Subgroups — #72261873

Order 2048.

At least 7289 conjugacy classes of subgroups; only the 7508 normal subgroups are shown.

The subgroup lattice has 901 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261797	C₂	1	2	yes	maximal, complemented
2	#72261773	C₂	1	16	yes	maximal, complemented
3	#72261762	C₂	1	16	yes	maximal, complemented
4	#72261660	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6343491	C₂	1	1	yes	maximal, characteristic, complemented
6	#72260872	C₂	1	2	yes	maximal, complemented
7	#72256539	C₂	1	1	yes	maximal, characteristic, complemented
8	#72235226	C₂	1	4	yes	maximal, complemented
9	#72235220	C₂	1	4	yes	maximal, complemented
10	#72235217	C₂	1	4	yes	maximal, complemented
11	C₂×#6342764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#234591	C₂	1	4	yes	maximal, complemented
13	#72233872	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10574840	C₂	1	1	yes	maximal, characteristic, complemented
15	#72231702	C₂	1	2	yes	maximal, complemented
16	#72231671	C₂	1	2	yes	maximal, complemented
17	C₂²×#35680	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×#62811	C₂²	1	1	yes	characteristic
20	C₂³×#546	C₂²	1	1	yes	characteristic
21	C₂×#60373	C₂²	1	8	yes	complemented
22	C₂×#60372	C₂²	1	8	yes	complemented
23	C₂×#60359	C₂²	1	2	yes	complemented
24	C₂×#60359	C₂²	1	4	yes	complemented
25	C₂²×#3003	C₂²	1	2	yes	complemented
26	C₂²×#3003	C₂²	1	4	yes	complemented
27	C₂×#60064	C₂²	1	1	yes	characteristic
28	C₂×#60064	C₂²	1	1	yes	characteristic
29	#7656808	C₂²	1	8	yes	complemented
30	#7656741	C₂²	1	8	yes	complemented
31	#7641875	C₂²	1	4	yes	complemented
32	#7641850	C₂²	1	2	yes	complemented
33	C₂×#35680	C₂²	1	16	yes	complemented
34	#7628282	C₂²	1	2	yes	complemented
35	C₂×#35050	C₂²	1	4	yes	complemented
36	C₂²×#2430	C₂²	1	2	yes	complemented
37	C₂²×#2404	C₂²	1	2	yes	complemented
38	C₂²×#2433	C₂²	1	1	yes	characteristic, complemented
39	C₂²×#2408	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#2615	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#2613	C₂²	1	2	yes	complemented
42	C₂²×#2388	C₂²	1	1	yes	characteristic, complemented
43	C₂³×#392	C₂²	1	2	yes	complemented
44	#7625442	C₂²	1	1	yes	characteristic
45	C₂²×#2339	C₂²	1	1	yes	characteristic
46	#6370722	C₂²	1	16	yes	complemented
47	#6370715	C₂²	1	2	yes	complemented
48	#6370715	C₂²	1	4	yes	complemented
49	C₂×#20598	C₂²	1	2	yes	complemented
50	C₂×#20598	C₂²	1	4	yes	complemented
51	C₂×#17608	C₂²	1	8	yes	complemented
52	C₂×#17603	C₂²	1	8	yes	complemented
53	C₂×#17592	C₂²	1	2	yes	complemented
54	C₂×#17587	C₂²	1	4	yes	complemented
55	C₂×#17542	C₂²	1	2	yes	complemented
56	C₂²×#1504	C₂²	1	4	yes	complemented
57	C₂×#17411	C₂²	1	16	yes	complemented
58	C₂×#17396	C₂²	1	2	yes	complemented
59	C₂×#17392	C₂²	1	4	yes	complemented
60	C₂×#17362	C₂²	1	2	yes	complemented
61	C₂²×#1462	C₂²	1	4	yes	complemented
62	#234615	C₂²	1	32	yes	complemented
63	#234612	C₂²	1	8	yes	complemented
64	#234611	C₂²	1	8	yes	complemented
65	#234594	C₂²	1	4	yes	complemented
66	#234593	C₂²	1	8	yes	complemented
67	#234593	C₂²	1	4	yes	complemented
68	#234592	C₂²	1	8	yes	complemented
69	#234592	C₂²	1	4	yes	complemented
70	#234591	C₂²	1	8	yes	complemented
71	#234591	C₂²	1	8	yes	complemented
72	#234591	C₂²	1	4	yes	complemented
73	#234591	C₂²	1	8	yes	complemented
74	#234591	C₂²	1	8	yes	complemented
75	#234591	C₂²	1	32	yes	complemented
76	#234590	C₂²	1	8	yes	complemented
77	#234589	C₂²	1	8	yes	complemented
78	#234569	C₂²	1	16	yes	complemented
79	#234568	C₂²	1	16	yes	complemented
80	#234567	C₂²	1	16	yes	complemented
81	#234551	C₂²	1	16	yes	complemented
82	#234548	C₂²	1	16	yes	complemented
83	#234547	C₂²	1	16	yes	complemented
84	#234529	C₂²	1	32	yes	complemented
85	#234522	C₂²	1	8	yes	complemented
86	#234521	C₂²	1	8	yes	complemented
87	#234503	C₂²	1	32	yes	complemented
88	#234500	C₂²	1	8	yes	complemented
89	#234499	C₂²	1	8	yes	complemented
90	#234481	C₂²	1	16	yes	complemented
91	#234478	C₂²	1	16	yes	complemented
92	#234477	C₂²	1	16	yes	complemented
93	#234459	C₂²	1	16	yes	complemented
94	C₂×#9922	C₂²	1	16	yes	complemented
95	C₂×#9914	C₂²	1	16	yes	complemented
96	#181744	C₂²	1	2	yes	complemented
97	#181740	C₂²	1	4	yes	complemented
98	#181528	C₂²	1	16	yes	complemented
99	#181500	C₂²	1	2	yes	complemented
100	C₂×#8020	C₂²	1	4	yes	complemented
101	C₂²×#585	D₄	1	1	yes	characteristic, complemented
102	C₂³×H(5,𝔽₂)	D₄	1	16	yes	complemented
103	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
104	C₂⁴×#41	C₂³	1	2	yes	—
105	C₂⁴×#41	C₂³	1	1	yes	characteristic
106	C₂⁴×#41	C₂³	1	1	yes	characteristic
107	C₂⁵×D₄	D₄	1	1	yes	characteristic
108	C₂⁵×D₄	C₂³	1	1	yes	characteristic
109	C₂⁵×D₄	C₂³	1	2	yes	—
110	C₂×#3489	D₄	1	4	yes	complemented
111	C₂×#3489	C₂³	1	4	yes	—
112	C₂×#3488	D₄	1	4	yes	complemented
113	C₂×#3488	C₂³	1	4	yes	—
114	C₂²×#546	D₄	1	8	yes	—
115	C₂²×#546	C₂³	1	8	yes	—
116	C₂×#3449	D₄	1	4	yes	complemented
117	C₂×#3449	D₄	1	2	yes	complemented
118	C₂³×#124	D₄	1	1	yes	characteristic
119	C₂²×#525	C₂³	1	4	yes	—
120	C₂²×#525	C₂³	1	2	yes	—
