Subgroups — #72263560

Order 2048.

At least 10237 conjugacy classes of subgroups; only the 1156 normal subgroups are shown.

The subgroup lattice has 773 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263548	C₂	1	1	yes	maximal, characteristic
2	#72238031	C₂	1	1	yes	maximal, characteristic, complemented
3	#72236670	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#106766	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493370	C₂	1	1	yes	maximal, characteristic
6	C₂×#128073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#359509	C₂	1	1	yes	maximal, characteristic
8	#72210473	C₂	1	4	yes	maximal, complemented
9	#72210462	C₂	1	4	yes	maximal, complemented
10	C₂³×#535	C₂²	1	1	yes	characteristic
11	C₂×#34171	C₂²	1	1	yes	characteristic
12	C₂²×#2127	C₄	1	4	yes	complemented
13	C₂²×#1783	C₂²	1	1	yes	characteristic
14	C₂²×#1781	C₂²	1	1	yes	characteristic
15	C₂²×#1781	C₂²	1	1	yes	characteristic
16	#581605	C₂²	1	2	yes	—
17	#581603	C₂²	1	2	yes	—
18	#559859	C₄	1	1	yes	characteristic, complemented
19	#559850	C₄	1	1	yes	characteristic, complemented
20	#552678	C₄	1	2	yes	complemented
21	#552671	C₄	1	2	yes	complemented
22	#532187	C₄	1	1	yes	characteristic, complemented
23	#531766	C₄	1	1	yes	characteristic, complemented
24	#517411	C₂²	1	1	yes	characteristic
25	C₂×#13867	C₂²	1	1	yes	characteristic
26	#493370	C₄	1	4	yes	complemented
27	#493370	C₂²	1	2	yes	—
28	#493370	C₂²	1	2	yes	—
29	#359509	C₄	1	4	yes	complemented
30	#359509	C₂²	1	2	yes	—
31	#359509	C₂²	1	2	yes	—
32	C₂×#10989	C₄	1	4	yes	complemented
33	#128073	C₂²	1	4	yes	complemented
34	#128073	C₂²	1	4	yes	complemented
35	#106766	C₂²	1	4	yes	complemented
36	#106766	C₂²	1	4	yes	complemented
37	C₂⁴×#41	D₄	1	1	yes	characteristic
38	C₂⁵×D₄	C₂³	1	1	yes	characteristic
39	C₂²×#535	C₂×C₄	1	2	yes	—
40	C₂²×#535	C₂×C₄	1	2	yes	—
41	C₂²×#535	C₂×C₄	1	1	yes	characteristic
42	C₂²×#535	C₂×C₄	1	1	yes	characteristic
43	C₂²×#535	C₂×C₄	1	2	yes	—
44	C₂²×#535	C₂×C₄	1	2	yes	—
45	C₂²×#535	D₄	1	2	yes	—
46	C₂²×#535	D₄	1	2	yes	—
47	C₂²×#535	D₄	1	1	yes	characteristic
48	C₂²×#535	D₄	1	1	yes	characteristic
49	C₂²×#535	D₄	1	1	yes	characteristic
50	C₂²×#535	D₄	1	1	yes	characteristic
51	C₂²×#535	Q₈	1	2	yes	—
52	C₂²×#535	Q₈	1	2	yes	—
53	C₂²×#535	C₂³	1	1	yes	characteristic
54	C₂²×#535	C₂³	1	1	yes	characteristic
55	C₂³×#127	C₂×C₄	1	1	yes	characteristic
56	C₂³×#127	D₄	1	1	yes	characteristic
57	C₂³×#124	C₂×C₄	1	1	yes	characteristic
58	C₂³×#124	D₄	1	1	yes	characteristic
59	C₂³×#117	D₄	1	1	yes	characteristic
60	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
61	C₂³×#100	C₂×C₄	1	2	yes	complemented
62	C₂³×#99	C₂×C₄	1	2	yes	complemented
63	C₂³×#99	C₂×C₄	1	2	yes	complemented
64	#34171	C₂×C₄	1	2	yes	complemented
65	#34171	C₂³	1	2	yes	—
66	C₂×#2309	C₂×C₄	1	2	yes	complemented
67	C₂²×#379	D₄	1	1	yes	characteristic
68	C₂²×#379	D₄	1	1	yes	characteristic
69	C₂²×#379	D₄	1	1	yes	characteristic
70	C₂×#2127	C₂×C₄	1	8	yes	complemented
71	C₂×#2127	C₂×C₄	1	8	yes	complemented
72	C₂×#1783	C₂×C₄	1	2	yes	complemented
73	C₂×#1783	C₂³	1	2	yes	—
74	C₂×#1781	C₂×C₄	1	2	yes	complemented
75	C₂×#1781	C₂×C₄	1	2	yes	complemented
76	C₂×#1781	C₂³	1	2	yes	—
77	C₂×#1781	C₂³	1	2	yes	—
78	#14662	C₂×C₄	1	2	yes	complemented
79	#14661	C₂×C₄	1	2	yes	complemented
80	#14492	C₂×C₄	1	2	yes	complemented
81	#14492	C₂×C₄	1	2	yes	complemented
82	#14419	C₂×C₄	1	2	yes	complemented
83	#14419	C₂×C₄	1	2	yes	complemented
84	#14335	C₂×C₄	1	2	yes	—
85	#14335	D₄	1	2	yes	—
86	#14169	C₂×C₄	1	2	yes	complemented
87	#14154	C₂×C₄	1	2	yes	complemented
88	#13867	C₂×C₄	1	1	yes	characteristic
89	#13867	C₂×C₄	1	1	yes	characteristic
90	#13867	C₂×C₄	1	1	yes	characteristic
91	#13867	C₂×C₄	1	1	yes	characteristic
92	#13867	D₄	1	1	yes	characteristic
93	#13867	D₄	1	1	yes	characteristic
94	#13867	D₄	1	1	yes	characteristic
95	#13867	D₄	1	1	yes	characteristic
96	#13867	D₄	1	2	yes	—
97	#13867	D₄	1	2	yes	—
98	#13867	C₂³	1	2	yes	—
99	#13867	C₂³	1	2	yes	—
