Subgroups — #72260676

Order 2048.

At least 8801 conjugacy classes of subgroups; only the 1584 normal subgroups are shown.

The subgroup lattice has 750 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72260562	C₂	1	2	yes	maximal, complemented
2	#72260517	C₂	1	4	yes	maximal, complemented
3	#72260398	C₂	1	4	yes	maximal, complemented
4	#72260376	C₂	1	4	yes	maximal, complemented
5	#72252021	C₂	1	2	yes	maximal, complemented
6	#72240132	C₂	1	2	yes	maximal, complemented
7	C₂×#139718	C₂	1	2	yes	maximal, complemented
8	#72235246	C₂	1	2	yes	maximal, complemented
9	#72234663	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233654	C₂	1	1	yes	maximal, characteristic, complemented
11	#72232743	C₂	1	4	yes	maximal, complemented
12	#72225786	C₂	1	2	yes	maximal, complemented
13	#72215608	C₂	1	1	yes	maximal, characteristic
14	C₂²×#3498	C₂²	1	1	yes	characteristic
15	C₂²×#3484	C₂²	1	1	yes	characteristic
16	C₂×#35680	C₄	1	2	yes	complemented
17	#6385972	C₂²	1	4	yes	complemented
18	#6385971	C₂²	1	4	yes	complemented
19	#6374251	C₂²	1	2	yes	complemented
20	C₂×#21746	C₂²	1	2	yes	complemented
21	#6370693	C₂²	1	2	yes	—
22	#6370693	C₂²	1	2	yes	—
23	#763336	C₄	1	1	yes	characteristic, complemented
24	#763333	C₄	1	1	yes	characteristic, complemented
25	#763333	C₂²	1	1	yes	characteristic
26	#686207	C₂²	1	2	yes	—
27	#686202	C₄	1	2	yes	complemented
28	#686202	C₂²	1	2	yes	—
29	#649038	C₂²	1	2	yes	—
30	#649035	C₄	1	2	yes	complemented
31	#649035	C₂²	1	2	yes	—
32	#617715	C₄	1	1	yes	characteristic, complemented
33	#617710	C₄	1	1	yes	characteristic, complemented
34	#617710	C₂²	1	1	yes	characteristic
35	#616967	C₄	1	1	yes	characteristic, complemented
36	#616961	C₄	1	1	yes	characteristic, complemented
37	#616961	C₂²	1	1	yes	characteristic
38	#608791	C₄	1	1	yes	characteristic, complemented
39	C₂×#15258	C₄	1	1	yes	characteristic, complemented
40	C₂×#15258	C₂²	1	1	yes	characteristic
41	#518972	C₄	1	2	yes	complemented
42	#517592	C₂²	1	1	yes	characteristic
43	#493372	C₂²	1	4	yes	complemented
44	#493370	C₂²	1	4	yes	complemented
45	#493370	C₂²	1	4	yes	complemented
46	#493365	C₂²	1	4	yes	complemented
47	C₂×#12693	C₂²	1	4	yes	complemented
48	C₂×#12693	C₂²	1	4	yes	complemented
49	#188049	C₂²	1	2	yes	complemented
50	#188037	C₂²	1	4	yes	complemented
51	#188035	C₂²	1	4	yes	complemented
52	C₂×#8541	C₂²	1	2	yes	complemented
53	#139795	C₂²	1	8	yes	complemented
54	#139794	C₂²	1	8	yes	complemented
55	#139794	C₂²	1	8	yes	complemented
56	#139794	C₂²	1	8	yes	complemented
57	#139720	C₂²	1	8	yes	complemented
58	#139718	C₂²	1	8	yes	complemented
59	#139718	C₂²	1	8	yes	complemented
60	#139718	C₂²	1	8	yes	complemented
61	#128058	C₂²	1	8	yes	complemented
62	#128057	C₂²	1	8	yes	complemented
63	#128009	C₂²	1	4	yes	complemented
64	C₂×#7307	C₂²	1	4	yes	complemented
65	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
67	C₂⁵×D₄	D₄	1	1	yes	characteristic
68	C₂²×#546	C₂×C₄	1	2	yes	—
69	C₂²×#546	C₂×C₄	1	2	yes	—
70	C₂²×#546	D₄	1	2	yes	—
71	C₂²×#546	C₂³	1	2	yes	—
72	C₂²×D₄²	D₄	1	2	yes	—
73	C₂²×D₄²	D₄	1	2	yes	—
74	C₂²×D₄²	D₄	1	2	yes	—
75	C₂²×D₄²	C₂³	1	2	yes	—
76	C₂²×#535	C₂×C₄	1	1	yes	characteristic
77	C₂²×#535	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂²×#535	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂²×#535	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂²×#535	D₄	1	1	yes	characteristic
81	C₂²×#535	C₂³	1	1	yes	characteristic
82	C₂²×#535	C₂³	1	1	yes	characteristic
83	C₂²×#535	C₂³	1	1	yes	characteristic
84	C₂²×#534	C₂×C₄	1	1	yes	characteristic
85	C₂²×#534	D₄	1	1	yes	characteristic
86	C₂²×#534	D₄	1	1	yes	characteristic
87	C₂²×#534	C₂³	1	1	yes	characteristic
88	C₂²×#532	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂²×#532	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂²×#532	C₂³	1	1	yes	characteristic
91	C₂³×#127	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂³×#127	C₂³	1	1	yes	characteristic
93	C₂³×#127	C₂³	1	1	yes	characteristic
94	C₂²×#525	C₂×C₄	1	1	yes	characteristic
95	C₂²×#525	D₄	1	1	yes	characteristic
96	C₂³×#120	C₂×C₄	1	1	yes	characteristic
97	C₂³×#120	D₄	1	1	yes	characteristic
98	C₂³×#120	D₄	1	1	yes	characteristic
99	C₂³×#120	C₂³	1	1	yes	characteristic
100	C₂²×#518	D₄	1	1	yes	characteristic
101	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂×#2883	D₄	1	4	yes	complemented
103	C₂×#2430	C₂×C₄	1	2	yes	complemented
104	C₂×#2430	C₂×C₄	1	2	yes	complemented
105	C₂×#2404	C₂×C₄	1	2	yes	complemented