121	C₂³×#123	C₂³	1	2	yes	—
122	C₂³×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₂³×#121	D₄	1	2	yes	—
124	C₂³×#121	C₂³	1	1	yes	characteristic
125	C₂³×#120	D₄	1	2	yes	—
126	C₂×#3428	D₄	1	1	yes	characteristic, complemented
127	C₂×#3428	D₄	1	2	yes	complemented
128	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
129	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
130	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×#3007	C₂³	1	8	yes	complemented
132	C₂×#3007	C₂³	1	4	yes	complemented
133	C₂×#3006	C₂³	1	8	yes	complemented
134	C₂×#3006	C₂³	1	4	yes	complemented
135	C₂×#3004	C₂³	1	4	yes	—
136	C₂×#3003	C₂³	1	8	yes	—
137	C₂×#3003	C₂³	1	4	yes	—
138	C₂×#3003	C₂³	1	8	yes	complemented
139	C₂×#3003	C₂³	1	16	yes	complemented
140	C₂×#3002	C₂³	1	16	yes	complemented
141	C₂×#3002	C₂³	1	8	yes	complemented
142	C₂²×#450	C₂³	1	4	yes	complemented
143	C₂²×#450	C₂³	1	8	yes	complemented
144	C₂²×#447	C₂³	1	4	yes	complemented
145	C₂²×#447	C₂³	1	8	yes	complemented
146	#60064	D₄	1	16	yes	complemented
147	C₂×#2880	C₂³	1	8	yes	—
148	C₂×#2880	C₂³	1	8	yes	—
149	C₂²×#407	C₂³	1	4	yes	—
150	C₂²×#407	C₂³	1	2	yes	—
151	C₂²×#407	C₂³	1	4	yes	—
152	C₂²×#407	C₂³	1	2	yes	—
153	#37452	C₂³	1	16	yes	complemented
154	#37451	C₂³	1	4	yes	complemented
155	#37450	C₂³	1	4	yes	complemented
156	#37441	C₂³	1	8	yes	complemented
157	#37440	C₂³	1	8	yes	complemented
158	#37439	C₂³	1	8	yes	complemented
159	#35057	C₂³	1	4	yes	—
160	#35050	C₂³	1	8	yes	—
161	#35050	C₂³	1	4	yes	—
162	#35050	C₂³	1	16	yes	complemented
163	#35010	C₂³	1	4	yes	complemented
164	#35000	C₂³	1	4	yes	complemented
165	C₂×#2430	C₂³	1	16	yes	—
166	C₂×#2404	C₂³	1	16	yes	—
167	C₂×#2433	C₂³	1	8	yes	—
168	C₂×#2408	C₂³	1	8	yes	—
169	C₂×#2615	C₂³	1	8	yes	—
170	#34562	C₂³	1	8	yes	complemented
171	C₂×#2626	C₂³	1	8	yes	complemented
172	C₂×#2617	C₂³	1	8	yes	complemented
173	C₂×#2613	C₂³	1	16	yes	—
174	C₂×#2388	C₂³	1	8	yes	—
175	C₂²×#395	C₂³	1	1	yes	characteristic
176	C₂²×#394	C₂³	1	2	yes	—
177	C₂²×#394	C₂³	1	1	yes	characteristic
178	C₂²×#393	C₂³	1	1	yes	characteristic
179	C₂²×#393	C₂³	1	2	yes	—
180	C₂²×#392	C₂³	1	2	yes	—
181	C₂²×#392	C₂³	1	2	yes	—
182	C₂²×#392	C₂³	1	2	yes	—
183	C₂²×#392	C₂³	1	1	yes	characteristic
184	C₂²×#392	C₂³	1	2	yes	—
185	C₂²×#392	C₂³	1	16	yes	—
186	#34175	D₄	1	8	yes	complemented
187	#34175	C₂³	1	8	yes	—
188	C₂×#2339	D₄	1	16	yes	complemented
189	C₂×#2339	C₂³	1	8	yes	—
190	#34044	D₄	1	4	yes	complemented
191	#34044	D₄	1	2	yes	complemented
192	C₂×#2280	C₂³	1	4	yes	—
193	C₂×#2280	C₂³	1	2	yes	—
194	C₂²×#381	C₂³	1	2	yes	—
195	C₂²×#380	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂³×#95	C₂³	1	2	yes	—
198	#20601	C₂³	1	16	yes	complemented
199	#20601	C₂³	1	8	yes	complemented
200	#20599	C₂³	1	4	yes	—
201	#20598	C₂³	1	8	yes	—
202	#20598	C₂³	1	4	yes	—
203	#20598	C₂³	1	8	yes	complemented
204	#20598	C₂³	1	16	yes	complemented
205	#20597	C₂³	1	16	yes	complemented
206	#20597	C₂³	1	8	yes	complemented
207	C₂×#1786	C₂³	1	8	yes	complemented
208	C₂×#1786	C₂³	1	16	yes	complemented
209	C₂×#1516	C₂³	1	16	yes	complemented
210	C₂×#1520	C₂³	1	4	yes	complemented
211	C₂×#1519	C₂³	1	4	yes	complemented
212	C₂×#1513	C₂³	1	8	yes	complemented
213	C₂×#1511	C₂³	1	8	yes	complemented
214	C₂×#1510	C₂³	1	8	yes	complemented
215	C₂×#1504	C₂³	1	4	yes	—
216	C₂×#1504	C₂³	1	8	yes	—
217	C₂×#1504	C₂³	1	4	yes	—
218	C₂×#1504	C₂³	1	16	yes	complemented
219	C₂×#1508	C₂³	1	4	yes	complemented
220	C₂×#1507	C₂³	1	4	yes	complemented
221	C₂×#1501	C₂³	1	8	yes	complemented
222	C₂²×#328	C₂³	1	8	yes	complemented
223	C₂²×#327	C₂³	1	8	yes	complemented
224	C₂×#1471	C₂³	1	8	yes	complemented
225	C₂×#1471	C₂³	1	8	yes	complemented
226	C₂×#1468	C₂³	1	16	yes	complemented
227	C₂×#1468	C₂³	1	16	yes	complemented
228	C₂×#1465	C₂³	1	8	yes	complemented
229	C₂×#1463	C₂³	1	4	yes	—
230	C₂×#1462	C₂³	1	4	yes	—
231	C₂×#1462	C₂³	1	8	yes	—
232	C₂×#1462	C₂³	1	16	yes	complemented
233	C₂×#1459	C₂³	1	8	yes	complemented
234	C₂²×#323	C₂³	1	16	yes	complemented
235	#9925	C₂³	1	16	yes	complemented
236	#9924	C₂³	1	16	yes	complemented
237	#9924	C₂³	1	32	yes	complemented
238	#9923	C₂³	1	32	yes	complemented
239	#9923	C₂³	1	16	yes	complemented
240	#9922	C₂³	1	32	yes	complemented
241	#9922	C₂³	1	32	yes	complemented
242	#9922	C₂³	1	32	yes	complemented
243	#9922	C₂³	1	16	yes	complemented
244	#9922	C₂³	1	32	yes	complemented
245	#9917	C₂³	1	16	yes	complemented
246	#9916	C₂³	1	16	yes	complemented
247	#9916	C₂³	1	32	yes	complemented
248	#9915	C₂³	1	32	yes	complemented
249	#9915	C₂³	1	16	yes	complemented
250	#9914	C₂³	1	32	yes	complemented
251	#9914	C₂³	1	32	yes	complemented
252	#9914	C₂³	1	32	yes	complemented
253	#9914	C₂³	1	16	yes	complemented
254	#9914	C₂³	1	32	yes	complemented
255	#8024	C₂³	1	16	yes	complemented
256	#8023	C₂³	1	8	yes	complemented
257	#8020	C₂³	1	4	yes	—
258	#8020	C₂³	1	4	yes	—
259	#8020	C₂³	1	8	yes	—
260	#8020	C₂³	1	16	yes	complemented
261	#8019	C₂³	1	8	yes	complemented
262	#8016	C₂³	1	8	yes	complemented
263	#8015	C₂³	1	16	yes	complemented
264	#8012	C₂³	1	8	yes	complemented
265	C₂×#1294	C₂³	1	16	yes	complemented
