Subgroups — #72315375

Order 4096.

Only the 1041 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 753 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315362	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315351	C₂	1	1	yes	maximal, characteristic, complemented
3	#72315335	C₂	1	1	yes	maximal, characteristic, complemented
4	#72315298	C₂	1	1	yes	maximal, characteristic, complemented
5	#72315275	C₂	1	1	yes	maximal, characteristic, complemented
6	#72315031	C₂	1	1	yes	maximal, characteristic, complemented
7	#72314996	C₂	1	1	yes	maximal, characteristic, complemented
8	#72314858	C₂	1	1	yes	maximal, characteristic, complemented
9	#72314855	C₂²	1	1	yes	characteristic, complemented
10	#72314750	C₂	1	1	yes	maximal, characteristic, complemented
11	#72314748	C₂²	1	1	yes	characteristic, complemented
12	#72314742	C₂	1	1	yes	maximal, characteristic, complemented
13	#72314739	C₂²	1	1	yes	characteristic, complemented
14	#72314736	C₂	1	1	yes	maximal, characteristic, complemented
15	#72314734	C₂²	1	1	yes	characteristic, complemented
16	#72314508	C₂	1	1	yes	maximal, characteristic, complemented
17	#72314456	C₂²	1	1	yes	characteristic, complemented
18	#72314452	C₂²	1	1	yes	characteristic, complemented
19	#72312604	C₂	1	1	yes	maximal, characteristic, complemented
20	#72312489	C₂	1	1	yes	maximal, characteristic, complemented
21	#72312214	C₂²	1	1	yes	characteristic, complemented
22	#72310370	C₂	1	1	yes	maximal, characteristic, complemented
23	#72310364	C₂	1	1	yes	maximal, characteristic, complemented
24	#72310322	C₂²	1	1	yes	characteristic, complemented
25	#72310283	C₂²	1	1	yes	characteristic, complemented
26	#72304521	C₂	1	1	yes	maximal, characteristic, complemented
27	#72300166	C₂	1	1	yes	maximal, characteristic, complemented
28	#72271172	C₂²	1	1	yes	characteristic, complemented
29	#72266863	C₂²	1	1	yes	characteristic, complemented
30	#72266863	C₂²	1	1	yes	characteristic, complemented
31	#72266835	C₂²	1	1	yes	characteristic
32	#72266835	C₂²	1	1	yes	characteristic, complemented
33	#72266378	C₂²	1	1	yes	characteristic, complemented
34	#72264779	C₂	1	1	yes	maximal, characteristic, complemented
35	#72264770	C₂²	1	1	yes	characteristic, complemented
36	#72263490	C₂²	1	1	yes	characteristic, complemented
37	#72260574	C₂	1	1	yes	maximal, characteristic, complemented
38	#72260562	C₂²	1	1	yes	characteristic, complemented
39	#72260537	C₂²	1	1	yes	characteristic, complemented
40	#72259136	C₂²	1	1	yes	characteristic, complemented
41	#72258368	C₂²	1	1	yes	characteristic, complemented
42	#72258334	C₂²	1	1	yes	characteristic, complemented
43	#72258108	C₂	1	1	yes	maximal, characteristic, complemented
44	#72258097	C₂²	1	1	yes	characteristic, complemented
45	#72258094	C₂²	1	1	yes	characteristic, complemented
46	#72258051	C₂	1	1	yes	maximal, characteristic, complemented
47	C₂×#139739	C₂²	1	1	yes	characteristic, complemented
48	C₂×#139742	C₂²	1	1	yes	characteristic, complemented
49	#72258028	C₂²	1	1	yes	characteristic, complemented
50	#72258020	C₂	1	1	yes	maximal, characteristic, complemented
51	#72258019	C₂²	1	1	yes	characteristic, complemented
52	#72256307	C₂	1	1	yes	maximal, characteristic, complemented
53	#72256303	C₂	1	1	yes	maximal, characteristic, complemented
54	#72256243	C₂	1	1	yes	maximal, characteristic, complemented
55	#72256239	C₂	1	1	yes	maximal, characteristic, complemented
56	#72255977	C₂²	1	1	yes	characteristic, complemented
57	#72255971	C₂²	1	1	yes	characteristic, complemented
58	#72255849	C₂²	1	1	yes	characteristic, complemented
59	#72255841	C₂²	1	1	yes	characteristic, complemented
60	#72255841	C₂²	1	1	yes	characteristic, complemented
61	#72255778	C₂²	1	1	yes	characteristic, complemented
62	#72255772	C₂²	1	1	yes	characteristic, complemented
63	#72255764	C₂²	1	1	yes	characteristic, complemented
64	#72251610	C₂	1	1	yes	maximal, characteristic, complemented
65	#72251595	C₂	1	1	yes	maximal, characteristic, complemented
66	#72251530	C₂²	1	1	yes	characteristic, complemented
67	#72251530	C₂²	1	1	yes	characteristic, complemented
68	#72251528	C₂²	1	1	yes	characteristic, complemented
69	#72251527	C₂²	1	1	yes	characteristic, complemented
70	#72251501	C₂²	1	1	yes	characteristic, complemented
71	#72251475	C₂²	1	1	yes	characteristic, complemented
72	#72251473	C₂²	1	1	yes	characteristic, complemented
73	#72251462	C₂²	1	1	yes	characteristic, complemented
74	#72251420	C₂²	1	1	yes	characteristic
75	#72251138	C₂	1	1	yes	maximal, characteristic, complemented
76	#72246450	C₂²	1	1	yes	characteristic, complemented
77	#72246299	C₂²	1	1	yes	characteristic, complemented
78	#72246287	C₂²	1	1	yes	characteristic, complemented
79	#72246286	C₂²	1	1	yes	characteristic, complemented
80	#72240419	C₂²	1	1	yes	characteristic, complemented
81	#72238976	C₂²	1	1	yes	characteristic, complemented
82	#72238974	C₂²	1	1	yes	characteristic, complemented
83	#72238613	C₂²	1	1	yes	characteristic, complemented
84	#72238613	C₂²	1	1	yes	characteristic, complemented
85	#72238443	C₂²	1	1	yes	characteristic, complemented
86	#72238349	C₂²	1	1	yes	characteristic, complemented
87	#72238343	C₂²	1	1	yes	characteristic, complemented
88	#72238342	C₂²	1	1	yes	characteristic
89	#72238342	C₂²	1	1	yes	characteristic
90	#72238342	C₂²	1	1	yes	characteristic, complemented
91	#72237899	C₂²	1	1	yes	characteristic, complemented
