Subgroups — #16859263

Order 3968.

1132 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521766	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521761	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521753	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521750	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521742	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521736	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521735	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521731	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521731	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521729	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521726	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521724	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521722	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521697	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521691	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521688	C₂	1	1	yes	maximal, characteristic, complemented
17	#14521603	C₂	1	1	yes	maximal, characteristic, complemented
18	#14521586	C₂	1	1	yes	maximal, characteristic, complemented
19	#14521579	C₂	1	1	yes	maximal, characteristic, complemented
20	#14521579	C₂	1	1	yes	maximal, characteristic, complemented
21	#14521577	C₂	1	1	yes	maximal, characteristic, complemented
22	#14521577	C₂	1	1	yes	maximal, characteristic, complemented
23	#14521558	C₂	1	1	yes	maximal, characteristic, complemented
24	#14521558	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
26	#14521517	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#92497	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#11758449	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#92497	C₂²	1	1	yes	characteristic
33	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
34	C₂×#92495	C₂²	1	1	yes	characteristic
35	C₂×#92495	C₂²	1	1	yes	characteristic
36	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#123	C₂²	1	1	yes	characteristic
43	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#121	C₂²	1	1	yes	characteristic
46	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
53	#11758524	C₂²	1	1	yes	characteristic, complemented
54	#11758523	C₂²	1	1	yes	characteristic
55	#11758523	C₂²	1	1	yes	characteristic, complemented
56	#11758521	C₂²	1	1	yes	characteristic, complemented
57	#11758516	C₂²	1	1	yes	characteristic
58	#11758516	C₂²	1	1	yes	characteristic
59	#11758516	C₂²	1	1	yes	characteristic, complemented
60	#11758516	C₂²	1	1	yes	characteristic, complemented
61	#11758514	C₂²	1	1	yes	characteristic
62	#11758514	C₂²	1	1	yes	characteristic
63	#11758512	C₂²	1	1	yes	characteristic
64	#11758512	C₂²	1	1	yes	characteristic, complemented
65	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
66	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
76	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
77	#11758503	C₂²	1	1	yes	characteristic, complemented
78	#11758503	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
83	#11758475	C₂²	1	1	yes	characteristic, complemented
84	#11758475	C₂²	1	1	yes	characteristic, complemented
85	#11758475	C₂²	1	1	yes	characteristic, complemented
86	#11758475	C₂²	1	1	yes	characteristic, complemented
87	#11758475	C₂²	1	1	yes	characteristic, complemented
88	#11758475	C₂²	1	1	yes	characteristic, complemented
89	#11758474	C₂²	1	1	yes	characteristic
90	#11758473	C₂²	1	1	yes	characteristic
91	#11758473	C₂²	1	1	yes	characteristic
92	#11758473	C₂²	1	1	yes	characteristic, complemented