106	C₂×#2404	C₂×C₄	1	2	yes	complemented
107	C₂×#2433	C₂×C₄	1	2	yes	complemented
108	C₂×#2408	C₂×C₄	1	2	yes	complemented
109	C₂×#2615	C₂×C₄	1	2	yes	complemented
110	C₂×#2613	C₂×C₄	1	2	yes	complemented
111	C₂×#2613	C₂×C₄	1	2	yes	complemented
112	C₂×#2388	C₂×C₄	1	2	yes	complemented
113	C₂²×#392	C₂×C₄	1	2	yes	complemented
114	C₂²×#392	C₂×C₄	1	2	yes	complemented
115	C₂×#2339	C₂×C₄	1	2	yes	complemented
116	#21793	C₂³	1	8	yes	—
117	#21746	C₂³	1	8	yes	—
118	#20586	D₄	1	4	yes	complemented
119	#20585	D₄	1	4	yes	complemented
120	#20585	D₄	1	4	yes	complemented
121	#20584	C₂³	1	4	yes	—
122	#20584	C₂³	1	4	yes	—
123	C₂×#1781	C₂³	1	4	yes	—
124	C₂×#1781	C₂³	1	4	yes	—
125	C₂×#1781	C₂³	1	4	yes	—
126	C₂×#1781	C₂³	1	4	yes	—
127	#15763	C₂×C₄	1	2	yes	complemented
128	#15763	C₂×C₄	1	2	yes	complemented
129	#15763	C₂×C₄	1	2	yes	complemented
130	#15761	C₂×C₄	1	2	yes	complemented
131	#15673	C₂×C₄	1	2	yes	complemented
132	#15673	C₂³	1	2	yes	—
133	#15310	C₂×C₄	1	2	yes	complemented
134	#15310	C₂×C₄	1	2	yes	complemented
135	#15310	C₂×C₄	1	2	yes	complemented
136	#15310	C₂³	1	2	yes	—
137	#15310	C₂³	1	2	yes	—
138	#15310	C₂³	1	2	yes	—
139	#15265	C₂×C₄	1	2	yes	complemented
140	#15264	C₂×C₄	1	2	yes	complemented
141	#15264	C₂×C₄	1	2	yes	complemented
142	#15264	C₂×C₄	1	2	yes	complemented
143	#15262	C₂×C₄	1	1	yes	characteristic, complemented
144	#15261	C₂×C₄	1	1	yes	characteristic, complemented
145	#15261	C₂×C₄	1	1	yes	characteristic, complemented
146	#15261	C₂×C₄	1	1	yes	characteristic, complemented
147	#15259	C₂×C₄	1	1	yes	characteristic, complemented
148	#15259	C₂×C₄	1	1	yes	characteristic, complemented
149	#15259	C₂×C₄	1	2	yes	complemented
150	#15259	C₂×C₄	1	1	yes	characteristic, complemented
151	#15259	C₂³	1	2	yes	—
152	#15258	C₂×C₄	1	1	yes	characteristic, complemented
153	#15258	C₂×C₄	1	1	yes	characteristic, complemented
154	#15258	C₂×C₄	1	1	yes	characteristic, complemented
155	#15258	C₂×C₄	1	1	yes	characteristic, complemented
156	#15258	C₂×C₄	1	1	yes	characteristic, complemented
157	#15258	C₂×C₄	1	1	yes	characteristic, complemented
158	#15258	C₂×C₄	1	2	yes	complemented
159	#15258	C₂×C₄	1	2	yes	complemented
160	#15258	C₂×C₄	1	2	yes	complemented
161	#15258	C₂×C₄	1	1	yes	characteristic, complemented
162	#15258	C₂×C₄	1	1	yes	characteristic, complemented
163	#15258	C₂×C₄	1	1	yes	characteristic, complemented
164	#15258	C₂³	1	2	yes	—
165	#15258	C₂³	1	2	yes	—
166	#15258	C₂³	1	2	yes	—
167	#14706	C₂×C₄	1	2	yes	complemented
168	#14706	C₂×C₄	1	2	yes	complemented
169	#14698	C₂×C₄	1	2	yes	complemented
170	#14337	C₂×C₄	1	1	yes	characteristic, complemented
171	#14335	C₂×C₄	1	1	yes	characteristic, complemented
172	#14335	C₂³	1	1	yes	characteristic
173	#14136	C₂×C₄	1	2	yes	complemented
174	#14135	C₂×C₄	1	2	yes	complemented
175	#14135	C₂×C₄	1	2	yes	complemented
176	#13956	C₂×C₄	1	2	yes	complemented
177	#13956	C₂³	1	2	yes	—
178	#13902	C₂³	1	2	yes	—
179	#13871	C₂×C₄	1	2	yes	complemented
180	#13868	C₂×C₄	1	2	yes	complemented
181	#13868	C₂×C₄	1	2	yes	complemented
182	#13851	C₂×C₄	1	1	yes	characteristic, complemented
183	C₂×#1438	C₂×C₄	1	1	yes	characteristic, complemented
184	C₂×#1438	C₂³	1	1	yes	characteristic
185	C₄×#386	C₂×C₄	1	2	yes	complemented
186	C₂×#1437	C₂×C₄	1	2	yes	complemented
187	C₂×#1437	C₂×C₄	1	2	yes	complemented
188	#12694	C₂³	1	8	yes	complemented
189	#12693	C₂³	1	8	yes	complemented
190	#12693	C₂³	1	8	yes	complemented
191	#12693	C₂³	1	8	yes	complemented
192	#8542	C₂³	1	8	yes	—
193	#8541	C₂³	1	8	yes	—
194	#7307	C₂³	1	16	yes	complemented
195	#7307	C₂³	1	16	yes	complemented
196	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
197	C₂⁷	C₂×D₄	1	1	yes	characteristic
198	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
199	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
200	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
201	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
202	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
203	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
204	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
205	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
206	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
207	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
208	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
209	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
210	C₂³×#41	C₂²×C₄	1	1	yes	characteristic, complemented
211	C₂³×#41	C₂²×C₄	1	1	yes	characteristic, complemented
