Subgroups — #72302755

Order 2048.

At least 8815 conjugacy classes of subgroups; only the 1312 normal subgroups are shown.

The subgroup lattice has 734 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72302701	C₂	1	1	yes	maximal, characteristic, complemented
2	#72302683	C₂	1	1	yes	maximal, characteristic, complemented
3	#72302667	C₂	1	2	yes	maximal, complemented
4	#72302342	C₂	1	2	yes	maximal, complemented
5	#72281679	C₂	1	2	yes	maximal, complemented
6	#72281452	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#7640519	C₂	1	1	yes	maximal, characteristic
8	#72281362	C₂	1	2	yes	maximal, complemented
9	#72281217	C₂	1	1	yes	maximal, characteristic, complemented
10	#72257904	C₂	1	1	yes	maximal, characteristic, complemented
11	#72257760	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#3481	C₂²	1	1	yes	characteristic
13	C₂²×#3460	C₂²	1	1	yes	characteristic
14	C₂×#36687	C₄	1	1	yes	characteristic, complemented
15	C₂×#36687	C₂²	1	1	yes	characteristic
16	C₂×#34963	C₄	1	1	yes	characteristic, complemented
17	C₂×#34936	C₄	1	1	yes	characteristic, complemented
18	C₂×#34876	C₄	1	1	yes	characteristic, complemented
19	C₂×#34876	C₂²	1	1	yes	characteristic
20	C₂×#34643	C₄	1	1	yes	characteristic, complemented
21	C₂×#34641	C₂²	1	1	yes	characteristic
22	C₂×#34609	C₂²	1	1	yes	characteristic
23	C₂×#34593	C₄	1	1	yes	characteristic, complemented
24	C₂×#34593	C₄	1	1	yes	characteristic, complemented
25	C₂²×#2397	C₄	1	1	yes	characteristic, complemented
26	C₂×#34123	C₂²	1	1	yes	characteristic
27	#6370997	C₂²	1	2	yes	complemented
28	#6370950	C₂²	1	1	yes	characteristic
29	#6370937	C₂²	1	1	yes	characteristic
30	#6344036	C₂²	1	2	yes	complemented
31	#6344036	C₂²	1	2	yes	complemented
32	#6343792	C₂²	1	2	yes	complemented
33	#6343377	C₂²	1	2	yes	complemented
34	#6343377	C₂²	1	2	yes	complemented
35	#6343354	C₂²	1	2	yes	complemented
36	#6342924	C₂²	1	2	yes	complemented
37	#6342561	C₂²	1	1	yes	characteristic
38	#6342561	C₂²	1	1	yes	characteristic
39	#353782	C₂²	1	2	yes	complemented
40	#181152	C₂²	1	2	yes	complemented
41	#181126	C₂²	1	2	yes	complemented
42	C₂×#7855	C₂²	1	2	yes	complemented
43	C₂²×#559	D₄	1	1	yes	characteristic
44	C₂²×#553	D₄	1	1	yes	characteristic
45	C₂²×#553	D₄	1	1	yes	characteristic
46	C₂²×#554	D₄	1	1	yes	characteristic
47	C₂²×#554	D₄	1	1	yes	characteristic
48	C₂²×#546	D₄	1	1	yes	characteristic
49	C₂²×#546	D₄	1	1	yes	characteristic
50	C₂²×D₄²	D₄	1	1	yes	characteristic
51	C₂²×#542	D₄	1	1	yes	characteristic
52	C₂²×#542	D₄	1	1	yes	characteristic
53	C₂²×#540	D₄	1	1	yes	characteristic
54	C₂²×#540	D₄	1	1	yes	characteristic
55	C₂²×#544	D₄	1	1	yes	characteristic
56	C₂²×#537	D₄	1	1	yes	characteristic
57	C₂²×#535	D₄	1	1	yes	characteristic
58	C₂²×#535	D₄	1	1	yes	characteristic
59	C₂²×#532	C₂×C₄	1	1	yes	characteristic
60	C₂²×#532	C₂³	1	1	yes	characteristic
61	C₂²×#532	C₂³	1	1	yes	characteristic
62	C₂²×#529	C₂×C₄	1	1	yes	characteristic
63	C₂²×#529	C₂×C₄	1	1	yes	characteristic
