Subgroups — #72261399

Order 4096.

Only the 2345 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 897 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261378	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261341	C₂	1	1	yes	maximal, characteristic, complemented
3	#72261323	C₂	1	1	yes	maximal, characteristic, complemented
4	#72261300	C₂	1	2	yes	maximal, complemented
5	#72261234	C₂	1	2	yes	maximal, complemented
6	#72261212	C₂	1	1	yes	maximal, characteristic, complemented
7	#72261187	C₂²	1	1	yes	characteristic, complemented
8	#72261184	C₂²	1	1	yes	characteristic, complemented
9	#72261177	C₂²	1	1	yes	characteristic, complemented
10	#72261153	C₂	1	2	yes	maximal, complemented
11	#72261142	C₂	1	2	yes	maximal, complemented
12	#72261111	C₂²	1	2	yes	complemented
13	#72261086	C₂	1	1	yes	maximal, characteristic, complemented
14	#72261073	C₂²	1	1	yes	characteristic, complemented
15	#72261064	C₂²	1	2	yes	complemented
16	#72260847	C₂	1	1	yes	maximal, characteristic, complemented
17	#72238588	C₂²	1	1	yes	characteristic
18	#72238586	C₂²	1	2	yes	—
19	#72238584	C₂²	1	1	yes	characteristic
20	#72238583	C₂²	1	2	yes	—
21	#72234424	C₂	1	2	yes	maximal, complemented
22	#72234423	C₂	1	4	yes	maximal, complemented
23	#72234421	C₂²	1	2	yes	complemented
24	#72234418	C₂²	1	2	yes	complemented
25	#72234416	C₂²	1	4	yes	complemented
26	#72234201	C₂	1	2	yes	maximal, complemented
27	#72234197	C₂²	1	2	yes	complemented
28	#72234193	C₂²	1	2	yes	complemented
29	#72234175	C₂	1	2	yes	maximal, complemented
30	#72234170	C₂²	1	2	yes	complemented
31	#72234167	C₂²	1	2	yes	complemented
32	#72234146	C₂²	1	2	yes	complemented
33	C₂×#7622880	C₂²	1	1	yes	characteristic, complemented
34	#72234104	C₂	1	1	yes	maximal, characteristic, complemented
35	#72234078	C₂²	1	1	yes	characteristic, complemented
36	#72234065	C₂²	1	1	yes	characteristic, complemented
37	#72233992	C₂²	1	1	yes	characteristic
38	#72233917	C₂²	1	2	yes	complemented
39	#72233911	C₂²	1	1	yes	characteristic, complemented
40	#72233902	C₂²	1	2	yes	complemented
41	#72233857	C₂²	1	1	yes	characteristic, complemented
42	#72233839	C₂²	1	1	yes	characteristic, complemented
43	#72233476	C₂²	1	2	yes	complemented
44	#72233417	C₂²	1	4	yes	complemented
45	#72233302	C₂²	1	2	yes	complemented
46	#72233262	C₂²	1	4	yes	complemented
47	#72233187	C₂²	1	2	yes	complemented
48	#72233169	C₂²	1	2	yes	complemented
49	#72233157	C₂	1	2	yes	maximal, complemented
50	#72233119	C₂²	1	4	yes	complemented
51	#72233095	C₂²	1	2	yes	complemented
52	#72233091	C₂²	1	2	yes	complemented
53	#72233063	C₂²	1	4	yes	complemented
54	#72233051	C₂²	1	4	yes	complemented
55	#72233038	C₂²	1	2	yes	complemented
56	#72233002	C₂²	1	2	yes	complemented
57	#72232927	C₂	1	4	yes	maximal, complemented
58	#72232895	C₂²	1	1	yes	characteristic, complemented
59	#72232864	C₂²	1	2	yes	complemented
60	#72232863	C₂²	1	2	yes	complemented
61	#72232850	C₂²	1	2	yes	complemented
62	#72232835	C₂²	1	4	yes	complemented
63	#72232831	C₂²	1	2	yes	complemented
64	#72232823	C₂²	1	4	yes	complemented
65	#72232811	C₂²	1	4	yes	complemented
66	#72232800	C₂²	1	2	yes	complemented
67	#72232794	C₂²	1	1	yes	characteristic, complemented
68	#72232788	C₂²	1	4	yes	complemented
69	#72232778	C₂²	1	4	yes	complemented
70	#72232771	C₂²	1	4	yes	complemented
71	#72232764	C₂²	1	4	yes	complemented
72	#72232751	C₂²	1	4	yes	complemented
73	#72232739	C₂²	1	4	yes	complemented
74	#72232729	C₂²	1	2	yes	complemented
75	#72232390	C₂²	1	2	yes	—
76	#72232200	C₂²	1	4	yes	—
77	#72232033	C₂²	1	2	yes	—
78	#72225779	C₂²	1	4	yes	complemented
79	#72219653	C₂²	1	2	yes	complemented
80	#72219306	C₂²	1	4	yes	complemented
81	#72219306	C₂²	1	4	yes	complemented
82	#72216646	C₂²	1	4	yes	complemented
83	C₂×#63011	C₂³	1	1	yes	characteristic
84	C₂×#41²	D₄	1	1	yes	characteristic, complemented
85	C₂³×D₄²	D₄	1	2	yes	complemented
86	C₂×#60399	C₂³	1	2	yes	complemented
87	C₂×#60399	C₂³	1	2	yes	complemented
88	C₂×#60388	C₂³	1	1	yes	characteristic, complemented
89	#8943527	D₄	1	4	yes	complemented
90	#8943482	D₄	1	4	yes	complemented
91	#8943077	D₄	1	4	yes	complemented
92	#8942728	D₄	1	2	yes	complemented
93	#8942673	D₄	1	4	yes	complemented
94	#8898169	C₂³	1	4	yes	—
95	#8898065	C₂³	1	2	yes	—
96	#8824131	D₄	1	2	yes	complemented
97	#8811246	D₄	1	2	yes	complemented
98	#8806945	D₄	1	2	yes	complemented
99	#8797683	D₄	1	4	yes	complemented
100	#8765601	D₄	1	4	yes	complemented
101	#8757654	D₄	1	4	yes	complemented
102	#8196400	D₄	1	2	yes	complemented
103	#8195815	D₄	1	2	yes	complemented
104	#8195113	D₄	1	2	yes	complemented
105	#8181081	D₄	1	4	yes	complemented
106	#8179068	D₄	1	4	yes	complemented
107	#8176553	D₄	1	4	yes	complemented
108	#8110542	D₄	1	2	yes	complemented
109	#8110000	D₄	1	1	yes	characteristic, complemented
110	#8109917	D₄	1	2	yes	complemented
111	#8108057	D₄	1	4	yes	complemented
112	#7849663	D₄	1	1	yes	characteristic, complemented
113	#7849663	C₂³	1	1	yes	characteristic
114	#7837029	D₄	1	2	yes	complemented
115	#7837029	C₂³	1	2	yes	—
116	#7829344	C₂³	1	2	yes	—
117	#7829278	D₄	1	2	yes	complemented
118	#7819715	D₄	1	4	yes	complemented
119	#7819605	C₂³	1	4	yes	—
120	#7739388	C₂³	1	1	yes	characteristic
121	#7739367	D₄	1	1	yes	characteristic, complemented
122	#7737957	D₄	1	2	yes	complemented
123	#7737955	C₂³	1	2	yes	—
124	#7737413	D₄	1	2	yes	complemented