92	#72237899	C₂²	1	1	yes	characteristic, complemented
93	#72237639	C₂	1	1	yes	maximal, characteristic, complemented
94	#72237638	C₂²	1	1	yes	characteristic, complemented
95	#72237638	C₂²	1	1	yes	characteristic, complemented
96	#72237638	C₂²	1	1	yes	characteristic, complemented
97	#72237638	C₂²	1	1	yes	characteristic, complemented
98	#72237638	C₂²	1	1	yes	characteristic, complemented
99	#72237637	C₂²	1	1	yes	characteristic, complemented
100	#72237599	C₂²	1	1	yes	characteristic, complemented
101	#72237599	C₂²	1	1	yes	characteristic, complemented
102	#72237473	C₂²	1	1	yes	characteristic, complemented
103	#72237472	C₂²	1	1	yes	characteristic, complemented
104	#72237467	C₂²	1	1	yes	characteristic, complemented
105	#72237402	C₂²	1	1	yes	characteristic, complemented
106	#72237402	C₂²	1	1	yes	characteristic, complemented
107	#72237302	C₂²	1	1	yes	characteristic, complemented
108	#72237045	C₂²	1	1	yes	characteristic, complemented
109	#72236948	C₂²	1	1	yes	characteristic, complemented
110	#72236928	C₂²	1	1	yes	characteristic, complemented
111	#72236928	C₂²	1	1	yes	characteristic, complemented
112	#72236678	C₂²	1	1	yes	characteristic, complemented
113	#72236674	C₂²	1	1	yes	characteristic, complemented
114	#72236631	C₂²	1	1	yes	characteristic, complemented
115	#72236521	C₂²	1	1	yes	characteristic, complemented
116	#72236508	C₂²	1	1	yes	characteristic, complemented
117	#72235242	C₂²	1	1	yes	characteristic, complemented
118	#72235130	C₂²	1	1	yes	characteristic
119	#72235130	C₂²	1	1	yes	characteristic, complemented
120	#72235130	C₂²	1	1	yes	characteristic, complemented
121	#72235130	C₂²	1	1	yes	characteristic, complemented
122	#72235130	C₂²	1	1	yes	characteristic, complemented
123	#72234953	C₂²	1	1	yes	characteristic
124	#72234953	C₂²	1	1	yes	characteristic, complemented
125	#72234693	C₂²	1	1	yes	characteristic
126	#72234693	C₂²	1	1	yes	characteristic, complemented
127	#72234100	C₂²	1	1	yes	characteristic, complemented
128	#72233800	C₂²	1	1	yes	characteristic, complemented
129	#72233581	C₂²	1	1	yes	characteristic
130	#72233581	C₂²	1	1	yes	characteristic, complemented
131	#72226366	C₂²	1	1	yes	characteristic, complemented
132	#72225778	C₂²	1	1	yes	characteristic, complemented
133	#72225742	C₂²	1	1	yes	characteristic, complemented
134	#72225742	C₂²	1	1	yes	characteristic, complemented
135	#72225735	C₂²	1	1	yes	characteristic
136	#72225735	C₂²	1	1	yes	characteristic, complemented
137	#72225735	C₂²	1	1	yes	characteristic, complemented
138	#72225712	C₂²	1	1	yes	characteristic, complemented
139	#72225657	C₂²	1	1	yes	characteristic, complemented
140	#72225644	C₂²	1	1	yes	characteristic, complemented
141	#72225641	C₂²	1	1	yes	characteristic, complemented
142	C₂×#139748	C₂²	1	1	yes	characteristic, complemented
143	#72219438	C₂²	1	1	yes	characteristic, complemented
144	#72219393	C₂²	1	1	yes	characteristic, complemented
145	#72219345	C₂²	1	1	yes	characteristic, complemented
146	C₂×#493474	C₂²	1	1	yes	characteristic, complemented
147	#72219293	C₂²	1	1	yes	characteristic, complemented
148	#72219268	C₂²	1	1	yes	characteristic, complemented
149	#72219240	C₂²	1	1	yes	characteristic, complemented
150	#72219160	C₂²	1	1	yes	characteristic, complemented
151	#72219160	C₂²	1	1	yes	characteristic, complemented
152	#72219158	C₂²	1	1	yes	characteristic, complemented
153	#72219158	C₂²	1	1	yes	characteristic, complemented
154	#72219158	C₂²	1	1	yes	characteristic, complemented
155	#72219157	C₂²	1	1	yes	characteristic, complemented
156	#72219040	C₂²	1	1	yes	characteristic
157	#72219040	C₂²	1	1	yes	characteristic, complemented
158	#72219040	C₂²	1	1	yes	characteristic, complemented
159	#72218980	C₂²	1	1	yes	characteristic, complemented
160	#72218840	C₂²	1	1	yes	characteristic, complemented
161	#72218838	C₂²	1	1	yes	characteristic, complemented
162	#72218521	C₂²	1	1	yes	characteristic, complemented
163	#72218475	C₂²	1	1	yes	characteristic, complemented
164	#72218391	C₂²	1	1	yes	characteristic, complemented
165	#72218391	C₂²	1	1	yes	characteristic, complemented
166	#72218215	C₂²	1	1	yes	characteristic, complemented
167	#72218215	C₂²	1	1	yes	characteristic, complemented
168	#72218121	C₂²	1	1	yes	characteristic, complemented
169	#72218114	C₂²	1	1	yes	characteristic, complemented
170	C₂×#144366	C₂²	1	1	yes	characteristic, complemented
171	C₂×#144366	C₂²	1	1	yes	characteristic, complemented
172	C₂×#144364	C₂²	1	1	yes	characteristic, complemented
173	C₂×#139750	C₂²	1	1	yes	characteristic, complemented
174	C₂×#139750	C₂²	1	1	yes	characteristic, complemented
175	C₂×#133839	C₂²	1	1	yes	characteristic, complemented
176	C₂×#144382	C₂²	1	1	yes	characteristic, complemented
177	C₂×#144382	C₂²	1	1	yes	characteristic, complemented
178	C₂×#144378	C₂²	1	1	yes	characteristic, complemented
179	C₂×#144378	C₂²	1	1	yes	characteristic, complemented
180	C₂×#144378	C₂²	1	1	yes	characteristic, complemented
181	C₂×#6499874	C₂²	1	1	yes	characteristic
182	C₂×#347042	C₂²	1	1	yes	characteristic, complemented
183	C₂×#347042	C₂²	1	1	yes	characteristic, complemented
184	C₂×#511790	C₂²	1	1	yes	characteristic
185	C₂×#511790	C₂²	1	1	yes	characteristic
186	C₂×#511790	C₂²	1	1	yes	characteristic, complemented
187	#10586422	C₂³	1	1	yes	characteristic
188	#10586422	C₂³	1	1	yes	characteristic
189	#10586404	C₂³	1	1	yes	characteristic
190	#10586404	C₂³	1	1	yes	characteristic
