Subgroups — #72315310

Order 4096.

Only the 1185 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 772 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315298	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315275	C₂	1	1	yes	maximal, characteristic, complemented
3	#72315264	C₂	1	1	yes	maximal, characteristic, complemented
4	#72315258	C₂	1	1	yes	maximal, characteristic, complemented
5	#72315242	C₂	1	1	yes	maximal, characteristic, complemented
6	#72315053	C₂	1	1	yes	maximal, characteristic, complemented
7	#72315025	C₂	1	1	yes	maximal, characteristic, complemented
8	#72315025	C₂	1	1	yes	maximal, characteristic, complemented
9	#72315022	C₂	1	1	yes	maximal, characteristic, complemented
10	#72314884	C₂	1	1	yes	maximal, characteristic, complemented
11	#72314855	C₂²	1	1	yes	characteristic, complemented
12	#72314843	C₂	1	1	yes	maximal, characteristic, complemented
13	#72314760	C₂	1	1	yes	maximal, characteristic, complemented
14	#72314748	C₂²	1	1	yes	characteristic, complemented
15	#72314748	C₂²	1	1	yes	characteristic, complemented
16	#72314729	C₂²	1	1	yes	characteristic, complemented
17	#72314498	C₂	1	1	yes	maximal, characteristic, complemented
18	#72314472	C₂²	1	1	yes	characteristic, complemented
19	#72314472	C₂²	1	1	yes	characteristic, complemented
20	#72313624	C₂	1	1	yes	maximal, characteristic, complemented
21	#72312545	C₂	1	1	yes	maximal, characteristic, complemented
22	#72312516	C₂	1	1	yes	maximal, characteristic, complemented
23	#72312312	C₂²	1	1	yes	characteristic, complemented
24	#72312218	C₂²	1	1	yes	characteristic, complemented
25	#72312214	C₂²	1	1	yes	characteristic, complemented
26	#72310373	C₂	1	1	yes	maximal, characteristic, complemented
27	#72310366	C₂²	1	1	yes	characteristic, complemented
28	#72310354	C₂	1	1	yes	maximal, characteristic, complemented
29	#72310216	C₂	1	1	yes	maximal, characteristic, complemented
30	#72309794	C₂²	1	1	yes	characteristic, complemented
31	#72309555	C₂²	1	1	yes	characteristic, complemented
32	#72309478	C₂²	1	1	yes	characteristic, complemented
33	#72301923	C₂	1	1	yes	maximal, characteristic, complemented
34	#72300162	C₂	1	1	yes	maximal, characteristic, complemented
35	#72271167	C₂²	1	1	yes	characteristic, complemented
36	#72266971	C₂	1	1	yes	maximal, characteristic, complemented
37	#72266864	C₂²	1	1	yes	characteristic
38	#72266864	C₂²	1	1	yes	characteristic, complemented
39	#72266834	C₂²	1	1	yes	characteristic
40	#72266834	C₂²	1	1	yes	characteristic, complemented
41	#72266368	C₂²	1	1	yes	characteristic, complemented
42	#72266366	C₂²	1	1	yes	characteristic, complemented
43	#72265779	C₂²	1	1	yes	characteristic, complemented
44	#72264761	C₂	1	1	yes	maximal, characteristic, complemented
45	#72264754	C₂²	1	1	yes	characteristic, complemented
46	#72260584	C₂²	1	1	yes	characteristic, complemented
47	#72259125	C₂²	1	1	yes	characteristic, complemented
48	C₂×#135516	C₂²	1	1	yes	characteristic, complemented
49	#72258334	C₂²	1	1	yes	characteristic, complemented
50	#72258051	C₂	1	1	yes	maximal, characteristic, complemented
51	C₂×#139739	C₂²	1	1	yes	characteristic, complemented
52	#72258028	C₂²	1	1	yes	characteristic
53	#72258028	C₂²	1	1	yes	characteristic
54	#72258020	C₂	1	1	yes	maximal, characteristic, complemented
55	#72258019	C₂²	1	1	yes	characteristic
56	#72258019	C₂²	1	1	yes	characteristic, complemented
57	#72256408	C₂	1	1	yes	maximal, characteristic, complemented
58	#72256348	C₂	1	1	yes	maximal, characteristic, complemented
59	#72256195	C₂²	1	1	yes	characteristic, complemented
60	#72256048	C₂²	1	1	yes	characteristic, complemented
61	#72256025	C₂²	1	1	yes	characteristic, complemented
62	#72255980	C₂²	1	1	yes	characteristic, complemented
63	#72255977	C₂²	1	1	yes	characteristic, complemented
64	#72255874	C₂²	1	1	yes	characteristic, complemented
65	#72255867	C₂²	1	1	yes	characteristic, complemented
66	#72255867	C₂²	1	1	yes	characteristic, complemented
67	#72255863	C₂²	1	1	yes	characteristic, complemented
68	#72255841	C₂²	1	1	yes	characteristic, complemented
69	#72255833	C₂²	1	1	yes	characteristic, complemented
70	#72255830	C₂²	1	1	yes	characteristic, complemented
71	#72255830	C₂²	1	1	yes	characteristic, complemented
72	#72255793	C₂²	1	1	yes	characteristic, complemented
73	#72255778	C₂²	1	1	yes	characteristic, complemented
74	#72255774	C₂²	1	1	yes	characteristic, complemented
75	#72251601	C₂	1	1	yes	maximal, characteristic, complemented
76	#72251595	C₂	1	1	yes	maximal, characteristic, complemented
77	#72251550	C₂²	1	1	yes	characteristic, complemented
78	#72251533	C₂²	1	1	yes	characteristic, complemented
79	#72251533	C₂²	1	1	yes	characteristic, complemented
80	#72251530	C₂²	1	1	yes	characteristic, complemented
81	#72251530	C₂²	1	1	yes	characteristic, complemented
82	#72251501	C₂²	1	1	yes	characteristic, complemented
83	#72251476	C₂²	1	1	yes	characteristic, complemented
84	#72251475	C₂²	1	1	yes	characteristic, complemented
85	#72251462	C₂²	1	1	yes	characteristic, complemented
86	#72251422	C₂²	1	1	yes	characteristic, complemented
87	#72251420	C₂²	1	1	yes	characteristic
88	#72251165	C₂	1	1	yes	maximal, characteristic, complemented
89	#72251157	C₂²	1	1	yes	characteristic, complemented
90	#72251140	C₂²	1	1	yes	characteristic, complemented
91	#72251108	C₂²	1	1	yes	characteristic, complemented
