Subgroups — #72249652

Order 1024.

At least 6312 conjugacy classes of subgroups; only the 1819 normal subgroups are shown.

The subgroup lattice has 737 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10586404	C₂	1	1	yes	maximal, characteristic
2	#7622451	C₂	1	2	yes	maximal, complemented
3	C₂×#33348	C₂	1	2	yes	maximal, complemented
4	#6374195	C₂	1	1	yes	maximal, characteristic, complemented
5	#6374187	C₂	1	1	yes	maximal, characteristic, complemented
6	#493478	C₂	1	4	yes	maximal, complemented
7	#493477	C₂	1	4	yes	maximal, complemented
8	#493476	C₂	1	4	yes	maximal, complemented
9	#493474	C₂	1	4	yes	maximal, complemented
10	#493458	C₂	1	2	yes	maximal, complemented
11	C₂×#12725	C₂	1	2	yes	maximal, complemented
12	#493424	C₂	1	2	yes	maximal, complemented
13	#493391	C₂	1	2	yes	maximal, complemented
14	#62862	C₄	1	2	yes	complemented
15	#62862	C₄	1	2	yes	complemented
16	#62862	C₂²	1	2	yes	—
17	#62862	C₂²	1	2	yes	—
18	#62844	C₄	1	1	yes	characteristic, complemented
19	#62844	C₄	1	1	yes	characteristic, complemented
20	#62844	C₄	1	1	yes	characteristic, complemented
21	#62844	C₂²	1	1	yes	characteristic
22	#62842	C₄	1	1	yes	characteristic, complemented
23	#62842	C₂²	1	1	yes	characteristic
24	#62842	C₂²	1	1	yes	characteristic
25	#62842	C₂²	1	1	yes	characteristic
26	#62820	C₄	1	2	yes	complemented
27	#62820	C₂²	1	2	yes	—
28	#62817	C₄	1	2	yes	complemented
29	#62817	C₂²	1	2	yes	—
30	C₂×#3490	C₄	1	1	yes	characteristic, complemented
31	C₂×#3490	C₂²	1	1	yes	characteristic
32	C₂×#3484	C₄	1	1	yes	characteristic, complemented
33	C₂×#3484	C₄	1	1	yes	characteristic, complemented
34	C₂×#3484	C₂²	1	1	yes	characteristic
35	C₂×#3484	C₂²	1	1	yes	characteristic
36	C₂²×#534	C₄	1	1	yes	characteristic, complemented
37	C₂×#2888	C₂²	1	2	yes	complemented
38	C₂×#2883	C₂²	1	2	yes	complemented
39	#33350	C₂²	1	8	yes	complemented
40	#33348	C₂²	1	8	yes	complemented
41	#33348	C₂²	1	8	yes	complemented
42	#33348	C₂²	1	8	yes	complemented
43	C₂×#2121	C₂²	1	4	yes	complemented
44	C₂×#2121	C₂²	1	4	yes	complemented
45	C₂×#2121	C₂²	1	4	yes	complemented
46	C₂²×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
47	#21779	C₂²	1	4	yes	complemented
48	#21778	C₂²	1	4	yes	complemented
49	#21777	C₂²	1	4	yes	complemented
50	#21776	C₂²	1	4	yes	complemented
51	C₂×#1829	C₂²	1	2	yes	complemented
52	C₂×#1828	C₂²	1	2	yes	complemented
53	#20592	C₂²	1	2	yes	complemented
54	#20585	C₂²	1	2	yes	complemented
55	#12726	C₂²	1	8	yes	complemented
56	#12725	C₂²	1	8	yes	complemented
57	#12725	C₂²	1	8	yes	complemented
58	#12725	C₂²	1	8	yes	complemented
59	#12706	C₂²	1	8	yes	complemented
60	#12705	C₂²	1	8	yes	complemented
61	#12691	C₂²	1	4	yes	complemented
62	#12690	C₂²	1	4	yes	complemented
63	#12689	C₂²	1	4	yes	complemented
64	#12687	C₂²	1	4	yes	complemented
65	C₂²×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
66	C₂²×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂²×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
68	C₂²×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂⁴×D₄	C₂×C₄	1	1	yes	characteristic
70	C₂⁴×D₄	C₂×C₄	1	1	yes	characteristic, complemented
71	#3491	C₂×C₄	1	2	yes	complemented
72	#3491	C₂×C₄	1	2	yes	complemented
73	#3491	C₂×C₄	1	2	yes	complemented
74	#3491	C₂×C₄	1	2	yes	complemented
75	#3491	C₂×C₄	1	2	yes	complemented
76	#3491	C₂×C₄	1	2	yes	complemented
77	#3491	C₂×C₄	1	2	yes	complemented
78	#3491	C₂³	1	2	yes	—
79	#3490	C₂×C₄	1	2	yes	complemented
80	#3490	C₂×C₄	1	2	yes	complemented
81	#3490	C₂×C₄	1	2	yes	complemented
82	#3490	C₂×C₄	1	2	yes	complemented
83	#3490	C₂×C₄	1	2	yes	complemented
84	#3490	C₂×C₄	1	2	yes	complemented
85	#3490	C₂×C₄	1	2	yes	complemented
86	#3490	C₂×C₄	1	2	yes	complemented
87	#3490	C₂×C₄	1	2	yes	complemented
88	#3490	C₂×C₄	1	2	yes	complemented
89	#3490	C₂×C₄	1	2	yes	complemented
90	#3490	C₂×C₄	1	2	yes	complemented
91	#3490	C₂×C₄	1	2	yes	complemented
92	#3490	C₂³	1	2	yes	—
93	#3490	C₂³	1	2	yes	—
94	#3490	C₂³	1	2	yes	—
95	#3485	C₂×C₄	1	2	yes	—
96	#3485	C₂×C₄	1	2	yes	—
97	#3485	C₂×C₄	1	2	yes	complemented
98	#3485	C₂×C₄	1	2	yes	complemented
99	#3485	C₂×C₄	1	2	yes	complemented
100	#3485	D₄	1	4	yes	—
