Subgroups — #72263027

Order 2048.

At least 14242 conjugacy classes of subgroups; only the 1360 normal subgroups are shown.

The subgroup lattice has 817 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261903	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261819	C₂	1	1	yes	maximal, characteristic, complemented
3	#72260901	C₂	1	1	yes	maximal, characteristic, complemented
4	#72260553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493584	C₂	1	1	yes	maximal, characteristic, complemented
6	#72250630	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#12755	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#147817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#146656	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#147573	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#359645	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#147577	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#12711	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#147782	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#7837029	C₂	1	1	yes	maximal, characteristic
16	C₂²×#3537	C₂²	1	1	yes	characteristic
17	C₂²×#3484	C₂²	1	1	yes	characteristic
18	C₂×#60087	C₂²	1	1	yes	characteristic, complemented
19	#7837029	C₄	1	8	yes	complemented
20	C₂×#37269	C₂²	1	1	yes	characteristic
21	C₂×#52163	C₂²	1	1	yes	characteristic
22	C₂×#35527	C₂²	1	1	yes	characteristic
23	C₂×#35512	C₂²	1	1	yes	characteristic
24	C₂×#34415	C₂²	1	1	yes	characteristic
25	C₂²×#2134	C₂²	1	1	yes	characteristic
26	C₂²×#2128	C₂²	1	1	yes	characteristic
27	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2120	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#1914	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#1910	C₂²	1	1	yes	characteristic
35	C₂²×#1891	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#1891	C₂²	1	1	yes	characteristic, complemented
37	C₂×#20961	C₂²	1	1	yes	characteristic, complemented
38	C₂×#20959	C₂²	1	1	yes	characteristic, complemented
39	C₂×#20959	C₂²	1	1	yes	characteristic, complemented
40	C₂×#20956	C₂²	1	1	yes	characteristic
41	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
44	C₂×#12587	C₂²	1	1	yes	characteristic, complemented
45	C₂×#12585	C₂²	1	1	yes	characteristic, complemented
46	C₂×#12583	C₂²	1	1	yes	characteristic, complemented
47	C₂×#12581	C₂²	1	1	yes	characteristic, complemented
48	C₂×#10751	C₂²	1	1	yes	characteristic, complemented
49	#353440	C₂²	1	1	yes	characteristic, complemented
50	#353437	C₂²	1	1	yes	characteristic, complemented
51	C₂×#10742	C₂²	1	1	yes	characteristic, complemented
52	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
53	C₂⁵×D₄	D₄	1	1	yes	characteristic
54	C₂²×#568	C₂³	1	1	yes	characteristic
55	C₂×#3484	C₂×C₄	1	4	yes	—
56	C₂×#3484	D₄	1	4	yes	—
57	C₂×#3537	C₂×C₄	1	4	yes	—
58	C₂×#3537	D₄	1	4	yes	—
59	C₂²×D₄²	D₄	1	2	yes	—
60	C₂²×#560	D₄	1	2	yes	—
61	C₂²×#535	D₄	1	1	yes	characteristic
62	C₂²×#535	D₄	1	1	yes	characteristic
63	C₂²×#535	C₂³	1	1	yes	characteristic
64	C₂²×#535	C₂³	1	1	yes	characteristic
65	C₂³×#127	D₄	1	1	yes	characteristic
66	C₂²×#525	D₄	1	1	yes	characteristic
67	C₂²×#525	D₄	1	1	yes	characteristic
68	C₂²×#525	C₂³	1	1	yes	characteristic
69	C₂²×#525	C₂³	1	1	yes	characteristic
70	C₂³×#121	D₄	1	1	yes	characteristic
71	C₂×#3428	C₂³	1	1	yes	characteristic
72	C₂²×#518	D₄	1	1	yes	characteristic
73	C₂²×#413	C₂³	1	1	yes	characteristic
74	C₂²×#413	C₂³	1	1	yes	characteristic
75	C₂²×#413	C₂³	1	1	yes	characteristic
76	C₂²×#410	C₂³	1	1	yes	characteristic
77	C₂²×#410	C₂³	1	1	yes	characteristic
78	C₂²×#410	C₂³	1	1	yes	characteristic
79	#52163	C₂×C₄	1	4	yes	—
80	#52163	D₄	1	4	yes	—
81	C₂×#2724	D₄	1	1	yes	characteristic
82	C₂×#2697	D₄	1	1	yes	characteristic
83	C₂×#2697	D₄	1	1	yes	characteristic
84	C₂×#2697	D₄	1	2	yes	—
85	C₂×#2679	D₄	1	1	yes	characteristic
86	C₂×#2679	D₄	1	2	yes	—
87	#37269	C₂×C₄	1	4	yes	—
88	#37269	D₄	1	4	yes	—
89	#35527	C₂×C₄	1	4	yes	—
90	#35527	D₄	1	4	yes	—
91	#35512	C₂×C₄	1	4	yes	—
92	#35512	D₄	1	4	yes	—
93	#34415	C₂×C₄	1	4	yes	—
94	#34415	D₄	1	4	yes	—
95	C₂×#2379	D₄	1	2	yes	—
96	C₂×#2372	D₄	1	2	yes	—
