54	C₂²×#1781	C₂²	1	2	yes	complemented
55	C₂×#14679	C₂²	1	2	yes	complemented
56	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
57	#393532	C₂²	1	4	yes	complemented
58	#392699	C₂²	1	4	yes	complemented
59	#392207	C₂²	1	2	yes	complemented
60	#392109	C₂²	1	2	yes	complemented
61	#391798	C₂²	1	8	yes	complemented
62	#391735	C₂²	1	4	yes	complemented
63	#391709	C₂²	1	4	yes	complemented
64	#387715	C₂²	1	4	yes	complemented
65	#387715	C₂²	1	8	yes	complemented
66	#387715	C₂²	1	4	yes	complemented
67	#387068	C₂²	1	4	yes	complemented
68	#387068	C₂²	1	8	yes	complemented
69	#387068	C₂²	1	4	yes	complemented
70	#386017	C₂²	1	4	yes	complemented
71	#386017	C₂²	1	8	yes	complemented
72	#386017	C₂²	1	4	yes	complemented
73	#385868	C₂²	1	4	yes	complemented
74	#385868	C₂²	1	8	yes	complemented
75	#385868	C₂²	1	4	yes	complemented
76	#383741	C₂²	1	8	yes	complemented
77	#383741	C₂²	1	8	yes	complemented
78	#383741	C₂²	1	8	yes	complemented
79	#383741	C₂²	1	8	yes	complemented
80	#383139	C₂²	1	8	yes	complemented
81	#383139	C₂²	1	8	yes	complemented
82	#383139	C₂²	1	8	yes	complemented
83	#383139	C₂²	1	8	yes	complemented
84	#382811	C₂²	1	8	yes	complemented
85	#382544	C₂²	1	4	yes	complemented
86	#382434	C₂²	1	4	yes	complemented
87	#382422	C₂²	1	2	yes	complemented
88	#382422	C₂²	1	2	yes	complemented
89	#381249	C₂²	1	8	yes	complemented
90	#381122	C₂²	1	8	yes	complemented
91	#380554	C₂²	1	8	yes	complemented
92	#379847	C₂²	1	4	yes	complemented
93	#379806	C₂²	1	8	yes	complemented
94	#379733	C₂²	1	4	yes	complemented
95	#375666	C₂²	1	4	yes	complemented
96	#375194	C₂²	1	8	yes	complemented
97	#374166	C₂²	1	8	yes	complemented
98	#374058	C₂²	1	8	yes	complemented
99	#374004	C₂²	1	4	yes	complemented
100	#368784	C₂²	1	8	yes	complemented
101	#368784	C₂²	1	8	yes	complemented
102	#368784	C₂²	1	8	yes	complemented
103	#368784	C₂²	1	8	yes	complemented
104	#364709	C₂²	1	8	yes	complemented
105	#364709	C₂²	1	8	yes	complemented
106	#364440	C₂²	1	8	yes	complemented
107	#364440	C₂²	1	8	yes	complemented
108	#364410	C₂²	1	8	yes	complemented
109	#364410	C₂²	1	8	yes	complemented
110	#364410	C₂²	1	8	yes	complemented
111	#364410	C₂²	1	8	yes	complemented
112	#364410	C₂²	1	8	yes	complemented
113	#364410	C₂²	1	8	yes	complemented
114	#364410	C₂²	1	8	yes	complemented
115	#364410	C₂²	1	8	yes	complemented
116	#364173	C₂²	1	8	yes	complemented
117	#364054	C₂²	1	8	yes	complemented
118	#363421	C₂²	1	8	yes	complemented
119	#361793	C₂²	1	8	yes	complemented
120	#361312	C₂²	1	8	yes	complemented
121	#361312	C₂²	1	8	yes	complemented
122	#361312	C₂²	1	8	yes	complemented
123	#361312	C₂²	1	8	yes	complemented
124	#359892	C₂²	1	8	yes	complemented
125	#359756	C₂²	1	8	yes	complemented
126	#359591	C₂²	1	8	yes	complemented
127	#359501	C₂²	1	8	yes	complemented
128	#359428	C₂²	1	8	yes	complemented
129	#359428	C₂²	1	8	yes	complemented
130	#359428	C₂²	1	8	yes	complemented
131	#359428	C₂²	1	8	yes	complemented
132	C₂×#11069	C₂²	1	4	yes	complemented
133	C₂×#10991	C₂²	1	4	yes	complemented
134	C₂×#10965	C₂²	1	2	yes	complemented
135	C₂×#10965	C₂²	1	2	yes	complemented
136	#355913	C₂²	1	2	yes	complemented
137	#355913	C₂²	1	2	yes	complemented
138	#355474	C₂²	1	8	yes	complemented
139	#355096	C₂²	1	4	yes	complemented
140	C₂×#10935	C₂²	1	4	yes	complemented
141	C₂×#10735	C₂²	1	2	yes	complemented
142	C₂×#10725	C₂²	1	2	yes	complemented
143	C₂×#10725	C₂²	1	2	yes	complemented
144	C₂⁸	C₂³	1	1	yes	characteristic
145	C₂⁵×D₄	C₂×C₄	1	2	yes	complemented
146	C₂⁵×D₄	C₂³	1	1	yes	characteristic
147	C₂×#3490	C₂×C₄	1	4	yes	—
148	C₂×#3490	D₄	1	8	yes	—
149	C₂×#3490	C₂³	1	2	yes	—
150	C₂×#3490	C₂³	1	4	yes	—
151	C₂×#3484	C₂×C₄	1	4	yes	—
152	C₂×#3484	D₄	1	8	yes	—
153	C₂×#3484	C₂³	1	2	yes	—
154	C₂×#3484	C₂³	1	4	yes	—
155	C₂×#3484	C₂³	1	4	yes	—
156	C₂×#3532	C₂×C₄	1	8	yes	—
157	C₂×#3532	D₄	1	16	yes	—
158	C₂³×#120	C₂×C₄	1	2	yes	complemented
159	C₂³×#120	C₂×C₄	1	2	yes	complemented
160	C₂³×#120	C₂×C₄	1	8	yes	complemented
161	C₂³×#120	C₂³	1	4	yes	—
162	C₂³×#120	C₂³	1	1	yes	characteristic
163	C₂³×#120	C₂³	1	1	yes	characteristic
164	C₂³×#120	C₂³	1	8	yes	—
165	C₂³×#120	C₂³	1	1	yes	characteristic
166	C₂³×#120	C₂³	1	1	yes	characteristic
167	C₂³×#120	C₂³	1	2	yes	—
168	C₂²×#518	C₂³	1	2	yes	complemented
169	C₂⁴×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
170	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×#2883	C₂³	1	8	yes	complemented
173	C₂³×#99	C₂³	1	4	yes	—
174	C₂³×#99	C₂³	1	4	yes	—
175	C₂³×#99	C₂³	1	4	yes	complemented
176	#37833	C₂×C₄	1	32	yes	complemented
177	#37832	C₂×C₄	1	32	yes	complemented
178	#37645	C₂×C₄	1	32	yes	complemented
179	#37644	C₂×C₄	1	32	yes	complemented
180	#37436	C₂×C₄	1	16	yes	complemented
181	#36714	C₂×C₄	1	8	yes	complemented
182	#36703	C₂×C₄	1	16	yes	complemented
183	#36702	C₂×C₄	1	8	yes	complemented
184	#36614	C₂×C₄	1	4	yes	complemented
185	#36614	C₂×C₄	1	8	yes	complemented
186	C₂×#2846	C₂×C₄	1	8	yes	complemented
187	C₂×#2846	C₂×C₄	1	8	yes	complemented
188	C₂×#2846	C₂×C₄	1	16	yes	complemented
189	C₂×#2846	C₂×C₄	1	4	yes	complemented
190	C₂×#2846	C₂³	1	8	yes	—
191	C₂×#2846	C₂³	1	4	yes	—
192	C₂×#2846	C₂³	1	4	yes	—
193	#36158	C₂×C₄	1	32	yes	complemented
194	#36152	C₂×C₄	1	32	yes	complemented
195	#36098	C₂×C₄	1	32	yes	complemented
196	D₄×#120	C₂×C₄	1	32	yes	complemented
197	#35390	C₂³	1	4	yes	—
198	#35367	C₂³	1	4	yes	—
199	#35350	C₂³	1	4	yes	—
200	#35348	C₂³	1	8	yes	—
201	#35348	C₂³	1	8	yes	—
202	#35346	C₂³	1	4	yes	—
203	#35222	C₂×C₄	1	8	yes	complemented
204	#35222	C₂×C₄	1	4	yes	complemented
205	#35222	C₂×C₄	1	8	yes	complemented
206	#35050	C₂×C₄	1	8	yes	complemented
207	#35050	C₂×C₄	1	8	yes	complemented
208	#35050	C₂×C₄	1	8	yes	complemented
209	#34992	C₂×C₄	1	8	yes	complemented
210	#34992	C₂³	1	4	yes	—
211	#34992	C₂³	1	4	yes	—
212	#34988	C₂×C₄	1	16	yes	complemented
213	#34982	C₂³	1	4	yes	—
214	#34981	C₂³	1	8	yes	—
215	#34981	C₂³	1	4	yes	—
216	#34980	C₂×C₄	1	8	yes	complemented
217	#34980	C₂×C₄	1	8	yes	complemented
218	#34980	C₂×C₄	1	4	yes	complemented
219	#34980	C₂×C₄	1	8	yes	complemented
220	#34980	C₂³	1	4	yes	—
221	#34980	C₂³	1	4	yes	—
222	#34980	C₂³	1	8	yes	—
223	#34356	C₂×C₄	1	8	yes	complemented
224	#34198	C₂³	1	8	yes	—
225	#34198	C₂³	1	8	yes	—
226	#34198	C₂³	1	8	yes	—
227	#34198	C₂³	1	8	yes	—
228	#34198	C₂³	1	8	yes	complemented
229	#34198	C₂³	1	8	yes	complemented
230	#34176	C₂×C₄	1	4	yes	complemented
231	#34176	C₂³	1	2	yes	—
232	#34176	C₂³	1	4	yes	complemented
233	#34171	C₂×C₄	1	4	yes	complemented
234	#34171	C₂³	1	4	yes	—
235	#34171	C₂³	1	2	yes	—
236	#34171	C₂³	1	4	yes	complemented
237	C₂×#2315	C₂³	1	2	yes	complemented
238	C₂×#2308	C₂³	1	2	yes	complemented
239	C₂²×#379	C₂³	1	4	yes	—
240	C₂²×#379	C₂³	1	4	yes	—
241	C₂²×#379	C₂³	1	2	yes	—
242	C₂²×#379	C₂³	1	4	yes	—
243	C₂²×#379	C₂³	1	2	yes	—
244	C₂²×#379	C₂³	1	2	yes	—
245	C₂²×#379	C₂³	1	4	yes	—
246	C₂²×#379	C₂³	1	4	yes	—
