Subgroups — #72234105

Order 4096.

At least 40144 conjugacy classes of subgroups; only the 1047 normal subgroups are shown.

The subgroup lattice has 882 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234099	C₂	1	2	yes	maximal, complemented
2	#72234097	C₂	1	2	yes	maximal, complemented
3	#72234094	C₂	1	2	yes	maximal, complemented
4	#72234092	C₂	1	2	yes	maximal, complemented
5	#72234090	C₂	1	2	yes	maximal, complemented
6	#72234088	C₂	1	2	yes	maximal, complemented
7	#72234085	C₂	1	2	yes	maximal, complemented
8	#72234082	C₂	1	2	yes	maximal, complemented
9	#72234079	C₂	1	1	yes	maximal, characteristic, complemented
10	#72234076	C₂²	1	2	yes	complemented
11	#72234075	C₂²	1	2	yes	complemented
12	#72234074	C₂²	1	2	yes	complemented
13	#72234073	C₂²	1	2	yes	complemented
14	#72234072	C₂	1	1	yes	maximal, characteristic, complemented
15	#72234070	C₂²	1	2	yes	complemented
16	#72234069	C₂²	1	2	yes	complemented
17	#72234068	C₂²	1	2	yes	complemented
18	#72234067	C₂²	1	2	yes	complemented
19	#72234066	C₂	1	1	yes	maximal, characteristic, complemented
20	#72234063	C₂²	1	2	yes	complemented
21	#72234062	C₂²	1	2	yes	complemented
22	#72234061	C₂²	1	2	yes	complemented
23	#72234060	C₂²	1	2	yes	complemented
24	#72234059	C₂	1	1	yes	maximal, characteristic, complemented
25	#72234058	C₂²	1	2	yes	complemented
26	#72234057	C₂²	1	2	yes	complemented
27	#72234056	C₂	1	1	yes	maximal, characteristic, complemented
28	#72234055	C₂²	1	1	yes	characteristic, complemented
29	#72234054	C₂²	1	1	yes	characteristic, complemented
30	#72234053	C₂²	1	1	yes	characteristic, complemented
31	#72234052	C₂²	1	1	yes	characteristic, complemented
32	#72234051	C₂²	1	1	yes	characteristic, complemented
33	#72234050	C₂²	1	1	yes	characteristic, complemented
34	#72234049	C₂²	1	1	yes	characteristic, complemented
35	#72234048	C₂²	1	1	yes	characteristic, complemented
36	#72233903	C₂	1	1	yes	maximal, characteristic, complemented
37	#72233901	C₂²	1	2	yes	complemented
38	#72233900	C₂²	1	2	yes	complemented
39	#72233898	C₂²	1	2	yes	complemented
40	#72233897	C₂²	1	2	yes	complemented
41	#72233858	C₂	1	1	yes	maximal, characteristic, complemented
42	#72233845	C₂²	1	2	yes	complemented
43	#72233844	C₂²	1	2	yes	complemented
44	#72233843	C₂²	1	1	yes	characteristic, complemented
45	#72233842	C₂²	1	1	yes	characteristic
46	#72233840	C₂	1	1	yes	maximal, characteristic, complemented
47	#72233828	C₂²	1	2	yes	complemented
48	#72233827	C₂²	1	2	yes	complemented
49	#72233826	C₂²	1	2	yes	complemented
50	#72233825	C₂²	1	2	yes	complemented
51	#72233824	C₂²	1	1	yes	characteristic
52	#72233822	C₂	1	1	yes	maximal, characteristic, complemented
53	#72233813	C₂²	1	2	yes	complemented
54	#72233812	C₂²	1	2	yes	complemented
55	#72233811	C₂²	1	2	yes	complemented
56	#72233810	C₂²	1	2	yes	complemented
57	#72233809	C₂²	1	1	yes	characteristic, complemented
58	#72233808	C₂	1	1	yes	maximal, characteristic, complemented
59	#72233799	C₂²	1	2	yes	complemented
60	#72233798	C₂²	1	2	yes	complemented
61	#72233797	C₂²	1	1	yes	characteristic, complemented
62	#72233796	C₂²	1	1	yes	characteristic
63	#72233795	C₂²	1	1	yes	characteristic, complemented
64	#72233794	C₂	1	1	yes	maximal, characteristic, complemented
65	#72233789	C₂²	1	2	yes	complemented
66	#72233788	C₂²	1	2	yes	complemented
67	#72233787	C₂²	1	1	yes	characteristic
68	#72233592	C₂	1	1	yes	maximal, characteristic, complemented
69	#72233591	C₂²	1	2	yes	complemented
70	#72233589	C₂²	1	2	yes	complemented
71	#72233588	C₂²	1	2	yes	complemented
72	#72233586	C₂²	1	2	yes	complemented
73	#72233530	C₂²	1	1	yes	characteristic
74	#72233401	C₂	1	1	yes	maximal, characteristic, complemented
75	#72233399	C₂²	1	2	yes	complemented
76	#72233398	C₂²	1	2	yes	complemented
77	#72233397	C₂²	1	2	yes	complemented
78	#72233394	C₂²	1	2	yes	complemented
79	#72233278	C₂²	1	1	yes	characteristic, complemented
80	#72233277	C₂²	1	1	yes	characteristic, complemented
81	#72233258	C₂²	1	1	yes	characteristic, complemented
82	#72233231	C₂	1	1	yes	maximal, characteristic, complemented
83	#72233228	C₂²	1	2	yes	complemented
84	#72233227	C₂²	1	2	yes	complemented
85	#72233226	C₂²	1	2	yes	complemented
86	#72233224	C₂²	1	1	yes	characteristic, complemented
87	#72233223	C₂²	1	1	yes	characteristic, complemented
88	#72233221	C₂²	1	1	yes	characteristic, complemented
89	#72233220	C₂²	1	1	yes	characteristic, complemented
90	#72233123	C₂²	1	1	yes	characteristic, complemented
91	#72233104	C₂²	1	1	yes	characteristic, complemented
92	#72233050	C₂	1	1	yes	maximal, characteristic, complemented
93	#72233048	C₂²	1	2	yes	complemented
94	#72233047	C₂²	1	2	yes	complemented
95	#72233046	C₂²	1	2	yes	complemented
96	#72233041	C₂²	1	1	yes	characteristic, complemented
97	#72233040	C₂²	1	1	yes	characteristic, complemented
98	#72233035	C₂²	1	1	yes	characteristic, complemented
99	#72233021	C₂²	1	1	yes	characteristic, complemented
100	#72232937	C₂²	1	1	yes	characteristic, complemented
101	#72232866	C₂²	1	1	yes	characteristic, complemented
102	#72232782	C₂²	1	1	yes	characteristic, complemented
103	#72232773	C₂²	1	1	yes	characteristic, complemented
104	#72232773	C₂²	1	1	yes	characteristic, complemented
105	#72232724	C₂²	1	1	yes	characteristic, complemented
106	#72232722	C₂²	1	1	yes	characteristic, complemented
107	#72232721	C₂²	1	1	yes	characteristic, complemented
108	#72232717	C₂²	1	1	yes	characteristic, complemented
109	#72232716	C₂²	1	1	yes	characteristic, complemented
110	#72232708	C₂²	1	1	yes	characteristic
111	#72232671	C₂²	1	1	yes	characteristic
112	#72231775	C₂²	1	2	yes	complemented
113	#72231764	C₂²	1	2	yes	complemented
114	#72231359	C₂²	1	2	yes	complemented
115	#72231339	C₂²	1	2	yes	complemented
116	#72231082	C₂²	1	2	yes	complemented
117	#72231013	C₂²	1	2	yes	complemented
118	#72216616	C₂²	1	1	yes	characteristic, complemented
119	#72213902	C₂²	1	2	yes	complemented
120	#72213874	C₂²	1	2	yes	complemented
121	#72213216	C₂²	1	2	yes	complemented