92	#72246450	C₂²	1	1	yes	characteristic, complemented
93	#72246292	C₂²	1	1	yes	characteristic, complemented
94	#72246287	C₂²	1	1	yes	characteristic, complemented
95	#72240471	C₂²	1	1	yes	characteristic, complemented
96	#72240419	C₂²	1	1	yes	characteristic, complemented
97	#72238976	C₂²	1	1	yes	characteristic, complemented
98	#72238976	C₂²	1	1	yes	characteristic, complemented
99	#72238609	C₂²	1	1	yes	characteristic
100	#72238589	C₂²	1	1	yes	characteristic, complemented
101	#72238351	C₂²	1	1	yes	characteristic, complemented
102	#72238351	C₂²	1	1	yes	characteristic, complemented
103	#72238343	C₂²	1	1	yes	characteristic
104	#72238343	C₂²	1	1	yes	characteristic
105	#72238342	C₂²	1	1	yes	characteristic
106	#72238342	C₂²	1	1	yes	characteristic
107	#72237900	C₂²	1	1	yes	characteristic, complemented
108	#72237900	C₂²	1	1	yes	characteristic, complemented
109	#72237636	C₂	1	1	yes	maximal, characteristic, complemented
110	#72237635	C₂²	1	1	yes	characteristic, complemented
111	#72237634	C₂²	1	1	yes	characteristic, complemented
112	#72237633	C₂²	1	1	yes	characteristic, complemented
113	#72237632	C₂²	1	1	yes	characteristic, complemented
114	#72237476	C₂²	1	1	yes	characteristic, complemented
115	#72237476	C₂²	1	1	yes	characteristic, complemented
116	#72237472	C₂²	1	1	yes	characteristic, complemented
117	#72237472	C₂²	1	1	yes	characteristic, complemented
118	#72237402	C₂²	1	1	yes	characteristic
119	#72237402	C₂²	1	1	yes	characteristic, complemented
120	#72237374	C₂²	1	1	yes	characteristic, complemented
121	#72237374	C₂²	1	1	yes	characteristic, complemented
122	#72237302	C₂²	1	1	yes	characteristic
123	#72237045	C₂²	1	1	yes	characteristic, complemented
124	#72237003	C₂²	1	1	yes	characteristic, complemented
125	#72236928	C₂²	1	1	yes	characteristic, complemented
126	#72236678	C₂²	1	1	yes	characteristic, complemented
127	#72236678	C₂²	1	1	yes	characteristic, complemented
128	#72236636	C₂²	1	1	yes	characteristic, complemented
129	#72235130	C₂²	1	1	yes	characteristic
130	#72235130	C₂²	1	1	yes	characteristic
131	#72234693	C₂²	1	1	yes	characteristic
132	#72234633	C₂²	1	1	yes	characteristic, complemented
133	#72234619	C₂²	1	1	yes	characteristic
134	#72234619	C₂²	1	1	yes	characteristic, complemented
135	#72234609	C₂²	1	1	yes	characteristic
136	#72234609	C₂²	1	1	yes	characteristic, complemented
137	#72234117	C₂²	1	1	yes	characteristic, complemented
138	#72233800	C₂²	1	1	yes	characteristic, complemented
139	#72233611	C₂²	1	1	yes	characteristic, complemented
140	#72233441	C₂²	1	1	yes	characteristic, complemented
141	#72225742	C₂²	1	1	yes	characteristic, complemented
142	#72225741	C₂²	1	1	yes	characteristic, complemented
143	#72225734	C₂²	1	1	yes	characteristic, complemented
144	#72225647	C₂²	1	1	yes	characteristic, complemented
145	#72225641	C₂²	1	1	yes	characteristic, complemented
146	C₂×#139748	C₂²	1	1	yes	characteristic, complemented
147	C₂×#139748	C₂²	1	1	yes	characteristic, complemented
148	#72219325	C₂²	1	1	yes	characteristic, complemented
149	C₂×#493474	C₂²	1	1	yes	characteristic
150	C₂×#493474	C₂²	1	1	yes	characteristic, complemented
151	#72219293	C₂²	1	1	yes	characteristic, complemented
152	#72219267	C₂²	1	1	yes	characteristic, complemented
153	#72219240	C₂²	1	1	yes	characteristic, complemented
154	#72219163	C₂²	1	1	yes	characteristic, complemented
155	#72219162	C₂²	1	1	yes	characteristic, complemented
156	#72219160	C₂²	1	1	yes	characteristic, complemented
157	#72219158	C₂²	1	1	yes	characteristic, complemented
158	#72219158	C₂²	1	1	yes	characteristic, complemented
159	#72219040	C₂²	1	1	yes	characteristic
160	#72219040	C₂²	1	1	yes	characteristic
161	#72218980	C₂²	1	1	yes	characteristic, complemented
162	#72218980	C₂²	1	1	yes	characteristic, complemented
163	#72218521	C₂²	1	1	yes	characteristic, complemented
164	#72218521	C₂²	1	1	yes	characteristic, complemented
165	#72218521	C₂²	1	1	yes	characteristic, complemented
166	#72218475	C₂²	1	1	yes	characteristic
167	#72218475	C₂²	1	1	yes	characteristic
168	#72218391	C₂²	1	1	yes	characteristic, complemented
169	#72218391	C₂²	1	1	yes	characteristic, complemented
170	#72218317	C₂²	1	1	yes	characteristic, complemented
171	#72218215	C₂²	1	1	yes	characteristic, complemented
172	#72218206	C₂²	1	1	yes	characteristic, complemented
173	#72218121	C₂²	1	1	yes	characteristic, complemented
174	#72218114	C₂²	1	1	yes	characteristic, complemented
175	C₂×#144366	C₂²	1	1	yes	characteristic, complemented
176	C₂×#139750	C₂²	1	1	yes	characteristic, complemented
177	C₂×#139750	C₂²	1	1	yes	characteristic, complemented
178	C₂×#139743	C₂²	1	1	yes	characteristic, complemented
179	C₂×#133839	C₂²	1	1	yes	characteristic, complemented
180	C₂×#144382	C₂²	1	1	yes	characteristic, complemented
181	C₂×#144378	C₂²	1	1	yes	characteristic, complemented
182	C₂×#6499874	C₂²	1	1	yes	characteristic
183	C₂×#347042	C₂²	1	1	yes	characteristic
184	C₂×#347042	C₂²	1	1	yes	characteristic, complemented
185	C₂×#511790	C₂²	1	1	yes	characteristic
186	C₂×#511790	C₂²	1	1	yes	characteristic
187	#10586797	D₄	1	2	yes	complemented
188	#10586796	D₄	1	2	yes	complemented
189	#10586489	D₄	1	2	yes	complemented
190	#10586472	D₄	1	2	yes	complemented
191	#10586422	C₂³	1	1	yes	characteristic
192	#10586422	C₂³	1	1	yes	characteristic