100	C₂×#1438	C₂×C₄	1	2	yes	—
101	C₂×#1438	D₄	1	2	yes	—
102	#10989	C₂×C₄	1	8	yes	complemented
103	#10989	C₂×C₄	1	8	yes	complemented
104	C₂⁷	C₂×D₄	1	1	yes	characteristic
105	C₂⁷	C₂×D₄	1	1	yes	characteristic
106	C₂³×#41	C₂²⋊C₄	1	2	yes	—
107	C₂³×#41	C₂²⋊C₄	1	2	yes	—
108	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×#41	C₄⋊C₄	1	2	yes	—
111	C₂³×#41	C₄⋊C₄	1	2	yes	—
112	C₂³×#41	C₂×D₄	1	1	yes	characteristic
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×Q₈	C₂²⋊C₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
122	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
123	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
125	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
126	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
132	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×D₄	C₂×Q₈	1	1	yes	characteristic
134	C₂⁴×D₄	C₂×Q₈	1	1	yes	characteristic
135	C₂⁴×D₄	#41	1	1	yes	characteristic
136	C₂⁴×D₄	#41	1	1	yes	characteristic
137	C₂⁴×D₄	#41	1	1	yes	characteristic
138	C₂⁴×D₄	#41	1	1	yes	characteristic
139	C₂⁴×D₄	#41	1	1	yes	characteristic
140	C₂⁴×D₄	#41	1	1	yes	characteristic
141	C₂⁴×D₄	#41	1	1	yes	characteristic
142	C₂⁴×D₄	#41	1	1	yes	characteristic
143	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
144	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂×#535	C₄²	1	2	yes	—
146	C₂×#535	C₄²	1	2	yes	—
147	C₂×#535	C₄²	1	2	yes	—
148	C₂×#535	C₄²	1	2	yes	—
149	C₂×#535	C₂²⋊C₄	1	2	yes	—
150	C₂×#535	C₂²⋊C₄	1	2	yes	—
151	C₂×#535	C₂²⋊C₄	1	2	yes	—
152	C₂×#535	C₂²⋊C₄	1	2	yes	—
153	C₂×#535	C₂²⋊C₄	1	2	yes	—
154	C₂×#535	C₂²⋊C₄	1	2	yes	—
155	C₂×#535	C₂²⋊C₄	1	2	yes	—
156	C₂×#535	C₂²⋊C₄	1	2	yes	—
157	C₂×#535	C₄⋊C₄	1	2	yes	—
158	C₂×#535	C₄⋊C₄	1	2	yes	—
159	C₂×#535	C₄⋊C₄	1	2	yes	—
160	C₂×#535	C₄⋊C₄	1	2	yes	—
161	C₂×#535	C₄⋊C₄	1	2	yes	—
162	C₂×#535	C₄⋊C₄	1	2	yes	—
163	C₂×#535	C₄⋊C₄	1	2	yes	—
164	C₂×#535	C₄⋊C₄	1	2	yes	—
165	C₂×#535	C₄⋊C₄	1	2	yes	—
166	C₂×#535	C₄⋊C₄	1	2	yes	—
167	C₂×#535	C₄⋊C₄	1	2	yes	—
168	C₂×#535	C₄⋊C₄	1	2	yes	—
169	C₂×#535	C₂²×C₄	1	2	yes	—
170	C₂×#535	C₂²×C₄	1	2	yes	—
171	C₂×#535	C₂²×C₄	1	2	yes	—
172	C₂×#535	C₂²×C₄	1	2	yes	—
173	C₂×#535	C₂×D₄	1	2	yes	—
174	C₂×#535	C₂×D₄	1	2	yes	—
175	C₂×#535	C₂×Q₈	1	2	yes	—
176	C₂×#535	C₂×Q₈	1	2	yes	—
177	C₂²×#127	C₄²	1	2	yes	—
178	C₂²×#127	C₄²	1	2	yes	—
179	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×#127	C₂²⋊C₄	1	2	yes	—
181	C₂²×#127	C₂²⋊C₄	1	2	yes	—
182	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×#127	C₄⋊C₄	1	2	yes	—
186	C₂²×#127	C₄⋊C₄	1	2	yes	—
187	C₂²×#127	C₄⋊C₄	1	2	yes	—
188	C₂²×#127	C₄⋊C₄	1	2	yes	—
189	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
190	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
191	C₂²×#127	C₂×D₄	1	1	yes	characteristic
192	C₂²×#127	C₂×D₄	1	1	yes	characteristic
193	C₂²×#124	C₄²	1	2	yes	—
194	C₂²×#124	C₄²	1	2	yes	—
195	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×#124	C₂²⋊C₄	1	2	yes	—
197	C₂²×#124	C₂²⋊C₄	1	2	yes	—
198	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×#124	C₄⋊C₄	1	2	yes	—
202	C₂²×#124	C₄⋊C₄	1	2	yes	—
203	C₂²×#124	C₄⋊C₄	1	2	yes	—
204	C₂²×#124	C₄⋊C₄	1	2	yes	—
205	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
206	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
207	C₂²×#124	C₂×D₄	1	1	yes	characteristic
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic
209	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×#117	C₂²⋊C₄	1	2	yes	—
211	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×#117	C₂²⋊C₄	1	2	yes	—
213	C₂²×#117	C₄⋊C₄	1	2	yes	—
214	C₂²×#117	C₄⋊C₄	1	2	yes	—
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
219	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
223	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
224	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
225	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×#100	C₂²×C₄	1	4	yes	—
228	C₂²×#99	C₂²×C₄	1	4	yes	—
229	C₂²×#99	C₂²×C₄	1	4	yes	—