101	#3485	D₄	1	2	yes	—
102	#3485	D₄	1	2	yes	—
103	#3485	C₂³	1	2	yes	—
104	#3485	C₂³	1	2	yes	—
105	#3485	C₂³	1	2	yes	—
106	#3484	C₂×C₄	1	2	yes	—
107	#3484	C₂×C₄	1	2	yes	—
108	#3484	C₂×C₄	1	2	yes	—
109	#3484	C₂×C₄	1	2	yes	—
110	#3484	C₂×C₄	1	2	yes	complemented
111	#3484	C₂×C₄	1	2	yes	complemented
112	#3484	C₂×C₄	1	2	yes	complemented
113	#3484	C₂×C₄	1	2	yes	complemented
114	#3484	C₂×C₄	1	2	yes	complemented
115	#3484	C₂×C₄	1	2	yes	complemented
116	#3484	C₂×C₄	1	2	yes	complemented
117	#3484	D₄	1	4	yes	—
118	#3484	D₄	1	4	yes	—
119	#3484	D₄	1	4	yes	—
120	#3484	D₄	1	2	yes	—
121	#3484	D₄	1	2	yes	—
122	#3484	C₂³	1	2	yes	—
123	#3484	C₂³	1	2	yes	—
124	#3484	C₂³	1	2	yes	—
125	#3484	C₂³	1	2	yes	—
126	#3484	C₂³	1	2	yes	—
127	C₂×#543	C₂×C₄	1	1	yes	characteristic, complemented
128	C₂×#543	C₂×C₄	1	1	yes	characteristic, complemented
129	#3449	D₄	1	4	yes	—
130	#3449	D₄	1	2	yes	—
131	#3449	D₄	1	2	yes	—
132	C₂×#535	C₂×C₄	1	2	yes	complemented
133	C₂×#535	C₂×C₄	1	1	yes	characteristic, complemented
134	C₂×#535	D₄	1	2	yes	—
135	C₂×#535	C₂³	1	1	yes	characteristic
136	C₂×#534	C₂×C₄	1	1	yes	characteristic
137	C₂×#534	C₂×C₄	1	1	yes	characteristic
138	C₂×#534	C₂×C₄	1	1	yes	characteristic
139	C₂×#534	C₂×C₄	1	1	yes	characteristic
140	C₂×#534	C₂×C₄	1	1	yes	characteristic
141	C₂×#534	C₂×C₄	1	1	yes	characteristic
142	C₂×#534	C₂×C₄	1	1	yes	characteristic
143	C₂×#534	C₂×C₄	1	1	yes	characteristic, complemented
144	C₂×#534	C₂×C₄	1	1	yes	characteristic, complemented
145	C₂×#534	C₂×C₄	1	1	yes	characteristic, complemented
146	C₂×#534	C₂×C₄	1	1	yes	characteristic, complemented
147	C₂×#534	C₂×C₄	1	2	yes	complemented
148	C₂×#534	C₂×C₄	1	1	yes	characteristic, complemented
149	C₂×#534	C₂×C₄	1	2	yes	complemented
150	C₂×#534	C₂×C₄	1	2	yes	complemented
151	C₂×#534	D₄	1	2	yes	—
152	C₂×#534	D₄	1	4	yes	—
153	C₂×#534	D₄	1	2	yes	—
154	C₂×#534	D₄	1	2	yes	—
155	C₂×#534	C₂³	1	1	yes	characteristic
156	C₂×#534	C₂³	1	1	yes	characteristic
157	C₂×#534	C₂³	1	1	yes	characteristic
158	C₂×#534	C₂³	1	1	yes	characteristic
159	C₂×#525	C₂×C₄	1	2	yes	complemented
160	C₂×#525	C₂×C₄	1	1	yes	characteristic, complemented
161	C₂×#525	D₄	1	2	yes	—
162	C₂×#525	C₂³	1	1	yes	characteristic
163	C₂²×#123	C₂×C₄	1	2	yes	complemented
164	C₂²×#120	C₂×C₄	1	1	yes	characteristic
165	C₂²×#120	C₂×C₄	1	1	yes	characteristic, complemented
166	C₂²×#120	C₂×C₄	1	1	yes	characteristic, complemented
167	C₂²×#120	C₂×C₄	1	2	yes	complemented
168	C₂²×#120	C₂×C₄	1	1	yes	characteristic, complemented
169	C₂²×#120	C₂×C₄	1	2	yes	complemented
170	C₂²×#120	D₄	1	2	yes	—
171	C₂²×#120	C₂³	1	1	yes	characteristic
172	C₂²×#120	C₂³	1	1	yes	characteristic
173	C₂×#518	C₂×C₄	1	1	yes	characteristic
174	C₂×#518	C₂×C₄	1	1	yes	characteristic
175	C₂×#518	C₂×C₄	1	1	yes	characteristic, complemented
176	C₂×#518	C₂×C₄	1	1	yes	characteristic, complemented
177	C₂×#518	C₂×C₄	1	1	yes	characteristic, complemented
178	C₂×#518	C₂×C₄	1	1	yes	characteristic, complemented
179	C₂×#518	C₂×C₄	1	1	yes	characteristic, complemented
180	C₂×#518	C₂³	1	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
182	#2888	C₂³	1	8	yes	complemented
183	C₂²×#100	C₂³	1	4	yes	—
184	#2883	C₂³	1	8	yes	complemented
185	C₂²×#99	C₂³	1	4	yes	—
186	#2121	C₂³	1	16	yes	—
187	#2121	C₂³	1	16	yes	complemented
188	C₂×#352	C₂³	1	8	yes	complemented
189	C₂×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
190	C₂×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
191	C₂×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
192	#1829	C₂³	1	8	yes	complemented
193	#1828	C₂³	1	8	yes	complemented
194	#1785	C₂³	1	4	yes	complemented
195	#1783	C₂³	1	4	yes	complemented
196	#1782	C₂³	1	4	yes	complemented
197	#1781	C₂³	1	4	yes	complemented
198	C₂⁶	C₂²⋊C₄	1	1	yes	characteristic, complemented
199	C₂⁶	C₂²×C₄	1	1	yes	characteristic
200	C₂⁶	C₂²×C₄	1	1	yes	characteristic, complemented
201	C₂×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
202	C₂×H(5,𝔽₂)	C₂²×C₄	1	2	yes	complemented
203	C₂×H(5,𝔽₂)	C₂²×C₄	1	2	yes	complemented
204	C₂×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
205	C₂×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
