Subgroups — #72265755

Order 2048.

At least 12534 conjugacy classes of subgroups; only the 2252 normal subgroups are shown.

The subgroup lattice has 768 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265754	C₂	1	2	yes	maximal, complemented
2	#72265753	C₂	1	2	yes	maximal, complemented
3	#72258069	C₂	1	1	yes	maximal, characteristic, complemented
4	#72236929	C₂	1	2	yes	maximal, complemented
5	#72225626	C₂	1	16	yes	maximal, complemented
6	C₂×#359428	C₂	1	2	yes	maximal, complemented
7	C₂×#7670203	C₂	1	1	yes	maximal, characteristic
8	#72218467	C₂	1	2	yes	maximal, complemented
9	#72217789	C₂	1	1	yes	maximal, characteristic, complemented
10	#72217666	C₂	1	2	yes	maximal, complemented
11	C₂²×#3484	C₄	1	1	yes	characteristic, complemented
12	C₂²×#3484	C₂²	1	1	yes	characteristic
13	C₂⁴×#120	C₂²	1	1	yes	characteristic
14	C₂⁴×#120	C₂²	1	1	yes	characteristic
15	#7670203	C₄	1	8	yes	complemented
16	#7670203	C₂²	1	8	yes	—
17	C₂²×#2846	C₂²	1	1	yes	characteristic
18	C₂×#35390	C₄	1	1	yes	characteristic, complemented
19	C₂×#35348	C₄	1	1	yes	characteristic, complemented
20	C₂×#35348	C₄	1	1	yes	characteristic, complemented
21	C₂×#35346	C₄	1	1	yes	characteristic, complemented
22	C₂×#34981	C₄	1	1	yes	characteristic, complemented
23	C₂×#34981	C₂²	1	1	yes	characteristic
24	C₂×#34980	C₄	1	1	yes	characteristic, complemented
25	C₂×#34980	C₂²	1	1	yes	characteristic
26	C₂×#34198	C₄	1	1	yes	characteristic, complemented
27	C₂×#34198	C₂²	1	1	yes	characteristic
28	C₂³×#379	C₂²	1	2	yes	complemented
29	C₂²×#1898	C₂²	1	8	yes	complemented
30	C₂×#14679	C₂²	1	2	yes	complemented
31	#392675	C₂²	1	8	yes	complemented
32	#392207	C₂²	1	2	yes	complemented
33	#392109	C₂²	1	2	yes	complemented
34	#374022	C₂²	1	8	yes	complemented
35	#359799	C₂²	1	4	yes	complemented
36	#359428	C₂²	1	4	yes	—
37	#359428	C₂²	1	4	yes	complemented
38	#359428	C₂²	1	4	yes	complemented
39	#359428	C₂²	1	8	yes	complemented
40	#359428	C₂²	1	8	yes	complemented
41	C₂×#8534	C₂²	1	16	yes	complemented
42	#154195	C₂²	1	8	yes	complemented
43	#154130	C₂²	1	2	yes	complemented
44	#154094	C₂²	1	2	yes	complemented
45	#115348	C₂²	1	16	yes	complemented
46	#111462	C₂²	1	16	yes	complemented
47	#106076	C₂²	1	16	yes	complemented
48	C₂⁸	C₂³	1	1	yes	characteristic
49	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂⁵×D₄	D₄	1	2	yes	—
52	C₂⁵×D₄	D₄	1	1	yes	characteristic
53	C₂⁵×D₄	D₄	1	1	yes	characteristic
54	C₂⁵×D₄	C₂³	1	1	yes	characteristic
55	C₂×#3484	C₂×C₄	1	8	yes	complemented
56	C₂×#3484	C₂×C₄	1	4	yes	complemented
57	C₂×#3484	C₂³	1	4	yes	—
58	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂³×#120	C₂×C₄	1	1	yes	characteristic
64	C₂³×#120	C₂×C₄	1	1	yes	characteristic
65	C₂³×#120	C₂×C₄	1	1	yes	characteristic
66	C₂³×#120	C₂×C₄	1	1	yes	characteristic
67	C₂³×#120	C₂×C₄	1	4	yes	—
68	C₂³×#120	C₂×C₄	1	1	yes	characteristic
69	C₂³×#120	C₂×C₄	1	1	yes	characteristic
70	C₂³×#120	C₂×C₄	1	4	yes	—
71	C₂³×#120	C₂×C₄	1	1	yes	characteristic
72	C₂³×#120	C₂×C₄	1	1	yes	characteristic
73	C₂³×#120	D₄	1	1	yes	characteristic
74	C₂³×#120	D₄	1	1	yes	characteristic
75	C₂³×#120	D₄	1	4	yes	—
76	C₂³×#120	D₄	1	1	yes	characteristic
77	C₂³×#120	D₄	1	1	yes	characteristic
78	C₂³×#120	D₄	1	2	yes	—
79	C₂³×#120	D₄	1	4	yes	—
80	C₂³×#120	D₄	1	2	yes	—
81	C₂³×#120	D₄	1	4	yes	—
82	C₂³×#120	D₄	1	2	yes	—
83	C₂³×#120	D₄	1	2	yes	—
84	C₂³×#120	D₄	1	4	yes	—
85	C₂³×#120	C₂³	1	1	yes	characteristic
86	C₂³×#120	C₂³	1	4	yes	—
87	C₂³×#120	C₂³	1	1	yes	characteristic
88	C₂³×#120	C₂³	1	1	yes	characteristic
89	C₂³×#120	C₂³	1	4	yes	—
90	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂⁴×C₂²⋊C₄	D₄	1	2	yes	—
94	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
97	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	complemented
98	C₂×#2846	C₂×C₄	1	4	yes	—
99	C₂×#2846	D₄	1	4	yes	—
100	C₂×#2846	D₄	1	4	yes	—
101	C₂×#2846	C₂³	1	4	yes	—
102	#35390	C₂×C₄	1	8	yes	complemented
103	#35348	C₂×C₄	1	8	yes	complemented
104	#35348	C₂×C₄	1	8	yes	complemented
105	#35346	C₂×C₄	1	8	yes	complemented
106	#34981	C₂×C₄	1	8	yes	complemented
107	#34981	C₂×C₄	1	4	yes	complemented
108	#34981	C₂³	1	4	yes	—
109	#34980	C₂×C₄	1	8	yes	complemented
110	#34980	C₂×C₄	1	4	yes	complemented
111	#34980	C₂³	1	4	yes	—
112	#34198	C₂×C₄	1	4	yes	complemented
