Subgroups — #72302147

Order 2048.

At least 8069 conjugacy classes of subgroups; only the 1108 normal subgroups are shown.

The subgroup lattice has 769 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72302144	C₂	1	1	yes	maximal, characteristic, complemented
2	#72281701	C₂	1	1	yes	maximal, characteristic, complemented
3	#72281325	C₂	1	2	yes	maximal, complemented
4	#72281067	C₂	1	2	yes	maximal, complemented
5	#72280709	C₂	1	1	yes	maximal, characteristic, complemented
6	#72280662	C₂	1	1	yes	maximal, characteristic, complemented
7	#72280430	C₂	1	1	yes	maximal, characteristic
8	#72280243	C₂	1	1	yes	maximal, characteristic, complemented
9	#72263920	C₂	1	1	yes	maximal, characteristic, complemented
10	#72239047	C₂	1	2	yes	maximal, complemented
11	#72216619	C₂	1	2	yes	maximal, complemented
12	C₂²×#3481	C₂²	1	1	yes	characteristic
13	#10574447	C₂²	1	1	yes	characteristic
14	#10574126	C₂²	1	1	yes	characteristic
15	C₂×#34593	C₂²	1	1	yes	characteristic
16	C₂²×#2397	C₂²	1	1	yes	characteristic
17	C₂×C₄×#535	C₂²	1	1	yes	characteristic
18	#6370977	C₂²	1	2	yes	—
19	#6370977	C₂²	1	2	yes	complemented
20	#6370937	C₂²	1	1	yes	characteristic
21	#6343354	C₂²	1	2	yes	—
22	#6343018	C₂²	1	2	yes	—
23	C₂×#17448	C₂²	1	2	yes	—
24	C₂×#17448	C₂²	1	2	yes	complemented
25	#6342561	C₂²	1	1	yes	characteristic
26	#758019	C₄	1	2	yes	complemented
27	#758017	C₄	1	2	yes	complemented
28	#754562	C₄	1	2	yes	complemented
29	#754560	C₄	1	2	yes	complemented
30	#514638	C₂²	1	1	yes	characteristic
31	#514210	C₂²	1	1	yes	characteristic
32	#514189	C₂²	1	1	yes	characteristic
33	#353782	C₂²	1	2	yes	complemented
34	#353774	C₂²	1	2	yes	complemented
35	#181778	C₂²	1	2	yes	complemented
36	#181430	C₂²	1	2	yes	complemented
37	#181176	C₂²	1	2	yes	complemented
38	C₂×#7855	C₂²	1	2	yes	complemented
39	C₂²×#559	C₂×C₄	1	1	yes	characteristic
40	C₂²×#553	C₂×C₄	1	1	yes	characteristic
41	C₂²×#553	D₄	1	1	yes	characteristic
42	C₂²×#554	C₂×C₄	1	1	yes	characteristic
43	C₂²×#554	D₄	1	1	yes	characteristic
44	C₂²×#546	C₂×C₄	1	1	yes	characteristic
45	C₂²×#546	D₄	1	1	yes	characteristic
46	C₂²×D₄²	D₄	1	1	yes	characteristic
47	C₂²×#535	D₄	1	1	yes	characteristic
48	C₂²×#532	D₄	1	1	yes	characteristic
49	C₂²×#529	D₄	1	1	yes	characteristic
50	C₂²×#529	C₂³	1	1	yes	characteristic
51	C₂²×C₄×#41	D₄	1	1	yes	characteristic
52	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
53	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
54	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
55	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
56	#60284	D₄	1	2	yes	complemented
57	#60282	D₄	1	2	yes	complemented
58	#60123	D₄	1	2	yes	complemented
59	C₂×#2920	C₂³	1	2	yes	—
60	C₂×#2920	C₂³	1	2	yes	—
61	C₂×#2920	C₂³	1	2	yes	—
62	C₄×#568	D₄	1	2	yes	complemented
63	C₂×#2633	C₂×C₄	1	2	yes	—
64	C₂×#2631	C₂×C₄	1	2	yes	—
65	C₂×#2397	C₂×C₄	1	2	yes	—
66	C₂×#2397	C₂×C₄	1	2	yes	—
67	C₂×#2328	C₂×C₄	1	2	yes	—
68	C₂×#2326	C₂×C₄	1	2	yes	—
69	C₂×#2317	D₄	1	1	yes	characteristic
70	C₂×#2311	D₄	1	1	yes	characteristic
71	C₂×#2309	D₄	1	1	yes	characteristic
72	C₂×C₄×#127	D₄	1	2	yes	—
73	C₂×C₄×#124	D₄	1	2	yes	—
74	#34012	C₂³	1	2	yes	—
75	C₂×#2283	C₂³	1	1	yes	characteristic
76	C₂×C₄×#117	C₂³	1	1	yes	characteristic
77	C₂²×#376	C₂³	1	1	yes	characteristic
78	#20632	D₄	1	2	yes	complemented
79	#20632	D₄	1	2	yes	complemented
80	#17480	D₄	1	8	yes	complemented