212	C₂³×#41	C₂×D₄	1	1	yes	characteristic
213	C₂³×#41	C₂×D₄	1	1	yes	characteristic
214	C₂³×#41	C₂⁴	1	1	yes	characteristic
215	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
216	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
217	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
218	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
219	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
220	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
221	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
222	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
223	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
224	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×D₄	C₂×D₄	1	2	yes	—
226	C₂⁴×D₄	C₂×D₄	1	2	yes	—
227	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
228	C₂⁴×D₄	C₂×D₄	1	2	yes	—
229	C₂⁴×D₄	C₂×D₄	1	2	yes	—
230	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
231	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
232	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
233	C₂⁴×D₄	C₂×D₄	1	2	yes	—
234	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
235	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
236	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
237	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
238	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
240	C₂²×#127	C₂²⋊C₄	1	2	yes	—
241	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
242	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
243	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
244	C₂²×#127	C₂²×C₄	1	1	yes	characteristic, complemented
245	C₂²×#127	C₂²×C₄	1	1	yes	characteristic, complemented
246	C₂²×#127	C₂²×C₄	1	1	yes	characteristic, complemented
247	C₂²×#127	C₂×D₄	1	2	yes	—
248	C₂²×#127	C₂⁴	1	1	yes	characteristic
249	C₂²×#127	C₂⁴	1	1	yes	characteristic
250	C₂²×#127	C₂⁴	1	1	yes	characteristic
251	C₂²×#124	C₂²⋊C₄	1	2	yes	—
252	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
253	C₂²×#124	C₂²×C₄	1	2	yes	—
254	C₂²×#124	C₂²×C₄	1	1	yes	characteristic, complemented
255	C₂²×#124	C₂²×C₄	1	1	yes	characteristic, complemented
256	C₂²×#124	C₂²×C₄	1	1	yes	characteristic, complemented
257	C₂²×#124	C₂²×C₄	1	1	yes	characteristic, complemented
258	C₂²×#124	C₂⁴	1	1	yes	characteristic
259	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×#123	C₂²⋊C₄	1	2	yes	—
262	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
263	C₂²×#123	C₂²×C₄	1	2	yes	—
264	C₂²×#123	C₂²×C₄	1	2	yes	—
265	C₂²×#123	C₂×D₄	1	2	yes	—
266	C₂²×#123	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	2	yes	—
268	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
269	C₂²×#121	C₂²⋊C₄	1	2	yes	—
270	C₂²×#121	C₂²⋊C₄	1	2	yes	—
271	C₂²×#121	C₂²⋊C₄	1	2	yes	—
272	C₂²×#121	C₂²⋊C₄	1	2	yes	—
273	C₂²×#121	C₂²⋊C₄	1	2	yes	—
274	C₂²×#121	C₂²⋊C₄	1	2	yes	—
275	C₂²×#121	C₂²⋊C₄	1	2	yes	—
276	C₂²×#121	C₂²×C₄	1	2	yes	—
277	C₂²×#121	C₂²×C₄	1	2	yes	—
278	C₂²×#121	C₂×D₄	1	2	yes	—
279	C₂²×#121	C₂×D₄	1	2	yes	—
280	C₂²×#121	C₂×D₄	1	2	yes	—
281	C₂²×#121	C₂×D₄	1	2	yes	—
282	C₂²×#121	C₂⁴	1	2	yes	—
283	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×#120	C₂²⋊C₄	1	2	yes	—
286	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×#120	C₂²⋊C₄	1	2	yes	—
289	C₂²×#120	C₂²⋊C₄	1	2	yes	—
290	C₂²×#120	C₂²⋊C₄	1	2	yes	—
291	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×#120	C₂²⋊C₄	1	2	yes	—
293	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
295	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
296	C₂²×#120	C₂²×C₄	1	2	yes	—
297	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
298	C₂²×#120	C₂×D₄	1	2	yes	—
299	C₂²×#120	C₂×D₄	1	1	yes	characteristic
300	C₂²×#120	C₂×D₄	1	1	yes	characteristic
301	C₂²×#120	C₂×D₄	1	1	yes	characteristic
302	C₂²×#120	C₂×D₄	1	2	yes	—
303	C₂²×#120	C₂×D₄	1	2	yes	—
304	C₂²×#120	C₂×D₄	1	2	yes	—
305	C₂²×#120	C₂×D₄	1	2	yes	—
306	C₂²×#120	C₂⁴	1	2	yes	—
307	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
308	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
309	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
310	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
311	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
313	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
314	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
315	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
318	C₂²×#117	C₂²×C₄	1	1	yes	characteristic, complemented