93	#11758473	C₂²	1	1	yes	characteristic, complemented
94	#11758473	C₂²	1	1	yes	characteristic, complemented
95	#11758473	C₂²	1	1	yes	characteristic, complemented
96	#11758472	C₂²	1	1	yes	characteristic
97	#11758471	C₂²	1	1	yes	characteristic
98	#11758471	C₂²	1	1	yes	characteristic
99	#11758471	C₂²	1	1	yes	characteristic
100	#11758471	C₂²	1	1	yes	characteristic
101	#11758471	C₂²	1	1	yes	characteristic, complemented
102	#11758471	C₂²	1	1	yes	characteristic, complemented
103	#11758470	C₂²	1	1	yes	characteristic
104	#11758470	C₂²	1	1	yes	characteristic
105	#11758470	C₂²	1	1	yes	characteristic
106	#11758469	C₂²	1	1	yes	characteristic
107	#11758469	C₂²	1	1	yes	characteristic
108	#11758469	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
111	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
112	#11758467	C₂²	1	1	yes	characteristic, complemented
113	#11758466	C₂²	1	1	yes	characteristic, complemented
114	#11758466	C₂²	1	1	yes	characteristic, complemented
115	#11758466	C₂²	1	1	yes	characteristic, complemented
116	#11758466	C₂²	1	1	yes	characteristic, complemented
117	#11758466	C₂²	1	1	yes	characteristic, complemented
118	#11758466	C₂²	1	1	yes	characteristic, complemented
119	#11758465	C₂²	1	1	yes	characteristic, complemented
120	#11758464	C₂²	1	1	yes	characteristic, complemented
121	#11758464	C₂²	1	1	yes	characteristic, complemented
122	#11758464	C₂²	1	1	yes	characteristic, complemented
123	#11758463	C₂²	1	1	yes	characteristic, complemented
124	#11758463	C₂²	1	1	yes	characteristic, complemented
125	#11758462	C₂²	1	1	yes	characteristic
126	#11758462	C₂²	1	1	yes	characteristic
127	#11758462	C₂²	1	1	yes	characteristic, complemented
128	#11758462	C₂²	1	1	yes	characteristic, complemented
129	#11758461	C₂²	1	1	yes	characteristic
130	#11758461	C₂²	1	1	yes	characteristic
131	#11758461	C₂²	1	1	yes	characteristic, complemented
132	#11758461	C₂²	1	1	yes	characteristic, complemented
133	#11758460	C₂²	1	1	yes	characteristic
134	#11758460	C₂²	1	1	yes	characteristic
135	#11758460	C₂²	1	1	yes	characteristic, complemented
136	#11758460	C₂²	1	1	yes	characteristic, complemented
137	#11758459	C₂²	1	1	yes	characteristic
138	#11758459	C₂²	1	1	yes	characteristic
139	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
140	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
141	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
142	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
143	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
144	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
145	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
149	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
151	#11758456	C₂²	1	1	yes	characteristic, complemented
152	#11758456	C₂²	1	1	yes	characteristic, complemented
153	#11758456	C₂²	1	1	yes	characteristic, complemented
154	#11758456	C₂²	1	1	yes	characteristic, complemented
155	#11758455	C₂²	1	1	yes	characteristic, complemented
156	#11758455	C₂²	1	1	yes	characteristic, complemented
157	#11758455	C₂²	1	1	yes	characteristic, complemented
158	#11758455	C₂²	1	1	yes	characteristic, complemented
159	#11758454	C₂²	1	1	yes	characteristic, complemented
160	#11758454	C₂²	1	1	yes	characteristic, complemented
161	#11758454	C₂²	1	1	yes	characteristic, complemented
162	#11758454	C₂²	1	1	yes	characteristic, complemented
163	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
164	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
165	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
166	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