125	#7737411	C₂³	1	2	yes	—
126	#7733150	D₄	1	4	yes	complemented
127	#7733149	C₂³	1	4	yes	—
128	#7712736	D₄	1	1	yes	characteristic, complemented
129	#7712669	D₄	1	2	yes	complemented
130	#7711942	D₄	1	2	yes	complemented
131	#7711937	D₄	1	1	yes	characteristic, complemented
132	#7711204	D₄	1	2	yes	complemented
133	#7711201	D₄	1	2	yes	complemented
134	#7708349	D₄	1	4	yes	complemented
135	#7708349	D₄	1	4	yes	complemented
136	#7672702	C₂³	1	1	yes	characteristic
137	#7671946	C₂³	1	2	yes	—
138	#7671874	C₂³	1	2	yes	—
139	#7670609	D₄	1	2	yes	complemented
140	#7670554	D₄	1	2	yes	complemented
141	#7670308	D₄	1	1	yes	characteristic, complemented
142	#7670203	D₄	1	4	yes	complemented
143	#7670203	C₂³	1	4	yes	—
144	#7659311	D₄	1	2	yes	complemented
145	#7659307	D₄	1	1	yes	characteristic, complemented
146	#7659307	C₂³	1	1	yes	characteristic
147	#7633646	D₄	1	1	yes	characteristic, complemented
148	C₂²×#2679	D₄	1	2	yes	complemented
149	#7627216	D₄	1	1	yes	characteristic, complemented
150	#7627211	D₄	1	2	yes	complemented
151	C₂×#33359	C₂³	1	1	yes	characteristic, complemented
152	C₂×#33348	C₂³	1	2	yes	complemented
153	C₂×#33348	C₂³	1	2	yes	complemented
154	#6628898	C₂³	1	1	yes	characteristic, complemented
155	#6628896	C₂³	1	4	yes	complemented
156	#6628876	C₂³	1	2	yes	complemented
157	#6628872	C₂³	1	2	yes	complemented
158	#6370747	C₂³	1	1	yes	characteristic, complemented
159	#494742	C₂³	1	2	yes	complemented
160	#494738	C₂³	1	2	yes	complemented
161	#494722	C₂³	1	2	yes	complemented
162	#494721	C₂³	1	4	yes	complemented
163	#494719	C₂³	1	2	yes	complemented
164	#494717	C₂³	1	4	yes	complemented
165	#494701	C₂³	1	2	yes	complemented
166	#494701	C₂³	1	2	yes	complemented
167	#494700	C₂³	1	4	yes	complemented
168	#494700	C₂³	1	4	yes	complemented
169	#494682	C₂³	1	4	yes	complemented
170	#494682	C₂³	1	4	yes	complemented
171	#493878	C₂³	1	1	yes	characteristic, complemented
172	#493867	C₂³	1	2	yes	complemented
173	#493441	C₂³	1	1	yes	characteristic, complemented
174	#493430	C₂³	1	2	yes	complemented
175	#493425	C₂³	1	2	yes	complemented
176	#493425	C₂³	1	2	yes	complemented
177	#493424	C₂³	1	4	yes	complemented
178	#493424	C₂³	1	4	yes	complemented
179	#492900	C₂³	1	1	yes	characteristic, complemented
180	#374036	C₂³	1	2	yes	complemented
181	#374034	C₂³	1	2	yes	complemented
182	#374006	C₂³	1	1	yes	characteristic, complemented
183	#374004	C₂³	1	4	yes	complemented
184	#359890	C₂³	1	1	yes	characteristic, complemented
185	#359888	C₂³	1	2	yes	complemented
186	#359605	C₂³	1	1	yes	characteristic, complemented
187	#359601	C₂³	1	2	yes	complemented
188	#359593	C₂³	1	2	yes	complemented
189	#359593	C₂³	1	2	yes	complemented
190	#359591	C₂³	1	4	yes	complemented
191	#359591	C₂³	1	4	yes	complemented
192	#214619	C₂³	1	4	yes	complemented
193	#214616	C₂³	1	4	yes	complemented
194	#213906	C₂³	1	4	yes	complemented
195	#213854	C₂³	1	4	yes	complemented
196	#213852	C₂³	1	2	yes	complemented
197	C₂×H(7,𝔽₂)	C₂⁴	1	1	yes	characteristic
198	C₂×#3498	C₂⁴	1	1	yes	characteristic
199	C₂×#3484	C₂×D₄	1	2	yes	—
200	C₂×#3484	C₂⁴	1	2	yes	—
201	C₂×#3484	C₂⁴	1	2	yes	—
202	C₂×#3549	C₂×D₄	1	1	yes	characteristic
203	C₂×#3543	C₂×D₄	1	2	yes	—
204	C₂×#3537	C₂×D₄	1	2	yes	—
205	C₂×#3537	C₂×D₄	1	2	yes	—
206	C₂×#3532	C₂×D₄	1	4	yes	—
207	C₂×#3532	C₂×D₄	1	4	yes	—
208	C₂×#3483	C₂×D₄	1	1	yes	characteristic
209	C₂×#3481	C₂×D₄	1	1	yes	characteristic
210	C₂×#3481	C₂×D₄	1	2	yes	—
211	C₂²×D₄²	C₂×D₄	1	2	yes	—
212	C₂²×D₄²	C₂×D₄	1	2	yes	—
213	C₂²×D₄²	C₂×D₄	1	4	yes	—
214	C₂×#3444	C₂×D₄	1	2	yes	—
215	C₂×#3444	C₂×D₄	1	1	yes	characteristic
216	C₂³×#127	C₂×D₄	1	2	yes	—
217	C₂³×#120	C₂×D₄	1	4	yes	—
218	C₂³×#120	C₂×D₄	1	4	yes	—
219	C₂×#2888	C₂⁴	1	1	yes	characteristic
220	C₂×#2888	C₂⁴	1	1	yes	characteristic
221	C₂×#2883	C₂⁴	1	2	yes	—
222	C₂×#2883	C₂⁴	1	2	yes	—
223	#60048	C₂×D₄	1	2	yes	—
224	#60045	C₂×D₄	1	2	yes	—
225	#59814	C₂×D₄	1	2	yes	—
226	#59179	C₂×D₄	1	4	yes	—
227	#59126	C₂×D₄	1	2	yes	—
228	#59126	C₂×D₄	1	2	yes	—
229	#59089	C₂×D₄	1	4	yes	—
230	#59089	C₂×D₄	1	4	yes	—
231	#59084	C₂×D₄	1	2	yes	—
232	#59056	C₂×D₄	1	2	yes	—
233	#59041	C₂×D₄	1	2	yes	—
234	#59041	C₂×D₄	1	2	yes	—
235	#59006	C₂×D₄	1	4	yes	—
236	#58990	C₂×D₄	1	4	yes	—
237	#58990	C₂×D₄	1	4	yes	—
238	#58990	C₂×D₄	1	4	yes	—
239	#58990	C₂×D₄	1	4	yes	—
240	#58990	C₂×D₄	1	4	yes	—
241	#52291	C₂×D₄	1	1	yes	characteristic
242	#52163	C₂×D₄	1	1	yes	characteristic
243	#52163	C₂×D₄	1	2	yes	—
244	C₂×#2679	C₂×D₄	1	2	yes	—
245	C₂×#2679	C₂×D₄	1	2	yes	—
246	C₂×#2679	C₂×D₄	1	4	yes	—
247	#52004	C₂×D₄	1	4	yes	—
248	#52004	C₂×D₄	1	4	yes	—
249	#51940	C₂×D₄	1	4	yes	—
250	#51930	C₂×D₄	1	4	yes	—
251	#51896	C₂×D₄	1	4	yes	—
252	#51815	C₂×D₄	1	4	yes	—
253	#50856	C₂×D₄	1	4	yes	—
254	#50856	C₂×D₄	1	4	yes	—
255	#50646	C₂×D₄	1	4	yes	—
256	#50635	C₂×D₄	1	4	yes	—
257	#49562	C₂×D₄	1	4	yes	—
258	#49545	C₂×D₄	1	4	yes	—
259	#49545	C₂×D₄	1	4	yes	—
260	#49545	C₂×D₄	1	4	yes	—
261	#47846	C₂×D₄	1	4	yes	—
262	#47827	C₂×D₄	1	4	yes	—
263	#47827	C₂×D₄	1	4	yes	—
264	#47827	C₂×D₄	1	4	yes	—
265	#46454	C₂×D₄	1	4	yes	—
266	#46452	C₂×D₄	1	4	yes	—
267	#46425	C₂×D₄	1	4	yes	—
268	#46424	C₂×D₄	1	4	yes	—
269	#46387	C₂×D₄	1	4	yes	—
270	#46386	C₂×D₄	1	4	yes	—
271	#46384	C₂×D₄	1	4	yes	—
272	#46355	C₂×D₄	1	4	yes	—
273	#46354	C₂×D₄	1	4	yes	—
274	#46318	C₂×D₄	1	2	yes	—
275	#46287	C₂×D₄	1	2	yes	—
276	#46089	C₂×D₄	1	2	yes	—