64	C₂²×#529	C₂×C₄	1	1	yes	characteristic
65	C₂²×#529	C₂³	1	1	yes	characteristic
66	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
68	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
69	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
72	C₂×#2920	C₂³	1	2	yes	—
73	C₂×#2920	C₂³	1	2	yes	—
74	C₂×#2920	C₂³	1	2	yes	—
75	#36687	D₄	1	8	yes	—
76	#34876	D₄	1	8	yes	—
77	#34641	D₄	1	8	yes	—
78	#34609	D₄	1	8	yes	—
79	C₂×#2399	C₂×C₄	1	1	yes	characteristic
80	C₂×#2398	C₂×C₄	1	1	yes	characteristic
81	C₂×#2398	C₂×C₄	1	1	yes	characteristic
82	C₂×#2398	C₂×C₄	1	1	yes	characteristic
83	C₂×#2398	C₂×C₄	1	1	yes	characteristic
84	C₂×#2398	C₂×C₄	1	1	yes	characteristic
85	C₂×#2398	C₂×C₄	1	1	yes	characteristic
86	C₂×#2397	C₂×C₄	1	1	yes	characteristic
87	C₂×#2397	C₂×C₄	1	1	yes	characteristic
88	C₂×#2397	C₂×C₄	1	1	yes	characteristic
89	C₂×#2397	C₂×C₄	1	1	yes	characteristic
90	C₂×#2397	C₂×C₄	1	1	yes	characteristic
91	C₂×#2397	C₂×C₄	1	1	yes	characteristic
92	C₂×#2397	C₂×C₄	1	1	yes	characteristic
93	C₂×#2397	C₂×C₄	1	1	yes	characteristic
94	C₂×#2397	C₂×C₄	1	1	yes	characteristic
95	C₂×#2295	D₄	1	2	yes	—
96	C₂×#2290	D₄	1	2	yes	—
97	C₂×#2290	D₄	1	2	yes	—
98	#34012	C₂³	1	2	yes	—
99	C₂×#2283	C₂×C₄	1	1	yes	characteristic
100	C₂×#2283	C₂×C₄	1	1	yes	characteristic
101	C₂×#2283	C₂³	1	1	yes	characteristic
102	C₂×C₄²×D₄	D₄	1	2	yes	—
103	C₂×C₄×#117	C₂×C₄	1	1	yes	characteristic
104	C₂²×#376	C₂×C₄	1	1	yes	characteristic
105	C₂²×#376	C₂³	1	1	yes	characteristic
106	#20728	D₄	1	4	yes	complemented
107	#20723	D₄	1	4	yes	complemented
108	#17366	D₄	1	4	yes	complemented
109	#17366	D₄	1	4	yes	complemented
110	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#532	C₂×D₄	1	4	yes	—
117	C₂×#532	C₂×D₄	1	4	yes	—
118	C₂×#532	C₂×D₄	1	4	yes	—
119	C₂×#532	C₂×D₄	1	4	yes	—
120	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
123	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#127	C₂×D₄	1	1	yes	characteristic
125	C₂²×#127	C₂×D₄	1	1	yes	characteristic
126	C₂×#529	C₂×D₄	1	4	yes	—
127	C₂×#529	C₂×D₄	1	4	yes	—
128	C₂²×#125	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#125	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#125	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×#125	C₂×D₄	1	1	yes	characteristic
132	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×#124	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
140	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×#121	C₂×D₄	1	1	yes	characteristic
146	C₂²×#121	C₂×D₄	1	1	yes	characteristic
147	C₂²×#121	C₂×D₄	1	1	yes	characteristic
148	C₂²×#121	C₂×D₄	1	1	yes	characteristic
149	C₂²×#121	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×#41	C₂×D₄	1	4	yes	—
151	C₂×C₄×#41	C₂×D₄	1	4	yes	—
152	C₂×C₄×#41	C₂×D₄	1	2	yes	—
153	C₂×C₄×#41	C₂×D₄	1	2	yes	—
154	C₂×C₄×#41	C₂×D₄	1	2	yes	—
155	C₂×C₄×#41	C₂×D₄	1	2	yes	—
156	C₂×C₄×#41	#41	1	2	yes	—
157	C₂×C₄×#41	#41	1	2	yes	—
158	C₂×C₄×#41	#41	1	2	yes	—