191	#10586404	C₂³	1	1	yes	characteristic, complemented
192	C₂×#62817	C₂³	1	1	yes	characteristic
193	C₂×#62817	C₂³	1	1	yes	characteristic
194	C₂²×#3532	C₂³	1	1	yes	characteristic
195	#10574873	D₄	1	2	yes	complemented
196	C₂×#60399	C₂³	1	1	yes	characteristic
197	#7642273	D₄	1	2	yes	complemented
198	#7642244	C₂³	1	1	yes	characteristic, complemented
199	C₂×#35390	C₂³	1	1	yes	characteristic
200	#6451863	D₄	1	2	yes	complemented
201	#6451863	D₄	1	2	yes	complemented
202	#6451863	D₄	1	2	yes	complemented
203	#6437629	D₄	1	2	yes	complemented
204	C₂×#23895	C₂³	1	1	yes	characteristic
205	C₂×#23895	C₂³	1	1	yes	characteristic
206	C₂×#23895	C₂³	1	1	yes	characteristic
207	C₂×#23895	C₂³	1	1	yes	characteristic
208	C₂×#23895	C₂³	1	1	yes	characteristic
209	C₂×#23895	C₂³	1	1	yes	characteristic
210	C₂×#23895	C₂³	1	1	yes	characteristic, complemented
211	#6437621	D₄	1	2	yes	complemented
212	#6437621	C₂³	1	1	yes	characteristic
213	#6437621	C₂³	1	1	yes	characteristic
214	#6437621	C₂³	1	1	yes	characteristic
215	#6437621	C₂³	1	1	yes	characteristic
216	#6437621	C₂³	1	1	yes	characteristic
217	#6437621	C₂³	1	1	yes	characteristic
218	#6437621	C₂³	1	1	yes	characteristic
219	#6437621	C₂³	1	1	yes	characteristic, complemented
220	C₂×#23900	D₄	1	2	yes	complemented
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
225	C₂×#23900	C₂³	1	1	yes	characteristic
226	C₂×#23900	C₂³	1	1	yes	characteristic
227	C₂×#23900	C₂³	1	1	yes	characteristic
228	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
229	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
230	C₂×#23897	C₂³	1	1	yes	characteristic
231	C₂×#23897	C₂³	1	1	yes	characteristic
232	C₂×#23897	C₂³	1	1	yes	characteristic
233	#6437445	C₂³	1	1	yes	characteristic
234	#6437445	C₂³	1	1	yes	characteristic
235	#6437445	C₂³	1	1	yes	characteristic
236	#6431795	C₂³	1	1	yes	characteristic
237	#6374251	C₂³	1	1	yes	characteristic
238	#6374251	C₂³	1	1	yes	characteristic
239	#6374251	C₂³	1	1	yes	characteristic, complemented
240	C₂×#21778	C₂³	1	1	yes	characteristic
241	#6374187	D₄	1	2	yes	complemented
242	C₂×#21776	C₂³	1	1	yes	characteristic
243	C₂×#21776	C₂³	1	1	yes	characteristic
244	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
245	#6372488	D₄	1	2	yes	complemented
246	#763333	C₂³	1	1	yes	characteristic
247	#616961	C₂³	1	1	yes	characteristic
248	#616960	C₂³	1	1	yes	characteristic
249	C₂×#15947	C₂³	1	1	yes	characteristic
250	#552677	C₂³	1	1	yes	characteristic
251	#511793	D₄	1	8	yes	complemented
252	#511776	D₄	1	2	yes	complemented
253	#511775	D₄	1	2	yes	complemented
254	#511772	D₄	1	2	yes	complemented
255	#511771	D₄	1	2	yes	complemented
256	C₂×#12707	C₂³	1	1	yes	characteristic
257	C₂×#12707	C₂³	1	1	yes	characteristic
258	C₂×#12707	C₂³	1	1	yes	characteristic
259	C₂×#12707	C₂³	1	1	yes	characteristic
260	C₂×#12707	C₂³	1	1	yes	characteristic, complemented
261	C₂×#12707	C₂³	1	1	yes	characteristic, complemented
262	C₂×#12707	C₂³	1	1	yes	characteristic, complemented
263	C₂×#12705	C₂³	1	1	yes	characteristic
264	C₂×#12705	C₂³	1	1	yes	characteristic
265	C₂×#12705	C₂³	1	1	yes	characteristic
266	C₂×#12705	C₂³	1	1	yes	characteristic
267	C₂×#12705	C₂³	1	1	yes	characteristic
268	C₂×#12705	C₂³	1	1	yes	characteristic
269	C₂×#12705	C₂³	1	1	yes	characteristic
270	C₂×#12705	C₂³	1	1	yes	characteristic
271	C₂×#12705	C₂³	1	1	yes	characteristic, complemented
272	C₂×#12705	C₂³	1	1	yes	characteristic, complemented
273	C₂×#12705	C₂³	1	1	yes	characteristic, complemented
274	#493370	C₂³	1	1	yes	characteristic
275	#493370	C₂³	1	1	yes	characteristic
276	#493370	C₂³	1	1	yes	characteristic
277	#493370	C₂³	1	1	yes	characteristic
278	#493357	C₂³	1	1	yes	characteristic
279	#493357	C₂³	1	1	yes	characteristic
280	#493357	C₂³	1	1	yes	characteristic
281	#493357	C₂³	1	1	yes	characteristic
282	#493357	C₂³	1	1	yes	characteristic, complemented
283	#493357	C₂³	1	1	yes	characteristic, complemented
284	C₂×#12687	C₂³	1	1	yes	characteristic
285	C₂×#12687	C₂³	1	1	yes	characteristic
286	C₂×#12687	C₂³	1	1	yes	characteristic
287	C₂×#12687	C₂³	1	1	yes	characteristic
288	C₂×#12687	C₂³	1	1	yes	characteristic, complemented
289	C₂×#12687	C₂³	1	1	yes	characteristic, complemented
290	#392030	C₂³	1	1	yes	characteristic, complemented
291	#392030	C₂³	1	1	yes	characteristic, complemented
292	#382436	C₂³	1	1	yes	characteristic
293	#382434	C₂³	1	1	yes	characteristic
294	#382434	C₂³	1	1	yes	characteristic
295	#382434	C₂³	1	1	yes	characteristic, complemented
296	#382434	C₂³	1	1	yes	characteristic, complemented
297	#382422	C₂³	1	1	yes	characteristic, complemented
298	#363969	D₄	1	2	yes	complemented
299	#359558	C₂³	1	1	yes	characteristic
300	#359549	C₂³	1	1	yes	characteristic
301	#359549	C₂³	1	1	yes	characteristic
302	#359549	C₂³	1	1	yes	characteristic, complemented
303	#359528	D₄	1	2	yes	complemented
304	#359509	C₂³	1	1	yes	characteristic
305	#359501	C₂³	1	1	yes	characteristic
306	#359442	C₂³	1	1	yes	characteristic
307	#359442	C₂³	1	1	yes	characteristic, complemented
308	#355096	C₂³	1	1	yes	characteristic, complemented
309	#347057	D₄	1	2	yes	complemented
310	#347056	D₄	1	2	yes	complemented
311	#347048	D₄	1	2	yes	complemented
312	#347048	D₄	1	2	yes	complemented
313	#347047	D₄	1	2	yes	complemented
314	#347045	D₄	1	2	yes	complemented
315	#347042	D₄	1	2	yes	complemented
316	#347042	D₄	1	2	yes	complemented