97	C₂×#2311	D₄	1	1	yes	characteristic
98	C₂×#2311	C₂³	1	1	yes	characteristic
99	C₂×#2309	D₄	1	1	yes	characteristic
100	C₂×#2309	D₄	1	1	yes	characteristic
101	C₂×#2297	D₄	1	1	yes	characteristic
102	C₂×#2297	C₂³	1	1	yes	characteristic
103	C₂×#2134	D₄	1	4	yes	complemented
104	C₂×#2128	D₄	1	4	yes	complemented
105	C₂×#1910	D₄	1	4	yes	complemented
106	#20956	D₄	1	4	yes	complemented
107	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
108	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
109	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
110	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	1	yes	characteristic
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂³×#41	C₂⁴	1	1	yes	characteristic
115	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×#568	C₂×D₄	1	2	yes	complemented
124	C₂×#560	C₂²⋊C₄	1	8	yes	complemented
125	C₂×D₄²	C₂²⋊C₄	1	8	yes	complemented
126	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
127	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
128	C₂×#535	C₂²×C₄	1	2	yes	—
129	C₂×#535	C₂²×C₄	1	2	yes	—
130	C₂×#535	C₂×D₄	1	2	yes	—
131	C₂×#535	C₂×D₄	1	2	yes	—
132	C₂×#535	C₂×D₄	1	2	yes	—
133	C₂×#535	C₂×D₄	1	2	yes	—
134	C₂×#535	C₂×D₄	1	2	yes	—
135	C₂×#535	C₂×D₄	1	2	yes	—
136	C₂×#535	C₂×D₄	1	2	yes	—
137	C₂×#535	C₂×D₄	1	2	yes	—
138	C₂×#535	C₂×D₄	1	2	yes	—
139	C₂×#535	C₂×D₄	1	2	yes	—
140	C₂×#535	#41	1	2	yes	—
141	C₂×#535	#41	1	2	yes	—
142	C₂×#535	#41	1	2	yes	—
143	C₂×#535	#41	1	2	yes	—
144	C₂²×#127	C₂²⋊C₄	1	4	yes	complemented
145	C₂²×#127	C₂×D₄	1	2	yes	—
146	C₂²×#124	C₂×D₄	1	2	yes	—
147	C₂×#525	C₂²⋊C₄	1	4	yes	complemented
148	C₂×#525	C₂²⋊C₄	1	4	yes	complemented
149	C₂×#525	C₂²×C₄	1	2	yes	—
150	C₂×#525	C₂²×C₄	1	2	yes	—
151	C₂×#525	C₂×D₄	1	2	yes	—
152	C₂×#525	C₂×D₄	1	2	yes	—
153	C₂×#525	C₂×D₄	1	2	yes	—
154	C₂×#525	C₂×D₄	1	2	yes	—
155	C₂×#525	C₂×D₄	1	2	yes	—
156	C₂×#525	C₂×D₄	1	2	yes	—
157	C₂²×#123	C₂×D₄	1	1	yes	characteristic
158	C₂²×#123	C₂×D₄	1	1	yes	characteristic
159	C₂²×#123	C₂×D₄	1	1	yes	characteristic
160	C₂²×#123	C₂×D₄	1	1	yes	characteristic
161	C₂²×#121	C₂²⋊C₄	1	4	yes	complemented
162	C₂²×#120	C₂×D₄	1	1	yes	characteristic
163	C₂²×#120	C₂×D₄	1	2	yes	—
164	C₂²×#120	C₂×D₄	1	1	yes	characteristic
165	C₂²×#120	C₂×D₄	1	2	yes	—
166	C₂²×#120	C₂×D₄	1	1	yes	characteristic
167	C₂²×#120	C₂×D₄	1	1	yes	characteristic
168	#3428	C₂×D₄	1	2	yes	complemented
169	C₂×#518	C₂²⋊C₄	1	4	yes	complemented
170	C₂²×#117	C₂×D₄	1	1	yes	characteristic
171	C₂²×#117	C₂×D₄	1	1	yes	characteristic
172	C₂²×#117	C₂×D₄	1	1	yes	characteristic
173	C₂²×#117	C₂×D₄	1	1	yes	characteristic
174	C₂²×#117	C₂×D₄	1	1	yes	characteristic
175	C₂²×#117	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
178	C₂×#413	C₂×D₄	1	2	yes	complemented
179	C₂×#413	C₂×D₄	1	2	yes	complemented
180	C₂×#413	C₂×D₄	1	2	yes	complemented
181	C₂×#410	C₂×D₄	1	2	yes	complemented
182	C₂×#410	C₂×D₄	1	2	yes	complemented
183	C₂×#410	C₂×D₄	1	2	yes	complemented
184	#2724	C₂²⋊C₄	1	4	yes	complemented
185	#2697	C₂²⋊C₄	1	8	yes	complemented
186	#2697	C₂²⋊C₄	1	4	yes	complemented
187	#2697	C₂²⋊C₄	1	4	yes	complemented
188	#2679	C₂²⋊C₄	1	8	yes	complemented
189	#2679	C₂²⋊C₄	1	4	yes	complemented
190	#2379	C₂²⋊C₄	1	8	yes	complemented
191	#2372	C₂²⋊C₄	1	8	yes	complemented
192	#2311	C₂²⋊C₄	1	4	yes	complemented
193	#2311	C₂²×C₄	1	2	yes	—
194	#2311	C₂×D₄	1	2	yes	—
195	#2311	C₂×D₄	1	2	yes	—
196	#2311	C₂×D₄	1	2	yes	—
197	#2309	C₂²⋊C₄	1	4	yes	complemented
198	#2309	C₂²⋊C₄	1	4	yes	complemented
199	#2297	C₂²⋊C₄	1	4	yes	complemented
200	#2297	C₂²×C₄	1	2	yes	—
201	#2297	C₂×D₄	1	2	yes	—
202	#2297	C₂×D₄	1	2	yes	—
203	#2297	C₂×D₄	1	2	yes	—
204	C₂×#391	C₂×D₄	1	1	yes	characteristic
205	C₂×#391	C₂×D₄	1	2	yes	—
206	C₂×#391	C₂×D₄	1	1	yes	characteristic
207	C₂×#390	C₂×D₄	1	2	yes	—
208	C₂×#390	C₂×D₄	1	1	yes	characteristic
209	C₂×#390	C₂×D₄	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	#120	1	2	yes	—
213	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂²×#41	#120	1	2	yes	—
217	C₂²×#41	#120	1	2	yes	—
218	C₂²×#41	#120	1	2	yes	—
219	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