159	C₂×C₄×#41	#41	1	2	yes	—
160	C₂²×C₄×Q₈	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂²×#117	C₂²⋊C₄	1	2	yes	—
187	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×#117	C₂×D₄	1	1	yes	characteristic
189	C₂²×#117	C₂×D₄	1	1	yes	characteristic
190	C₂²×#117	C₂×D₄	1	1	yes	characteristic
191	C₂²×#117	C₂×D₄	1	1	yes	characteristic
192	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₄²	C₂²⋊C₄	1	2	yes	—
196	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
197	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
198	C₂³×C₄²	C₂×D₄	1	2	yes	—
199	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
200	#2920	C₂×D₄	1	4	yes	complemented
201	#2920	C₂×D₄	1	4	yes	complemented
202	#2920	C₂×D₄	1	4	yes	complemented
203	#2399	C₂²⋊C₄	1	4	yes	—
204	#2398	C₂²⋊C₄	1	4	yes	—
205	#2398	C₂²⋊C₄	1	4	yes	—
206	#2398	C₂²⋊C₄	1	4	yes	—
207	#2398	C₂²⋊C₄	1	4	yes	—
208	#2398	C₂²⋊C₄	1	4	yes	—
209	#2398	C₂²⋊C₄	1	4	yes	—
210	#2397	C₂²⋊C₄	1	4	yes	—
211	#2397	C₂²⋊C₄	1	4	yes	—
212	#2397	C₂²⋊C₄	1	4	yes	—
213	#2397	C₂²⋊C₄	1	4	yes	—
214	#2397	C₂²⋊C₄	1	4	yes	—
215	#2397	C₂²⋊C₄	1	4	yes	—
216	#2397	C₂²⋊C₄	1	4	yes	—
217	#2397	C₂²⋊C₄	1	4	yes	—
218	#2397	C₂²⋊C₄	1	4	yes	—
219	#2283	C₂×D₄	1	4	yes	—
220	#2283	C₂×D₄	1	4	yes	—
221	#2283	C₂×D₄	1	4	yes	complemented
222	C₂×C₄×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
224	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
225	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
228	C₂×#376	C₂²⋊C₄	1	2	yes	—
229	C₂×#376	C₂²×C₄	1	1	yes	characteristic
230	C₂×#376	C₂²×C₄	1	1	yes	characteristic
231	C₂×#376	C₂²×C₄	1	1	yes	characteristic
232	C₂×#376	C₂²×C₄	1	1	yes	characteristic
233	C₂×#376	C₂×D₄	1	4	yes	—
234	C₂×#376	C₂×D₄	1	4	yes	—
235	C₂×#376	C₂×D₄	1	2	yes	—
236	C₂×C₄³	C₂²⋊C₄	1	2	yes	—
237	C₂²×#41	#120	1	4	yes	—
238	C₂²×#41	#120	1	2	yes	—
239	C₂²×#41	#121	1	2	yes	—
240	C₂²×#41	#121	1	2	yes	—
241	C₂²×#41	#123	1	2	yes	—
242	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂³×Q₈	#120	1	1	yes	characteristic
245	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂³×D₄	#120	1	1	yes	characteristic
252	C₂³×D₄	#120	1	1	yes	characteristic
253	C₂³×D₄	#120	1	1	yes	characteristic
254	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	#120	1	4	yes	—
264	C₂×C₄⋊Q₈	#120	1	4	yes	—
265	C₂×#127	#120	1	4	yes	—
266	C₂×#127	#120	1	4	yes	—
267	C₂×#125	#120	1	4	yes	—
268	C₂×#124	#120	1	4	yes	—
269	C₂×C₂²⋊Q₈	#120	1	4	yes	—
270	C₂×#121	#120	1	4	yes	—
271	C₂×#121	#120	1	4	yes	—
272	C₂×#121	#120	1	4	yes	—
273	C₂×#121	#120	1	4	yes	—
274	C₂×#121	#120	1	4	yes	—
275	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×C₄×Q₈	#120	1	4	yes	—
280	C₂×C₄×Q₈	#120	1	2	yes	—
281	C₂×C₄×Q₈	#121	1	2	yes	—
282	C₂×C₄×Q₈	#121	1	2	yes	—
283	C₂×C₄×Q₈	#121	1	2	yes	—
284	C₂×C₄×Q₈	#121	1	2	yes	—
285	C₂×C₄×Q₈	#123	1	2	yes	—
286	C₂×C₄×Q₈	#124	1	2	yes	—
287	C₂×C₄×Q₈	#127	1	2	yes	—
288	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×C₄×D₄	#120	1	4	yes	—