81	C₂×#1486	D₄	1	8	yes	complemented
82	#17349	D₄	1	2	yes	complemented
83	#17349	D₄	1	2	yes	complemented
84	#14170	C₂×C₄	1	2	yes	—
85	#14169	C₂×C₄	1	2	yes	—
86	#13961	C₂×C₄	1	2	yes	—
87	#13959	C₂×C₄	1	2	yes	—
88	#13959	C₂×C₄	1	2	yes	—
89	#13959	C₂×C₄	1	2	yes	—
90	#13957	D₄	1	2	yes	—
91	#13957	D₄	1	2	yes	—
92	C₄×#386	D₄	1	2	yes	—
93	C₄×#386	D₄	1	2	yes	—
94	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
95	C₂³×#41	C₂×D₄	1	1	yes	characteristic
96	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
98	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×#127	C₂²⋊C₄	1	2	yes	—
102	C₂×#529	C₂×D₄	1	4	yes	—
103	C₂×#529	#41	1	4	yes	—
104	C₂²×#125	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×#125	C₂²×C₄	1	1	yes	characteristic
106	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×#124	C₂²⋊C₄	1	2	yes	—
108	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
111	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×#121	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×#41	#41	1	1	yes	characteristic
124	C₂×C₄×#41	#41	1	1	yes	characteristic
125	C₂×C₄×#41	#41	1	1	yes	characteristic
126	C₂×C₄×#41	#41	1	1	yes	characteristic
127	C₂×C₄×#41	#41	1	1	yes	characteristic
128	C₂×C₄×#41	#41	1	1	yes	characteristic
129	C₂×C₄×#41	#41	1	1	yes	characteristic
130	C₂×C₄×#41	#41	1	1	yes	characteristic
131	C₂²×C₄×Q₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
143	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
147	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×D₄	#41	1	4	yes	—
153	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×#117	C₂×D₄	1	1	yes	characteristic
155	C₂²×#117	C₂×D₄	1	1	yes	characteristic
156	C₂²×#117	C₂×D₄	1	1	yes	characteristic
157	C₂²×#117	C₂×D₄	1	1	yes	characteristic
158	C₂²×#117	C₂×D₄	1	1	yes	characteristic
159	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₄²	C₂×D₄	1	2	yes	—
163	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
165	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
166	#2920	C₂×D₄	1	4	yes	—
167	#2920	C₂×D₄	1	4	yes	—
168	C₂×#431	C₂×D₄	1	4	yes	—
169	C₂×#431	C₂×D₄	1	4	yes	—
170	C₂×#431	C₂×D₄	1	4	yes	—
171	C₂×#423	C₂×D₄	1	4	yes	—
172	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
173	C₂×#391	C₂²⋊C₄	1	2	yes	—
174	C₂×#390	C₂²⋊C₄	1	2	yes	—
175	C₂×#390	C₂²⋊C₄	1	2	yes	—
176	C₂×#390	C₂²⋊C₄	1	2	yes	—
177	#2285	C₂×D₄	1	4	yes	—
178	C₂×#384	C₂²⋊C₄	1	2	yes	—
179	C₂×#383	C₂²×C₄	1	2	yes	—
180	C₂×#382	C₂²⋊C₄	1	2	yes	—
181	C₂×#382	C₂×D₄	1	2	yes	—
182	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
183	C₂×#376	C₂²×C₄	1	2	yes	—
184	C₂×#376	C₂²×C₄	1	2	yes	—
185	C₂×#376	C₂×D₄	1	2	yes	—
186	C₂×C₄³	C₂×D₄	1	2	yes	—
187	#1437	C₂²⋊C₄	1	4	yes	—
188	#1437	C₂²⋊C₄	1	4	yes	—
189	#1436	C₂²⋊C₄	1	4	yes	—
190	#1436	C₂²⋊C₄	1	4	yes	—
191	C₂²×#41	#120	1	1	yes	characteristic
192	C₂²×#41	#120	1	1	yes	characteristic
193	C₂²×#41	#121	1	1	yes	characteristic
194	C₂²×#41	#121	1	1	yes	characteristic
195	C₂²×#41	#121	1	1	yes	characteristic
196	C₂²×#41	#121	1	1	yes	characteristic
197	C₂²×#41	#123	1	1	yes	characteristic
198	C₂²×#41	#123	1	1	yes	characteristic
199	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×D₄	#120	1	1	yes	characteristic
207	C₂³×D₄	#120	1	1	yes	characteristic
208	C₂³×D₄	#121	1	4	yes	—
209	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂⁴×C₄	#120	1	1	yes	characteristic
212	C₂⁴×C₄	#120	1	1	yes	characteristic