220	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
221	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
222	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
223	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
224	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
225	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
226	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
227	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
228	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
229	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
230	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
231	C₂²×#41	C₂×#41	1	1	yes	characteristic
232	C₂²×#41	C₂×#41	1	1	yes	characteristic
233	C₂²×#41	C₂×#41	1	1	yes	characteristic
234	C₂²×#41	C₂×#41	1	1	yes	characteristic
235	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂³×Q₈	#120	1	1	yes	characteristic
244	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
245	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂³×D₄	#120	1	2	yes	—
251	C₂³×D₄	#120	1	2	yes	—
252	C₂³×D₄	#120	1	2	yes	—
253	C₂³×D₄	#120	1	2	yes	—
254	C₂³×D₄	#120	1	2	yes	—
255	C₂³×D₄	#120	1	2	yes	—
256	C₂³×D₄	#120	1	2	yes	—
257	C₂³×D₄	#120	1	1	yes	characteristic
258	C₂³×D₄	#120	1	1	yes	characteristic
259	C₂³×D₄	#120	1	1	yes	characteristic
260	C₂³×D₄	#121	1	2	yes	—
261	C₂³×D₄	#121	1	2	yes	—
262	C₂³×D₄	#123	1	2	yes	—
263	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
265	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
266	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂⁴×C₄	#120	1	2	yes	—
269	C₂⁴×C₄	#120	1	2	yes	—
270	C₂⁴×C₄	#120	1	1	yes	characteristic
271	C₂⁴×C₄	#120	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
274	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
275	#535	C₄×D₄	1	4	yes	—
276	#535	C₄×D₄	1	4	yes	—
277	#535	C₄×D₄	1	4	yes	—
278	#535	C₄×D₄	1	4	yes	—
279	#535	#120	1	4	yes	—
280	#535	#120	1	4	yes	—
281	#535	#121	1	4	yes	—
282	#535	#121	1	4	yes	—
283	#535	#121	1	4	yes	—
284	#535	#121	1	4	yes	—
285	#535	#121	1	4	yes	—
286	#535	#121	1	4	yes	—
287	#535	#123	1	4	yes	—
288	#535	#123	1	4	yes	—
289	#535	#124	1	4	yes	—
290	#535	#127	1	4	yes	—
291	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
292	C₂×#127	#120	1	4	yes	—
293	C₂×#127	#120	1	4	yes	—
294	C₂×#127	#121	1	4	yes	—
295	C₂×#127	#121	1	4	yes	—
296	C₂×#127	#123	1	4	yes	—
297	C₂×#124	C₂×C₂²⋊C₄	1	4	yes	—
298	C₂×#124	#120	1	4	yes	—
299	C₂×#124	#121	1	4	yes	—
300	C₂×#124	#121	1	4	yes	—
301	C₂×#124	#124	1	4	yes	—
302	C₂×#124	#127	1	4	yes	—
303	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂×#123	#120	1	2	yes	—
308	C₂×#123	#120	1	2	yes	—
309	C₂×#123	#120	1	2	yes	—
310	C₂×#123	#120	1	2	yes	—
311	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
312	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
314	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
315	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂×#120	#120	1	2	yes	—
318	C₂×#120	#120	1	2	yes	—
319	C₂×#120	#120	1	4	yes	—
320	C₂×#120	#120	1	4	yes	—
321	C₂×#120	#120	1	2	yes	—
322	C₂×#120	#120	1	2	yes	—
323	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
326	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×#117	#120	1	2	yes	—
330	C₂×#117	#120	1	2	yes	—
331	C₂×#117	#120	1	2	yes	—
332	C₂×#117	#120	1	2	yes	—
333	C₂×#117	#120	1	2	yes	—
334	C₂×#117	#120	1	2	yes	—
335	C₂×#117	#120	1	2	yes	—
336	C₂×#117	#121	1	2	yes	—
337	C₂×#117	#121	1	2	yes	—
338	C₂×#117	#123	1	2	yes	—
339	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂²×C₄⋊C₄	#120	1	2	yes	—
341	C₂²×C₄⋊C₄	#120	1	2	yes	—
342	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	#120	1	2	yes	—
347	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
349	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂²×C₄²	#120	1	2	yes	—
351	C₂²×C₄²	#120	1	1	yes	characteristic
352	C₂²×C₄²	#120	1	1	yes	characteristic
353	C₂²×C₄²	#120	1	2	yes	—
354	C₂²×C₄²	#120	1	2	yes	—
355	#391	C₂×C₂²⋊C₄	1	4	yes	—
356	#391	C₂×C₂²⋊C₄	1	2	yes	—
357	#391	C₂×C₂²⋊C₄	1	2	yes	—
358	#391	#120	1	4	yes	—
359	#391	#120	1	2	yes	—
360	#391	#120	1	2	yes	—