122	#72213205	C₂²	1	2	yes	complemented
123	#10586472	C₂³	1	1	yes	characteristic
124	C₂⁴×#127	D₄	1	1	yes	characteristic, complemented
125	#10577303	C₂³	1	2	yes	—
126	C₂×#56346	C₂³	1	1	yes	characteristic
127	C₂×#47830	C₂³	1	1	yes	characteristic
128	C₂×#46350	C₂³	1	1	yes	characteristic
129	C₂×#37674	C₂³	1	1	yes	characteristic
130	C₂×#37644	C₂³	1	1	yes	characteristic
131	C₂×#36152	C₂³	1	1	yes	characteristic
132	C₂×D₄×#120	C₂³	1	1	yes	characteristic
133	C₂×#35684	D₄	1	1	yes	characteristic, complemented
134	C₂×#35390	D₄	1	1	yes	characteristic, complemented
135	#6491103	C₂³	1	2	yes	—
136	#6491100	C₂³	1	2	yes	—
137	#6454047	C₂³	1	2	yes	—
138	#6454041	C₂³	1	2	yes	—
139	#6393515	C₂³	1	2	yes	—
140	#6385983	C₂³	1	1	yes	characteristic
141	#6385983	C₂³	1	1	yes	characteristic
142	#6385971	C₂³	1	1	yes	characteristic
143	#6385971	C₂³	1	1	yes	characteristic
144	#6347256	C₂³	1	2	yes	—
145	#6346631	C₂³	1	2	yes	—
146	#6346599	C₂³	1	2	yes	—
147	#6342375	D₄	1	1	yes	characteristic, complemented
148	#5522295	D₄	1	1	yes	characteristic, complemented
149	#5519537	D₄	1	1	yes	characteristic, complemented
150	#5482155	D₄	1	1	yes	characteristic, complemented
151	#5119558	D₄	1	1	yes	characteristic, complemented
152	#5118168	D₄	1	1	yes	characteristic, complemented
153	#5025138	D₄	1	1	yes	characteristic, complemented
154	#5024691	D₄	1	1	yes	characteristic, complemented
155	#5020746	D₄	1	1	yes	characteristic, complemented
156	#5020746	D₄	1	1	yes	characteristic, complemented
157	#4933002	D₄	1	1	yes	characteristic, complemented
158	#4932999	D₄	1	1	yes	characteristic, complemented
159	#4932979	D₄	1	1	yes	characteristic, complemented
160	#4930070	D₄	1	1	yes	characteristic, complemented
161	#4929342	D₄	1	1	yes	characteristic, complemented
162	#4867143	C₂³	1	1	yes	characteristic
163	#4867137	D₄	1	1	yes	characteristic
164	#4861302	C₂³	1	1	yes	characteristic
165	#4599084	D₄	1	1	yes	characteristic, complemented
166	#4443126	D₄	1	1	yes	characteristic, complemented
167	#4433768	D₄	1	1	yes	characteristic, complemented
168	#4421184	C₂³	1	1	yes	characteristic
169	#4417886	C₂³	1	1	yes	characteristic
170	#4397107	D₄	1	1	yes	characteristic, complemented
171	#4389661	D₄	1	1	yes	characteristic, complemented
172	#4389610	D₄	1	1	yes	characteristic, complemented
173	#4380225	D₄	1	1	yes	characteristic, complemented
174	#4378714	C₂³	1	1	yes	characteristic
175	#4341466	C₂³	1	1	yes	characteristic
176	#4312851	D₄	1	1	yes	characteristic
177	#4123398	D₄	1	1	yes	characteristic, complemented
178	#2805719	D₄	1	1	yes	characteristic, complemented
179	#2535814	D₄	1	1	yes	characteristic, complemented
180	#2177498	D₄	1	1	yes	characteristic, complemented
181	#2032594	D₄	1	1	yes	characteristic, complemented
182	#2031999	D₄	1	1	yes	characteristic, complemented
183	#1495037	D₄	1	1	yes	characteristic, complemented
184	#1494104	D₄	1	1	yes	characteristic, complemented
185	#1473807	D₄	1	1	yes	characteristic, complemented
186	#947571	D₄	1	1	yes	characteristic
187	#878571	C₂³	1	1	yes	characteristic
188	#876092	C₂³	1	1	yes	characteristic
189	#850480	C₂³	1	1	yes	characteristic
190	#850272	C₂³	1	1	yes	characteristic
191	#845677	D₄	1	1	yes	characteristic
192	#845297	D₄	1	1	yes	characteristic
193	#845297	D₄	1	1	yes	characteristic
194	#765212	D₄	1	1	yes	characteristic, complemented
195	#758216	C₂³	1	1	yes	characteristic
196	#758068	D₄	1	1	yes	characteristic, complemented
197	#719145	C₂³	1	1	yes	characteristic
198	#686591	D₄	1	1	yes	characteristic, complemented
199	#649052	D₄	1	1	yes	characteristic, complemented
200	#649051	D₄	1	1	yes	characteristic, complemented
201	#649038	C₂³	1	1	yes	characteristic
202	#649037	C₂³	1	1	yes	characteristic
203	#648360	D₄	1	1	yes	characteristic, complemented
204	#648360	D₄	1	1	yes	characteristic, complemented
205	#641002	D₄	1	1	yes	characteristic, complemented
206	#640973	C₂³	1	1	yes	characteristic
207	#634295	C₂³	1	1	yes	characteristic
208	#633915	C₂³	1	1	yes	characteristic
209	#619552	C₂³	1	1	yes	characteristic
210	#619533	C₂³	1	1	yes	characteristic
211	#616961	D₄	1	1	yes	characteristic, complemented
212	#616960	D₄	1	1	yes	characteristic
213	#612904	D₄	1	1	yes	characteristic, complemented
214	#612801	D₄	1	1	yes	characteristic, complemented
215	C₂×#15947	D₄	1	1	yes	characteristic
216	#607582	C₂³	1	1	yes	characteristic
217	#587425	C₂³	1	1	yes	characteristic
218	#576685	D₄	1	1	yes	characteristic, complemented
219	#572033	C₂³	1	1	yes	characteristic
220	#561507	D₄	1	1	yes	characteristic, complemented
221	#556476	C₂³	1	1	yes	characteristic
222	#553180	C₂³	1	1	yes	characteristic
223	#539756	C₂³	1	1	yes	characteristic
224	#530257	D₄	1	1	yes	characteristic, complemented
225	#516285	C₂³	1	1	yes	characteristic
226	#516177	C₂³	1	1	yes	characteristic
227	#513995	C₂³	1	1	yes	characteristic
228	#496333	C₂³	1	2	yes	—
229	#496330	C₂³	1	2	yes	—
230	#493998	C₂³	1	2	yes	—
231	#493995	C₂³	1	2	yes	—
232	#482377	C₂³	1	2	yes	—
233	#482360	C₂³	1	2	yes	—
234	#482360	C₂³	1	2	yes	—
235	#482357	C₂³	1	2	yes	—
236	#481985	C₂³	1	2	yes	—
237	#481961	C₂³	1	2	yes	—
238	#480710	C₂³	1	2	yes	—
239	#480708	C₂³	1	2	yes	—
240	#480382	C₂³	1	2	yes	—
241	#480376	C₂³	1	2	yes	—
242	#201876	C₂³	1	2	yes	—
243	#201743	C₂³	1	2	yes	—
244	#201549	C₂³	1	2	yes	—
245	#201386	C₂³	1	2	yes	—
246	#197340	C₂³	1	2	yes	—
247	#196338	C₂³	1	2	yes	—
248	#193892	C₂³	1	2	yes	—
249	#188151	C₂³	1	1	yes	characteristic
250	#188087	C₂³	1	1	yes	characteristic
251	#188087	C₂³	1	1	yes	characteristic
252	#186837	C₂³	1	2	yes	—
253	#186816	C₂³	1	2	yes	—
254	#185652	C₂³	1	2	yes	—
255	#185555	C₂³	1	2	yes	—
256	#185475	C₂³	1	2	yes	—
257	#185264	C₂³	1	2	yes	—
258	#185253	C₂³	1	2	yes	—
259	#185246	C₂³	1	2	yes	—
260	#128200	C₂³	1	2	yes	—
261	#128179	C₂³	1	2	yes	—
262	#128086	C₂³	1	2	yes	—
263	#128050	C₂³	1	2	yes	—
264	#127242	C₂³	1	2	yes	—
265	#127233	C₂³	1	2	yes	—
266	#127207	C₂³	1	2	yes	—
267	#127202	C₂³	1	2	yes	—
268	#127202	C₂³	1	2	yes	—
269	#127199	C₂³	1	2	yes	—