266	C₂⁷	C₂×D₄	1	2	yes	—
267	C₂²×2₋¹⁺⁴	C₂×D₄	1	4	yes	complemented
268	C₂²×H(5,𝔽₂)	C₂×D₄	1	64	yes	complemented
269	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
270	C₂³×#41	C₂×D₄	1	1	yes	characteristic
271	C₂³×#41	C₂×D₄	1	1	yes	characteristic
272	C₂³×#41	C₂×D₄	1	8	yes	—
273	C₂³×#41	C₂×D₄	1	4	yes	—
274	C₂³×#41	C₂×D₄	1	2	yes	—
275	C₂³×#41	C₂×D₄	1	1	yes	characteristic
276	C₂³×#41	C₂×D₄	1	8	yes	—
277	C₂³×#41	C₂×D₄	1	2	yes	—
278	C₂³×#41	C₂×D₄	1	1	yes	characteristic
279	C₂³×#41	C₂×D₄	1	4	yes	—
280	C₂³×#41	C₂×D₄	1	8	yes	—
281	C₂³×#41	C₂×D₄	1	4	yes	—
282	C₂³×#41	C₂×D₄	1	8	yes	complemented
283	C₂³×#41	C₂×D₄	1	16	yes	complemented
284	C₂³×#41	C₂×D₄	1	4	yes	complemented
285	C₂³×#41	C₂×D₄	1	2	yes	complemented
286	C₂³×#41	#41	1	8	yes	—
287	C₂³×#41	C₂⁴	1	4	yes	—
288	C₂³×#41	C₂⁴	1	8	yes	—
289	C₂³×#41	C₂⁴	1	4	yes	—
290	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
291	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
292	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂⁴×D₄	C₂×D₄	1	8	yes	—
294	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
295	C₂⁴×D₄	C₂×D₄	1	2	yes	—
296	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂⁴×D₄	C₂×D₄	1	2	yes	—
298	C₂⁴×D₄	C₂×D₄	1	2	yes	—
299	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
300	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
301	C₂⁴×D₄	C₂⁴	1	4	yes	—
302	C₂⁴×D₄	C₂⁴	1	8	yes	—
303	C₂⁴×D₄	C₂⁴	1	2	yes	—
304	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
305	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
306	C₂⁵×C₄	C₂×D₄	1	2	yes	—
307	C₂⁵×C₄	C₂⁴	1	2	yes	—
308	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
309	C₂×#537	C₂×D₄	1	8	yes	complemented
310	C₂×#537	C₂×D₄	1	4	yes	complemented
311	C₂×#537	C₂×D₄	1	4	yes	complemented
312	C₂×#537	C₂×D₄	1	8	yes	complemented
313	C₂×#536	C₂×D₄	1	8	yes	complemented
314	C₂×#536	C₂×D₄	1	4	yes	complemented
315	C₂×#535	C₂×D₄	1	8	yes	complemented
316	C₂×#535	C₂×D₄	1	4	yes	complemented
317	C₂²×#124	C₂×D₄	1	8	yes	—
318	C₂×#525	C₂×D₄	1	8	yes	complemented
319	C₂×#525	C₂×D₄	1	4	yes	complemented
320	C₂×#525	C₂×D₄	1	4	yes	complemented
321	C₂×#525	C₂×D₄	1	8	yes	complemented
322	C₂×#525	C₂⁴	1	4	yes	—
323	C₂×#525	C₂⁴	1	4	yes	—
324	C₂×#525	C₂⁴	1	8	yes	—
325	C₂²×#123	C₂×D₄	1	8	yes	—
326	C₂²×#123	C₂⁴	1	8	yes	—
327	C₂²×C₂²⋊Q₈	C₂×D₄	1	8	yes	—
328	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
329	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	complemented
330	C₂²×C₂²⋊Q₈	C₂⁴	1	4	yes	—
331	C₂²×C₂²⋊Q₈	C₂⁴	1	2	yes	—
332	C₂²×#121	C₂×D₄	1	4	yes	—
333	C₂²×#121	C₂×D₄	1	16	yes	—
334	C₂²×#121	C₂×D₄	1	4	yes	complemented
335	C₂²×#121	C₂×D₄	1	2	yes	complemented
336	C₂²×#121	C₂⁴	1	4	yes	—
337	C₂²×#121	C₂⁴	1	2	yes	—
338	C₂²×#121	C₂⁴	1	4	yes	—
339	C₂²×#120	C₂×D₄	1	16	yes	—
340	C₂×#520	C₂×D₄	1	4	yes	complemented
341	C₂×#520	C₂×D₄	1	4	yes	complemented
342	C₂×#520	C₂×D₄	1	16	yes	complemented
343	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
344	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
345	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
346	C₂²×#117	C₂×D₄	1	4	yes	complemented
347	C₂²×#117	C₂×D₄	1	2	yes	complemented
348	C₂²×#117	C₂×D₄	1	8	yes	complemented
349	C₂²×#117	C₂×D₄	1	4	yes	complemented
350	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
351	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
352	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
353	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
354	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
358	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
359	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
360	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
361	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
362	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
363	C₂×#451	C₂⁴	1	8	yes	—
364	C₂×#448	C₂⁴	1	8	yes	—
365	C₂×#450	C₂⁴	1	16	yes	—
366	C₂×#450	C₂⁴	1	8	yes	—
367	C₂×#447	C₂⁴	1	16	yes	—
368	C₂×#447	C₂⁴	1	8	yes	—
369	#2880	C₂×D₄	1	64	yes	complemented
370	C₂×#407	C₂×D₄	1	32	yes	complemented
371	C₂×#407	C₂×D₄	1	16	yes	complemented
372	C₂×#407	C₂⁴	1	4	yes	—
373	C₂×#407	C₂⁴	1	4	yes	—
374	C₂×#407	C₂⁴	1	8	yes	—
375	C₂×#407	C₂⁴	1	4	yes	—
376	C₂×#407	C₂⁴	1	8	yes	—
377	C₂×#407	C₂⁴	1	4	yes	—
378	C₂²×C₂²⋊C₈	C₂⁴	1	8	yes	—
379	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
380	C₂²×C₂²⋊C₈	C₂⁴	1	8	yes	—
381	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
382	#2627	C₂⁴	1	8	yes	—
383	#2626	C₂⁴	1	8	yes	—
384	#2626	C₂⁴	1	16	yes	—
385	#2618	C₂⁴	1	8	yes	—
386	#2617	C₂⁴	1	8	yes	—
387	#2617	C₂⁴	1	16	yes	—
388	C₂×#395	C₂⁴	1	4	yes	—
389	C₂×#394	C₂⁴	1	8	yes	—
390	C₂×#394	C₂⁴	1	4	yes	—
391	C₂×#393	C₂⁴	1	8	yes	—
392	C₂×#393	C₂⁴	1	4	yes	—
393	C₂×#392	C₂⁴	1	8	yes	—
394	C₂×#392	C₂⁴	1	8	yes	—
395	C₂×#392	C₂⁴	1	8	yes	—
396	C₂×#392	C₂⁴	1	8	yes	—
397	C₂×#392	C₂⁴	1	4	yes	—
398	#2339	C₂×D₄	1	64	yes	complemented
399	#2311	C₂×D₄	1	16	yes	complemented
400	#2311	C₂×D₄	1	32	yes	complemented
401	#2280	C₂×D₄	1	4	yes	complemented
402	#2280	C₂×D₄	1	8	yes	complemented