277	#45452	C₂×D₄	1	4	yes	—
278	#45439	C₂×D₄	1	4	yes	—
279	#45438	C₂×D₄	1	4	yes	—
280	#37297	C₂×D₄	1	1	yes	characteristic
281	#37297	C₂×D₄	1	1	yes	characteristic
282	#37273	C₂×D₄	1	2	yes	—
283	#37273	C₂×D₄	1	2	yes	—
284	#37269	C₂×D₄	1	2	yes	—
285	#37269	C₂×D₄	1	2	yes	—
286	#37269	C₂×D₄	1	2	yes	—
287	#37232	C₂×D₄	1	4	yes	—
288	#37134	C₂×D₄	1	2	yes	—
289	#37129	C₂×D₄	1	2	yes	—
290	#36818	C₂×D₄	1	4	yes	—
291	#36812	C₂×D₄	1	4	yes	—
292	#36717	C₂×D₄	1	2	yes	—
293	#36714	C₂×D₄	1	4	yes	—
294	#36714	C₂×D₄	1	4	yes	—
295	#36714	C₂×D₄	1	4	yes	—
296	#36703	C₂×D₄	1	4	yes	—
297	#36702	C₂×D₄	1	4	yes	—
298	#36702	C₂×D₄	1	4	yes	—
299	#36626	C₂×D₄	1	2	yes	—
300	#36624	C₂×D₄	1	2	yes	—
301	C₂×#2856	C₂×D₄	1	1	yes	characteristic
302	C₂×#2846	C₂×D₄	1	4	yes	—
303	#35563	C₂×D₄	1	1	yes	characteristic
304	#35563	C₂×D₄	1	1	yes	characteristic
305	#35556	C₂×D₄	1	2	yes	—
306	#35533	C₂×D₄	1	2	yes	—
307	#35528	C₂×D₄	1	2	yes	—
308	#35528	C₂×D₄	1	2	yes	—
309	#35527	C₂×D₄	1	2	yes	—
310	#35527	C₂⁴	1	2	yes	—
311	#35515	C₂×D₄	1	2	yes	—
312	#35513	C₂⁴	1	2	yes	—
313	#35512	C₂×D₄	1	1	yes	characteristic
314	#35512	C₂⁴	1	1	yes	characteristic
315	#35439	C₂×D₄	1	4	yes	—
316	#35438	C₂×D₄	1	4	yes	—
317	#35390	C₂×D₄	1	4	yes	—
318	#35390	C₂×D₄	1	4	yes	—
319	#35348	C₂×D₄	1	4	yes	—
320	#35348	C₂×D₄	1	4	yes	—
321	#35347	C₂×D₄	1	2	yes	—
322	#35346	C₂×D₄	1	4	yes	—
323	#35346	C₂⁴	1	4	yes	—
324	#35285	C₂×D₄	1	1	yes	characteristic
325	#35280	C₂×D₄	1	1	yes	characteristic
326	#35274	C₂×D₄	1	2	yes	—
327	#35272	C₂×D₄	1	2	yes	—
328	#35256	C₂×D₄	1	2	yes	—
329	#35254	C₂×D₄	1	2	yes	—
330	#35254	C₂×D₄	1	1	yes	characteristic
331	#35254	C₂×D₄	1	1	yes	characteristic
332	#35223	C₂×D₄	1	2	yes	—
333	#35222	C₂×D₄	1	2	yes	—
334	#35222	C₂×D₄	1	2	yes	—
335	#35222	C₂×D₄	1	2	yes	—
336	#34981	C₂×D₄	1	4	yes	—
337	#34981	C₂×D₄	1	4	yes	—
338	#34980	C₂×D₄	1	4	yes	—
339	#34980	C₂×D₄	1	4	yes	—
340	#34415	C₂×D₄	1	2	yes	—
341	#34415	C₂×D₄	1	2	yes	—
342	#34408	C₂×D₄	1	4	yes	—
343	#34368	C₂×D₄	1	1	yes	characteristic
344	#34364	C₂×D₄	1	2	yes	—
345	#34360	C₂×D₄	1	2	yes	—
346	#34356	C₂×D₄	1	4	yes	—
347	#34356	C₂×D₄	1	4	yes	—
348	#34269	C₂×D₄	1	2	yes	—
349	#34258	C₂×D₄	1	1	yes	characteristic
350	#34258	C₂⁴	1	1	yes	characteristic
351	#34210	C₂×D₄	1	2	yes	—
352	#34207	C₂×D₄	1	1	yes	characteristic
353	#34200	C₂×D₄	1	2	yes	—
354	#34198	C₂×D₄	1	4	yes	—
355	#34198	C₂×D₄	1	4	yes	—
356	C₄×#525	C₂×D₄	1	1	yes	characteristic
357	C₄×#525	C₂×D₄	1	2	yes	—
358	C₂²×#390	C₂×D₄	1	2	yes	—
359	#20592	C₂⁴	1	2	yes	—
360	#20592	C₂⁴	1	2	yes	—
361	#20586	C₂⁴	1	1	yes	characteristic
362	#20585	C₂⁴	1	4	yes	—
363	C₂⁷	#120	1	4	yes	complemented
364	C₂²×H(5,𝔽₂)	#120	1	2	yes	complemented
365	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
366	C₂²×H(5,𝔽₂)	C₂⁵	1	1	yes	characteristic
367	C₂⁴×D₄	#120	1	2	yes	complemented
368	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
369	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
370	C₂×H(3,𝔽₄)	#120	1	2	yes	—
371	C₂×H(3,𝔽₄)	#120	1	4	yes	complemented
372	C₂×#560	#120	1	4	yes	—
373	C₂×#560	#120	1	4	yes	complemented
374	C₂×#560	#120	1	4	yes	complemented
375	C₂×#559	#120	1	1	yes	characteristic
376	C₂×#559	#120	1	2	yes	complemented
377	C₂×Q₈²	#120	1	1	yes	characteristic, complemented
378	C₂×#555	#120	1	1	yes	characteristic, complemented
379	C₂×#555	#120	1	2	yes	complemented
380	C₂×#551	#120	1	2	yes	—
381	C₂×#551	#120	1	4	yes	complemented
382	C₂×#551	#120	1	2	yes	complemented
383	C₂×#551	#120	1	2	yes	complemented
384	C₂×D₄²	#120	1	4	yes	—
385	C₂×D₄²	#120	1	2	yes	—
386	C₂×D₄²	#120	1	1	yes	characteristic
387	C₂×D₄²	#120	1	4	yes	complemented
388	C₂×D₄²	#120	1	4	yes	complemented
389	C₂×D₄²	#120	1	2	yes	complemented
390	C₂×D₄²	#120	1	4	yes	complemented
391	C₂×D₄²	#120	1	4	yes	complemented
392	C₂×D₄²	#120	1	4	yes	complemented
393	C₂×D₄²	#120	1	4	yes	complemented
394	C₂×D₄²	#120	1	4	yes	complemented
395	C₂×D₄²	#120	1	2	yes	complemented
396	C₂×D₄²	#120	1	2	yes	complemented
397	C₂×#538	#120	1	4	yes	complemented
398	C₂×#537	C₂²×D₄	1	2	yes	—
399	C₂×#535	#120	1	2	yes	complemented
400	C₂×#535	#120	1	2	yes	complemented
401	C₂×#535	#120	1	2	yes	complemented
402	C₂×#535	C₂²×D₄	1	2	yes	—
403	C₂×#535	C₂²×D₄	1	2	yes	—
404	C₂×#535	C₂²×D₄	1	2	yes	—
405	C₂×#535	C₂²×D₄	1	2	yes	—
406	C₂×#535	C₂²×D₄	1	2	yes	—
407	C₂×#535	C₂²×D₄	1	1	yes	characteristic
408	C₂×#535	C₂²×D₄	1	2	yes	—
409	C₂×#535	C₂²×D₄	1	2	yes	—
410	C₂×#535	C₂²×D₄	1	1	yes	characteristic
411	C₂×#535	C₂²×D₄	1	2	yes	—
412	C₂×#535	C₂²×D₄	1	2	yes	—
413	C₂×#534	#120	1	4	yes	complemented
414	C₂×#534	#120	1	4	yes	complemented
415	C₂×#534	#120	1	2	yes	complemented
416	C₂×#534	C₂²×D₄	1	4	yes	—
417	C₂×#534	C₂²×D₄	1	4	yes	—
418	C₂×#534	C₂²×D₄	1	4	yes	—
419	C₂×#534	C₂²×D₄	1	4	yes	—
420	C₂×#533	#120	1	2	yes	complemented
421	C₂×#533	#120	1	1	yes	characteristic, complemented
422	C₂×#532	C₂²×D₄	1	2	yes	—
423	C₂×#532	C₂²×D₄	1	1	yes	characteristic
424	C₂×#532	C₂²×D₄	1	2	yes	—
425	C₂²×#127	#120	1	2	yes	complemented
426	C₂²×#127	#120	1	2	yes	complemented
427	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
428	C₂²×#127	C₂²×D₄	1	2	yes	—
429	C₂²×#127	C₂²×D₄	1	2	yes	—
430	C₂×#525	#120	1	2	yes	complemented
431	C₂×#525	#120	1	2	yes	complemented
432	C₂×#525	#120	1	1	yes	characteristic, complemented
433	C₂×#525	C₂²×D₄	1	1	yes	characteristic
434	C₂×#525	C₂²×D₄	1	2	yes	—