301	C₂×C₄×D₄	#120	1	2	yes	—
302	C₂×C₄×D₄	#120	1	2	yes	—
303	C₂×C₄×D₄	#120	1	2	yes	—
304	C₂×C₄×D₄	#121	1	2	yes	—
305	C₂×C₄×D₄	#121	1	2	yes	—
306	C₂×C₄×D₄	#121	1	2	yes	—
307	C₂×C₄×D₄	#121	1	2	yes	—
308	C₂×C₄×D₄	#121	1	2	yes	—
309	C₂×C₄×D₄	#121	1	2	yes	—
310	C₂×C₄×D₄	#121	1	2	yes	—
311	C₂×C₄×D₄	#121	1	2	yes	—
312	C₂×C₄×D₄	#121	1	2	yes	—
313	C₂×C₄×D₄	#121	1	2	yes	—
314	C₂×C₄×D₄	#121	1	2	yes	—
315	C₂×C₄×D₄	#121	1	2	yes	—
316	C₂×C₄×D₄	#123	1	2	yes	—
317	C₂×C₄×D₄	#123	1	2	yes	—
318	C₂×C₄×D₄	#123	1	2	yes	—
319	C₂×C₄×D₄	#124	1	2	yes	—
320	C₂×C₄×D₄	#124	1	2	yes	—
321	C₂×C₄×D₄	#124	1	2	yes	—
322	C₂×C₄×D₄	#127	1	2	yes	—
323	C₂×C₄×D₄	#127	1	2	yes	—
324	C₂×C₄×D₄	#127	1	2	yes	—
325	C₂×#117	#120	1	4	yes	—
326	C₂×#117	#120	1	2	yes	—
327	C₂×#117	#120	1	2	yes	—
328	C₂×#117	#120	1	2	yes	—
329	C₂×#117	#121	1	2	yes	—
330	C₂×#117	#121	1	2	yes	—
331	C₂×#117	#121	1	2	yes	—
332	C₂×#117	#121	1	2	yes	—
333	C₂×#117	#121	1	2	yes	—
334	C₂×#117	#121	1	2	yes	—
335	C₂×#117	#123	1	2	yes	—
336	C₂×#117	#123	1	2	yes	—
337	C₂×#117	#123	1	2	yes	—
338	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
358	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
368	C₂²×C₄²	C₄×D₄	1	2	yes	—
369	C₂²×C₄²	C₄×D₄	1	2	yes	—
370	C₂²×C₄²	C₄×D₄	1	2	yes	—
371	C₂²×C₄²	C₄×D₄	1	2	yes	—
372	C₂²×C₄²	C₄×D₄	1	2	yes	—
373	C₂²×C₄²	C₄×D₄	1	2	yes	—
374	C₂²×C₄²	C₄×D₄	1	2	yes	—
375	C₂²×C₄²	C₄×D₄	1	2	yes	—
376	C₂²×C₄²	#120	1	8	yes	—
377	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×D₄	1	2	yes	—
379	C₂²×C₄²	C₂²×D₄	1	2	yes	—
380	C₂²×C₄²	C₂²×D₄	1	2	yes	—
381	C₂²×C₄²	C₂²×D₄	1	2	yes	—
382	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
385	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
390	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
391	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
392	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
393	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
394	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
395	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
396	C₂²×C₄²	H(5,𝔽₂)	1	2	yes	—
397	C₄×C₄⋊C₄	#120	1	8	yes	—
398	C₄×C₂²⋊C₄	#120	1	8	yes	—
399	#376	C₂×C₂²⋊C₄	1	2	yes	—
400	#376	C₂×C₂²⋊C₄	1	2	yes	—
401	#376	C₂×C₂²⋊C₄	1	2	yes	—
402	#376	C₂×C₂²⋊C₄	1	2	yes	—
403	#376	C₂×C₂²⋊C₄	1	2	yes	—
404	#376	C₂×C₂²⋊C₄	1	2	yes	—
405	#376	C₂×C₂²⋊C₄	1	2	yes	—
406	#376	C₂×C₂²⋊C₄	1	2	yes	—
407	#376	#120	1	8	yes	—
408	C₂⁵	#379	1	1	yes	characteristic
409	C₂⁵	#379	1	1	yes	characteristic
410	C₂⁵	C₂×#120	1	1	yes	characteristic
411	C₂²×Q₈	#379	1	2	yes	—
412	C₂²×Q₈	#379	1	2	yes	—
413	C₂²×Q₈	#392	1	2	yes	—
414	C₂²×Q₈	#394	1	2	yes	—
415	C₂²×D₄	#379	1	2	yes	—
416	C₂²×D₄	#379	1	2	yes	—
417	C₂²×D₄	#379	1	2	yes	—
418	C₂²×D₄	#379	1	2	yes	—
419	C₂²×D₄	#379	1	2	yes	—
420	C₂²×D₄	#379	1	2	yes	—
421	C₂²×D₄	#392	1	2	yes	—
422	C₂²×D₄	#392	1	2	yes	—
423	C₂²×D₄	#392	1	2	yes	—
424	C₂²×D₄	#394	1	2	yes	—
425	C₂²×D₄	#394	1	2	yes	—
426	C₂²×D₄	#394	1	2	yes	—