319	C₂²×#117	C₂²×C₄	1	1	yes	characteristic, complemented
320	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
323	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
324	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
325	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
326	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
327	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
329	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic, complemented
330	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic, complemented
331	C₂×#410	C₂×D₄	1	8	yes	complemented
332	C₂²×#99	C₂×D₄	1	8	yes	complemented
333	C₂²×#99	C₂×D₄	1	8	yes	complemented
334	C₂×#395	C₂²×C₄	1	2	yes	complemented
335	C₂×#394	C₂²×C₄	1	2	yes	complemented
336	C₂×#394	C₂²×C₄	1	2	yes	complemented
337	C₂×#394	C₂²×C₄	1	2	yes	complemented
338	C₂×#393	C₂²×C₄	1	2	yes	—
339	C₂×#393	C₂²×C₄	1	2	yes	—
340	C₂×#393	C₂²×C₄	1	2	yes	complemented
341	C₂×#392	C₂²×C₄	1	2	yes	—
342	C₂×#392	C₂²×C₄	1	2	yes	—
343	C₂×#392	C₂²×C₄	1	2	yes	—
344	C₂×#392	C₂²×C₄	1	2	yes	—
345	C₂×#392	C₂²×C₄	1	2	yes	—
346	C₂×#392	C₂²×C₄	1	2	yes	—
347	C₂×#392	C₂²×C₄	1	2	yes	complemented
348	C₂×#392	C₂²×C₄	1	2	yes	complemented
349	C₂×#392	C₂²×C₄	1	2	yes	complemented
350	C₂×#381	C₂²×C₄	1	2	yes	—
351	C₂×#381	C₂²×C₄	1	2	yes	complemented
352	C₂×#380	C₂²×C₄	1	2	yes	complemented
353	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
354	C₂²×#95	C₂²×C₄	1	2	yes	—
355	C₂²×#95	C₂²×C₄	1	2	yes	complemented
356	#1782	C₂×D₄	1	8	yes	complemented
357	#1781	C₂×D₄	1	8	yes	complemented
358	#1781	C₂×D₄	1	8	yes	complemented
359	#1781	C₂⁴	1	8	yes	—
360	#1781	C₂⁴	1	8	yes	—
361	#1446	C₂²×C₄	1	2	yes	complemented
362	#1446	C₂²×C₄	1	2	yes	complemented
363	#1438	C₂²×C₄	1	1	yes	characteristic
364	#1438	C₂²×C₄	1	1	yes	characteristic
365	#1438	C₂²×C₄	1	1	yes	characteristic
366	#1438	C₂²×C₄	1	1	yes	characteristic
367	#1438	C₂²×C₄	1	2	yes	complemented
368	#1438	C₂²×C₄	1	2	yes	complemented
369	#1438	C₂⁴	1	2	yes	—
370	#1438	C₂⁴	1	2	yes	—
371	#1437	C₂²×C₄	1	2	yes	—
372	#1437	C₂²×C₄	1	2	yes	—
373	#1437	C₂²×C₄	1	2	yes	—
374	#1437	C₂²×C₄	1	2	yes	—
375	#1437	C₂²×C₄	1	2	yes	—
376	#1437	C₂²×C₄	1	2	yes	—
377	#1437	C₂²×C₄	1	2	yes	—
378	#1437	C₂²×C₄	1	2	yes	—
379	#1437	C₂²×C₄	1	2	yes	complemented
380	#1437	C₂²×C₄	1	2	yes	complemented
381	#1437	C₂²×C₄	1	2	yes	complemented
382	#1437	C₂²×C₄	1	2	yes	complemented
383	#1436	C₂²×C₄	1	2	yes	complemented
384	#1436	C₂²×C₄	1	2	yes	complemented
385	#1436	C₂²×C₄	1	2	yes	complemented
386	#1436	C₂²×C₄	1	2	yes	complemented
387	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
390	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
392	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂⁶	C₂²×D₄	1	1	yes	characteristic
396	C₂⁶	C₂²×D₄	1	2	yes	—
397	C₂⁶	C₂²×D₄	1	1	yes	characteristic
398	C₂⁶	C₂²×D₄	1	1	yes	characteristic
399	C₂⁶	C₂²×D₄	1	1	yes	characteristic
400	C₂²×#41	C₄×D₄	1	2	yes	—
401	C₂²×#41	C₄×D₄	1	2	yes	—
402	C₂²×#41	C₄×D₄	1	2	yes	—
403	C₂²×#41	C₄×D₄	1	2	yes	—
404	C₂²×#41	C₄×D₄	1	2	yes	—
405	C₂²×#41	C₄×D₄	1	2	yes	—
406	C₂²×#41	C₄×D₄	1	2	yes	—
407	C₂²×#41	C₄×D₄	1	2	yes	—
408	C₂²×#41	C₄×D₄	1	2	yes	—
409	C₂²×#41	C₄×D₄	1	2	yes	—
410	C₂²×#41	C₄×D₄	1	2	yes	—
411	C₂²×#41	C₄×D₄	1	2	yes	—
412	C₂²×#41	#120	1	2	yes	—
413	C₂²×#41	#120	1	2	yes	—
414	C₂²×#41	#121	1	2	yes	—
415	C₂²×#41	#121	1	2	yes	—
416	C₂²×#41	#121	1	2	yes	—
417	C₂²×#41	#121	1	2	yes	—
418	C₂²×#41	#123	1	2	yes	—
419	C₂²×#41	#123	1	2	yes	—
420	C₂²×#41	C₂²×D₄	1	2	yes	—
421	C₂²×#41	C₂²×D₄	1	2	yes	—
422	C₂²×#41	C₂×#41	1	2	yes	—
423	C₂²×#41	C₂×#41	1	2	yes	—
424	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
425	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
426	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
427	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
430	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
431	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
432	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
433	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
434	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
435	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
436	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
439	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
440	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
444	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
445	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