193	#10586404	C₂³	1	1	yes	characteristic
194	#10586404	C₂³	1	1	yes	characteristic
195	C₂×#62817	C₂³	1	1	yes	characteristic
196	C₂×#62817	C₂³	1	1	yes	characteristic
197	C₂²×#3532	C₂³	1	1	yes	characteristic
198	#10574873	D₄	1	2	yes	complemented
199	C₂×#60399	C₂³	1	1	yes	characteristic
200	#7642244	D₄	1	2	yes	complemented
201	#7642244	C₂³	1	1	yes	characteristic, complemented
202	C₂×#35348	C₂³	1	1	yes	characteristic
203	#6453039	D₄	1	2	yes	complemented
204	C₂×#23984	D₄	1	2	yes	complemented
205	#6451863	D₄	1	2	yes	complemented
206	#6451863	D₄	1	2	yes	complemented
207	#6440460	C₂³	1	1	yes	characteristic
208	#6440460	C₂³	1	1	yes	characteristic
209	#6440460	C₂³	1	1	yes	characteristic
210	#6440460	C₂³	1	1	yes	characteristic
211	#6440460	C₂³	1	1	yes	characteristic, complemented
212	C₂×#23895	C₂³	1	1	yes	characteristic
213	C₂×#23895	C₂³	1	1	yes	characteristic
214	C₂×#23895	C₂³	1	1	yes	characteristic
215	C₂×#23895	C₂³	1	1	yes	characteristic
216	#6437621	C₂³	1	1	yes	characteristic
217	#6437621	C₂³	1	1	yes	characteristic
218	C₂×#23900	C₂³	1	1	yes	characteristic
219	C₂×#23900	C₂³	1	1	yes	characteristic
220	C₂×#23900	C₂³	1	1	yes	characteristic
221	C₂×#23900	C₂³	1	1	yes	characteristic
222	C₂×#23900	C₂³	1	1	yes	characteristic
223	C₂×#23900	C₂³	1	1	yes	characteristic
224	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
225	C₂×#23897	C₂³	1	1	yes	characteristic
226	C₂×#23897	C₂³	1	1	yes	characteristic
227	#6437445	C₂³	1	1	yes	characteristic
228	#6437445	C₂³	1	1	yes	characteristic
229	#6374210	C₂³	1	1	yes	characteristic, complemented
230	C₂×#21778	C₂³	1	1	yes	characteristic
231	C₂×#21778	C₂³	1	1	yes	characteristic
232	#6374187	D₄	1	2	yes	complemented
233	#6374187	D₄	1	2	yes	complemented
234	C₂×#21776	C₂³	1	1	yes	characteristic
235	C₂×#21776	C₂³	1	1	yes	characteristic
236	C₂×#21776	C₂³	1	1	yes	characteristic
237	C₂×#21776	C₂³	1	1	yes	characteristic
238	#6374128	C₂³	1	1	yes	characteristic
239	#6374128	C₂³	1	1	yes	characteristic
240	#6371558	C₂³	1	1	yes	characteristic
241	#6371551	D₄	1	2	yes	complemented
242	#6371504	D₄	1	2	yes	complemented
243	#763514	C₂³	1	1	yes	characteristic
244	#617161	C₂³	1	1	yes	characteristic
245	#616961	C₂³	1	1	yes	characteristic
246	C₂×#15947	C₂³	1	1	yes	characteristic
247	#552670	C₂³	1	1	yes	characteristic
248	#493879	C₂³	1	1	yes	characteristic, complemented
249	#493879	C₂³	1	1	yes	characteristic, complemented
250	#493477	D₄	1	8	yes	complemented
251	C₂×#12707	C₂³	1	1	yes	characteristic
252	C₂×#12707	C₂³	1	1	yes	characteristic
253	C₂×#12707	C₂³	1	1	yes	characteristic
254	C₂×#12707	C₂³	1	1	yes	characteristic
255	C₂×#12707	C₂³	1	1	yes	characteristic, complemented
256	C₂×#12707	C₂³	1	1	yes	characteristic, complemented
257	C₂×#12705	C₂³	1	1	yes	characteristic
258	C₂×#12705	C₂³	1	1	yes	characteristic
259	C₂×#12705	C₂³	1	1	yes	characteristic
260	C₂×#12705	C₂³	1	1	yes	characteristic
261	C₂×#12705	C₂³	1	1	yes	characteristic
262	C₂×#12705	C₂³	1	1	yes	characteristic
263	C₂×#12705	C₂³	1	1	yes	characteristic
264	C₂×#12705	C₂³	1	1	yes	characteristic
265	C₂×#12705	C₂³	1	1	yes	characteristic, complemented
266	C₂×#12705	C₂³	1	1	yes	characteristic, complemented
267	#493370	C₂³	1	1	yes	characteristic
268	#493370	C₂³	1	1	yes	characteristic
269	#493370	C₂³	1	1	yes	characteristic
270	#493370	C₂³	1	1	yes	characteristic
271	#493357	C₂³	1	1	yes	characteristic
272	#493357	C₂³	1	1	yes	characteristic
273	#493357	C₂³	1	1	yes	characteristic
274	#493357	C₂³	1	1	yes	characteristic
275	C₂×#12687	C₂³	1	1	yes	characteristic
276	C₂×#12687	C₂³	1	1	yes	characteristic
277	C₂×#12687	C₂³	1	1	yes	characteristic
278	C₂×#12687	C₂³	1	1	yes	characteristic
279	C₂×#12687	C₂³	1	1	yes	characteristic, complemented
280	C₂×#12687	C₂³	1	1	yes	characteristic, complemented
281	#392030	C₂³	1	1	yes	characteristic, complemented
282	#392030	C₂³	1	1	yes	characteristic, complemented
283	#382707	C₂³	1	1	yes	characteristic, complemented
284	#382544	C₂³	1	1	yes	characteristic, complemented
285	#382544	C₂³	1	1	yes	characteristic, complemented
286	#382434	C₂³	1	1	yes	characteristic, complemented
287	#382434	C₂³	1	1	yes	characteristic, complemented
288	#382422	C₂³	1	1	yes	characteristic, complemented
289	#363969	D₄	1	2	yes	complemented
290	#363969	D₄	1	2	yes	complemented
291	#359811	C₂³	1	1	yes	characteristic, complemented
292	#359558	C₂³	1	1	yes	characteristic
293	#359558	C₂³	1	1	yes	characteristic
294	#359549	C₂³	1	1	yes	characteristic
295	#359549	C₂³	1	1	yes	characteristic
296	#359549	C₂³	1	1	yes	characteristic
297	#359549	C₂³	1	1	yes	characteristic
298	#359549	C₂³	1	1	yes	characteristic, complemented
299	#359549	C₂³	1	1	yes	characteristic, complemented
300	#359509	C₂³	1	1	yes	characteristic
301	#359509	C₂³	1	1	yes	characteristic
302	#359501	C₂³	1	1	yes	characteristic
303	#359501	C₂³	1	1	yes	characteristic
304	#359501	C₂³	1	1	yes	characteristic, complemented
305	#359442	C₂³	1	1	yes	characteristic
306	#359442	C₂³	1	1	yes	characteristic
307	#190147	C₂³	1	1	yes	characteristic, complemented
308	#190116	C₂³	1	1	yes	characteristic, complemented
309	C₂×#8547	C₂³	1	1	yes	characteristic, complemented
310	#188050	C₂³	1	1	yes	characteristic
311	#188050	C₂³	1	1	yes	characteristic
312	C₂×#8541	C₂³	1	1	yes	characteristic
313	C₂×#8541	C₂³	1	1	yes	characteristic