435	C₂×#525	C₂²×D₄	1	2	yes	—
436	C₂×#525	C₂²×D₄	1	2	yes	—
437	C₂×#525	C₂²×D₄	1	2	yes	—
438	C₂×#525	C₂²×D₄	1	1	yes	characteristic
439	C₂²×#121	#120	1	1	yes	characteristic, complemented
440	C₂²×#121	C₂²×D₄	1	1	yes	characteristic
441	C₂²×#120	#120	1	4	yes	complemented
442	C₂²×#120	#120	1	4	yes	complemented
443	C₂²×#120	#120	1	4	yes	complemented
444	C₂²×#120	#120	1	4	yes	complemented
445	C₂²×#120	C₂²×D₄	1	4	yes	—
446	C₂²×#120	C₂²×D₄	1	4	yes	—
447	C₂²×#120	C₂²×D₄	1	4	yes	—
448	C₂²×#120	C₂²×D₄	1	4	yes	—
449	C₂²×#120	C₂²×D₄	1	4	yes	—
450	C₂²×#120	C₂²×D₄	1	4	yes	—
451	C₂²×#120	C₂²×D₄	1	4	yes	—
452	C₂×#520	#120	1	1	yes	characteristic, complemented
453	C₂×#520	C₂²×D₄	1	1	yes	characteristic
454	C₂×#518	#120	1	2	yes	complemented
455	C₂×#518	C₂²×D₄	1	2	yes	—
456	C₂×#518	C₂²×D₄	1	2	yes	—
457	C₂×C₄×#41	#120	1	1	yes	characteristic, complemented
458	C₂×C₄×#41	#120	1	2	yes	complemented
459	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
461	C₂³×C₄⋊C₄	#120	1	2	yes	complemented
462	C₂³×C₂²⋊C₄	#120	1	4	yes	complemented
463	C₂³×C₂²⋊C₄	#120	1	4	yes	complemented
464	C₂³×C₄²	#120	1	1	yes	characteristic, complemented
465	C₂³×C₄²	#120	1	2	yes	complemented
466	C₂³×C₄²	#120	1	2	yes	complemented
467	#2842	#120	1	4	yes	complemented
468	#2816	#120	1	4	yes	complemented
469	#2815	#120	1	4	yes	complemented
470	#2811	#120	1	1	yes	characteristic, complemented
471	#2809	#120	1	2	yes	complemented
472	#2809	#120	1	1	yes	characteristic, complemented
473	#2804	#120	1	2	yes	complemented
474	#2748	#120	1	4	yes	complemented
475	#2733	#120	1	2	yes	complemented
476	#2733	#120	1	4	yes	complemented
477	#2733	#120	1	2	yes	complemented
478	#2731	#120	1	4	yes	complemented
479	#2724	#120	1	1	yes	characteristic
480	#2724	#120	1	2	yes	complemented
481	#2709	#120	1	4	yes	complemented
482	#2709	#120	1	4	yes	complemented
483	#2709	#120	1	4	yes	complemented
484	#2697	#120	1	4	yes	—
485	#2697	#120	1	2	yes	—
486	#2697	#120	1	4	yes	complemented
487	#2697	#120	1	4	yes	complemented
488	#2697	#120	1	2	yes	complemented
489	#2697	#120	1	4	yes	complemented
490	#2697	#120	1	2	yes	complemented
491	#2684	#120	1	4	yes	complemented
492	#2684	#120	1	4	yes	complemented
493	#2684	#120	1	4	yes	complemented
494	#2684	#120	1	4	yes	complemented
495	#2684	#120	1	4	yes	complemented
496	#2683	#120	1	2	yes	complemented
497	#2679	#120	1	2	yes	—
498	#2679	#120	1	2	yes	—
499	#2679	#120	1	4	yes	—
500	#2679	#120	1	1	yes	characteristic
501	#2679	#120	1	2	yes	complemented
502	#2679	#120	1	4	yes	complemented
503	#2679	#120	1	4	yes	complemented
504	#2679	#120	1	4	yes	complemented
505	#2679	#120	1	4	yes	complemented
506	#2679	#120	1	2	yes	complemented
507	#2679	#120	1	4	yes	complemented
508	#2679	#120	1	4	yes	complemented
509	#2679	#120	1	4	yes	complemented
510	#2679	#120	1	2	yes	complemented
511	#2679	#120	1	4	yes	complemented
512	#2669	#120	1	4	yes	complemented
513	#2669	#120	1	4	yes	complemented
514	#2669	#120	1	4	yes	complemented
515	#2669	#120	1	4	yes	complemented
516	#2669	#120	1	4	yes	complemented
517	#2669	#120	1	4	yes	complemented
518	#2669	#120	1	4	yes	complemented
519	#2669	#120	1	4	yes	complemented
520	#2608	#120	1	4	yes	complemented
521	#2607	#120	1	4	yes	complemented
522	#2561	#120	1	4	yes	complemented
523	#2539	#120	1	4	yes	complemented
524	#2539	#120	1	4	yes	complemented
525	#2539	#120	1	4	yes	complemented
526	#2435	C₂²×D₄	1	4	yes	—
527	#2433	C₂²×D₄	1	4	yes	—
528	#2433	C₂²×D₄	1	4	yes	—
529	#2433	C₂²×D₄	1	4	yes	—
530	#2432	C₂²×D₄	1	4	yes	—
531	#2431	C₂²×D₄	1	4	yes	—
532	#2431	C₂²×D₄	1	4	yes	—
533	#2431	C₂²×D₄	1	4	yes	—
534	#2405	#120	1	4	yes	complemented
535	#2405	C₂²×D₄	1	4	yes	—
536	#2404	C₂²×D₄	1	4	yes	—
537	#2404	C₂²×D₄	1	4	yes	—
538	#2404	C₂²×D₄	1	4	yes	—
539	#2404	C₂²×D₄	1	4	yes	—
540	#2403	#120	1	4	yes	complemented
541	#2403	#120	1	4	yes	complemented
542	#2403	C₂²×D₄	1	4	yes	—
543	#2403	C₂²×D₄	1	4	yes	—
544	#2403	C₂²×D₄	1	4	yes	—
545	#2403	C₂²×D₄	1	4	yes	—
546	#2403	C₂²×D₄	1	4	yes	—
547	#2380	#120	1	4	yes	complemented
548	#2379	#120	1	2	yes	complemented
549	#2379	#120	1	4	yes	complemented
550	#2376	#120	1	4	yes	complemented
551	#2376	#120	1	4	yes	complemented
552	#2375	#120	1	4	yes	complemented
553	#2375	#120	1	4	yes	complemented
554	#2375	#120	1	4	yes	complemented
555	#2375	#120	1	4	yes	complemented
556	#2375	#120	1	4	yes	complemented
557	#2375	#120	1	4	yes	complemented
558	#2374	#120	1	4	yes	complemented
559	#2372	#120	1	4	yes	complemented
560	#2369	#120	1	2	yes	complemented
561	#2366	#120	1	2	yes	complemented
562	#2366	#120	1	2	yes	complemented
563	#2358	#120	1	4	yes	complemented
564	#2358	#120	1	4	yes	complemented
565	#2358	#120	1	4	yes	complemented
566	#2358	#120	1	4	yes	complemented
567	#2358	#120	1	4	yes	complemented
568	#2358	#120	1	4	yes	complemented
569	#2358	#120	1	4	yes	complemented
570	#2333	#120	1	4	yes	complemented
571	#2333	#120	1	4	yes	complemented
572	#2333	#120	1	4	yes	complemented
573	#2332	#120	1	4	yes	complemented
574	#2317	#120	1	2	yes	complemented
575	#2316	#120	1	2	yes	complemented
576	#2316	#120	1	1	yes	characteristic, complemented
577	#2316	#120	1	1	yes	characteristic, complemented
578	#2315	#120	1	4	yes	complemented
579	#2315	#120	1	4	yes	complemented
580	#2312	#120	1	4	yes	complemented
581	#2312	#120	1	2	yes	complemented
582	#2311	#120	1	2	yes	complemented