446	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
447	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
448	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
449	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂³×D₄	C₄×D₄	1	2	yes	—
451	C₂³×D₄	C₄×D₄	1	2	yes	—
452	C₂³×D₄	C₄×D₄	1	2	yes	—
453	C₂³×D₄	C₄×D₄	1	2	yes	—
454	C₂³×D₄	#120	1	2	yes	—
455	C₂³×D₄	#120	1	2	yes	—
456	C₂³×D₄	#120	1	1	yes	characteristic
457	C₂³×D₄	#120	1	1	yes	characteristic
458	C₂³×D₄	#120	1	1	yes	characteristic
459	C₂³×D₄	#120	1	2	yes	—
460	C₂³×D₄	#120	1	2	yes	—
461	C₂³×D₄	#120	1	1	yes	characteristic
462	C₂³×D₄	#121	1	2	yes	—
463	C₂³×D₄	#121	1	2	yes	—
464	C₂³×D₄	#121	1	2	yes	—
465	C₂³×D₄	#121	1	2	yes	—
466	C₂³×D₄	#121	1	2	yes	—
467	C₂³×D₄	#121	1	2	yes	—
468	C₂³×D₄	#121	1	2	yes	—
469	C₂³×D₄	#121	1	2	yes	—
470	C₂³×D₄	#121	1	2	yes	—
471	C₂³×D₄	#121	1	2	yes	—
472	C₂³×D₄	#121	1	2	yes	—
473	C₂³×D₄	#121	1	2	yes	—
474	C₂³×D₄	#123	1	2	yes	—
475	C₂³×D₄	#123	1	2	yes	—
476	C₂³×D₄	#123	1	1	yes	characteristic
477	C₂³×D₄	#123	1	1	yes	characteristic
478	C₂³×D₄	#123	1	1	yes	characteristic
479	C₂³×D₄	#123	1	1	yes	characteristic
480	C₂³×D₄	#123	1	2	yes	—
481	C₂³×D₄	#123	1	2	yes	—
482	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
483	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
484	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
485	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
486	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
487	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
488	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
489	C₂³×D₄	C₂²×D₄	1	2	yes	—
490	C₂³×D₄	C₂²×D₄	1	2	yes	—
491	C₂³×D₄	C₂²×D₄	1	2	yes	—
492	C₂³×D₄	C₂²×D₄	1	2	yes	—
493	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
494	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
495	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
496	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
497	C₂³×D₄	C₂²×D₄	1	2	yes	—
498	C₂³×D₄	C₂²×D₄	1	2	yes	—
499	C₂³×D₄	C₂²×D₄	1	2	yes	—
500	C₂³×D₄	C₂²×D₄	1	2	yes	—
501	C₂³×D₄	C₂×#41	1	2	yes	—
502	C₂³×D₄	C₂×#41	1	2	yes	—
503	C₂³×D₄	C₂×#41	1	2	yes	—
504	C₂³×D₄	C₂×#41	1	2	yes	—
505	C₂³×D₄	C₂⁵	1	1	yes	characteristic
506	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
507	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
508	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
510	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
511	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
512	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
517	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
518	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
519	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×#120	#99	1	8	yes	—
523	C₂×#120	#99	1	8	yes	—
524	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
525	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
526	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
527	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
528	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
529	C₂²×C₄⋊C₄	C₂³×C₄	1	2	yes	—
530	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
531	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
532	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
533	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
534	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
535	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
536	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
537	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
538	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
539	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
540	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
541	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
542	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
543	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
544	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
545	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
546	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
547	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
548	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
549	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
550	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
551	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