167	#11758449	C₂²	1	1	yes	characteristic
168	#11758449	C₂²	1	1	yes	characteristic
169	#11758449	C₂²	1	1	yes	characteristic
170	#11758449	C₂²	1	1	yes	characteristic
171	#11758449	C₂²	1	1	yes	characteristic
172	#11758449	C₂²	1	1	yes	characteristic, complemented
173	#11758449	C₂²	1	1	yes	characteristic, complemented
174	#11758449	C₂²	1	1	yes	characteristic, complemented
175	#11758449	C₂²	1	1	yes	characteristic, complemented
176	#11758449	C₂²	1	1	yes	characteristic, complemented
177	#11758449	C₂²	1	1	yes	characteristic, complemented
178	#11758449	C₂²	1	1	yes	characteristic, complemented
179	C₄²×D₃₁	C₂²	1	1	yes	characteristic
180	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₃₁	C₂³	1	1	yes	characteristic
188	C₂³×D₃₁	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
206	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
211	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
212	#92497	—	2	4	no	—
213	D₄×D₃₁	—	2	4	no	—
214	#92495	—	2	4	no	—
215	#92495	—	2	4	no	—
216	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
217	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
218	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
219	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₃₁	—	2	4	no	—
221	C₂×C₄×D₃₁	—	2	4	no	—
222	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
238	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
239	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
240	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
241	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₄²×C₃₁	C₂³	1	1	yes	characteristic
265	C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₄²×C₃₁	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
276	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
308	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
332	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
333	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
334	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
335	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
336	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
337	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
338	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
339	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
340	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
341	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
342	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
343	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
344	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
345	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
346	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
347	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
348	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×D₃₁	—	2	2	no	—
352	C₂²×D₃₁	—	2	2	no	—
353	C₂²×D₃₁	—	2	2	no	—
354	C₂²×D₃₁	—	2	2	no	—
355	C₂²×D₃₁	—	4	1	no	—
356	C₂²×D₃₁	—	4	1	no	—
357	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
358	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
360	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
361	Q₈×C₃₁	—	4	1	no	—
362	D₄×C₃₁	—	2	2	no	—
363	D₄×C₃₁	—	2	2	no	—
364	D₄×C₃₁	—	4	1	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	4	1	no	—
370	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂²⋊D₃₁	—	2	2	no	—
383	C₂²⋊D₃₁	—	2	2	no	—
384	C₂²⋊D₃₁	—	2	2	no	—
385	C₂²⋊D₃₁	—	2	2	no	—
386	C₂²⋊D₃₁	—	2	2	no	—
387	C₂²⋊D₃₁	—	4	1	no	—
388	C₂²⋊D₃₁	—	4	1	no	—