403	#2280	C₂×D₄	1	4	yes	complemented
404	#2280	C₂×D₄	1	8	yes	complemented
405	#2280	C₂⁴	1	4	yes	—
406	#2280	C₂⁴	1	4	yes	—
407	#2280	C₂⁴	1	8	yes	—
408	C₂×#381	C₂×D₄	1	16	yes	complemented
409	C₂×#381	C₂⁴	1	8	yes	—
410	C₂×#380	C₂×D₄	1	8	yes	complemented
411	C₂×#380	C₂×D₄	1	8	yes	complemented
412	C₂×#380	C₂×D₄	1	4	yes	complemented
413	C₂×#380	C₂⁴	1	4	yes	—
414	C₂×#380	C₂⁴	1	4	yes	—
415	C₂×#380	C₂⁴	1	8	yes	—
416	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
417	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	—
418	C₂²×#95	C₂×D₄	1	16	yes	complemented
419	C₂²×#95	C₂⁴	1	8	yes	—
420	C₂²×#95	C₂⁴	1	1	yes	characteristic
421	C₂²×#95	C₂⁴	1	2	yes	—
422	C₂²×#95	C₂⁴	1	1	yes	characteristic
423	#1787	C₂⁴	1	16	yes	—
424	#1786	C₂⁴	1	32	yes	—
425	#1786	C₂⁴	1	16	yes	—
426	C₂×#328	C₂⁴	1	8	yes	—
427	C₂×#328	C₂⁴	1	16	yes	—
428	C₂×#328	C₂⁴	1	8	yes	—
429	C₂×#327	C₂⁴	1	8	yes	—
430	C₂×#327	C₂⁴	1	16	yes	—
431	C₂×#327	C₂⁴	1	8	yes	—
432	C₂×#324	C₂⁴	1	16	yes	—
433	C₂×#323	C₂⁴	1	16	yes	—
434	C₂×#323	C₂⁴	1	32	yes	—
435	#1294	C₂⁴	1	16	yes	—
436	#1294	C₂⁴	1	32	yes	—
437	#1294	C₂⁴	1	16	yes	—
438	C₂⁶	C₂²×D₄	1	1	yes	characteristic
439	C₂⁶	C₂²×D₄	1	2	yes	—
440	C₂⁶	C₂²×D₄	1	8	yes	—
441	C₂⁶	C₂²×D₄	1	2	yes	—
442	C₂⁶	C₂²×D₄	1	1	yes	characteristic
443	C₂²×#41	#120	1	4	yes	—
444	C₂²×#41	#120	1	4	yes	—
445	C₂²×#41	#120	1	32	yes	—
446	C₂²×#41	#120	1	8	yes	—
447	C₂²×#41	#120	1	4	yes	—
448	C₂²×#41	#120	1	8	yes	—
449	C₂²×#41	#120	1	4	yes	—
450	C₂²×#41	#120	1	8	yes	—
451	C₂²×#41	#120	1	16	yes	—
452	C₂²×#41	#120	1	8	yes	—
453	C₂²×#41	#120	1	32	yes	—
454	C₂²×#41	#121	1	32	yes	—
455	C₂²×#41	#121	1	8	yes	—
456	C₂²×#41	#121	1	8	yes	—
457	C₂²×#41	#121	1	32	yes	—
458	C₂²×#41	#121	1	16	yes	—
459	C₂²×#41	#121	1	8	yes	—
460	C₂²×#41	#121	1	16	yes	—
461	C₂²×#41	#121	1	8	yes	—
462	C₂²×#41	#121	1	32	yes	—
463	C₂²×#41	#127	1	8	yes	—
464	C₂²×#41	#127	1	16	yes	—
465	C₂²×#41	#127	1	8	yes	—
466	C₂²×#41	#127	1	32	yes	—
467	C₂²×#41	C₂²×D₄	1	4	yes	—
468	C₂²×#41	C₂²×D₄	1	16	yes	—
469	C₂²×#41	C₂²×D₄	1	32	yes	—
470	C₂²×#41	C₂²×D₄	1	4	yes	—
471	C₂²×#41	C₂²×D₄	1	4	yes	—
472	C₂²×#41	C₂²×D₄	1	8	yes	—
473	C₂²×#41	C₂²×D₄	1	4	yes	—
474	C₂²×#41	C₂²×D₄	1	16	yes	—
475	C₂²×#41	C₂²×D₄	1	8	yes	—
476	C₂²×#41	C₂²×D₄	1	4	yes	—
477	C₂²×#41	C₂²×D₄	1	16	yes	—
478	C₂²×#41	C₂²×D₄	1	16	yes	—
479	C₂²×#41	C₂²×D₄	1	4	yes	complemented
480	C₂²×#41	C₂²×D₄	1	8	yes	complemented
481	C₂²×#41	C₂×#41	1	16	yes	—
482	C₂³×Q₈	#120	1	1	yes	characteristic
483	C₂³×Q₈	#120	1	1	yes	characteristic
484	C₂³×Q₈	#120	1	2	yes	—
485	C₂³×Q₈	#120	1	8	yes	—
486	C₂³×Q₈	#120	1	4	yes	—
487	C₂³×Q₈	#121	1	8	yes	—
488	C₂³×Q₈	C₂²×D₄	1	4	yes	—
489	C₂³×Q₈	C₂²×D₄	1	4	yes	—
490	C₂³×Q₈	C₂²×D₄	1	4	yes	complemented
491	C₂³×Q₈	C₂²×D₄	1	2	yes	complemented
492	C₂³×Q₈	C₂⁵	1	2	yes	—
493	C₂³×D₄	#120	1	2	yes	—
494	C₂³×D₄	#120	1	2	yes	—
495	C₂³×D₄	#120	1	8	yes	—
496	C₂³×D₄	#120	1	1	yes	characteristic
497	C₂³×D₄	#120	1	4	yes	—
498	C₂³×D₄	#120	1	2	yes	—
499	C₂³×D₄	#120	1	2	yes	—
500	C₂³×D₄	#120	1	16	yes	—
501	C₂³×D₄	#120	1	2	yes	—
502	C₂³×D₄	#120	1	8	yes	—
503	C₂³×D₄	#120	1	1	yes	characteristic
504	C₂³×D₄	#121	1	8	yes	—
505	C₂³×D₄	#121	1	16	yes	—
506	C₂³×D₄	C₂²×D₄	1	4	yes	—
507	C₂³×D₄	C₂²×D₄	1	4	yes	—
508	C₂³×D₄	C₂²×D₄	1	8	yes	—
509	C₂³×D₄	C₂²×D₄	1	4	yes	—
510	C₂³×D₄	C₂²×D₄	1	8	yes	—
511	C₂³×D₄	C₂²×D₄	1	8	yes	—
512	C₂³×D₄	C₂²×D₄	1	4	yes	—
513	C₂³×D₄	C₂²×D₄	1	32	yes	—
514	C₂³×D₄	C₂²×D₄	1	16	yes	—
515	C₂³×D₄	C₂²×D₄	1	8	yes	—
516	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
517	C₂³×D₄	C₂²×D₄	1	2	yes	complemented
518	C₂³×D₄	C₂⁵	1	4	yes	—
519	C₂³×D₄	C₂⁵	1	2	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
522	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
524	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
527	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
529	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
531	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
532	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
533	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
534	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
535	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
536	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
537	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
538	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
539	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
540	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
541	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
542	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
543	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
544	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
545	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
546	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
548	C₂⁴×C₄	C₂×#41	1	8	yes	—
549	C₂⁴×C₄	C₂×#41	1	4	yes	—
550	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
551	C₂⁴×C₄	C₂⁵	1	4	yes	—
552	C₂⁴×C₄	C₂⁵	1	2	yes	—
553	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