213	C₂⁴×C₄	#120	1	1	yes	characteristic
214	C₂⁴×C₄	#120	1	1	yes	characteristic
215	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
216	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
217	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
218	C₂×#125	C₄×D₄	1	4	yes	—
219	C₂×#124	C₄×D₄	1	4	yes	—
220	C₂×C₂²⋊Q₈	#121	1	4	yes	—
221	C₂×#121	#121	1	4	yes	—
222	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×Q₈	#120	1	2	yes	—
231	C₂×C₄×Q₈	#120	1	1	yes	characteristic
232	C₂×C₄×Q₈	#120	1	1	yes	characteristic
233	C₂×C₄×Q₈	#121	1	1	yes	characteristic
234	C₂×C₄×Q₈	#121	1	1	yes	characteristic
235	C₂×C₄×Q₈	#121	1	1	yes	characteristic
236	C₂×C₄×Q₈	#121	1	1	yes	characteristic
237	C₂×C₄×Q₈	#123	1	2	yes	—
238	C₂×C₄×Q₈	#123	1	1	yes	characteristic
239	C₂×C₄×Q₈	#123	1	1	yes	characteristic
240	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
241	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
242	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×D₄	#120	1	2	yes	—
251	C₂×C₄×D₄	#120	1	2	yes	—
252	C₂×C₄×D₄	#120	1	2	yes	—
253	C₂×C₄×D₄	#120	1	1	yes	characteristic
254	C₂×C₄×D₄	#120	1	1	yes	characteristic
255	C₂×C₄×D₄	#120	1	1	yes	characteristic
256	C₂×C₄×D₄	#120	1	1	yes	characteristic
257	C₂×C₄×D₄	#120	1	1	yes	characteristic
258	C₂×C₄×D₄	#120	1	1	yes	characteristic
259	C₂×C₄×D₄	#121	1	1	yes	characteristic
260	C₂×C₄×D₄	#121	1	1	yes	characteristic
261	C₂×C₄×D₄	#121	1	1	yes	characteristic
262	C₂×C₄×D₄	#121	1	1	yes	characteristic
263	C₂×C₄×D₄	#121	1	1	yes	characteristic
264	C₂×C₄×D₄	#121	1	1	yes	characteristic
265	C₂×C₄×D₄	#121	1	1	yes	characteristic
266	C₂×C₄×D₄	#121	1	1	yes	characteristic
267	C₂×C₄×D₄	#121	1	1	yes	characteristic
268	C₂×C₄×D₄	#121	1	1	yes	characteristic
269	C₂×C₄×D₄	#121	1	1	yes	characteristic
270	C₂×C₄×D₄	#121	1	1	yes	characteristic
271	C₂×C₄×D₄	#121	1	1	yes	characteristic
272	C₂×C₄×D₄	#121	1	1	yes	characteristic
273	C₂×C₄×D₄	#121	1	1	yes	characteristic
274	C₂×C₄×D₄	#121	1	1	yes	characteristic
275	C₂×C₄×D₄	#121	1	1	yes	characteristic
276	C₂×C₄×D₄	#121	1	1	yes	characteristic
277	C₂×C₄×D₄	#121	1	1	yes	characteristic
278	C₂×C₄×D₄	#121	1	1	yes	characteristic
279	C₂×C₄×D₄	#123	1	2	yes	—
280	C₂×C₄×D₄	#123	1	2	yes	—
281	C₂×C₄×D₄	#123	1	2	yes	—
282	C₂×C₄×D₄	#123	1	1	yes	characteristic
283	C₂×C₄×D₄	#123	1	1	yes	characteristic
284	C₂×C₄×D₄	#123	1	1	yes	characteristic
285	C₂×C₄×D₄	#123	1	1	yes	characteristic
286	C₂×C₄×D₄	#123	1	1	yes	characteristic
287	C₂×C₄×D₄	#123	1	1	yes	characteristic
288	C₂×C₄×D₄	#124	1	1	yes	characteristic
289	C₂×C₄×D₄	#124	1	1	yes	characteristic
290	C₂×C₄×D₄	#124	1	1	yes	characteristic
291	C₂×C₄×D₄	#124	1	1	yes	characteristic
292	C₂×C₄×D₄	#127	1	1	yes	characteristic
293	C₂×C₄×D₄	#127	1	1	yes	characteristic
294	C₂×C₄×D₄	#127	1	1	yes	characteristic
295	C₂×C₄×D₄	#127	1	1	yes	characteristic
296	C₂×#117	#120	1	1	yes	characteristic
297	C₂×#117	#120	1	1	yes	characteristic
298	C₂×#117	#121	1	1	yes	characteristic
299	C₂×#117	#121	1	1	yes	characteristic
300	C₂×#117	#121	1	1	yes	characteristic
301	C₂×#117	#121	1	1	yes	characteristic
302	C₂×#117	#121	1	1	yes	characteristic
303	C₂×#117	#121	1	1	yes	characteristic
304	C₂×#117	#121	1	1	yes	characteristic
305	C₂×#117	#121	1	1	yes	characteristic
306	C₂×#117	#121	1	1	yes	characteristic
307	C₂×#117	#121	1	1	yes	characteristic
308	C₂×#117	#121	1	1	yes	characteristic
309	C₂×#117	#121	1	1	yes	characteristic