230	#2309	C₂²×C₄	1	4	yes	—
231	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
235	C₂×#379	C₂²⋊C₄	1	2	yes	—
236	C₂×#379	C₂²⋊C₄	1	2	yes	—
237	C₂×#379	C₂×D₄	1	2	yes	—
238	C₂×#379	C₂×D₄	1	2	yes	—
239	#1438	C₂²⋊C₄	1	2	yes	—
240	#1438	C₂²⋊C₄	1	2	yes	—
241	#1438	C₂²⋊C₄	1	2	yes	—
242	#1438	C₂²⋊C₄	1	2	yes	—
243	#1438	C₂²⋊C₄	1	2	yes	—
244	#1438	C₂²⋊C₄	1	2	yes	—
245	#1438	C₂²⋊C₄	1	2	yes	—
246	#1438	C₂²⋊C₄	1	2	yes	—
247	#1438	C₂²×C₄	1	2	yes	—
248	#1438	C₂²×C₄	1	2	yes	—
249	#1438	C₂²×C₄	1	2	yes	—
250	#1438	C₂²×C₄	1	2	yes	—
251	#1438	C₂×D₄	1	2	yes	—
252	#1438	C₂×D₄	1	2	yes	—
253	#1438	C₂×D₄	1	2	yes	—
254	#1438	C₂×D₄	1	2	yes	—
255	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂⁶	C₄×D₄	1	1	yes	characteristic
260	C₂⁶	C₄×D₄	1	1	yes	characteristic
261	C₂⁶	C₄×D₄	1	1	yes	characteristic
262	C₂⁶	C₄×D₄	1	1	yes	characteristic
263	C₂⁶	C₄×D₄	1	1	yes	characteristic
264	C₂⁶	C₄×D₄	1	1	yes	characteristic
265	C₂⁶	C₄×D₄	1	1	yes	characteristic
266	C₂⁶	C₄×D₄	1	1	yes	characteristic
267	C₂⁶	#120	1	1	yes	characteristic
268	C₂⁶	#120	1	1	yes	characteristic
269	C₂⁶	#120	1	1	yes	characteristic
270	C₂⁶	#120	1	1	yes	characteristic
271	C₂⁶	#120	1	1	yes	characteristic
272	C₂⁶	#120	1	1	yes	characteristic
273	C₂⁶	#120	1	1	yes	characteristic
274	C₂⁶	#121	1	1	yes	characteristic
275	C₂⁶	#121	1	1	yes	characteristic
276	C₂⁶	#121	1	1	yes	characteristic
277	C₂⁶	#121	1	1	yes	characteristic
278	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
279	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
280	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
281	C₂⁶	C₂²⋊Q₈	1	1	yes	characteristic
282	C₂⁶	C₂²×D₄	1	1	yes	characteristic
283	C₂⁶	C₂²×D₄	1	1	yes	characteristic
284	C₂²×#41	#95	1	2	yes	—
285	C₂²×#41	#95	1	2	yes	—
286	C₂²×#41	#95	1	2	yes	—
287	C₂²×#41	#95	1	2	yes	—
288	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂²×#41	C₂×C₄⋊C₄	1	2	yes	—
291	C₂²×#41	C₂×C₄⋊C₄	1	2	yes	—
292	C₂³×Q₈	#95	1	2	yes	—
293	C₂³×Q₈	#95	1	2	yes	—
294	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂³×D₄	#95	1	2	yes	—
297	C₂³×D₄	#95	1	2	yes	—
298	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
299	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
300	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
301	C₂³×D₄	C₂×C₄²	1	1	yes	characteristic
302	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
317	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
318	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
319	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
320	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
321	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
322	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
323	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
324	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
325	C₂³×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
326	C₂³×D₄	#117	1	1	yes	characteristic
327	C₂³×D₄	#117	1	1	yes	characteristic
328	C₂³×D₄	#117	1	1	yes	characteristic
329	C₂³×D₄	#117	1	1	yes	characteristic
330	C₂³×D₄	#117	1	1	yes	characteristic
331	C₂³×D₄	#117	1	1	yes	characteristic
332	C₂³×D₄	#117	1	1	yes	characteristic
333	C₂³×D₄	#117	1	1	yes	characteristic
334	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
335	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
336	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
337	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
338	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
339	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
340	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
342	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
343	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
345	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
346	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
347	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
348	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