554	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	complemented
555	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	complemented
556	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	complemented
557	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	complemented
558	C₂×C₂²⋊Q₈	C₂⁵	1	4	yes	—
559	C₂×#121	C₂²×D₄	1	4	yes	—
560	C₂×#121	C₂²×D₄	1	8	yes	complemented
561	C₂×#121	C₂²×D₄	1	4	yes	complemented
562	C₂×#121	C₂²×D₄	1	8	yes	complemented
563	C₂×#121	C₂²×D₄	1	4	yes	complemented
564	C₂×#121	C₂⁵	1	4	yes	—
565	C₂×#117	C₂²×D₄	1	4	yes	—
566	C₂×#117	C₂²×D₄	1	8	yes	—
567	C₂×#117	C₂²×D₄	1	4	yes	complemented
568	C₂×#117	C₂²×D₄	1	8	yes	complemented
569	C₂×#117	C₂²×D₄	1	8	yes	complemented
570	C₂×#117	C₂²×D₄	1	16	yes	complemented
571	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
572	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	—
573	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
574	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
575	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
576	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	complemented
577	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	complemented
578	C₂²×C₄⋊C₄	C₂²×D₄	1	16	yes	complemented
579	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	complemented
580	C₂²×C₄⋊C₄	C₂⁵	1	2	yes	—
581	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
582	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
583	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
584	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
585	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
586	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
587	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
588	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
589	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
590	C₂²×C₄²	C₂²×D₄	1	4	yes	—
591	#407	C₂²×D₄	1	16	yes	—
592	#407	C₂²×D₄	1	32	yes	complemented
593	#407	C₂²×D₄	1	16	yes	complemented
594	C₂×C₂²⋊C₈	C₂²×D₄	1	32	yes	complemented
595	C₂×C₂²⋊C₈	C₂²×D₄	1	16	yes	complemented
596	C₂×C₂²⋊C₈	C₂⁵	1	8	yes	—
597	C₂×C₂²⋊C₈	C₂⁵	1	8	yes	—
598	#381	C₂²×D₄	1	32	yes	—
599	#380	C₂²×D₄	1	8	yes	—
600	#380	C₂²×D₄	1	16	yes	—
601	#380	C₂²×D₄	1	8	yes	complemented
602	#380	C₂²×D₄	1	8	yes	complemented
603	#380	C₂²×D₄	1	16	yes	complemented
604	#380	C₂²×D₄	1	16	yes	complemented
605	#380	C₂⁵	1	8	yes	—
606	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
607	C₂×#95	C₂²×D₄	1	32	yes	—
608	C₂×#95	C₂²×D₄	1	4	yes	—
609	C₂×#95	C₂²×D₄	1	8	yes	—
610	C₂×#95	C₂²×D₄	1	4	yes	—
611	C₂×#95	C₂⁵	1	2	yes	—
612	C₂×#95	C₂⁵	1	4	yes	—
613	C₂×#95	C₂⁵	1	2	yes	—
614	C₂⁵	C₂×#120	1	4	yes	—
615	C₂⁵	C₂×#120	1	1	yes	characteristic
616	C₂⁵	C₂×#120	1	2	yes	—
617	C₂⁵	C₂×#120	1	8	yes	—
618	C₂⁵	C₂×#120	1	1	yes	characteristic
619	C₂⁵	C₂×#120	1	2	yes	—
620	C₂⁵	C₂×#120	1	4	yes	—
621	C₂⁵	C₂×#120	1	2	yes	—
622	C₂⁵	C₂×#121	1	8	yes	—
623	C₂⁵	C₂×#121	1	4	yes	—
624	C₂⁵	C₂³×D₄	1	1	yes	characteristic
625	C₂⁵	C₂³×D₄	1	4	yes	—
626	C₂⁵	C₂³×D₄	1	4	yes	—
627	C₂⁵	C₂³×D₄	1	2	yes	—
628	C₂⁵	C₂³×D₄	1	2	yes	—
629	C₂×#41	#392	1	32	yes	—
630	C₂×#41	#392	1	32	yes	—
631	C₂×#41	#392	1	64	yes	—
632	C₂×#41	#392	1	32	yes	—
633	C₂×#41	#392	1	64	yes	—
634	C₂×#41	#392	1	32	yes	—
635	C₂×#41	C₂×#120	1	16	yes	—
636	C₂×#41	C₂×#120	1	32	yes	—
637	C₂×#41	C₂×#120	1	16	yes	—
638	C₂×#41	C₂×#121	1	16	yes	—
639	C₂×#41	C₂×#121	1	16	yes	—
640	C₂×#41	C₂×#121	1	32	yes	—
641	C₂×#41	C₂×#121	1	16	yes	—
642	C₂×#41	C₂×#121	1	32	yes	—
643	C₂×#41	C₂×#121	1	16	yes	—
644	C₂×#41	C₂×#127	1	16	yes	—
645	C₂×#41	C₂×#127	1	32	yes	—
646	C₂×#41	C₂×#127	1	16	yes	—
647	C₂²×Q₈	#392	1	8	yes	—
648	C₂²×Q₈	#392	1	8	yes	—
649	C₂²×Q₈	#392	1	16	yes	—
650	C₂²×Q₈	#392	1	32	yes	—
651	C₂²×Q₈	C₂×#120	1	4	yes	—
652	C₂²×Q₈	C₂×#120	1	4	yes	—
653	C₂²×Q₈	C₂×#120	1	8	yes	—
654	C₂²×Q₈	C₂×#120	1	16	yes	—
655	C₂²×Q₈	C₂×#121	1	16	yes	—
656	C₂²×Q₈	C₂³×D₄	1	4	yes	—
657	C₂²×Q₈	C₂³×D₄	1	4	yes	—
658	C₂²×D₄	#392	1	16	yes	—
659	C₂²×D₄	#392	1	8	yes	—
660	C₂²×D₄	#392	1	32	yes	—
661	C₂²×D₄	#392	1	16	yes	—
662	C₂²×D₄	#392	1	16	yes	—
663	C₂²×D₄	#392	1	16	yes	—
664	C₂²×D₄	#392	1	16	yes	—
665	C₂²×D₄	#392	1	64	yes	—
666	C₂²×D₄	#392	1	8	yes	—
667	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
668	C₂²×D₄	C₂×#120	1	16	yes	—
669	C₂²×D₄	C₂×#120	1	8	yes	—
670	C₂²×D₄	C₂×#120	1	8	yes	—
671	C₂²×D₄	C₂×#120	1	8	yes	—
672	C₂²×D₄	C₂×#120	1	4	yes	—
673	C₂²×D₄	C₂×#120	1	8	yes	—
674	C₂²×D₄	C₂×#120	1	8	yes	—
675	C₂²×D₄	C₂×#120	1	32	yes	—
676	C₂²×D₄	C₂×#120	1	4	yes	—
677	C₂²×D₄	C₂×#121	1	16	yes	—
678	C₂²×D₄	C₂×#121	1	32	yes	—
679	C₂²×D₄	C₂³×D₄	1	4	yes	—
680	C₂²×D₄	C₂³×D₄	1	4	yes	—
681	C₂²×D₄	C₂³×D₄	1	8	yes	—
682	C₂³×C₄	C₂×#120	1	2	yes	—
683	C₂³×C₄	C₂×#120	1	4	yes	—
684	C₂³×C₄	C₂×#120	1	2	yes	—
685	C₂³×C₄	C₂×#120	1	4	yes	—
686	C₂³×C₄	C₂×#120	1	4	yes	—
687	C₂³×C₄	C₂×#120	1	2	yes	—
688	C₂³×C₄	C₂×#120	1	1	yes	characteristic
689	C₂³×C₄	C₂×#120	1	2	yes	—
690	C₂³×C₄	C₂×#120	1	2	yes	—
691	C₂³×C₄	C₂×#120	1	8	yes	—
692	C₂³×C₄	C₂×#120	1	4	yes	—
693	C₂³×C₄	C₂×#120	1	4	yes	—