270	#108241	C₂³	1	2	yes	—
271	#106763	C₂³	1	2	yes	—
272	#106601	C₂³	1	2	yes	—
273	#106573	C₂³	1	2	yes	—
274	#106385	C₂³	1	2	yes	—
275	#106107	C₂³	1	2	yes	—
276	#105582	C₂³	1	2	yes	—
277	#105580	C₂³	1	2	yes	—
278	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
279	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic, complemented
280	#62773	C₂⁴	1	2	yes	—
281	C₂²×#546	C₂⁴	1	1	yes	characteristic
282	C₂²×D₄²	C₂⁴	1	1	yes	characteristic
283	C₂²×#535	C₂×D₄	1	1	yes	characteristic
284	C₂²×#534	C₂×D₄	1	1	yes	characteristic
285	C₂²×#534	C₂×D₄	1	1	yes	characteristic, complemented
286	C₂³×#127	C₂×D₄	1	1	yes	characteristic
287	C₂³×#127	C₂×D₄	1	1	yes	characteristic
288	C₂³×#127	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂³×#127	C₂×D₄	1	1	yes	characteristic, complemented
290	C₂³×#120	C₂×D₄	1	1	yes	characteristic
291	C₂³×#120	C₂×D₄	1	1	yes	characteristic
292	C₂³×#120	C₂×D₄	1	1	yes	characteristic
293	C₂³×#120	C₂×D₄	1	1	yes	characteristic
294	C₂⁴×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
295	#60230	C₂⁴	1	2	yes	—
296	C₂×#2735	C₂×D₄	1	1	yes	characteristic, complemented
297	C₂×#2693	C₂×D₄	1	1	yes	characteristic, complemented
298	C₂×#2675	C₂×D₄	1	1	yes	characteristic, complemented
299	C₂×#2668	C₂×D₄	1	1	yes	characteristic, complemented
300	C₂×#2815	C₂×D₄	1	1	yes	characteristic
301	C₂×#2812	C₂×D₄	1	1	yes	characteristic, complemented
302	C₂×#2812	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂×#2850	C₂×D₄	1	1	yes	characteristic
304	C₂×#2848	C₂×D₄	1	1	yes	characteristic, complemented
305	C₂×#2847	C₂×D₄	1	1	yes	characteristic
306	C₂×#2846	C₂×D₄	1	1	yes	characteristic
307	C₂×#2846	C₂×D₄	1	1	yes	characteristic
308	C₂×#2846	C₂×D₄	1	1	yes	characteristic
309	C₂×#2541	C₂×D₄	1	1	yes	characteristic
310	C₂×#2541	C₂×D₄	1	1	yes	characteristic
311	C₂×#2544	C₂×D₄	1	1	yes	characteristic
312	C₂×#2535	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×#2535	C₂⁴	1	1	yes	characteristic
314	C₂×#2605	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂×#2539	C₂×D₄	1	1	yes	characteristic
316	C₂×#2539	C₂×D₄	1	1	yes	characteristic, complemented
317	C₂×#2539	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#2534	C₂⁴	1	1	yes	characteristic
319	C₂×#2404	C₂×D₄	1	1	yes	characteristic, complemented
320	C₂×#2404	C₂×D₄	1	1	yes	characteristic, complemented
321	C₂×#2431	C₂×D₄	1	1	yes	characteristic
322	C₂×#2435	C₂×D₄	1	1	yes	characteristic
323	C₂×#2435	C₂×D₄	1	1	yes	characteristic, complemented
324	C₂×#2435	C₂×D₄	1	1	yes	characteristic, complemented
325	C₂×#2433	C₂×D₄	1	1	yes	characteristic
326	C₂×#2433	C₂×D₄	1	1	yes	characteristic
327	C₂×#2433	C₂×D₄	1	1	yes	characteristic
328	C₂×#2433	C₂×D₄	1	1	yes	characteristic
329	C₂×#2433	C₂×D₄	1	1	yes	characteristic
330	C₂×#2408	C₂⁴	1	1	yes	characteristic
331	C₂×#2408	C₂⁴	1	1	yes	characteristic
332	C₂×#2412	C₂×D₄	1	1	yes	characteristic
333	C₂×#2405	C₂×D₄	1	1	yes	characteristic
334	C₂×#2410	C₂×D₄	1	1	yes	characteristic
335	C₂×#2410	C₂×D₄	1	1	yes	characteristic
336	C₂×#2410	C₂×D₄	1	1	yes	characteristic
337	C₂×#2403	C₂×D₄	1	1	yes	characteristic
338	C₂×#2403	C₂×D₄	1	1	yes	characteristic
339	C₂×#2403	C₂×D₄	1	1	yes	characteristic
340	C₂×#2403	C₂×D₄	1	1	yes	characteristic, complemented
341	C₂×#2403	C₂×D₄	1	1	yes	characteristic, complemented
342	C₂×#2657	C₂×D₄	1	1	yes	characteristic
343	C₂×#2619	C₂×D₄	1	1	yes	characteristic
344	C₂×#2615	C₂×D₄	1	1	yes	characteristic, complemented
345	C₂×#2631	C₂×D₄	1	1	yes	characteristic, complemented
346	C₂×#2635	C₂⁴	1	1	yes	characteristic
347	C₂×#2617	C₂×D₄	1	1	yes	characteristic
348	C₂×#2613	C₂×D₄	1	1	yes	characteristic
349	C₂×#2397	C₂×D₄	1	1	yes	characteristic
350	C₂×#2377	C₂×D₄	1	1	yes	characteristic, complemented
351	C₂×#2372	C₂×D₄	1	1	yes	characteristic, complemented
352	C₂×#2353	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
356	C₂×#2337	C₂×D₄	1	1	yes	characteristic, complemented
357	C₂×#2328	C₂×D₄	1	1	yes	characteristic
358	C₂×#2321	C₂⁴	1	1	yes	characteristic
359	C₂×#2318	C₂×D₄	1	1	yes	characteristic
360	C₂×C₄×#120	C₂⁴	1	1	yes	characteristic
361	C₂×#2290	C₂⁴	1	1	yes	characteristic
362	C₂×#2275	C₂×D₄	1	1	yes	characteristic, complemented
363	C₂×#2273	C₂×D₄	1	1	yes	characteristic, complemented
364	#20726	C₂⁴	1	2	yes	—
365	#20722	C₂⁴	1	2	yes	—
366	#20722	C₂⁴	1	2	yes	—
367	#17364	C₂⁴	1	2	yes	—
368	#17362	C₂⁴	1	2	yes	—
369	#17362	C₂⁴	1	2	yes	—
370	#17141	C₂×D₄	1	1	yes	characteristic, complemented
371	#17141	C₂×D₄	1	1	yes	characteristic, complemented
372	#17082	C₂×D₄	1	1	yes	characteristic, complemented
373	#17082	C₂×D₄	1	1	yes	characteristic, complemented
374	#16242	C₂×D₄	1	1	yes	characteristic, complemented
375	#16186	C₂×D₄	1	1	yes	characteristic, complemented
376	#16171	C₂×D₄	1	1	yes	characteristic, complemented
377	#16014	C₂×D₄	1	1	yes	characteristic
378	#15964	C₂×D₄	1	1	yes	characteristic, complemented
379	#15948	C₂×D₄	1	1	yes	characteristic
380	#15948	C₂×D₄	1	1	yes	characteristic
381	#15948	C₂×D₄	1	1	yes	characteristic
382	#15947	C₂×D₄	1	1	yes	characteristic
383	#15947	C₂×D₄	1	1	yes	characteristic
384	#15947	C₂×D₄	1	1	yes	characteristic
385	#15947	C₂×D₄	1	1	yes	characteristic
386	#15947	C₂×D₄	1	1	yes	characteristic
387	#15947	C₂×D₄	1	1	yes	characteristic
388	#15730	C₂×D₄	1	1	yes	characteristic, complemented
389	#15674	C₂×D₄	1	1	yes	characteristic
390	#15674	C₂×D₄	1	1	yes	characteristic
391	#15635	C₂×D₄	1	1	yes	characteristic, complemented
392	#15579	C₂×D₄	1	1	yes	characteristic, complemented
393	#15561	C₂×D₄	1	1	yes	characteristic, complemented
394	#15561	C₂×D₄	1	1	yes	characteristic, complemented
395	#15561	C₂×D₄	1	1	yes	characteristic, complemented
396	#15539	C₂×D₄	1	1	yes	characteristic, complemented
397	#15480	C₂×D₄	1	1	yes	characteristic, complemented
398	#15480	C₂×D₄	1	1	yes	characteristic, complemented
399	#15463	C₂×D₄	1	1	yes	characteristic
400	#15420	C₂×D₄	1	1	yes	characteristic, complemented
401	#15310	C₂×D₄	1	1	yes	characteristic