317	#188109	C₂³	1	1	yes	characteristic, complemented
318	C₂×#8547	C₂³	1	1	yes	characteristic, complemented
319	#188050	C₂³	1	1	yes	characteristic
320	#188050	C₂³	1	1	yes	characteristic
321	#188049	C₂³	1	1	yes	characteristic, complemented
322	C₂×#8541	C₂³	1	1	yes	characteristic
323	C₂×#8541	C₂³	1	1	yes	characteristic
324	C₂×#8541	C₂³	1	1	yes	characteristic, complemented
325	#187944	C₂³	1	1	yes	characteristic
326	#187944	C₂³	1	1	yes	characteristic
327	#187944	C₂³	1	1	yes	characteristic
328	#187944	C₂³	1	1	yes	characteristic
329	#187944	C₂³	1	1	yes	characteristic, complemented
330	#187944	C₂³	1	1	yes	characteristic, complemented
331	C₂×#8534	C₂³	1	1	yes	characteristic
332	C₂×#8534	C₂³	1	1	yes	characteristic
333	C₂×#8534	C₂³	1	1	yes	characteristic
334	C₂×#8534	C₂³	1	1	yes	characteristic
335	C₂×#8534	C₂³	1	1	yes	characteristic, complemented
336	#186835	C₂³	1	1	yes	characteristic, complemented
337	C₂×#8453	C₂³	1	1	yes	characteristic, complemented
338	C₂×#8453	C₂³	1	1	yes	characteristic, complemented
339	#146479	C₂³	1	1	yes	characteristic, complemented
340	#146475	C₂³	1	1	yes	characteristic, complemented
341	#128033	C₂³	1	1	yes	characteristic, complemented
342	#128033	C₂³	1	1	yes	characteristic, complemented
343	C₂×#7304	C₂³	1	1	yes	characteristic, complemented
344	C₂×#7304	C₂³	1	1	yes	characteristic, complemented
345	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
346	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
347	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
348	C₂×#7316	C₂³	1	1	yes	characteristic, complemented
349	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
350	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
351	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
352	C₂×#7314	C₂³	1	1	yes	characteristic, complemented
353	C₂×#7311	C₂³	1	1	yes	characteristic, complemented
354	C₂×#7311	C₂³	1	1	yes	characteristic, complemented
355	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
356	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
357	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
358	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
359	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
360	C₂×#7310	C₂³	1	1	yes	characteristic, complemented
361	#128009	C₂³	1	1	yes	characteristic, complemented
362	#128009	C₂³	1	1	yes	characteristic, complemented
363	C₂×#7307	C₂³	1	1	yes	characteristic, complemented
364	C₂×#7307	C₂³	1	1	yes	characteristic, complemented
365	#108238	C₂³	1	1	yes	characteristic, complemented
366	#108222	C₂³	1	1	yes	characteristic, complemented
367	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
368	#62863	C₂×D₄	1	4	yes	complemented
369	#62844	C₂×D₄	1	2	yes	—
370	#62844	C₂×D₄	1	2	yes	—
371	#62842	C₂×D₄	1	2	yes	—
372	#62842	C₂×D₄	1	2	yes	—
373	#62842	C₂×D₄	1	1	yes	characteristic, complemented
374	#62832	C₂×D₄	1	2	yes	—
375	#62824	C₂×D₄	1	2	yes	—
376	#62817	C₂×D₄	1	2	yes	—
377	#62817	C₂×D₄	1	2	yes	—
378	C₂×#3490	C₂×D₄	1	2	yes	—
379	C₂×#3484	C₂×D₄	1	2	yes	—
380	C₂×#3484	C₂⁴	1	1	yes	characteristic
381	C₂×#3484	C₂⁴	1	1	yes	characteristic
382	C₂×#3484	C₂⁴	1	1	yes	characteristic
383	C₂×#3484	C₂⁴	1	1	yes	characteristic
384	C₂×#3484	C₂⁴	1	1	yes	characteristic
385	C₂×#3484	C₂⁴	1	1	yes	characteristic
386	C₂×#3484	C₂⁴	1	1	yes	characteristic
387	C₂²×#551	C₂×D₄	1	1	yes	characteristic, complemented
388	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
389	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
390	C₂²×#560	C₂×D₄	1	1	yes	characteristic, complemented
391	C₂²×#535	C₂⁴	1	1	yes	characteristic
392	C₂²×#534	C₂×D₄	1	1	yes	characteristic, complemented
393	C₂²×#534	C₂⁴	1	1	yes	characteristic
394	C₂²×#534	C₂⁴	1	1	yes	characteristic
395	C₂³×#120	C₂×D₄	1	1	yes	characteristic, complemented
396	C₂³×#120	C₂×D₄	1	1	yes	characteristic, complemented
397	C₂³×#120	C₂⁴	1	1	yes	characteristic
398	C₂³×#120	C₂⁴	1	1	yes	characteristic
399	C₂×#3026	C₂×D₄	1	2	yes	—
400	C₂×#3026	C₂×D₄	1	2	yes	—
401	C₂×#3026	C₂×D₄	1	2	yes	—
402	C₂×#3026	C₂×D₄	1	2	yes	—
403	C₂×#3026	C₂×D₄	1	2	yes	—
404	C₂×#3026	C₂×D₄	1	2	yes	complemented
405	C₂×#2883	C₂×D₄	1	2	yes	—
406	C₂×#2883	C₂×D₄	1	1	yes	characteristic
407	C₂×#2883	C₂×D₄	1	1	yes	characteristic
408	C₂×#2883	C₂×D₄	1	1	yes	characteristic
409	C₂×#2883	C₂×D₄	1	1	yes	characteristic, complemented
410	C₂×#2883	C₂×D₄	1	1	yes	characteristic, complemented
411	C₂×#2846	C₂×D₄	1	2	yes	—
412	C₂×#2846	C₂×D₄	1	2	yes	complemented
413	#34980	C₂×D₄	1	2	yes	—
414	#34980	C₂×D₄	1	2	yes	complemented
415	#34176	C₂×D₄	1	2	yes	complemented
416	#34171	C₂⁴	1	1	yes	characteristic
417	C₂×#2273	C₂×D₄	1	1	yes	characteristic, complemented
418	#23907	C₂×D₄	1	2	yes	—
419	#23906	C₂×D₄	1	2	yes	—
420	#23903	C₂×D₄	1	4	yes	—
421	#23901	C₂×D₄	1	2	yes	—
422	#23901	C₂×D₄	1	2	yes	—
423	#23901	C₂×D₄	1	2	yes	—
424	#23901	C₂×D₄	1	2	yes	complemented
425	#23901	C₂×D₄	1	2	yes	complemented
426	#23900	C₂×D₄	1	2	yes	—
427	#23900	C₂×D₄	1	2	yes	—
428	#23900	C₂×D₄	1	2	yes	—
429	#23900	C₂×D₄	1	2	yes	—
430	#23900	C₂×D₄	1	2	yes	—
431	#23900	C₂×D₄	1	2	yes	complemented
432	#23900	C₂×D₄	1	2	yes	complemented
433	#23897	C₂×D₄	1	4	yes	—
434	#23895	C₂×D₄	1	4	yes	—
435	C₂×#1913	C₂×D₄	1	2	yes	—
436	C₂×#1913	C₂×D₄	1	2	yes	—
437	C₂×#1913	C₂×D₄	1	2	yes	—
438	C₂×#1913	C₂×D₄	1	2	yes	—
439	C₂×#1913	C₂×D₄	1	2	yes	complemented
440	C₂×#1913	C₂×D₄	1	2	yes	complemented