206	C₂×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
207	C₂×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
208	C₂×H(5,𝔽₂)	C₂⁴	1	2	yes	—
209	C₂²×#41	C₂²⋊C₄	1	2	yes	complemented
210	C₂²×#41	C₂²⋊C₄	1	2	yes	complemented
211	C₂²×#41	C₂²×C₄	1	2	yes	—
212	C₂²×#41	C₂²×C₄	1	1	yes	characteristic
213	C₂²×#41	C₂×D₄	1	1	yes	characteristic
214	C₂²×#41	C₂×D₄	1	1	yes	characteristic
215	C₂²×#41	C₂×D₄	1	1	yes	characteristic
216	C₂²×#41	C₂×D₄	1	2	yes	—
217	C₂²×#41	C₂×D₄	1	2	yes	—
218	C₂²×#41	C₂×D₄	1	2	yes	—
219	C₂²×#41	C₂×D₄	1	1	yes	characteristic
220	C₂²×#41	C₂⁴	1	1	yes	characteristic
221	C₂³×D₄	C₂²⋊C₄	1	2	yes	complemented
222	C₂³×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
223	C₂³×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
224	C₂³×D₄	C₂²⋊C₄	1	2	yes	complemented
225	C₂³×D₄	C₂²⋊C₄	1	2	yes	complemented
226	C₂³×D₄	C₂²⋊C₄	1	2	yes	complemented
227	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
230	C₂³×D₄	C₂²×C₄	1	2	yes	—
231	C₂³×D₄	C₂²×C₄	1	2	yes	—
232	C₂³×D₄	C₂²×C₄	1	2	yes	—
233	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
235	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
237	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic
238	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
239	C₂³×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
240	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
241	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
242	C₂³×D₄	C₂×D₄	1	2	yes	—
243	C₂³×D₄	C₂×D₄	1	2	yes	—
244	C₂³×D₄	C₂×D₄	1	2	yes	—
245	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
246	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
247	C₂³×D₄	C₂⁴	1	1	yes	characteristic
248	C₂³×D₄	C₂⁴	1	1	yes	characteristic
249	C₂⁴×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
250	C₂⁴×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
251	#543	C₂²×C₄	1	2	yes	complemented
252	#543	C₂²×C₄	1	2	yes	complemented
253	#543	C₂²×C₄	1	2	yes	complemented
254	#543	C₂²×C₄	1	2	yes	complemented
255	#536	C₂²⋊C₄	1	4	yes	—
256	#536	C₂²⋊C₄	1	4	yes	complemented
257	#536	C₂×D₄	1	4	yes	—
258	#536	C₂×D₄	1	4	yes	—
259	#535	C₂²⋊C₄	1	4	yes	—
260	#535	C₂²⋊C₄	1	4	yes	complemented
261	#535	C₂²⋊C₄	1	4	yes	complemented
262	#535	C₂²⋊C₄	1	4	yes	complemented
263	#535	C₂×D₄	1	4	yes	—
264	#535	C₂×D₄	1	4	yes	—
265	#535	C₂×D₄	1	4	yes	—
266	#535	C₂×D₄	1	4	yes	—
267	#534	C₂²⋊C₄	1	2	yes	—
268	#534	C₂²⋊C₄	1	2	yes	—
269	#534	C₂²⋊C₄	1	2	yes	—
270	#534	C₂²⋊C₄	1	2	yes	—
271	#534	C₂²⋊C₄	1	2	yes	—
272	#534	C₂²⋊C₄	1	2	yes	—
273	#534	C₂²⋊C₄	1	2	yes	—
274	#534	C₂²⋊C₄	1	2	yes	—
275	#534	C₂²⋊C₄	1	2	yes	—
276	#534	C₂²⋊C₄	1	2	yes	—
277	#534	C₂²⋊C₄	1	2	yes	—
278	#534	C₂²⋊C₄	1	2	yes	—
279	#534	C₂²⋊C₄	1	4	yes	—
280	#534	C₂²⋊C₄	1	4	yes	—
281	#534	C₂²⋊C₄	1	4	yes	complemented
282	#534	C₂²⋊C₄	1	4	yes	complemented
283	#534	C₂²⋊C₄	1	4	yes	complemented
284	#534	C₂²⋊C₄	1	4	yes	complemented
285	#534	C₂²⋊C₄	1	4	yes	complemented
286	#534	C₂²⋊C₄	1	4	yes	complemented
287	#534	C₂²⋊C₄	1	4	yes	complemented
288	#534	C₂²⋊C₄	1	4	yes	complemented
289	#534	C₂²×C₄	1	2	yes	—
290	#534	C₂²×C₄	1	2	yes	—
291	#534	C₂²×C₄	1	2	yes	—
292	#534	C₂²×C₄	1	2	yes	—
293	#534	C₂²×C₄	1	2	yes	—
294	#534	C₂²×C₄	1	2	yes	—
295	#534	C₂²×C₄	1	2	yes	—
296	#534	C₂²×C₄	1	2	yes	—
297	#534	C₂²×C₄	1	2	yes	—
298	#534	C₂²×C₄	1	2	yes	—
299	#534	C₂×D₄	1	4	yes	—
300	#534	C₂×D₄	1	4	yes	—
301	#534	C₂×D₄	1	4	yes	—
302	#534	C₂×D₄	1	4	yes	—
303	#534	C₂×D₄	1	4	yes	—
304	#534	C₂×D₄	1	4	yes	—
305	#534	C₂×D₄	1	4	yes	—
306	#534	C₂×D₄	1	4	yes	—
307	#534	C₂×D₄	1	4	yes	—
308	#534	C₂×D₄	1	4	yes	—
309	#534	C₂⁴	1	2	yes	—
310	#534	C₂⁴	1	2	yes	—
311	#525	C₂²⋊C₄	1	4	yes	—
312	#525	C₂²⋊C₄	1	4	yes	—
313	#525	C₂²⋊C₄	1	4	yes	complemented
314	#525	C₂²⋊C₄	1	4	yes	complemented
315	#525	C₂²⋊C₄	1	4	yes	complemented
316	#525	C₂²⋊C₄	1	4	yes	complemented
317	#525	C₂×D₄	1	4	yes	—
318	#525	C₂×D₄	1	4	yes	—
319	#525	C₂×D₄	1	4	yes	—
320	#525	C₂×D₄	1	4	yes	—
321	#525	C₂×D₄	1	4	yes	—
322	#525	C₂×D₄	1	4	yes	—
323	C₂×#123	C₂²⋊C₄	1	2	yes	—
324	C₂×#123	C₂²⋊C₄	1	2	yes	—
325	C₂×#123	C₂²⋊C₄	1	4	yes	—
326	C₂×#123	C₂²⋊C₄	1	2	yes	complemented
327	C₂×#123	C₂²⋊C₄	1	2	yes	complemented
328	C₂×#123	C₂²⋊C₄	1	4	yes	complemented