310	C₂×#117	#123	1	1	yes	characteristic
311	C₂×#117	#123	1	1	yes	characteristic
312	C₂×#117	#124	1	1	yes	characteristic
313	C₂×#117	#124	1	1	yes	characteristic
314	C₂×#117	#124	1	1	yes	characteristic
315	C₂×#117	#124	1	1	yes	characteristic
316	C₂×#117	#127	1	1	yes	characteristic
317	C₂×#117	#127	1	1	yes	characteristic
318	C₂×#117	#127	1	1	yes	characteristic
319	C₂×#117	#127	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	#121	1	4	yes	—
332	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
338	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
341	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂²×C₄²	#120	1	1	yes	characteristic
344	C₂²×C₄²	#120	1	1	yes	characteristic
345	C₂²×C₄²	#120	1	1	yes	characteristic
346	C₂²×C₄²	#120	1	1	yes	characteristic
347	C₂²×C₄²	#120	1	1	yes	characteristic
348	C₂²×C₄²	#120	1	1	yes	characteristic
349	C₂²×C₄²	#120	1	1	yes	characteristic
350	C₂²×C₄²	#120	1	1	yes	characteristic
351	C₂²×C₄²	#121	1	1	yes	characteristic
352	C₂²×C₄²	#121	1	1	yes	characteristic
353	C₂²×C₄²	#121	1	1	yes	characteristic
354	C₂²×C₄²	#121	1	1	yes	characteristic
355	C₂²×C₄²	#121	1	1	yes	characteristic
356	C₂²×C₄²	#121	1	1	yes	characteristic
357	C₂²×C₄²	#121	1	1	yes	characteristic
358	C₂²×C₄²	#121	1	1	yes	characteristic
359	C₂²×C₄²	#123	1	1	yes	characteristic
360	C₂²×C₄²	#123	1	1	yes	characteristic
361	C₂²×C₄²	#123	1	1	yes	characteristic
362	C₂²×C₄²	#123	1	1	yes	characteristic
363	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
364	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
366	C₂²×C₄²	C₂²×D₄	1	2	yes	—
367	C₂²×C₄²	C₂²×D₄	1	2	yes	—
368	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
373	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
374	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
375	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
376	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
377	C₂²×C₄²	C₂×#41	1	2	yes	—
378	C₂²×C₄²	C₂×#41	1	2	yes	—
379	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
381	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
382	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
383	#423	#120	1	8	yes	complemented
384	C₂×C₄×C₈	#120	1	8	yes	complemented
385	C₂×#95	C₂×C₂²⋊C₄	1	4	yes	—
386	C₂⁵	#379	1	1	yes	characteristic
387	C₂⁵	#379	1	1	yes	characteristic
388	C₂⁵	C₂×#120	1	1	yes	characteristic
389	C₂²×Q₈	#386	1	2	yes	—
390	C₂²×Q₈	#386	1	1	yes	characteristic
391	C₂²×Q₈	#386	1	1	yes	characteristic
392	C₂²×Q₈	#386	1	1	yes	characteristic
393	C₂²×Q₈	#386	1	1	yes	characteristic
394	C₂²×D₄	#386	1	1	yes	characteristic
395	C₂²×D₄	#386	1	1	yes	characteristic
396	C₂²×D₄	#386	1	2	yes	—
397	C₂²×D₄	#386	1	2	yes	—
398	C₂²×D₄	#386	1	1	yes	characteristic
399	C₂²×D₄	#386	1	1	yes	characteristic
400	C₂²×D₄	#386	1	2	yes	—
401	C₂²×D₄	#392	1	1	yes	characteristic
402	C₂²×D₄	#392	1	1	yes	characteristic
403	C₂²×D₄	#392	1	1	yes	characteristic
404	C₂²×D₄	#392	1	1	yes	characteristic
405	C₂²×D₄	#394	1	1	yes	characteristic
406	C₂²×D₄	#394	1	1	yes	characteristic
407	C₂²×D₄	#394	1	1	yes	characteristic
408	C₂²×D₄	#394	1	1	yes	characteristic
409	C₂³×C₄	#379	1	1	yes	characteristic
410	C₂³×C₄	#379	1	1	yes	characteristic
411	C₂³×C₄	#379	1	1	yes	characteristic
412	C₂³×C₄	#379	1	1	yes	characteristic
413	C₂³×C₄	#379	1	1	yes	characteristic
414	C₂³×C₄	#379	1	1	yes	characteristic
415	C₂³×C₄	#386	1	1	yes	characteristic