247	C₂²×#379	C₂³	1	2	yes	—
248	C₂²×#379	C₂³	1	2	yes	—
249	C₂²×#379	C₂³	1	2	yes	—
250	C₂²×#379	C₂³	1	2	yes	—
251	C₂²×#379	C₂³	1	2	yes	—
252	C₂×#2273	C₂³	1	2	yes	complemented
253	#21333	C₂³	1	8	yes	complemented
254	#21333	C₂³	1	8	yes	complemented
255	#21213	C₂³	1	8	yes	complemented
256	#21213	C₂³	1	8	yes	complemented
257	C₂×#1913	C₂³	1	8	yes	complemented
258	C₂×#1913	C₂³	1	8	yes	complemented
259	C₂×#1913	C₂³	1	8	yes	complemented
260	C₂×#1913	C₂³	1	8	yes	complemented
261	#20984	C₂³	1	8	yes	complemented
262	#20984	C₂³	1	8	yes	complemented
263	#20984	C₂³	1	8	yes	complemented
264	#20984	C₂³	1	8	yes	complemented
265	C₂×#1898	C₂³	1	8	yes	—
266	C₂×#1898	C₂³	1	8	yes	—
267	C₂×#1898	C₂³	1	8	yes	—
268	C₂×#1898	C₂³	1	8	yes	—
269	C₂×#1898	C₂³	1	4	yes	—
270	C₂×#1898	C₂³	1	4	yes	—
271	C₂×#1898	C₂³	1	4	yes	—
272	C₂×#1898	C₂³	1	4	yes	—
273	C₂×#1898	C₂³	1	8	yes	—
274	C₂×#1898	C₂³	1	8	yes	—
275	C₂×#1898	C₂³	1	4	yes	—
276	C₂×#1898	C₂³	1	4	yes	—
277	C₂×#1898	C₂³	1	4	yes	—
278	C₂×#1898	C₂³	1	4	yes	—
279	C₂×#1898	C₂³	1	4	yes	complemented
280	C₂×#1898	C₂³	1	4	yes	complemented
281	C₂×#1898	C₂³	1	4	yes	complemented
282	C₂×#1898	C₂³	1	4	yes	complemented
283	C₂×#1889	C₂³	1	8	yes	—
284	C₂×#1889	C₂³	1	8	yes	—
285	C₂×#1889	C₂³	1	8	yes	—
286	C₂×#1889	C₂³	1	8	yes	—
287	C₂×#1889	C₂³	1	8	yes	complemented
288	C₂×#1889	C₂³	1	8	yes	complemented
289	C₂×#1889	C₂³	1	8	yes	complemented
290	C₂×#1889	C₂³	1	8	yes	complemented
291	C₂×#1828	C₂³	1	8	yes	complemented
292	C₂×#1828	C₂³	1	8	yes	complemented
293	#20689	C₂³	1	8	yes	complemented
294	C₂×#1819	C₂³	1	4	yes	—
295	C₂×#1819	C₂³	1	2	yes	—
296	C₂×#1819	C₂³	1	2	yes	—
297	C₂×#1819	C₂³	1	4	yes	complemented
298	#20633	C₂³	1	8	yes	complemented
299	#20633	C₂³	1	8	yes	complemented
300	#20585	C₂³	1	8	yes	complemented
301	C₂×#1781	C₂³	1	4	yes	—
302	C₂×#1781	C₂³	1	4	yes	—
303	C₂×#1781	C₂³	1	4	yes	—
304	C₂×#1781	C₂³	1	4	yes	—
305	C₂×#1781	C₂³	1	8	yes	—
306	C₂×#1781	C₂³	1	4	yes	—
307	C₂×#1781	C₂³	1	2	yes	—
308	C₂×#1781	C₂³	1	2	yes	—
309	C₂×#1781	C₂³	1	8	yes	—
310	C₂×#1781	C₂³	1	4	yes	complemented
311	#20392	C₂³	1	8	yes	complemented
312	#20392	C₂³	1	8	yes	complemented
313	#20354	C₂³	1	8	yes	complemented
314	C₂²×#342	C₂³	1	4	yes	—
315	C₂²×#342	C₂³	1	4	yes	—
316	C₂²×#342	C₂³	1	4	yes	complemented
317	C₂²×#342	C₂³	1	4	yes	complemented
318	C₂²×#342	C₂³	1	4	yes	complemented
319	C₂²×#342	C₂³	1	4	yes	complemented
320	C₂²×#342	C₂³	1	4	yes	complemented
321	#14679	C₂³	1	8	yes	—
322	#14679	C₂³	1	8	yes	—
323	#14679	C₂³	1	4	yes	—
324	#14679	C₂³	1	4	yes	—
325	#11351	C₂³	1	8	yes	complemented
326	#11351	C₂³	1	8	yes	complemented
327	#11351	C₂³	1	8	yes	complemented
328	#11351	C₂³	1	8	yes	complemented
329	#11205	C₂³	1	8	yes	complemented
330	#11205	C₂³	1	8	yes	complemented
331	#11205	C₂³	1	8	yes	complemented
332	#11205	C₂³	1	8	yes	complemented
333	#11172	C₂³	1	8	yes	complemented
334	#11172	C₂³	1	8	yes	complemented
335	#11172	C₂³	1	8	yes	complemented
336	#11172	C₂³	1	8	yes	complemented
337	#11169	C₂³	1	8	yes	complemented
338	#11169	C₂³	1	8	yes	complemented
339	#11166	C₂³	1	8	yes	complemented
340	#11166	C₂³	1	8	yes	complemented
341	#11069	C₂³	1	8	yes	—
342	#11069	C₂³	1	8	yes	—
343	#11069	C₂³	1	8	yes	—
344	#11069	C₂³	1	8	yes	—
345	#11069	C₂³	1	8	yes	complemented
346	#11069	C₂³	1	8	yes	complemented
347	#11069	C₂³	1	8	yes	complemented
348	#11069	C₂³	1	8	yes	complemented
349	#11046	C₂³	1	8	yes	complemented
350	#11046	C₂³	1	8	yes	complemented
351	#11046	C₂³	1	8	yes	complemented
352	#11046	C₂³	1	8	yes	complemented
353	#10991	C₂³	1	8	yes	—
354	#10991	C₂³	1	8	yes	—
355	#10991	C₂³	1	8	yes	—
356	#10991	C₂³	1	8	yes	—
357	#10991	C₂³	1	8	yes	complemented
358	#10991	C₂³	1	8	yes	complemented
359	#10991	C₂³	1	8	yes	complemented
360	#10991	C₂³	1	8	yes	complemented
361	#10972	C₂³	1	8	yes	complemented
362	#10972	C₂³	1	8	yes	complemented
363	#10972	C₂³	1	8	yes	complemented
364	#10972	C₂³	1	8	yes	complemented
365	#10965	C₂³	1	4	yes	—
366	#10965	C₂³	1	4	yes	—
367	#10965	C₂³	1	8	yes	—
368	#10965	C₂³	1	4	yes	—
369	#10965	C₂³	1	4	yes	—
370	#10965	C₂³	1	4	yes	—
371	#10965	C₂³	1	8	yes	—
372	#10965	C₂³	1	4	yes	—
373	#10965	C₂³	1	4	yes	—
374	#10965	C₂³	1	8	yes	—
375	#10965	C₂³	1	4	yes	—
376	#10965	C₂³	1	8	yes	—
377	#10938	C₂³	1	8	yes	complemented
378	#10938	C₂³	1	8	yes	complemented
379	#10938	C₂³	1	8	yes	complemented
380	#10938	C₂³	1	8	yes	complemented
381	#10935	C₂³	1	8	yes	—
382	#10935	C₂³	1	8	yes	—
383	#10935	C₂³	1	8	yes	—
384	#10935	C₂³	1	8	yes	—
385	#10935	C₂³	1	8	yes	complemented
386	#10935	C₂³	1	8	yes	complemented
387	#10935	C₂³	1	8	yes	complemented
388	#10935	C₂³	1	8	yes	complemented
389	#10915	C₂³	1	8	yes	complemented
390	#10915	C₂³	1	8	yes	complemented
391	#10915	C₂³	1	8	yes	complemented
392	#10915	C₂³	1	8	yes	complemented
393	#10829	C₂³	1	8	yes	complemented
394	#10829	C₂³	1	8	yes	complemented
395	#10829	C₂³	1	8	yes	complemented
396	#10829	C₂³	1	8	yes	complemented
397	#10768	C₂³	1	8	yes	complemented
398	#10768	C₂³	1	8	yes	complemented
399	#10754	C₂³	1	8	yes	complemented
400	#10754	C₂³	1	8	yes	complemented
401	#10754	C₂³	1	8	yes	complemented
402	#10754	C₂³	1	8	yes	complemented
403	#10735	C₂³	1	8	yes	—
404	#10735	C₂³	1	8	yes	—
405	#10735	C₂³	1	4	yes	complemented
406	#10735	C₂³	1	4	yes	complemented
407	#10735	C₂³	1	8	yes	complemented
408	#10735	C₂³	1	8	yes	complemented
409	#10735	C₂³	1	4	yes	complemented
410	#10735	C₂³	1	4	yes	complemented
411	#10725	C₂³	1	8	yes	—
412	#10725	C₂³	1	4	yes	—
413	#10725	C₂³	1	4	yes	—
414	#10725	C₂³	1	4	yes	—
415	#10725	C₂³	1	8	yes	—
416	#10725	C₂³	1	4	yes	—
417	#10725	C₂³	1	8	yes	—
418	#10725	C₂³	1	8	yes	—
419	#10725	C₂³	1	8	yes	complemented
420	#10725	C₂³	1	8	yes	complemented
421	C₂⁷	C₂²×C₄	1	2	yes	—
422	C₂⁷	C₂²×C₄	1	2	yes	—
423	C₂⁷	C₂²×C₄	1	4	yes	—
424	C₂⁷	C₂²×C₄	1	1	yes	characteristic, complemented
425	C₂⁷	C₂⁴	1	1	yes	characteristic
426	C₂⁷	C₂⁴	1	4	yes	—
427	C₂⁷	C₂⁴	1	1	yes	characteristic
428	C₂⁷	C₂⁴	1	1	yes	characteristic
429	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	complemented
430	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
431	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
432	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
433	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
434	C₂⁴×D₄	C₂²×C₄	1	4	yes	complemented
435	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
436	C₂⁴×D₄	C₂²×C₄	1	16	yes	complemented
437	C₂⁴×D₄	C₂²×C₄	1	2	yes	complemented
438	C₂⁴×D₄	C₂²×C₄	1	2	yes	complemented
439	C₂⁴×D₄	C₂×D₄	1	4	yes	—
440	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
441	C₂⁴×D₄	C₂⁴	1	4	yes	—
442	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
443	C₂⁴×D₄	C₂⁴	1	2	yes	—
444	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
445	C₂⁵×C₄	C₂²×C₄	1	2	yes	complemented
446	C₂×H(3,𝔽₄)	C₂²⋊C₄	1	8	yes	complemented
447	C₂×#560	C₂²⋊C₄	1	8	yes	complemented