349	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
350	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
351	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
352	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
353	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
354	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
355	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
356	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
357	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
358	C₂³×D₄	#120	1	1	yes	characteristic
359	C₂³×D₄	#120	1	1	yes	characteristic
360	C₂³×D₄	#120	1	1	yes	characteristic
361	C₂³×D₄	#120	1	1	yes	characteristic
362	C₂³×D₄	#120	1	1	yes	characteristic
363	C₂³×D₄	#120	1	1	yes	characteristic
364	C₂³×D₄	#121	1	1	yes	characteristic
365	C₂³×D₄	#121	1	1	yes	characteristic
366	C₂³×D₄	#121	1	1	yes	characteristic
367	C₂³×D₄	#121	1	1	yes	characteristic
368	C₂³×D₄	#121	1	1	yes	characteristic
369	C₂³×D₄	#121	1	1	yes	characteristic
370	C₂³×D₄	#121	1	1	yes	characteristic
371	C₂³×D₄	#121	1	1	yes	characteristic
372	C₂³×D₄	#121	1	1	yes	characteristic
373	C₂³×D₄	#121	1	1	yes	characteristic
374	C₂³×D₄	#121	1	1	yes	characteristic
375	C₂³×D₄	#121	1	1	yes	characteristic
376	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
377	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
378	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
379	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
380	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
381	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
382	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
383	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
384	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
385	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
386	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
387	C₂³×D₄	C₂²⋊Q₈	1	1	yes	characteristic
388	C₂³×D₄	#123	1	1	yes	characteristic
389	C₂³×D₄	#123	1	1	yes	characteristic
390	C₂³×D₄	#123	1	1	yes	characteristic
391	C₂³×D₄	#123	1	1	yes	characteristic
392	C₂³×D₄	#123	1	1	yes	characteristic
393	C₂³×D₄	#123	1	1	yes	characteristic
394	C₂³×D₄	#123	1	1	yes	characteristic
395	C₂³×D₄	#123	1	1	yes	characteristic
396	C₂³×D₄	#123	1	1	yes	characteristic
397	C₂³×D₄	#123	1	1	yes	characteristic
398	C₂³×D₄	#123	1	1	yes	characteristic
399	C₂³×D₄	#123	1	1	yes	characteristic
400	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
401	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
402	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
403	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
404	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
405	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
406	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
407	C₂³×D₄	C₂²×Q₈	1	1	yes	characteristic
408	C₂³×D₄	C₂×#41	1	1	yes	characteristic
409	C₂³×D₄	C₂×#41	1	1	yes	characteristic
410	C₂³×D₄	C₂×#41	1	1	yes	characteristic
411	C₂³×D₄	C₂×#41	1	1	yes	characteristic
412	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
413	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
414	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
415	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
416	C₂⁴×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
417	C₂⁴×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
418	C₂⁴×C₄	#120	1	1	yes	characteristic
419	C₂⁴×C₄	#120	1	1	yes	characteristic
420	C₂⁴×C₄	#120	1	1	yes	characteristic
421	C₂⁴×C₄	#123	1	1	yes	characteristic
422	C₂⁴×C₄	#123	1	1	yes	characteristic
423	C₂⁴×C₄	#123	1	1	yes	characteristic
424	C₂⁴×C₄	#123	1	1	yes	characteristic
425	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
426	#535	#99	1	16	yes	—
427	C₂×#127	#95	1	2	yes	—
428	C₂×#127	#95	1	2	yes	—
429	C₂×#127	#95	1	2	yes	—
430	C₂×#127	#95	1	2	yes	—
431	C₂×#127	#95	1	2	yes	—
432	C₂×#127	#95	1	2	yes	—