416	C₂³×C₄	#386	1	1	yes	characteristic
417	C₂³×C₄	#386	1	1	yes	characteristic
418	C₂³×C₄	#386	1	1	yes	characteristic
419	C₂³×C₄	#386	1	1	yes	characteristic
420	C₂³×C₄	#386	1	1	yes	characteristic
421	C₂³×C₄	#386	1	1	yes	characteristic
422	C₂³×C₄	#386	1	1	yes	characteristic
423	C₂³×C₄	#392	1	1	yes	characteristic
424	C₂³×C₄	#392	1	1	yes	characteristic
425	C₂³×C₄	#392	1	1	yes	characteristic
426	C₂³×C₄	#392	1	1	yes	characteristic
427	C₂³×C₄	#392	1	1	yes	characteristic
428	C₂³×C₄	#392	1	1	yes	characteristic
429	C₂³×C₄	#392	1	1	yes	characteristic
430	C₂³×C₄	#392	1	1	yes	characteristic
431	C₂³×C₄	#394	1	1	yes	characteristic
432	C₂³×C₄	#394	1	1	yes	characteristic
433	C₂³×C₄	#394	1	1	yes	characteristic
434	C₂³×C₄	#394	1	1	yes	characteristic
435	C₂³×C₄	#394	1	1	yes	characteristic
436	C₂³×C₄	#394	1	1	yes	characteristic
437	C₂³×C₄	#394	1	1	yes	characteristic
438	C₂³×C₄	#394	1	1	yes	characteristic
439	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
440	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
441	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
442	C₂³×C₄	C₂×#120	1	1	yes	characteristic
443	C₂³×C₄	C₂×#120	1	1	yes	characteristic
444	C₂³×C₄	C₂×#120	1	1	yes	characteristic
445	C₂³×C₄	C₂×#120	1	1	yes	characteristic
446	C₂³×C₄	C₂×#120	1	1	yes	characteristic
447	C₂³×C₄	C₂×#121	1	1	yes	characteristic
448	C₂³×C₄	C₂×#121	1	2	yes	—
449	C₂³×C₄	C₂×#121	1	1	yes	characteristic
450	C₂³×C₄	C₂×#121	1	1	yes	characteristic
451	C₂³×C₄	C₂×#121	1	1	yes	characteristic
452	C₂³×C₄	C₂×#121	1	1	yes	characteristic
453	C₂³×C₄	C₂×#121	1	1	yes	characteristic
454	C₂³×C₄	C₂×#121	1	2	yes	—
455	C₂³×C₄	C₂×#123	1	1	yes	characteristic
456	C₂³×C₄	C₂×#123	1	1	yes	characteristic
457	C₂³×C₄	C₂×#124	1	1	yes	characteristic
458	C₂³×C₄	C₂×#127	1	1	yes	characteristic
459	C₂³×C₄	#534	1	2	yes	—
460	C₂³×C₄	#534	1	2	yes	—
461	C₂³×C₄	D₄²	1	2	yes	—
462	C₂³×C₄	D₄²	1	2	yes	—
463	C₂³×C₄	D₄²	1	2	yes	—
464	C₂³×C₄	D₄²	1	2	yes	—
465	C₂³×C₄	#546	1	2	yes	—
466	C₂³×C₄	#546	1	2	yes	—
467	C₂³×C₄	#546	1	2	yes	—
468	C₂³×C₄	#546	1	2	yes	—
469	C₂×C₄⋊C₄	#386	1	2	yes	—
470	C₂×C₄⋊C₄	#386	1	2	yes	—
471	C₂×C₄⋊C₄	#386	1	2	yes	—
472	C₂×C₄⋊C₄	#386	1	2	yes	—
473	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
474	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
475	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
476	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
477	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
478	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
479	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
480	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
481	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
482	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
483	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
484	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
485	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
486	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
487	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
488	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
489	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
490	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
491	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
492	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