441	C₂×#1898	C₂×D₄	1	2	yes	—
442	C₂×#1898	C₂×D₄	1	2	yes	—
443	C₂×#1898	C₂×D₄	1	2	yes	complemented
444	C₂×#1898	C₂×D₄	1	2	yes	complemented
445	#20960	C₂×D₄	1	2	yes	—
446	#20960	C₂×D₄	1	2	yes	—
447	#20960	C₂×D₄	1	2	yes	—
448	#20960	C₂×D₄	1	2	yes	complemented
449	C₂×#1828	C₂×D₄	1	2	yes	—
450	C₂×#1828	C₂×D₄	1	2	yes	complemented
451	C₂×#1783	C₂⁴	1	1	yes	characteristic
452	C₂×#1783	C₂⁴	1	1	yes	characteristic
453	C₂×#1783	C₂⁴	1	1	yes	characteristic
454	C₂×#1783	C₂⁴	1	1	yes	characteristic
455	#20585	C₂×D₄	1	2	yes	complemented
456	C₂×#1781	C₂×D₄	1	2	yes	complemented
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	C₂×#1781	C₂⁴	1	1	yes	characteristic
463	C₂×#1781	C₂⁴	1	1	yes	characteristic
464	C₂×#1781	C₂⁴	1	1	yes	characteristic
465	C₂×#1781	C₂⁴	1	1	yes	characteristic
466	C₂×#1781	C₂⁴	1	1	yes	characteristic
467	C₂×#1781	C₂⁴	1	1	yes	characteristic
468	C₂×#1781	C₂⁴	1	1	yes	characteristic
469	#20354	C₂×D₄	1	1	yes	characteristic, complemented
470	#15948	C₂×D₄	1	1	yes	characteristic, complemented
471	#15948	C₂×D₄	1	1	yes	characteristic, complemented
472	#15947	C₂×D₄	1	1	yes	characteristic, complemented
473	#15947	C₂×D₄	1	1	yes	characteristic, complemented
474	#15262	C₂×D₄	1	1	yes	characteristic, complemented
475	#15261	C₂×D₄	1	1	yes	characteristic, complemented
476	#15259	C₂×D₄	1	1	yes	characteristic, complemented
477	#15258	C₂×D₄	1	1	yes	characteristic, complemented
478	#14335	C₂⁴	1	1	yes	characteristic
479	C₂×#1438	C₂⁴	1	1	yes	characteristic
480	#12707	C₂×D₄	1	4	yes	complemented
481	#12705	C₂×D₄	1	4	yes	complemented
482	#12694	C₂×D₄	1	2	yes	complemented
483	#12693	C₂×D₄	1	2	yes	complemented
484	#12690	C₂×D₄	1	4	yes	complemented
485	#12688	C₂×D₄	1	2	yes	complemented
486	#12687	C₂×D₄	1	2	yes	complemented
487	#12687	C₂×D₄	1	2	yes	complemented
488	#12687	C₂×D₄	1	2	yes	complemented
489	#8546	C₂×D₄	1	2	yes	complemented
490	#8544	C₂×D₄	1	2	yes	complemented
491	#8541	C₂×D₄	1	2	yes	complemented
492	#8541	C₂×D₄	1	2	yes	complemented
493	#8534	C₂×D₄	1	2	yes	—
494	#8534	C₂×D₄	1	2	yes	—
495	#8534	C₂×D₄	1	2	yes	—
496	#8534	C₂×D₄	1	2	yes	—
497	#8534	C₂×D₄	1	2	yes	complemented
498	#8534	C₂×D₄	1	2	yes	complemented
499	#8534	C₂×D₄	1	2	yes	complemented
500	#8534	C₂×D₄	1	2	yes	complemented
501	C₂⁷	C₂²×D₄	1	1	yes	characteristic
502	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
504	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
505	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
506	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
507	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
508	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
509	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
511	C₂³×#41	H(5,𝔽₂)	1	1	yes	characteristic
512	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
513	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
514	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
523	#3484	H(5,𝔽₂)	1	2	yes	—
524	#3484	H(5,𝔽₂)	1	2	yes	—
525	C₂×#543	#120	1	2	yes	—
526	C₂×#534	#120	1	2	yes	—
527	C₂×#534	#120	1	2	yes	—
528	C₂×#534	#120	1	2	yes	—
529	C₂×#534	C₂²×D₄	1	2	yes	—
530	C₂×#534	C₂²×D₄	1	2	yes	—
531	C₂×#534	C₂²×D₄	1	2	yes	—
532	C₂×#534	C₂²×D₄	1	2	yes	—
533	C₂×#534	C₂²×D₄	1	2	yes	—
534	C₂×#534	H(5,𝔽₂)	1	2	yes	—
535	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
536	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
537	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
538	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
539	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
540	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
541	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
542	C₂²×#123	H(5,𝔽₂)	1	1	yes	characteristic
543	C₂²×#120	C₂²×D₄	1	2	yes	—
544	C₂²×#120	C₂²×D₄	1	2	yes	—
545	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
546	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
547	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
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	C₂×#518	#120	1	2	yes	—
554	C₂×#518	#120	1	2	yes	—
555	C₂×#518	#120	1	2	yes	—
556	C₂×#518	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
565	C₂²×#117	H(5,𝔽₂)	1	1	yes	characteristic
566	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×#458	#120	1	4	yes	complemented
571	C₂×B(4,𝔽₂)	#120	1	4	yes	complemented
572	C₂²×#99	C₂²×D₄	1	2	yes	—
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	#2849	#120	1	4	yes	complemented
577	#2846	#120	1	4	yes	complemented
578	C₂×#379	C₂²×D₄	1	2	yes	—
579	C₂×#379	C₂²×D₄	1	2	yes	—
580	#1898	#120	1	4	yes	complemented
581	#1898	#120	1	4	yes	complemented
582	#1890	#120	1	4	yes	complemented
583	#1889	#120	1	4	yes	complemented
584	#1783	C₂²×D₄	1	2	yes	—
585	#1783	C₂²×D₄	1	2	yes	—
586	#1781	C₂²×D₄	1	2	yes	—
587	#1781	C₂²×D₄	1	2	yes	—
588	#1781	C₂²×D₄	1	2	yes	—
589	#1781	C₂²×D₄	1	2	yes	—
590	#1781	C₂²×D₄	1	2	yes	—
591	#1781	C₂²×D₄	1	2	yes	—
592	#1781	C₂²×D₄	1	2	yes	—
593	#1781	C₂²×D₄	1	2	yes	—
594	#1438	C₂²×D₄	1	1	yes	characteristic
595	#1438	C₂²×D₄	1	1	yes	characteristic
596	#1438	C₂²×D₄	1	1	yes	characteristic
597	#1438	C₂²×D₄	1	1	yes	characteristic
598	C₂⁶	C₂×#120	1	1	yes	characteristic
599	C₂⁶	D₄²	1	1	yes	characteristic
600	C₂⁶	D₄²	1	1	yes	characteristic
601	C₂⁶	D₄²	1	1	yes	characteristic
602	C₂⁶	C₂³×D₄	1	1	yes	characteristic
603	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