113	#34198	C₂×C₄	1	8	yes	complemented
114	#34198	C₂³	1	4	yes	—
115	C₂×#2315	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂×#2315	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
121	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
122	C₂²×#379	C₂×C₄	1	1	yes	characteristic
123	C₂²×#379	C₂×C₄	1	1	yes	characteristic
124	C₂²×#379	D₄	1	2	yes	—
125	C₂²×#379	D₄	1	2	yes	—
126	C₂²×#379	C₂³	1	4	yes	—
127	C₂²×#379	C₂³	1	1	yes	characteristic
128	C₂²×#379	C₂³	1	4	yes	complemented
129	C₂²×#379	C₂³	1	4	yes	complemented
130	C₂×#2273	C₂×C₄	1	1	yes	characteristic, complemented
131	C₂×#1898	C₂³	1	16	yes	—
132	C₂×#1898	C₂³	1	16	yes	complemented
133	C₂×#1898	C₂³	1	16	yes	complemented
134	C₂×#1781	C₂³	1	8	yes	complemented
135	#14679	C₂³	1	4	yes	—
136	#14679	C₂³	1	4	yes	complemented
137	C₂×#1438	C₂³	1	8	yes	complemented
138	#10735	C₂³	1	16	yes	complemented
139	#10725	C₂³	1	8	yes	complemented
140	#7555	C₂³	1	8	yes	complemented
141	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
142	C₂⁷	C₂²×C₄	1	1	yes	characteristic
143	C₂⁷	C₂²×C₄	1	1	yes	characteristic
144	C₂⁷	C₂²×C₄	1	2	yes	—
145	C₂⁷	C₂×D₄	1	1	yes	characteristic
146	C₂⁷	C₂×D₄	1	2	yes	—
147	C₂⁷	C₂×D₄	1	1	yes	characteristic
148	C₂⁷	C₂×D₄	1	1	yes	characteristic
149	C₂⁷	C₂×D₄	1	2	yes	—
150	C₂⁷	C₂×D₄	1	1	yes	characteristic
151	C₂⁷	C₂×D₄	1	2	yes	—
152	C₂⁷	C₂×D₄	1	2	yes	—
153	C₂⁷	C₂×D₄	1	2	yes	—
154	C₂⁷	C₂×D₄	1	2	yes	—
155	C₂⁷	C₂×D₄	1	2	yes	—
156	C₂⁷	C₂×D₄	1	1	yes	characteristic
157	C₂⁷	C₂×D₄	1	2	yes	—
158	C₂⁷	C₂×D₄	1	2	yes	—
159	C₂⁷	C₂×D₄	1	2	yes	—
160	C₂⁷	C₂⁴	1	2	yes	—
161	C₂⁷	C₂⁴	1	1	yes	characteristic
162	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
163	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
168	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
171	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
173	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
175	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
176	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
177	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
178	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
179	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
180	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
181	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	complemented
182	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
186	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
190	C₂⁴×D₄	C₂×D₄	1	2	yes	—
191	C₂⁴×D₄	C₂×D₄	1	4	yes	—
192	C₂⁴×D₄	C₂×D₄	1	4	yes	—
193	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	2	yes	—
196	C₂⁴×D₄	C₂×D₄	1	2	yes	—
197	C₂⁴×D₄	C₂×D₄	1	2	yes	—
198	C₂⁴×D₄	C₂×D₄	1	4	yes	—
199	C₂⁴×D₄	C₂×D₄	1	2	yes	—
200	C₂⁴×D₄	C₂×D₄	1	4	yes	—
201	C₂⁴×D₄	C₂⁴	1	2	yes	—
202	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	complemented
203	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
204	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
205	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
206	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
207	C₂×#534	C₂²×C₄	1	4	yes	—
208	C₂×#534	C₂²×C₄	1	4	yes	—
209	C₂×#534	C₂²×C₄	1	4	yes	—
210	C₂×#534	C₂²×C₄	1	4	yes	—
211	C₂×#534	C₂²×C₄	1	4	yes	—
212	C₂²×#120	C₂²⋊C₄	1	4	yes	—
213	C₂²×#120	C₂²⋊C₄	1	4	yes	—
214	C₂²×#120	C₂²⋊C₄	1	4	yes	—
215	C₂²×#120	C₂²⋊C₄	1	4	yes	—
216	C₂²×#120	C₂²⋊C₄	1	4	yes	—
217	C₂²×#120	C₂²⋊C₄	1	4	yes	—
218	C₂²×#120	C₂²⋊C₄	1	4	yes	—
219	C₂²×#120	C₂²⋊C₄	1	4	yes	—
220	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
221	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
222	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
223	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
224	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
225	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
226	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
227	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
228	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
229	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
230	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
231	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
232	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