493	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
494	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
495	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
496	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
521	C₂×C₄²	#386	1	1	yes	characteristic
522	C₂×C₄²	#386	1	1	yes	characteristic
523	C₂×C₄²	#386	1	1	yes	characteristic
524	C₂×C₄²	#386	1	1	yes	characteristic
525	C₂×C₄²	#386	1	1	yes	characteristic
526	C₂×C₄²	#386	1	1	yes	characteristic
527	C₂×C₄²	#386	1	1	yes	characteristic
528	C₂×C₄²	#386	1	1	yes	characteristic
529	C₂×C₄²	#392	1	1	yes	characteristic
530	C₂×C₄²	#392	1	1	yes	characteristic
531	C₂×C₄²	#392	1	1	yes	characteristic
532	C₂×C₄²	#392	1	1	yes	characteristic
533	C₂×C₄²	#392	1	1	yes	characteristic
534	C₂×C₄²	#392	1	1	yes	characteristic
535	C₂×C₄²	#392	1	1	yes	characteristic
536	C₂×C₄²	#392	1	1	yes	characteristic
537	C₂×C₄²	#394	1	1	yes	characteristic
538	C₂×C₄²	#394	1	1	yes	characteristic
539	C₂×C₄²	#394	1	1	yes	characteristic
540	C₂×C₄²	#394	1	1	yes	characteristic
541	C₂×C₄²	#394	1	1	yes	characteristic
542	C₂×C₄²	#394	1	1	yes	characteristic
543	C₂×C₄²	#394	1	1	yes	characteristic
544	C₂×C₄²	#394	1	1	yes	characteristic
545	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
546	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
547	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
548	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
549	C₂×C₄²	C₂×C₄×D₄	1	2	yes	—
550	C₂×C₄²	C₂×C₄×D₄	1	2	yes	—
551	C₂×C₄²	#518	1	2	yes	—
552	C₂×C₄²	#518	1	2	yes	—
553	C₂×C₄²	C₂×#120	1	1	yes	characteristic
554	C₂×C₄²	C₂×#120	1	1	yes	characteristic
555	C₂×C₄²	C₂×#120	1	1	yes	characteristic
556	C₂×C₄²	C₂×#120	1	2	yes	—
557	C₂×C₄²	C₂×#120	1	2	yes	—
558	C₂×C₄²	C₂×#120	1	1	yes	characteristic
559	C₂×C₄²	C₂×#121	1	1	yes	characteristic
560	C₂×C₄²	C₂×#121	1	1	yes	characteristic
561	C₂×C₄²	C₂×#121	1	1	yes	characteristic
562	C₂×C₄²	C₂×#121	1	1	yes	characteristic
563	C₂×C₄²	C₂×#121	1	1	yes	characteristic
564	C₂×C₄²	C₂×#121	1	1	yes	characteristic
565	C₂×C₄²	C₂×#123	1	1	yes	characteristic
566	C₂×C₄²	C₂×#123	1	1	yes	characteristic
567	C₂×C₄²	C₂×#123	1	1	yes	characteristic
568	C₂×C₄²	C₂×#123	1	1	yes	characteristic
569	C₂×C₄²	#525	1	2	yes	—
570	C₂×C₄²	#525	1	2	yes	—
571	C₂×C₄²	#525	1	2	yes	—
572	C₂×C₄²	#525	1	2	yes	—
573	C₂×C₄²	#525	1	2	yes	—
574	C₂×C₄²	#525	1	2	yes	—
575	C₂×C₄²	C₂×#124	1	1	yes	characteristic
576	C₂×C₄²	C₂×#127	1	1	yes	characteristic
577	C₂×C₄²	#534	1	2	yes	—
578	C₂×C₄²	#534	1	2	yes	—
579	C₂×C₄²	#534	1	1	yes	characteristic
580	C₂×C₄²	#534	1	1	yes	characteristic
581	C₂×C₄²	#534	1	1	yes	characteristic
582	C₂×C₄²	#534	1	1	yes	characteristic
583	C₂×C₄²	#535	1	2	yes	—
584	C₂×C₄²	#535	1	2	yes	—
585	C₂×C₄²	#538	1	2	yes	—
586	C₂×C₄²	#538	1	2	yes	—
587	C₂×C₄²	#538	1	2	yes	—
588	C₂×C₄²	#538	1	2	yes	—
589	C₂×C₄²	D₄²	1	2	yes	—
590	C₂×C₄²	D₄²	1	2	yes	—
591	C₂×C₄²	D₄²	1	2	yes	—
592	C₂×C₄²	D₄²	1	2	yes	—
593	C₂×C₄²	D₄²	1	2	yes	—
594	C₂×C₄²	D₄²	1	2	yes	—
595	C₂×C₄²	D₄²	1	2	yes	—
596	C₂×C₄²	D₄²	1	2	yes	—
597	C₂×C₄²	#546	1	2	yes	—
598	C₂×C₄²	#546	1	2	yes	—
599	C₂×C₄²	#546	1	2	yes	—
600	C₂×C₄²	#546	1	2	yes	—
601	C₂×C₄²	#546	1	2	yes	—
602	C₂×C₄²	#546	1	2	yes	—
603	C₂×C₄²	#546	1	2	yes	—
604	C₂×C₄²	#546	1	2	yes	—
605	C₂×C₄²	#546	1	2	yes	—
606	C₂×C₄²	#546	1	2	yes	—
607	C₂×C₄²	#546	1	2	yes	—
608	C₂×C₄²	#546	1	2	yes	—
609	C₂×C₄²	#551	1	2	yes	—
610	C₂×C₄²	#551	1	2	yes	—