402	#15310	C₂×D₄	1	1	yes	characteristic
403	#15310	C₂×D₄	1	1	yes	characteristic
404	#15310	C₂×D₄	1	1	yes	characteristic
405	#15310	C₂×D₄	1	1	yes	characteristic
406	#15310	C₂×D₄	1	1	yes	characteristic
407	#15284	C₂×D₄	1	1	yes	characteristic, complemented
408	#15283	C₂×D₄	1	1	yes	characteristic
409	#15283	C₂×D₄	1	1	yes	characteristic
410	#15283	C₂×D₄	1	1	yes	characteristic
411	#15283	C₂×D₄	1	1	yes	characteristic
412	#15283	C₂×D₄	1	1	yes	characteristic
413	#15283	C₂×D₄	1	1	yes	characteristic
414	#15267	C₂×D₄	1	1	yes	characteristic, complemented
415	#15267	C₂×D₄	1	1	yes	characteristic, complemented
416	#15267	C₂×D₄	1	1	yes	characteristic, complemented
417	#15267	C₂×D₄	1	1	yes	characteristic, complemented
418	#15267	C₂×D₄	1	1	yes	characteristic, complemented
419	#15266	C₂×D₄	1	1	yes	characteristic
420	#15266	C₂×D₄	1	1	yes	characteristic
421	#15266	C₂×D₄	1	1	yes	characteristic
422	#15266	C₂×D₄	1	1	yes	characteristic
423	#15266	C₂×D₄	1	1	yes	characteristic
424	#15258	C₂×D₄	1	1	yes	characteristic
425	#15258	C₂×D₄	1	1	yes	characteristic
426	#15258	C₂×D₄	1	1	yes	characteristic
427	#15258	C₂×D₄	1	1	yes	characteristic
428	#15258	C₂×D₄	1	1	yes	characteristic
429	#15258	C₂×D₄	1	1	yes	characteristic
430	#15258	C₂×D₄	1	1	yes	characteristic
431	#15258	C₂×D₄	1	1	yes	characteristic
432	#15258	C₂×D₄	1	1	yes	characteristic
433	#15258	C₂×D₄	1	1	yes	characteristic
434	#14702	C₂×D₄	1	1	yes	characteristic, complemented
435	#14698	C₂×D₄	1	1	yes	characteristic
436	#14682	C₂×D₄	1	1	yes	characteristic, complemented
437	#14662	C₂×D₄	1	1	yes	characteristic, complemented
438	#14661	C₂×D₄	1	1	yes	characteristic
439	#14659	C₂×D₄	1	1	yes	characteristic
440	#14654	C₂×D₄	1	1	yes	characteristic, complemented
441	#14641	C₂×D₄	1	1	yes	characteristic, complemented
442	#14641	C₂×D₄	1	1	yes	characteristic, complemented
443	#14617	C₂×D₄	1	1	yes	characteristic, complemented
444	#14571	C₂×D₄	1	1	yes	characteristic, complemented
445	#14365	C₂×D₄	1	1	yes	characteristic, complemented
446	#14365	C₂×D₄	1	1	yes	characteristic, complemented
447	#14345	C₂×D₄	1	1	yes	characteristic, complemented
448	#14345	C₂⁴	1	1	yes	characteristic
449	#14335	C₂×D₄	1	1	yes	characteristic
450	#14335	C₂×D₄	1	1	yes	characteristic
451	#14290	C₂×D₄	1	1	yes	characteristic
452	#14290	C₂×D₄	1	1	yes	characteristic
453	#14290	C₂×D₄	1	1	yes	characteristic, complemented
454	#14272	C₂×D₄	1	1	yes	characteristic
455	#14272	C₂×D₄	1	1	yes	characteristic
456	#14271	C₂×D₄	1	1	yes	characteristic
457	#14252	C₂×D₄	1	1	yes	characteristic, complemented
458	#14181	C₂×D₄	1	1	yes	characteristic, complemented
459	#14181	C₂×D₄	1	1	yes	characteristic, complemented
460	#14168	C₂×D₄	1	1	yes	characteristic, complemented
461	#14168	C₂×D₄	1	1	yes	characteristic, complemented
462	#14152	C₂×D₄	1	1	yes	characteristic
463	#14136	C₂×D₄	1	1	yes	characteristic, complemented
464	#14129	C₂×D₄	1	1	yes	characteristic, complemented
465	#13964	C₂×D₄	1	1	yes	characteristic, complemented
466	#13959	C₂×D₄	1	1	yes	characteristic, complemented
467	#13959	C₂×D₄	1	1	yes	characteristic, complemented
468	#13959	C₂⁴	1	1	yes	characteristic
469	#13954	C₂×D₄	1	1	yes	characteristic, complemented
470	#13953	C₂×D₄	1	1	yes	characteristic, complemented
471	#13940	C₂⁴	1	1	yes	characteristic
472	#13905	C₂×D₄	1	1	yes	characteristic
473	#13902	C₂×D₄	1	1	yes	characteristic
474	#13902	C₂×D₄	1	1	yes	characteristic
475	#13902	C₂×D₄	1	1	yes	characteristic
476	#13902	C₂×D₄	1	1	yes	characteristic, complemented
477	#13902	C₂×D₄	1	1	yes	characteristic, complemented
478	#13902	C₂×D₄	1	1	yes	characteristic, complemented
479	#13868	C₂×D₄	1	1	yes	characteristic, complemented
480	#13868	C₂×D₄	1	1	yes	characteristic, complemented
481	#13851	C₂×D₄	1	1	yes	characteristic, complemented
482	#13847	C₂×D₄	1	1	yes	characteristic, complemented
483	C₂×#1438	C₂×D₄	1	1	yes	characteristic
484	#13831	C₂×D₄	1	1	yes	characteristic, complemented
485	#13827	C₂×D₄	1	1	yes	characteristic, complemented
486	#13827	C₂×D₄	1	1	yes	characteristic, complemented
487	#13823	C₂×D₄	1	1	yes	characteristic, complemented
488	C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
489	C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
490	#13785	C₂⁴	1	1	yes	characteristic
491	#13781	C₂×D₄	1	1	yes	characteristic, complemented
492	#13780	C₂×D₄	1	1	yes	characteristic, complemented
493	C₄×#379	C₂×D₄	1	1	yes	characteristic, complemented
494	C₄×#385	C₂×D₄	1	1	yes	characteristic, complemented
495	C₄×#386	C₂⁴	1	1	yes	characteristic
496	#13753	C₂×D₄	1	1	yes	characteristic, complemented
497	C₂⁷	#120	1	1	yes	characteristic
498	C₂⁷	#120	1	1	yes	characteristic
499	C₂⁷	#120	1	1	yes	characteristic
500	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
501	C₂⁴×D₄	#120	1	1	yes	characteristic
502	C₂⁴×D₄	#120	1	1	yes	characteristic
503	C₂⁴×D₄	#120	1	1	yes	characteristic
504	C₂⁴×D₄	#120	1	1	yes	characteristic
505	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
506	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
507	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
508	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
509	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
510	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
511	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
512	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
513	#3501	H(5,𝔽₂)	1	2	yes	complemented
514	#3496	H(5,𝔽₂)	1	2	yes	complemented
515	C₂²×#127	#120	1	1	yes	characteristic
516	C₂²×#127	#120	1	1	yes	characteristic
517	C₂²×#127	#120	1	1	yes	characteristic
518	C₂²×#127	#120	1	1	yes	characteristic
519	C₂²×#127	#120	1	1	yes	characteristic
520	C₂²×#127	#120	1	1	yes	characteristic
521	C₂²×#127	#120	1	1	yes	characteristic
522	C₂²×#127	#120	1	1	yes	characteristic
523	C₂²×#127	#120	1	1	yes	characteristic
524	C₂²×#127	#120	1	1	yes	characteristic
525	C₂²×#127	#120	1	1	yes	characteristic
526	C₂²×#127	#120	1	1	yes	characteristic