361	#390	C₂×C₂²⋊C₄	1	4	yes	—
362	#390	C₂×C₂²⋊C₄	1	2	yes	—
363	#390	C₂×C₂²⋊C₄	1	2	yes	—
364	#390	#120	1	4	yes	—
365	#390	#120	1	2	yes	—
366	#390	#120	1	2	yes	—
367	C₂⁵	#379	1	2	yes	—
368	C₂⁵	#379	1	2	yes	—
369	C₂⁵	#379	1	4	yes	—
370	C₂⁵	C₂×#120	1	1	yes	characteristic
371	C₂⁵	C₂×#120	1	1	yes	characteristic
372	C₂⁵	C₂×#120	1	1	yes	characteristic
373	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
376	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
377	C₂×#41	#518	1	1	yes	characteristic
378	C₂×#41	#518	1	1	yes	characteristic
379	C₂×#41	#518	1	1	yes	characteristic
380	C₂×#41	#518	1	1	yes	characteristic
381	C₂×#41	C₂×#120	1	1	yes	characteristic
382	C₂×#41	C₂×#120	1	1	yes	characteristic
383	C₂×#41	C₂×#121	1	1	yes	characteristic
384	C₂×#41	C₂×#121	1	1	yes	characteristic
385	C₂×#41	C₂×#121	1	1	yes	characteristic
386	C₂×#41	C₂×#121	1	1	yes	characteristic
387	C₂×#41	C₂×#121	1	1	yes	characteristic
388	C₂×#41	C₂×#121	1	1	yes	characteristic
389	C₂×#41	C₂×#123	1	1	yes	characteristic
390	C₂×#41	C₂×#123	1	1	yes	characteristic
391	C₂×#41	C₂×#124	1	1	yes	characteristic
392	C₂×#41	C₂×#127	1	1	yes	characteristic
393	C₂×#41	#534	1	1	yes	characteristic
394	C₂×#41	#534	1	1	yes	characteristic
395	C₂×#41	#534	1	1	yes	characteristic
396	C₂×#41	#534	1	1	yes	characteristic
397	C₂×#41	#534	1	1	yes	characteristic
398	C₂×#41	#534	1	1	yes	characteristic
399	C₂×#41	#534	1	1	yes	characteristic
400	C₂×#41	#534	1	1	yes	characteristic
401	C₂×#41	#535	1	1	yes	characteristic
402	C₂×#41	#535	1	1	yes	characteristic
403	C₂×#41	#535	1	1	yes	characteristic
404	C₂×#41	#535	1	1	yes	characteristic
405	C₂×#41	D₄²	1	1	yes	characteristic
406	C₂×#41	D₄²	1	1	yes	characteristic
407	C₂×#41	D₄²	1	1	yes	characteristic
408	C₂×#41	D₄²	1	1	yes	characteristic
409	C₂×#41	D₄²	1	1	yes	characteristic
410	C₂×#41	D₄²	1	1	yes	characteristic
411	C₂×#41	D₄²	1	1	yes	characteristic
412	C₂×#41	D₄²	1	1	yes	characteristic
413	C₂×#41	D₄²	1	1	yes	characteristic
414	C₂×#41	D₄²	1	1	yes	characteristic
415	C₂×#41	D₄²	1	1	yes	characteristic
416	C₂×#41	D₄²	1	1	yes	characteristic
417	C₂×#41	D₄²	1	1	yes	characteristic
418	C₂×#41	D₄²	1	1	yes	characteristic
419	C₂×#41	D₄²	1	1	yes	characteristic
420	C₂×#41	D₄²	1	1	yes	characteristic
421	C₂×#41	#546	1	1	yes	characteristic
422	C₂×#41	#546	1	1	yes	characteristic
423	C₂×#41	#546	1	1	yes	characteristic
424	C₂×#41	#546	1	1	yes	characteristic
425	C₂×#41	#546	1	1	yes	characteristic
426	C₂×#41	#546	1	1	yes	characteristic
427	C₂×#41	#546	1	1	yes	characteristic
428	C₂×#41	#546	1	1	yes	characteristic
429	C₂×#41	#546	1	1	yes	characteristic
430	C₂×#41	#546	1	1	yes	characteristic
431	C₂×#41	#546	1	1	yes	characteristic
432	C₂×#41	#546	1	1	yes	characteristic
433	C₂×#41	#546	1	1	yes	characteristic
434	C₂×#41	#546	1	1	yes	characteristic
435	C₂×#41	#546	1	1	yes	characteristic
436	C₂×#41	#546	1	1	yes	characteristic
437	C₂²×Q₈	#379	1	2	yes	—
438	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
439	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
440	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
441	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
442	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
443	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
444	C₂²×Q₈	C₂×#124	1	1	yes	characteristic
445	C₂²×Q₈	C₂×#127	1	1	yes	characteristic
446	C₂²×Q₈	#535	1	1	yes	characteristic
447	C₂²×Q₈	#535	1	1	yes	characteristic
448	C₂²×Q₈	#535	1	1	yes	characteristic
449	C₂²×Q₈	#535	1	1	yes	characteristic
450	C₂²×D₄	#379	1	2	yes	—
451	C₂²×D₄	#379	1	2	yes	—
452	C₂²×D₄	#379	1	2	yes	—
453	C₂²×D₄	#379	1	4	yes	—
454	C₂²×D₄	#386	1	4	yes	—
455	C₂²×D₄	#386	1	4	yes	—
456	C₂²×D₄	#392	1	4	yes	—
457	C₂²×D₄	#392	1	4	yes	—
458	C₂²×D₄	#394	1	4	yes	—
459	C₂²×D₄	#394	1	4	yes	—
460	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
461	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
462	C₂²×D₄	#458	1	2	yes	—
463	C₂²×D₄	#458	1	2	yes	—
464	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×D₄	C₂×#120	1	1	yes	characteristic
468	C₂²×D₄	C₂×#120	1	1	yes	characteristic