611	C₂×C₄²	#551	1	2	yes	—
612	C₂×C₄²	#551	1	2	yes	—
613	C₂⁴	#1438	1	1	yes	characteristic
614	C₂⁴	#1438	1	1	yes	characteristic
615	C₂⁴	#1438	1	1	yes	characteristic
616	C₂⁴	#1438	1	1	yes	characteristic
617	C₂⁴	C₂×#379	1	1	yes	characteristic
618	C₂⁴	C₂×#392	1	1	yes	characteristic
619	C₂⁴	C₂×#394	1	1	yes	characteristic
620	C₂⁴	#2410	1	2	yes	—
621	C₂⁴	#2410	1	2	yes	—
622	C₂×D₄	#2010	1	4	yes	—
623	C₂²×C₄	#1438	1	1	yes	characteristic
624	C₂²×C₄	#1438	1	1	yes	characteristic
625	C₂²×C₄	#1438	1	1	yes	characteristic
626	C₂²×C₄	#1438	1	1	yes	characteristic
627	C₂²×C₄	#1438	1	1	yes	characteristic
628	C₂²×C₄	#1438	1	1	yes	characteristic
629	C₂²×C₄	#1438	1	1	yes	characteristic
630	C₂²×C₄	#1438	1	1	yes	characteristic
631	C₂²×C₄	#1438	1	1	yes	characteristic
632	C₂²×C₄	#1438	1	1	yes	characteristic
633	C₂²×C₄	#1438	1	1	yes	characteristic
634	C₂²×C₄	#1438	1	1	yes	characteristic
635	C₂²×C₄	C₂×#386	1	1	yes	characteristic
636	C₂²×C₄	C₂×#386	1	1	yes	characteristic
637	C₂²×C₄	C₂×#386	1	1	yes	characteristic
638	C₂²×C₄	C₂×#386	1	1	yes	characteristic
639	C₂²×C₄	C₂×#386	1	1	yes	characteristic
640	C₂²×C₄	C₂×#386	1	1	yes	characteristic
641	C₂²×C₄	C₂×#390	1	1	yes	characteristic
642	C₂²×C₄	C₂×#390	1	1	yes	characteristic
643	C₂²×C₄	#2308	1	1	yes	characteristic
644	C₂²×C₄	#2308	1	1	yes	characteristic
645	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
646	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
647	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
648	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
649	C₂²×C₄	C₂×#392	1	1	yes	characteristic
650	C₂²×C₄	C₂×#392	1	1	yes	characteristic
651	C₂²×C₄	C₂×#392	1	1	yes	characteristic
652	C₂²×C₄	C₂×#394	1	1	yes	characteristic
653	C₂²×C₄	C₂×#394	1	1	yes	characteristic
654	C₂²×C₄	C₂×#394	1	1	yes	characteristic
655	C₂²×C₄	#2403	1	2	yes	—
656	C₂²×C₄	#2403	1	1	yes	characteristic
657	C₂²×C₄	#2403	1	1	yes	characteristic
658	C₂²×C₄	#2403	1	1	yes	characteristic
659	C₂²×C₄	#2403	1	1	yes	characteristic
660	C₂²×C₄	#2404	1	2	yes	—
661	C₂²×C₄	#2405	1	1	yes	characteristic
662	C₂²×C₄	#2405	1	1	yes	characteristic
663	C₂²×C₄	#2405	1	1	yes	characteristic
664	C₂²×C₄	#2405	1	1	yes	characteristic
665	C₂²×C₄	#2408	1	2	yes	—
666	C₂²×C₄	#2410	1	2	yes	—
667	C₂²×C₄	#2410	1	2	yes	—
668	C₂²×C₄	#2410	1	2	yes	—
669	C₂²×C₄	#2410	1	2	yes	—
670	C₂²×C₄	#2410	1	2	yes	—
671	C₂²×C₄	#2411	1	2	yes	—
672	C₂²×C₄	#2412	1	2	yes	—
673	C₂²×C₄	#2412	1	2	yes	—
674	C₂²×C₄	#2418	1	2	yes	—
675	C₂²×C₄	#2418	1	2	yes	—
676	C₂²×C₄	#2424	1	2	yes	—
677	C₂²×C₄	#2424	1	2	yes	—
678	C₂²×C₄	#2424	1	2	yes	—
679	C₂²×C₄	#2424	1	2	yes	—
680	C₂²×C₄	#2433	1	2	yes	—
681	C₂²×C₄	#2472	1	2	yes	—
682	C₂²×C₄	#2472	1	2	yes	—
683	C₂²×C₄	#2534	1	2	yes	—
684	C₂²×C₄	#2539	1	2	yes	—
685	C₂²×C₄	#2617	1	2	yes	—
686	C₂²×C₄	#2617	1	2	yes	—
687	C₂²×C₄	#2847	1	2	yes	—
688	C₂²×C₄	#2847	1	2	yes	—
689	C₄²	C₄×#120	1	2	yes	—
690	C₄²	C₄×#120	1	2	yes	—
691	C₄²	#2321	1	2	yes	—
692	C₄²	#2321	1	2	yes	—
693	C₄²	#2358	1	2	yes	—
694	C₄²	#2358	1	2	yes	—
695	C₄²	#2358	1	2	yes	—
696	C₄²	#2358	1	2	yes	—
697	C₄²	#2403	1	2	yes	—
698	C₄²	#2404	1	2	yes	—
699	C₄²	#2408	1	2	yes	—
700	C₄²	#2410	1	1	yes	characteristic
701	C₄²	#2410	1	1	yes	characteristic
702	C₄²	#2410	1	1	yes	characteristic
703	C₄²	#2410	1	1	yes	characteristic
704	C₄²	#2410	1	2	yes	—
705	C₄²	#2411	1	2	yes	—
706	C₄²	#2412	1	1	yes	characteristic
707	C₄²	#2412	1	1	yes	characteristic