448	C₂×#560	C₂²⋊C₄	1	16	yes	complemented
449	C₂×#551	C₂²⋊C₄	1	16	yes	complemented
450	C₂×#551	C₂²⋊C₄	1	8	yes	complemented
451	C₂×#551	C₂²×C₄	1	16	yes	—
452	C₂×#551	C₂×D₄	1	16	yes	—
453	C₂×#551	C₂×D₄	1	16	yes	—
454	C₂×#546	C₂²⋊C₄	1	16	yes	complemented
455	C₂×#546	C₂²⋊C₄	1	16	yes	complemented
456	C₂×#546	C₂²⋊C₄	1	16	yes	complemented
457	C₂×#546	C₂²×C₄	1	16	yes	—
458	C₂×#546	C₂²×C₄	1	16	yes	—
459	C₂×#546	C₂×D₄	1	16	yes	—
460	C₂×#546	C₂×D₄	1	16	yes	—
461	C₂×#546	C₂×D₄	1	16	yes	—
462	C₂×#546	C₂×D₄	1	16	yes	—
463	C₂×D₄²	C₂²⋊C₄	1	16	yes	complemented
464	C₂×D₄²	C₂²⋊C₄	1	8	yes	complemented
465	C₂×D₄²	C₂²×C₄	1	16	yes	—
466	C₂×D₄²	C₂×D₄	1	16	yes	—
467	C₂×D₄²	C₂×D₄	1	16	yes	—
468	C₂×#543	C₂²⋊C₄	1	4	yes	complemented
469	C₂×#543	C₂⁴	1	2	yes	—
470	C₂×#538	C₂²⋊C₄	1	16	yes	complemented
471	C₂×#538	C₂²⋊C₄	1	16	yes	complemented
472	C₂×#538	C₂²⋊C₄	1	8	yes	complemented
473	C₂×#538	C₂²⋊C₄	1	8	yes	complemented
474	C₂×#538	C₂²×C₄	1	8	yes	—
475	C₂×#538	C₂×D₄	1	16	yes	—
476	C₂×#535	C₂²⋊C₄	1	16	yes	complemented
477	C₂×#535	C₂²⋊C₄	1	8	yes	complemented
478	C₂×#535	C₂²×C₄	1	4	yes	—
479	C₂×#535	C₂²×C₄	1	8	yes	complemented
480	C₂×#535	C₂×D₄	1	8	yes	—
481	C₂×#534	C₂²⋊C₄	1	8	yes	complemented
482	C₂×#534	C₂²⋊C₄	1	4	yes	complemented
483	C₂×#534	C₂²⋊C₄	1	16	yes	complemented
484	C₂×#534	C₂²⋊C₄	1	8	yes	complemented
485	C₂×#534	C₂²×C₄	1	4	yes	—
486	C₂×#534	C₂²×C₄	1	8	yes	complemented
487	C₂×#534	C₂×D₄	1	8	yes	—
488	C₂×#534	C₂⁴	1	8	yes	—
489	C₂×#534	C₂⁴	1	4	yes	—
490	C₂×#534	C₂⁴	1	2	yes	—
491	C₂×#525	C₂²×C₄	1	8	yes	—
492	C₂×#525	C₂²×C₄	1	4	yes	—
493	C₂×#525	C₂²×C₄	1	8	yes	complemented
494	C₂×#525	C₂×D₄	1	16	yes	—
495	C₂×#525	C₂×D₄	1	8	yes	—
496	C₂²×#120	C₂²×C₄	1	8	yes	—
497	C₂²×#120	C₂²×C₄	1	8	yes	—
498	C₂²×#120	C₂²×C₄	1	4	yes	—
499	C₂²×#120	C₂²×C₄	1	4	yes	—
500	C₂²×#120	C₂²×C₄	1	4	yes	—
501	C₂²×#120	C₂²×C₄	1	16	yes	complemented
502	C₂²×#120	C₂²×C₄	1	16	yes	complemented
503	C₂²×#120	C₂²×C₄	1	8	yes	complemented
504	C₂²×#120	C₂²×C₄	1	16	yes	complemented
505	C₂²×#120	C₂²×C₄	1	16	yes	complemented
506	C₂²×#120	C₂²×C₄	1	4	yes	complemented
507	C₂²×#120	C₂²×C₄	1	4	yes	complemented
508	C₂²×#120	C₂×D₄	1	8	yes	—
509	C₂²×#120	C₂×D₄	1	8	yes	—
510	C₂²×#120	C₂×D₄	1	8	yes	—
511	C₂²×#120	C₂×D₄	1	8	yes	—
512	C₂²×#120	C₂×D₄	1	8	yes	—
513	C₂²×#120	C₂×D₄	1	8	yes	—
514	C₂²×#120	C₂⁴	1	8	yes	—
515	C₂²×#120	C₂⁴	1	8	yes	—
516	C₂²×#120	C₂⁴	1	4	yes	—
517	C₂²×#120	C₂⁴	1	4	yes	—
518	C₂²×#120	C₂⁴	1	4	yes	—
519	C₂²×#120	C₂⁴	1	4	yes	—
520	C₂²×#120	C₂⁴	1	4	yes	—
521	C₂²×#120	C₂⁴	1	4	yes	—
522	C₂×#518	C₂²⋊C₄	1	8	yes	complemented
523	C₂×#518	C₂²⋊C₄	1	4	yes	complemented
524	C₂×#518	C₂⁴	1	8	yes	—
525	C₂×#518	C₂⁴	1	8	yes	—
526	C₂×#518	C₂⁴	1	4	yes	—
527	C₂×#518	C₂⁴	1	2	yes	—
528	C₂×#518	C₂⁴	1	4	yes	—
529	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
530	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
531	C₂³×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
532	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
533	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
534	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
535	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
536	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
537	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
538	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
539	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
540	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
541	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
542	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
543	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
544	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
545	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
546	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
547	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
548	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
549	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
550	C₂²×#99	C₂⁴	1	8	yes	—
551	C₂²×#99	C₂⁴	1	8	yes	—
552	C₂²×#99	C₂⁴	1	8	yes	—
553	C₂²×#99	C₂⁴	1	8	yes	—
554	C₂²×#99	C₂⁴	1	8	yes	—
555	C₂²×#99	C₂⁴	1	8	yes	—
556	C₂²×#99	C₂⁴	1	8	yes	—
557	C₂²×#99	C₂⁴	1	8	yes	—
558	C₂²×#99	C₂⁴	1	8	yes	—
559	C₂²×#99	C₂⁴	1	2	yes	—
560	C₂²×#99	C₂⁴	1	4	yes	—
561	C₂²×#99	C₂⁴	1	4	yes	—
562	C₂²×#99	C₂⁴	1	4	yes	—
563	C₂²×#99	C₂⁴	1	8	yes	—
564	C₂²×#99	C₂⁴	1	2	yes	—
565	#2849	C₂²×C₄	1	16	yes	complemented
566	#2849	C₂²×C₄	1	16	yes	complemented
567	#2849	C₂²×C₄	1	8	yes	complemented
568	#2848	C₂²×C₄	1	16	yes	complemented
569	#2847	C₂²×C₄	1	16	yes	complemented
570	#2846	C₂²×C₄	1	32	yes	—
571	#2846	C₂²×C₄	1	32	yes	—
572	#2846	C₂²×C₄	1	8	yes	complemented
573	#2846	C₂²×C₄	1	16	yes	complemented
574	#2846	C₂²×C₄	1	16	yes	complemented
575	#2846	C₂²×C₄	1	16	yes	complemented
576	#2846	C₂²×C₄	1	8	yes	complemented
577	#2846	C₂²×C₄	1	16	yes	complemented
578	#2846	C₂²×C₄	1	8	yes	complemented
579	#2626	C₂²×C₄	1	16	yes	complemented
580	#2622	C₂²×C₄	1	16	yes	complemented
581	#2617	C₂²×C₄	1	16	yes	complemented
582	#2613	C₂²×C₄	1	16	yes	complemented
583	#2613	C₂²×C₄	1	16	yes	complemented
584	#2613	C₂²×C₄	1	16	yes	complemented
585	#2561	C₂²×C₄	1	16	yes	complemented
586	#2539	C₂²×C₄	1	16	yes	complemented
587	#2534	C₂²×C₄	1	32	yes	complemented
588	#2483	C₂²×C₄	1	16	yes	complemented
589	#2482	C₂²×C₄	1	16	yes	complemented
590	#2435	C₂²×C₄	1	16	yes	complemented
591	#2433	C₂²×C₄	1	16	yes	complemented
592	#2412	C₂²×C₄	1	32	yes	—
593	#2411	C₂²×C₄	1	32	yes	complemented
594	#2410	C₂²×C₄	1	32	yes	—
595	#2410	C₂²×C₄	1	32	yes	complemented
596	#2408	C₂²×C₄	1	32	yes	complemented
597	#2405	C₂²×C₄	1	16	yes	complemented
598	#2405	C₂²×C₄	1	16	yes	complemented
599	#2405	C₂²×C₄	1	16	yes	complemented
600	#2404	C₂²×C₄	1	16	yes	complemented
601	#2403	C₂²×C₄	1	16	yes	complemented
602	#2403	C₂²×C₄	1	16	yes	complemented
603	#2342	C₂²×C₄	1	32	yes	complemented
604	D₄×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
605	#2321	C₂²×C₄	1	32	yes	complemented
606	#2315	C₂⁴	1	8	yes	—
607	#2315	C₂⁴	1	8	yes	—
608	#2315	C₂⁴	1	8	yes	—
609	#2315	C₂⁴	1	4	yes	—
610	#2312	C₂²×C₄	1	8	yes	complemented
611	#2309	C₂²×C₄	1	4	yes	complemented
612	#2309	C₂²×C₄	1	8	yes	complemented
613	#2308	C₂²×C₄	1	4	yes	complemented
614	#2308	C₂²×C₄	1	8	yes	complemented
615	#2308	C₂⁴	1	8	yes	—
616	#2308	C₂⁴	1	8	yes	—
617	#2308	C₂⁴	1	8	yes	—
618	#2308	C₂⁴	1	4	yes	—
619	#2308	C₂⁴	1	8	yes	—
620	C₄×#120	C₂²×C₄	1	32	yes	complemented
621	#2280	C₂²×C₄	1	8	yes	complemented
622	#2280	C₂²×C₄	1	8	yes	complemented
623	#2280	C₂²×C₄	1	4	yes	complemented
624	C₂×#379	C₂²×C₄	1	8	yes	—
625	C₂×#379	C₂²×C₄	1	8	yes	—
626	C₂×#379	C₂²×C₄	1	16	yes	complemented
627	C₂×#379	C₂²×C₄	1	16	yes	complemented
628	C₂×#379	C₂²×C₄	1	8	yes	complemented
629	C₂×#379	C₂²×C₄	1	4	yes	complemented
630	C₂×#379	C₂⁴	1	4	yes	—
631	C₂×#379	C₂⁴	1	4	yes	—