583	#2311	#120	1	1	yes	characteristic, complemented
584	#2311	C₂²×D₄	1	1	yes	characteristic
585	#2311	C₂²×D₄	1	1	yes	characteristic
586	#2311	C₂²×D₄	1	2	yes	—
587	#2311	C₂²×D₄	1	2	yes	—
588	#2311	C₂²×D₄	1	1	yes	characteristic
589	#2309	#120	1	2	yes	complemented
590	#2309	#120	1	2	yes	complemented
591	#2309	#120	1	2	yes	complemented
592	#2309	#120	1	2	yes	complemented
593	#2309	#120	1	1	yes	characteristic, complemented
594	#2309	#120	1	1	yes	characteristic, complemented
595	#2309	#120	1	4	yes	complemented
596	#2309	C₂²×D₄	1	1	yes	characteristic
597	#2309	C₂²×D₄	1	2	yes	—
598	#2309	C₂²×D₄	1	2	yes	—
599	#2309	C₂²×D₄	1	1	yes	characteristic
600	#2308	#120	1	4	yes	complemented
601	#2308	#120	1	4	yes	complemented
602	#2308	#120	1	4	yes	complemented
603	#2308	#120	1	2	yes	complemented
604	#2308	C₂²×D₄	1	4	yes	—
605	#2308	C₂²×D₄	1	4	yes	—
606	#2308	C₂²×D₄	1	4	yes	—
607	#2297	#120	1	2	yes	complemented
608	#2297	C₂²×D₄	1	2	yes	—
609	#2297	C₂²×D₄	1	2	yes	—
610	#2297	C₂²×D₄	1	2	yes	—
611	#2297	C₂²×D₄	1	2	yes	—
612	#2297	C₂²×D₄	1	1	yes	characteristic
613	#2296	#120	1	2	yes	complemented
614	#2296	#120	1	2	yes	complemented
615	#2296	#120	1	1	yes	characteristic, complemented
616	#2296	#120	1	2	yes	complemented
617	C₂×#390	#120	1	1	yes	characteristic, complemented
618	C₂×#390	#120	1	2	yes	complemented
619	C₂×#390	#120	1	2	yes	complemented
620	C₂×#390	C₂²×D₄	1	2	yes	—
621	C₂×#390	C₂²×D₄	1	1	yes	characteristic
622	C₂×#390	C₂²×D₄	1	2	yes	—
623	#2285	#120	1	2	yes	complemented
624	C₂×#384	#120	1	1	yes	characteristic, complemented
625	#2280	#120	1	2	yes	complemented
626	#2280	#120	1	2	yes	complemented
627	#2280	#120	1	1	yes	characteristic, complemented
628	C₂×#379	#120	1	4	yes	complemented
629	C₂×#379	#120	1	4	yes	complemented
630	C₂×#379	#120	1	4	yes	complemented
631	#2274	#120	1	2	yes	complemented
632	#2273	#120	1	4	yes	complemented
633	#2273	#120	1	4	yes	complemented
634	C₄×#117	#120	1	1	yes	characteristic, complemented
635	C₄×#117	#120	1	2	yes	complemented
636	C₂⁶	C₂×#120	1	4	yes	—
637	C₂⁶	C₂×#120	1	4	yes	—
638	C₂⁶	C₂×#120	1	4	yes	—
639	C₂²×#41	C₂×#120	1	1	yes	characteristic
640	C₂²×#41	C₂×#120	1	2	yes	—
641	C₂²×#41	C₂×#120	1	2	yes	—
642	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
643	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
644	C₂²×#41	C₂³×D₄	1	2	yes	—
645	C₂²×#41	C₂³×D₄	1	2	yes	—
646	C₂³×D₄	C₂×#120	1	4	yes	—
647	C₂³×D₄	C₂×#120	1	4	yes	—
648	C₂³×D₄	C₂×#120	1	2	yes	—
649	C₂³×D₄	C₂×#120	1	4	yes	—
650	C₂³×D₄	C₂×#120	1	4	yes	—
651	C₂³×D₄	C₂×#120	1	2	yes	—
652	C₂³×D₄	C₂×#120	1	2	yes	—
653	C₂³×D₄	C₂×#120	1	1	yes	characteristic
654	C₂³×D₄	C₂×#120	1	2	yes	—
655	C₂³×D₄	C₂×#120	1	2	yes	—
656	C₂³×D₄	C₂³×D₄	1	2	yes	—
657	C₂³×D₄	C₂³×D₄	1	2	yes	—
658	C₂³×D₄	C₂³×D₄	1	4	yes	—
659	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
660	C₂⁴×C₄	C₂×#120	1	2	yes	—
661	C₂⁴×C₄	C₂×#120	1	2	yes	—
662	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
663	D₄²	B(4,𝔽₂)	1	4	yes	complemented
664	C₂×C₄⋊Q₈	C₂×#120	1	1	yes	characteristic
665	C₂×C₄⋊Q₈	C₂×#120	1	2	yes	—
666	C₂×#127	C₂×#120	1	1	yes	characteristic
667	C₂×#127	C₂×#120	1	2	yes	—
668	C₂×#127	C₂×#120	1	2	yes	—
669	C₂×#127	C₂×#120	1	2	yes	—
670	C₂×#127	C₂×#120	1	2	yes	—
671	C₂×#127	C₂×#120	1	4	yes	—
672	C₂×#127	C₂×#120	1	4	yes	—
673	C₂×#127	C₂×#120	1	4	yes	—
674	C₂×#127	C₂×#120	1	4	yes	—
675	C₂×#127	C₂×#120	1	2	yes	—
676	C₂×#124	C₂×#120	1	4	yes	—
677	C₂×#124	C₂×#120	1	1	yes	characteristic
678	C₂×#124	C₂×#120	1	2	yes	—
679	C₂×#124	C₂×#120	1	2	yes	—
680	C₂×#124	C₂×#120	1	2	yes	—
681	C₂×#124	C₂×#120	1	1	yes	characteristic
682	C₂×#124	C₂×#120	1	2	yes	—
683	C₂×#124	C₂×#120	1	4	yes	—
684	C₂×#123	C₂×#120	1	4	yes	—
685	C₂×#123	C₂×#120	1	2	yes	—
686	C₂×#123	C₂×#120	1	2	yes	—
687	C₂×#123	C₂×#120	1	2	yes	—
688	C₂×#123	C₂×#120	1	2	yes	—
689	C₂×#123	C₂×#120	1	4	yes	—
690	C₂×#123	C₂×#120	1	2	yes	—
691	C₂×#123	C₂×#120	1	2	yes	—
692	C₂×C₂²⋊Q₈	C₂×#120	1	4	yes	—
693	C₂×#121	C₂×#120	1	4	yes	—
694	C₂×#121	C₂×#120	1	4	yes	—
695	C₂×#121	C₂×#120	1	4	yes	—
696	C₂×#120	C₂×#120	1	2	yes	—
697	C₂×#120	C₂×#120	1	4	yes	—
698	C₂×#120	C₂×#120	1	4	yes	—
699	C₂×#120	C₂×#120	1	2	yes	—
700	C₂×#120	C₂×#120	1	4	yes	—
701	C₂×#120	C₂×#120	1	4	yes	—
702	C₂×#120	C₂×#120	1	4	yes	—
703	C₂×#120	C₂×#120	1	4	yes	—
704	C₂×#120	C₂×#120	1	2	yes	—
705	C₂×#120	C₂×#120	1	2	yes	—
706	C₂×#120	C₂×#120	1	4	yes	—
707	C₂×#120	C₂×#120	1	4	yes	—
708	C₂×#120	C₂×#120	1	4	yes	—
709	C₂×#120	C₂×#120	1	4	yes	—
710	C₂×#120	C₂×#120	1	4	yes	—
711	C₂×#120	C₂×#120	1	4	yes	—
712	C₂×#120	C₂×#120	1	2	yes	—
713	C₂×#120	C₂×#120	1	4	yes	—
714	C₂×#120	C₂×#120	1	2	yes	—
715	C₂×#120	C₂×#120	1	4	yes	—
716	C₂×#120	C₂×#120	1	4	yes	—
717	C₂×#120	C₂×#120	1	4	yes	—
718	C₂×#120	C₂×#120	1	4	yes	—
719	C₂×#120	C₂×#120	1	4	yes	—
720	C₂×#117	C₂×#120	1	2	yes	—
721	C₂×#117	C₂×#120	1	2	yes	—
722	C₂×#117	C₂×#120	1	1	yes	characteristic
723	C₂×#117	C₂×#120	1	2	yes	—
724	C₂×#117	C₂×#120	1	2	yes	—
725	C₂×#117	C₂×#120	1	1	yes	characteristic
726	C₂×#117	C₂×#120	1	2	yes	—
727	C₂×#117	C₂×#120	1	1	yes	characteristic
728	C₂×#117	C₂×#120	1	1	yes	characteristic
729	C₂×#117	C₂×#120	1	2	yes	—
730	C₂×#117	C₂×#120	1	2	yes	—
731	C₂×#117	C₂×#120	1	2	yes	—
732	C₂×#117	C₂×#120	1	1	yes	characteristic
733	C₂×#117	C₂×#120	1	2	yes	—
734	C₂×#117	C₂×#120	1	2	yes	—
735	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