233	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
234	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
235	C₂²×#120	C₂²×C₄	1	4	yes	—
236	C₂²×#120	C₂²×C₄	1	2	yes	—
237	C₂²×#120	C₂²×C₄	1	4	yes	—
238	C₂²×#120	C₂²×C₄	1	4	yes	—
239	C₂²×#120	C₂²×C₄	1	2	yes	—
240	C₂²×#120	C₂²×C₄	1	4	yes	—
241	C₂²×#120	C₂²×C₄	1	4	yes	—
242	C₂²×#120	C₂²×C₄	1	4	yes	—
243	C₂²×#120	C₂²×C₄	1	4	yes	—
244	C₂²×#120	C₂²×C₄	1	2	yes	—
245	C₂²×#120	C₂²×C₄	1	4	yes	—
246	C₂²×#120	C₂×D₄	1	4	yes	—
247	C₂²×#120	C₂×D₄	1	4	yes	—
248	C₂²×#120	C₂×D₄	1	4	yes	—
249	C₂²×#120	C₂×D₄	1	4	yes	—
250	C₂²×#120	C₂×D₄	1	4	yes	—
251	C₂²×#120	C₂×D₄	1	4	yes	—
252	C₂²×#120	C₂×D₄	1	4	yes	—
253	C₂²×#120	C₂×D₄	1	4	yes	—
254	C₂²×#120	C₂×D₄	1	4	yes	—
255	C₂²×#120	C₂×D₄	1	4	yes	—
256	C₂²×#120	C₂×D₄	1	4	yes	—
257	C₂²×#120	C₂×D₄	1	4	yes	—
258	C₂²×#120	C₂×D₄	1	4	yes	—
259	C₂²×#120	C₂×D₄	1	4	yes	—
260	C₂²×#120	C₂×D₄	1	4	yes	—
261	C₂²×#120	C₂⁴	1	2	yes	—
262	C₂²×#120	C₂⁴	1	2	yes	—
263	C₂²×#120	C₂⁴	1	2	yes	—
264	C₂×#518	C₂²×C₄	1	4	yes	—
265	C₂×#518	C₂²×C₄	1	4	yes	—
266	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
270	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
271	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
272	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
273	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
274	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
275	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
276	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
277	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
278	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
279	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
280	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
281	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
282	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
283	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
284	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
285	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
286	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
287	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
288	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
289	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
290	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
292	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
293	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
294	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
295	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
296	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
297	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
298	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
299	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
300	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
301	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
305	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
306	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
307	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
308	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
309	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
310	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
311	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
313	#2315	C₂²×C₄	1	4	yes	—
314	#2315	C₂²×C₄	1	4	yes	—
315	#2308	C₂²×C₄	1	4	yes	—
316	#2308	C₂²×C₄	1	4	yes	—
317	#2308	C₂²×C₄	1	4	yes	—
318	#2308	C₂²×C₄	1	4	yes	—
319	#2308	C₂²×C₄	1	4	yes	—
320	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
321	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
322	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
323	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
324	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
325	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
326	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
327	C₂×#379	C₂²×C₄	1	2	yes	—
328	C₂×#379	C₂²×C₄	1	4	yes	—
329	C₂×#379	C₂²×C₄	1	4	yes	—
330	C₂×#379	C₂×D₄	1	4	yes	—
331	C₂×#379	C₂×D₄	1	4	yes	—
332	C₂×#379	C₂×D₄	1	4	yes	—
333	C₂×#379	C₂×D₄	1	4	yes	—
334	C₂×#379	C₂×D₄	1	4	yes	—
335	C₂×#379	C₂⁴	1	8	yes	—