389	C₂²⋊D₃₁	#41	1	4	yes	complemented
390	C₂×Dic₃₁	—	2	2	no	—
391	C₂×Dic₃₁	—	2	2	no	—
392	C₂×Dic₃₁	—	2	2	no	—
393	C₂×Dic₃₁	—	2	2	no	—
394	C₂×Dic₃₁	—	4	1	no	—
395	C₂×Dic₃₁	—	4	1	no	—
396	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
408	D₁₂₄	—	2	2	no	—
409	D₁₂₄	—	2	2	no	—
410	D₁₂₄	—	2	2	no	—
411	D₁₂₄	—	4	1	no	—
412	C₄×D₃₁	—	2	2	no	—
413	C₄×D₃₁	—	2	2	no	—
414	C₄×D₃₁	—	2	2	no	—
415	C₄×D₃₁	—	2	2	no	—
416	C₄×D₃₁	—	2	2	no	—
417	C₄×D₃₁	—	2	2	no	—
418	C₄×D₃₁	—	2	2	no	—
419	C₄×D₃₁	—	2	2	no	—
420	C₄×D₃₁	—	2	2	no	—
421	C₄×D₃₁	—	2	2	no	—
422	C₄×D₃₁	—	2	2	no	—
423	C₄×D₃₁	—	4	1	no	—
424	C₄×D₃₁	—	4	1	no	—
425	C₄×D₃₁	—	4	1	no	—
426	C₄×D₃₁	—	4	1	no	—
427	C₄×D₃₁	#41	1	4	yes	complemented
428	Dic₆₂	—	2	2	no	—
429	Dic₆₂	—	2	2	no	—
430	Dic₆₂	—	2	2	no	—
431	Dic₆₂	—	4	1	no	—
432	#3475	—	31	1	no	maximal, Sylow
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	2	1	no	—
435	C₂²×C₃₁	—	2	1	no	—
436	C₂²×C₃₁	—	2	1	no	—
437	C₂²×C₃₁	—	2	1	no	—
438	C₂²×C₃₁	—	2	1	no	—
439	C₂²×C₃₁	—	2	1	no	—
440	C₂²×C₃₁	—	2	1	no	—
441	C₂²×C₃₁	C₂×#41	1	2	yes	—
442	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
443	C₂×D₃₁	—	2	1	no	—
444	C₂×D₃₁	—	2	1	no	—
445	C₂×D₃₁	—	2	1	no	—
446	C₂×D₃₁	—	2	1	no	—
447	C₂×D₃₁	—	2	1	no	—
448	C₂×D₃₁	—	2	1	no	—
449	C₂×D₃₁	—	2	1	no	—
450	C₂×D₃₁	—	2	1	no	—
451	C₂×D₃₁	—	2	1	no	—
452	C₂×D₃₁	—	2	1	no	—
453	C₂×D₃₁	—	4	4	no	—
454	C₂×D₃₁	—	4	4	no	—
455	C₂×D₃₁	C₂×#41	1	2	yes	—
456	C₂×D₃₁	C₂×#41	1	2	yes	—
457	C₄×C₃₁	—	2	1	no	—
458	C₄×C₃₁	—	2	1	no	—
459	C₄×C₃₁	—	2	1	no	—
460	C₄×C₃₁	—	2	1	no	—
461	C₄×C₃₁	—	2	1	no	—
462	C₄×C₃₁	—	2	1	no	—
463	C₄×C₃₁	—	2	1	no	—
464	C₄×C₃₁	—	2	1	no	—
465	C₄×C₃₁	—	2	1	no	—
466	C₄×C₃₁	—	2	1	no	—
467	C₄×C₃₁	—	2	1	no	—
468	C₄×C₃₁	C₂×#41	1	2	yes	—
469	Dic₃₁	—	2	1	no	—
470	Dic₃₁	—	2	1	no	—
471	Dic₃₁	—	2	1	no	—
472	Dic₃₁	—	2	1	no	—
473	Dic₃₁	—	2	1	no	—
474	Dic₃₁	—	2	1	no	—
475	Dic₃₁	—	2	1	no	—
476	Dic₃₁	—	2	1	no	—
477	Dic₃₁	—	2	1	no	—
478	Dic₃₁	—	2	1	no	—
479	Dic₃₁	C₂×#41	1	2	yes	—
480	Dic₃₁	C₂×#41	1	2	yes	—
481	#556	—	31	1	no	—
482	#555	—	31	1	no	—
483	#554	—	31	1	no	—
484	#553	—	31	1	no	—
485	#553	—	31	1	no	—
486	#552	—	31	1	no	—
487	#552	—	31	1	no	—
488	#552	—	31	1	no	—
489	#552	—	31	1	no	—
490	#551	—	31	1	no	—
491	#551	—	31	1	no	—
492	#551	—	31	1	no	—
493	#551	—	31	1	no	—
494	#547	—	31	1	no	—
495	#546	—	31	1	no	—
496	#546	—	31	1	no	—
497	#533	—	31	1	no	—
498	#529	—	31	1	no	—
499	#529	—	31	1	no	—
500	#529	—	31	1	no	—
501	#529	—	31	1	no	—
502	#529	—	31	1	no	—
503	#529	D₃₁	1	1	yes	characteristic, complemented
504	#525	—	31	1	no	—
505	#525	—	31	1	no	—
506	C₄×#41	—	31	1	no	—
507	C₄×#41	—	31	1	no	—
508	C₄×#41	—	31	1	no	—
509	C₂×C₄×D₄	—	31	1	no	—
510	C₂×#117	—	31	1	no	—
511	C₂×#117	—	31	1	no	—
512	C₂×C₃₁	—	2	2	no	—
513	C₂×C₃₁	—	4	1	no	—
514	C₂×C₃₁	—	4	1	no	—
515	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
516	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
517	C₂×C₃₁	#585	1	1	yes	characteristic
518	D₃₁	—	2	2	no	—
519	D₃₁	—	2	2	no	—
520	D₃₁	—	4	1	no	—
521	D₃₁	—	4	1	no	—
522	C₂×#41	—	31	1	no	—
523	C₂×#41	—	31	1	no	—
524	C₂×#41	—	31	1	no	—
525	C₂²×D₄	—	31	1	no	—
526	C₂³×C₄	—	31	1	no	—
527	C₂³×C₄	—	31	1	no	—
528	C₄⋊Q₈	—	31	1	no	—
529	C₄⋊Q₈	—	31	1	no	—
530	#126	—	31	1	no	—
531	#126	—	31	1	no	—
532	#126	—	31	1	no	—
533	#126	—	31	1	no	—
534	#126	—	31	1	no	—
535	#126	—	31	1	no	—
536	#126	—	31	1	no	—
537	#126	—	31	1	no	—
538	#126	—	31	1	no	—
539	#126	—	31	1	no	—
540	#126	C₂×D₃₁	1	1	yes	characteristic, complemented
541	#126	C₂×D₃₁	1	1	yes	characteristic, complemented
542	#125	—	31	1	no	—
543	#125	—	31	1	no	—
544	#125	—	31	1	no	—
545	#125	—	31	1	no	—