527	C₂²×#127	#120	1	1	yes	characteristic
528	C₂²×#127	#120	1	1	yes	characteristic
529	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
530	C₂²×#124	#120	1	1	yes	characteristic
531	C₂²×#124	#120	1	1	yes	characteristic
532	C₂²×#124	#120	1	1	yes	characteristic
533	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
534	C₂²×#123	#120	1	1	yes	characteristic
535	C₂²×#123	#120	1	1	yes	characteristic
536	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
537	C₂²×C₂²⋊Q₈	C₂²×D₄	1	1	yes	characteristic
538	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
539	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
540	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
541	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
542	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
543	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
544	C₂²×#120	#120	1	1	yes	characteristic
545	C₂²×#120	#120	1	1	yes	characteristic
546	C₂²×#120	#120	1	1	yes	characteristic
547	C₂²×#120	#120	1	1	yes	characteristic
548	C₂²×#120	#120	1	1	yes	characteristic
549	C₂²×#120	#120	1	1	yes	characteristic
550	C₂²×#120	#120	1	1	yes	characteristic
551	C₂²×#120	#120	1	1	yes	characteristic
552	C₂²×#120	#120	1	1	yes	characteristic
553	C₂²×#120	#120	1	1	yes	characteristic
554	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
555	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
556	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
557	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
558	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
559	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
560	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
561	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
562	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
563	C₂²×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
564	C₂²×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
565	C₂²×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
566	C₂²×C₄×D₄	C₂⁵	1	1	yes	characteristic
567	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
569	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
570	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
571	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
572	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
573	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
576	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
577	C₂×#400	C₂²×D₄	1	1	yes	characteristic
578	C₂×#399	#120	1	1	yes	characteristic
579	C₂×#399	#120	1	1	yes	characteristic
580	C₂×#399	C₂²×D₄	1	1	yes	characteristic
581	C₂×#397	#120	1	1	yes	characteristic
582	C₂×#397	#120	1	1	yes	characteristic
583	C₂×#397	C₂²×D₄	1	1	yes	characteristic
584	C₂×#397	C₂²×D₄	1	1	yes	characteristic
585	C₂×#394	C₂²×D₄	1	1	yes	characteristic
586	C₂×#394	C₂²×D₄	1	1	yes	characteristic
587	C₂×#394	C₂²×D₄	1	1	yes	characteristic
588	C₂×#392	#120	1	1	yes	characteristic
589	C₂×#392	#120	1	1	yes	characteristic
590	C₂×#392	#120	1	1	yes	characteristic
591	C₂×#392	#120	1	1	yes	characteristic
592	C₂×#392	#120	1	1	yes	characteristic
593	C₂×#392	#120	1	1	yes	characteristic
594	C₂×#392	#120	1	1	yes	characteristic
595	C₂×#392	#120	1	1	yes	characteristic
596	C₂×#392	C₂²×D₄	1	1	yes	characteristic
597	C₂×#392	C₂²×D₄	1	1	yes	characteristic
598	C₂×#392	C₂²×D₄	1	1	yes	characteristic
599	C₂×#392	C₂²×D₄	1	1	yes	characteristic
600	C₂×#392	C₂²×D₄	1	1	yes	characteristic
601	C₂×#391	#120	1	1	yes	characteristic
602	C₂×#390	#120	1	1	yes	characteristic
603	C₂×#390	#120	1	1	yes	characteristic
604	C₂×#390	#120	1	1	yes	characteristic
605	C₂×#390	#120	1	1	yes	characteristic
606	C₂×#390	#120	1	1	yes	characteristic
607	C₂×#390	#120	1	1	yes	characteristic
608	C₂×#390	#120	1	1	yes	characteristic
609	C₂×#390	#120	1	1	yes	characteristic
610	C₂×#390	#120	1	1	yes	characteristic
611	C₂×#386	#120	1	1	yes	characteristic
612	C₂×#386	#120	1	1	yes	characteristic
613	C₂×#386	#120	1	1	yes	characteristic
614	C₂×#386	#120	1	1	yes	characteristic
615	C₂×#386	C₂²×D₄	1	1	yes	characteristic
616	C₂×#386	C₂²×D₄	1	1	yes	characteristic
617	C₂×#385	C₂²×D₄	1	1	yes	characteristic
618	C₂×#385	C₂²×D₄	1	1	yes	characteristic
619	C₂×#383	C₂²×D₄	1	1	yes	characteristic
620	C₂×#383	C₂²×D₄	1	1	yes	characteristic
621	C₂×#382	#120	1	1	yes	characteristic
622	C₂×#382	C₂²×D₄	1	1	yes	characteristic
623	C₂×#382	C₂²×D₄	1	1	yes	characteristic
624	C₂×#381	#120	1	1	yes	characteristic
625	C₂×#381	#120	1	1	yes	characteristic
626	C₂×#381	C₂²×D₄	1	1	yes	characteristic
627	C₂×#381	C₂²×D₄	1	1	yes	characteristic
628	C₂×#381	C₂²×D₄	1	1	yes	characteristic
629	C₂×#380	#120	1	1	yes	characteristic
630	C₂×#380	#120	1	1	yes	characteristic
631	C₂×#380	C₂²×D₄	1	1	yes	characteristic
632	C₂×#380	C₂²×D₄	1	1	yes	characteristic
633	C₂×#380	C₂²×D₄	1	1	yes	characteristic
634	C₂×#379	#120	1	1	yes	characteristic
635	C₂×#379	#120	1	1	yes	characteristic
636	C₂×#379	#120	1	1	yes	characteristic
637	C₂×#379	#120	1	1	yes	characteristic
638	C₂×#379	C₂²×D₄	1	1	yes	characteristic
639	C₂×#379	C₂²×D₄	1	1	yes	characteristic
640	C₂×#379	C₂²×D₄	1	1	yes	characteristic
641	C₂×#379	C₂²×D₄	1	1	yes	characteristic
642	C₂×#379	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
646	C₂×C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
647	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
648	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
653	C₂×#376	C₂²×D₄	1	1	yes	characteristic
654	C₂×#376	C₂²×D₄	1	1	yes	characteristic
655	C₂×#376	C₂²×D₄	1	1	yes	characteristic
656	C₂²×#95	#120	1	1	yes	characteristic
657	C₂²×#95	#120	1	1	yes	characteristic
658	#1799	H(5,𝔽₂)	1	4	yes	complemented
659	C₄×#99	H(5,𝔽₂)	1	4	yes	complemented
660	#1445	C₂²×D₄	1	1	yes	characteristic
661	#1445	C₂²×D₄	1	1	yes	characteristic
662	#1445	C₂²×D₄	1	1	yes	characteristic
663	#1445	C₂²×D₄	1	1	yes	characteristic
664	#1438	#120	1	1	yes	characteristic
665	#1438	#120	1	1	yes	characteristic