708	C₄²	#2412	1	1	yes	characteristic
709	C₄²	#2412	1	1	yes	characteristic
710	C₄²	#2418	1	2	yes	—
711	C₄²	#2418	1	2	yes	—
712	C₄²	#2424	1	2	yes	—
713	C₄²	#2424	1	2	yes	—
714	C₄²	#2424	1	2	yes	—
715	C₄²	#2424	1	2	yes	—
716	C₄²	#2433	1	2	yes	—
717	C₄²	#2472	1	2	yes	—
718	C₄²	#2472	1	2	yes	—
719	C₄²	#2534	1	2	yes	—
720	C₄²	#2539	1	2	yes	—
721	C₄²	#2613	1	1	yes	characteristic
722	C₄²	#2613	1	1	yes	characteristic
723	C₄²	#2622	1	1	yes	characteristic
724	C₄²	#2622	1	1	yes	characteristic
725	C₄²	#2846	1	1	yes	characteristic
726	C₄²	#2849	1	1	yes	characteristic
727	C₄²	#2849	1	1	yes	characteristic
728	C₄²	#2849	1	1	yes	characteristic
729	C₂³	#10994	1	2	yes	—
730	C₂³	C₂×#1438	1	1	yes	characteristic
731	C₂³	#13867	1	1	yes	characteristic
732	C₂³	#13867	1	1	yes	characteristic
733	C₂³	#14716	1	2	yes	—
734	C₂³	#14725	1	2	yes	—
735	C₂³	C₂×#2010	1	2	yes	—
736	C₂³	#23414	1	2	yes	—
737	C₂×C₄	#10994	1	2	yes	—
738	C₂×C₄	#13967	1	2	yes	—
739	C₂×C₄	#13967	1	2	yes	—
740	C₂×C₄	#13995	1	2	yes	—
741	C₂×C₄	#13995	1	2	yes	—
742	C₂×C₄	#14134	1	1	yes	characteristic
743	C₂×C₄	#14134	1	1	yes	characteristic
744	C₂×C₄	#14255	1	1	yes	characteristic
745	C₂×C₄	#14694	1	1	yes	characteristic
746	C₂×C₄	#14715	1	1	yes	characteristic
747	C₂×C₄	#14715	1	1	yes	characteristic
748	C₂×C₄	#14716	1	2	yes	—
749	C₂×C₄	#14718	1	1	yes	characteristic
750	C₂×C₄	#14718	1	1	yes	characteristic
751	C₂×C₄	#14718	1	1	yes	characteristic
752	C₂×C₄	#14718	1	1	yes	characteristic
753	C₂×C₄	#14725	1	2	yes	—
754	C₂×C₄	#14911	1	1	yes	characteristic
755	C₂×C₄	#14911	1	1	yes	characteristic
756	C₂×C₄	#23882	1	4	yes	—
757	C₂²	#154195	1	1	yes	characteristic
758	C₂²	C₂×#10994	1	1	yes	characteristic
759	C₂²	#357548	1	1	yes	characteristic
760	C₂²	#359562	1	2	yes	—
761	C₂²	#359645	1	2	yes	—
762	C₂²	#394261	1	4	yes	—
763	C₄	#394022	1	2	yes	—
764	C₄	#394539	1	2	yes	—
765	C₂	#72237271	1	1	yes	characteristic
766	C₂	#72256165	1	1	yes	characteristic
767	C₂	#72280584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14715
commutator	C₂²×C₄²	C₂³×C₄
Frattini, cosocle	C₂³×C₄²	C₂⁴
socle	C₂²	#154195
prime radical	#72280430	C₂
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂³×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72302144	C₂	semidirect
2. #72281701	C₂	semidirect
3. #72281325	C₂	semidirect
4. #72281067	C₂	semidirect
5. #72280709	C₂	semidirect
6. #72280662	C₂	semidirect
8. #72280243	C₂	semidirect
9. #72263920	C₂	semidirect
10. #72239047	C₂	semidirect
11. #72216619	C₂	semidirect
19. #6370977	C₂²	semidirect
24. C₂×#17448	C₂²	semidirect
26. #758019	C₄	semidirect
27. #758017	C₄	semidirect
28. #754562	C₄	semidirect
29. #754560	C₄	semidirect
33. #353782	C₂²	semidirect
34. #353774	C₂²	semidirect
35. #181778	C₂²	semidirect
36. #181430	C₂²	semidirect
37. #181176	C₂²	semidirect
38. C₂×#7855	C₂²	semidirect
56. #60284	D₄	semidirect
57. #60282	D₄	semidirect
58. #60123	D₄	semidirect
62. C₄×#568	D₄	semidirect
78. #20632	D₄	semidirect
79. #20632	D₄	semidirect
80. #17480	D₄	semidirect
81. C₂×#1486	D₄	semidirect
82. #17349	D₄	semidirect
83. #17349	D₄	semidirect
383. #423	#120	semidirect
384. C₂×C₄×C₈	#120	semidirect

Maximal subgroups

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

subgroup	index
#72302144	2
#72281701	2
#72281325	2
#72281067	2
#72280709	2
#72280662	2
#72280430	2
#72280243	2
#72263920	2
#72239047	2
#72216619	2