329	C₂×#123	C₂²×C₄	1	2	yes	—
330	C₂×#123	C₂²×C₄	1	2	yes	—
331	C₂×#123	C₂²×C₄	1	2	yes	—
332	C₂×#123	C₂²×C₄	1	1	yes	characteristic
333	C₂×#123	C₂²×C₄	1	2	yes	complemented
334	C₂×#123	C₂²×C₄	1	2	yes	complemented
335	C₂×#123	C₂²×C₄	1	2	yes	complemented
336	C₂×#123	C₂²×C₄	1	1	yes	characteristic, complemented
337	C₂×#123	C₂²×C₄	1	1	yes	characteristic, complemented
338	C₂×#123	C₂×D₄	1	2	yes	—
339	C₂×#123	C₂×D₄	1	4	yes	—
340	C₂×#123	C₂×D₄	1	2	yes	—
341	C₂×#123	C₂×D₄	1	4	yes	—
342	C₂×#123	C₂⁴	1	1	yes	characteristic
343	C₂×#120	C₂²⋊C₄	1	2	yes	—
344	C₂×#120	C₂²⋊C₄	1	2	yes	—
345	C₂×#120	C₂²⋊C₄	1	4	yes	—
346	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
347	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
348	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
349	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
350	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
351	C₂×#120	C₂²⋊C₄	1	4	yes	complemented
352	C₂×#120	C₂²⋊C₄	1	4	yes	complemented
353	C₂×#120	C₂²⋊C₄	1	2	yes	complemented
354	C₂×#120	C₂²⋊C₄	1	4	yes	complemented
355	C₂×#120	C₂²×C₄	1	2	yes	—
356	C₂×#120	C₂²×C₄	1	2	yes	—
357	C₂×#120	C₂²×C₄	1	1	yes	characteristic
358	C₂×#120	C₂²×C₄	1	2	yes	—
359	C₂×#120	C₂²×C₄	1	2	yes	—
360	C₂×#120	C₂²×C₄	1	2	yes	—
361	C₂×#120	C₂²×C₄	1	1	yes	characteristic
362	C₂×#120	C₂²×C₄	1	1	yes	characteristic
363	C₂×#120	C₂²×C₄	1	2	yes	complemented
364	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
365	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
366	C₂×#120	C₂²×C₄	1	2	yes	complemented
367	C₂×#120	C₂²×C₄	1	2	yes	complemented
368	C₂×#120	C₂²×C₄	1	2	yes	complemented
369	C₂×#120	C₂²×C₄	1	2	yes	complemented
370	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
371	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
372	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
373	C₂×#120	C₂²×C₄	1	1	yes	characteristic, complemented
374	C₂×#120	C₂×D₄	1	2	yes	—
375	C₂×#120	C₂×D₄	1	2	yes	—
376	C₂×#120	C₂×D₄	1	4	yes	—
377	C₂×#120	C₂×D₄	1	4	yes	—
378	C₂×#120	C₂×D₄	1	2	yes	—
379	C₂×#120	C₂×D₄	1	2	yes	—
380	C₂×#120	C₂×D₄	1	2	yes	—
381	C₂×#120	C₂×D₄	1	4	yes	—
382	C₂×#120	C₂×D₄	1	2	yes	—
383	C₂×#120	C₂×D₄	1	4	yes	—
384	C₂×#120	C₂⁴	1	1	yes	characteristic
385	C₂×#120	C₂⁴	1	1	yes	characteristic
386	C₂×#120	C₂⁴	1	1	yes	characteristic
387	#518	C₂²⋊C₄	1	4	yes	complemented
388	#518	C₂²⋊C₄	1	4	yes	complemented
389	#518	C₂²×C₄	1	2	yes	—
390	#518	C₂²×C₄	1	2	yes	—
391	#518	C₂²×C₄	1	2	yes	—
392	#518	C₂²×C₄	1	2	yes	—
393	#518	C₂²×C₄	1	2	yes	—
394	#518	C₂²×C₄	1	2	yes	complemented
395	#518	C₂²×C₄	1	2	yes	complemented
396	#518	C₂²×C₄	1	2	yes	complemented
397	#518	C₂²×C₄	1	2	yes	complemented
398	#518	C₂²×C₄	1	2	yes	complemented
399	#518	C₂²×C₄	1	2	yes	complemented
400	#518	C₂×D₄	1	2	yes	—
401	#518	C₂×D₄	1	2	yes	—
402	#518	C₂⁴	1	2	yes	—
403	C₂×#117	C₂²⋊C₄	1	2	yes	complemented
404	C₂×#117	C₂²⋊C₄	1	2	yes	complemented
405	C₂×#117	C₂²×C₄	1	2	yes	complemented
406	C₂×#117	C₂²×C₄	1	1	yes	characteristic, complemented
407	C₂×#117	C₂²×C₄	1	1	yes	characteristic, complemented
408	C₂×#117	C₂×D₄	1	2	yes	—
409	C₂²×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
410	C₂²×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
411	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
418	C₂²×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
419	C₂²×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
420	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
421	C₂²×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
422	C₂²×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₂×#100	C₂⁴	1	8	yes	—
424	C₂×#99	C₂⁴	1	8	yes	—
425	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
426	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂⁵	C₂×C₂²⋊C₄	1	2	yes	—
434	C₂⁵	C₂×C₂²⋊C₄	1	2	yes	—
435	C₂⁵	C₂×C₂²⋊C₄	1	2	yes	—
436	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂⁵	C₂×C₂²⋊C₄	1	1	yes	characteristic
438	C₂⁵	#120	1	2	yes	—
439	C₂⁵	C₂³×C₄	1	1	yes	characteristic
440	C₂⁵	C₂³×C₄	1	1	yes	characteristic
441	C₂⁵	C₂³×C₄	1	1	yes	characteristic
442	C₂⁵	C₂³×C₄	1	1	yes	characteristic
443	C₂⁵	C₂³×C₄	1	1	yes	characteristic