666	#1438	#120	1	1	yes	characteristic
667	#1438	#120	1	1	yes	characteristic
668	#1438	#120	1	1	yes	characteristic
669	#1438	#120	1	1	yes	characteristic
670	#1438	#120	1	1	yes	characteristic
671	#1438	#120	1	1	yes	characteristic
672	#1438	#120	1	1	yes	characteristic
673	#1438	#120	1	1	yes	characteristic
674	#1438	#120	1	1	yes	characteristic
675	#1438	#120	1	1	yes	characteristic
676	#1438	#120	1	1	yes	characteristic
677	#1438	#120	1	1	yes	characteristic
678	#1438	#120	1	1	yes	characteristic
679	#1438	#120	1	1	yes	characteristic
680	#1438	#120	1	1	yes	characteristic
681	#1438	#120	1	1	yes	characteristic
682	#1438	#120	1	1	yes	characteristic
683	#1438	#120	1	1	yes	characteristic
684	#1438	C₂²×D₄	1	1	yes	characteristic
685	#1438	C₂²×D₄	1	1	yes	characteristic
686	#1438	C₂²×D₄	1	1	yes	characteristic
687	#1438	C₂²×D₄	1	1	yes	characteristic
688	#1437	#120	1	1	yes	characteristic
689	#1437	#120	1	1	yes	characteristic
690	#1437	#120	1	1	yes	characteristic
691	#1437	#120	1	1	yes	characteristic
692	#1437	#120	1	1	yes	characteristic
693	#1437	#120	1	1	yes	characteristic
694	#1437	#120	1	1	yes	characteristic
695	#1437	#120	1	1	yes	characteristic
696	#1437	#120	1	1	yes	characteristic
697	#1437	#120	1	1	yes	characteristic
698	#1437	#120	1	1	yes	characteristic
699	#1437	#120	1	1	yes	characteristic
700	#1437	C₂²×D₄	1	1	yes	characteristic
701	#1437	C₂²×D₄	1	1	yes	characteristic
702	#1437	C₂²×D₄	1	1	yes	characteristic
703	#1437	C₂²×D₄	1	1	yes	characteristic
704	#1437	C₂²×D₄	1	1	yes	characteristic
705	#1437	C₂²×D₄	1	1	yes	characteristic
706	#1437	C₂²×D₄	1	1	yes	characteristic
707	#1437	C₂²×D₄	1	1	yes	characteristic
708	#1436	C₂²×D₄	1	1	yes	characteristic
709	#1436	C₂²×D₄	1	1	yes	characteristic
710	#1436	C₂²×D₄	1	1	yes	characteristic
711	#1436	C₂²×D₄	1	1	yes	characteristic
712	C₂⁶	C₂×#120	1	1	yes	characteristic
713	C₂⁶	C₂×#120	1	1	yes	characteristic
714	C₂⁶	C₂×#120	1	1	yes	characteristic
715	C₂⁶	C₂×#120	1	1	yes	characteristic
716	C₂⁶	C₂×#120	1	1	yes	characteristic
717	C₂⁶	C₂×#120	1	1	yes	characteristic
718	C₂⁶	C₂×#120	1	1	yes	characteristic
719	C₂⁶	C₂×#120	1	1	yes	characteristic
720	C₂⁶	C₂×#120	1	1	yes	characteristic
721	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
722	C₂³×D₄	C₂×#120	1	1	yes	characteristic
723	C₂³×D₄	C₂×#120	1	1	yes	characteristic
724	C₂³×D₄	C₂×#120	1	1	yes	characteristic
725	C₂³×D₄	C₂×#120	1	1	yes	characteristic
726	C₂³×D₄	C₂×#120	1	1	yes	characteristic
727	C₂³×D₄	C₂×#120	1	1	yes	characteristic
728	C₂³×D₄	C₂×#120	1	1	yes	characteristic
729	C₂³×D₄	C₂×#120	1	1	yes	characteristic
730	C₂³×D₄	C₂×#120	1	1	yes	characteristic
731	C₂³×D₄	C₂×#120	1	1	yes	characteristic
732	C₂³×D₄	C₂×#120	1	1	yes	characteristic
733	C₂³×D₄	C₂×#120	1	1	yes	characteristic
734	C₂³×D₄	C₂×#120	1	1	yes	characteristic
735	C₂³×D₄	C₂×#120	1	1	yes	characteristic
736	C₂³×D₄	C₂×#120	1	1	yes	characteristic
737	C₂³×D₄	C₂×#120	1	1	yes	characteristic
738	C₂³×D₄	C₂×#120	1	1	yes	characteristic
739	C₂³×D₄	C₂×#120	1	1	yes	characteristic
740	C₂³×D₄	C₂×#120	1	1	yes	characteristic
741	C₂³×D₄	C₂×#120	1	1	yes	characteristic
742	C₂³×D₄	C₂×#120	1	1	yes	characteristic
743	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
744	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
745	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
746	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
747	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
748	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
749	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
750	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
751	C₂×#127	B(4,𝔽₂)	1	2	yes	—
752	C₂×#127	B(4,𝔽₂)	1	2	yes	—
753	C₂×C₄×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
754	C₂×C₄×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
755	C₂×C₄×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
756	C₂×C₄×D₄	#585	1	2	yes	—
757	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
758	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
759	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
760	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
761	C₂²×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
762	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
763	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
764	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
765	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
766	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
767	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
768	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
769	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
770	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
771	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
772	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
773	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
774	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
775	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
776	C₂²×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
777	C₂²×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
778	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
779	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
780	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
781	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
782	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
783	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
784	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
785	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
786	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
787	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
788	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
789	C₂×#95	C₂×#120	1	1	yes	characteristic
790	C₂×#95	C₂×#120	1	1	yes	characteristic
791	C₂×#95	C₂×#120	1	1	yes	characteristic