546	#125	—	31	1	no	—
547	#125	—	31	1	no	—
548	#125	—	31	1	no	—
549	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
550	#124	—	31	1	no	—
551	#124	—	31	1	no	—
552	#124	—	31	1	no	—
553	#124	—	31	1	no	—
554	#124	—	31	1	no	—
555	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
556	#123	—	31	1	no	—
557	#123	—	31	1	no	—
558	#123	—	31	1	no	—
559	#123	—	31	1	no	—
560	#123	—	31	1	no	—
561	#123	—	31	1	no	—
562	#123	—	31	1	no	—
563	#123	—	31	1	no	—
564	#123	—	31	1	no	—
565	#123	—	31	1	no	—
566	#123	—	31	1	no	—
567	#123	—	31	1	no	—
568	#123	—	31	1	no	—
569	#123	—	31	1	no	—
570	#123	C₂×D₃₁	1	1	yes	characteristic
571	#123	C₂×D₃₁	1	1	yes	characteristic, complemented
572	C₂²⋊Q₈	—	31	1	no	—
573	C₂²⋊Q₈	—	31	1	no	—
574	C₂²⋊Q₈	—	31	1	no	—
575	C₂²⋊Q₈	—	31	1	no	—
576	C₂²⋊Q₈	—	31	1	no	—
577	C₂²⋊Q₈	—	31	1	no	—
578	C₂²⋊Q₈	—	31	1	no	—
579	C₂²⋊Q₈	—	31	1	no	—
580	C₂²⋊Q₈	—	31	1	no	—
581	C₂²⋊Q₈	—	31	1	no	—
582	C₂²⋊Q₈	—	31	1	no	—
583	C₂²⋊Q₈	—	31	1	no	—
584	C₂²⋊Q₈	—	31	1	no	—
585	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
586	#121	—	31	1	no	—
587	#121	—	31	1	no	—
588	#121	—	31	1	no	—
589	#121	—	31	1	no	—
590	#121	—	31	1	no	—
591	#121	—	31	1	no	—
592	#121	—	31	1	no	—
593	#121	—	31	1	no	—
594	#121	—	31	1	no	—
595	#121	C₂×D₃₁	1	1	yes	characteristic
596	#120	—	31	1	no	—
597	#120	—	31	1	no	—
598	#120	—	31	1	no	—
599	#120	—	31	1	no	—
600	C₄×Q₈	—	31	1	no	—
601	C₄×Q₈	—	31	1	no	—
602	C₄×Q₈	—	31	1	no	—
603	C₄×Q₈	—	31	1	no	—
604	C₄×Q₈	—	31	1	no	—
605	C₄×Q₈	—	31	1	no	—
606	C₄×Q₈	—	31	1	no	—
607	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
608	C₄×D₄	—	31	1	no	—
609	C₄×D₄	—	31	1	no	—
610	C₄×D₄	—	31	1	no	—
611	C₄×D₄	—	31	1	no	—
612	C₄×D₄	—	31	1	no	—
613	C₄×D₄	—	31	1	no	—
614	C₄×D₄	—	31	1	no	—
615	C₄×D₄	—	31	1	no	—
616	C₄×D₄	—	31	1	no	—
617	C₄×D₄	—	31	1	no	—
618	C₄×D₄	—	31	1	no	—
619	C₄×D₄	—	31	1	no	—
620	C₄×D₄	—	31	1	no	—
621	C₄×D₄	—	31	1	no	—
622	C₄×D₄	—	31	1	no	—
623	C₄×D₄	—	31	1	no	—
624	C₄×D₄	—	31	1	no	—
625	C₄×D₄	—	31	1	no	—
626	C₄×D₄	—	31	1	no	—
627	C₄×D₄	—	31	1	no	—
628	C₄×D₄	—	31	1	no	—
629	C₄×D₄	—	31	1	no	—
630	C₄×D₄	—	31	1	no	—
631	C₄×D₄	—	31	1	no	—
632	C₄×D₄	—	31	1	no	—
633	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
634	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
635	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
636	#117	—	31	1	no	—
637	#117	—	31	1	no	—
638	#117	—	31	1	no	—
639	#117	—	31	1	no	—
640	#117	—	31	1	no	—
641	#117	—	31	1	no	—
642	#117	—	31	1	no	—
643	#117	—	31	1	no	—
644	#117	—	31	1	no	—
645	#117	—	31	1	no	—
646	#117	—	31	1	no	—
647	#117	—	31	1	no	—
648	#117	—	31	1	no	—
649	#117	—	31	1	no	—
650	#117	—	31	1	no	—
651	#117	—	31	1	no	—
652	#117	—	31	1	no	—
653	#117	—	31	1	no	—
654	#117	—	31	1	no	—
655	#117	—	31	1	no	—
656	#117	—	31	1	no	—
657	#117	C₂×D₃₁	1	1	yes	characteristic, complemented
658	#117	C₂×D₃₁	1	1	yes	characteristic, complemented
659	C₂×C₄⋊C₄	—	31	1	no	—
660	C₂×C₄⋊C₄	—	31	1	no	—
661	C₂×C₄⋊C₄	—	31	1	no	—
662	C₂×C₄⋊C₄	—	31	1	no	—
663	C₂×C₄⋊C₄	—	31	1	no	—
664	C₂×C₂²⋊C₄	—	31	1	no	—
665	C₂×C₂²⋊C₄	—	31	1	no	—
666	C₂×C₂²⋊C₄	—	31	1	no	—
667	C₂×C₂²⋊C₄	—	31	1	no	—
668	C₂×C₂²⋊C₄	—	31	1	no	—
669	C₂×C₂²⋊C₄	—	31	1	no	—
670	C₂×C₄²	—	31	1	no	—
671	C₂×C₄²	—	31	1	no	—
672	C₂×C₄²	—	31	1	no	—
673	C₂×C₄²	—	31	1	no	—
674	C₂×C₄²	—	31	1	no	—
675	C₂×C₄²	—	31	1	no	—
676	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
677	C₃₁	#3475	1	1	yes	characteristic, complemented, Sylow
678	C₂⁴	—	31	1	no	—
679	C₂⁴	—	31	1	no	—
680	#41	—	62	4	no	—
681	#41	—	62	4	no	—
682	#41	—	62	4	no	—
683	C₂×Q₈	—	31	1	no	—
684	C₂×Q₈	—	31	1	no	—