632	C₂×#379	C₂⁴	1	4	yes	—
633	C₂×#379	C₂⁴	1	4	yes	—
634	C₂×#379	C₂⁴	1	4	yes	—
635	C₂×#379	C₂⁴	1	4	yes	—
636	C₂×#379	C₂⁴	1	8	yes	—
637	C₂×#379	C₂⁴	1	8	yes	—
638	C₂×#379	C₂⁴	1	4	yes	—
639	C₂×#379	C₂⁴	1	4	yes	—
640	C₂×#379	C₂⁴	1	4	yes	—
641	C₂×#379	C₂⁴	1	2	yes	—
642	C₂×#379	C₂⁴	1	2	yes	—
643	C₂×#379	C₂⁴	1	8	yes	—
644	C₂×#379	C₂⁴	1	4	yes	—
645	C₂×#379	C₂⁴	1	4	yes	—
646	C₂×#379	C₂⁴	1	8	yes	—
647	C₂×#379	C₂⁴	1	4	yes	—
648	C₂×#379	C₂⁴	1	2	yes	—
649	C₂×#379	C₂⁴	1	8	yes	—
650	C₂×#379	C₂⁴	1	4	yes	—
651	C₂×#379	C₂⁴	1	4	yes	—
652	C₂×#379	C₂⁴	1	8	yes	—
653	C₂×#379	C₂⁴	1	2	yes	—
654	#2273	C₂⁴	1	4	yes	—
655	#2273	C₂⁴	1	8	yes	—
656	#2273	C₂⁴	1	8	yes	—
657	C₂×#342	C₂⁴	1	8	yes	—
658	C₂×#342	C₂⁴	1	8	yes	—
659	C₂×#342	C₂⁴	1	8	yes	—
660	C₂×#342	C₂⁴	1	8	yes	—
661	C₂×#342	C₂⁴	1	8	yes	—
662	C₂×#342	C₂⁴	1	8	yes	—
663	C₂×#342	C₂⁴	1	8	yes	—
664	C₂×#342	C₂⁴	1	8	yes	—
665	C₂×#342	C₂⁴	1	8	yes	—
666	C₂×#342	C₂⁴	1	8	yes	—
667	C₂×#342	C₂⁴	1	2	yes	—
668	C₂×#342	C₂⁴	1	8	yes	—
669	C₂×#342	C₂⁴	1	4	yes	—
670	C₂×#342	C₂⁴	1	4	yes	—
671	C₂×#342	C₂⁴	1	4	yes	—
672	C₂×#342	C₂⁴	1	8	yes	—
673	C₂×#342	C₂⁴	1	8	yes	—
674	C₂×#342	C₂⁴	1	8	yes	—
675	C₂×#342	C₂⁴	1	8	yes	—
676	C₂×#342	C₂⁴	1	8	yes	—
677	C₂×#342	C₂⁴	1	8	yes	—
678	C₂×#342	C₂⁴	1	8	yes	—
679	C₂×#342	C₂⁴	1	8	yes	—
680	C₂×#342	C₂⁴	1	8	yes	—
681	C₂×#342	C₂⁴	1	8	yes	—
682	C₂×#342	C₂⁴	1	8	yes	—
683	C₂×#342	C₂⁴	1	8	yes	—
684	C₂×#342	C₂⁴	1	8	yes	—
685	C₂×#342	C₂⁴	1	8	yes	—
686	C₂×#342	C₂⁴	1	8	yes	—
687	C₂×#342	C₂⁴	1	2	yes	—
688	C₂⁶	C₂³×C₄	1	1	yes	characteristic
689	C₂⁶	C₂³×C₄	1	1	yes	characteristic
690	C₂⁶	C₂³×C₄	1	2	yes	—
691	C₂⁶	C₂³×C₄	1	8	yes	—
692	C₂⁶	C₂³×C₄	1	8	yes	—
693	C₂⁶	C₂³×C₄	1	2	yes	—
694	C₂⁶	C₂³×C₄	1	1	yes	characteristic
695	C₂⁶	C₂³×C₄	1	2	yes	—
696	C₂⁶	C₂³×C₄	1	4	yes	—
697	C₂⁶	C₂³×C₄	1	1	yes	characteristic
698	C₂⁶	C₂³×C₄	1	2	yes	—
699	C₂⁶	C₂³×C₄	1	2	yes	—
700	C₂⁶	C₂²×D₄	1	2	yes	—
701	C₂⁶	C₂²×D₄	1	4	yes	—
702	C₂⁶	C₂²×D₄	1	4	yes	—
703	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
704	C₂⁶	H(5,𝔽₂)	1	4	yes	—
705	C₂⁶	H(5,𝔽₂)	1	2	yes	—
706	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
707	C₂⁶	H(5,𝔽₂)	1	2	yes	—
708	C₂⁶	H(5,𝔽₂)	1	4	yes	—
709	C₂⁶	H(5,𝔽₂)	1	2	yes	—
710	C₂⁶	C₂⁵	1	2	yes	—
711	C₂⁶	C₂⁵	1	2	yes	—
712	C₂⁶	C₂⁵	1	1	yes	characteristic
713	C₂⁶	C₂⁵	1	2	yes	—
714	C₂²×#41	C₂×C₂²⋊C₄	1	8	yes	complemented
715	C₂²×#41	C₂×C₂²⋊C₄	1	16	yes	complemented
716	C₂²×#41	C₂³×C₄	1	4	yes	—
717	C₂²×#41	C₂²×D₄	1	8	yes	—
718	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
719	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
720	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
721	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
722	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
723	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
724	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
725	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	complemented
726	C₂³×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
727	C₂³×D₄	C₂³×C₄	1	8	yes	—
728	C₂³×D₄	C₂³×C₄	1	4	yes	—
729	C₂³×D₄	C₂³×C₄	1	2	yes	—
730	C₂³×D₄	C₂³×C₄	1	8	yes	—
731	C₂³×D₄	C₂³×C₄	1	4	yes	—
732	C₂³×D₄	C₂³×C₄	1	4	yes	—
733	C₂³×D₄	C₂³×C₄	1	2	yes	—
734	C₂³×D₄	C₂³×C₄	1	8	yes	—
735	C₂³×D₄	C₂³×C₄	1	8	yes	—
736	C₂³×D₄	C₂³×C₄	1	8	yes	—
737	C₂³×D₄	C₂²×D₄	1	8	yes	—
738	C₂³×D₄	C₂²×D₄	1	8	yes	—
739	C₂³×D₄	C₂²×D₄	1	8	yes	—
740	C₂³×D₄	C₂²×D₄	1	4	yes	—
741	C₂³×D₄	C₂²×D₄	1	8	yes	—
742	C₂³×D₄	C₂²×D₄	1	8	yes	—
743	C₂³×D₄	C₂⁵	1	2	yes	—
744	C₂³×D₄	C₂⁵	1	2	yes	—
745	C₂³×D₄	C₂⁵	1	4	yes	—
746	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
747	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
748	C₂⁴×C₄	C₂³×C₄	1	4	yes	—
749	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
750	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
751	C₂⁴×C₄	C₂³×C₄	1	8	yes	—
752	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
753	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
754	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	complemented
755	C₂×#127	C₂×C₂²⋊C₄	1	16	yes	complemented
756	C₂×#126	C₂×C₂²⋊C₄	1	16	yes	complemented
757	C₂×#126	C₂×C₂²⋊C₄	1	16	yes	complemented
758	C₂×#126	C₂×C₂²⋊C₄	1	16	yes	complemented
759	C₂×#124	C₂×C₂²⋊C₄	1	16	yes	complemented
760	C₂×#124	C₂×C₂²⋊C₄	1	16	yes	complemented
761	C₂×#124	C₂×C₂²⋊C₄	1	16	yes	complemented
762	C₂×#124	C₂×C₂²⋊C₄	1	16	yes	complemented
763	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	complemented
764	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
765	C₂×#123	C₂×C₂²⋊C₄	1	8	yes	complemented
766	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
767	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
768	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
769	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
770	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
771	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
772	C₂×#123	C₂³×C₄	1	16	yes	—
773	C₂×#123	C₂³×C₄	1	8	yes	—
774	C₂×#123	C₂²×D₄	1	8	yes	—
775	C₂×#123	C₂²×D₄	1	8	yes	—
776	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
777	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
778	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	16	yes	complemented
779	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	16	yes	complemented
780	C₂×C₂²⋊Q₈	C₂³×C₄	1	8	yes	—
781	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	—
782	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
783	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
784	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
785	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
786	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
787	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
788	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
789	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
790	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
791	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
792	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
793	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
794	C₂×#121	C₂×C₂²⋊C₄	1	16	yes	complemented
795	C₂×#121	C₂³×C₄	1	8	yes	—
796	C₂×#121	C₂²×D₄	1	16	yes	—
797	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
798	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
799	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
800	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
801	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
802	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
803	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
804	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	complemented
805	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	complemented
806	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	complemented