605	C₂×H(5,𝔽₂)	D₄²	1	2	yes	—
606	C₂×H(5,𝔽₂)	D₄²	1	2	yes	—
607	C₂×H(5,𝔽₂)	D₄²	1	2	yes	—
608	C₂×H(5,𝔽₂)	D₄²	1	2	yes	—
609	C₂³×Q₈	D₄²	1	1	yes	characteristic
610	C₂³×D₄	C₂×#120	1	2	yes	—
611	C₂³×D₄	C₂×#120	1	2	yes	—
612	C₂³×D₄	C₂×#120	1	2	yes	—
613	C₂³×D₄	D₄²	1	2	yes	—
614	C₂³×D₄	D₄²	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	C₂³×D₄	1	1	yes	characteristic
618	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
619	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
620	C₂³×D₄	C₂³×D₄	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	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
628	C₂⁴×C₄	D₄²	1	1	yes	characteristic
629	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	#534	D₄²	1	4	yes	—
631	#534	D₄²	1	4	yes	—
632	C₂×#123	B(4,𝔽₂)	1	4	yes	complemented
633	C₂×#123	C₂×#120	1	2	yes	—
634	C₂×#123	#534	1	2	yes	—
635	C₂×#123	D₄²	1	2	yes	—
636	C₂×#123	D₄²	1	2	yes	—
637	C₂×#120	B(4,𝔽₂)	1	4	yes	complemented
638	C₂×#120	C₂×#120	1	4	yes	—
639	C₂×#120	C₂×#120	1	2	yes	—
640	C₂×#120	#534	1	4	yes	—
641	C₂×#120	#534	1	2	yes	—
642	C₂×#120	D₄²	1	2	yes	—
643	C₂×#120	D₄²	1	2	yes	—
644	#518	C₂×#120	1	2	yes	—
645	#518	D₄²	1	2	yes	—
646	#518	D₄²	1	2	yes	—
647	#518	D₄²	1	2	yes	—
648	#518	D₄²	1	2	yes	—
649	C₂×#117	B(4,𝔽₂)	1	4	yes	complemented
650	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	complemented
651	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
652	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
653	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
654	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
655	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
656	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
657	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
658	C₂²×C₂²⋊C₄	D₄²	1	2	yes	—
659	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
660	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
661	C₂²×C₄²	D₄²	1	1	yes	characteristic
662	C₂²×C₄²	D₄²	1	1	yes	characteristic
663	C₂×#99	C₂×#120	1	4	yes	—
664	#379	C₂×#120	1	4	yes	—
665	C₂⁵	#2403	1	2	yes	—
666	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
667	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
668	C₂⁵	C₂²×#120	1	1	yes	characteristic
669	C₂⁵	C₂²×#120	1	1	yes	characteristic
670	C₂⁵	C₂×#534	1	1	yes	characteristic
671	C₂⁵	C₂×D₄²	1	1	yes	characteristic
672	C₂⁵	C₂×D₄²	1	1	yes	characteristic
673	C₂⁵	C₂×D₄²	1	1	yes	characteristic
674	C₂⁵	#3484	1	1	yes	characteristic
675	C₂⁵	#3484	1	1	yes	characteristic
676	C₂⁵	#3484	1	1	yes	characteristic
677	C₂⁵	#3484	1	1	yes	characteristic
678	C₂⁵	#3484	1	1	yes	characteristic
679	C₂⁵	#3484	1	1	yes	characteristic
680	C₂⁵	#3532	1	1	yes	characteristic
681	C₂²×D₄	#2403	1	4	yes	—
682	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
683	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
684	C₂²×D₄	C₂×#534	1	1	yes	characteristic
685	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
686	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
687	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
688	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
689	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
690	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
691	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
692	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
693	C₂²×D₄	#3484	1	1	yes	characteristic
694	C₂²×D₄	#3484	1	1	yes	characteristic
695	C₂²×D₄	#3484	1	1	yes	characteristic
696	C₂²×D₄	#3484	1	1	yes	characteristic
697	C₂²×D₄	#3532	1	1	yes	characteristic
698	C₂²×D₄	#3532	1	1	yes	characteristic
699	C₂³×C₄	#2403	1	2	yes	—
700	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
701	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
702	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
703	C₂³×C₄	#3484	1	1	yes	characteristic
704	C₂³×C₄	#3484	1	1	yes	characteristic
705	C₂³×C₄	#3484	1	1	yes	characteristic
706	C₂³×C₄	#3484	1	1	yes	characteristic
707	C₂³×C₄	#3532	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	#2403	1	2	yes	—
709	C₂×C₂²⋊C₄	#2403	1	2	yes	—
710	C₂×C₂²⋊C₄	#2403	1	4	yes	—
711	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
712	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
713	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
714	C₂⁴	#23900	1	4	yes	—
715	C₂⁴	C₂×#2403	1	1	yes	characteristic
716	C₂⁴	C₂×#2403	1	1	yes	characteristic
717	C₂⁴	#35346	1	1	yes	characteristic
718	C₂⁴	D₄×#120	1	1	yes	characteristic
719	C₂⁴	D₄×#120	1	1	yes	characteristic
720	C₂⁴	D₄×#120	1	1	yes	characteristic
721	C₂⁴	#37644	1	1	yes	characteristic
722	C₂⁴	#37644	1	1	yes	characteristic
723	C₂⁴	#37644	1	1	yes	characteristic
724	C₂⁴	#58990	1	1	yes	characteristic
725	C₂⁴	#58990	1	1	yes	characteristic
726	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
727	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
728	C₂²×C₄	#23900	1	4	yes	—
729	C₂²×C₄	D₄×#120	1	1	yes	characteristic
730	C₂²×C₄	#37644	1	1	yes	characteristic
731	C₂²×C₄	#58990	1	1	yes	characteristic
732	C₂²×C₄	#58990	1	1	yes	characteristic
733	C₂²⋊C₄	#23900	1	4	yes	—
734	C₂²⋊C₄	#23900	1	4	yes	—
735	C₂³	#647656	1	1	yes	characteristic
736	C₂³	C₂×#23900	1	2	yes	—
737	C₂³	C₂×#23900	1	2	yes	—
738	C₂³	#6499867	1	1	yes	characteristic
739	C₂³	#6499867	1	1	yes	characteristic