469	C₂²×D₄	C₂×#120	1	1	yes	characteristic
470	C₂²×D₄	C₂×#120	1	1	yes	characteristic
471	C₂²×D₄	C₂×#120	1	1	yes	characteristic
472	C₂²×D₄	C₂×#120	1	1	yes	characteristic
473	C₂²×D₄	C₂×#120	1	1	yes	characteristic
474	C₂²×D₄	C₂×#120	1	1	yes	characteristic
475	C₂²×D₄	C₂×#120	1	1	yes	characteristic
476	C₂²×D₄	C₂×#120	1	1	yes	characteristic
477	C₂²×D₄	C₂×#121	1	1	yes	characteristic
478	C₂²×D₄	C₂×#121	1	1	yes	characteristic
479	C₂²×D₄	C₂×#123	1	1	yes	characteristic
480	C₂²×D₄	#534	1	1	yes	characteristic
481	C₂²×D₄	#534	1	1	yes	characteristic
482	C₂²×D₄	#534	1	1	yes	characteristic
483	C₂²×D₄	#534	1	1	yes	characteristic
484	C₂²×D₄	D₄²	1	1	yes	characteristic
485	C₂²×D₄	D₄²	1	1	yes	characteristic
486	C₂²×D₄	D₄²	1	1	yes	characteristic
487	C₂²×D₄	D₄²	1	1	yes	characteristic
488	C₂²×D₄	D₄²	1	1	yes	characteristic
489	C₂²×D₄	D₄²	1	1	yes	characteristic
490	C₂²×D₄	D₄²	1	1	yes	characteristic
491	C₂²×D₄	D₄²	1	1	yes	characteristic
492	C₂²×D₄	#546	1	1	yes	characteristic
493	C₂²×D₄	#546	1	1	yes	characteristic
494	C₂²×D₄	#546	1	1	yes	characteristic
495	C₂²×D₄	#546	1	1	yes	characteristic
496	C₂²×D₄	#546	1	1	yes	characteristic
497	C₂²×D₄	#546	1	1	yes	characteristic
498	C₂²×D₄	#546	1	1	yes	characteristic
499	C₂²×D₄	#546	1	1	yes	characteristic
500	C₂³×C₄	#379	1	2	yes	—
501	C₂³×C₄	#379	1	2	yes	—
502	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
503	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
504	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
505	C₂³×C₄	C₂×#120	1	1	yes	characteristic
506	C₂³×C₄	C₂×#120	1	1	yes	characteristic
507	C₂³×C₄	C₂×#120	1	1	yes	characteristic
508	C₂³×C₄	C₂×#120	1	1	yes	characteristic
509	C₂³×C₄	C₂×#120	1	1	yes	characteristic
510	C₂³×C₄	C₂×#120	1	1	yes	characteristic
511	C₂³×C₄	C₂×#120	1	1	yes	characteristic
512	C₂³×C₄	C₂×#120	1	1	yes	characteristic
513	C₂³×C₄	C₂×#120	1	1	yes	characteristic
514	C₂³×C₄	C₂×#120	1	1	yes	characteristic
515	C₂³×C₄	C₂×#120	1	1	yes	characteristic
516	C₂³×C₄	C₂×#120	1	1	yes	characteristic
517	C₂³×C₄	C₂×#120	1	1	yes	characteristic
518	C₂³×C₄	C₂×#120	1	1	yes	characteristic
519	C₂³×C₄	C₂×#121	1	1	yes	characteristic
520	C₂³×C₄	C₂×#121	1	1	yes	characteristic
521	C₂³×C₄	C₂×#123	1	1	yes	characteristic
522	C₂³×C₄	#534	1	1	yes	characteristic
523	C₂³×C₄	#534	1	1	yes	characteristic
524	C₂³×C₄	#534	1	1	yes	characteristic
525	C₂³×C₄	#534	1	1	yes	characteristic
526	C₂³×C₄	D₄²	1	1	yes	characteristic
527	C₂³×C₄	D₄²	1	1	yes	characteristic
528	C₂³×C₄	D₄²	1	1	yes	characteristic
529	C₂³×C₄	D₄²	1	1	yes	characteristic
530	C₂³×C₄	D₄²	1	1	yes	characteristic
531	C₂³×C₄	D₄²	1	1	yes	characteristic
532	C₂³×C₄	D₄²	1	1	yes	characteristic
533	C₂³×C₄	D₄²	1	1	yes	characteristic
534	C₂³×C₄	#546	1	1	yes	characteristic
535	C₂³×C₄	#546	1	1	yes	characteristic
536	C₂³×C₄	#546	1	1	yes	characteristic
537	C₂³×C₄	#546	1	1	yes	characteristic
538	C₂³×C₄	#546	1	1	yes	characteristic
539	C₂³×C₄	#546	1	1	yes	characteristic
540	C₂³×C₄	#546	1	1	yes	characteristic
541	C₂³×C₄	#546	1	1	yes	characteristic
542	#127	#386	1	8	yes	—
543	#127	#386	1	8	yes	—
544	#127	#392	1	8	yes	—
545	#127	#394	1	8	yes	—
546	#124	#390	1	8	yes	—
547	#124	#390	1	8	yes	—
548	#124	#392	1	8	yes	—
549	#124	#394	1	8	yes	—
550	#117	#386	1	4	yes	—
551	#117	#386	1	4	yes	—
552	#117	#392	1	4	yes	—
553	#117	#394	1	4	yes	—
554	C₂×C₄⋊C₄	#379	1	4	yes	—
555	C₂×C₄⋊C₄	#379	1	2	yes	—
556	C₂×C₄⋊C₄	#379	1	2	yes	—
557	C₂×C₂²⋊C₄	#379	1	2	yes	—
558	C₂×C₂²⋊C₄	#379	1	2	yes	—
559	C₂×C₂²⋊C₄	#379	1	4	yes	—
560	C₂×C₂²⋊C₄	#379	1	2	yes	—
561	C₂×C₂²⋊C₄	#379	1	2	yes	—
562	C₂×C₄²	#379	1	4	yes	—
563	C₂×C₄²	#379	1	4	yes	—
564	C₂×C₄²	#379	1	2	yes	—
565	C₂×C₄²	#379	1	2	yes	—
566	C₂×C₄²	#392	1	4	yes	—
567	C₂×C₄²	#394	1	4	yes	—
568	C₂⁴	C₂×#379	1	1	yes	characteristic
569	C₂⁴	C₂×#379	1	1	yes	characteristic
570	C₂⁴	C₂×#379	1	1	yes	characteristic
571	C₂⁴	#2403	1	1	yes	characteristic
572	C₂⁴	#2403	1	1	yes	characteristic
573	C₂⁴	#2403	1	1	yes	characteristic
574	C₂⁴	#2405	1	1	yes	characteristic
575	C₂⁴	#2405	1	1	yes	characteristic
576	C₂⁴	#2405	1	1	yes	characteristic
577	C₂⁴	#2410	1	1	yes	characteristic
578	C₂⁴	#2410	1	1	yes	characteristic