427	C₂³×C₄	#379	1	1	yes	characteristic
428	C₂³×C₄	#379	1	1	yes	characteristic
429	C₂³×C₄	#379	1	1	yes	characteristic
430	C₂³×C₄	#379	1	1	yes	characteristic
431	C₂³×C₄	#379	1	1	yes	characteristic
432	C₂³×C₄	#379	1	1	yes	characteristic
433	C₂³×C₄	#386	1	2	yes	—
434	C₂³×C₄	#386	1	2	yes	—
435	C₂³×C₄	#386	1	2	yes	—
436	C₂³×C₄	#386	1	2	yes	—
437	C₂³×C₄	#386	1	2	yes	—
438	C₂³×C₄	#386	1	2	yes	—
439	C₂³×C₄	#386	1	2	yes	—
440	C₂³×C₄	#386	1	2	yes	—
441	C₂³×C₄	#390	1	2	yes	—
442	C₂³×C₄	#390	1	2	yes	—
443	C₂³×C₄	#390	1	2	yes	—
444	C₂³×C₄	#390	1	2	yes	—
445	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
446	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
447	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
448	C₂³×C₄	C₂×#120	1	2	yes	—
449	C₂³×C₄	C₂×#120	1	1	yes	characteristic
450	C₂³×C₄	C₂×#120	1	1	yes	characteristic
451	C₂³×C₄	C₂×#120	1	1	yes	characteristic
452	C₂³×C₄	C₂×#120	1	2	yes	—
453	C₂³×C₄	C₂×#120	1	1	yes	characteristic
454	C₂³×C₄	C₂×#120	1	2	yes	—
455	C₂³×C₄	C₂×#120	1	2	yes	—
456	C₂³×C₄	C₂×#120	1	2	yes	—
457	C₂³×C₄	C₂×#120	1	2	yes	—
458	C₂³×C₄	C₂×#120	1	1	yes	characteristic
459	C₂³×C₄	C₂×#121	1	1	yes	characteristic
460	C₂³×C₄	C₂×#121	1	1	yes	characteristic
461	C₂³×C₄	C₂×#121	1	1	yes	characteristic
462	C₂³×C₄	C₂×#121	1	1	yes	characteristic
463	C₂³×C₄	C₂×#121	1	1	yes	characteristic
464	C₂³×C₄	C₂×#121	1	1	yes	characteristic
465	C₂³×C₄	C₂×#123	1	1	yes	characteristic
466	C₂³×C₄	C₂×#123	1	1	yes	characteristic
467	C₂³×C₄	C₂×#124	1	1	yes	characteristic
468	C₂³×C₄	C₂×#127	1	1	yes	characteristic
469	C₂³×C₄	#534	1	2	yes	—
470	C₂³×C₄	#534	1	2	yes	—
471	C₂³×C₄	#534	1	2	yes	—
472	C₂³×C₄	#534	1	2	yes	—
473	C₂³×C₄	#535	1	2	yes	—
474	C₂³×C₄	#535	1	2	yes	—
475	C₂×C₄⋊C₄	#379	1	2	yes	—
476	C₂×C₄⋊C₄	#379	1	2	yes	—
477	C₂×C₄⋊C₄	#379	1	2	yes	—
478	C₂×C₄⋊C₄	#379	1	2	yes	—
479	C₂×C₄⋊C₄	#379	1	2	yes	—
480	C₂×C₄⋊C₄	#379	1	2	yes	—
481	C₂×C₄⋊C₄	#379	1	2	yes	—
482	C₂×C₄⋊C₄	#379	1	2	yes	—
483	C₂×C₄⋊C₄	#392	1	2	yes	—
484	C₂×C₄⋊C₄	#392	1	2	yes	—
485	C₂×C₄⋊C₄	#392	1	2	yes	—
486	C₂×C₄⋊C₄	#392	1	2	yes	—
487	C₂×C₄⋊C₄	#392	1	2	yes	—
488	C₂×C₄⋊C₄	#392	1	2	yes	—
489	C₂×C₄⋊C₄	#394	1	2	yes	—
490	C₂×C₄⋊C₄	#394	1	2	yes	—
491	C₂×C₄⋊C₄	#394	1	2	yes	—
492	C₂×C₄⋊C₄	#394	1	2	yes	—
493	C₂×C₄⋊C₄	#394	1	2	yes	—
494	C₂×C₄⋊C₄	#394	1	2	yes	—
495	C₂×C₂²⋊C₄	#392	1	2	yes	—
496	C₂×C₂²⋊C₄	#392	1	2	yes	—
497	C₂×C₂²⋊C₄	#392	1	2	yes	—
498	C₂×C₂²⋊C₄	#392	1	2	yes	—
499	C₂×C₂²⋊C₄	#392	1	2	yes	—
500	C₂×C₂²⋊C₄	#392	1	2	yes	—
501	C₂×C₂²⋊C₄	#394	1	2	yes	—
502	C₂×C₂²⋊C₄	#394	1	2	yes	—
503	C₂×C₂²⋊C₄	#394	1	2	yes	—
504	C₂×C₂²⋊C₄	#394	1	2	yes	—
505	C₂×C₂²⋊C₄	#394	1	2	yes	—
506	C₂×C₂²⋊C₄	#394	1	2	yes	—
507	C₂×C₄²	#379	1	4	yes	—
508	C₂×C₄²	#379	1	4	yes	—
509	C₂×C₄²	#379	1	4	yes	—
510	C₂×C₄²	#379	1	4	yes	—
511	C₂×C₄²	#386	1	2	yes	—
512	C₂×C₄²	#386	1	2	yes	—
513	C₂×C₄²	#386	1	2	yes	—
514	C₂×C₄²	#386	1	2	yes	—
515	C₂×C₄²	#386	1	2	yes	—
516	C₂×C₄²	#386	1	2	yes	—
517	C₂×C₄²	#386	1	2	yes	—