444	C₂⁵	C₂²×D₄	1	1	yes	characteristic
445	C₂⁵	C₂²×D₄	1	1	yes	characteristic
446	C₂×#41	C₂×C₂²⋊C₄	1	4	yes	—
447	C₂×#41	C₂×C₂²⋊C₄	1	4	yes	—
448	C₂×#41	C₂×C₂²⋊C₄	1	4	yes	—
449	C₂×#41	#120	1	4	yes	—
450	C₂×#41	#120	1	4	yes	—
451	C₂×#41	#120	1	4	yes	—
452	C₂×#41	#120	1	4	yes	—
453	C₂×#41	#120	1	4	yes	—
454	C₂×#41	#120	1	4	yes	—
455	C₂×#41	C₂²×D₄	1	4	yes	—
456	C₂×#41	C₂²×D₄	1	4	yes	—
457	C₂×#41	C₂²×D₄	1	4	yes	—
458	C₂²×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
460	C₂²×Q₈	#120	1	2	yes	—
461	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
462	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
469	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
470	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
471	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
472	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
475	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
478	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
479	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
480	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
481	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
482	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
483	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
484	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
485	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
486	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
487	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
488	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
489	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
490	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
491	C₂²×D₄	C₂×C₂²⋊C₄	1	2	yes	—
492	C₂²×D₄	C₂×C₂²⋊C₄	1	4	yes	—
493	C₂²×D₄	C₂×C₂²⋊C₄	1	4	yes	—
494	C₂²×D₄	C₂×C₂²⋊C₄	1	4	yes	—
495	C₂²×D₄	#120	1	2	yes	—
496	C₂²×D₄	#120	1	4	yes	—
497	C₂²×D₄	#120	1	4	yes	—
498	C₂²×D₄	#120	1	4	yes	—
499	C₂²×D₄	#120	1	2	yes	—
500	C₂²×D₄	#120	1	2	yes	—
501	C₂²×D₄	#120	1	4	yes	—
502	C₂²×D₄	#120	1	4	yes	—
503	C₂²×D₄	#120	1	4	yes	—
504	C₂²×D₄	C₂³×C₄	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₄	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₄	1	2	yes	—
507	C₂²×D₄	C₂³×C₄	1	2	yes	—
508	C₂²×D₄	C₂³×C₄	1	2	yes	—
509	C₂²×D₄	C₂³×C₄	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₄	1	2	yes	—
511	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
512	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
513	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
514	C₂²×D₄	C₂²×D₄	1	4	yes	—
515	C₂²×D₄	C₂²×D₄	1	2	yes	—
516	C₂²×D₄	C₂²×D₄	1	2	yes	—
517	C₂²×D₄	C₂²×D₄	1	2	yes	—
518	C₂²×D₄	C₂²×D₄	1	2	yes	—
519	C₂²×D₄	C₂²×D₄	1	4	yes	—
520	C₂²×D₄	C₂²×D₄	1	4	yes	—
521	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
522	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
523	C₂²×D₄	C₂⁵	1	1	yes	characteristic
524	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
525	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
526	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
527	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
528	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
529	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
530	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
531	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
532	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
533	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
534	C₂³×C₄	C₂×C₂²⋊C₄	1	2	yes	—
535	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
536	C₂³×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
537	C₂³×C₄	#120	1	2	yes	—
538	C₂³×C₄	#120	1	2	yes	—
539	C₂³×C₄	#120	1	2	yes	—
540	C₂³×C₄	C₂³×C₄	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₄	1	1	yes	characteristic
542	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
545	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
546	#123	C₂×C₂²⋊C₄	1	4	yes	—
547	#123	C₂×C₂²⋊C₄	1	4	yes	—
548	#123	C₂×C₂²⋊C₄	1	4	yes	—
549	#123	C₂×C₂²⋊C₄	1	4	yes	—
550	#123	C₂×C₂²⋊C₄	1	4	yes	—
551	#123	C₂×C₂²⋊C₄	1	4	yes	—
552	#123	C₂×C₂²⋊C₄	1	4	yes	—