314	C₂×#8541	C₂³	1	1	yes	characteristic, complemented
315	#187952	D₄	1	2	yes	complemented
316	#187949	D₄	1	2	yes	complemented
317	#187944	C₂³	1	1	yes	characteristic
318	#187944	C₂³	1	1	yes	characteristic
319	#187944	C₂³	1	1	yes	characteristic
320	#187944	C₂³	1	1	yes	characteristic
321	#187944	C₂³	1	1	yes	characteristic, complemented
322	#187943	D₄	1	2	yes	complemented
323	#187940	D₄	1	2	yes	complemented
324	C₂×#8534	C₂³	1	1	yes	characteristic
325	C₂×#8534	C₂³	1	1	yes	characteristic
326	C₂×#8534	C₂³	1	1	yes	characteristic
327	C₂×#8534	C₂³	1	1	yes	characteristic
328	C₂×#8534	C₂³	1	1	yes	characteristic, complemented
329	#186835	C₂³	1	1	yes	characteristic, complemented
330	C₂×#8453	C₂³	1	1	yes	characteristic, complemented
331	#146479	C₂³	1	1	yes	characteristic, complemented
332	#146479	C₂³	1	1	yes	characteristic, complemented
333	#146475	C₂³	1	1	yes	characteristic, complemented
334	#146475	C₂³	1	1	yes	characteristic, complemented
335	#128033	C₂³	1	1	yes	characteristic, complemented
336	#128033	C₂³	1	1	yes	characteristic, complemented
337	C₂×#7304	C₂³	1	1	yes	characteristic, complemented
338	C₂×#7304	C₂³	1	1	yes	characteristic, complemented
339	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
340	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
341	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
342	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
343	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
344	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
345	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
346	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
347	C₂×#7311	C₂³	1	1	yes	characteristic, complemented
348	C₂×#7311	C₂³	1	1	yes	characteristic, complemented
349	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
350	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
351	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
352	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
353	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
354	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
355	#128009	C₂³	1	1	yes	characteristic, complemented
356	#128009	C₂³	1	1	yes	characteristic, complemented
357	C₂×#7307	C₂³	1	1	yes	characteristic, complemented
358	C₂×#7307	C₂³	1	1	yes	characteristic, complemented
359	#108238	C₂³	1	1	yes	characteristic, complemented
360	#108222	C₂³	1	1	yes	characteristic, complemented
361	#107130	C₂³	1	1	yes	characteristic, complemented
362	#107114	C₂³	1	1	yes	characteristic, complemented
363	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
364	#62862	C₂×D₄	1	4	yes	—
365	#62862	#41	1	4	yes	—
366	#62844	C₂×D₄	1	2	yes	—
367	#62844	C₂×D₄	1	2	yes	—
368	#62842	C₂×D₄	1	2	yes	—
369	#62842	C₂×D₄	1	2	yes	—
370	#62832	C₂×D₄	1	2	yes	—
371	#62832	C₂×D₄	1	2	yes	—
372	#62824	C₂×D₄	1	2	yes	—
373	#62824	C₂×D₄	1	2	yes	—
374	#62820	C₂×D₄	1	2	yes	—
375	#62820	C₂×D₄	1	2	yes	—
376	#62820	C₂×D₄	1	2	yes	—
377	#62817	C₂×D₄	1	2	yes	—
378	#62817	C₂×D₄	1	2	yes	—
379	#62817	C₂×D₄	1	2	yes	—
380	#62817	C₂×D₄	1	2	yes	—
381	#62817	C₂×D₄	1	2	yes	—
382	#62817	C₂×D₄	1	2	yes	—
383	#62817	C₂×D₄	1	2	yes	—
384	C₂×#3490	C₂×D₄	1	2	yes	—
385	C₂×#3484	C₂×D₄	1	2	yes	—
386	C₂×#3484	C₂⁴	1	1	yes	characteristic
387	C₂×#3484	C₂⁴	1	1	yes	characteristic
388	C₂×#3484	C₂⁴	1	1	yes	characteristic
389	C₂×#3484	C₂⁴	1	1	yes	characteristic
390	C₂×#3484	C₂⁴	1	1	yes	characteristic
391	C₂×#3484	C₂⁴	1	1	yes	characteristic
392	C₂²×#551	C₂×D₄	1	1	yes	characteristic
393	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
394	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
395	C₂²×#560	C₂×D₄	1	1	yes	characteristic
396	C₂²×#535	C₂⁴	1	1	yes	characteristic
397	C₂²×#534	C₂⁴	1	1	yes	characteristic
398	C₂³×#120	C₂×D₄	1	1	yes	characteristic, complemented
399	C₂³×#120	C₂⁴	1	1	yes	characteristic
400	C₂³×#120	C₂⁴	1	1	yes	characteristic
401	#62652	C₂×D₄	1	1	yes	characteristic, complemented
402	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
403	C₂×#3026	C₂×D₄	1	2	yes	—
404	C₂×#3026	C₂×D₄	1	2	yes	—
405	C₂×#3026	C₂×D₄	1	2	yes	—
406	C₂×#3026	C₂×D₄	1	2	yes	—
407	C₂×#2883	C₂×D₄	1	2	yes	—
408	C₂×#2883	C₂×D₄	1	1	yes	characteristic
409	C₂×#2883	C₂×D₄	1	1	yes	characteristic
410	C₂×#2883	C₂×D₄	1	1	yes	characteristic
411	C₂×#2883	C₂×D₄	1	2	yes	complemented
412	C₂×#2883	C₂×D₄	1	1	yes	characteristic, complemented
413	C₂×#2846	C₂×D₄	1	2	yes	—
414	C₂×#2846	C₂×D₄	1	2	yes	complemented
415	#34992	C₂×D₄	1	2	yes	—
416	#34992	C₂×D₄	1	2	yes	complemented
417	#34171	C₂×D₄	1	2	yes	complemented
418	#34171	C₂⁴	1	1	yes	characteristic
419	#34171	C₂⁴	1	1	yes	characteristic
420	C₂×#2315	C₂×D₄	1	1	yes	characteristic, complemented
421	C₂×#2308	C₂⁴	1	1	yes	characteristic
422	C₂²×#379	C₂×D₄	1	1	yes	characteristic, complemented
423	#21778	C₂×D₄	1	4	yes	—
424	#21776	C₂×D₄	1	4	yes	—
425	#21747	C₂×D₄	1	2	yes	complemented
426	#21746	C₂×D₄	1	2	yes	complemented
427	C₂×#1913	C₂×D₄	1	2	yes	—
428	C₂×#1913	C₂×D₄	1	2	yes	—
429	C₂×#1913	C₂×D₄	1	2	yes	—
430	C₂×#1913	C₂×D₄	1	2	yes	—
431	C₂×#1913	C₂×D₄	1	2	yes	complemented
432	C₂×#1913	C₂×D₄	1	2	yes	complemented
433	C₂×#1913	C₂×D₄	1	2	yes	complemented
434	C₂×#1913	C₂×D₄	1	2	yes	complemented
435	C₂×#1898	C₂×D₄	1	2	yes	—
436	C₂×#1898	C₂×D₄	1	2	yes	—
437	C₂×#1898	C₂×D₄	1	2	yes	complemented