579	C₂⁴	#2410	1	1	yes	characteristic
580	C₂⁴	#2410	1	1	yes	characteristic
581	C₂⁴	#2410	1	1	yes	characteristic
582	C₂⁴	#2410	1	1	yes	characteristic
583	C₂⁴	#2846	1	1	yes	characteristic
584	C₂⁴	#2846	1	1	yes	characteristic
585	C₂⁴	#2846	1	1	yes	characteristic
586	C₂⁴	#2846	1	1	yes	characteristic
587	C₂×Q₈	C₂×#390	1	1	yes	characteristic
588	C₂×Q₈	C₂×#390	1	1	yes	characteristic
589	C₂×Q₈	#2309	1	1	yes	characteristic
590	C₂×Q₈	#2309	1	1	yes	characteristic
591	C₂×Q₈	C₂×#392	1	1	yes	characteristic
592	C₂×Q₈	C₂×#394	1	1	yes	characteristic
593	C₂×Q₈	#2408	1	1	yes	characteristic
594	C₂×Q₈	#2408	1	1	yes	characteristic
595	C₂×Q₈	#2408	1	1	yes	characteristic
596	C₂×Q₈	#2408	1	1	yes	characteristic
597	C₂×Q₈	#2433	1	1	yes	characteristic
598	C₂×Q₈	#2433	1	1	yes	characteristic
599	C₂×Q₈	#2435	1	1	yes	characteristic
600	C₂×Q₈	#2435	1	1	yes	characteristic
601	C₂×Q₈	#2613	1	1	yes	characteristic
602	C₂×Q₈	#2613	1	1	yes	characteristic
603	C₂×D₄	#1438	1	8	yes	—
604	C₂×D₄	#1790	1	4	yes	—
605	C₂×D₄	#1790	1	4	yes	—
606	C₂×D₄	C₂×#386	1	1	yes	characteristic
607	C₂×D₄	C₂×#386	1	1	yes	characteristic
608	C₂×D₄	#2308	1	1	yes	characteristic
609	C₂×D₄	#2308	1	1	yes	characteristic
610	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
611	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
612	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
613	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
614	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
615	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
616	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
617	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
618	C₂×D₄	C₂×#392	1	1	yes	characteristic
619	C₂×D₄	C₂×#394	1	1	yes	characteristic
620	C₂×D₄	#2403	1	1	yes	characteristic
621	C₂×D₄	#2403	1	1	yes	characteristic
622	C₂×D₄	#2403	1	1	yes	characteristic
623	C₂×D₄	#2403	1	1	yes	characteristic
624	C₂×D₄	#2403	1	1	yes	characteristic
625	C₂×D₄	#2403	1	1	yes	characteristic
626	C₂×D₄	#2405	1	1	yes	characteristic
627	C₂×D₄	#2405	1	1	yes	characteristic
628	C₂×D₄	#2405	1	1	yes	characteristic
629	C₂×D₄	#2405	1	1	yes	characteristic
630	C₂×D₄	#2405	1	1	yes	characteristic
631	C₂×D₄	#2405	1	1	yes	characteristic
632	C₂×D₄	#2408	1	1	yes	characteristic
633	C₂×D₄	#2408	1	1	yes	characteristic
634	C₂×D₄	#2408	1	1	yes	characteristic
635	C₂×D₄	#2408	1	1	yes	characteristic
636	C₂×D₄	#2410	1	1	yes	characteristic
637	C₂×D₄	#2410	1	1	yes	characteristic
638	C₂×D₄	#2410	1	1	yes	characteristic
639	C₂×D₄	#2410	1	1	yes	characteristic
640	C₂×D₄	#2410	1	1	yes	characteristic
641	C₂×D₄	#2410	1	1	yes	characteristic
642	C₂×D₄	#2410	1	1	yes	characteristic
643	C₂×D₄	#2410	1	1	yes	characteristic
644	C₂×D₄	#2410	1	1	yes	characteristic
645	C₂×D₄	#2410	1	1	yes	characteristic
646	C₂×D₄	#2410	1	1	yes	characteristic
647	C₂×D₄	#2410	1	1	yes	characteristic
648	C₂×D₄	#2433	1	1	yes	characteristic
649	C₂×D₄	#2433	1	1	yes	characteristic
650	C₂×D₄	#2435	1	1	yes	characteristic
651	C₂×D₄	#2435	1	1	yes	characteristic
652	C₂×D₄	#2613	1	1	yes	characteristic
653	C₂×D₄	#2613	1	1	yes	characteristic
654	C₂²×C₄	C₂×#379	1	1	yes	characteristic
655	C₂²×C₄	C₂×#379	1	1	yes	characteristic
656	C₂²×C₄	C₂×#379	1	1	yes	characteristic
657	C₂²×C₄	C₂×#379	1	1	yes	characteristic
658	C₂²×C₄	C₂×#386	1	1	yes	characteristic
659	C₂²×C₄	C₂×#386	1	1	yes	characteristic
660	C₂²×C₄	#2308	1	1	yes	characteristic
661	C₂²×C₄	#2308	1	1	yes	characteristic
662	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
663	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
664	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
665	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
666	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
667	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
668	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
669	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×#392	1	1	yes	characteristic
671	C₂²×C₄	C₂×#392	1	1	yes	characteristic
672	C₂²×C₄	C₂×#394	1	1	yes	characteristic
673	C₂²×C₄	C₂×#394	1	1	yes	characteristic
674	C₂²×C₄	#2403	1	1	yes	characteristic