807	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	complemented
808	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	complemented
809	C₂×#120	C₂³×C₄	1	16	yes	—
810	C₂×#120	C₂³×C₄	1	16	yes	—
811	C₂×#120	C₂³×C₄	1	32	yes	—
812	C₂×#120	C₂³×C₄	1	16	yes	—
813	C₂×#120	C₂³×C₄	1	16	yes	—
814	C₂×#120	C₂³×C₄	1	8	yes	—
815	C₂×#120	C₂³×C₄	1	8	yes	—
816	C₂×#120	C₂³×C₄	1	8	yes	—
817	C₂×#120	C₂²×D₄	1	8	yes	—
818	C₂×#120	C₂²×D₄	1	8	yes	—
819	C₂×#120	C₂²×D₄	1	8	yes	—
820	C₂×#120	C₂²×D₄	1	16	yes	—
821	C₂×#120	C₂²×D₄	1	16	yes	—
822	C₂×#120	C₂²×D₄	1	8	yes	—
823	C₂×#120	C₂²×D₄	1	8	yes	—
824	C₂×#120	C₂²×D₄	1	8	yes	—
825	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
826	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
827	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
828	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
829	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
830	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	16	yes	complemented
831	C₂×C₄×D₄	C₂³×C₄	1	16	yes	—
832	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
833	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
834	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	complemented
835	C₂×#117	C₂×C₂²⋊C₄	1	16	yes	complemented
836	C₂×#117	C₂³×C₄	1	8	yes	—
837	C₂×#117	C₂³×C₄	1	4	yes	—
838	C₂×#117	C₂²×D₄	1	8	yes	—
839	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
840	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
841	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
842	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
843	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
844	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
845	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
846	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	complemented
847	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
848	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
849	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
850	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
851	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
852	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
853	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
854	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
855	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
856	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
857	C₂²×C₂²⋊C₄	C₂³×C₄	1	16	yes	—
858	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
859	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
860	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
861	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
862	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
863	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
864	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
865	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
866	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
867	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
868	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
869	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
870	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
871	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
872	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
873	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
874	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
875	#386	C₂³×C₄	1	32	yes	—
876	#385	C₂³×C₄	1	32	yes	—
877	#381	C₂³×C₄	1	16	yes	—
878	#381	C₂³×C₄	1	8	yes	—
879	#380	C₂³×C₄	1	16	yes	—
880	#379	C₂³×C₄	1	32	yes	—
881	#379	C₂³×C₄	1	8	yes	—
882	#379	C₂³×C₄	1	16	yes	—
883	#379	C₂³×C₄	1	8	yes	—
884	#379	C₂³×C₄	1	16	yes	—
885	#379	C₂³×C₄	1	16	yes	—
886	#379	C₂³×C₄	1	16	yes	—
887	#379	C₂³×C₄	1	8	yes	—
888	#379	H(5,𝔽₂)	1	8	yes	complemented
889	C₄×C₂²⋊C₄	C₂³×C₄	1	16	yes	—
890	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
891	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
892	C₂⁵	C₂²×C₂²⋊C₄	1	8	yes	—
893	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
894	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
895	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
896	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
897	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
898	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	complemented
899	C₂⁵	#518	1	2	yes	—
900	C₂⁵	#518	1	2	yes	—
901	C₂⁵	#518	1	2	yes	—
902	C₂⁵	#518	1	4	yes	—
903	C₂⁵	#518	1	2	yes	—
904	C₂⁵	#518	1	2	yes	—
905	C₂⁵	#518	1	4	yes	—
906	C₂⁵	#518	1	2	yes	—
907	C₂⁵	#518	1	4	yes	—
908	C₂⁵	#518	1	4	yes	—
909	C₂⁵	#518	1	2	yes	—
910	C₂⁵	#518	1	2	yes	—
911	C₂⁵	#534	1	4	yes	—
912	C₂⁵	#534	1	4	yes	—
913	C₂⁵	#534	1	4	yes	—
914	C₂⁵	#534	1	4	yes	—
915	C₂⁵	#534	1	4	yes	—
916	C₂⁵	#534	1	4	yes	—
917	C₂⁵	#534	1	4	yes	—
918	C₂⁵	#534	1	4	yes	—
919	C₂⁵	#534	1	4	yes	—
920	C₂⁵	#534	1	4	yes	—
921	C₂⁵	#534	1	4	yes	—
922	C₂⁵	#534	1	4	yes	—
923	C₂⁵	#534	1	4	yes	—
924	C₂⁵	#534	1	4	yes	—
925	C₂⁵	#534	1	4	yes	—
926	C₂⁵	#534	1	4	yes	—
927	C₂⁵	C₂⁴×C₄	1	4	yes	—
928	C₂⁵	C₂⁴×C₄	1	2	yes	—
929	C₂⁵	C₂⁴×C₄	1	2	yes	—
930	C₂⁵	C₂⁴×C₄	1	2	yes	—
931	C₂⁵	C₂⁴×C₄	1	2	yes	—
932	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
933	C₂⁵	C₂⁴×C₄	1	4	yes	—
934	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
935	C₂⁵	C₂³×D₄	1	4	yes	—
936	C₂⁵	C₂³×D₄	1	2	yes	—
937	C₂⁵	C₂³×D₄	1	4	yes	—
938	C₂⁵	C₂³×D₄	1	4	yes	—
939	C₂⁵	C₂³×D₄	1	2	yes	—
940	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
941	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
942	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
943	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
946	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
947	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
948	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
949	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
950	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
951	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂⁵	#585	1	4	yes	—
953	C₂⁵	C₂⁶	1	1	yes	characteristic
954	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	complemented
955	C₂²×Q₈	C₂²×C₂²⋊C₄	1	8	yes	complemented
956	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
957	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
958	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
959	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
960	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
961	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
962	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
963	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
964	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
965	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