552	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
553	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
554	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
555	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
556	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
557	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
558	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
559	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
560	C₂×#99	C₂²×D₄	1	16	yes	—
561	C₂×#95	C₂³×C₄	1	2	yes	—
562	C₂×#95	C₂³×C₄	1	2	yes	—
563	C₂×#95	C₂³×C₄	1	2	yes	—
564	C₂×#95	C₂³×C₄	1	2	yes	—
565	C₂⁵	#386	1	1	yes	characteristic
566	C₂⁵	#386	1	1	yes	characteristic
567	C₂⁵	#386	1	1	yes	characteristic
568	C₂⁵	#386	1	2	yes	—
569	C₂⁵	#386	1	2	yes	—
570	C₂⁵	#386	1	1	yes	characteristic
571	C₂⁵	C₂×#99	1	4	yes	—
572	C₂⁵	C₂×#99	1	4	yes	—
573	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
574	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
575	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
576	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
577	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
578	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
579	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
580	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
581	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
582	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
583	C₂⁵	C₂×#120	1	2	yes	—
584	C₂⁵	C₂×#120	1	1	yes	characteristic
585	C₂⁵	C₂×#120	1	1	yes	characteristic
586	C₂⁵	C₂×#121	1	2	yes	—
587	C₂⁵	C₂×#121	1	2	yes	—
588	C₂⁵	C₂×#121	1	2	yes	—
589	C₂⁵	C₂×#121	1	2	yes	—
590	C₂⁵	C₂×#123	1	1	yes	characteristic
591	C₂⁵	C₂×#123	1	1	yes	characteristic
592	C₂⁵	C₂×#123	1	2	yes	—
593	C₂⁵	C₂³×D₄	1	1	yes	characteristic
594	C₂⁵	C₂³×D₄	1	1	yes	characteristic
595	C₂²×Q₈	#386	1	2	yes	—
596	C₂²×Q₈	#386	1	2	yes	—
597	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
598	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
599	C₂²×D₄	#386	1	1	yes	characteristic
600	C₂²×D₄	#386	1	1	yes	characteristic
601	C₂²×D₄	#386	1	1	yes	characteristic
602	C₂²×D₄	#386	1	2	yes	—
603	C₂²×D₄	#386	1	1	yes	characteristic
604	C₂²×D₄	#386	1	1	yes	characteristic
605	C₂²×D₄	#386	1	2	yes	—
606	C₂²×D₄	#386	1	2	yes	—
607	C₂²×D₄	#386	1	2	yes	—
608	C₂²×D₄	#386	1	2	yes	—
609	C₂²×D₄	#386	1	2	yes	—
610	C₂²×D₄	#386	1	2	yes	—
611	C₂²×D₄	#386	1	1	yes	characteristic
612	C₂²×D₄	#386	1	1	yes	characteristic
613	C₂²×D₄	#386	1	2	yes	—
614	C₂²×D₄	#386	1	1	yes	characteristic
615	C₂²×D₄	#386	1	2	yes	—
616	C₂²×D₄	#386	1	2	yes	—
617	C₂²×D₄	#386	1	2	yes	—
618	C₂²×D₄	#386	1	2	yes	—
619	C₂²×D₄	#386	1	2	yes	—
620	C₂²×D₄	#386	1	2	yes	—
621	C₂²×D₄	C₂×#99	1	4	yes	—
622	C₂²×D₄	C₂×#99	1	4	yes	—
623	C₂²×D₄	C₂×#99	1	8	yes	—
624	C₂²×D₄	C₂×#99	1	8	yes	—
625	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
626	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
627	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
628	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
629	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
630	C₂²×D₄	C₂×#120	1	1	yes	characteristic
631	C₂²×D₄	C₂×#120	1	1	yes	characteristic
632	C₂²×D₄	C₂×#120	1	2	yes	—
633	C₂²×D₄	C₂×#120	1	1	yes	characteristic
634	C₂²×D₄	C₂×#120	1	1	yes	characteristic
635	C₂²×D₄	C₂×#121	1	2	yes	—
636	C₂²×D₄	C₂×#121	1	2	yes	—
637	C₂²×D₄	C₂×#121	1	2	yes	—
638	C₂²×D₄	C₂×#121	1	2	yes	—
639	C₂²×D₄	C₂×#121	1	2	yes	—
640	C₂²×D₄	C₂×#121	1	2	yes	—
641	C₂²×D₄	C₂×#123	1	1	yes	characteristic
642	C₂²×D₄	C₂×#123	1	1	yes	characteristic
643	C₂²×D₄	C₂×#123	1	1	yes	characteristic
644	C₂²×D₄	C₂×#123	1	1	yes	characteristic
645	C₂²×D₄	C₂×#123	1	2	yes	—
646	C₂²×D₄	C₂³×D₄	1	2	yes	—
647	C₂²×D₄	C₂²×#41	1	2	yes	—
648	C₂³×C₄	#386	1	1	yes	characteristic
649	C₂³×C₄	#386	1	1	yes	characteristic
650	C₂³×C₄	#386	1	2	yes	—
651	C₂³×C₄	#386	1	1	yes	characteristic
652	C₂³×C₄	#386	1	2	yes	—
653	C₂³×C₄	#386	1	2	yes	—
654	C₂³×C₄	#386	1	2	yes	—
655	C₂³×C₄	#386	1	2	yes	—
656	C₂³×C₄	#386	1	2	yes	—
657	C₂³×C₄	#386	1	1	yes	characteristic
658	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
659	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
660	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
661	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
662	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
663	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