438	C₂×#1898	C₂×D₄	1	2	yes	complemented
439	#20960	C₂×D₄	1	2	yes	—
440	#20960	C₂×D₄	1	2	yes	—
441	#20960	C₂×D₄	1	2	yes	—
442	#20960	C₂×D₄	1	2	yes	—
443	C₂×#1828	C₂×D₄	1	2	yes	—
444	C₂×#1828	C₂×D₄	1	2	yes	complemented
445	C₂×#1819	C₂×D₄	1	2	yes	complemented
446	C₂×#1783	C₂⁴	1	1	yes	characteristic
447	C₂×#1783	C₂⁴	1	1	yes	characteristic
448	C₂×#1783	C₂⁴	1	1	yes	characteristic
449	C₂×#1783	C₂⁴	1	1	yes	characteristic
450	C₂×#1781	C₂⁴	1	1	yes	characteristic
451	C₂×#1781	C₂⁴	1	1	yes	characteristic
452	C₂×#1781	C₂⁴	1	1	yes	characteristic
453	C₂×#1781	C₂⁴	1	1	yes	characteristic
454	C₂×#1781	C₂⁴	1	1	yes	characteristic
455	C₂×#1781	C₂⁴	1	1	yes	characteristic
456	C₂×#1781	C₂⁴	1	1	yes	characteristic
457	C₂×#1781	C₂⁴	1	1	yes	characteristic
458	C₂×#1781	C₂⁴	1	1	yes	characteristic
459	C₂×#1781	C₂⁴	1	1	yes	characteristic
460	C₂×#1781	C₂⁴	1	1	yes	characteristic
461	C₂×#1781	C₂⁴	1	1	yes	characteristic
462	#20354	C₂×D₄	1	1	yes	characteristic, complemented
463	#20354	C₂×D₄	1	1	yes	characteristic, complemented
464	#14658	C₂×D₄	1	1	yes	characteristic, complemented
465	#14657	C₂×D₄	1	1	yes	characteristic, complemented
466	#14335	C₂⁴	1	1	yes	characteristic
467	#14167	C₂×D₄	1	1	yes	characteristic, complemented
468	#14134	C₂×D₄	1	1	yes	characteristic, complemented
469	C₂×#1438	C₂⁴	1	1	yes	characteristic
470	#12705	C₂×D₄	1	4	yes	—
471	#12705	C₂×D₄	1	4	yes	—
472	#12690	C₂×D₄	1	4	yes	—
473	#12690	C₂×D₄	1	4	yes	—
474	#8534	C₂×D₄	1	2	yes	—
475	#8534	C₂×D₄	1	2	yes	—
476	#8534	C₂×D₄	1	2	yes	—
477	#8534	C₂×D₄	1	2	yes	—
478	#8534	C₂×D₄	1	2	yes	complemented
479	#8534	C₂×D₄	1	2	yes	complemented
480	#8534	C₂×D₄	1	2	yes	complemented
481	#8534	C₂×D₄	1	2	yes	complemented
482	C₂⁷	C₂²×D₄	1	1	yes	characteristic
483	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
484	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
485	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
486	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
487	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
488	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
489	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
490	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
491	C₂³×#41	H(5,𝔽₂)	1	1	yes	characteristic
492	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
493	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
494	#3491	#120	1	4	yes	—
495	#3491	#121	1	4	yes	—
496	#3491	#121	1	4	yes	—
497	#3491	#127	1	4	yes	—
498	#3490	#120	1	4	yes	—
499	#3490	#120	1	4	yes	—
500	#3490	#120	1	4	yes	—
501	#3490	#121	1	4	yes	—
502	#3490	#121	1	4	yes	—
503	#3490	#121	1	4	yes	—
504	#3490	#121	1	4	yes	—
505	#3490	#127	1	4	yes	—
506	#3485	#120	1	4	yes	—
507	#3485	#121	1	4	yes	—
508	#3485	#121	1	4	yes	—
509	#3485	#127	1	4	yes	—
510	#3484	#120	1	4	yes	—
511	#3484	#121	1	4	yes	—
512	#3484	#121	1	4	yes	—
513	#3484	#127	1	4	yes	—
514	#3484	C₂²×D₄	1	2	yes	—
515	#3484	C₂²×D₄	1	2	yes	—
516	#3484	C₂²×D₄	1	2	yes	—
517	#3484	C₂²×D₄	1	2	yes	—
518	#3484	C₂²×D₄	1	2	yes	—
519	#3484	C₂²×D₄	1	2	yes	—
520	#3484	C₂²×D₄	1	2	yes	—
521	#3484	C₂²×D₄	1	2	yes	—
522	#3484	C₂×#41	1	2	yes	—
523	#3484	C₂×#41	1	2	yes	—
524	#3484	H(5,𝔽₂)	1	2	yes	—
525	#3484	H(5,𝔽₂)	1	2	yes	—
526	C₂×#543	#120	1	2	yes	—
527	C₂×#535	#121	1	4	yes	—
528	C₂×#534	#120	1	2	yes	—
529	C₂×#534	#120	1	2	yes	—
530	C₂×#534	#120	1	2	yes	—
531	C₂×#534	#121	1	4	yes	—
532	C₂×#534	C₂²×D₄	1	2	yes	—
533	C₂×#534	C₂²×D₄	1	2	yes	—
534	C₂×#534	C₂²×D₄	1	2	yes	—
535	C₂×#534	C₂²×D₄	1	2	yes	—
536	C₂×#534	C₂²×D₄	1	2	yes	—
537	C₂×#534	C₂×#41	1	2	yes	—
538	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
539	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
540	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
541	C₂²×#124	H(5,𝔽₂)	1	1	yes	characteristic
542	C₂×#525	#120	1	4	yes	—
543	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
544	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
545	C₂²×#120	#120	1	4	yes	—
546	C₂²×#120	C₂²×D₄	1	2	yes	—
547	C₂²×#120	C₂²×D₄	1	2	yes	—
548	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
549	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
550	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
551	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
552	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
554	C₂×#518	#120	1	2	yes	—
555	C₂×#518	#120	1	2	yes	—
556	C₂×#518	#120	1	2	yes	—
557	C₂×#518	C₂²×D₄	1	1	yes	characteristic
558	C₂×#518	C₂²×D₄	1	1	yes	characteristic
559	C₂×#518	C₂²×D₄	1	1	yes	characteristic
560	C₂×#518	C₂²×D₄	1	1	yes	characteristic
561	C₂×#518	C₂²×D₄	1	1	yes	characteristic
562	C₂×#518	C₂²×D₄	1	1	yes	characteristic
563	C₂×#518	C₂²×D₄	1	1	yes	characteristic
564	C₂×#518	C₂²×D₄	1	1	yes	characteristic
565	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
566	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
567	C₂²×#117	H(5,𝔽₂)	1	1	yes	characteristic
568	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
573	C₂²×#99	C₂²×D₄	1	2	yes	—
574	C₂²×#99	C₂²×D₄	1	2	yes	—
575	C₂²×#99	C₂²×D₄	1	2	yes	—
576	C₂²×#99	C₂²×D₄	1	2	yes	—
577	C₂×#379	C₂²×D₄	1	2	yes	—
578	C₂×#379	C₂²×D₄	1	2	yes	—
579	#1783	C₂²×D₄	1	2	yes	—
580	#1783	C₂²×D₄	1	2	yes	—
581	#1781	C₂²×D₄	1	2	yes	—
582	#1781	C₂²×D₄	1	2	yes	—
583	#1781	C₂²×D₄	1	2	yes	—
584	#1781	C₂²×D₄	1	2	yes	—
585	#1438	C₂²×D₄	1	1	yes	characteristic