966	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
967	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
968	C₂²×D₄	C₂⁴×C₄	1	8	yes	—
969	C₂²×D₄	C₂³×D₄	1	8	yes	—
970	C₂²×D₄	C₂³×D₄	1	8	yes	—
971	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
972	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
973	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
974	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
975	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
976	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
977	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
978	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
979	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
980	C₂³×C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
981	C₂³×C₄	C₂⁴×C₄	1	2	yes	—
982	C₂³×C₄	C₂⁴×C₄	1	2	yes	—
983	C₂³×C₄	C₂⁴×C₄	1	4	yes	—
984	C₂³×C₄	C₂⁴×C₄	1	4	yes	—
985	C₂³×C₄	C₂³×D₄	1	4	yes	—
986	C₂³×C₄	C₂³×D₄	1	8	yes	—
987	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
988	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
989	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
990	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
991	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
992	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
993	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
994	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
995	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
996	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
997	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
998	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
999	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
1000	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
1001	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
1002	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
1003	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
1004	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	complemented
1005	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	complemented
1006	C₂×C₂²⋊C₄	C₂⁴×C₄	1	16	yes	—
1007	C₂×C₂²⋊C₄	C₂⁴×C₄	1	8	yes	—
1008	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
1009	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
1010	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	8	yes	—
1011	C₂×C₄²	C₂²×C₂²⋊C₄	1	8	yes	complemented
1012	C₂×C₄²	C₂²×C₂²⋊C₄	1	16	yes	complemented
1013	C₂⁴	#2308	1	4	yes	—
1014	C₂⁴	#2308	1	2	yes	—
1015	C₂⁴	#2308	1	2	yes	—
1016	C₂⁴	#2308	1	4	yes	—
1017	C₂⁴	#2308	1	4	yes	—
1018	C₂⁴	#2308	1	4	yes	—
1019	C₂⁴	#2308	1	4	yes	—
1020	C₂⁴	#2308	1	2	yes	—
1021	C₂⁴	#2308	1	2	yes	—
1022	C₂⁴	#2308	1	4	yes	—
1023	C₂⁴	#2308	1	4	yes	—
1024	C₂⁴	#2308	1	4	yes	—
1025	C₂⁴	#2308	1	2	yes	—
1026	C₂⁴	#2308	1	4	yes	—
1027	C₂⁴	#2308	1	4	yes	—
1028	C₂⁴	#2308	1	4	yes	—
1029	C₂⁴	#2308	1	2	yes	—
1030	C₂⁴	#2308	1	2	yes	—
1031	C₂⁴	#2308	1	4	yes	—
1032	C₂⁴	#2308	1	2	yes	—
1033	C₂⁴	C₂³×C₂²⋊C₄	1	2	yes	—
1034	C₂⁴	C₂³×C₂²⋊C₄	1	4	yes	—
1035	C₂⁴	C₂³×C₂²⋊C₄	1	4	yes	—
1036	C₂⁴	C₂³×C₂²⋊C₄	1	8	yes	—
1037	C₂⁴	C₂³×C₂²⋊C₄	1	4	yes	—
1038	C₂⁴	C₂³×C₂²⋊C₄	1	2	yes	—
1039	C₂⁴	C₂×#518	1	1	yes	characteristic
1040	C₂⁴	C₂×#518	1	4	yes	—
1041	C₂⁴	C₂×#518	1	4	yes	—
1042	C₂⁴	C₂×#518	1	2	yes	—
1043	C₂⁴	C₂×#518	1	4	yes	—
1044	C₂⁴	C₂×#518	1	4	yes	—
1045	C₂⁴	C₂×#518	1	1	yes	characteristic
1046	C₂⁴	C₂×#518	1	1	yes	characteristic
1047	C₂⁴	C₂×#518	1	2	yes	—
1048	C₂⁴	C₂×#518	1	1	yes	characteristic
1049	C₂⁴	C₄×H(5,𝔽₂)	1	4	yes	—
1050	C₂⁴	C₄×H(5,𝔽₂)	1	4	yes	—
1051	C₂⁴	C₂×#534	1	2	yes	—
1052	C₂⁴	C₂×#534	1	4	yes	—
1053	C₂⁴	C₂×#534	1	4	yes	—
1054	C₂⁴	C₂×#534	1	4	yes	—
1055	C₂⁴	C₂×#534	1	4	yes	—
1056	C₂⁴	C₂×#534	1	4	yes	—
1057	C₂⁴	C₂×#534	1	4	yes	—
1058	C₂⁴	C₂×#534	1	4	yes	—
1059	C₂⁴	C₂×#534	1	4	yes	—
1060	C₂⁴	C₂×#534	1	4	yes	—
1061	C₂⁴	C₂×#534	1	4	yes	—
1062	C₂⁴	C₂×#534	1	2	yes	—
1063	C₂⁴	C₂×#534	1	2	yes	—
1064	C₂⁴	C₂×#534	1	2	yes	—
1065	C₂⁴	C₂⁵×C₄	1	1	yes	characteristic
1066	C₂⁴	C₂⁴×D₄	1	2	yes	—
1067	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1069	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
1070	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
1071	C₂⁴	C₂×#585	1	2	yes	—
1072	C₂⁴	H(7,𝔽₂)	1	4	yes	—
1073	C₂²×C₄	C₂³×C₂²⋊C₄	1	4	yes	—
1074	C₂²×C₄	C₂³×C₂²⋊C₄	1	8	yes	—
1075	C₂²×C₄	C₂³×C₂²⋊C₄	1	8	yes	—
1076	C₂²×C₄	C₂³×C₂²⋊C₄	1	16	yes	—
1077	C₂³	#21776	1	8	yes	complemented
1078	C₂³	C₂×#2308	1	4	yes	—
1079	C₂³	C₂×#2308	1	4	yes	—
1080	C₂³	C₂×#2308	1	2	yes	—
1081	C₂³	C₂×#2308	1	2	yes	—
1082	C₂³	C₂×#2308	1	4	yes	—
1083	C₂³	C₂×#2308	1	2	yes	—
1084	C₂³	C₂×#2308	1	4	yes	—
1085	C₂³	C₂×#2308	1	2	yes	—
1086	C₂³	C₂⁴×C₂²⋊C₄	1	1	yes	characteristic
1087	C₂³	C₂²×#518	1	1	yes	characteristic
1088	C₂³	C₂²×#518	1	1	yes	characteristic
1089	C₂³	C₂×C₄×H(5,𝔽₂)	1	2	yes	—
1090	C₂³	#62652	1	2	yes	—
1091	C₂³	C₂²×#534	1	2	yes	—
1092	C₂³	C₂²×#534	1	2	yes	—
1093	C₂³	#62817	1	1	yes	characteristic
1094	C₂³	#62818	1	2	yes	—
1095	C₂³	#62820	1	1	yes	characteristic
1096	C₂³	#62862	1	2	yes	—
1097	C₂³	#62863	1	2	yes	—
1098	C₂³	#62892	1	4	yes	—
1099	C₂³	#62900	1	4	yes	—
1100	C₂³	D₄×H(5,𝔽₂)	1	4	yes	—
1101	C₂³	#62987	1	4	yes	—
1102	C₂²	C₂×#21776	1	4	yes	—
1103	C₂²	C₂×#21776	1	8	yes	—
1104	C₂²	C₂²×#2308	1	1	yes	characteristic
1105	C₂²	C₂²⋊C₄×H(5,𝔽₂)	1	2	yes	—
1106	C₂²	#7626243	1	1	yes	characteristic
1107	C₂²	#7626386	1	1	yes	characteristic
1108	C₂²	#7626663	1	2	yes	—
1109	C₂²	#7648640	1	2	yes	—
1110	C₂²	#7648649	1	4	yes	—
1111	C₂²	#7649027	1	2	yes	—
1112	C₂	C₂²×#21776	1	2	yes	—
1113	C₂	#72258969	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2308
commutator	C₂⁴	C₂⁵×C₄
Frattini, cosocle	C₂⁵	C₂⁶
prime radical	#72217511	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72309339	C₂	semidirect
2. #72309335	C₂	semidirect
3. #72309329	C₂	semidirect
4. #72309325	C₂	semidirect
5. #72309324	C₂	semidirect
6. #72309322	C₂	semidirect
7. #72309321	C₂	semidirect
8. #72237627	C₂	semidirect
9. #72234591	C₂	semidirect
10. #72225698	C₂	semidirect
11. #72225631	C₂	semidirect
12. #72225617	C₂	semidirect
13. C₂×#359428	C₂	semidirect
14. C₂×#364410	C₂	semidirect
15. #72217818	C₂	semidirect
16. #72217789	C₂	semidirect
20. #7708349	C₄	semidirect
23. #7642273	C₄	semidirect
25. #7642244	C₄	semidirect
29. #7630944	C₄	semidirect
31. #7630939	C₄	semidirect
34. #7626202	C₂²	semidirect
35. C₂×#34198	C₂²	semidirect
36. C₂³×#379	C₂²	semidirect
37. #6379246	C₂²	semidirect
38. #6379246	C₂²	semidirect
39. #6379010	C₂²	semidirect
40. #6379010	C₂²	semidirect
41. #6374548	C₂²	semidirect
42. #6374210	C₂²	semidirect
43. C₂×#21776	C₂²	semidirect
45. C₂×#21746	C₂²	semidirect
46. C₂×#21746	C₂²	semidirect
47. C₂×#21746	C₂²	semidirect
48. #6372488	C₂²	semidirect
49. #6371504	C₂²	semidirect
51. C₂²×#1898	C₂²	semidirect
52. C₂²×#1898	C₂²	semidirect
53. C₂²×#1889	C₂²	semidirect