736	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
737	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
738	C₂²×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
739	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
740	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
741	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
742	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
743	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
744	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
745	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
746	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
747	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
748	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
749	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
750	C₂²×C₄²	C₂×#120	1	2	yes	—
751	C₂²×C₄²	C₂×#120	1	2	yes	—
752	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
753	C₂²×C₄²	C₂×#120	1	2	yes	—
754	C₂²×C₄²	C₂×#120	1	2	yes	—
755	#391	C₂×#120	1	2	yes	—
756	#391	C₂×#120	1	1	yes	characteristic
757	#391	C₂×#120	1	4	yes	—
758	#391	C₂×#120	1	2	yes	—
759	#391	C₂×#120	1	2	yes	—
760	#391	C₂×#120	1	1	yes	characteristic
761	#390	C₂×#120	1	2	yes	—
762	#390	C₂×#120	1	1	yes	characteristic
763	#390	C₂×#120	1	2	yes	—
764	#390	C₂×#120	1	2	yes	—
765	#390	C₂×#120	1	2	yes	—
766	#390	C₂×#120	1	4	yes	—
767	#390	C₂×#120	1	4	yes	—
768	#390	C₂×#120	1	4	yes	—
769	#390	C₂×#120	1	2	yes	—
770	#390	C₂×#120	1	4	yes	—
771	#390	C₂×#120	1	2	yes	—
772	#390	C₂×#120	1	4	yes	—
773	#390	C₂×#120	1	1	yes	characteristic
774	#390	C₂×#120	1	2	yes	—
775	#386	C₂×#120	1	4	yes	—
776	#386	C₂×#120	1	4	yes	—
777	#386	C₂×#120	1	4	yes	—
778	#386	C₂×#120	1	4	yes	—
779	#386	C₂×#120	1	4	yes	—
780	#386	C₂×#120	1	4	yes	—
781	#386	C₂×#120	1	4	yes	—
782	#386	C₂×#120	1	4	yes	—
783	#386	C₂×#120	1	4	yes	—
784	#386	C₂×#120	1	4	yes	—
785	#381	C₂×#120	1	4	yes	—
786	#381	C₂×#120	1	4	yes	—
787	#379	C₂×#120	1	4	yes	—
788	#379	C₂×#120	1	4	yes	—
789	#379	C₂×#120	1	4	yes	—
790	C₄×C₂²⋊C₄	C₂×#120	1	4	yes	—
791	C₄×C₂²⋊C₄	C₂×#120	1	4	yes	—
792	C₄×C₂²⋊C₄	C₂×#120	1	4	yes	—
793	C₄×C₂²⋊C₄	C₂×#120	1	4	yes	—
794	C₂⁵	#2846	1	4	yes	—
795	C₂⁵	#2846	1	4	yes	—
796	C₂⁵	#2846	1	1	yes	characteristic
797	C₂⁵	#2846	1	2	yes	—
798	C₂⁵	#2846	1	4	yes	—
799	C₂⁵	#2846	1	4	yes	—
800	C₂⁵	#2846	1	2	yes	—
801	C₂⁵	C₂²×#120	1	4	yes	—
802	C₂⁵	C₂²×#120	1	2	yes	—
803	C₂²×Q₈	#2846	1	2	yes	—
804	C₂²×Q₈	#2846	1	1	yes	characteristic
805	C₂²×Q₈	C₂²×#120	1	1	yes	characteristic
806	C₂²×Q₈	C₂²×#120	1	1	yes	characteristic
807	C₂²×D₄	#2846	1	4	yes	—
808	C₂²×D₄	#2846	1	2	yes	—
809	C₂²×D₄	#2846	1	2	yes	—
810	C₂²×D₄	#2846	1	1	yes	characteristic
811	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
812	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
813	C₂²×D₄	C₂²×#120	1	4	yes	—
814	C₂²×D₄	C₂²×#120	1	4	yes	—
815	C₂²×D₄	C₂²×#120	1	2	yes	—
816	C₂²×D₄	C₂²×#120	1	2	yes	—
817	C₂²×D₄	C₂²×#120	1	2	yes	—
818	C₂²×D₄	C₂²×#120	1	2	yes	—
819	C₂³×C₄	#2846	1	1	yes	characteristic
820	C₂³×C₄	#2846	1	4	yes	—
821	C₂³×C₄	#2846	1	4	yes	—
822	C₂³×C₄	#2846	1	2	yes	—
823	C₂³×C₄	#2846	1	2	yes	—
824	C₂³×C₄	#2846	1	2	yes	—
825	C₂³×C₄	C₂²×#120	1	4	yes	—
826	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
827	C₂³×C₄	C₂²×#120	1	2	yes	—
828	C₂³×C₄	C₂²×#120	1	2	yes	—
829	#127	C₂×B(4,𝔽₂)	1	2	yes	—
830	#127	#3026	1	2	yes	—
831	#120	C₂×B(4,𝔽₂)	1	4	yes	—
832	#120	#3026	1	4	yes	—
833	C₂×C₄⋊C₄	#2846	1	2	yes	—
834	C₂×C₄⋊C₄	#2846	1	1	yes	characteristic
835	C₂×C₄⋊C₄	#2846	1	4	yes	—
836	C₂×C₄⋊C₄	#2846	1	1	yes	characteristic
837	C₂×C₄⋊C₄	#2846	1	2	yes	—
838	C₂×C₄⋊C₄	#2846	1	2	yes	—
839	C₂×C₂²⋊C₄	#2846	1	2	yes	—
840	C₂×C₂²⋊C₄	#2846	1	2	yes	—
841	C₂×C₂²⋊C₄	#2846	1	4	yes	—
842	C₂×C₂²⋊C₄	#2846	1	2	yes	—
843	C₂×C₂²⋊C₄	#2846	1	4	yes	—
844	C₂×C₂²⋊C₄	#2846	1	2	yes	—
845	C₂×C₂²⋊C₄	#2846	1	4	yes	—
846	C₂×C₂²⋊C₄	#2846	1	4	yes	—
847	C₂×C₂²⋊C₄	#2846	1	4	yes	—
848	C₂×C₂²⋊C₄	#2846	1	4	yes	—
849	C₂×C₂²⋊C₄	#2846	1	2	yes	—
850	C₂×C₂²⋊C₄	#2846	1	2	yes	—
851	C₂×C₄²	#2846	1	1	yes	characteristic
852	C₂×C₄²	#2846	1	1	yes	characteristic
853	C₂×C₄²	#2846	1	2	yes	—
854	C₂×C₄²	#2846	1	2	yes	—
855	C₂×C₄²	#2846	1	1	yes	characteristic
856	C₂×C₄²	#2846	1	4	yes	—
857	C₂×C₄²	#2846	1	4	yes	—
858	C₂×C₄²	#2846	1	2	yes	—
859	C₂×C₄²	#2846	1	2	yes	—
860	C₂×C₄²	#2846	1	2	yes	—
861	C₂×C₄²	#2846	1	2	yes	—
862	C₂×C₄²	#2846	1	1	yes	characteristic
863	C₂⁴	#32898	1	4	yes	—
864	C₂⁴	C₂×#2846	1	2	yes	—
865	C₂⁴	C₂×#2846	1	2	yes	—
866	C₂⁴	C₂×#2846	1	1	yes	characteristic
867	C₂⁴	C₂×#2846	1	4	yes	—
868	C₂×D₄	#32898	1	2	yes	—
869	C₂×D₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
870	C₂×D₄	C₂×#3026	1	1	yes	characteristic
871	C₂×D₄	C₂×#3026	1	2	yes	—
872	C₂×D₄	#60399	1	1	yes	characteristic
873	C₂×D₄	#60399	1	2	yes	—
874	C₂×D₄	#60401	1	1	yes	characteristic
875	C₂²×C₄	C₂×#2846	1	1	yes	characteristic
876	C₂²×C₄	C₂×#2846	1	1	yes	characteristic
877	C₂²×C₄	C₂×#2846	1	2	yes	—
878	C₂²×C₄	C₂×#2846	1	2	yes	—
879	C₂²⋊C₄	#32898	1	4	yes	—
880	C₄²	#32898	1	2	yes	—
881	C₂³	#6342371	1	1	yes	characteristic
882	C₂³	C₂×#32898	1	2	yes	—
883	C₂³	#6628892	1	2	yes	—
884	C₂³	#6628896	1	2	yes	—
885	C₂³	#6628900	1	2	yes	—
886	C₂×C₄	C₂×#32898	1	1	yes	characteristic
887	C₂×C₄	#6628892	1	1	yes	characteristic
888	C₂×C₄	#6628898	1	1	yes	characteristic
889	C₂×C₄	#6628901	1	1	yes	characteristic