336	C₂×#379	C₂⁴	1	2	yes	—
337	#2273	C₂²×C₄	1	4	yes	—
338	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
351	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
352	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
353	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
358	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
361	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
369	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
371	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
373	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂⁶	#120	1	2	yes	—
376	C₂⁶	#120	1	2	yes	—
377	C₂⁶	#120	1	2	yes	—
378	C₂⁶	#120	1	2	yes	—
379	C₂⁶	#120	1	2	yes	—
380	C₂⁶	#120	1	2	yes	—
381	C₂⁶	#120	1	2	yes	—
382	C₂⁶	#120	1	2	yes	—
383	C₂⁶	#120	1	2	yes	—
384	C₂⁶	#120	1	2	yes	—
385	C₂⁶	#120	1	2	yes	—
386	C₂⁶	#120	1	2	yes	—
387	C₂⁶	#120	1	2	yes	—
388	C₂⁶	#120	1	2	yes	—
389	C₂⁶	#120	1	2	yes	—
390	C₂⁶	#120	1	2	yes	—
391	C₂⁶	#120	1	2	yes	—
392	C₂⁶	#120	1	2	yes	—
393	C₂⁶	#120	1	2	yes	—
394	C₂⁶	#120	1	2	yes	—
395	C₂⁶	#120	1	2	yes	—
396	C₂⁶	#120	1	2	yes	—
397	C₂⁶	#120	1	2	yes	—
398	C₂⁶	#120	1	2	yes	—
399	C₂⁶	#120	1	2	yes	—
400	C₂⁶	#120	1	2	yes	—
401	C₂⁶	#120	1	2	yes	—
402	C₂⁶	#120	1	2	yes	—
403	C₂⁶	#120	1	2	yes	—
404	C₂⁶	#120	1	2	yes	—
405	C₂⁶	#120	1	2	yes	—
406	C₂⁶	#120	1	2	yes	—
407	C₂⁶	C₂³×C₄	1	1	yes	characteristic
408	C₂⁶	C₂³×C₄	1	2	yes	—
409	C₂⁶	C₂³×C₄	1	2	yes	—
410	C₂⁶	C₂³×C₄	1	1	yes	characteristic
411	C₂⁶	C₂²×D₄	1	2	yes	—
412	C₂⁶	C₂²×D₄	1	1	yes	characteristic
413	C₂⁶	C₂²×D₄	1	2	yes	—
414	C₂⁶	C₂²×D₄	1	2	yes	—
415	C₂⁶	C₂²×D₄	1	2	yes	—
416	C₂⁶	C₂²×D₄	1	1	yes	characteristic
417	C₂⁶	C₂²×D₄	1	2	yes	—
418	C₂⁶	C₂²×D₄	1	2	yes	—
419	C₂⁶	C₂²×D₄	1	2	yes	—
420	C₂⁶	C₂²×D₄	1	2	yes	—
421	C₂⁶	C₂²×D₄	1	2	yes	—
422	C₂⁶	C₂²×D₄	1	1	yes	characteristic
423	C₂⁶	C₂²×D₄	1	1	yes	characteristic
424	C₂⁶	C₂²×D₄	1	2	yes	—
425	C₂⁶	C₂²×D₄	1	2	yes	—
426	C₂⁶	C₂²×D₄	1	2	yes	—
427	C₂⁶	C₂²×D₄	1	2	yes	—
428	C₂⁶	C₂²×D₄	1	2	yes	—
429	C₂⁶	C₂²×D₄	1	2	yes	—
430	C₂⁶	C₂²×D₄	1	2	yes	—
431	C₂⁶	C₂²×D₄	1	2	yes	—
432	C₂⁶	C₂⁵	1	1	yes	characteristic
433	C₂³×D₄	#99	1	8	yes	complemented
434	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
435	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
436	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
437	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
438	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
439	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
440	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
441	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
442	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
443	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
444	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
445	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
446	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
447	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
448	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
449	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
450	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
451	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
452	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
453	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
454	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
455	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
456	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
457	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
458	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
459	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
460	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
461	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
462	C₂³×D₄	C₂³×C₄	1	2	yes	—
463	C₂³×D₄	C₂³×C₄	1	2	yes	—
464	C₂³×D₄	C₂³×C₄	1	2	yes	—
465	C₂³×D₄	C₂³×C₄	1	2	yes	—
466	C₂³×D₄	C₂³×C₄	1	2	yes	—
467	C₂³×D₄	C₂²×D₄	1	2	yes	—
468	C₂³×D₄	C₂²×D₄	1	2	yes	—
469	C₂³×D₄	C₂²×D₄	1	4	yes	—
470	C₂³×D₄	C₂²×D₄	1	4	yes	—
471	C₂³×D₄	C₂²×D₄	1	4	yes	—
472	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
474	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
475	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