586	#1438	C₂²×D₄	1	1	yes	characteristic
587	#1438	C₂²×D₄	1	1	yes	characteristic
588	#1438	C₂²×D₄	1	1	yes	characteristic
589	C₂⁶	C₂×#120	1	1	yes	characteristic
590	C₂⁶	#534	1	1	yes	characteristic
591	C₂⁶	#534	1	1	yes	characteristic
592	C₂⁶	C₂³×D₄	1	1	yes	characteristic
593	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
595	C₂×H(5,𝔽₂)	C₂×#121	1	2	yes	—
596	C₂×H(5,𝔽₂)	C₂×#121	1	2	yes	—
597	C₂×H(5,𝔽₂)	C₂×#127	1	2	yes	—
598	C₂×H(5,𝔽₂)	#534	1	2	yes	—
599	C₂×H(5,𝔽₂)	#534	1	2	yes	—
600	C₂²×#41	#392	1	4	yes	—
601	C₂²×#41	B(4,𝔽₂)	1	4	yes	—
602	C₂²×#41	B(4,𝔽₂)	1	4	yes	—
603	C₂³×Q₈	#534	1	1	yes	characteristic
604	C₂³×D₄	#392	1	4	yes	—
605	C₂³×D₄	B(4,𝔽₂)	1	4	yes	—
606	C₂³×D₄	B(4,𝔽₂)	1	4	yes	—
607	C₂³×D₄	C₂×#120	1	2	yes	—
608	C₂³×D₄	C₂×#120	1	2	yes	—
609	C₂³×D₄	C₂×#120	1	2	yes	—
610	C₂³×D₄	C₂×#121	1	2	yes	—
611	C₂³×D₄	#534	1	1	yes	characteristic
612	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
613	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
614	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
615	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
616	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
617	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
618	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
623	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
625	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	#543	#392	1	4	yes	—
627	#543	#392	1	4	yes	—
628	#534	#392	1	4	yes	—
629	#534	#392	1	4	yes	—
630	#534	C₂×#120	1	4	yes	—
631	#534	C₂×#121	1	4	yes	—
632	#534	C₂×#121	1	4	yes	—
633	#534	C₂×#127	1	4	yes	—
634	C₂×#123	#392	1	4	yes	—
635	C₂×#123	#392	1	4	yes	—
636	C₂×#123	C₂×#120	1	2	yes	—
637	C₂×#123	C₂×#121	1	2	yes	—
638	C₂×#123	C₂×#121	1	2	yes	—
639	C₂×#123	C₂×#127	1	2	yes	—
640	C₂×#120	#392	1	4	yes	—
641	C₂×#120	#392	1	4	yes	—
642	C₂×#120	C₂×#120	1	4	yes	—
643	C₂×#120	C₂×#120	1	4	yes	—
644	C₂×#120	C₂×#120	1	2	yes	—
645	C₂×#120	C₂×#121	1	4	yes	—
646	C₂×#120	C₂×#121	1	4	yes	—
647	C₂×#120	C₂×#121	1	2	yes	—
648	C₂×#120	C₂×#121	1	2	yes	—
649	C₂×#120	C₂×#127	1	2	yes	—
650	#518	#392	1	4	yes	—
651	#518	#392	1	4	yes	—
652	#518	#392	1	4	yes	—
653	#518	#392	1	4	yes	—
654	#518	C₂×#120	1	2	yes	—
655	#518	C₂×#121	1	2	yes	—
656	#518	C₂×#121	1	2	yes	—
657	#518	C₂×#127	1	2	yes	—
658	#518	#534	1	2	yes	—
659	#518	#534	1	2	yes	—
660	C₂×#117	#392	1	4	yes	—
661	C₂²×C₂²⋊C₄	#392	1	4	yes	—
662	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
663	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
664	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
665	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
666	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
667	C₂²×C₂²⋊C₄	C₂×#121	1	2	yes	—
668	C₂²×C₂²⋊C₄	#534	1	1	yes	characteristic
669	C₂²×C₂²⋊C₄	#534	1	1	yes	characteristic
670	C₂²×C₄²	#534	1	1	yes	characteristic
671	C₂²×C₄²	#534	1	1	yes	characteristic
672	C₂⁵	#2021	1	4	yes	complemented
673	C₂⁵	C₂×#392	1	2	yes	—
674	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
675	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
676	C₂⁵	C₂²×#120	1	1	yes	characteristic
677	C₂⁵	C₂²×#120	1	1	yes	characteristic
678	C₂⁵	C₂²×#121	1	1	yes	characteristic
679	C₂⁵	C₂×#534	1	1	yes	characteristic
680	C₂⁵	#3484	1	1	yes	characteristic
681	C₂⁵	#3484	1	1	yes	characteristic
682	C₂⁵	#3484	1	1	yes	characteristic
683	C₂⁵	#3484	1	1	yes	characteristic
684	C₂⁵	#3484	1	1	yes	characteristic
685	C₂⁵	#3484	1	1	yes	characteristic
686	C₂⁵	#3484	1	1	yes	characteristic
687	C₂⁵	#3484	1	1	yes	characteristic
688	C₂⁵	#3490	1	1	yes	characteristic
689	C₂²×Q₈	#2021	1	4	yes	complemented
690	C₂²×D₄	#2021	1	4	yes	complemented
691	C₂²×D₄	#2021	1	4	yes	complemented
692	C₂²×D₄	#2021	1	4	yes	complemented
693	C₂²×D₄	C₂×#392	1	4	yes	—
694	C₂²×D₄	C₂×#392	1	4	yes	—
695	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
696	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
697	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
698	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
699	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
700	C₂²×D₄	C₂²×#121	1	1	yes	characteristic
701	C₂²×D₄	C₂²×#121	1	1	yes	characteristic
702	C₂²×D₄	C₂²×#127	1	1	yes	characteristic
703	C₂²×D₄	C₂×#534	1	1	yes	characteristic
704	C₂²×D₄	C₂×#534	1	1	yes	characteristic
705	C₂²×D₄	#3484	1	1	yes	characteristic
706	C₂²×D₄	#3484	1	1	yes	characteristic
707	C₂²×D₄	#3484	1	1	yes	characteristic
708	C₂²×D₄	#3484	1	1	yes	characteristic
709	C₂²×D₄	#3484	1	1	yes	characteristic
710	C₂²×D₄	#3484	1	1	yes	characteristic
711	C₂²×D₄	#3484	1	1	yes	characteristic
712	C₂²×D₄	#3484	1	1	yes	characteristic
713	C₂²×D₄	#3490	1	1	yes	characteristic
714	C₂²×D₄	#3490	1	1	yes	characteristic
715	C₂³×C₄	#2021	1	4	yes	complemented
716	C₂³×C₄	#2021	1	4	yes	complemented
717	C₂³×C₄	#2021	1	4	yes	complemented
718	C₂³×C₄	C₂×#392	1	2	yes	—
719	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
720	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
721	C₂³×C₄	C₂×#534	1	1	yes	characteristic
722	C₂³×C₄	#3484	1	1	yes	characteristic
723	C₂³×C₄	#3484	1	1	yes	characteristic
724	C₂³×C₄	#3484	1	1	yes	characteristic
725	C₂³×C₄	#3484	1	1	yes	characteristic