694	C₂³×C₄	C₂×#120	1	8	yes	—
695	C₂³×C₄	C₂×#120	1	4	yes	—
696	C₂³×C₄	C₂×#120	1	4	yes	—
697	C₂³×C₄	C₂×#120	1	16	yes	—
698	C₂³×C₄	C₂×#120	1	2	yes	—
699	C₂³×C₄	C₂×#120	1	2	yes	—
700	C₂³×C₄	C₂×#120	1	8	yes	—
701	C₂³×C₄	C₂×#120	1	16	yes	—
702	C₂³×C₄	C₂×#120	1	8	yes	—
703	C₂³×C₄	C₂×#120	1	8	yes	—
704	C₂³×C₄	C₂×#120	1	4	yes	—
705	C₂³×C₄	C₂×#120	1	1	yes	characteristic
706	C₂³×C₄	C₂×#121	1	4	yes	—
707	C₂³×C₄	C₂×#121	1	8	yes	—
708	C₂³×C₄	C₂×#121	1	8	yes	—
709	C₂³×C₄	C₂×#121	1	4	yes	—
710	C₂³×C₄	C₂×#121	1	4	yes	—
711	C₂³×C₄	C₂×#121	1	8	yes	—
712	C₂³×C₄	C₂×#121	1	16	yes	—
713	C₂³×C₄	C₂×#121	1	8	yes	—
714	C₂³×C₄	C₂×#121	1	16	yes	—
715	C₂³×C₄	C₂×#121	1	16	yes	—
716	C₂³×C₄	C₂×#121	1	8	yes	—
717	C₂³×C₄	C₂×#121	1	8	yes	—
718	C₂³×C₄	C₂×#121	1	8	yes	—
719	C₂³×C₄	C₂×#121	1	8	yes	—
720	C₂³×C₄	C₂×#121	1	4	yes	—
721	C₂³×C₄	C₂×#121	1	4	yes	—
722	C₂³×C₄	C₂×#127	1	8	yes	—
723	C₂³×C₄	C₂×#127	1	4	yes	—
724	C₂³×C₄	C₂×#127	1	16	yes	—
725	C₂³×C₄	C₂×#127	1	8	yes	—
726	C₂³×C₄	C₂×#127	1	8	yes	—
727	C₂³×C₄	C₂×#127	1	4	yes	—
728	C₂³×C₄	C₂³×D₄	1	2	yes	—
729	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
730	C₂³×C₄	C₂³×D₄	1	4	yes	—
731	C₂³×C₄	C₂³×D₄	1	2	yes	—
732	C₂³×C₄	C₂³×D₄	1	4	yes	—
733	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
734	C₂³×C₄	C₂³×D₄	1	2	yes	—
735	C₂³×C₄	C₂³×D₄	1	2	yes	—
736	C₂³×C₄	C₂³×D₄	1	2	yes	—
737	C₂³×C₄	C₂³×D₄	1	4	yes	—
738	C₂³×C₄	C₂³×D₄	1	2	yes	—
739	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
740	C₂³×C₄	C₂³×D₄	1	2	yes	—
741	C₂³×C₄	C₂³×D₄	1	8	yes	—
742	C₂³×C₄	C₂³×D₄	1	4	yes	—
743	C₂³×C₄	C₂³×D₄	1	4	yes	—
744	C₂³×C₄	C₂³×D₄	1	2	yes	—
745	C₂³×C₄	C₂³×D₄	1	2	yes	—
746	C₂³×C₄	C₂³×D₄	1	8	yes	—
747	C₂³×C₄	C₂³×D₄	1	4	yes	—
748	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
749	C₂³×C₄	C₂³×D₄	1	2	yes	—
750	C₂³×C₄	C₂³×D₄	1	4	yes	—
751	C₂³×C₄	C₂³×D₄	1	8	yes	—
752	C₂³×C₄	C₂³×D₄	1	2	yes	—
753	C₂³×C₄	C₂³×D₄	1	4	yes	—
754	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
755	C₂³×C₄	C₂³×D₄	1	4	yes	—
756	C₂³×C₄	C₂²×#41	1	2	yes	—
757	C₂³×C₄	C₂²×#41	1	8	yes	—
758	C₂³×C₄	C₂²×#41	1	4	yes	—
759	C₂³×C₄	C₂⁶	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
761	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
762	C₂×C₄⋊C₄	C₂³×D₄	1	16	yes	—
763	C₂²⋊C₈	C₂³×D₄	1	16	yes	—
764	#95	C₂³×D₄	1	4	yes	—
765	#95	C₂³×D₄	1	8	yes	—
766	#95	C₂³×D₄	1	4	yes	—
767	C₂⁴	C₂×#392	1	16	yes	—
768	C₂⁴	C₂×#392	1	4	yes	—
769	C₂⁴	C₂×#392	1	8	yes	—
770	C₂⁴	C₂×#392	1	8	yes	—
771	C₂⁴	C₂×#392	1	4	yes	—
772	C₂⁴	C₂×#392	1	8	yes	—
773	C₂⁴	C₂×B(4,𝔽₂)	1	16	yes	—
774	C₂⁴	C₂²×#120	1	2	yes	—
775	C₂⁴	C₂²×#120	1	4	yes	—
776	C₂⁴	C₂²×#120	1	2	yes	—
777	C₂⁴	C₂²×#120	1	2	yes	—
778	C₂⁴	C₂²×#120	1	8	yes	—
779	C₂⁴	C₂²×#120	1	1	yes	characteristic
780	C₂⁴	C₂²×#120	1	1	yes	characteristic
781	C₂⁴	C₂²×#120	1	4	yes	—
782	C₂⁴	C₂²×#120	1	4	yes	—
783	C₂⁴	C₂²×#121	1	2	yes	—
784	C₂⁴	C₂²×#121	1	8	yes	—
785	C₂⁴	C₂²×#121	1	4	yes	—
786	C₂⁴	#3585	1	4	yes	complemented
787	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
788	C₂×Q₈	C₂×#392	1	16	yes	—
789	C₂×Q₈	C₂×#392	1	16	yes	—
790	C₂×Q₈	C₂×#392	1	32	yes	—
791	C₂×D₄	#2021	1	64	yes	—
792	C₂×D₄	C₂×#392	1	32	yes	—
793	C₂×D₄	C₂×#392	1	32	yes	—
794	C₂×D₄	C₂×#392	1	16	yes	—
795	C₂×D₄	C₂×#392	1	32	yes	—
796	C₂×D₄	C₂×#392	1	32	yes	—
797	C₂×D₄	C₂×#392	1	32	yes	—
798	C₂×D₄	C₂×#392	1	16	yes	—
799	C₂×D₄	C₂×B(4,𝔽₂)	1	32	yes	—
800	C₂²×C₄	C₂×#392	1	16	yes	—
801	C₂²×C₄	C₂×#392	1	8	yes	—
802	C₂²×C₄	C₂×#392	1	4	yes	—
803	C₂²×C₄	C₂×#392	1	8	yes	—
804	C₂²×C₄	C₂×#392	1	8	yes	—
805	C₂²×C₄	C₂×#392	1	8	yes	—
806	C₂²×C₄	C₂×#392	1	16	yes	—
807	C₂²×C₄	C₂×#392	1	8	yes	—
808	C₂²×C₄	C₂×#392	1	16	yes	—
809	C₂²×C₄	C₂×#392	1	16	yes	—
810	C₂²×C₄	C₂×#392	1	16	yes	—
811	C₂²×C₄	C₂×#392	1	8	yes	—
812	C₂²×C₄	C₂×#392	1	8	yes	—
813	C₂²×C₄	C₂×#392	1	4	yes	—
814	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	—
815	C₂²×C₄	C₂²×#120	1	2	yes	—
816	C₂²×C₄	C₂²×#120	1	8	yes	—
817	C₂²×C₄	C₂²×#120	1	4	yes	—
818	C₂²×C₄	C₂²×#120	1	4	yes	—
819	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
820	C₂²×C₄	C₂²×#120	1	4	yes	—
821	C₂²×C₄	C₂²×#120	1	2	yes	—
822	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
823	C₂²×C₄	C₂²×#120	1	4	yes	—
824	C₂²×C₄	C₂²×#120	1	2	yes	—
825	C₂²×C₄	C₂²×#120	1	8	yes	—
826	C₂²×C₄	C₂²×#120	1	4	yes	—
827	C₂²×C₄	C₂²×#120	1	2	yes	—
828	C₂²×C₄	C₂²×#120	1	8	yes	—
829	C₂²×C₄	C₂²×#120	1	2	yes	—
830	C₂²×C₄	C₂²×#121	1	2	yes	—
831	C₂²×C₄	C₂²×#121	1	2	yes	—
832	C₂²×C₄	C₂²×#121	1	8	yes	—
833	C₂²×C₄	C₂²×#121	1	8	yes	—
834	C₂²×C₄	C₂²×#121	1	4	yes	—
835	C₂²×C₄	C₂²×#121	1	4	yes	—
836	C₂²×C₄	C₂²×#121	1	4	yes	—
837	C₂²×C₄	C₂²×#121	1	2	yes	—
838	C₂²×C₄	C₂²×#121	1	2	yes	—
839	C₂²×C₄	C₂²×#121	1	8	yes	—
840	C₂²×C₄	C₂²×#121	1	8	yes	—
841	C₂²×C₄	C₂²×#121	1	4	yes	—
842	C₂²×C₄	C₂²×#121	1	4	yes	—
843	C₂²×C₄	C₂²×#121	1	2	yes	—
844	C₂²×C₄	C₂²×#121	1	8	yes	—
845	C₂²×C₄	C₂²×#127	1	8	yes	—
846	C₂²×C₄	C₂²×#127	1	2	yes	—
847	C₂²×C₄	C₂²×#127	1	4	yes	—
848	C₂²×C₄	C₂²×#127	1	2	yes	—
849	C₂²×C₄	C₂²×#127	1	8	yes	—
850	C₂²×C₄	C₂²×#127	1	4	yes	—
851	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂³×#41	1	1	yes	characteristic