477	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
478	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
479	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
480	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
481	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
482	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
483	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
484	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
485	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
486	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
487	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
488	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
489	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
490	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
491	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
492	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
493	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
494	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
495	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
496	C₂×#120	H(5,𝔽₂)	1	16	yes	—
497	C₂²×C₂²⋊C₄	#99	1	8	yes	complemented
498	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
499	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
500	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
501	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
502	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
503	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
504	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
505	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
506	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
507	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
508	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
509	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
510	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
511	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
512	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
513	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
514	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
515	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
516	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
517	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
518	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
519	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
520	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
521	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
522	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
523	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
524	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
525	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
526	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
527	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
528	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
529	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
530	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
531	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
532	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
533	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
534	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
535	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
536	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
537	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
538	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
539	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
540	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
541	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
542	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
543	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
544	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
545	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
546	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
547	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
548	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
549	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
550	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
551	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
552	C₂⁵	#379	1	1	yes	characteristic
553	C₂⁵	#379	1	2	yes	—
554	C₂⁵	#379	1	2	yes	—
555	C₂⁵	#379	1	2	yes	—
556	C₂⁵	#379	1	2	yes	—
557	C₂⁵	#379	1	1	yes	characteristic
558	C₂⁵	#379	1	2	yes	—
559	C₂⁵	#379	1	2	yes	—
560	C₂⁵	#379	1	2	yes	—
561	C₂⁵	#379	1	2	yes	—
562	C₂⁵	#379	1	2	yes	—
563	C₂⁵	#379	1	1	yes	characteristic
564	C₂⁵	#379	1	1	yes	characteristic
565	C₂⁵	#379	1	1	yes	characteristic
566	C₂⁵	#379	1	2	yes	—
567	C₂⁵	#379	1	2	yes	—
568	C₂⁵	#379	1	2	yes	—
569	C₂⁵	#379	1	2	yes	—
570	C₂⁵	#379	1	2	yes	—
571	C₂⁵	#379	1	2	yes	—
572	C₂⁵	#379	1	2	yes	—
573	C₂⁵	#379	1	2	yes	—
574	C₂⁵	#379	1	2	yes	—
575	C₂⁵	#379	1	2	yes	—
576	C₂⁵	#379	1	2	yes	—
577	C₂⁵	#379	1	1	yes	characteristic
578	C₂⁵	#379	1	2	yes	—
579	C₂⁵	#379	1	2	yes	—
580	C₂⁵	#379	1	2	yes	—
581	C₂⁵	#379	1	2	yes	—
582	C₂⁵	#379	1	1	yes	characteristic
583	C₂⁵	#379	1	2	yes	—
584	C₂⁵	#379	1	2	yes	—
585	C₂⁵	#379	1	2	yes	—
586	C₂⁵	#379	1	2	yes	—
587	C₂⁵	#379	1	1	yes	characteristic
588	C₂⁵	C₂×#99	1	4	yes	—
589	C₂⁵	C₂×#99	1	4	yes	—
590	C₂⁵	C₂×#99	1	4	yes	complemented
591	C₂⁵	B(4,𝔽₂)	1	8	yes	—
592	C₂⁵	#458	1	8	yes	—
593	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
596	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
597	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
598	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
599	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
600	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
601	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
602	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
603	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
604	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
605	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
606	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
607	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
608	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
609	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
610	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
611	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
612	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
613	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
614	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
615	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
616	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
617	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
618	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
619	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
620	C₂⁵	C₂×#120	1	2	yes	—
621	C₂⁵	C₂×#120	1	2	yes	—
622	C₂⁵	C₂×#120	1	2	yes	—
623	C₂⁵	C₂×#120	1	2	yes	—
624	C₂⁵	C₂×#120	1	2	yes	—
625	C₂⁵	C₂×#120	1	2	yes	—
626	C₂⁵	C₂×#120	1	2	yes	—
627	C₂⁵	C₂×#120	1	2	yes	—
628	C₂⁵	C₂×#120	1	2	yes	—
629	C₂⁵	C₂×#120	1	2	yes	—
630	C₂⁵	C₂×#120	1	2	yes	—
631	C₂⁵	C₂×#120	1	2	yes	—
632	C₂⁵	C₂×#120	1	2	yes	—
633	C₂⁵	C₂×#120	1	2	yes	—
634	C₂⁵	C₂×#120	1	2	yes	—
635	C₂⁵	C₂×#120	1	2	yes	—
636	C₂⁵	C₂×#120	1	2	yes	—
637	C₂⁵	C₂×#120	1	2	yes	—
638	C₂⁵	C₂×#120	1	2	yes	—
639	C₂⁵	C₂×#120	1	2	yes	—
640	C₂⁵	C₂×#120	1	2	yes	—
641	C₂⁵	C₂×#120	1	2	yes	—
642	C₂⁵	C₂×#120	1	2	yes	—
643	C₂⁵	C₂×#120	1	2	yes	—
644	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
645	C₂⁵	C₂³×D₄	1	1	yes	characteristic
646	C₂⁵	C₂³×D₄	1	2	yes	—
647	C₂⁵	C₂³×D₄	1	2	yes	—
648	C₂⁵	C₂³×D₄	1	1	yes	characteristic
649	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
650	C₂²×D₄	C₂×#99	1	16	yes	complemented
651	C₂²×D₄	#518	1	8	yes	—
652	C₂²×D₄	#534	1	16	yes	—
653	C₂³×C₄	C₂×#99	1	4	yes	complemented
654	C₂³×C₄	C₂×#99	1	4	yes	complemented
655	C₂³×C₄	C₂×#99	1	4	yes	complemented
656	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
657	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
658	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
659	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
660	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
661	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
662	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