553	#123	C₂×C₂²⋊C₄	1	4	yes	—
554	#123	C₂×C₂²⋊C₄	1	4	yes	—
555	#123	C₂×C₂²⋊C₄	1	4	yes	—
556	#123	C₂×C₂²⋊C₄	1	4	yes	—
557	#123	C₂×C₂²⋊C₄	1	4	yes	—
558	#123	C₂×C₂²⋊C₄	1	4	yes	—
559	#123	C₂×C₂²⋊C₄	1	4	yes	—
560	#123	C₂×C₂²⋊C₄	1	4	yes	—
561	#123	C₂×C₂²⋊C₄	1	4	yes	—
562	#123	C₂×C₂²⋊C₄	1	4	yes	—
563	#123	C₂²×D₄	1	4	yes	—
564	#123	C₂²×D₄	1	4	yes	—
565	#123	C₂²×D₄	1	4	yes	—
566	#120	C₂×C₂²⋊C₄	1	4	yes	—
567	#120	C₂×C₂²⋊C₄	1	4	yes	—
568	#120	C₂×C₂²⋊C₄	1	4	yes	—
569	#120	C₂×C₂²⋊C₄	1	2	yes	—
570	#120	C₂×C₂²⋊C₄	1	4	yes	—
571	#120	C₂×C₂²⋊C₄	1	4	yes	—
572	#120	C₂×C₂²⋊C₄	1	4	yes	—
573	#120	C₂×C₂²⋊C₄	1	2	yes	—
574	#120	C₂×C₂²⋊C₄	1	4	yes	—
575	#120	C₂×C₂²⋊C₄	1	4	yes	—
576	#120	C₂×C₂²⋊C₄	1	4	yes	—
577	#120	C₂×C₂²⋊C₄	1	4	yes	—
578	#120	C₂×C₂²⋊C₄	1	4	yes	—
579	#120	C₂×C₂²⋊C₄	1	4	yes	—
580	#120	C₂×C₂²⋊C₄	1	4	yes	—
581	#120	C₂×C₂²⋊C₄	1	4	yes	—
582	#120	C₂×C₂²⋊C₄	1	2	yes	—
583	#120	C₂×C₂²⋊C₄	1	4	yes	—
584	#120	C₂×C₂²⋊C₄	1	4	yes	—
585	#120	C₂×C₂²⋊C₄	1	4	yes	—
586	#120	C₂×C₂²⋊C₄	1	4	yes	—
587	#120	C₂×C₂²⋊C₄	1	4	yes	—
588	#120	C₂×C₂²⋊C₄	1	4	yes	—
589	#120	C₂×C₂²⋊C₄	1	4	yes	—
590	#120	C₂×C₂²⋊C₄	1	2	yes	—
591	#120	C₂²×D₄	1	2	yes	—
592	#120	C₂²×D₄	1	2	yes	—
593	#120	C₂²×D₄	1	4	yes	—
594	#120	C₂²×D₄	1	2	yes	—
595	#120	C₂²×D₄	1	4	yes	—
596	#120	C₂²×D₄	1	2	yes	—
597	#120	C₂²×D₄	1	4	yes	—
598	#117	C₂×C₂²⋊C₄	1	4	yes	—
599	#117	C₂×C₂²⋊C₄	1	4	yes	—
600	#117	C₂×C₂²⋊C₄	1	4	yes	—
601	#117	C₂×C₂²⋊C₄	1	4	yes	—
602	#117	C₂×C₂²⋊C₄	1	4	yes	—
603	#117	C₂²×D₄	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
611	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
619	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
630	C₂⁴	#379	1	2	yes	—
631	C₂⁴	#379	1	2	yes	—
632	C₂⁴	#379	1	2	yes	—
633	C₂⁴	#379	1	4	yes	—
634	C₂⁴	#379	1	2	yes	—
635	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
636	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
637	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
638	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
639	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
640	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
641	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
642	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
643	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
644	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
645	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
646	C₂⁴	C₂²×C₂²⋊C₄	1	2	yes	—
647	C₂⁴	C₂²×C₂²⋊C₄	1	2	yes	—
648	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
649	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
650	C₂⁴	C₂²×C₂²⋊C₄	1	2	yes	—
651	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
652	C₂⁴	C₂²×C₂²⋊C₄	1	2	yes	—
653	C₂⁴	C₂²×C₂²⋊C₄	1	2	yes	—
654	C₂⁴	C₂²×C₂²⋊C₄	1	1	yes	characteristic
655	C₂⁴	C₂×#120	1	2	yes	—
656	C₂⁴	C₂×#120	1	2	yes	—
657	C₂⁴	C₂×#120	1	4	yes	—
658	C₂⁴	C₂⁴×C₄	1	1	yes	characteristic
659	C₂⁴	C₂³×D₄	1	1	yes	characteristic
660	C₂×Q₈	#379	1	4	yes	—
661	C₂×Q₈	C₂×#120	1	4	yes	—
662	C₂×D₄	#379	1	4	yes	—
663	C₂×D₄	#379	1	4	yes	—
664	C₂×D₄	#379	1	4	yes	—
665	C₂×D₄	#379	1	4	yes	—
666	C₂×D₄	#379	1	4	yes	—
667	C₂×D₄	#379	1	4	yes	—
668	C₂×D₄	#379	1	4	yes	—
669	C₂×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
670	C₂×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
671	C₂×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
672	C₂×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
673	C₂×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
674	C₂×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
675	C₂×D₄	C₂×#120	1	2	yes	—
676	C₂×D₄	C₂×#120	1	2	yes	—
677	C₂×D₄	C₂×#120	1	4	yes	—
678	C₂×D₄	C₂×#120	1	2	yes	—
679	C₂×D₄	C₂×#120	1	2	yes	—
680	C₂×D₄	C₂×#120	1	4	yes	—
681	C₂×D₄	C₂×#120	1	4	yes	—
682	C₂×D₄	C₂³×D₄	1	2	yes	—
683	C₂×D₄	C₂³×D₄	1	2	yes	—
684	C₂²×C₄	#379	1	2	yes	—
685	C₂²×C₄	#379	1	2	yes	—
686	C₂²×C₄	#379	1	2	yes	—
687	C₂²×C₄	#379	1	2	yes	—
688	C₂²×C₄	#379	1	4	yes	—
689	C₂²×C₄	#379	1	4	yes	—
690	C₂²×C₄	#379	1	4	yes	—
691	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
692	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
693	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