518	C₂×C₄²	#386	1	2	yes	—
519	C₂×C₄²	#390	1	2	yes	—
520	C₂×C₄²	#390	1	2	yes	—
521	C₂×C₄²	#390	1	2	yes	—
522	C₂×C₄²	#390	1	2	yes	—
523	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
524	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
525	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
526	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
527	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
528	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
529	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
530	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
531	C₂×C₄²	#518	1	1	yes	characteristic
532	C₂×C₄²	#518	1	1	yes	characteristic
533	C₂×C₄²	#518	1	1	yes	characteristic
534	C₂×C₄²	#518	1	1	yes	characteristic
535	C₂×C₄²	C₂×#120	1	1	yes	characteristic
536	C₂×C₄²	C₂×#120	1	1	yes	characteristic
537	C₂×C₄²	C₂×#120	1	2	yes	—
538	C₂×C₄²	C₂×#120	1	2	yes	—
539	C₂×C₄²	C₂×#120	1	2	yes	—
540	C₂×C₄²	C₂×#120	1	2	yes	—
541	C₂×C₄²	C₂×#120	1	2	yes	—
542	C₂×C₄²	C₂×#120	1	2	yes	—
543	C₂×C₄²	C₂×#121	1	1	yes	characteristic
544	C₂×C₄²	C₂×#121	1	1	yes	characteristic
545	C₂×C₄²	C₂×#121	1	1	yes	characteristic
546	C₂×C₄²	C₂×#121	1	1	yes	characteristic
547	C₂×C₄²	C₂×#121	1	1	yes	characteristic
548	C₂×C₄²	C₂×#121	1	1	yes	characteristic
549	C₂×C₄²	C₂×#123	1	1	yes	characteristic
550	C₂×C₄²	C₂×#123	1	1	yes	characteristic
551	C₂×C₄²	C₂×#124	1	1	yes	characteristic
552	C₂×C₄²	C₂×#127	1	1	yes	characteristic
553	C₂×C₄²	#534	1	2	yes	—
554	C₂×C₄²	#534	1	2	yes	—
555	C₂×C₄²	#534	1	2	yes	—
556	C₂×C₄²	#534	1	2	yes	—
557	C₂×C₄²	#535	1	2	yes	—
558	C₂×C₄²	#535	1	2	yes	—
559	C₂×C₄²	D₄²	1	2	yes	—
560	C₂×C₄²	D₄²	1	2	yes	—
561	C₂×C₄²	D₄²	1	2	yes	—
562	C₂×C₄²	D₄²	1	2	yes	—
563	C₂×C₄²	D₄²	1	2	yes	—
564	C₂×C₄²	D₄²	1	2	yes	—
565	C₂×C₄²	D₄²	1	2	yes	—
566	C₂×C₄²	D₄²	1	2	yes	—
567	C₂×C₄²	D₄²	1	2	yes	—
568	C₂×C₄²	D₄²	1	2	yes	—
569	C₂×C₄²	D₄²	1	2	yes	—
570	C₂×C₄²	D₄²	1	2	yes	—
571	C₂×C₄²	D₄²	1	2	yes	—
572	C₂×C₄²	D₄²	1	2	yes	—
573	C₂×C₄²	D₄²	1	2	yes	—
574	C₂×C₄²	D₄²	1	2	yes	—
575	C₂×C₄²	#546	1	2	yes	—
576	C₂×C₄²	#546	1	2	yes	—
577	C₂×C₄²	#546	1	2	yes	—
578	C₂×C₄²	#546	1	2	yes	—
579	C₂×C₄²	#546	1	2	yes	—
580	C₂×C₄²	#546	1	2	yes	—
581	C₂×C₄²	#546	1	2	yes	—
582	C₂×C₄²	#546	1	2	yes	—
583	C₂×C₄²	#546	1	2	yes	—
584	C₂×C₄²	#546	1	2	yes	—
585	C₂×C₄²	#546	1	2	yes	—
586	C₂×C₄²	#546	1	2	yes	—
587	C₂×C₄²	#546	1	2	yes	—
588	C₂×C₄²	#546	1	2	yes	—
589	C₂×C₄²	#546	1	2	yes	—
590	C₂×C₄²	#546	1	2	yes	—
591	C₂⁴	#1438	1	2	yes	—
592	C₂⁴	#1438	1	2	yes	—
593	C₂⁴	C₂×#379	1	1	yes	characteristic
594	C₂⁴	C₂×#392	1	1	yes	characteristic
595	C₂⁴	C₂×#394	1	1	yes	characteristic
596	C₂⁴	#2613	1	2	yes	—
597	C₂⁴	#2846	1	2	yes	—
598	C₂²×C₄	#1438	1	2	yes	—
599	C₂²×C₄	#1438	1	2	yes	—
600	C₂²×C₄	#1438	1	2	yes	—
601	C₂²×C₄	#1438	1	2	yes	—
602	C₂²×C₄	#1438	1	2	yes	—
603	C₂²×C₄	#1438	1	2	yes	—
604	C₂²×C₄	C₂×#379	1	1	yes	characteristic
605	C₂²×C₄	C₂×#379	1	1	yes	characteristic
606	C₂²×C₄	C₂×#379	1	1	yes	characteristic