726	C₂³×C₄	#3490	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂×#392	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂×#392	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂×#392	1	4	yes	—
730	C₂×C₂²⋊C₄	C₂×#392	1	4	yes	—
731	C₂⁴	C₂×#2021	1	4	yes	—
732	C₂⁴	C₂×#2021	1	4	yes	—
733	C₂⁴	C₂×#2021	1	4	yes	—
734	C₂⁴	C₂²×#392	1	1	yes	characteristic
735	C₂⁴	#34980	1	1	yes	characteristic
736	C₂⁴	#34980	1	1	yes	characteristic
737	C₂⁴	#34980	1	1	yes	characteristic
738	C₂⁴	#34981	1	1	yes	characteristic
739	C₂⁴	#35346	1	1	yes	characteristic
740	C₂⁴	#35346	1	1	yes	characteristic
741	C₂⁴	#35348	1	1	yes	characteristic
742	C₂⁴	#35348	1	1	yes	characteristic
743	C₂⁴	#35348	1	1	yes	characteristic
744	C₂⁴	#35390	1	1	yes	characteristic
745	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
746	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
747	C₂²×C₄	C₂×#2021	1	4	yes	—
748	C₂²×C₄	C₂×#2021	1	4	yes	—
749	C₂²×C₄	C₂×#2021	1	4	yes	—
750	C₂²×C₄	#34980	1	1	yes	characteristic
751	C₂²×C₄	#34981	1	1	yes	characteristic
752	C₂²×C₄	#35348	1	1	yes	characteristic
753	C₂²×C₄	#35390	1	1	yes	characteristic
754	C₂³	#5955303	1	1	yes	characteristic
755	C₂³	C₂²×#2021	1	2	yes	—
756	C₂³	#6499867	1	1	yes	characteristic
757	C₂³	#6499867	1	2	yes	—
758	C₂³	#6499867	1	1	yes	characteristic
759	C₂³	#6499874	1	1	yes	characteristic
760	C₂³	#6499875	1	1	yes	characteristic
761	C₂³	#6499876	1	1	yes	characteristic
762	C₂³	#6499876	1	1	yes	characteristic
763	C₂²	#72217699	1	1	yes	characteristic
764	C₂²	#72234630	1	1	yes	characteristic
765	C₂²	#72241003	1	1	yes	characteristic
766	C₂²	#72241004	1	1	yes	characteristic
767	C₂²	#72241021	1	1	yes	characteristic
768	C₂²	#72252234	1	1	yes	characteristic
769	C₂²	#72258442	1	1	yes	characteristic
770	C₂	#72266206	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266206
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72315298	C₂	semidirect
2. #72315275	C₂	semidirect
3. #72315264	C₂	semidirect
4. #72315258	C₂	semidirect
5. #72315242	C₂	semidirect
6. #72315053	C₂	semidirect
7. #72315025	C₂	semidirect
8. #72315025	C₂	semidirect
9. #72315022	C₂	semidirect
10. #72314884	C₂	semidirect
11. #72314855	C₂²	semidirect
12. #72314843	C₂	semidirect
13. #72314760	C₂	semidirect
14. #72314748	C₂²	semidirect
15. #72314748	C₂²	semidirect
16. #72314729	C₂²	semidirect
17. #72314498	C₂	semidirect
18. #72314472	C₂²	semidirect
19. #72314472	C₂²	semidirect
20. #72313624	C₂	semidirect
21. #72312545	C₂	semidirect
22. #72312516	C₂	semidirect
23. #72312312	C₂²	semidirect
24. #72312218	C₂²	semidirect
25. #72312214	C₂²	semidirect
26. #72310373	C₂	semidirect
27. #72310366	C₂²	semidirect
28. #72310354	C₂	semidirect
29. #72310216	C₂	semidirect
30. #72309794	C₂²	semidirect
31. #72309555	C₂²	semidirect
32. #72309478	C₂²	semidirect
33. #72301923	C₂	semidirect
34. #72300162	C₂	semidirect
35. #72271167	C₂²	semidirect
36. #72266971	C₂	semidirect
38. #72266864	C₂²	semidirect
40. #72266834	C₂²	semidirect
41. #72266368	C₂²	semidirect
42. #72266366	C₂²	semidirect
43. #72265779	C₂²	semidirect
44. #72264761	C₂	semidirect
45. #72264754	C₂²	semidirect
46. #72260584	C₂²	semidirect
47. #72259125	C₂²	semidirect
48. C₂×#135516	C₂²	semidirect
49. #72258334	C₂²	semidirect
50. #72258051	C₂	semidirect
51. C₂×#139739	C₂²	semidirect
54. #72258020	C₂	semidirect
56. #72258019	C₂²	semidirect
57. #72256408	C₂	semidirect
58. #72256348	C₂	semidirect
59. #72256195	C₂²	semidirect
60. #72256048	C₂²	semidirect
61. #72256025	C₂²	semidirect
62. #72255980	C₂²	semidirect
63. #72255977	C₂²	semidirect
64. #72255874	C₂²	semidirect
65. #72255867	C₂²	semidirect
66. #72255867	C₂²	semidirect
67. #72255863	C₂²	semidirect
68. #72255841	C₂²	semidirect
69. #72255833	C₂²	semidirect
70. #72255830	C₂²	semidirect
71. #72255830	C₂²	semidirect
72. #72255793	C₂²	semidirect
73. #72255778	C₂²	semidirect
74. #72255774	C₂²	semidirect
75. #72251601	C₂	semidirect
76. #72251595	C₂	semidirect
77. #72251550	C₂²	semidirect
78. #72251533	C₂²	semidirect
79. #72251533	C₂²	semidirect
80. #72251530	C₂²	semidirect
81. #72251530	C₂²	semidirect
82. #72251501	C₂²	semidirect
83. #72251476	C₂²	semidirect
84. #72251475	C₂²	semidirect
85. #72251462	C₂²	semidirect
86. #72251422	C₂²	semidirect
88. #72251165	C₂	semidirect
89. #72251157	C₂²	semidirect
90. #72251140	C₂²	semidirect
91. #72251108	C₂²	semidirect
92. #72246450	C₂²	semidirect
93. #72246292	C₂²	semidirect
94. #72246287	C₂²	semidirect
95. #72240471	C₂²	semidirect
96. #72240419	C₂²	semidirect
97. #72238976	C₂²	semidirect
98. #72238976	C₂²	semidirect
100. #72238589	C₂²	semidirect
101. #72238351	C₂²	semidirect
102. #72238351	C₂²	semidirect
107. #72237900	C₂²	semidirect
108. #72237900	C₂²	semidirect
109. #72237636	C₂	semidirect
110. #72237635	C₂²	semidirect
111. #72237634	C₂²	semidirect
112. #72237633	C₂²	semidirect
113. #72237632	C₂²	semidirect
114. #72237476	C₂²	semidirect
115. #72237476	C₂²	semidirect
116. #72237472	C₂²	semidirect
117. #72237472	C₂²	semidirect
119. #72237402	C₂²	semidirect
120. #72237374	C₂²	semidirect
121. #72237374	C₂²	semidirect
123. #72237045	C₂²	semidirect
124. #72237003	C₂²	semidirect
125. #72236928	C₂²	semidirect
126. #72236678	C₂²	semidirect
127. #72236678	C₂²	semidirect
128. #72236636	C₂²	semidirect
132. #72234633	C₂²	semidirect
134. #72234619	C₂²	semidirect
136. #72234609	C₂²	semidirect
137. #72234117	C₂²	semidirect