433	C₂×#127	#95	1	2	yes	—
434	C₂×#127	#95	1	2	yes	—
435	C₂×#127	C₂×C₄²	1	2	yes	—
436	C₂×#127	C₂×C₄²	1	2	yes	—
437	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
439	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
440	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
441	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
442	C₂×#127	C₂×C₄⋊C₄	1	2	yes	—
443	C₂×#124	#95	1	2	yes	—
444	C₂×#124	#95	1	2	yes	—
445	C₂×#124	#95	1	2	yes	—
446	C₂×#124	#95	1	2	yes	—
447	C₂×#124	#95	1	2	yes	—
448	C₂×#124	#95	1	2	yes	—
449	C₂×#124	#95	1	2	yes	—
450	C₂×#124	#95	1	2	yes	—
451	C₂×#124	C₂×C₄²	1	2	yes	—
452	C₂×#124	C₂×C₄²	1	2	yes	—
453	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
454	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
455	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
456	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
457	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
458	C₂×#124	C₂×C₄⋊C₄	1	2	yes	—
459	C₂×#117	#95	1	2	yes	—
460	C₂×#117	#95	1	2	yes	—
461	C₂×#117	#95	1	2	yes	—
462	C₂×#117	#95	1	2	yes	—
463	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
464	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
465	C₂×#117	C₂×C₄⋊C₄	1	2	yes	—
466	C₂×#117	C₂×C₄⋊C₄	1	2	yes	—
467	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
468	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
469	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
470	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
471	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
472	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
473	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
474	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
475	C₂²×C₄²	#95	1	2	yes	—
476	C₂²×C₄²	#95	1	2	yes	—
477	C₂²×C₄²	#95	1	2	yes	—
478	C₂²×C₄²	#95	1	2	yes	—
479	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
480	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
481	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
482	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
483	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
484	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
485	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
486	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
487	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
488	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
489	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
490	C₂⁵	C₄×C₂²⋊C₄	1	1	yes	characteristic
491	C₂⁵	#379	1	1	yes	characteristic
492	C₂⁵	#379	1	1	yes	characteristic
493	C₂⁵	#379	1	1	yes	characteristic
494	C₂⁵	#379	1	1	yes	characteristic
495	C₂⁵	#379	1	1	yes	characteristic
496	C₂⁵	#379	1	1	yes	characteristic
497	C₂⁵	#380	1	1	yes	characteristic
498	C₂⁵	#380	1	1	yes	characteristic
499	C₂⁵	#380	1	1	yes	characteristic
500	C₂⁵	#380	1	1	yes	characteristic
501	C₂⁵	#380	1	1	yes	characteristic
502	C₂⁵	#380	1	1	yes	characteristic
503	C₂⁵	#380	1	1	yes	characteristic
504	C₂⁵	#380	1	1	yes	characteristic
505	C₂⁵	#385	1	1	yes	characteristic
506	C₂⁵	#385	1	1	yes	characteristic
507	C₂⁵	#385	1	1	yes	characteristic
508	C₂⁵	#385	1	1	yes	characteristic
509	C₂⁵	#385	1	1	yes	characteristic
510	C₂⁵	#385	1	1	yes	characteristic
511	C₂⁵	#385	1	1	yes	characteristic
512	C₂⁵	#385	1	1	yes	characteristic
513	C₂⁵	#385	1	1	yes	characteristic
514	C₂⁵	#385	1	1	yes	characteristic
515	C₂⁵	#385	1	1	yes	characteristic
516	C₂⁵	#385	1	1	yes	characteristic
517	C₂⁵	#385	1	1	yes	characteristic
518	C₂⁵	#385	1	1	yes	characteristic
519	C₂⁵	#386	1	1	yes	characteristic
520	C₂⁵	#386	1	1	yes	characteristic
521	C₂⁵	#386	1	1	yes	characteristic
522	C₂⁵	#386	1	1	yes	characteristic
523	C₂⁵	#386	1	1	yes	characteristic
524	C₂⁵	#386	1	1	yes	characteristic
525	C₂⁵	#386	1	1	yes	characteristic
526	C₂⁵	#386	1	1	yes	characteristic
527	C₂⁵	#386	1	1	yes	characteristic
528	C₂⁵	#386	1	1	yes	characteristic