607	C₂²×C₄	C₂×#379	1	1	yes	characteristic
608	C₂²×C₄	C₂×#379	1	1	yes	characteristic
609	C₂²×C₄	C₂×#379	1	1	yes	characteristic
610	C₂²×C₄	C₂×#386	1	1	yes	characteristic
611	C₂²×C₄	C₂×#386	1	1	yes	characteristic
612	C₂²×C₄	C₂×#386	1	1	yes	characteristic
613	C₂²×C₄	C₂×#386	1	1	yes	characteristic
614	C₂²×C₄	C₂×#390	1	1	yes	characteristic
615	C₂²×C₄	C₂×#390	1	1	yes	characteristic
616	C₂²×C₄	#2308	1	1	yes	characteristic
617	C₂²×C₄	#2308	1	1	yes	characteristic
618	C₂²×C₄	#2308	1	1	yes	characteristic
619	C₂²×C₄	#2308	1	1	yes	characteristic
620	C₂²×C₄	#2309	1	1	yes	characteristic
621	C₂²×C₄	#2309	1	1	yes	characteristic
622	C₂²×C₄	C₂×#392	1	1	yes	characteristic
623	C₂²×C₄	C₂×#392	1	1	yes	characteristic
624	C₂²×C₄	C₂×#392	1	1	yes	characteristic
625	C₂²×C₄	C₂×#394	1	1	yes	characteristic
626	C₂²×C₄	C₂×#394	1	1	yes	characteristic
627	C₂²×C₄	C₂×#394	1	1	yes	characteristic
628	C₂²×C₄	#2403	1	2	yes	—
629	C₂²×C₄	#2403	1	2	yes	—
630	C₂²×C₄	#2403	1	2	yes	—
631	C₂²×C₄	#2403	1	2	yes	—
632	C₂²×C₄	#2405	1	2	yes	—
633	C₂²×C₄	#2405	1	2	yes	—
634	C₂²×C₄	#2405	1	2	yes	—
635	C₂²×C₄	#2405	1	2	yes	—
636	C₂²×C₄	#2408	1	2	yes	—
637	C₂²×C₄	#2408	1	2	yes	—
638	C₂²×C₄	#2408	1	2	yes	—
639	C₂²×C₄	#2408	1	2	yes	—
640	C₂²×C₄	#2410	1	2	yes	—
641	C₂²×C₄	#2410	1	2	yes	—
642	C₂²×C₄	#2410	1	2	yes	—
643	C₂²×C₄	#2410	1	2	yes	—
644	C₂²×C₄	#2410	1	2	yes	—
645	C₂²×C₄	#2410	1	2	yes	—
646	C₂²×C₄	#2410	1	2	yes	—
647	C₂²×C₄	#2410	1	2	yes	—
648	C₂²×C₄	#2433	1	2	yes	—
649	C₂²×C₄	#2433	1	2	yes	—
650	C₂²×C₄	#2435	1	2	yes	—
651	C₂²×C₄	#2435	1	2	yes	—
652	C₂²×C₄	#2613	1	2	yes	—
653	C₂²×C₄	#2613	1	2	yes	—
654	C₂²×C₄	#2613	1	2	yes	—
655	C₂²×C₄	#2846	1	2	yes	—
656	C₂²×C₄	#2846	1	2	yes	—
657	C₂²×C₄	#2846	1	2	yes	—
658	C₄²	#1795	1	8	yes	—
659	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
660	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
661	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
662	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
663	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
664	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
665	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
666	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
667	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
668	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
669	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
670	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
671	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
672	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
673	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
674	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
675	C₄²	#2403	1	2	yes	—
676	C₄²	#2403	1	2	yes	—
677	C₄²	#2403	1	2	yes	—
678	C₄²	#2403	1	2	yes	—
679	C₄²	#2405	1	2	yes	—
680	C₄²	#2405	1	2	yes	—
681	C₄²	#2405	1	2	yes	—
682	C₄²	#2405	1	2	yes	—
683	C₄²	#2408	1	2	yes	—
684	C₄²	#2408	1	2	yes	—