792	C₂×#95	C₂×#120	1	1	yes	characteristic
793	C₂×#95	C₂×#120	1	1	yes	characteristic
794	C₂×#95	C₂×#120	1	1	yes	characteristic
795	C₂×#95	C₂×#120	1	1	yes	characteristic
796	C₂×#95	C₂×#120	1	1	yes	characteristic
797	C₂×#95	C₂×#120	1	1	yes	characteristic
798	C₂×#95	C₂×#120	1	1	yes	characteristic
799	C₂×#95	C₂×#120	1	1	yes	characteristic
800	C₂×#95	C₂×#120	1	1	yes	characteristic
801	C₂×#95	C₂×#120	1	1	yes	characteristic
802	C₂×#95	C₂×#120	1	1	yes	characteristic
803	C₂×#95	C₂×#120	1	1	yes	characteristic
804	C₂×#95	C₂×#120	1	1	yes	characteristic
805	C₂×#95	C₂×#120	1	1	yes	characteristic
806	C₂×#95	C₂×#120	1	1	yes	characteristic
807	C₂×#95	C₂×#120	1	1	yes	characteristic
808	C₂×#95	C₂×#120	1	1	yes	characteristic
809	C₂⁵	#2846	1	1	yes	characteristic
810	C₂⁵	#2846	1	1	yes	characteristic
811	C₂⁵	#2846	1	1	yes	characteristic
812	C₂⁵	#2846	1	1	yes	characteristic
813	C₂⁵	#2846	1	1	yes	characteristic
814	C₂⁵	#2846	1	1	yes	characteristic
815	C₂⁵	C₂²×#120	1	1	yes	characteristic
816	C₂⁵	C₂²×#120	1	1	yes	characteristic
817	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
818	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
819	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
820	C₂²×D₄	#3026	1	1	yes	characteristic
821	C₂²×D₄	#3026	1	1	yes	characteristic
822	C₂²×D₄	#3484	1	1	yes	characteristic
823	C₂²×D₄	#3484	1	1	yes	characteristic
824	C₂²×D₄	#3484	1	1	yes	characteristic
825	C₂²×D₄	#3485	1	1	yes	characteristic
826	C₂³×C₄	#2846	1	1	yes	characteristic
827	C₂³×C₄	#2846	1	1	yes	characteristic
828	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
829	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
830	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
831	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
832	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
833	C₂³×C₄	#3484	1	2	yes	—
834	C₂³×C₄	#3484	1	2	yes	—
835	C₂³×C₄	#3496	1	2	yes	—
836	C₂³×C₄	#3496	1	2	yes	—
837	C₂×C₄⋊C₄	#3488	1	2	yes	—
838	C₂×C₄⋊C₄	#3498	1	2	yes	—
839	C₂×C₂²⋊C₄	#3484	1	2	yes	—
840	C₂×C₂²⋊C₄	#3484	1	2	yes	—
841	C₂×C₂²⋊C₄	#3496	1	2	yes	—
842	C₂×C₂²⋊C₄	#3496	1	2	yes	—
843	C₂×C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
844	C₂×C₄²	#3488	1	2	yes	—
845	C₂×C₄²	#3498	1	2	yes	—
846	C₂⁴	#32898	1	1	yes	characteristic
847	C₂⁴	#32898	1	1	yes	characteristic
848	C₂⁴	#32898	1	1	yes	characteristic
849	C₂⁴	#32898	1	1	yes	characteristic
850	C₂⁴	#35346	1	1	yes	characteristic
851	C₂⁴	#35346	1	1	yes	characteristic
852	C₂⁴	#35347	1	1	yes	characteristic
853	C₂⁴	#35347	1	1	yes	characteristic
854	C₂⁴	C₂×#2846	1	1	yes	characteristic
855	C₂²×C₄	#35512	1	1	yes	characteristic
856	C₂²×C₄	#35527	1	1	yes	characteristic
857	C₂²×C₄	#35680	1	2	yes	—
858	C₂²×C₄	#35680	1	2	yes	—
859	C₂²×C₄	#35680	1	2	yes	—
860	C₂²×C₄	#35680	1	2	yes	—
861	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
862	C₂²×C₄	C₂×#3026	1	1	yes	characteristic
863	C₂²×C₄	#60399	1	2	yes	—
864	C₂³	#511790	1	2	yes	—
865	C₂³	#4928938	1	1	yes	characteristic
866	C₂³	#6499855	1	2	yes	—
867	C₂³	C₂×#32898	1	1	yes	characteristic
868	C₂³	#6628896	1	1	yes	characteristic
869	C₂×C₄	#6533135	1	2	yes	—
870	C₂×C₄	#6533339	1	2	yes	—
871	C₂²	C₂×#511790	1	1	yes	characteristic
872	C₂²	#72219645	1	1	yes	characteristic
873	C₂²	#72233203	1	1	yes	characteristic
874	C₂²	#72233205	1	1	yes	characteristic
875	C₂²	#72234100	1	1	yes	characteristic
876	C₂²	#72234102	1	1	yes	characteristic
877	C₂²	#72234103	1	1	yes	characteristic
878	C₂	#72233207	1	1	yes	characteristic
879	C₂	#72234101	1	1	yes	characteristic
880	C₂	#72234104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72233203
commutator, Frattini, cosocle	C₂²×C₄×D₄	C₂⁵
LCS	G ▷ C₂²×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#37674 ◁ G
LECS	G ▷ C₂²×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72234099	C₂	semidirect
2. #72234097	C₂	semidirect
3. #72234094	C₂	semidirect
4. #72234092	C₂	semidirect
5. #72234090	C₂	semidirect
6. #72234088	C₂	semidirect
7. #72234085	C₂	semidirect
8. #72234082	C₂	semidirect
9. #72234079	C₂	semidirect
10. #72234076	C₂²	semidirect
11. #72234075	C₂²	semidirect
12. #72234074	C₂²	semidirect
13. #72234073	C₂²	semidirect
14. #72234072	C₂	semidirect
15. #72234070	C₂²	semidirect
16. #72234069	C₂²	semidirect
17. #72234068	C₂²	semidirect
18. #72234067	C₂²	semidirect
19. #72234066	C₂	semidirect
20. #72234063	C₂²	semidirect
21. #72234062	C₂²	semidirect
22. #72234061	C₂²	semidirect
23. #72234060	C₂²	semidirect
24. #72234059	C₂	semidirect
25. #72234058	C₂²	semidirect
26. #72234057	C₂²	semidirect
27. #72234056	C₂	semidirect
28. #72234055	C₂²	semidirect
29. #72234054	C₂²	semidirect
30. #72234053	C₂²	semidirect
31. #72234052	C₂²	semidirect
32. #72234051	C₂²	semidirect
33. #72234050	C₂²	semidirect
34. #72234049	C₂²	semidirect
35. #72234048	C₂²	semidirect
36. #72233903	C₂	semidirect
37. #72233901	C₂²	semidirect
38. #72233900	C₂²	semidirect
39. #72233898	C₂²	semidirect
40. #72233897	C₂²	semidirect
41. #72233858	C₂	semidirect
42. #72233845	C₂²	semidirect
43. #72233844	C₂²	semidirect
44. #72233843	C₂²	semidirect
46. #72233840	C₂	semidirect
47. #72233828	C₂²	semidirect
48. #72233827	C₂²	semidirect
49. #72233826	C₂²	semidirect
50. #72233825	C₂²	semidirect
52. #72233822	C₂	semidirect
53. #72233813	C₂²	semidirect
54. #72233812	C₂²	semidirect
55. #72233811	C₂²	semidirect
56. #72233810	C₂²	semidirect
57. #72233809	C₂²	semidirect
58. #72233808	C₂	semidirect
59. #72233799	C₂²	semidirect
60. #72233798	C₂²	semidirect
61. #72233797	C₂²	semidirect
63. #72233795	C₂²	semidirect
64. #72233794	C₂	semidirect
65. #72233789	C₂²	semidirect
66. #72233788	C₂²	semidirect
68. #72233592	C₂	semidirect
69. #72233591	C₂²	semidirect
70. #72233589	C₂²	semidirect
71. #72233588	C₂²	semidirect
72. #72233586	C₂²	semidirect
74. #72233401	C₂	semidirect
75. #72233399	C₂²	semidirect
76. #72233398	C₂²	semidirect
77. #72233397	C₂²	semidirect
78. #72233394	C₂²	semidirect
79. #72233278	C₂²	semidirect