685	C₂×Q₈	—	31	1	no	—
686	C₂×Q₈	—	31	1	no	—
687	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
688	C₂×D₄	—	31	1	no	—
689	C₂×D₄	—	31	1	no	—
690	C₂×D₄	—	31	1	no	—
691	C₂×D₄	—	31	1	no	—
692	C₂×D₄	—	31	1	no	—
693	C₂×D₄	—	31	1	no	—
694	C₂×D₄	—	31	1	no	—
695	C₂×D₄	—	31	1	no	—
696	C₂×D₄	—	31	1	no	—
697	C₂×D₄	—	31	1	no	—
698	C₂×D₄	—	31	1	no	—
699	C₂×D₄	—	31	1	no	—
700	C₂×D₄	—	62	4	no	—
701	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
702	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
703	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
704	C₂²×C₄	—	31	1	no	—
705	C₂²×C₄	—	31	1	no	—
706	C₂²×C₄	—	31	1	no	—
707	C₂²×C₄	—	31	1	no	—
708	C₂²×C₄	—	31	1	no	—
709	C₂²×C₄	—	31	1	no	—
710	C₂²×C₄	—	31	1	no	—
711	C₂²×C₄	—	31	1	no	—
712	C₂²×C₄	—	31	1	no	—
713	C₂²×C₄	—	31	1	no	—
714	C₂²×C₄	—	31	1	no	—
715	C₂²×C₄	—	31	1	no	—
716	C₂²×C₄	—	31	1	no	—
717	C₂²×C₄	—	31	1	no	—
718	C₂²×C₄	—	31	1	no	—
719	C₂²×C₄	—	31	1	no	—
720	C₂²×C₄	—	31	1	no	—
721	C₂²×C₄	—	31	1	no	—
722	C₂²×C₄	—	31	1	no	—
723	C₂²×C₄	—	31	1	no	—
724	C₂²×C₄	—	31	1	no	—
725	C₂²×C₄	—	31	1	no	—
726	C₂²×C₄	—	62	4	no	—
727	C₂²×C₄	—	62	4	no	—
728	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
733	C₄⋊C₄	—	31	1	no	—
734	C₄⋊C₄	—	31	1	no	—
735	C₄⋊C₄	—	31	1	no	—
736	C₄⋊C₄	—	31	1	no	—
737	C₄⋊C₄	—	31	1	no	—
738	C₄⋊C₄	—	31	1	no	—
739	C₄⋊C₄	—	31	1	no	—
740	C₄⋊C₄	—	31	1	no	—
741	C₄⋊C₄	—	31	1	no	—
742	C₄⋊C₄	—	31	1	no	—
743	C₄⋊C₄	—	31	1	no	—
744	C₄⋊C₄	—	31	1	no	—
745	C₄⋊C₄	—	31	1	no	—
746	C₄⋊C₄	—	31	1	no	—
747	C₄⋊C₄	—	31	1	no	—
748	C₄⋊C₄	—	31	1	no	—
749	C₄⋊C₄	—	31	1	no	—
750	C₄⋊C₄	—	31	1	no	—
751	C₄⋊C₄	—	31	1	no	—
752	C₄⋊C₄	—	31	1	no	—
753	C₄⋊C₄	—	31	1	no	—
754	C₄⋊C₄	—	31	1	no	—
755	C₄⋊C₄	—	31	1	no	—
756	C₄⋊C₄	—	31	1	no	—
757	C₄⋊C₄	—	31	1	no	—
758	C₄⋊C₄	—	31	1	no	—
759	C₄⋊C₄	—	31	1	no	—
760	C₄⋊C₄	—	31	1	no	—
761	C₄⋊C₄	—	31	1	no	—
762	C₄⋊C₄	—	31	1	no	—
763	C₄⋊C₄	—	31	1	no	—
764	C₄⋊C₄	—	31	1	no	—
765	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
775	C₂²⋊C₄	—	31	1	no	—
776	C₂²⋊C₄	—	31	1	no	—
777	C₂²⋊C₄	—	31	1	no	—
778	C₂²⋊C₄	—	31	1	no	—
779	C₂²⋊C₄	—	31	1	no	—
780	C₂²⋊C₄	—	31	1	no	—
781	C₂²⋊C₄	—	31	1	no	—
782	C₂²⋊C₄	—	31	1	no	—
783	C₂²⋊C₄	—	31	1	no	—
784	C₂²⋊C₄	—	31	1	no	—
785	C₂²⋊C₄	—	31	1	no	—
786	C₂²⋊C₄	—	31	1	no	—
787	C₂²⋊C₄	—	31	1	no	—
788	C₂²⋊C₄	—	31	1	no	—
789	C₂²⋊C₄	—	31	1	no	—
790	C₂²⋊C₄	—	31	1	no	—
791	C₂²⋊C₄	—	31	1	no	—
792	C₂²⋊C₄	—	31	1	no	—
793	C₂²⋊C₄	—	31	1	no	—
794	C₂²⋊C₄	—	31	1	no	—
795	C₂²⋊C₄	—	31	1	no	—
796	C₂²⋊C₄	—	31	1	no	—
797	C₂²⋊C₄	—	31	1	no	—
798	C₂²⋊C₄	—	31	1	no	—
799	C₂²⋊C₄	—	31	1	no	—
800	C₂²⋊C₄	—	31	1	no	—
801	C₂²⋊C₄	—	31	1	no	—
802	C₂²⋊C₄	—	31	1	no	—
803	C₂²⋊C₄	—	31	1	no	—
804	C₂²⋊C₄	—	31	1	no	—
805	C₂²⋊C₄	—	31	1	no	—
806	C₂²⋊C₄	—	31	1	no	—
807	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
817	C₄²	—	31	1	no	—
818	C₄²	—	31	1	no	—
819	C₄²	—	31	1	no	—
820	C₄²	—	31	1	no	—
821	C₄²	—	31	1	no	—
822	C₄²	—	31	1	no	—
823	C₄²	—	31	1	no	—
824	C₄²	—	31	1	no	—
825	C₄²	—	31	1	no	—
826	C₄²	—	31	1	no	—
827	C₄²	—	31	1	no	—
828	C₄²	—	31	1	no	—
829	C₄²	—	31	1	no	—
830	C₄²	—	31	1	no	—
831	C₄²	—	31	1	no	—
832	C₄²	—	31	1	no	—
833	C₄²	C₂²×D₃₁	1	1	yes	characteristic
834	C₄²	C₂²×D₃₁	1	1	yes	characteristic
835	C₄²	C₂²×D₃₁	1	1	yes	characteristic
836	C₄²	C₂²×D₃₁	1	1	yes	characteristic
837	C₄²	C₂²×D₃₁	1	1	yes	characteristic
838	C₄²	C₂²×D₃₁	1	1	yes	characteristic
839	C₂³	—	31	1	no	—
840	C₂³	—	31	1	no	—
841	C₂³	—	31	1	no	—
842	C₂³	—	31	1	no	—
843	C₂³	—	62	2	no	—
844	C₂³	—	62	2	no	—
845	C₂³	—	62	2	no	—
846	C₂³	—	62	2	no	—
847	C₂³	—	124	1	no	—
848	C₂³	—	124	1	no	—