890	C₂²	#72210025	1	1	yes	characteristic
891	C₂²	#72219118	1	1	yes	characteristic
892	C₂²	#72241173	1	1	yes	characteristic
893	C₂	#72258964	1	1	yes	characteristic
894	C₂	#72260582	1	1	yes	characteristic
895	C₂	#72260648	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72210025
commutator, Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁵
LCS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261378	C₂	semidirect
2. #72261341	C₂	semidirect
3. #72261323	C₂	semidirect
4. #72261300	C₂	semidirect
5. #72261234	C₂	semidirect
6. #72261212	C₂	semidirect
7. #72261187	C₂²	semidirect
8. #72261184	C₂²	semidirect
9. #72261177	C₂²	semidirect
10. #72261153	C₂	semidirect
11. #72261142	C₂	semidirect
12. #72261111	C₂²	semidirect
13. #72261086	C₂	semidirect
14. #72261073	C₂²	semidirect
15. #72261064	C₂²	semidirect
16. #72260847	C₂	semidirect
21. #72234424	C₂	semidirect
22. #72234423	C₂	semidirect
23. #72234421	C₂²	semidirect
24. #72234418	C₂²	semidirect
25. #72234416	C₂²	semidirect
26. #72234201	C₂	semidirect
27. #72234197	C₂²	semidirect
28. #72234193	C₂²	semidirect
29. #72234175	C₂	semidirect
30. #72234170	C₂²	semidirect
31. #72234167	C₂²	semidirect
32. #72234146	C₂²	semidirect
33. C₂×#7622880	C₂²	semidirect
34. #72234104	C₂	semidirect
35. #72234078	C₂²	semidirect
36. #72234065	C₂²	semidirect
38. #72233917	C₂²	semidirect
39. #72233911	C₂²	semidirect
40. #72233902	C₂²	semidirect
41. #72233857	C₂²	semidirect
42. #72233839	C₂²	semidirect
43. #72233476	C₂²	semidirect
44. #72233417	C₂²	semidirect
45. #72233302	C₂²	semidirect
46. #72233262	C₂²	semidirect
47. #72233187	C₂²	semidirect
48. #72233169	C₂²	semidirect
49. #72233157	C₂	semidirect
50. #72233119	C₂²	semidirect
51. #72233095	C₂²	semidirect
52. #72233091	C₂²	semidirect
53. #72233063	C₂²	semidirect
54. #72233051	C₂²	semidirect
55. #72233038	C₂²	semidirect
56. #72233002	C₂²	semidirect
57. #72232927	C₂	semidirect
58. #72232895	C₂²	semidirect
59. #72232864	C₂²	semidirect
60. #72232863	C₂²	semidirect
61. #72232850	C₂²	semidirect
62. #72232835	C₂²	semidirect
63. #72232831	C₂²	semidirect
64. #72232823	C₂²	semidirect
65. #72232811	C₂²	semidirect
66. #72232800	C₂²	semidirect
67. #72232794	C₂²	semidirect
68. #72232788	C₂²	semidirect
69. #72232778	C₂²	semidirect
70. #72232771	C₂²	semidirect
71. #72232764	C₂²	semidirect
72. #72232751	C₂²	semidirect
73. #72232739	C₂²	semidirect
74. #72232729	C₂²	semidirect
78. #72225779	C₂²	semidirect
79. #72219653	C₂²	semidirect
80. #72219306	C₂²	semidirect
81. #72219306	C₂²	semidirect
82. #72216646	C₂²	semidirect
84. C₂×#41²	D₄	semidirect
85. C₂³×D₄²	D₄	semidirect
86. C₂×#60399	C₂³	semidirect
87. C₂×#60399	C₂³	semidirect
88. C₂×#60388	C₂³	semidirect
89. #8943527	D₄	semidirect
90. #8943482	D₄	semidirect
91. #8943077	D₄	semidirect
92. #8942728	D₄	semidirect
93. #8942673	D₄	semidirect
96. #8824131	D₄	semidirect
97. #8811246	D₄	semidirect
98. #8806945	D₄	semidirect
99. #8797683	D₄	semidirect
100. #8765601	D₄	semidirect
101. #8757654	D₄	semidirect
102. #8196400	D₄	semidirect
103. #8195815	D₄	semidirect
104. #8195113	D₄	semidirect
105. #8181081	D₄	semidirect
106. #8179068	D₄	semidirect
107. #8176553	D₄	semidirect
108. #8110542	D₄	semidirect
109. #8110000	D₄	semidirect
110. #8109917	D₄	semidirect
111. #8108057	D₄	semidirect
112. #7849663	D₄	semidirect
114. #7837029	D₄	semidirect
117. #7829278	D₄	semidirect
118. #7819715	D₄	semidirect
121. #7739367	D₄	semidirect
122. #7737957	D₄	semidirect
124. #7737413	D₄	semidirect
126. #7733150	D₄	semidirect
128. #7712736	D₄	semidirect
129. #7712669	D₄	semidirect
130. #7711942	D₄	semidirect
131. #7711937	D₄	semidirect
132. #7711204	D₄	semidirect
133. #7711201	D₄	semidirect
134. #7708349	D₄	semidirect
135. #7708349	D₄	semidirect
139. #7670609	D₄	semidirect
140. #7670554	D₄	semidirect
141. #7670308	D₄	semidirect
142. #7670203	D₄	semidirect
144. #7659311	D₄	semidirect
145. #7659307	D₄	semidirect
147. #7633646	D₄	semidirect
148. C₂²×#2679	D₄	semidirect
149. #7627216	D₄	semidirect
150. #7627211	D₄	semidirect
151. C₂×#33359	C₂³	semidirect
152. C₂×#33348	C₂³	semidirect
153. C₂×#33348	C₂³	semidirect
154. #6628898	C₂³	semidirect
155. #6628896	C₂³	semidirect
156. #6628876	C₂³	semidirect
157. #6628872	C₂³	semidirect
158. #6370747	C₂³	semidirect
159. #494742	C₂³	semidirect
160. #494738	C₂³	semidirect
161. #494722	C₂³	semidirect
162. #494721	C₂³	semidirect
163. #494719	C₂³	semidirect
164. #494717	C₂³	semidirect
165. #494701	C₂³	semidirect
166. #494701	C₂³	semidirect
167. #494700	C₂³	semidirect
168. #494700	C₂³	semidirect
169. #494682	C₂³	semidirect
170. #494682	C₂³	semidirect
171. #493878	C₂³	semidirect
172. #493867	C₂³	semidirect
173. #493441	C₂³	semidirect
174. #493430	C₂³	semidirect
175. #493425	C₂³	semidirect
176. #493425	C₂³	semidirect
177. #493424	C₂³	semidirect
178. #493424	C₂³	semidirect
179. #492900	C₂³	semidirect
180. #374036	C₂³	semidirect
181. #374034	C₂³	semidirect
182. #374006	C₂³	semidirect
183. #374004	C₂³	semidirect
184. #359890	C₂³	semidirect
185. #359888	C₂³	semidirect
186. #359605	C₂³	semidirect
187. #359601	C₂³	semidirect
188. #359593	C₂³	semidirect
189. #359593	C₂³	semidirect
190. #359591	C₂³	semidirect
191. #359591	C₂³	semidirect
192. #214619	C₂³	semidirect
193. #214616	C₂³	semidirect
194. #213906	C₂³	semidirect