663	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
664	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
665	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
666	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
667	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
668	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
669	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
670	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
671	C₂×C₂²⋊C₄	C₂×#99	1	16	yes	complemented
672	C₂×C₂²⋊C₄	#518	1	8	yes	—
673	C₂×C₂²⋊C₄	#534	1	16	yes	—
674	C₂⁴	#1781	1	4	yes	—
675	C₂⁴	#1781	1	8	yes	—
676	C₂⁴	#1781	1	4	yes	—
677	C₂⁴	#1790	1	8	yes	—
678	C₂⁴	#1790	1	8	yes	—
679	C₂⁴	#1790	1	8	yes	—
680	C₂⁴	#1790	1	8	yes	—
681	C₂⁴	C₂×#379	1	2	yes	—
682	C₂⁴	C₂×#379	1	2	yes	—
683	C₂⁴	C₂×#379	1	2	yes	—
684	C₂⁴	C₂×#379	1	2	yes	—
685	C₂⁴	C₂×#379	1	1	yes	characteristic
686	C₂⁴	C₂×#379	1	1	yes	characteristic
687	C₂⁴	C₂×#379	1	1	yes	characteristic
688	C₂⁴	C₂×#379	1	2	yes	—
689	C₂⁴	C₂×#379	1	2	yes	—
690	C₂⁴	C₂×#379	1	2	yes	—
691	C₂⁴	C₂×#379	1	2	yes	—
692	C₂⁴	C₂×#379	1	2	yes	—
693	C₂⁴	C₂×#379	1	2	yes	—
694	C₂⁴	C₂×#379	1	1	yes	characteristic
695	C₂⁴	#2308	1	4	yes	complemented
696	C₂⁴	C₂²×#99	1	4	yes	—
697	C₂⁴	C₂²×#99	1	4	yes	—
698	C₂⁴	C₂²×#99	1	2	yes	—
699	C₂⁴	C₂²×#99	1	2	yes	—
700	C₂⁴	C₂²×#99	1	4	yes	—
701	C₂⁴	#2883	1	4	yes	—
702	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
703	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
704	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
705	C₂⁴	C₂×#458	1	4	yes	—
706	C₂⁴	C₂×#458	1	4	yes	—
707	C₂⁴	C₂×#458	1	4	yes	—
708	C₂⁴	#3026	1	8	yes	—
709	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
710	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
711	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
712	C₂⁴	C₂×#518	1	4	yes	—
713	C₂⁴	C₂²×#120	1	2	yes	—
714	C₂⁴	C₂²×#120	1	2	yes	—
715	C₂⁴	C₂×#534	1	8	yes	—
716	C₂⁴	#3484	1	4	yes	—
717	C₂⁴	#3484	1	8	yes	—
718	C₂⁴	#3484	1	4	yes	—
719	C₂²×C₄	#2308	1	8	yes	complemented
720	C₂²×C₄	#2308	1	4	yes	complemented
721	C₂²×C₄	C₂²×#99	1	4	yes	—
722	C₂²×C₄	C₂²×#99	1	4	yes	—
723	C₂²×C₄	C₂²×#99	1	4	yes	—
724	C₂³	#8534	1	16	yes	complemented
725	C₂³	C₂×#1781	1	4	yes	—
726	C₂³	C₂×#1781	1	2	yes	—
727	C₂³	C₂×#1781	1	4	yes	—
728	C₂³	C₂×#1781	1	2	yes	—
729	C₂³	#20585	1	2	yes	—
730	C₂³	#20585	1	2	yes	—
731	C₂³	C₂×#1790	1	4	yes	—
732	C₂³	C₂×#1790	1	4	yes	—
733	C₂³	C₂×#1790	1	4	yes	—
734	C₂³	C₂×#1790	1	4	yes	—
735	C₂³	C₂×#1790	1	4	yes	—
736	C₂³	C₂×#1790	1	4	yes	—
737	C₂³	#20609	1	4	yes	—
738	C₂³	#20609	1	4	yes	—
739	C₂³	C₂²×#379	1	1	yes	characteristic
740	C₂³	C₂×#2308	1	2	yes	—
741	C₂³	#34171	1	2	yes	—
742	C₂³	#34171	1	2	yes	—
743	C₂³	#34980	1	4	yes	—
744	C₂³	#34980	1	4	yes	—
745	C₂³	C₂³×#99	1	1	yes	characteristic
746	C₂³	C₂³×#99	1	1	yes	characteristic
747	C₂³	C₂×#2883	1	2	yes	—
748	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
749	C₂³	C₂²×#458	1	2	yes	—
750	C₂³	C₂×#3026	1	4	yes	—
751	C₂²	C₂×#8534	1	4	yes	—
752	C₂²	C₂×#8534	1	8	yes	—
753	C₂²	#517411	1	1	yes	characteristic
754	C₂²	C₂²×#1781	1	1	yes	characteristic
755	C₂²	C₂×#20585	1	1	yes	characteristic
756	C₂²	C₂²×#1790	1	2	yes	—
757	C₂²	C₂×#20609	1	2	yes	—
758	C₂²	#6385971	1	2	yes	—
759	C₂²	#6385971	1	2	yes	—
760	C₂²	#6470225	1	4	yes	—
761	C₂²	#6470226	1	4	yes	—
762	C₂	C₂²×#8534	1	1	yes	characteristic
763	C₂	#72219307	1	1	yes	characteristic
764	C₂	#72236437	1	2	yes	—
765	C₂	#72237398	1	1	yes	characteristic
766	C₂	#72250200	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂²×#379
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂⁶	C₂⁵
prime radical	C₂×#7670203	C₂
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁸ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265754	C₂	semidirect
2. #72265753	C₂	semidirect
3. #72258069	C₂	semidirect
4. #72236929	C₂	semidirect
5. #72225626	C₂	semidirect
6. C₂×#359428	C₂	semidirect
8. #72218467	C₂	semidirect
9. #72217789	C₂	semidirect
10. #72217666	C₂	semidirect
11. C₂²×#3484	C₄	semidirect
15. #7670203	C₄	semidirect
18. C₂×#35390	C₄	semidirect
19. C₂×#35348	C₄	semidirect
20. C₂×#35348	C₄	semidirect
21. C₂×#35346	C₄	semidirect
22. C₂×#34981	C₄	semidirect