80. #72233277	C₂²	semidirect
81. #72233258	C₂²	semidirect
82. #72233231	C₂	semidirect
83. #72233228	C₂²	semidirect
84. #72233227	C₂²	semidirect
85. #72233226	C₂²	semidirect
86. #72233224	C₂²	semidirect
87. #72233223	C₂²	semidirect
88. #72233221	C₂²	semidirect
89. #72233220	C₂²	semidirect
90. #72233123	C₂²	semidirect
91. #72233104	C₂²	semidirect
92. #72233050	C₂	semidirect
93. #72233048	C₂²	semidirect
94. #72233047	C₂²	semidirect
95. #72233046	C₂²	semidirect
96. #72233041	C₂²	semidirect
97. #72233040	C₂²	semidirect
98. #72233035	C₂²	semidirect
99. #72233021	C₂²	semidirect
100. #72232937	C₂²	semidirect
101. #72232866	C₂²	semidirect
102. #72232782	C₂²	semidirect
103. #72232773	C₂²	semidirect
104. #72232773	C₂²	semidirect
105. #72232724	C₂²	semidirect
106. #72232722	C₂²	semidirect
107. #72232721	C₂²	semidirect
108. #72232717	C₂²	semidirect
109. #72232716	C₂²	semidirect
112. #72231775	C₂²	semidirect
113. #72231764	C₂²	semidirect
114. #72231359	C₂²	semidirect
115. #72231339	C₂²	semidirect
116. #72231082	C₂²	semidirect
117. #72231013	C₂²	semidirect
118. #72216616	C₂²	semidirect
119. #72213902	C₂²	semidirect
120. #72213874	C₂²	semidirect
121. #72213216	C₂²	semidirect
122. #72213205	C₂²	semidirect
124. C₂⁴×#127	D₄	semidirect
133. C₂×#35684	D₄	semidirect
134. C₂×#35390	D₄	semidirect
147. #6342375	D₄	semidirect
148. #5522295	D₄	semidirect
149. #5519537	D₄	semidirect
150. #5482155	D₄	semidirect
151. #5119558	D₄	semidirect
152. #5118168	D₄	semidirect
153. #5025138	D₄	semidirect
154. #5024691	D₄	semidirect
155. #5020746	D₄	semidirect
156. #5020746	D₄	semidirect
157. #4933002	D₄	semidirect
158. #4932999	D₄	semidirect
159. #4932979	D₄	semidirect
160. #4930070	D₄	semidirect
161. #4929342	D₄	semidirect
165. #4599084	D₄	semidirect
166. #4443126	D₄	semidirect
167. #4433768	D₄	semidirect
170. #4397107	D₄	semidirect
171. #4389661	D₄	semidirect
172. #4389610	D₄	semidirect
173. #4380225	D₄	semidirect
177. #4123398	D₄	semidirect
178. #2805719	D₄	semidirect
179. #2535814	D₄	semidirect
180. #2177498	D₄	semidirect
181. #2032594	D₄	semidirect
182. #2031999	D₄	semidirect
183. #1495037	D₄	semidirect
184. #1494104	D₄	semidirect
185. #1473807	D₄	semidirect
194. #765212	D₄	semidirect
196. #758068	D₄	semidirect
198. #686591	D₄	semidirect
199. #649052	D₄	semidirect
200. #649051	D₄	semidirect
203. #648360	D₄	semidirect
204. #648360	D₄	semidirect
205. #641002	D₄	semidirect
211. #616961	D₄	semidirect
213. #612904	D₄	semidirect
214. #612801	D₄	semidirect
218. #576685	D₄	semidirect
220. #561507	D₄	semidirect
224. #530257	D₄	semidirect
279. C₂⁵×D₄	C₂×D₄	semidirect
285. C₂²×#534	C₂×D₄	semidirect
288. C₂³×#127	C₂×D₄	semidirect
289. C₂³×#127	C₂×D₄	semidirect
294. C₂⁴×C₄²	C₂×D₄	semidirect
296. C₂×#2735	C₂×D₄	semidirect
297. C₂×#2693	C₂×D₄	semidirect
298. C₂×#2675	C₂×D₄	semidirect
299. C₂×#2668	C₂×D₄	semidirect
301. C₂×#2812	C₂×D₄	semidirect
302. C₂×#2812	C₂×D₄	semidirect
304. C₂×#2848	C₂×D₄	semidirect
312. C₂×#2535	C₂×D₄	semidirect
314. C₂×#2605	C₂×D₄	semidirect
316. C₂×#2539	C₂×D₄	semidirect
317. C₂×#2539	C₂×D₄	semidirect
319. C₂×#2404	C₂×D₄	semidirect
320. C₂×#2404	C₂×D₄	semidirect
323. C₂×#2435	C₂×D₄	semidirect
324. C₂×#2435	C₂×D₄	semidirect
340. C₂×#2403	C₂×D₄	semidirect
341. C₂×#2403	C₂×D₄	semidirect
344. C₂×#2615	C₂×D₄	semidirect
345. C₂×#2631	C₂×D₄	semidirect
350. C₂×#2377	C₂×D₄	semidirect
351. C₂×#2372	C₂×D₄	semidirect
355. C₂×D₄×C₂²⋊C₄	C₂×D₄	semidirect
356. C₂×#2337	C₂×D₄	semidirect
362. C₂×#2275	C₂×D₄	semidirect
363. C₂×#2273	C₂×D₄	semidirect
370. #17141	C₂×D₄	semidirect
371. #17141	C₂×D₄	semidirect
372. #17082	C₂×D₄	semidirect
373. #17082	C₂×D₄	semidirect
374. #16242	C₂×D₄	semidirect
375. #16186	C₂×D₄	semidirect
376. #16171	C₂×D₄	semidirect
378. #15964	C₂×D₄	semidirect
388. #15730	C₂×D₄	semidirect
391. #15635	C₂×D₄	semidirect
392. #15579	C₂×D₄	semidirect
393. #15561	C₂×D₄	semidirect
394. #15561	C₂×D₄	semidirect
395. #15561	C₂×D₄	semidirect
396. #15539	C₂×D₄	semidirect
397. #15480	C₂×D₄	semidirect
398. #15480	C₂×D₄	semidirect
400. #15420	C₂×D₄	semidirect
407. #15284	C₂×D₄	semidirect
414. #15267	C₂×D₄	semidirect
415. #15267	C₂×D₄	semidirect
416. #15267	C₂×D₄	semidirect
417. #15267	C₂×D₄	semidirect
418. #15267	C₂×D₄	semidirect
434. #14702	C₂×D₄	semidirect
436. #14682	C₂×D₄	semidirect
437. #14662	C₂×D₄	semidirect
440. #14654	C₂×D₄	semidirect
441. #14641	C₂×D₄	semidirect
442. #14641	C₂×D₄	semidirect
443. #14617	C₂×D₄	semidirect
444. #14571	C₂×D₄	semidirect
445. #14365	C₂×D₄	semidirect
446. #14365	C₂×D₄	semidirect
447. #14345	C₂×D₄	semidirect
453. #14290	C₂×D₄	semidirect
457. #14252	C₂×D₄	semidirect
458. #14181	C₂×D₄	semidirect
459. #14181	C₂×D₄	semidirect
460. #14168	C₂×D₄	semidirect
461. #14168	C₂×D₄	semidirect
463. #14136	C₂×D₄	semidirect
464. #14129	C₂×D₄	semidirect
465. #13964	C₂×D₄	semidirect
466. #13959	C₂×D₄	semidirect
467. #13959	C₂×D₄	semidirect
469. #13954	C₂×D₄	semidirect
470. #13953	C₂×D₄	semidirect
476. #13902	C₂×D₄	semidirect
477. #13902	C₂×D₄	semidirect
478. #13902	C₂×D₄	semidirect
479. #13868	C₂×D₄	semidirect
480. #13868	C₂×D₄	semidirect
481. #13851	C₂×D₄	semidirect
482. #13847	C₂×D₄	semidirect
484. #13831	C₂×D₄	semidirect
485. #13827	C₂×D₄	semidirect
486. #13827	C₂×D₄	semidirect
487. #13823	C₂×D₄	semidirect
488. C₂²⋊C₄²	C₂×D₄	semidirect
489. C₂²⋊C₄²	C₂×D₄	semidirect
491. #13781	C₂×D₄	semidirect
492. #13780	C₂×D₄	semidirect
493. C₄×#379	C₂×D₄	semidirect
494. C₄×#385	C₂×D₄	semidirect
496. #13753	C₂×D₄	semidirect
513. #3501	H(5,𝔽₂)	semidirect
514. #3496	H(5,𝔽₂)	semidirect
658. #1799	H(5,𝔽₂)	semidirect
659. C₄×#99	H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72234099	2
#72234097	2
#72234094	2
#72234092	2
#72234090	2
#72234088	2
#72234085	2
#72234082	2
#72234079	2
#72234072	2
#72234066	2
#72234059	2
#72234056	2
#72233903	2
#72233858	2
#72233840	2
#72233822	2
#72233808	2
#72233794	2
#72233592	2
#72233401	2
#72233231	2
#72233050	2