849	C₂³	C₂³×D₃₁	1	1	yes	characteristic
850	C₂³	C₂³×D₃₁	1	1	yes	characteristic
851	C₂³	C₂³×D₃₁	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	62	2	no	—
854	Q₈	—	62	2	no	—
855	Q₈	—	62	2	no	—
856	Q₈	—	124	1	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	4	1	no	—
860	D₄	—	31	4	no	—
861	D₄	—	62	2	no	—
862	D₄	—	62	2	no	—
863	D₄	—	62	2	no	—
864	D₄	—	62	2	no	—
865	D₄	—	62	2	no	—
866	D₄	—	62	2	no	—
867	D₄	—	62	2	no	—
868	D₄	—	62	2	no	—
869	D₄	—	124	1	no	—
870	D₄	—	124	1	no	—
871	D₄	—	124	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	31	1	no	—
878	C₂×C₄	—	31	1	no	—
879	C₂×C₄	—	31	4	no	—
880	C₂×C₄	—	31	1	no	—
881	C₂×C₄	—	31	1	no	—
882	C₂×C₄	—	31	1	no	—
883	C₂×C₄	—	31	1	no	—
884	C₂×C₄	—	31	1	no	—
885	C₂×C₄	—	31	1	no	—
886	C₂×C₄	—	31	1	no	—
887	C₂×C₄	—	31	1	no	—
888	C₂×C₄	—	31	1	no	—
889	C₂×C₄	—	31	1	no	—
890	C₂×C₄	—	62	2	no	—
891	C₂×C₄	—	62	2	no	—
892	C₂×C₄	—	62	2	no	—
893	C₂×C₄	—	62	2	no	—
894	C₂×C₄	—	62	2	no	—
895	C₂×C₄	—	62	2	no	—
896	C₂×C₄	—	62	2	no	—
897	C₂×C₄	—	62	2	no	—
898	C₂×C₄	—	62	2	no	—
899	C₂×C₄	—	62	2	no	—
900	C₂×C₄	—	62	2	no	—
901	C₂×C₄	—	62	2	no	—
902	C₂×C₄	—	62	2	no	—
903	C₂×C₄	—	62	2	no	—
904	C₂×C₄	—	62	2	no	—
905	C₂×C₄	—	124	1	no	—
906	C₂×C₄	—	124	1	no	—
907	C₂×C₄	—	124	1	no	—
908	C₂×C₄	—	124	1	no	—
909	C₂×C₄	—	124	1	no	—
910	C₂×C₄	—	124	1	no	—
911	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	31	2	no	—
932	C₂²	—	31	2	no	—
933	C₂²	—	62	1	no	—
934	C₂²	—	62	1	no	—
935	C₂²	—	62	1	no	—
936	C₂²	—	62	1	no	—
937	C₂²	—	62	1	no	—
938	C₂²	—	62	1	no	—
939	C₂²	—	62	1	no	—
940	C₂²	—	62	1	no	—
941	C₂²	—	62	1	no	—
942	C₂²	—	62	1	no	—
943	C₂²	—	124	4	no	—
944	C₂²	—	124	4	no	—
945	C₂²	#41×D₃₁	1	2	yes	—
946	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	31	2	no	—
959	C₄	—	31	2	no	—
960	C₄	—	62	1	no	—
961	C₄	—	62	1	no	—
962	C₄	—	62	1	no	—
963	C₄	—	62	1	no	—
964	C₄	—	62	1	no	—
965	C₄	—	62	1	no	—
966	C₄	—	62	1	no	—
967	C₄	—	62	1	no	—
968	C₄	—	62	1	no	—
969	C₄	—	62	1	no	—
970	C₄	#41×D₃₁	1	2	yes	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	62	2	no	—
975	C₂	—	62	2	no	—
976	C₂	—	124	1	no	—
977	C₂	—	124	1	no	—
978	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
979	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
980	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₃₁×#529	C₂
hypercenter	#529	D₃₁
hypocenter	C₃₁	#3475
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14521766	C₂	semidirect
2. #14521761	C₂	semidirect
3. #14521753	C₂	semidirect
4. #14521750	C₂	semidirect
5. #14521742	C₂	semidirect
6. #14521736	C₂	semidirect
7. #14521735	C₂	semidirect
8. #14521731	C₂	semidirect
9. #14521731	C₂	semidirect
10. #14521729	C₂	semidirect
11. #14521726	C₂	semidirect
12. #14521724	C₂	semidirect
13. #14521722	C₂	semidirect
14. #14521697	C₂	semidirect
15. #14521691	C₂	semidirect
16. #14521688	C₂	semidirect
17. #14521603	C₂	semidirect
18. #14521586	C₂	semidirect
19. #14521579	C₂	semidirect
20. #14521579	C₂	semidirect
21. #14521577	C₂	semidirect
22. #14521577	C₂	semidirect
23. #14521558	C₂	semidirect
24. #14521558	C₂	semidirect
25. C₄×#92495	C₂	semidirect
26. #14521517	C₂	semidirect
27. C₄×#92497	C₂	semidirect
28. C₄×D₄×D₃₁	C₂	semidirect
29. C₂×#11758449	C₂	semidirect
30. #117×D₃₁	C₂	semidirect
31. C₃₁×#529	C₂	semidirect
38. C₃₁×#126	C₂²	semidirect
39. C₃₁×#126	C₂²	semidirect
40. C₃₁×#125	C₂²	semidirect
41. C₃₁×#124	C₂²	semidirect
43. C₃₁×#123	C₂²	semidirect
44. C₃₁×C₂²⋊Q₈	C₂²	semidirect
46. C₄×Q₈×C₃₁	C₂²	semidirect
48. C₄×D₄×C₃₁	C₂²	semidirect
49. C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#117	C₂²	semidirect