195. #213854	C₂³	semidirect
196. #213852	C₂³	semidirect
363. C₂⁷	#120	semidirect
364. C₂²×H(5,𝔽₂)	#120	semidirect
367. C₂⁴×D₄	#120	semidirect
371. C₂×H(3,𝔽₄)	#120	semidirect
373. C₂×#560	#120	semidirect
374. C₂×#560	#120	semidirect
376. C₂×#559	#120	semidirect
377. C₂×Q₈²	#120	semidirect
378. C₂×#555	#120	semidirect
379. C₂×#555	#120	semidirect
381. C₂×#551	#120	semidirect
382. C₂×#551	#120	semidirect
383. C₂×#551	#120	semidirect
387. C₂×D₄²	#120	semidirect
388. C₂×D₄²	#120	semidirect
389. C₂×D₄²	#120	semidirect
390. C₂×D₄²	#120	semidirect
391. C₂×D₄²	#120	semidirect
392. C₂×D₄²	#120	semidirect
393. C₂×D₄²	#120	semidirect
394. C₂×D₄²	#120	semidirect
395. C₂×D₄²	#120	semidirect
396. C₂×D₄²	#120	semidirect
397. C₂×#538	#120	semidirect
399. C₂×#535	#120	semidirect
400. C₂×#535	#120	semidirect
401. C₂×#535	#120	semidirect
413. C₂×#534	#120	semidirect
414. C₂×#534	#120	semidirect
415. C₂×#534	#120	semidirect
420. C₂×#533	#120	semidirect
421. C₂×#533	#120	semidirect
425. C₂²×#127	#120	semidirect
426. C₂²×#127	#120	semidirect
430. C₂×#525	#120	semidirect
431. C₂×#525	#120	semidirect
432. C₂×#525	#120	semidirect
439. C₂²×#121	#120	semidirect
441. C₂²×#120	#120	semidirect
442. C₂²×#120	#120	semidirect
443. C₂²×#120	#120	semidirect
444. C₂²×#120	#120	semidirect
452. C₂×#520	#120	semidirect
454. C₂×#518	#120	semidirect
457. C₂×C₄×#41	#120	semidirect
458. C₂×C₄×#41	#120	semidirect
461. C₂³×C₄⋊C₄	#120	semidirect
462. C₂³×C₂²⋊C₄	#120	semidirect
463. C₂³×C₂²⋊C₄	#120	semidirect
464. C₂³×C₄²	#120	semidirect
465. C₂³×C₄²	#120	semidirect
466. C₂³×C₄²	#120	semidirect
467. #2842	#120	semidirect
468. #2816	#120	semidirect
469. #2815	#120	semidirect
470. #2811	#120	semidirect
471. #2809	#120	semidirect
472. #2809	#120	semidirect
473. #2804	#120	semidirect
474. #2748	#120	semidirect
475. #2733	#120	semidirect
476. #2733	#120	semidirect
477. #2733	#120	semidirect
478. #2731	#120	semidirect
480. #2724	#120	semidirect
481. #2709	#120	semidirect
482. #2709	#120	semidirect
483. #2709	#120	semidirect
486. #2697	#120	semidirect
487. #2697	#120	semidirect
488. #2697	#120	semidirect
489. #2697	#120	semidirect
490. #2697	#120	semidirect
491. #2684	#120	semidirect
492. #2684	#120	semidirect
493. #2684	#120	semidirect
494. #2684	#120	semidirect
495. #2684	#120	semidirect
496. #2683	#120	semidirect
501. #2679	#120	semidirect
502. #2679	#120	semidirect
503. #2679	#120	semidirect
504. #2679	#120	semidirect
505. #2679	#120	semidirect
506. #2679	#120	semidirect
507. #2679	#120	semidirect
508. #2679	#120	semidirect
509. #2679	#120	semidirect
510. #2679	#120	semidirect
511. #2679	#120	semidirect
512. #2669	#120	semidirect
513. #2669	#120	semidirect
514. #2669	#120	semidirect
515. #2669	#120	semidirect
516. #2669	#120	semidirect
517. #2669	#120	semidirect
518. #2669	#120	semidirect
519. #2669	#120	semidirect
520. #2608	#120	semidirect
521. #2607	#120	semidirect
522. #2561	#120	semidirect
523. #2539	#120	semidirect
524. #2539	#120	semidirect
525. #2539	#120	semidirect
534. #2405	#120	semidirect
540. #2403	#120	semidirect
541. #2403	#120	semidirect
547. #2380	#120	semidirect
548. #2379	#120	semidirect
549. #2379	#120	semidirect
550. #2376	#120	semidirect
551. #2376	#120	semidirect
552. #2375	#120	semidirect
553. #2375	#120	semidirect
554. #2375	#120	semidirect
555. #2375	#120	semidirect
556. #2375	#120	semidirect
557. #2375	#120	semidirect
558. #2374	#120	semidirect
559. #2372	#120	semidirect
560. #2369	#120	semidirect
561. #2366	#120	semidirect
562. #2366	#120	semidirect
563. #2358	#120	semidirect
564. #2358	#120	semidirect
565. #2358	#120	semidirect
566. #2358	#120	semidirect
567. #2358	#120	semidirect
568. #2358	#120	semidirect
569. #2358	#120	semidirect
570. #2333	#120	semidirect
571. #2333	#120	semidirect
572. #2333	#120	semidirect
573. #2332	#120	semidirect
574. #2317	#120	semidirect
575. #2316	#120	semidirect
576. #2316	#120	semidirect
577. #2316	#120	semidirect
578. #2315	#120	semidirect
579. #2315	#120	semidirect
580. #2312	#120	semidirect
581. #2312	#120	semidirect
582. #2311	#120	semidirect
583. #2311	#120	semidirect
589. #2309	#120	semidirect
590. #2309	#120	semidirect
591. #2309	#120	semidirect
592. #2309	#120	semidirect
593. #2309	#120	semidirect
594. #2309	#120	semidirect
595. #2309	#120	semidirect
600. #2308	#120	semidirect
601. #2308	#120	semidirect
602. #2308	#120	semidirect
603. #2308	#120	semidirect
607. #2297	#120	semidirect
613. #2296	#120	semidirect
614. #2296	#120	semidirect
615. #2296	#120	semidirect
616. #2296	#120	semidirect
617. C₂×#390	#120	semidirect
618. C₂×#390	#120	semidirect
619. C₂×#390	#120	semidirect
623. #2285	#120	semidirect
624. C₂×#384	#120	semidirect
625. #2280	#120	semidirect
626. #2280	#120	semidirect
627. #2280	#120	semidirect
628. C₂×#379	#120	semidirect
629. C₂×#379	#120	semidirect
630. C₂×#379	#120	semidirect
631. #2274	#120	semidirect
632. #2273	#120	semidirect
633. #2273	#120	semidirect
634. C₄×#117	#120	semidirect
635. C₄×#117	#120	semidirect
663. D₄²	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
#72261378	2
#72261341	2
#72261323	2
#72261300	2
#72261234	2
#72261212	2
#72261153	2
#72261142	2
#72261086	2
#72260847	2
#72234424	2
#72234423	2
#72234201	2
#72234175	2
#72234104	2
#72233157	2
#72232927	2