Subgroups — C₃₁×#62098 #21518857

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3380	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3337	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3303	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3297	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#556	—	2	1	no	—
19	C₃₁×#556	C₂²	1	1	yes	characteristic
20	C₃₁×#555	C₂²	1	1	yes	characteristic
21	C₃₁×#555	C₂²	1	2	yes	complemented
22	C₃₁×#554	C₂²	1	1	yes	characteristic
23	C₃₁×#554	C₂²	1	2	yes	complemented
24	C₃₁×#553	—	2	1	no	—
25	C₃₁×#553	C₂²	1	4	yes	—
26	C₃₁×#552	—	2	1	no	—
27	C₃₁×#552	C₂²	1	2	yes	—
28	C₃₁×#551	—	2	2	no	—
29	C₃₁×#548	—	2	2	no	—
30	C₃₁×#547	—	2	1	no	—
31	C₃₁×#547	C₂²	1	1	yes	characteristic
32	C₃₁×#546	C₂²	1	2	yes	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#537	—	2	1	no	—
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	2	yes	complemented
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#532	C₂²	1	2	yes	complemented
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#529	C₂²	1	2	yes	—
42	C₃₁×#525	—	2	1	no	—
43	C₃₁×#520	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	2	yes	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	—	2	1	no	—
48	C₃₁×#500	C₂²	1	2	yes	complemented
49	C₃₁×#499	C₂²	1	4	yes	complemented
50	C₃₁×#488	C₂²	1	4	yes	—
51	C₃₁×#487	C₂²	1	2	yes	complemented
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#484	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	4	yes	—
55	C₃₁×#482	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	2	yes	—
57	C₃₁×#479	C₂²	1	4	yes	complemented
58	C₃₁×#478	C₂²	1	4	yes	—
59	C₃₁×#478	C₂²	1	4	yes	complemented
60	C₃₁×#477	C₂²	1	2	yes	complemented
61	C₃₁×#477	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	2	yes	—
63	C₃₁×#476	C₂²	1	2	yes	—
64	C₃₁×#476	C₂²	1	2	yes	—
65	C₃₁×#476	C₂²	1	2	yes	—
66	C₃₁×#476	C₂²	1	2	yes	complemented
67	C₃₁×#475	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	1	yes	characteristic
69	C₃₁×#474	C₂²	1	1	yes	characteristic
70	C₃₁×#466	C₂²	1	4	yes	—
71	C₃₁×#465	C₂²	1	4	yes	—
72	C₃₁×#465	C₂²	1	4	yes	complemented
73	C₃₁×#463	C₂²	1	4	yes	—
74	C₃₁×#461	C₂²	1	2	yes	complemented
75	C₃₁×#460	C₂²	1	2	yes	complemented
76	C₃₁×#459	C₂²	1	1	yes	characteristic
77	C₃₁×#459	C₂²	1	1	yes	characteristic
78	C₃₁×#449	C₂²	1	4	yes	—
79	C₃₁×#447	C₂²	1	2	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
82	C₄×D₈×C₃₁	C₂²	1	2	yes	—
83	C₄×D₈×C₃₁	C₂²	1	2	yes	—
84	C₄×D₈×C₃₁	C₂²	1	4	yes	—
85	C₈×D₄×C₃₁	C₂²	1	4	yes	—
86	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#431	C₂²	1	1	yes	characteristic
88	C₃₁×#431	C₂²	1	2	yes	complemented
89	C₃₁×#427	C₂²	1	4	yes	complemented
90	C₂×C₃₁×#106	C₂²	1	2	yes	—
91	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₃₁×#416	C₂²	1	4	yes	—
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
98	C₂×#41×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	—	2	1	no	—
102	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×D₈×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×#127	C₂³	1	1	yes	characteristic
115	C₃₁×#126	—	2	2	no	—
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	2	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	—	2	1	no	—
121	C₃₁×#125	C₂³	1	4	yes	—
122	C₃₁×#125	C₂³	1	2	yes	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	—	2	1	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	C₂³	1	2	yes	—
128	C₃₁×#123	—	2	2	no	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₃₁×#121	—	2	1	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	4	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#121	C₂³	1	4	yes	—
152	C₃₁×#121	C₂³	1	2	yes	—
153	C₃₁×#120	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	4	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
170	C₄×D₄×C₃₁	D₄	1	2	yes	—
171	C₄×D₄×C₃₁	C₂³	1	2	yes	—
172	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	C₂³	1	4	yes	—
176	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₃₁	C₂³	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₃₁×#117	—	2	1	no	—
181	C₃₁×#117	—	2	1	no	—
182	C₃₁×#117	—	2	1	no	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	—	2	2	no	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	D₄	1	1	yes	characteristic