740	C₂³	#6499874	1	1	yes	characteristic
741	C₂³	#6499874	1	1	yes	characteristic
742	C₂³	#6499874	1	1	yes	characteristic
743	C₂³	#6499876	1	1	yes	characteristic
744	C₂²	#72210439	1	1	yes	characteristic
745	C₂²	#72216646	1	1	yes	characteristic
746	C₂²	#72217546	1	1	yes	characteristic
747	C₂²	#72233072	1	1	yes	characteristic
748	C₂²	#72240631	1	1	yes	characteristic
749	C₂²	#72240643	1	1	yes	characteristic
750	C₂²	#72241017	1	1	yes	characteristic
751	C₂	#72241290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72241290
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. #72315362	C₂	semidirect
2. #72315351	C₂	semidirect
3. #72315335	C₂	semidirect
4. #72315298	C₂	semidirect
5. #72315275	C₂	semidirect
6. #72315031	C₂	semidirect
7. #72314996	C₂	semidirect
8. #72314858	C₂	semidirect
9. #72314855	C₂²	semidirect
10. #72314750	C₂	semidirect
11. #72314748	C₂²	semidirect
12. #72314742	C₂	semidirect
13. #72314739	C₂²	semidirect
14. #72314736	C₂	semidirect
15. #72314734	C₂²	semidirect
16. #72314508	C₂	semidirect
17. #72314456	C₂²	semidirect
18. #72314452	C₂²	semidirect
19. #72312604	C₂	semidirect
20. #72312489	C₂	semidirect
21. #72312214	C₂²	semidirect
22. #72310370	C₂	semidirect
23. #72310364	C₂	semidirect
24. #72310322	C₂²	semidirect
25. #72310283	C₂²	semidirect
26. #72304521	C₂	semidirect
27. #72300166	C₂	semidirect
28. #72271172	C₂²	semidirect
29. #72266863	C₂²	semidirect
30. #72266863	C₂²	semidirect
32. #72266835	C₂²	semidirect
33. #72266378	C₂²	semidirect
34. #72264779	C₂	semidirect
35. #72264770	C₂²	semidirect
36. #72263490	C₂²	semidirect
37. #72260574	C₂	semidirect
38. #72260562	C₂²	semidirect
39. #72260537	C₂²	semidirect
40. #72259136	C₂²	semidirect
41. #72258368	C₂²	semidirect
42. #72258334	C₂²	semidirect
43. #72258108	C₂	semidirect
44. #72258097	C₂²	semidirect
45. #72258094	C₂²	semidirect
46. #72258051	C₂	semidirect
47. C₂×#139739	C₂²	semidirect
48. C₂×#139742	C₂²	semidirect
49. #72258028	C₂²	semidirect
50. #72258020	C₂	semidirect
51. #72258019	C₂²	semidirect
52. #72256307	C₂	semidirect
53. #72256303	C₂	semidirect
54. #72256243	C₂	semidirect
55. #72256239	C₂	semidirect
56. #72255977	C₂²	semidirect
57. #72255971	C₂²	semidirect
58. #72255849	C₂²	semidirect
59. #72255841	C₂²	semidirect
60. #72255841	C₂²	semidirect
61. #72255778	C₂²	semidirect
62. #72255772	C₂²	semidirect
63. #72255764	C₂²	semidirect
64. #72251610	C₂	semidirect
65. #72251595	C₂	semidirect
66. #72251530	C₂²	semidirect
67. #72251530	C₂²	semidirect
68. #72251528	C₂²	semidirect
69. #72251527	C₂²	semidirect
70. #72251501	C₂²	semidirect
71. #72251475	C₂²	semidirect
72. #72251473	C₂²	semidirect
73. #72251462	C₂²	semidirect
75. #72251138	C₂	semidirect
76. #72246450	C₂²	semidirect
77. #72246299	C₂²	semidirect
78. #72246287	C₂²	semidirect
79. #72246286	C₂²	semidirect
80. #72240419	C₂²	semidirect
81. #72238976	C₂²	semidirect
82. #72238974	C₂²	semidirect
83. #72238613	C₂²	semidirect
84. #72238613	C₂²	semidirect
85. #72238443	C₂²	semidirect
86. #72238349	C₂²	semidirect
87. #72238343	C₂²	semidirect
90. #72238342	C₂²	semidirect
91. #72237899	C₂²	semidirect
92. #72237899	C₂²	semidirect
93. #72237639	C₂	semidirect
94. #72237638	C₂²	semidirect
95. #72237638	C₂²	semidirect
96. #72237638	C₂²	semidirect
97. #72237638	C₂²	semidirect
98. #72237638	C₂²	semidirect
99. #72237637	C₂²	semidirect
100. #72237599	C₂²	semidirect
101. #72237599	C₂²	semidirect
102. #72237473	C₂²	semidirect
103. #72237472	C₂²	semidirect
104. #72237467	C₂²	semidirect
105. #72237402	C₂²	semidirect
106. #72237402	C₂²	semidirect
107. #72237302	C₂²	semidirect
108. #72237045	C₂²	semidirect
109. #72236948	C₂²	semidirect
110. #72236928	C₂²	semidirect
111. #72236928	C₂²	semidirect
112. #72236678	C₂²	semidirect
113. #72236674	C₂²	semidirect
114. #72236631	C₂²	semidirect
115. #72236521	C₂²	semidirect
116. #72236508	C₂²	semidirect
117. #72235242	C₂²	semidirect
119. #72235130	C₂²	semidirect
120. #72235130	C₂²	semidirect
121. #72235130	C₂²	semidirect
122. #72235130	C₂²	semidirect
124. #72234953	C₂²	semidirect
126. #72234693	C₂²	semidirect
127. #72234100	C₂²	semidirect
128. #72233800	C₂²	semidirect
130. #72233581	C₂²	semidirect
131. #72226366	C₂²	semidirect
132. #72225778	C₂²	semidirect
133. #72225742	C₂²	semidirect
134. #72225742	C₂²	semidirect
136. #72225735	C₂²	semidirect
137. #72225735	C₂²	semidirect
138. #72225712	C₂²	semidirect
139. #72225657	C₂²	semidirect
140. #72225644	C₂²	semidirect
141. #72225641	C₂²	semidirect
142. C₂×#139748	C₂²	semidirect
143. #72219438	C₂²	semidirect
144. #72219393	C₂²	semidirect
145. #72219345	C₂²	semidirect
146. C₂×#493474	C₂²	semidirect
147. #72219293	C₂²	semidirect
148. #72219268	C₂²	semidirect
149. #72219240	C₂²	semidirect
150. #72219160	C₂²	semidirect
151. #72219160	C₂²	semidirect
152. #72219158	C₂²	semidirect
153. #72219158	C₂²	semidirect
154. #72219158	C₂²	semidirect
155. #72219157	C₂²	semidirect
157. #72219040	C₂²	semidirect
158. #72219040	C₂²	semidirect
159. #72218980	C₂²	semidirect
160. #72218840	C₂²	semidirect
161. #72218838	C₂²	semidirect
162. #72218521	C₂²	semidirect
163. #72218475	C₂²	semidirect
164. #72218391	C₂²	semidirect
165. #72218391	C₂²	semidirect
166. #72218215	C₂²	semidirect
167. #72218215	C₂²	semidirect
168. #72218121	C₂²	semidirect
169. #72218114	C₂²	semidirect
170. C₂×#144366	C₂²	semidirect
171. C₂×#144366	C₂²	semidirect