675	C₂²×C₄	#2403	1	1	yes	characteristic
676	C₂²×C₄	#2403	1	1	yes	characteristic
677	C₂²×C₄	#2403	1	1	yes	characteristic
678	C₂²×C₄	#2403	1	1	yes	characteristic
679	C₂²×C₄	#2403	1	1	yes	characteristic
680	C₂²×C₄	#2403	1	1	yes	characteristic
681	C₂²×C₄	#2405	1	1	yes	characteristic
682	C₂²×C₄	#2405	1	1	yes	characteristic
683	C₂²×C₄	#2405	1	1	yes	characteristic
684	C₂²×C₄	#2405	1	1	yes	characteristic
685	C₂²×C₄	#2405	1	1	yes	characteristic
686	C₂²×C₄	#2405	1	1	yes	characteristic
687	C₂²×C₄	#2405	1	1	yes	characteristic
688	C₂²×C₄	#2408	1	1	yes	characteristic
689	C₂²×C₄	#2408	1	1	yes	characteristic
690	C₂²×C₄	#2408	1	1	yes	characteristic
691	C₂²×C₄	#2408	1	1	yes	characteristic
692	C₂²×C₄	#2408	1	1	yes	characteristic
693	C₂²×C₄	#2408	1	1	yes	characteristic
694	C₂²×C₄	#2408	1	1	yes	characteristic
695	C₂²×C₄	#2408	1	1	yes	characteristic
696	C₂²×C₄	#2410	1	1	yes	characteristic
697	C₂²×C₄	#2410	1	1	yes	characteristic
698	C₂²×C₄	#2410	1	1	yes	characteristic
699	C₂²×C₄	#2410	1	1	yes	characteristic
700	C₂²×C₄	#2410	1	1	yes	characteristic
701	C₂²×C₄	#2410	1	1	yes	characteristic
702	C₂²×C₄	#2410	1	1	yes	characteristic
703	C₂²×C₄	#2410	1	1	yes	characteristic
704	C₂²×C₄	#2410	1	1	yes	characteristic
705	C₂²×C₄	#2410	1	1	yes	characteristic
706	C₂²×C₄	#2410	1	1	yes	characteristic
707	C₂²×C₄	#2410	1	1	yes	characteristic
708	C₂²×C₄	#2410	1	1	yes	characteristic
709	C₂²×C₄	#2410	1	1	yes	characteristic
710	C₂²×C₄	#2433	1	1	yes	characteristic
711	C₂²×C₄	#2433	1	1	yes	characteristic
712	C₂²×C₄	#2433	1	1	yes	characteristic
713	C₂²×C₄	#2433	1	1	yes	characteristic
714	C₂²×C₄	#2435	1	1	yes	characteristic
715	C₂²×C₄	#2435	1	1	yes	characteristic
716	C₂²×C₄	#2435	1	1	yes	characteristic
717	C₂²×C₄	#2435	1	1	yes	characteristic
718	C₂²×C₄	#2613	1	1	yes	characteristic
719	C₂²×C₄	#2613	1	1	yes	characteristic
720	C₂²×C₄	#2613	1	1	yes	characteristic
721	C₂²×C₄	#2613	1	1	yes	characteristic
722	C₂²×C₄	#2846	1	1	yes	characteristic
723	C₂²×C₄	#2846	1	1	yes	characteristic
724	C₂²×C₄	#2846	1	1	yes	characteristic
725	C₂²×C₄	#2846	1	1	yes	characteristic
726	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
727	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
728	C₂²×C₄	C₂×#458	1	1	yes	characteristic
729	C₂²×C₄	C₂×#458	1	1	yes	characteristic
730	C₂²×C₄	#3026	1	1	yes	characteristic
731	C₂²×C₄	#3026	1	1	yes	characteristic
732	C₂²×C₄	#3026	1	1	yes	characteristic
733	C₂²×C₄	#3026	1	1	yes	characteristic
734	C₄²	#1438	1	8	yes	—
735	C₂³	#13867	1	1	yes	characteristic
736	C₂³	#13867	1	1	yes	characteristic
737	C₂³	#13867	1	1	yes	characteristic
738	C₂³	#13867	1	1	yes	characteristic
739	C₂³	#13867	1	1	yes	characteristic
740	C₂³	#13867	1	1	yes	characteristic
741	C₂³	#14679	1	1	yes	characteristic
742	C₂³	#14715	1	1	yes	characteristic
743	C₂³	#14715	1	1	yes	characteristic
744	C₂³	#14715	1	1	yes	characteristic
745	C₂³	#14715	1	1	yes	characteristic
746	C₂³	#14724	1	1	yes	characteristic
747	C₂³	#14724	1	1	yes	characteristic
748	C₂³	#14724	1	1	yes	characteristic
749	C₂³	#14724	1	1	yes	characteristic
750	C₂³	#32898	1	1	yes	characteristic
751	C₂³	#32898	1	1	yes	characteristic
752	C₂³	#32900	1	1	yes	characteristic
753	C₂³	#32900	1	1	yes	characteristic
754	C₂×C₄	C₂×#1438	1	1	yes	characteristic
755	C₂×C₄	#13867	1	1	yes	characteristic
756	C₂×C₄	#13867	1	1	yes	characteristic
757	C₂×C₄	#13902	1	1	yes	characteristic
758	C₂×C₄	#13902	1	1	yes	characteristic
759	C₂×C₄	#13902	1	1	yes	characteristic
760	C₂×C₄	#13902	1	1	yes	characteristic
761	C₂×C₄	#14335	1	1	yes	characteristic
762	C₂×C₄	#14715	1	1	yes	characteristic
763	C₂×C₄	#14715	1	1	yes	characteristic
764	C₂×C₄	#14715	1	1	yes	characteristic
765	C₂×C₄	#14715	1	1	yes	characteristic
766	C₂×C₄	#14724	1	1	yes	characteristic
767	C₂×C₄	#14724	1	1	yes	characteristic
768	C₂×C₄	#14724	1	1	yes	characteristic
769	C₂×C₄	#14724	1	1	yes	characteristic
770	C₂×C₄	C₂×#1790	1	1	yes	characteristic
771	C₂×C₄	C₂×#1790	1	1	yes	characteristic
772	C₂×C₄	#20609	1	1	yes	characteristic
773	C₂×C₄	#20609	1	1	yes	characteristic
774	C₂×C₄	#23900	1	1	yes	characteristic
775	C₂×C₄	#23901	1	1	yes	characteristic