529	C₂⁵	#386	1	1	yes	characteristic
530	C₂⁵	#386	1	1	yes	characteristic
531	C₂⁵	#386	1	1	yes	characteristic
532	C₂⁵	#386	1	1	yes	characteristic
533	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
534	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
535	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
536	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
537	C₂⁵	#458	1	1	yes	characteristic
538	C₂⁵	#458	1	1	yes	characteristic
539	C₂⁵	#458	1	1	yes	characteristic
540	C₂⁵	#458	1	1	yes	characteristic
541	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
542	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
543	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
544	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
545	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
546	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
547	C₂⁵	C₂×#120	1	1	yes	characteristic
548	C₂⁵	C₂×#120	1	1	yes	characteristic
549	C₂⁵	C₂×#120	1	1	yes	characteristic
550	C₂⁵	C₂×#121	1	1	yes	characteristic
551	C₂⁵	C₂×#121	1	1	yes	characteristic
552	C₂⁵	C₂×C₂²⋊Q₈	1	1	yes	characteristic
553	C₂⁵	C₂×C₂²⋊Q₈	1	1	yes	characteristic
554	C₂×#41	#342	1	8	yes	complemented
555	C₂²×Q₈	C₂×#95	1	2	yes	—
556	C₂²×Q₈	C₂×#95	1	2	yes	—
557	C₂²×D₄	C₂×#95	1	2	yes	—
558	C₂²×D₄	C₂×#95	1	1	yes	characteristic
559	C₂²×D₄	C₂×#95	1	1	yes	characteristic
560	C₂²×D₄	C₂×#95	1	1	yes	characteristic
561	C₂²×D₄	C₂×#95	1	2	yes	—
562	C₂²×D₄	C₂×#95	1	1	yes	characteristic
563	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
564	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
565	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
566	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
567	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
568	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
569	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
570	C₂²×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
571	C₂²×D₄	#380	1	1	yes	characteristic
572	C₂²×D₄	#380	1	1	yes	characteristic
573	C₂²×D₄	#380	1	1	yes	characteristic
574	C₂²×D₄	#380	1	1	yes	characteristic
575	C₂²×D₄	#380	1	1	yes	characteristic
576	C₂²×D₄	#380	1	1	yes	characteristic
577	C₂²×D₄	#380	1	1	yes	characteristic
578	C₂²×D₄	#380	1	1	yes	characteristic
579	C₂²×D₄	#381	1	1	yes	characteristic
580	C₂²×D₄	#381	1	1	yes	characteristic
581	C₂²×D₄	#381	1	1	yes	characteristic
582	C₂²×D₄	#381	1	1	yes	characteristic
583	C₂²×D₄	#385	1	1	yes	characteristic
584	C₂²×D₄	#385	1	1	yes	characteristic
585	C₂²×D₄	#385	1	1	yes	characteristic
586	C₂²×D₄	#385	1	1	yes	characteristic
587	C₂²×D₄	#385	1	1	yes	characteristic
588	C₂²×D₄	#385	1	1	yes	characteristic
589	C₂²×D₄	#385	1	1	yes	characteristic
590	C₂²×D₄	#385	1	1	yes	characteristic
591	C₂²×D₄	#385	1	1	yes	characteristic
592	C₂²×D₄	#385	1	1	yes	characteristic
593	C₂²×D₄	#385	1	1	yes	characteristic
594	C₂²×D₄	#385	1	1	yes	characteristic
595	C₂²×D₄	#386	1	1	yes	characteristic
596	C₂²×D₄	#386	1	1	yes	characteristic
597	C₂²×D₄	#386	1	1	yes	characteristic
598	C₂²×D₄	#386	1	1	yes	characteristic
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	1	yes	characteristic
603	C₂²×D₄	#386	1	1	yes	characteristic
604	C₂²×D₄	#386	1	1	yes	characteristic
605	C₂²×D₄	#386	1	1	yes	characteristic
606	C₂²×D₄	#386	1	1	yes	characteristic
607	C₂²×D₄	C₂×#99	1	8	yes	—
608	C₂²×D₄	C₂²×C₄²	1	1	yes	characteristic
609	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
610	C₂²×D₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
611	C₂²×D₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
612	C₂²×D₄	C₂×#117	1	1	yes	characteristic
613	C₂²×D₄	C₂×#117	1	1	yes	characteristic
614	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
615	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
616	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
617	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
618	C₂²×D₄	C₂×#121	1	1	yes	characteristic