664	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
665	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
666	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
667	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
668	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
669	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
670	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
671	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
672	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
673	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
674	C₂³×C₄	C₂×#120	1	2	yes	—
675	C₂³×C₄	C₂×#121	1	2	yes	—
676	C₂³×C₄	C₂×#121	1	2	yes	—
677	C₂³×C₄	C₂×#123	1	2	yes	—
678	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂×#99	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂×#99	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	—
682	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	—
683	C₂⁴	#1889	1	4	yes	—
684	C₂⁴	C₂×#386	1	1	yes	characteristic
685	C₂⁴	C₂×#386	1	1	yes	characteristic
686	C₂⁴	C₂×#386	1	2	yes	—
687	C₂⁴	C₂×#386	1	2	yes	—
688	C₂⁴	C₂×#386	1	1	yes	characteristic
689	C₂⁴	C₂×#386	1	1	yes	characteristic
690	C₂⁴	C₂×#386	1	1	yes	characteristic
691	C₂⁴	C₂×#386	1	1	yes	characteristic
692	C₂⁴	C₂×#386	1	1	yes	characteristic
693	C₂⁴	C₂×#386	1	2	yes	—
694	C₂⁴	C₂×#386	1	1	yes	characteristic
695	C₂⁴	C₂²×#99	1	4	yes	—
696	C₂⁴	C₂²×#99	1	2	yes	—
697	C₂⁴	C₂²×#99	1	4	yes	—
698	C₂⁴	C₂²×#99	1	2	yes	—
699	C₂⁴	C₂²×#99	1	4	yes	—
700	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
701	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
702	C₂⁴	C₂²×#120	1	1	yes	characteristic
703	C₂⁴	C₂²×#121	1	2	yes	—
704	C₂⁴	C₂²×#123	1	1	yes	characteristic
705	C₂×D₄	#1889	1	4	yes	—
706	C₂×D₄	#1889	1	4	yes	—
707	C₂×D₄	#1898	1	8	yes	—
708	C₂×D₄	#1898	1	8	yes	—
709	C₂×D₄	#1913	1	4	yes	—
710	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
711	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
712	C₂²×C₄	#1889	1	4	yes	—
713	C₂²×C₄	C₂×#386	1	1	yes	characteristic
714	C₂²×C₄	C₂×#386	1	2	yes	—
715	C₂²×C₄	C₂×#386	1	2	yes	—
716	C₂²×C₄	C₂×#386	1	1	yes	characteristic
717	C₂²×C₄	C₂×#386	1	1	yes	characteristic
718	C₂²×C₄	C₂×#386	1	1	yes	characteristic
719	C₂²×C₄	C₂×#386	1	2	yes	—
720	C₂²×C₄	C₂²×#99	1	4	yes	—
721	C₂²×C₄	C₂²×#99	1	4	yes	—
722	C₂²×C₄	C₂²×#99	1	4	yes	—
723	C₂²×C₄	C₂²×C₄×D₄	1	2	yes	—
724	C₂³	C₂×#1889	1	2	yes	—
725	C₂³	C₂×#1889	1	2	yes	—
726	C₂³	C₂×#1889	1	2	yes	—
727	C₂³	C₂×#1889	1	2	yes	—
728	C₂³	C₂×#1898	1	2	yes	—
729	C₂³	C₂×#1898	1	4	yes	—
730	C₂³	C₂×#1898	1	2	yes	—
731	C₂³	C₂×#1913	1	2	yes	—
732	C₂³	C₂×#1913	1	2	yes	—
733	C₂³	#33359	1	4	yes	complemented
734	C₂³	C₂²×#386	1	1	yes	characteristic
735	C₂³	C₂³×#99	1	2	yes	—
736	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
737	C₂×C₄	C₂×#1889	1	2	yes	—
738	C₂×C₄	C₂×#1889	1	2	yes	—
739	C₂×C₄	C₂×#1898	1	4	yes	—
740	C₂×C₄	C₂×#1913	1	2	yes	—
741	C₂²	#201664	1	4	yes	—
742	C₂²	C₂²×#1889	1	1	yes	characteristic
743	C₂²	C₂²×#1898	1	1	yes	characteristic
744	C₂²	C₂²×#1913	1	1	yes	characteristic
745	C₂²	C₂×#33359	1	2	yes	—
746	C₂²	#7622467	1	2	yes	—
747	C₂	#72234836	1	2	yes	—
748	C₂	C₂×#201664	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1898
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72215608	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×D₄ ◁ C₂²×#3484 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72260562	C₂	semidirect
2. #72260517	C₂	semidirect
3. #72260398	C₂	semidirect
4. #72260376	C₂	semidirect
5. #72252021	C₂	semidirect
6. #72240132	C₂	semidirect
7. C₂×#139718	C₂	semidirect
8. #72235246	C₂	semidirect
9. #72234663	C₂	semidirect
10. #72233654	C₂	semidirect
11. #72232743	C₂	semidirect
12. #72225786	C₂	semidirect
16. C₂×#35680	C₄	semidirect
17. #6385972	C₂²	semidirect
18. #6385971	C₂²	semidirect
19. #6374251	C₂²	semidirect
20. C₂×#21746	C₂²	semidirect
23. #763336	C₄	semidirect
24. #763333	C₄	semidirect
27. #686202	C₄	semidirect
30. #649035	C₄	semidirect
32. #617715	C₄	semidirect
33. #617710	C₄	semidirect
35. #616967	C₄	semidirect
36. #616961	C₄	semidirect
38. #608791	C₄	semidirect
39. C₂×#15258	C₄	semidirect
41. #518972	C₄	semidirect
43. #493372	C₂²	semidirect
44. #493370	C₂²	semidirect
45. #493370	C₂²	semidirect
46. #493365	C₂²	semidirect
47. C₂×#12693	C₂²	semidirect
48. C₂×#12693	C₂²	semidirect
49. #188049	C₂²	semidirect
50. #188037	C₂²	semidirect
51. #188035	C₂²	semidirect
52. C₂×#8541	C₂²	semidirect