776	C₂×C₄	#23903	1	1	yes	characteristic
777	C₂×C₄	#23903	1	1	yes	characteristic
778	C₂×C₄	#24056	1	1	yes	characteristic
779	C₂×C₄	#24056	1	1	yes	characteristic
780	C₂×C₄	#24058	1	1	yes	characteristic
781	C₂×C₄	#24058	1	1	yes	characteristic
782	C₂×C₄	#24404	1	1	yes	characteristic
783	C₂×C₄	#24404	1	1	yes	characteristic
784	C₂×C₄	#24404	1	1	yes	characteristic
785	C₂×C₄	#24404	1	1	yes	characteristic
786	C₂×C₄	#24405	1	1	yes	characteristic
787	C₂×C₄	#24405	1	1	yes	characteristic
788	C₂×C₄	#24405	1	1	yes	characteristic
789	C₂×C₄	#24405	1	1	yes	characteristic
790	C₂×C₄	#32898	1	1	yes	characteristic
791	C₂×C₄	#32898	1	1	yes	characteristic
792	C₂×C₄	#32900	1	1	yes	characteristic
793	C₂×C₄	#32900	1	1	yes	characteristic
794	C₂²	#154094	1	1	yes	characteristic
795	C₂²	#392125	1	1	yes	characteristic
796	C₂²	#392125	1	1	yes	characteristic
797	C₂²	#394066	1	1	yes	characteristic
798	C₂²	#394068	1	1	yes	characteristic
799	C₂²	#395418	1	1	yes	characteristic
800	C₂²	#395418	1	1	yes	characteristic
801	C₂²	#511819	1	2	yes	—
802	C₂²	#511827	1	2	yes	—
803	C₄	#359531	1	1	yes	characteristic
804	C₄	#359531	1	1	yes	characteristic
805	C₄	#359552	1	1	yes	characteristic
806	C₄	#359554	1	1	yes	characteristic
807	C₄	#394066	1	1	yes	characteristic
808	C₄	#394068	1	1	yes	characteristic
809	C₄	#395418	1	1	yes	characteristic
810	C₄	#395418	1	1	yes	characteristic
811	C₂	#72215601	1	2	yes	—
812	C₂	#72225622	1	1	yes	characteristic
813	C₂	#72238617	1	1	yes	characteristic
814	C₂	#72260944	1	2	yes	—
815	C₂	#72261267	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#32898
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
prime radical	C₂×#7837029	C₂
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261903	C₂	semidirect
2. #72261819	C₂	semidirect
3. #72260901	C₂	semidirect
4. #72260553	C₂	semidirect
5. C₂×#493584	C₂	semidirect
6. #72250630	C₂	semidirect
7. C₂²×#12755	C₂	semidirect
8. C₂×#147817	C₂	semidirect
9. C₂×#146656	C₂	semidirect
10. C₂×#147573	C₂	semidirect
11. C₂×#359645	C₂	semidirect
12. C₂×#147577	C₂	semidirect
13. C₂²×#12711	C₂	semidirect
14. C₂×#147782	C₂	semidirect
18. C₂×#60087	C₂²	semidirect
19. #7837029	C₄	semidirect
27. C₂²×#2122	C₂²	semidirect
28. C₂²×#2122	C₂²	semidirect
29. C₂²×#2120	C₂²	semidirect
30. C₂²×#2120	C₂²	semidirect
31. C₂²×#2120	C₂²	semidirect
32. C₂²×#2120	C₂²	semidirect
33. C₂²×#1914	C₂²	semidirect
35. C₂²×#1891	C₂²	semidirect
36. C₂²×#1891	C₂²	semidirect
37. C₂×#20961	C₂²	semidirect
38. C₂×#20959	C₂²	semidirect
39. C₂×#20959	C₂²	semidirect
41. C₂²×#1795	C₂²	semidirect
42. C₂²×#1795	C₂²	semidirect
43. C₂²×#1795	C₂²	semidirect
44. C₂×#12587	C₂²	semidirect
45. C₂×#12585	C₂²	semidirect
46. C₂×#12583	C₂²	semidirect
47. C₂×#12581	C₂²	semidirect
48. C₂×#10751	C₂²	semidirect
49. #353440	C₂²	semidirect
50. #353437	C₂²	semidirect
51. C₂×#10742	C₂²	semidirect
103. C₂×#2134	D₄	semidirect
104. C₂×#2128	D₄	semidirect
105. C₂×#1910	D₄	semidirect
106. #20956	D₄	semidirect
115. C₂⁴×D₄	C₂²⋊C₄	semidirect
123. C₂×#568	C₂×D₄	semidirect
124. C₂×#560	C₂²⋊C₄	semidirect
125. C₂×D₄²	C₂²⋊C₄	semidirect
126. C₂×#535	C₂²⋊C₄	semidirect
127. C₂×#535	C₂²⋊C₄	semidirect
144. C₂²×#127	C₂²⋊C₄	semidirect
147. C₂×#525	C₂²⋊C₄	semidirect
148. C₂×#525	C₂²⋊C₄	semidirect
161. C₂²×#121	C₂²⋊C₄	semidirect
168. #3428	C₂×D₄	semidirect
169. C₂×#518	C₂²⋊C₄	semidirect
178. C₂×#413	C₂×D₄	semidirect
179. C₂×#413	C₂×D₄	semidirect
180. C₂×#413	C₂×D₄	semidirect
181. C₂×#410	C₂×D₄	semidirect
182. C₂×#410	C₂×D₄	semidirect
183. C₂×#410	C₂×D₄	semidirect
184. #2724	C₂²⋊C₄	semidirect
185. #2697	C₂²⋊C₄	semidirect
186. #2697	C₂²⋊C₄	semidirect
187. #2697	C₂²⋊C₄	semidirect
188. #2679	C₂²⋊C₄	semidirect
189. #2679	C₂²⋊C₄	semidirect
190. #2379	C₂²⋊C₄	semidirect
191. #2372	C₂²⋊C₄	semidirect
192. #2311	C₂²⋊C₄	semidirect
197. #2309	C₂²⋊C₄	semidirect
198. #2309	C₂²⋊C₄	semidirect
199. #2297	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72261903	2
#72261819	2
#72260901	2
#72260553	2
C₂×#493584	2
#72250630	2
C₂²×#12755	2
C₂×#147817	2
C₂×#146656	2
C₂×#147573	2
C₂×#359645	2
C₂×#147577	2
C₂²×#12711	2
C₂×#147782	2
C₂×#7837029	2