619	C₂²×D₄	C₂×#121	1	1	yes	characteristic
620	C₂²×D₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
621	C₂²×D₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
622	C₂²×D₄	C₂×#123	1	1	yes	characteristic
623	C₂²×D₄	C₂×#123	1	1	yes	characteristic
624	C₂³×C₄	C₂×#95	1	1	yes	characteristic
625	C₂³×C₄	C₂×#95	1	1	yes	characteristic
626	C₂³×C₄	C₂×#95	1	1	yes	characteristic
627	C₂³×C₄	C₂×#95	1	1	yes	characteristic
628	C₂³×C₄	#379	1	1	yes	characteristic
629	C₂³×C₄	#379	1	1	yes	characteristic
630	C₂³×C₄	#381	1	1	yes	characteristic
631	C₂³×C₄	#381	1	1	yes	characteristic
632	C₂³×C₄	#381	1	1	yes	characteristic
633	C₂³×C₄	#381	1	1	yes	characteristic
634	C₂³×C₄	#385	1	1	yes	characteristic
635	C₂³×C₄	#385	1	1	yes	characteristic
636	C₂³×C₄	#385	1	1	yes	characteristic
637	C₂³×C₄	#385	1	1	yes	characteristic
638	C₂³×C₄	#385	1	1	yes	characteristic
639	C₂³×C₄	#385	1	1	yes	characteristic
640	C₂³×C₄	#386	1	1	yes	characteristic
641	C₂³×C₄	#386	1	1	yes	characteristic
642	C₂³×C₄	#386	1	1	yes	characteristic
643	C₂³×C₄	#386	1	1	yes	characteristic
644	C₂³×C₄	#386	1	1	yes	characteristic
645	C₂³×C₄	#386	1	1	yes	characteristic
646	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
647	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
648	C₂³×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
649	C₂³×C₄	C₂×#120	1	1	yes	characteristic
650	C₂³×C₄	C₂×#123	1	1	yes	characteristic
651	C₂³×C₄	C₂×#123	1	1	yes	characteristic
652	#127	#342	1	8	yes	complemented
653	#127	C₂×#99	1	8	yes	—
654	#124	#342	1	8	yes	complemented
655	#124	C₂×#99	1	8	yes	—
656	#117	#342	1	8	yes	complemented
657	C₂×C₄²	C₂×#95	1	2	yes	—
658	C₂×C₄²	C₂×#95	1	2	yes	—
659	C₂×C₄²	C₂×#95	1	2	yes	—
660	C₂×C₄²	C₂×#95	1	2	yes	—
661	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
662	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
663	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
664	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
665	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
666	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
667	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
668	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
669	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
670	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
671	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
672	C₂⁴	C₂²⋊#95	1	1	yes	characteristic
673	C₂⁴	#1790	1	1	yes	characteristic
674	C₂⁴	#1790	1	1	yes	characteristic
675	C₂⁴	#1790	1	1	yes	characteristic
676	C₂⁴	#1790	1	1	yes	characteristic
677	C₂⁴	#1790	1	1	yes	characteristic
678	C₂⁴	#1790	1	1	yes	characteristic
679	C₂⁴	#1790	1	1	yes	characteristic
680	C₂⁴	#1790	1	1	yes	characteristic
681	C₂⁴	#1867	1	1	yes	characteristic
682	C₂⁴	#1867	1	1	yes	characteristic
683	C₂⁴	#1867	1	1	yes	characteristic
684	C₂⁴	#1867	1	1	yes	characteristic
685	C₂⁴	#1867	1	1	yes	characteristic
686	C₂⁴	#1867	1	1	yes	characteristic
687	C₂⁴	#1867	1	1	yes	characteristic
688	C₂⁴	#1867	1	1	yes	characteristic
689	C₂⁴	#1889	1	1	yes	characteristic
690	C₂⁴	#1889	1	1	yes	characteristic
691	C₂⁴	#1889	1	1	yes	characteristic
692	C₂⁴	#1889	1	1	yes	characteristic
693	C₂⁴	#1890	1	1	yes	characteristic
694	C₂⁴	#1890	1	1	yes	characteristic
695	C₂⁴	#1890	1	1	yes	characteristic
696	C₂⁴	#1890	1	1	yes	characteristic
697	C₂⁴	#1898	1	4	yes	—
698	C₂⁴	#1898	1	4	yes	—
699	C₂⁴	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
700	C₂⁴	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
701	C₂⁴	C₂×#379	1	1	yes	characteristic
702	C₂⁴	C₂×#380	1	1	yes	characteristic
703	C₂⁴	C₂×#380	1	1	yes	characteristic
704	C₂⁴	C₂×#385	1	1	yes	characteristic
705	C₂⁴	C₂×#385	1	1	yes	characteristic
706	C₂⁴	C₂×#385	1	1	yes	characteristic
707	C₂⁴	C₂×#386	1	1	yes	characteristic
708	C₂⁴	C₂×#386	1	1	yes	characteristic
709	C₂⁴	C₂×#386	1	1	yes	characteristic
710	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
711	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