138. #72233800	C₂²	semidirect
139. #72233611	C₂²	semidirect
140. #72233441	C₂²	semidirect
141. #72225742	C₂²	semidirect
142. #72225741	C₂²	semidirect
143. #72225734	C₂²	semidirect
144. #72225647	C₂²	semidirect
145. #72225641	C₂²	semidirect
146. C₂×#139748	C₂²	semidirect
147. C₂×#139748	C₂²	semidirect
148. #72219325	C₂²	semidirect
150. C₂×#493474	C₂²	semidirect
151. #72219293	C₂²	semidirect
152. #72219267	C₂²	semidirect
153. #72219240	C₂²	semidirect
154. #72219163	C₂²	semidirect
155. #72219162	C₂²	semidirect
156. #72219160	C₂²	semidirect
157. #72219158	C₂²	semidirect
158. #72219158	C₂²	semidirect
161. #72218980	C₂²	semidirect
162. #72218980	C₂²	semidirect
163. #72218521	C₂²	semidirect
164. #72218521	C₂²	semidirect
165. #72218521	C₂²	semidirect
168. #72218391	C₂²	semidirect
169. #72218391	C₂²	semidirect
170. #72218317	C₂²	semidirect
171. #72218215	C₂²	semidirect
172. #72218206	C₂²	semidirect
173. #72218121	C₂²	semidirect
174. #72218114	C₂²	semidirect
175. C₂×#144366	C₂²	semidirect
176. C₂×#139750	C₂²	semidirect
177. C₂×#139750	C₂²	semidirect
178. C₂×#139743	C₂²	semidirect
179. C₂×#133839	C₂²	semidirect
180. C₂×#144382	C₂²	semidirect
181. C₂×#144378	C₂²	semidirect
184. C₂×#347042	C₂²	semidirect
187. #10586797	D₄	semidirect
188. #10586796	D₄	semidirect
189. #10586489	D₄	semidirect
190. #10586472	D₄	semidirect
198. #10574873	D₄	semidirect
200. #7642244	D₄	semidirect
201. #7642244	C₂³	semidirect
203. #6453039	D₄	semidirect
204. C₂×#23984	D₄	semidirect
205. #6451863	D₄	semidirect
206. #6451863	D₄	semidirect
211. #6440460	C₂³	semidirect
224. C₂×#23900	C₂³	semidirect
229. #6374210	C₂³	semidirect
232. #6374187	D₄	semidirect
233. #6374187	D₄	semidirect
241. #6371551	D₄	semidirect
242. #6371504	D₄	semidirect
248. #493879	C₂³	semidirect
249. #493879	C₂³	semidirect
250. #493477	D₄	semidirect
255. C₂×#12707	C₂³	semidirect
256. C₂×#12707	C₂³	semidirect
265. C₂×#12705	C₂³	semidirect
266. C₂×#12705	C₂³	semidirect
279. C₂×#12687	C₂³	semidirect
280. C₂×#12687	C₂³	semidirect
281. #392030	C₂³	semidirect
282. #392030	C₂³	semidirect
283. #382707	C₂³	semidirect
284. #382544	C₂³	semidirect
285. #382544	C₂³	semidirect
286. #382434	C₂³	semidirect
287. #382434	C₂³	semidirect
288. #382422	C₂³	semidirect
289. #363969	D₄	semidirect
290. #363969	D₄	semidirect
291. #359811	C₂³	semidirect
298. #359549	C₂³	semidirect
299. #359549	C₂³	semidirect
304. #359501	C₂³	semidirect
307. #190147	C₂³	semidirect
308. #190116	C₂³	semidirect
309. C₂×#8547	C₂³	semidirect
314. C₂×#8541	C₂³	semidirect
315. #187952	D₄	semidirect
316. #187949	D₄	semidirect
321. #187944	C₂³	semidirect
322. #187943	D₄	semidirect
323. #187940	D₄	semidirect
328. C₂×#8534	C₂³	semidirect
329. #186835	C₂³	semidirect
330. C₂×#8453	C₂³	semidirect
331. #146479	C₂³	semidirect
332. #146479	C₂³	semidirect
333. #146475	C₂³	semidirect
334. #146475	C₂³	semidirect
335. #128033	C₂³	semidirect
336. #128033	C₂³	semidirect
337. C₂×#7304	C₂³	semidirect
338. C₂×#7304	C₂³	semidirect
339. C₂×#7316	C₂³	semidirect
340. C₂×#7316	C₂³	semidirect
341. C₂×#7316	C₂³	semidirect
342. C₂×#7316	C₂³	semidirect
343. C₂×#7314	C₂³	semidirect
344. C₂×#7314	C₂³	semidirect
345. C₂×#7314	C₂³	semidirect
346. C₂×#7314	C₂³	semidirect
347. C₂×#7311	C₂³	semidirect
348. C₂×#7311	C₂³	semidirect
349. C₂×#7310	C₂³	semidirect
350. C₂×#7310	C₂³	semidirect
351. C₂×#7310	C₂³	semidirect
352. C₂×#7310	C₂³	semidirect
353. C₂×#7310	C₂³	semidirect
354. C₂×#7310	C₂³	semidirect
355. #128009	C₂³	semidirect
356. #128009	C₂³	semidirect
357. C₂×#7307	C₂³	semidirect
358. C₂×#7307	C₂³	semidirect
359. #108238	C₂³	semidirect
360. #108222	C₂³	semidirect
361. #107130	C₂³	semidirect
362. #107114	C₂³	semidirect
398. C₂³×#120	C₂×D₄	semidirect
401. #62652	C₂×D₄	semidirect
402. C₂²×#518	C₂×D₄	semidirect
411. C₂×#2883	C₂×D₄	semidirect
412. C₂×#2883	C₂×D₄	semidirect
414. C₂×#2846	C₂×D₄	semidirect
416. #34992	C₂×D₄	semidirect
417. #34171	C₂×D₄	semidirect
420. C₂×#2315	C₂×D₄	semidirect
422. C₂²×#379	C₂×D₄	semidirect
425. #21747	C₂×D₄	semidirect
426. #21746	C₂×D₄	semidirect
431. C₂×#1913	C₂×D₄	semidirect
432. C₂×#1913	C₂×D₄	semidirect
433. C₂×#1913	C₂×D₄	semidirect
434. C₂×#1913	C₂×D₄	semidirect
437. C₂×#1898	C₂×D₄	semidirect
438. C₂×#1898	C₂×D₄	semidirect
444. C₂×#1828	C₂×D₄	semidirect
445. C₂×#1819	C₂×D₄	semidirect
462. #20354	C₂×D₄	semidirect
463. #20354	C₂×D₄	semidirect
464. #14658	C₂×D₄	semidirect
465. #14657	C₂×D₄	semidirect
467. #14167	C₂×D₄	semidirect
468. #14134	C₂×D₄	semidirect
478. #8534	C₂×D₄	semidirect
479. #8534	C₂×D₄	semidirect
480. #8534	C₂×D₄	semidirect
481. #8534	C₂×D₄	semidirect
672. C₂⁵	#2021	semidirect
689. C₂²×Q₈	#2021	semidirect
690. C₂²×D₄	#2021	semidirect
691. C₂²×D₄	#2021	semidirect
692. C₂²×D₄	#2021	semidirect
715. C₂³×C₄	#2021	semidirect
716. C₂³×C₄	#2021	semidirect
717. C₂³×C₄	#2021	semidirect

Maximal subgroups

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

subgroup	index
#72315298	2
#72315275	2
#72315264	2
#72315258	2
#72315242	2
#72315053	2
#72315025	2
#72315022	2
#72314884	2
#72314843	2
#72314760	2
#72314498	2
#72313624	2
#72312545	2
#72312516	2
#72310373	2
#72310354	2
#72310216	2
#72301923	2
#72300162	2
#72266971	2
#72264761	2
#72258051	2
#72258020	2
#72256408	2
#72256348	2
#72251601	2
#72251595	2
#72251165	2
#72237636	2