694	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
695	C₂²×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
696	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
697	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
698	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
699	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
700	C₂²×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
701	C₂²×C₄	C₂×#120	1	2	yes	—
702	C₂²×C₄	C₂×#120	1	2	yes	—
703	C₂²×C₄	C₂×#120	1	4	yes	—
704	C₂²×C₄	C₂×#120	1	4	yes	—
705	C₂²×C₄	C₂×#120	1	4	yes	—
706	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
707	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
708	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
709	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
710	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
711	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
712	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
713	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
714	C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
715	C₂³	C₂×#379	1	4	yes	—
716	C₂³	C₂×#379	1	1	yes	characteristic
717	C₂³	C₂×#379	1	4	yes	—
718	C₂³	C₂×#379	1	2	yes	—
719	C₂³	C₂×#379	1	1	yes	characteristic
720	C₂³	C₂×#379	1	1	yes	characteristic
721	C₂³	C₂×#379	1	1	yes	characteristic
722	C₂³	#2883	1	4	yes	—
723	C₂³	C₂³×C₂²⋊C₄	1	1	yes	characteristic
724	C₂³	C₂³×C₂²⋊C₄	1	1	yes	characteristic
725	C₂³	C₂³×C₂²⋊C₄	1	1	yes	characteristic
726	C₂³	C₂²×#120	1	2	yes	—
727	C₂×C₄	C₂×#379	1	2	yes	—
728	C₂×C₄	C₂×#379	1	4	yes	—
729	C₂×C₄	C₂×#379	1	4	yes	—
730	C₂×C₄	C₂²×#120	1	2	yes	—
731	C₂²	#20585	1	2	yes	—
732	C₂²	#20585	1	2	yes	—
733	C₂²	C₂²×#379	1	1	yes	characteristic
734	C₂²	C₂×#2883	1	2	yes	—
735	C₂	C₂×#20585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#20585
commutator	C₂⁴	C₂⁴×C₄
Frattini, cosocle	C₂²×D₄	C₂⁵
prime radical	#10586404	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #62842 ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #7622451	C₂	semidirect
3. C₂×#33348	C₂	semidirect
4. #6374195	C₂	semidirect
5. #6374187	C₂	semidirect
6. #493478	C₂	semidirect
7. #493477	C₂	semidirect
8. #493476	C₂	semidirect
9. #493474	C₂	semidirect
10. #493458	C₂	semidirect
11. C₂×#12725	C₂	semidirect
12. #493424	C₂	semidirect
13. #493391	C₂	semidirect
14. #62862	C₄	semidirect
15. #62862	C₄	semidirect
18. #62844	C₄	semidirect
19. #62844	C₄	semidirect
20. #62844	C₄	semidirect
22. #62842	C₄	semidirect
26. #62820	C₄	semidirect
28. #62817	C₄	semidirect
30. C₂×#3490	C₄	semidirect
32. C₂×#3484	C₄	semidirect
33. C₂×#3484	C₄	semidirect
36. C₂²×#534	C₄	semidirect
37. C₂×#2888	C₂²	semidirect
38. C₂×#2883	C₂²	semidirect
39. #33350	C₂²	semidirect
40. #33348	C₂²	semidirect
41. #33348	C₂²	semidirect
42. #33348	C₂²	semidirect
43. C₂×#2121	C₂²	semidirect
44. C₂×#2121	C₂²	semidirect
45. C₂×#2121	C₂²	semidirect
46. C₂²×AΣL(1,𝔽₁₆)	C₂²	semidirect
47. #21779	C₂²	semidirect
48. #21778	C₂²	semidirect
49. #21777	C₂²	semidirect
50. #21776	C₂²	semidirect
51. C₂×#1829	C₂²	semidirect
52. C₂×#1828	C₂²	semidirect
53. #20592	C₂²	semidirect
54. #20585	C₂²	semidirect
55. #12726	C₂²	semidirect
56. #12725	C₂²	semidirect
57. #12725	C₂²	semidirect
58. #12725	C₂²	semidirect
59. #12706	C₂²	semidirect
60. #12705	C₂²	semidirect
61. #12691	C₂²	semidirect
62. #12690	C₂²	semidirect
63. #12689	C₂²	semidirect
64. #12687	C₂²	semidirect
66. C₂²×H(5,𝔽₂)	C₂×C₄	semidirect
70. C₂⁴×D₄	C₂×C₄	semidirect
71. #3491	C₂×C₄	semidirect
72. #3491	C₂×C₄	semidirect
73. #3491	C₂×C₄	semidirect
74. #3491	C₂×C₄	semidirect
75. #3491	C₂×C₄	semidirect
76. #3491	C₂×C₄	semidirect
77. #3491	C₂×C₄	semidirect
79. #3490	C₂×C₄	semidirect
80. #3490	C₂×C₄	semidirect
81. #3490	C₂×C₄	semidirect
82. #3490	C₂×C₄	semidirect
83. #3490	C₂×C₄	semidirect
84. #3490	C₂×C₄	semidirect
85. #3490	C₂×C₄	semidirect
86. #3490	C₂×C₄	semidirect
87. #3490	C₂×C₄	semidirect
88. #3490	C₂×C₄	semidirect
89. #3490	C₂×C₄	semidirect
90. #3490	C₂×C₄	semidirect
91. #3490	C₂×C₄	semidirect
97. #3485	C₂×C₄	semidirect
98. #3485	C₂×C₄	semidirect
99. #3485	C₂×C₄	semidirect