172. C₂×#144364	C₂²	semidirect
173. C₂×#139750	C₂²	semidirect
174. C₂×#139750	C₂²	semidirect
175. C₂×#133839	C₂²	semidirect
176. C₂×#144382	C₂²	semidirect
177. C₂×#144382	C₂²	semidirect
178. C₂×#144378	C₂²	semidirect
179. C₂×#144378	C₂²	semidirect
180. C₂×#144378	C₂²	semidirect
182. C₂×#347042	C₂²	semidirect
183. C₂×#347042	C₂²	semidirect
186. C₂×#511790	C₂²	semidirect
191. #10586404	C₂³	semidirect
195. #10574873	D₄	semidirect
197. #7642273	D₄	semidirect
198. #7642244	C₂³	semidirect
200. #6451863	D₄	semidirect
201. #6451863	D₄	semidirect
202. #6451863	D₄	semidirect
203. #6437629	D₄	semidirect
210. C₂×#23895	C₂³	semidirect
211. #6437621	D₄	semidirect
219. #6437621	C₂³	semidirect
220. C₂×#23900	D₄	semidirect
228. C₂×#23900	C₂³	semidirect
229. C₂×#23900	C₂³	semidirect
239. #6374251	C₂³	semidirect
241. #6374187	D₄	semidirect
244. C₂×#21776	C₂³	semidirect
245. #6372488	D₄	semidirect
251. #511793	D₄	semidirect
252. #511776	D₄	semidirect
253. #511775	D₄	semidirect
254. #511772	D₄	semidirect
255. #511771	D₄	semidirect
260. C₂×#12707	C₂³	semidirect
261. C₂×#12707	C₂³	semidirect
262. C₂×#12707	C₂³	semidirect
271. C₂×#12705	C₂³	semidirect
272. C₂×#12705	C₂³	semidirect
273. C₂×#12705	C₂³	semidirect
282. #493357	C₂³	semidirect
283. #493357	C₂³	semidirect
288. C₂×#12687	C₂³	semidirect
289. C₂×#12687	C₂³	semidirect
290. #392030	C₂³	semidirect
291. #392030	C₂³	semidirect
295. #382434	C₂³	semidirect
296. #382434	C₂³	semidirect
297. #382422	C₂³	semidirect
298. #363969	D₄	semidirect
302. #359549	C₂³	semidirect
303. #359528	D₄	semidirect
307. #359442	C₂³	semidirect
308. #355096	C₂³	semidirect
309. #347057	D₄	semidirect
310. #347056	D₄	semidirect
311. #347048	D₄	semidirect
312. #347048	D₄	semidirect
313. #347047	D₄	semidirect
314. #347045	D₄	semidirect
315. #347042	D₄	semidirect
316. #347042	D₄	semidirect
317. #188109	C₂³	semidirect
318. C₂×#8547	C₂³	semidirect
321. #188049	C₂³	semidirect
324. C₂×#8541	C₂³	semidirect
329. #187944	C₂³	semidirect
330. #187944	C₂³	semidirect
335. C₂×#8534	C₂³	semidirect
336. #186835	C₂³	semidirect
337. C₂×#8453	C₂³	semidirect
338. C₂×#8453	C₂³	semidirect
339. #146479	C₂³	semidirect
340. #146475	C₂³	semidirect
341. #128033	C₂³	semidirect
342. #128033	C₂³	semidirect
343. C₂×#7304	C₂³	semidirect
344. C₂×#7304	C₂³	semidirect
345. C₂×#7316	C₂³	semidirect
346. C₂×#7316	C₂³	semidirect
347. C₂×#7316	C₂³	semidirect
348. C₂×#7316	C₂³	semidirect
349. C₂×#7314	C₂³	semidirect
350. C₂×#7314	C₂³	semidirect
351. C₂×#7314	C₂³	semidirect
352. C₂×#7314	C₂³	semidirect
353. C₂×#7311	C₂³	semidirect
354. C₂×#7311	C₂³	semidirect
355. C₂×#7310	C₂³	semidirect
356. C₂×#7310	C₂³	semidirect
357. C₂×#7310	C₂³	semidirect
358. C₂×#7310	C₂³	semidirect
359. C₂×#7310	C₂³	semidirect
360. C₂×#7310	C₂³	semidirect
361. #128009	C₂³	semidirect
362. #128009	C₂³	semidirect
363. C₂×#7307	C₂³	semidirect
364. C₂×#7307	C₂³	semidirect
365. #108238	C₂³	semidirect
366. #108222	C₂³	semidirect
368. #62863	C₂×D₄	semidirect
373. #62842	C₂×D₄	semidirect
387. C₂²×#551	C₂×D₄	semidirect
388. C₂²×D₄²	C₂×D₄	semidirect
389. C₂²×H(3,𝔽₄)	C₂×D₄	semidirect
390. C₂²×#560	C₂×D₄	semidirect
392. C₂²×#534	C₂×D₄	semidirect
395. C₂³×#120	C₂×D₄	semidirect
396. C₂³×#120	C₂×D₄	semidirect
404. C₂×#3026	C₂×D₄	semidirect
409. C₂×#2883	C₂×D₄	semidirect
410. C₂×#2883	C₂×D₄	semidirect
412. C₂×#2846	C₂×D₄	semidirect
414. #34980	C₂×D₄	semidirect
415. #34176	C₂×D₄	semidirect
417. C₂×#2273	C₂×D₄	semidirect
424. #23901	C₂×D₄	semidirect
425. #23901	C₂×D₄	semidirect
431. #23900	C₂×D₄	semidirect
432. #23900	C₂×D₄	semidirect
439. C₂×#1913	C₂×D₄	semidirect
440. C₂×#1913	C₂×D₄	semidirect
443. C₂×#1898	C₂×D₄	semidirect
444. C₂×#1898	C₂×D₄	semidirect
448. #20960	C₂×D₄	semidirect
450. C₂×#1828	C₂×D₄	semidirect
455. #20585	C₂×D₄	semidirect
456. C₂×#1781	C₂×D₄	semidirect
469. #20354	C₂×D₄	semidirect
470. #15948	C₂×D₄	semidirect
471. #15948	C₂×D₄	semidirect
472. #15947	C₂×D₄	semidirect
473. #15947	C₂×D₄	semidirect
474. #15262	C₂×D₄	semidirect
475. #15261	C₂×D₄	semidirect
476. #15259	C₂×D₄	semidirect
477. #15258	C₂×D₄	semidirect
480. #12707	C₂×D₄	semidirect
481. #12705	C₂×D₄	semidirect
482. #12694	C₂×D₄	semidirect
483. #12693	C₂×D₄	semidirect
484. #12690	C₂×D₄	semidirect
485. #12688	C₂×D₄	semidirect
486. #12687	C₂×D₄	semidirect
487. #12687	C₂×D₄	semidirect
488. #12687	C₂×D₄	semidirect
489. #8546	C₂×D₄	semidirect
490. #8544	C₂×D₄	semidirect
491. #8541	C₂×D₄	semidirect
492. #8541	C₂×D₄	semidirect
497. #8534	C₂×D₄	semidirect
498. #8534	C₂×D₄	semidirect
499. #8534	C₂×D₄	semidirect
500. #8534	C₂×D₄	semidirect
570. C₂×#458	#120	semidirect
571. C₂×B(4,𝔽₂)	#120	semidirect
576. #2849	#120	semidirect
577. #2846	#120	semidirect
580. #1898	#120	semidirect
581. #1898	#120	semidirect
582. #1890	#120	semidirect
583. #1889	#120	semidirect
632. C₂×#123	B(4,𝔽₂)	semidirect
637. C₂×#120	B(4,𝔽₂)	semidirect
649. C₂×#117	B(4,𝔽₂)	semidirect
650. C₂²×C₂²⋊C₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72315362	2
#72315351	2
#72315335	2
#72315298	2
#72315275	2
#72315031	2
#72314996	2
#72314858	2
#72314750	2
#72314742	2
#72314736	2
#72314508	2
#72312604	2
#72312489	2
#72310370	2
#72310364	2
#72304521	2
#72300166	2
#72264779	2
#72260574	2
#72258108	2
#72258051	2
#72258020	2
#72256307	2
#72256303	2
#72256243	2
#72256239	2
#72251610	2
#72251595	2
#72251138	2
#72237639	2