54. C₂²×#1781	C₂²	semidirect
55. C₂×#14679	C₂²	semidirect
56. C₂×#14679	C₂²	semidirect
57. #393532	C₂²	semidirect
58. #392699	C₂²	semidirect
59. #392207	C₂²	semidirect
60. #392109	C₂²	semidirect
61. #391798	C₂²	semidirect
62. #391735	C₂²	semidirect
63. #391709	C₂²	semidirect
64. #387715	C₂²	semidirect
65. #387715	C₂²	semidirect
66. #387715	C₂²	semidirect
67. #387068	C₂²	semidirect
68. #387068	C₂²	semidirect
69. #387068	C₂²	semidirect
70. #386017	C₂²	semidirect
71. #386017	C₂²	semidirect
72. #386017	C₂²	semidirect
73. #385868	C₂²	semidirect
74. #385868	C₂²	semidirect
75. #385868	C₂²	semidirect
76. #383741	C₂²	semidirect
77. #383741	C₂²	semidirect
78. #383741	C₂²	semidirect
79. #383741	C₂²	semidirect
80. #383139	C₂²	semidirect
81. #383139	C₂²	semidirect
82. #383139	C₂²	semidirect
83. #383139	C₂²	semidirect
84. #382811	C₂²	semidirect
85. #382544	C₂²	semidirect
86. #382434	C₂²	semidirect
87. #382422	C₂²	semidirect
88. #382422	C₂²	semidirect
89. #381249	C₂²	semidirect
90. #381122	C₂²	semidirect
91. #380554	C₂²	semidirect
92. #379847	C₂²	semidirect
93. #379806	C₂²	semidirect
94. #379733	C₂²	semidirect
95. #375666	C₂²	semidirect
96. #375194	C₂²	semidirect
97. #374166	C₂²	semidirect
98. #374058	C₂²	semidirect
99. #374004	C₂²	semidirect
100. #368784	C₂²	semidirect
101. #368784	C₂²	semidirect
102. #368784	C₂²	semidirect
103. #368784	C₂²	semidirect
104. #364709	C₂²	semidirect
105. #364709	C₂²	semidirect
106. #364440	C₂²	semidirect
107. #364440	C₂²	semidirect
108. #364410	C₂²	semidirect
109. #364410	C₂²	semidirect
110. #364410	C₂²	semidirect
111. #364410	C₂²	semidirect
112. #364410	C₂²	semidirect
113. #364410	C₂²	semidirect
114. #364410	C₂²	semidirect
115. #364410	C₂²	semidirect
116. #364173	C₂²	semidirect
117. #364054	C₂²	semidirect
118. #363421	C₂²	semidirect
119. #361793	C₂²	semidirect
120. #361312	C₂²	semidirect
121. #361312	C₂²	semidirect
122. #361312	C₂²	semidirect
123. #361312	C₂²	semidirect
124. #359892	C₂²	semidirect
125. #359756	C₂²	semidirect
126. #359591	C₂²	semidirect
127. #359501	C₂²	semidirect
128. #359428	C₂²	semidirect
129. #359428	C₂²	semidirect
130. #359428	C₂²	semidirect
131. #359428	C₂²	semidirect
132. C₂×#11069	C₂²	semidirect
133. C₂×#10991	C₂²	semidirect
134. C₂×#10965	C₂²	semidirect
135. C₂×#10965	C₂²	semidirect
136. #355913	C₂²	semidirect
137. #355913	C₂²	semidirect
138. #355474	C₂²	semidirect
139. #355096	C₂²	semidirect
140. C₂×#10935	C₂²	semidirect
141. C₂×#10735	C₂²	semidirect
142. C₂×#10725	C₂²	semidirect
143. C₂×#10725	C₂²	semidirect
145. C₂⁵×D₄	C₂×C₄	semidirect
158. C₂³×#120	C₂×C₄	semidirect
159. C₂³×#120	C₂×C₄	semidirect
160. C₂³×#120	C₂×C₄	semidirect
168. C₂²×#518	C₂³	semidirect
169. C₂⁴×C₂²⋊C₄	C₂×C₄	semidirect
172. C₂×#2883	C₂³	semidirect
175. C₂³×#99	C₂³	semidirect
176. #37833	C₂×C₄	semidirect
177. #37832	C₂×C₄	semidirect
178. #37645	C₂×C₄	semidirect
179. #37644	C₂×C₄	semidirect
180. #37436	C₂×C₄	semidirect
181. #36714	C₂×C₄	semidirect
182. #36703	C₂×C₄	semidirect
183. #36702	C₂×C₄	semidirect
184. #36614	C₂×C₄	semidirect
185. #36614	C₂×C₄	semidirect
186. C₂×#2846	C₂×C₄	semidirect
187. C₂×#2846	C₂×C₄	semidirect
188. C₂×#2846	C₂×C₄	semidirect
189. C₂×#2846	C₂×C₄	semidirect
193. #36158	C₂×C₄	semidirect
194. #36152	C₂×C₄	semidirect
195. #36098	C₂×C₄	semidirect
196. D₄×#120	C₂×C₄	semidirect
203. #35222	C₂×C₄	semidirect
204. #35222	C₂×C₄	semidirect
205. #35222	C₂×C₄	semidirect
206. #35050	C₂×C₄	semidirect
207. #35050	C₂×C₄	semidirect
208. #35050	C₂×C₄	semidirect
209. #34992	C₂×C₄	semidirect
212. #34988	C₂×C₄	semidirect
216. #34980	C₂×C₄	semidirect
217. #34980	C₂×C₄	semidirect
218. #34980	C₂×C₄	semidirect
219. #34980	C₂×C₄	semidirect
223. #34356	C₂×C₄	semidirect
228. #34198	C₂³	semidirect
229. #34198	C₂³	semidirect
230. #34176	C₂×C₄	semidirect
232. #34176	C₂³	semidirect
233. #34171	C₂×C₄	semidirect
236. #34171	C₂³	semidirect
237. C₂×#2315	C₂³	semidirect
238. C₂×#2308	C₂³	semidirect
252. C₂×#2273	C₂³	semidirect
253. #21333	C₂³	semidirect
254. #21333	C₂³	semidirect
255. #21213	C₂³	semidirect
256. #21213	C₂³	semidirect
257. C₂×#1913	C₂³	semidirect
258. C₂×#1913	C₂³	semidirect
259. C₂×#1913	C₂³	semidirect
260. C₂×#1913	C₂³	semidirect
261. #20984	C₂³	semidirect
262. #20984	C₂³	semidirect
263. #20984	C₂³	semidirect
264. #20984	C₂³	semidirect
279. C₂×#1898	C₂³	semidirect
280. C₂×#1898	C₂³	semidirect
281. C₂×#1898	C₂³	semidirect
282. C₂×#1898	C₂³	semidirect
287. C₂×#1889	C₂³	semidirect
288. C₂×#1889	C₂³	semidirect
289. C₂×#1889	C₂³	semidirect
290. C₂×#1889	C₂³	semidirect
291. C₂×#1828	C₂³	semidirect
292. C₂×#1828	C₂³	semidirect
293. #20689	C₂³	semidirect
297. C₂×#1819	C₂³	semidirect
298. #20633	C₂³	semidirect
299. #20633	C₂³	semidirect
300. #20585	C₂³	semidirect
310. C₂×#1781	C₂³	semidirect
311. #20392	C₂³	semidirect
312. #20392	C₂³	semidirect
313. #20354	C₂³	semidirect
316. C₂²×#342	C₂³	semidirect
317. C₂²×#342	C₂³	semidirect
318. C₂²×#342	C₂³	semidirect
319. C₂²×#342	C₂³	semidirect
320. C₂²×#342	C₂³	semidirect
325. #11351	C₂³	semidirect
326. #11351	C₂³	semidirect
327. #11351	C₂³	semidirect
328. #11351	C₂³	semidirect
329. #11205	C₂³	semidirect
330. #11205	C₂³	semidirect
331. #11205	C₂³	semidirect
332. #11205	C₂³	semidirect
333. #11172	C₂³	semidirect
334. #11172	C₂³	semidirect
335. #11172	C₂³	semidirect
336. #11172	C₂³	semidirect
337. #11169	C₂³	semidirect
338. #11169	C₂³	semidirect
339. #11166	C₂³	semidirect
340. #11166	C₂³	semidirect
345. #11069	C₂³	semidirect
346. #11069	C₂³	semidirect
347. #11069	C₂³	semidirect
348. #11069	C₂³	semidirect
349. #11046	C₂³	semidirect
350. #11046	C₂³	semidirect
351. #11046	C₂³	semidirect
352. #11046	C₂³	semidirect
357. #10991	C₂³	semidirect
358. #10991	C₂³	semidirect
359. #10991	C₂³	semidirect
360. #10991	C₂³	semidirect
361. #10972	C₂³	semidirect
362. #10972	C₂³	semidirect
363. #10972	C₂³	semidirect
364. #10972	C₂³	semidirect
377. #10938	C₂³	semidirect
378. #10938	C₂³	semidirect
379. #10938	C₂³	semidirect
380. #10938	C₂³	semidirect
385. #10935	C₂³	semidirect
386. #10935	C₂³	semidirect
387. #10935	C₂³	semidirect
388. #10935	C₂³	semidirect
389. #10915	C₂³	semidirect
390. #10915	C₂³	semidirect
391. #10915	C₂³	semidirect
392. #10915	C₂³	semidirect
393. #10829	C₂³	semidirect
394. #10829	C₂³	semidirect
395. #10829	C₂³	semidirect
396. #10829	C₂³	semidirect
397. #10768	C₂³	semidirect
398. #10768	C₂³	semidirect
399. #10754	C₂³	semidirect
400. #10754	C₂³	semidirect
401. #10754	C₂³	semidirect
402. #10754	C₂³	semidirect
405. #10735	C₂³	semidirect
406. #10735	C₂³	semidirect
407. #10735	C₂³	semidirect
408. #10735	C₂³	semidirect
409. #10735	C₂³	semidirect
410. #10735	C₂³	semidirect
419. #10725	C₂³	semidirect
420. #10725	C₂³	semidirect
424. C₂⁷	C₂²×C₄	semidirect
429. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
433. C₂⁴×D₄	C₂²×C₄	semidirect