110. #3484	C₂×C₄	semidirect
111. #3484	C₂×C₄	semidirect
112. #3484	C₂×C₄	semidirect
113. #3484	C₂×C₄	semidirect
114. #3484	C₂×C₄	semidirect
115. #3484	C₂×C₄	semidirect
116. #3484	C₂×C₄	semidirect
127. C₂×#543	C₂×C₄	semidirect
128. C₂×#543	C₂×C₄	semidirect
132. C₂×#535	C₂×C₄	semidirect
133. C₂×#535	C₂×C₄	semidirect
143. C₂×#534	C₂×C₄	semidirect
144. C₂×#534	C₂×C₄	semidirect
145. C₂×#534	C₂×C₄	semidirect
146. C₂×#534	C₂×C₄	semidirect
147. C₂×#534	C₂×C₄	semidirect
148. C₂×#534	C₂×C₄	semidirect
149. C₂×#534	C₂×C₄	semidirect
150. C₂×#534	C₂×C₄	semidirect
159. C₂×#525	C₂×C₄	semidirect
160. C₂×#525	C₂×C₄	semidirect
163. C₂²×#123	C₂×C₄	semidirect
165. C₂²×#120	C₂×C₄	semidirect
166. C₂²×#120	C₂×C₄	semidirect
167. C₂²×#120	C₂×C₄	semidirect
168. C₂²×#120	C₂×C₄	semidirect
169. C₂²×#120	C₂×C₄	semidirect
175. C₂×#518	C₂×C₄	semidirect
176. C₂×#518	C₂×C₄	semidirect
177. C₂×#518	C₂×C₄	semidirect
178. C₂×#518	C₂×C₄	semidirect
179. C₂×#518	C₂×C₄	semidirect
181. C₂³×C₂²⋊C₄	C₂×C₄	semidirect
182. #2888	C₂³	semidirect
184. #2883	C₂³	semidirect
187. #2121	C₂³	semidirect
188. C₂×#352	C₂³	semidirect
189. C₂×AΣL(1,𝔽₁₆)	C₂³	semidirect
190. C₂×AΣL(1,𝔽₁₆)	C₂³	semidirect
191. C₂×AΣL(1,𝔽₁₆)	C₂³	semidirect
192. #1829	C₂³	semidirect
193. #1828	C₂³	semidirect
194. #1785	C₂³	semidirect
195. #1783	C₂³	semidirect
196. #1782	C₂³	semidirect
197. #1781	C₂³	semidirect
198. C₂⁶	C₂²⋊C₄	semidirect
200. C₂⁶	C₂²×C₄	semidirect
202. C₂×H(5,𝔽₂)	C₂²×C₄	semidirect
203. C₂×H(5,𝔽₂)	C₂²×C₄	semidirect
209. C₂²×#41	C₂²⋊C₄	semidirect
210. C₂²×#41	C₂²⋊C₄	semidirect
221. C₂³×D₄	C₂²⋊C₄	semidirect
222. C₂³×D₄	C₂²⋊C₄	semidirect
223. C₂³×D₄	C₂²⋊C₄	semidirect
224. C₂³×D₄	C₂²⋊C₄	semidirect
225. C₂³×D₄	C₂²⋊C₄	semidirect
226. C₂³×D₄	C₂²⋊C₄	semidirect
238. C₂³×D₄	C₂²×C₄	semidirect
239. C₂³×D₄	C₂²×C₄	semidirect
249. C₂⁴×C₄	C₂²⋊C₄	semidirect
250. C₂⁴×C₄	C₂²×C₄	semidirect
251. #543	C₂²×C₄	semidirect
252. #543	C₂²×C₄	semidirect
253. #543	C₂²×C₄	semidirect
254. #543	C₂²×C₄	semidirect
256. #536	C₂²⋊C₄	semidirect
260. #535	C₂²⋊C₄	semidirect
261. #535	C₂²⋊C₄	semidirect
262. #535	C₂²⋊C₄	semidirect
281. #534	C₂²⋊C₄	semidirect
282. #534	C₂²⋊C₄	semidirect
283. #534	C₂²⋊C₄	semidirect
284. #534	C₂²⋊C₄	semidirect
285. #534	C₂²⋊C₄	semidirect
286. #534	C₂²⋊C₄	semidirect
287. #534	C₂²⋊C₄	semidirect
288. #534	C₂²⋊C₄	semidirect
313. #525	C₂²⋊C₄	semidirect
314. #525	C₂²⋊C₄	semidirect
315. #525	C₂²⋊C₄	semidirect
316. #525	C₂²⋊C₄	semidirect
326. C₂×#123	C₂²⋊C₄	semidirect
327. C₂×#123	C₂²⋊C₄	semidirect
328. C₂×#123	C₂²⋊C₄	semidirect
333. C₂×#123	C₂²×C₄	semidirect
334. C₂×#123	C₂²×C₄	semidirect
335. C₂×#123	C₂²×C₄	semidirect
336. C₂×#123	C₂²×C₄	semidirect
337. C₂×#123	C₂²×C₄	semidirect
346. C₂×#120	C₂²⋊C₄	semidirect
347. C₂×#120	C₂²⋊C₄	semidirect
348. C₂×#120	C₂²⋊C₄	semidirect
349. C₂×#120	C₂²⋊C₄	semidirect
350. C₂×#120	C₂²⋊C₄	semidirect
351. C₂×#120	C₂²⋊C₄	semidirect
352. C₂×#120	C₂²⋊C₄	semidirect
353. C₂×#120	C₂²⋊C₄	semidirect
354. C₂×#120	C₂²⋊C₄	semidirect
363. C₂×#120	C₂²×C₄	semidirect
364. C₂×#120	C₂²×C₄	semidirect
365. C₂×#120	C₂²×C₄	semidirect
366. C₂×#120	C₂²×C₄	semidirect
367. C₂×#120	C₂²×C₄	semidirect
368. C₂×#120	C₂²×C₄	semidirect
369. C₂×#120	C₂²×C₄	semidirect
370. C₂×#120	C₂²×C₄	semidirect
371. C₂×#120	C₂²×C₄	semidirect
372. C₂×#120	C₂²×C₄	semidirect
373. C₂×#120	C₂²×C₄	semidirect
387. #518	C₂²⋊C₄	semidirect
388. #518	C₂²⋊C₄	semidirect
394. #518	C₂²×C₄	semidirect
395. #518	C₂²×C₄	semidirect
396. #518	C₂²×C₄	semidirect
397. #518	C₂²×C₄	semidirect
398. #518	C₂²×C₄	semidirect
399. #518	C₂²×C₄	semidirect
403. C₂×#117	C₂²⋊C₄	semidirect
404. C₂×#117	C₂²⋊C₄	semidirect
405. C₂×#117	C₂²×C₄	semidirect
406. C₂×#117	C₂²×C₄	semidirect
407. C₂×#117	C₂²×C₄	semidirect
409. C₂²×C₂²⋊C₄	C₂²⋊C₄	semidirect
410. C₂²×C₂²⋊C₄	C₂²⋊C₄	semidirect
417. C₂²×C₂²⋊C₄	C₂²×C₄	semidirect
418. C₂²×C₂²⋊C₄	C₂²×C₄	semidirect
419. C₂²×C₂²⋊C₄	C₂²×C₄	semidirect
420. C₂²×C₂²⋊C₄	C₂²×C₄	semidirect
421. C₂²×C₂²⋊C₄	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
#10586404	2
#7622451	2
C₂×#33348	2
#6374195	2
#6374187	2
#493478	2
#493477	2
#493476	2
#493474	2
#493458	2
C₂×#12725	2
#493424	2
#493391	2