712	C₂⁴	C₂×#458	1	1	yes	characteristic
713	C₂⁴	C₂×#458	1	1	yes	characteristic
714	C₂×Q₈	C₂×#342	1	4	yes	complemented
715	C₂×D₄	C₂×#342	1	4	yes	—
716	C₂×D₄	C₂×#342	1	4	yes	complemented
717	C₂×D₄	#1898	1	4	yes	—
718	C₂×D₄	#1898	1	4	yes	—
719	C₂×D₄	C₂²×#99	1	4	yes	—
720	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
721	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
722	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
723	C₂²×C₄	C₂²⋊#95	1	1	yes	characteristic
724	C₂²×C₄	C₂×#342	1	4	yes	—
725	C₂²×C₄	#1913	1	4	yes	—
726	C₂²×C₄	C₂²×#95	1	1	yes	characteristic
727	C₂²×C₄	C₂×#381	1	1	yes	characteristic
728	C₂²×C₄	C₂×#385	1	1	yes	characteristic
729	C₂²×C₄	C₂×#386	1	1	yes	characteristic
730	C₄²	C₂×#342	1	4	yes	complemented
731	C₄²	C₂×#342	1	4	yes	complemented
732	C₂³	#10735	1	2	yes	—
733	C₂³	#10735	1	2	yes	—
734	C₂³	#10735	1	2	yes	—
735	C₂³	#10745	1	1	yes	characteristic
736	C₂³	#10745	1	1	yes	characteristic
737	C₂³	#10745	1	1	yes	characteristic
738	C₂³	#10745	1	1	yes	characteristic
739	C₂³	#10745	1	1	yes	characteristic
740	C₂³	#10745	1	1	yes	characteristic
741	C₂³	#10745	1	1	yes	characteristic
742	C₂³	#10745	1	1	yes	characteristic
743	C₂³	#10754	1	2	yes	—
744	C₂³	#12753	1	2	yes	—
745	C₂³	#12754	1	2	yes	—
746	C₂³	C₂×C₂²⋊#95	1	1	yes	characteristic
747	C₂³	C₂×#1790	1	1	yes	characteristic
748	C₂³	C₂×#1790	1	1	yes	characteristic
749	C₂³	C₂×#1867	1	1	yes	characteristic
750	C₂³	C₂×#1867	1	1	yes	characteristic
751	C₂³	C₂×#1889	1	1	yes	characteristic
752	C₂³	C₂×#1890	1	1	yes	characteristic
753	C₂³	C₂×#1898	1	2	yes	—
754	C₂³	C₂×#1898	1	2	yes	—
755	C₂×C₄	#10735	1	2	yes	—
756	C₂×C₄	#10754	1	2	yes	—
757	C₂×C₄	C₂²×#342	1	2	yes	—
758	C₂×C₄	C₂×#1913	1	2	yes	—
759	C₂²	#106766	1	2	yes	—
760	C₂²	#106766	1	2	yes	—
761	C₂²	#146654	1	2	yes	—
762	C₂²	#146654	1	2	yes	—
763	C₂²	C₂×#10735	1	1	yes	characteristic
764	C₂²	C₂×#10745	1	1	yes	characteristic
765	C₂²	C₂×#10754	1	1	yes	characteristic
766	C₂²	C₂×#12753	1	1	yes	characteristic
767	C₂²	C₂×#12754	1	1	yes	characteristic
768	C₂²	#493562	1	2	yes	—
769	C₂	C₂×#146654	1	1	yes	characteristic
770	C₂	C₂×#106766	1	1	yes	characteristic
771	C₂	#72256611	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#10745
commutator	C₂²×D₄	C₂²×C₄²
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	C₂³×#535	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72238031	C₂	semidirect
3. #72236670	C₂	semidirect
4. C₂×#106766	C₂	semidirect
6. C₂×#128073	C₂	semidirect
8. #72210473	C₂	semidirect
9. #72210462	C₂	semidirect
12. C₂²×#2127	C₄	semidirect
18. #559859	C₄	semidirect
19. #559850	C₄	semidirect
20. #552678	C₄	semidirect
21. #552671	C₄	semidirect
22. #532187	C₄	semidirect
23. #531766	C₄	semidirect
26. #493370	C₄	semidirect
29. #359509	C₄	semidirect
32. C₂×#10989	C₄	semidirect
33. #128073	C₂²	semidirect
34. #128073	C₂²	semidirect
35. #106766	C₂²	semidirect
36. #106766	C₂²	semidirect
61. C₂³×#100	C₂×C₄	semidirect
62. C₂³×#99	C₂×C₄	semidirect
63. C₂³×#99	C₂×C₄	semidirect
64. #34171	C₂×C₄	semidirect
66. C₂×#2309	C₂×C₄	semidirect
70. C₂×#2127	C₂×C₄	semidirect
71. C₂×#2127	C₂×C₄	semidirect
72. C₂×#1783	C₂×C₄	semidirect
74. C₂×#1781	C₂×C₄	semidirect
75. C₂×#1781	C₂×C₄	semidirect
78. #14662	C₂×C₄	semidirect
79. #14661	C₂×C₄	semidirect
80. #14492	C₂×C₄	semidirect
81. #14492	C₂×C₄	semidirect
82. #14419	C₂×C₄	semidirect
83. #14419	C₂×C₄	semidirect
86. #14169	C₂×C₄	semidirect
87. #14154	C₂×C₄	semidirect
102. #10989	C₂×C₄	semidirect
103. #10989	C₂×C₄	semidirect
554. C₂×#41	#342	semidirect
652. #127	#342	semidirect
654. #124	#342	semidirect
656. #117	#342	semidirect
714. C₂×Q₈	C₂×#342	semidirect
716. C₂×D₄	C₂×#342	semidirect
730. C₄²	C₂×#342	semidirect
731. C₄²	C₂×#342	semidirect

Maximal subgroups

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

subgroup	index
#72263548	2
#72238031	2
#72236670	2
C₂×#106766	2
C₂×#493370	2
C₂×#128073	2
C₂×#359509	2
#72210473	2
#72210462	2