434. C₂⁴×D₄	C₂²×C₄	semidirect
435. C₂⁴×D₄	C₂²×C₄	semidirect
436. C₂⁴×D₄	C₂²×C₄	semidirect
437. C₂⁴×D₄	C₂²×C₄	semidirect
438. C₂⁴×D₄	C₂²×C₄	semidirect
444. C₂⁵×C₄	C₂²×C₄	semidirect
445. C₂⁵×C₄	C₂²×C₄	semidirect
446. C₂×H(3,𝔽₄)	C₂²⋊C₄	semidirect
447. C₂×#560	C₂²⋊C₄	semidirect
448. C₂×#560	C₂²⋊C₄	semidirect
449. C₂×#551	C₂²⋊C₄	semidirect
450. C₂×#551	C₂²⋊C₄	semidirect
454. C₂×#546	C₂²⋊C₄	semidirect
455. C₂×#546	C₂²⋊C₄	semidirect
456. C₂×#546	C₂²⋊C₄	semidirect
463. C₂×D₄²	C₂²⋊C₄	semidirect
464. C₂×D₄²	C₂²⋊C₄	semidirect
468. C₂×#543	C₂²⋊C₄	semidirect
470. C₂×#538	C₂²⋊C₄	semidirect
471. C₂×#538	C₂²⋊C₄	semidirect
472. C₂×#538	C₂²⋊C₄	semidirect
473. C₂×#538	C₂²⋊C₄	semidirect
476. C₂×#535	C₂²⋊C₄	semidirect
477. C₂×#535	C₂²⋊C₄	semidirect
479. C₂×#535	C₂²×C₄	semidirect
481. C₂×#534	C₂²⋊C₄	semidirect
482. C₂×#534	C₂²⋊C₄	semidirect
483. C₂×#534	C₂²⋊C₄	semidirect
484. C₂×#534	C₂²⋊C₄	semidirect
486. C₂×#534	C₂²×C₄	semidirect
493. C₂×#525	C₂²×C₄	semidirect
501. C₂²×#120	C₂²×C₄	semidirect
502. C₂²×#120	C₂²×C₄	semidirect
503. C₂²×#120	C₂²×C₄	semidirect
504. C₂²×#120	C₂²×C₄	semidirect
505. C₂²×#120	C₂²×C₄	semidirect
506. C₂²×#120	C₂²×C₄	semidirect
507. C₂²×#120	C₂²×C₄	semidirect
522. C₂×#518	C₂²⋊C₄	semidirect
523. C₂×#518	C₂²⋊C₄	semidirect
531. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
532. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
533. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
534. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
535. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
565. #2849	C₂²×C₄	semidirect
566. #2849	C₂²×C₄	semidirect
567. #2849	C₂²×C₄	semidirect
568. #2848	C₂²×C₄	semidirect
569. #2847	C₂²×C₄	semidirect
572. #2846	C₂²×C₄	semidirect
573. #2846	C₂²×C₄	semidirect
574. #2846	C₂²×C₄	semidirect
575. #2846	C₂²×C₄	semidirect
576. #2846	C₂²×C₄	semidirect
577. #2846	C₂²×C₄	semidirect
578. #2846	C₂²×C₄	semidirect
579. #2626	C₂²×C₄	semidirect
580. #2622	C₂²×C₄	semidirect
581. #2617	C₂²×C₄	semidirect
582. #2613	C₂²×C₄	semidirect
583. #2613	C₂²×C₄	semidirect
584. #2613	C₂²×C₄	semidirect
585. #2561	C₂²×C₄	semidirect
586. #2539	C₂²×C₄	semidirect
587. #2534	C₂²×C₄	semidirect
588. #2483	C₂²×C₄	semidirect
589. #2482	C₂²×C₄	semidirect
590. #2435	C₂²×C₄	semidirect
591. #2433	C₂²×C₄	semidirect
593. #2411	C₂²×C₄	semidirect
595. #2410	C₂²×C₄	semidirect
596. #2408	C₂²×C₄	semidirect
597. #2405	C₂²×C₄	semidirect
598. #2405	C₂²×C₄	semidirect
599. #2405	C₂²×C₄	semidirect
600. #2404	C₂²×C₄	semidirect
601. #2403	C₂²×C₄	semidirect
602. #2403	C₂²×C₄	semidirect
603. #2342	C₂²×C₄	semidirect
604. D₄×C₂²⋊C₄	C₂²×C₄	semidirect
605. #2321	C₂²×C₄	semidirect
610. #2312	C₂²×C₄	semidirect
611. #2309	C₂²×C₄	semidirect
612. #2309	C₂²×C₄	semidirect
613. #2308	C₂²×C₄	semidirect
614. #2308	C₂²×C₄	semidirect
620. C₄×#120	C₂²×C₄	semidirect
621. #2280	C₂²×C₄	semidirect
622. #2280	C₂²×C₄	semidirect
623. #2280	C₂²×C₄	semidirect
626. C₂×#379	C₂²×C₄	semidirect
627. C₂×#379	C₂²×C₄	semidirect
628. C₂×#379	C₂²×C₄	semidirect
629. C₂×#379	C₂²×C₄	semidirect
714. C₂²×#41	C₂×C₂²⋊C₄	semidirect
715. C₂²×#41	C₂×C₂²⋊C₄	semidirect
725. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
726. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
754. C₂×#127	C₂×C₂²⋊C₄	semidirect
755. C₂×#127	C₂×C₂²⋊C₄	semidirect
756. C₂×#126	C₂×C₂²⋊C₄	semidirect
757. C₂×#126	C₂×C₂²⋊C₄	semidirect
758. C₂×#126	C₂×C₂²⋊C₄	semidirect
759. C₂×#124	C₂×C₂²⋊C₄	semidirect
760. C₂×#124	C₂×C₂²⋊C₄	semidirect
761. C₂×#124	C₂×C₂²⋊C₄	semidirect
762. C₂×#124	C₂×C₂²⋊C₄	semidirect
763. C₂×#124	C₂×C₂²⋊C₄	semidirect
764. C₂×#123	C₂×C₂²⋊C₄	semidirect
765. C₂×#123	C₂×C₂²⋊C₄	semidirect
766. C₂×#123	C₂×C₂²⋊C₄	semidirect
767. C₂×#123	C₂×C₂²⋊C₄	semidirect
768. C₂×#123	C₂×C₂²⋊C₄	semidirect
769. C₂×#123	C₂×C₂²⋊C₄	semidirect
770. C₂×#123	C₂×C₂²⋊C₄	semidirect
771. C₂×#123	C₂×C₂²⋊C₄	semidirect
776. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
777. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
778. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
779. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
782. C₂×#121	C₂×C₂²⋊C₄	semidirect
783. C₂×#121	C₂×C₂²⋊C₄	semidirect
784. C₂×#121	C₂×C₂²⋊C₄	semidirect
785. C₂×#121	C₂×C₂²⋊C₄	semidirect
786. C₂×#121	C₂×C₂²⋊C₄	semidirect
787. C₂×#121	C₂×C₂²⋊C₄	semidirect
788. C₂×#121	C₂×C₂²⋊C₄	semidirect
789. C₂×#121	C₂×C₂²⋊C₄	semidirect
790. C₂×#121	C₂×C₂²⋊C₄	semidirect
791. C₂×#121	C₂×C₂²⋊C₄	semidirect
792. C₂×#121	C₂×C₂²⋊C₄	semidirect
793. C₂×#121	C₂×C₂²⋊C₄	semidirect
794. C₂×#121	C₂×C₂²⋊C₄	semidirect
804. C₂×#120	C₂×C₂²⋊C₄	semidirect
805. C₂×#120	C₂×C₂²⋊C₄	semidirect
806. C₂×#120	C₂×C₂²⋊C₄	semidirect
807. C₂×#120	C₂×C₂²⋊C₄	semidirect
808. C₂×#120	C₂×C₂²⋊C₄	semidirect
825. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
826. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
827. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
828. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
829. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
830. C₂×C₄×D₄	C₂×C₂²⋊C₄	semidirect
834. C₂×#117	C₂×C₂²⋊C₄	semidirect
835. C₂×#117	C₂×C₂²⋊C₄	semidirect
846. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
847. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
888. #379	H(5,𝔽₂)	semidirect
898. C₂⁵	C₂²×C₂²⋊C₄	semidirect
954. C₂²×Q₈	C₂²×C₂²⋊C₄	semidirect
955. C₂²×Q₈	C₂²×C₂²⋊C₄	semidirect
964. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
965. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
966. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
967. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
977. C₂³×C₄	C₂²×C₂²⋊C₄	semidirect
978. C₂³×C₄	C₂²×C₂²⋊C₄	semidirect
979. C₂³×C₄	C₂²×C₂²⋊C₄	semidirect
980. C₂³×C₄	C₂²×C₂²⋊C₄	semidirect
987. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
988. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
989. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
990. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
991. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
992. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
1001. C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
1002. C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
1003. C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
1004. C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
1005. C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	semidirect
1011. C₂×C₄²	C₂²×C₂²⋊C₄	semidirect
1012. C₂×C₄²	C₂²×C₂²⋊C₄	semidirect
1077. C₂³	#21776	semidirect

Maximal subgroups

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

subgroup	index
#72309339	2
#72309335	2
#72309329	2
#72309325	2
#72309324	2
#72309322	2
#72309321	2
#72237627	2
#72234591	2
#72225698	2
#72225631	2
#72225617	2
C₂×#359428	2
C₂×#364410	2
#72217818	2
#72217789	2
#72217511	2