51. C₃₁×#117	C₂²	semidirect
52. C₂×C₄²×C₃₁	C₂²	semidirect
53. #11758524	C₂²	semidirect
55. #11758523	C₂²	semidirect
56. #11758521	C₂²	semidirect
59. #11758516	C₂²	semidirect
60. #11758516	C₂²	semidirect
64. #11758512	C₂²	semidirect
66. D₄×Dic₃₁	C₂²	semidirect
70. C₄×C₂²⋊D₃₁	C₂²	semidirect
71. C₄×C₂²⋊D₃₁	C₂²	semidirect
72. C₄×C₂²⋊D₃₁	C₂²	semidirect
73. C₄×C₂²⋊D₃₁	C₂²	semidirect
74. C₄×C₂²⋊D₃₁	C₂²	semidirect
77. #11758503	C₂²	semidirect
78. #11758503	C₂²	semidirect
79. C₂×Dic₃₁⋊C₄	C₂²	semidirect
80. C₂×Dic₃₁⋊C₄	C₂²	semidirect
81. C₂×C₄×Dic₃₁	C₂²	semidirect
82. C₂×C₄×Dic₃₁	C₂²	semidirect
83. #11758475	C₂²	semidirect
84. #11758475	C₂²	semidirect
85. #11758475	C₂²	semidirect
86. #11758475	C₂²	semidirect
87. #11758475	C₂²	semidirect
88. #11758475	C₂²	semidirect
92. #11758473	C₂²	semidirect
93. #11758473	C₂²	semidirect
94. #11758473	C₂²	semidirect
95. #11758473	C₂²	semidirect
101. #11758471	C₂²	semidirect
102. #11758471	C₂²	semidirect
108. #11758469	C₂²	semidirect
110. C₄⋊C₄×D₃₁	C₂²	semidirect
111. C₄⋊C₄×D₃₁	C₂²	semidirect
112. #11758467	C₂²	semidirect
113. #11758466	C₂²	semidirect
114. #11758466	C₂²	semidirect
115. #11758466	C₂²	semidirect
116. #11758466	C₂²	semidirect
117. #11758466	C₂²	semidirect
118. #11758466	C₂²	semidirect
119. #11758465	C₂²	semidirect
120. #11758464	C₂²	semidirect
121. #11758464	C₂²	semidirect
122. #11758464	C₂²	semidirect
123. #11758463	C₂²	semidirect
124. #11758463	C₂²	semidirect
127. #11758462	C₂²	semidirect
128. #11758462	C₂²	semidirect
131. #11758461	C₂²	semidirect
132. #11758461	C₂²	semidirect
135. #11758460	C₂²	semidirect
136. #11758460	C₂²	semidirect
144. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
145. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
146. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
151. #11758456	C₂²	semidirect
152. #11758456	C₂²	semidirect
153. #11758456	C₂²	semidirect
154. #11758456	C₂²	semidirect
155. #11758455	C₂²	semidirect
156. #11758455	C₂²	semidirect
157. #11758455	C₂²	semidirect
158. #11758455	C₂²	semidirect
159. #11758454	C₂²	semidirect
160. #11758454	C₂²	semidirect
161. #11758454	C₂²	semidirect
162. #11758454	C₂²	semidirect
164. C₄×D₁₂₄	C₂²	semidirect
165. C₄×D₁₂₄	C₂²	semidirect
166. C₄×D₁₂₄	C₂²	semidirect
172. #11758449	C₂²	semidirect
173. #11758449	C₂²	semidirect
174. #11758449	C₂²	semidirect
175. #11758449	C₂²	semidirect
176. #11758449	C₂²	semidirect
177. #11758449	C₂²	semidirect
178. #11758449	C₂²	semidirect
180. C₄²×D₃₁	C₂²	semidirect
181. C₄²×D₃₁	C₂²	semidirect
182. C₄²×D₃₁	C₂²	semidirect
183. C₄×Dic₆₂	C₂²	semidirect
184. C₄×Dic₆₂	C₂²	semidirect
185. C₄×Dic₆₂	C₂²	semidirect
186. C₄×Dic₆₂	C₂²	semidirect
389. C₂²⋊D₃₁	#41	semidirect
427. C₄×D₃₁	#41	semidirect
503. #529	D₃₁	semidirect
540. #126	C₂×D₃₁	semidirect
541. #126	C₂×D₃₁	semidirect
549. #125	C₂×D₃₁	semidirect
555. #124	C₂×D₃₁	semidirect
571. #123	C₂×D₃₁	semidirect
585. C₂²⋊Q₈	C₂×D₃₁	semidirect
607. C₄×Q₈	C₂×D₃₁	semidirect
634. C₄×D₄	C₂×D₃₁	semidirect
635. C₄×D₄	C₂×D₃₁	semidirect
657. #117	C₂×D₃₁	semidirect
658. #117	C₂×D₃₁	semidirect
676. C₂×C₄²	C₂×D₃₁	semidirect
677. C₃₁	#3475	semidirect

Maximal subgroups

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

subgroup	index
#14521766	2
#14521761	2
#14521753	2
#14521750	2
#14521742	2
#14521736	2
#14521735	2
#14521731	2
#14521729	2
#14521726	2
#14521724	2
#14521722	2
#14521697	2
#14521691	2
#14521688	2
#14521603	2
#14521586	2
#14521579	2
#14521577	2
#14521558	2
C₄×#92495	2
#14521517	2
C₄×#92497	2
C₄×D₄×D₃₁	2
C₂×#11758449	2
#117×D₃₁	2
C₃₁×#529	2
#3475	31