857	C₂³	C₂×#2021	1	32	yes	—
858	C₂³	C₂²×#392	1	8	yes	—
859	C₂³	C₂²×#392	1	4	yes	—
860	C₂³	C₂²×#392	1	4	yes	—
861	C₂³	C₂²×#392	1	2	yes	—
862	C₂³	C₂²×#392	1	8	yes	—
863	C₂³	C₂²×#392	1	2	yes	—
864	C₂³	#60388	1	4	yes	—
865	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
866	C₂³	C₂²×B(4,𝔽₂)	1	16	yes	—
867	C₂³	C₂³×#120	1	1	yes	characteristic
868	C₂³	C₂³×#120	1	1	yes	characteristic
869	C₂³	C₂³×#121	1	1	yes	characteristic
870	C₂³	C₂×#3585	1	2	yes	—
871	C₂³	#63090	1	2	yes	—
872	D₄	C₂×#2021	1	64	yes	—
873	C₂×C₄	C₂×#2021	1	16	yes	—
874	C₂×C₄	C₂²×#392	1	2	yes	—
875	C₂×C₄	C₂²×#392	1	8	yes	—
876	C₂×C₄	C₂²×#392	1	4	yes	—
877	C₂×C₄	C₂²×#392	1	8	yes	—
878	C₂×C₄	C₂²×#392	1	2	yes	—
879	C₂×C₄	C₂²×#392	1	4	yes	—
880	C₂×C₄	C₂²×B(4,𝔽₂)	1	8	yes	—
881	C₂×C₄	C₂³×#120	1	1	yes	characteristic
882	C₂×C₄	C₂³×#121	1	1	yes	characteristic
883	C₂×C₄	C₂³×#121	1	1	yes	characteristic
884	C₂×C₄	C₂³×#127	1	1	yes	characteristic
885	C₂²	#6431723	1	4	yes	—
886	C₂²	C₂²×#2021	1	4	yes	—
887	C₂²	C₂²×#2021	1	16	yes	—
888	C₂²	C₂³×#392	1	1	yes	characteristic
889	C₂²	C₂×#60388	1	2	yes	—
890	C₂²	#10574840	1	1	yes	characteristic
891	C₂²	#10574842	1	1	yes	characteristic
892	C₂²	#10574845	1	2	yes	—
893	C₂²	C₂³×B(4,𝔽₂)	1	2	yes	—
894	C₂²	#10574920	1	2	yes	—
895	C₄	C₂²×#2021	1	8	yes	—
896	C₂	C₂³×#2021	1	1	yes	characteristic
897	C₂	#72260479	1	4	yes	—
898	C₂	C₂×#6431723	1	1	yes	characteristic
899	C₂	#72260873	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×#120
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×#41 ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261797	C₂	semidirect
2. #72261773	C₂	semidirect
3. #72261762	C₂	semidirect
4. #72261660	C₂	semidirect
5. C₂×#6343491	C₂	semidirect
6. #72260872	C₂	semidirect
7. #72256539	C₂	semidirect
8. #72235226	C₂	semidirect
9. #72235220	C₂	semidirect
10. #72235217	C₂	semidirect
11. C₂×#6342764	C₂	semidirect
12. C₂×#234591	C₂	semidirect
13. #72233872	C₂	semidirect
14. C₂×#10574840	C₂	semidirect
15. #72231702	C₂	semidirect
16. #72231671	C₂	semidirect
17. C₂²×#35680	C₂	semidirect
21. C₂×#60373	C₂²	semidirect
22. C₂×#60372	C₂²	semidirect
23. C₂×#60359	C₂²	semidirect
24. C₂×#60359	C₂²	semidirect
25. C₂²×#3003	C₂²	semidirect
26. C₂²×#3003	C₂²	semidirect
29. #7656808	C₂²	semidirect
30. #7656741	C₂²	semidirect
31. #7641875	C₂²	semidirect
32. #7641850	C₂²	semidirect
33. C₂×#35680	C₂²	semidirect
34. #7628282	C₂²	semidirect
35. C₂×#35050	C₂²	semidirect
36. C₂²×#2430	C₂²	semidirect
37. C₂²×#2404	C₂²	semidirect
38. C₂²×#2433	C₂²	semidirect
39. C₂²×#2408	C₂²	semidirect
40. C₂²×#2615	C₂²	semidirect
41. C₂²×#2613	C₂²	semidirect
42. C₂²×#2388	C₂²	semidirect
43. C₂³×#392	C₂²	semidirect
46. #6370722	C₂²	semidirect
47. #6370715	C₂²	semidirect
48. #6370715	C₂²	semidirect
49. C₂×#20598	C₂²	semidirect
50. C₂×#20598	C₂²	semidirect
51. C₂×#17608	C₂²	semidirect
52. C₂×#17603	C₂²	semidirect
53. C₂×#17592	C₂²	semidirect
54. C₂×#17587	C₂²	semidirect
55. C₂×#17542	C₂²	semidirect
56. C₂²×#1504	C₂²	semidirect
57. C₂×#17411	C₂²	semidirect
58. C₂×#17396	C₂²	semidirect
59. C₂×#17392	C₂²	semidirect
60. C₂×#17362	C₂²	semidirect
61. C₂²×#1462	C₂²	semidirect
62. #234615	C₂²	semidirect
63. #234612	C₂²	semidirect
64. #234611	C₂²	semidirect
65. #234594	C₂²	semidirect
66. #234593	C₂²	semidirect
67. #234593	C₂²	semidirect
68. #234592	C₂²	semidirect
69. #234592	C₂²	semidirect
70. #234591	C₂²	semidirect
71. #234591	C₂²	semidirect
72. #234591	C₂²	semidirect
73. #234591	C₂²	semidirect
74. #234591	C₂²	semidirect
75. #234591	C₂²	semidirect
76. #234590	C₂²	semidirect
77. #234589	C₂²	semidirect
78. #234569	C₂²	semidirect
79. #234568	C₂²	semidirect
80. #234567	C₂²	semidirect
81. #234551	C₂²	semidirect
82. #234548	C₂²	semidirect
83. #234547	C₂²	semidirect
84. #234529	C₂²	semidirect
85. #234522	C₂²	semidirect
86. #234521	C₂²	semidirect
87. #234503	C₂²	semidirect
88. #234500	C₂²	semidirect
89. #234499	C₂²	semidirect
90. #234481	C₂²	semidirect
91. #234478	C₂²	semidirect
92. #234477	C₂²	semidirect
93. #234459	C₂²	semidirect
94. C₂×#9922	C₂²	semidirect
95. C₂×#9914	C₂²	semidirect
96. #181744	C₂²	semidirect
97. #181740	C₂²	semidirect
98. #181528	C₂²	semidirect
99. #181500	C₂²	semidirect
100. C₂×#8020	C₂²	semidirect
101. C₂²×#585	D₄	semidirect
102. C₂³×H(5,𝔽₂)	D₄	semidirect
110. C₂×#3489	D₄	semidirect
112. C₂×#3488	D₄	semidirect
116. C₂×#3449	D₄	semidirect
117. C₂×#3449	D₄	semidirect
126. C₂×#3428	D₄	semidirect
127. C₂×#3428	D₄	semidirect
131. C₂×#3007	C₂³	semidirect
132. C₂×#3007	C₂³	semidirect
133. C₂×#3006	C₂³	semidirect
134. C₂×#3006	C₂³	semidirect
138. C₂×#3003	C₂³	semidirect
139. C₂×#3003	C₂³	semidirect
140. C₂×#3002	C₂³	semidirect
141. C₂×#3002	C₂³	semidirect
142. C₂²×#450	C₂³	semidirect
143. C₂²×#450	C₂³	semidirect
144. C₂²×#447	C₂³	semidirect
145. C₂²×#447	C₂³	semidirect
146. #60064	D₄	semidirect
153. #37452	C₂³	semidirect
154. #37451	C₂³	semidirect
155. #37450	C₂³	semidirect
156. #37441	C₂³	semidirect
157. #37440	C₂³	semidirect
158. #37439	C₂³	semidirect
162. #35050	C₂³	semidirect