685	C₄²	#2408	1	2	yes	—
686	C₄²	#2408	1	2	yes	—
687	C₄²	#2410	1	2	yes	—
688	C₄²	#2410	1	2	yes	—
689	C₄²	#2410	1	2	yes	—
690	C₄²	#2410	1	2	yes	—
691	C₄²	#2410	1	2	yes	—
692	C₄²	#2410	1	2	yes	—
693	C₄²	#2410	1	2	yes	—
694	C₄²	#2410	1	2	yes	—
695	C₄²	#2433	1	2	yes	—
696	C₄²	#2433	1	2	yes	—
697	C₄²	#2435	1	2	yes	—
698	C₄²	#2435	1	2	yes	—
699	C₂³	#11000	1	4	yes	—
700	C₂³	C₂×#1438	1	1	yes	characteristic
701	C₂³	#14335	1	1	yes	characteristic
702	C₂³	#14679	1	1	yes	characteristic
703	C₂³	#14715	1	2	yes	—
704	C₂³	#14724	1	2	yes	—
705	C₂×C₄	#13867	1	1	yes	characteristic
706	C₂×C₄	#13867	1	1	yes	characteristic
707	C₂×C₄	#13867	1	1	yes	characteristic
708	C₂×C₄	#13867	1	1	yes	characteristic
709	C₂×C₄	#13867	1	1	yes	characteristic
710	C₂×C₄	#13867	1	1	yes	characteristic
711	C₂×C₄	#13867	1	1	yes	characteristic
712	C₂×C₄	#13867	1	1	yes	characteristic
713	C₂×C₄	#13902	1	1	yes	characteristic
714	C₂×C₄	#13902	1	1	yes	characteristic
715	C₂×C₄	#13902	1	1	yes	characteristic
716	C₂×C₄	#13902	1	1	yes	characteristic
717	C₂×C₄	#14715	1	2	yes	—
718	C₂×C₄	#14715	1	2	yes	—
719	C₂×C₄	#14715	1	2	yes	—
720	C₂×C₄	#14724	1	2	yes	—
721	C₂×C₄	#14724	1	2	yes	—
722	C₂×C₄	#14724	1	2	yes	—
723	C₂×C₄	C₂×#1795	1	4	yes	—
724	C₂²	#154094	1	1	yes	characteristic
725	C₂²	C₂×#11000	1	2	yes	—
726	C₂²	#382440	1	2	yes	—
727	C₂²	#392132	1	2	yes	—
728	C₄	#361631	1	2	yes	—
729	C₄	#361634	1	2	yes	—
730	C₂	#72237193	1	1	yes	characteristic
731	C₂	#72265377	1	1	yes	characteristic
732	C₂	#72280172	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13902
commutator	C₂²×C₄²	C₂³×C₄
Frattini, cosocle	C₂³×C₄²	C₂⁴
socle	C₂²	#154094
prime radical	C₂×#7640519	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. #72302701	C₂	semidirect
2. #72302683	C₂	semidirect
3. #72302667	C₂	semidirect
4. #72302342	C₂	semidirect
5. #72281679	C₂	semidirect
6. #72281452	C₂	semidirect
8. #72281362	C₂	semidirect
9. #72281217	C₂	semidirect
10. #72257904	C₂	semidirect
11. #72257760	C₂	semidirect
14. C₂×#36687	C₄	semidirect
16. C₂×#34963	C₄	semidirect
17. C₂×#34936	C₄	semidirect
18. C₂×#34876	C₄	semidirect
20. C₂×#34643	C₄	semidirect
23. C₂×#34593	C₄	semidirect
24. C₂×#34593	C₄	semidirect
25. C₂²×#2397	C₄	semidirect
27. #6370997	C₂²	semidirect
30. #6344036	C₂²	semidirect
31. #6344036	C₂²	semidirect
32. #6343792	C₂²	semidirect
33. #6343377	C₂²	semidirect
34. #6343377	C₂²	semidirect
35. #6343354	C₂²	semidirect
36. #6342924	C₂²	semidirect
39. #353782	C₂²	semidirect
40. #181152	C₂²	semidirect
41. #181126	C₂²	semidirect
42. C₂×#7855	C₂²	semidirect
106. #20728	D₄	semidirect
107. #20723	D₄	semidirect
108. #17366	D₄	semidirect
109. #17366	D₄	semidirect
200. #2920	C₂×D₄	semidirect
201. #2920	C₂×D₄	semidirect
202. #2920	C₂×D₄	semidirect
221. #2283	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72302701	2
#72302683	2
#72302667	2
#72302342	2
#72281679	2
#72281452	2
C₂×#7640519	2
#72281362	2
#72281217	2
#72257904	2
#72257760	2