53. #139795	C₂²	semidirect
54. #139794	C₂²	semidirect
55. #139794	C₂²	semidirect
56. #139794	C₂²	semidirect
57. #139720	C₂²	semidirect
58. #139718	C₂²	semidirect
59. #139718	C₂²	semidirect
60. #139718	C₂²	semidirect
61. #128058	C₂²	semidirect
62. #128057	C₂²	semidirect
63. #128009	C₂²	semidirect
64. C₂×#7307	C₂²	semidirect
65. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
77. C₂²×#535	C₂×C₄	semidirect
78. C₂²×#535	C₂×C₄	semidirect
79. C₂²×#535	C₂×C₄	semidirect
88. C₂²×#532	C₂×C₄	semidirect
89. C₂²×#532	C₂×C₄	semidirect
91. C₂³×#127	C₂×C₄	semidirect
101. C₂²×C₄×#41	C₂×C₄	semidirect
102. C₂×#2883	D₄	semidirect
103. C₂×#2430	C₂×C₄	semidirect
104. C₂×#2430	C₂×C₄	semidirect
105. C₂×#2404	C₂×C₄	semidirect
106. C₂×#2404	C₂×C₄	semidirect
107. C₂×#2433	C₂×C₄	semidirect
108. C₂×#2408	C₂×C₄	semidirect
109. C₂×#2615	C₂×C₄	semidirect
110. C₂×#2613	C₂×C₄	semidirect
111. C₂×#2613	C₂×C₄	semidirect
112. C₂×#2388	C₂×C₄	semidirect
113. C₂²×#392	C₂×C₄	semidirect
114. C₂²×#392	C₂×C₄	semidirect
115. C₂×#2339	C₂×C₄	semidirect
118. #20586	D₄	semidirect
119. #20585	D₄	semidirect
120. #20585	D₄	semidirect
127. #15763	C₂×C₄	semidirect
128. #15763	C₂×C₄	semidirect
129. #15763	C₂×C₄	semidirect
130. #15761	C₂×C₄	semidirect
131. #15673	C₂×C₄	semidirect
133. #15310	C₂×C₄	semidirect
134. #15310	C₂×C₄	semidirect
135. #15310	C₂×C₄	semidirect
139. #15265	C₂×C₄	semidirect
140. #15264	C₂×C₄	semidirect
141. #15264	C₂×C₄	semidirect
142. #15264	C₂×C₄	semidirect
143. #15262	C₂×C₄	semidirect
144. #15261	C₂×C₄	semidirect
145. #15261	C₂×C₄	semidirect
146. #15261	C₂×C₄	semidirect
147. #15259	C₂×C₄	semidirect
148. #15259	C₂×C₄	semidirect
149. #15259	C₂×C₄	semidirect
150. #15259	C₂×C₄	semidirect
152. #15258	C₂×C₄	semidirect
153. #15258	C₂×C₄	semidirect
154. #15258	C₂×C₄	semidirect
155. #15258	C₂×C₄	semidirect
156. #15258	C₂×C₄	semidirect
157. #15258	C₂×C₄	semidirect
158. #15258	C₂×C₄	semidirect
159. #15258	C₂×C₄	semidirect
160. #15258	C₂×C₄	semidirect
161. #15258	C₂×C₄	semidirect
162. #15258	C₂×C₄	semidirect
163. #15258	C₂×C₄	semidirect
167. #14706	C₂×C₄	semidirect
168. #14706	C₂×C₄	semidirect
169. #14698	C₂×C₄	semidirect
170. #14337	C₂×C₄	semidirect
171. #14335	C₂×C₄	semidirect
173. #14136	C₂×C₄	semidirect
174. #14135	C₂×C₄	semidirect
175. #14135	C₂×C₄	semidirect
176. #13956	C₂×C₄	semidirect
179. #13871	C₂×C₄	semidirect
180. #13868	C₂×C₄	semidirect
181. #13868	C₂×C₄	semidirect
182. #13851	C₂×C₄	semidirect
183. C₂×#1438	C₂×C₄	semidirect
185. C₄×#386	C₂×C₄	semidirect
186. C₂×#1437	C₂×C₄	semidirect
187. C₂×#1437	C₂×C₄	semidirect
188. #12694	C₂³	semidirect
189. #12693	C₂³	semidirect
190. #12693	C₂³	semidirect
191. #12693	C₂³	semidirect
194. #7307	C₂³	semidirect
195. #7307	C₂³	semidirect
210. C₂³×#41	C₂²×C₄	semidirect
211. C₂³×#41	C₂²×C₄	semidirect
222. C₂⁴×D₄	C₂²×C₄	semidirect
223. C₂⁴×D₄	C₂²×C₄	semidirect
239. C₂²×C₄⋊Q₈	C₂²×C₄	semidirect
244. C₂²×#127	C₂²×C₄	semidirect
245. C₂²×#127	C₂²×C₄	semidirect
246. C₂²×#127	C₂²×C₄	semidirect
254. C₂²×#124	C₂²×C₄	semidirect
255. C₂²×#124	C₂²×C₄	semidirect
256. C₂²×#124	C₂²×C₄	semidirect
257. C₂²×#124	C₂²×C₄	semidirect
318. C₂²×#117	C₂²×C₄	semidirect
319. C₂²×#117	C₂²×C₄	semidirect
329. C₂³×C₄²	C₂²×C₄	semidirect
330. C₂³×C₄²	C₂²×C₄	semidirect
331. C₂×#410	C₂×D₄	semidirect
332. C₂²×#99	C₂×D₄	semidirect
333. C₂²×#99	C₂×D₄	semidirect
334. C₂×#395	C₂²×C₄	semidirect
335. C₂×#394	C₂²×C₄	semidirect
336. C₂×#394	C₂²×C₄	semidirect
337. C₂×#394	C₂²×C₄	semidirect
340. C₂×#393	C₂²×C₄	semidirect
347. C₂×#392	C₂²×C₄	semidirect
348. C₂×#392	C₂²×C₄	semidirect
349. C₂×#392	C₂²×C₄	semidirect
351. C₂×#381	C₂²×C₄	semidirect
352. C₂×#380	C₂²×C₄	semidirect
353. C₂×C₄×C₂²⋊C₄	C₂²×C₄	semidirect
355. C₂²×#95	C₂²×C₄	semidirect
356. #1782	C₂×D₄	semidirect
357. #1781	C₂×D₄	semidirect
358. #1781	C₂×D₄	semidirect
361. #1446	C₂²×C₄	semidirect
362. #1446	C₂²×C₄	semidirect
367. #1438	C₂²×C₄	semidirect
368. #1438	C₂²×C₄	semidirect
379. #1437	C₂²×C₄	semidirect
380. #1437	C₂²×C₄	semidirect
381. #1437	C₂²×C₄	semidirect
382. #1437	C₂²×C₄	semidirect
383. #1436	C₂²×C₄	semidirect
384. #1436	C₂²×C₄	semidirect
385. #1436	C₂²×C₄	semidirect
386. #1436	C₂²×C₄	semidirect
733. C₂³	#33359	semidirect

Maximal subgroups

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

subgroup	index
#72260562	2
#72260517	2
#72260398	2
#72260376	2
#72252021	2
#72240132	2
C₂×#139718	2
#72235246	2
#72234663	2
#72233654	2
#72232743	2
#72225786	2
#72215608	2