24. C₂×#34980	C₄	semidirect
26. C₂×#34198	C₄	semidirect
28. C₂³×#379	C₂²	semidirect
29. C₂²×#1898	C₂²	semidirect
30. C₂×#14679	C₂²	semidirect
31. #392675	C₂²	semidirect
32. #392207	C₂²	semidirect
33. #392109	C₂²	semidirect
34. #374022	C₂²	semidirect
35. #359799	C₂²	semidirect
37. #359428	C₂²	semidirect
38. #359428	C₂²	semidirect
39. #359428	C₂²	semidirect
40. #359428	C₂²	semidirect
41. C₂×#8534	C₂²	semidirect
42. #154195	C₂²	semidirect
43. #154130	C₂²	semidirect
44. #154094	C₂²	semidirect
45. #115348	C₂²	semidirect
46. #111462	C₂²	semidirect
47. #106076	C₂²	semidirect
49. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
55. C₂×#3484	C₂×C₄	semidirect
56. C₂×#3484	C₂×C₄	semidirect
58. C₂²×#534	C₂×C₄	semidirect
59. C₂²×#534	C₂×C₄	semidirect
60. C₂²×#534	C₂×C₄	semidirect
61. C₂²×#534	C₂×C₄	semidirect
62. C₂²×#534	C₂×C₄	semidirect
90. C₂²×#518	C₂×C₄	semidirect
91. C₂²×#518	C₂×C₄	semidirect
97. C₂⁴×C₂²⋊C₄	C₂³	semidirect
102. #35390	C₂×C₄	semidirect
103. #35348	C₂×C₄	semidirect
104. #35348	C₂×C₄	semidirect
105. #35346	C₂×C₄	semidirect
106. #34981	C₂×C₄	semidirect
107. #34981	C₂×C₄	semidirect
109. #34980	C₂×C₄	semidirect
110. #34980	C₂×C₄	semidirect
112. #34198	C₂×C₄	semidirect
113. #34198	C₂×C₄	semidirect
115. C₂×#2315	C₂×C₄	semidirect
116. C₂×#2315	C₂×C₄	semidirect
117. C₂×#2308	C₂×C₄	semidirect
118. C₂×#2308	C₂×C₄	semidirect
119. C₂×#2308	C₂×C₄	semidirect
120. C₂×#2308	C₂×C₄	semidirect
121. C₂×#2308	C₂×C₄	semidirect
128. C₂²×#379	C₂³	semidirect
129. C₂²×#379	C₂³	semidirect
130. C₂×#2273	C₂×C₄	semidirect
132. C₂×#1898	C₂³	semidirect
133. C₂×#1898	C₂³	semidirect
134. C₂×#1781	C₂³	semidirect
136. #14679	C₂³	semidirect
137. C₂×#1438	C₂³	semidirect
138. #10735	C₂³	semidirect
139. #10725	C₂³	semidirect
140. #7555	C₂³	semidirect
141. C₂⁷	C₂²⋊C₄	semidirect
173. C₂⁴×D₄	C₂²⋊C₄	semidirect
174. C₂⁴×D₄	C₂²⋊C₄	semidirect
175. C₂⁴×D₄	C₂²⋊C₄	semidirect
176. C₂⁴×D₄	C₂²⋊C₄	semidirect
177. C₂⁴×D₄	C₂²⋊C₄	semidirect
178. C₂⁴×D₄	C₂²⋊C₄	semidirect
179. C₂⁴×D₄	C₂²⋊C₄	semidirect
180. C₂⁴×D₄	C₂²⋊C₄	semidirect
181. C₂⁴×D₄	C₂²⋊C₄	semidirect
182. C₂⁴×D₄	C₂²⋊C₄	semidirect
202. C₂⁵×C₄	C₂²⋊C₄	semidirect
203. C₂⁵×C₄	C₂²⋊C₄	semidirect
220. C₂²×#120	C₂²⋊C₄	semidirect
221. C₂²×#120	C₂²⋊C₄	semidirect
222. C₂²×#120	C₂²⋊C₄	semidirect
223. C₂²×#120	C₂²⋊C₄	semidirect
224. C₂²×#120	C₂²⋊C₄	semidirect
225. C₂²×#120	C₂²⋊C₄	semidirect
226. C₂²×#120	C₂²⋊C₄	semidirect
227. C₂²×#120	C₂²⋊C₄	semidirect
228. C₂²×#120	C₂²⋊C₄	semidirect
229. C₂²×#120	C₂²⋊C₄	semidirect
230. C₂²×#120	C₂²⋊C₄	semidirect
231. C₂²×#120	C₂²⋊C₄	semidirect
232. C₂²×#120	C₂²⋊C₄	semidirect
233. C₂²×#120	C₂²⋊C₄	semidirect
234. C₂²×#120	C₂²⋊C₄	semidirect
276. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
277. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
278. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
279. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
280. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
281. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
282. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
283. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
284. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
285. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
286. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
287. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
288. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
320. C₂×#379	C₂²⋊C₄	semidirect
321. C₂×#379	C₂²⋊C₄	semidirect
322. C₂×#379	C₂²⋊C₄	semidirect
323. C₂×#379	C₂²⋊C₄	semidirect
324. C₂×#379	C₂²⋊C₄	semidirect
325. C₂×#379	C₂²⋊C₄	semidirect
326. C₂×#379	C₂²⋊C₄	semidirect
433. C₂³×D₄	#99	semidirect
497. C₂²×C₂²⋊C₄	#99	semidirect
590. C₂⁵	C₂×#99	semidirect
650. C₂²×D₄	C₂×#99	semidirect
653. C₂³×C₄	C₂×#99	semidirect
654. C₂³×C₄	C₂×#99	semidirect
655. C₂³×C₄	C₂×#99	semidirect
671. C₂×C₂²⋊C₄	C₂×#99	semidirect
695. C₂⁴	#2308	semidirect
719. C₂²×C₄	#2308	semidirect
720. C₂²×C₄	#2308	semidirect
724. C₂³	#8534	semidirect

Maximal subgroups

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

subgroup	index
#72265754	2
#72265753	2
#72258069	2
#72236929	2
#72225626	2
C₂×#359428	2
C₂×#7670203	2
#72218467	2
#72217789	2
#72217666	2