163. #35010	C₂³	semidirect
164. #35000	C₂³	semidirect
170. #34562	C₂³	semidirect
171. C₂×#2626	C₂³	semidirect
172. C₂×#2617	C₂³	semidirect
186. #34175	D₄	semidirect
188. C₂×#2339	D₄	semidirect
190. #34044	D₄	semidirect
191. #34044	D₄	semidirect
198. #20601	C₂³	semidirect
199. #20601	C₂³	semidirect
203. #20598	C₂³	semidirect
204. #20598	C₂³	semidirect
205. #20597	C₂³	semidirect
206. #20597	C₂³	semidirect
207. C₂×#1786	C₂³	semidirect
208. C₂×#1786	C₂³	semidirect
209. C₂×#1516	C₂³	semidirect
210. C₂×#1520	C₂³	semidirect
211. C₂×#1519	C₂³	semidirect
212. C₂×#1513	C₂³	semidirect
213. C₂×#1511	C₂³	semidirect
214. C₂×#1510	C₂³	semidirect
218. C₂×#1504	C₂³	semidirect
219. C₂×#1508	C₂³	semidirect
220. C₂×#1507	C₂³	semidirect
221. C₂×#1501	C₂³	semidirect
222. C₂²×#328	C₂³	semidirect
223. C₂²×#327	C₂³	semidirect
224. C₂×#1471	C₂³	semidirect
225. C₂×#1471	C₂³	semidirect
226. C₂×#1468	C₂³	semidirect
227. C₂×#1468	C₂³	semidirect
228. C₂×#1465	C₂³	semidirect
232. C₂×#1462	C₂³	semidirect
233. C₂×#1459	C₂³	semidirect
234. C₂²×#323	C₂³	semidirect
235. #9925	C₂³	semidirect
236. #9924	C₂³	semidirect
237. #9924	C₂³	semidirect
238. #9923	C₂³	semidirect
239. #9923	C₂³	semidirect
240. #9922	C₂³	semidirect
241. #9922	C₂³	semidirect
242. #9922	C₂³	semidirect
243. #9922	C₂³	semidirect
244. #9922	C₂³	semidirect
245. #9917	C₂³	semidirect
246. #9916	C₂³	semidirect
247. #9916	C₂³	semidirect
248. #9915	C₂³	semidirect
249. #9915	C₂³	semidirect
250. #9914	C₂³	semidirect
251. #9914	C₂³	semidirect
252. #9914	C₂³	semidirect
253. #9914	C₂³	semidirect
254. #9914	C₂³	semidirect
255. #8024	C₂³	semidirect
256. #8023	C₂³	semidirect
260. #8020	C₂³	semidirect
261. #8019	C₂³	semidirect
262. #8016	C₂³	semidirect
263. #8015	C₂³	semidirect
264. #8012	C₂³	semidirect
265. C₂×#1294	C₂³	semidirect
267. C₂²×2₋¹⁺⁴	C₂×D₄	semidirect
268. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
269. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
282. C₂³×#41	C₂×D₄	semidirect
283. C₂³×#41	C₂×D₄	semidirect
284. C₂³×#41	C₂×D₄	semidirect
285. C₂³×#41	C₂×D₄	semidirect
299. C₂⁴×D₄	C₂×D₄	semidirect
300. C₂⁴×D₄	C₂×D₄	semidirect
309. C₂×#537	C₂×D₄	semidirect
310. C₂×#537	C₂×D₄	semidirect
311. C₂×#537	C₂×D₄	semidirect
312. C₂×#537	C₂×D₄	semidirect
313. C₂×#536	C₂×D₄	semidirect
314. C₂×#536	C₂×D₄	semidirect
315. C₂×#535	C₂×D₄	semidirect
316. C₂×#535	C₂×D₄	semidirect
318. C₂×#525	C₂×D₄	semidirect
319. C₂×#525	C₂×D₄	semidirect
320. C₂×#525	C₂×D₄	semidirect
321. C₂×#525	C₂×D₄	semidirect
328. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
329. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
334. C₂²×#121	C₂×D₄	semidirect
335. C₂²×#121	C₂×D₄	semidirect
340. C₂×#520	C₂×D₄	semidirect
341. C₂×#520	C₂×D₄	semidirect
342. C₂×#520	C₂×D₄	semidirect
346. C₂²×#117	C₂×D₄	semidirect
347. C₂²×#117	C₂×D₄	semidirect
348. C₂²×#117	C₂×D₄	semidirect
349. C₂²×#117	C₂×D₄	semidirect
369. #2880	C₂×D₄	semidirect
370. C₂×#407	C₂×D₄	semidirect
371. C₂×#407	C₂×D₄	semidirect
398. #2339	C₂×D₄	semidirect
399. #2311	C₂×D₄	semidirect
400. #2311	C₂×D₄	semidirect
401. #2280	C₂×D₄	semidirect
402. #2280	C₂×D₄	semidirect
403. #2280	C₂×D₄	semidirect
404. #2280	C₂×D₄	semidirect
408. C₂×#381	C₂×D₄	semidirect
410. C₂×#380	C₂×D₄	semidirect
411. C₂×#380	C₂×D₄	semidirect
412. C₂×#380	C₂×D₄	semidirect
416. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
418. C₂²×#95	C₂×D₄	semidirect
479. C₂²×#41	C₂²×D₄	semidirect
480. C₂²×#41	C₂²×D₄	semidirect
490. C₂³×Q₈	C₂²×D₄	semidirect
491. C₂³×Q₈	C₂²×D₄	semidirect
516. C₂³×D₄	C₂²×D₄	semidirect
517. C₂³×D₄	C₂²×D₄	semidirect
554. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
555. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
556. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
557. C₂×C₂²⋊Q₈	C₂²×D₄	semidirect
560. C₂×#121	C₂²×D₄	semidirect
561. C₂×#121	C₂²×D₄	semidirect
562. C₂×#121	C₂²×D₄	semidirect
563. C₂×#121	C₂²×D₄	semidirect
567. C₂×#117	C₂²×D₄	semidirect
568. C₂×#117	C₂²×D₄	semidirect
569. C₂×#117	C₂²×D₄	semidirect
570. C₂×#117	C₂²×D₄	semidirect
574. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
575. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
576. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
577. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
578. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
579. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
592. #407	C₂²×D₄	semidirect
593. #407	C₂²×D₄	semidirect
594. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
595. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
601. #380	C₂²×D₄	semidirect
602. #380	C₂²×D₄	semidirect
603. #380	C₂²×D₄	semidirect
604. #380	C₂²×D₄	semidirect
786. C₂⁴	#3585	semidirect

Maximal subgroups

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

subgroup	index
#72261797	2
#72261773	2
#72261762	2
#72261660	2
C₂×#6343491	2
#72260872	2
#72256539	2
#72235226	2
#72235220	2
#72235217	2
C₂×#6342764	2
C₂×#234591	2
#72233872	2
C₂×#10574840	2
#72231702	2
#72231671	2
C₂²×#35680	2