188	C₃₁×#117	D₄	1	2	yes	—
189	C₃₁×#117	C₂³	1	4	yes	—
190	C₃₁×#117	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄²×C₃₁	—	2	2	no	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	1	no	—
229	#41×C₃₁	—	2	4	no	—
230	#41×C₃₁	—	2	4	no	—
231	#41×C₃₁	—	4	2	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	8	4	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	8	2	no	—
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	—	2	2	no	—
242	C₂×D₄×C₃₁	—	2	2	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	4	no	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	4	1	no	—
250	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	—	2	1	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	1	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	1	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	4	4	no	—
266	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
272	SD₁₆×C₃₁	—	4	4	no	—
273	D₈×C₃₁	—	2	4	no	—
274	D₈×C₃₁	—	4	2	no	—
275	C₂×C₈×C₃₁	—	4	4	no	—
276	C₂×C₈×C₃₁	—	4	2	no	—
277	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
279	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	1	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	2	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	4	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	1	no	—
310	C₂²⋊C₄×C₃₁	—	2	2	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	1	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	1	no	—
315	C₂²⋊C₄×C₃₁	—	2	4	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	4	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	2	no	—
327	C₄²×C₃₁	—	2	4	no	—
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂×D₄	1	2	yes	—
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₄²×C₃₁	C₂⁴	1	2	yes	—
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	#62098	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	1	no	—
338	C₂³×C₃₁	—	2	2	no	—
339	C₂³×C₃₁	—	4	2	no	—
340	C₂³×C₃₁	—	4	2	no	—
341	C₂³×C₃₁	—	8	1	no	—
342	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	Q₈×C₃₁	—	8	1	no	—
350	Q₈×C₃₁	—	8	2	no	—
351	D₄×C₃₁	—	2	4	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	1	no	—
355	D₄×C₃₁	—	2	1	no	—
356	D₄×C₃₁	—	2	1	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	4	2	no	—
359	D₄×C₃₁	—	4	2	no	—
360	D₄×C₃₁	—	4	4	no	—
361	D₄×C₃₁	—	4	4	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	8	4	no	—
365	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	1	no	—
368	C₂×C₄×C₃₁	—	2	2	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	4	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	4	1	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	4	no	—
380	C₂×C₄×C₃₁	—	4	2	no	—
381	C₂×C₄×C₃₁	—	4	2	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	4	2	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	4	no	—
386	C₂×C₄×C₃₁	—	8	2	no	—
387	C₂×C₄×C₃₁	—	8	4	no	—
388	C₂×C₄×C₃₁	—	8	2	no	—
389	C₂×C₄×C₃₁	#135	1	4	yes	—
390	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
399	C₈×C₃₁	—	2	2	no	—
400	C₈×C₃₁	—	2	2	no	—
401	C₈×C₃₁	—	2	4	no	—
402	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
404	#3380	C₂×C₃₁	1	2	yes	complemented
405	#3360	C₂×C₃₁	1	2	yes	complemented
406	#3341	C₂×C₃₁	1	2	yes	complemented
407	#3337	C₂×C₃₁	1	4	yes	complemented
408	#3303	C₂×C₃₁	1	2	yes	complemented
409	#3297	C₂×C₃₁	1	4	yes	complemented
410	#3247	C₂×C₃₁	1	2	yes	complemented
411	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3233	C₂×C₃₁	1	2	yes	complemented
413	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3106	C₂×C₃₁	1	2	yes	complemented
415	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3076	C₂×C₃₁	1	2	yes	complemented
417	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
418	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	1	no	—
421	C₂²×C₃₁	—	2	2	no	—
422	C₂²×C₃₁	—	2	2	no	—
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	4	1	no	—
426	C₂²×C₃₁	—	4	1	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	4	1	no	—
429	C₂²×C₃₁	—	4	1	no	—
430	C₂²×C₃₁	—	4	2	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	2	no	—
433	C₂²×C₃₁	—	8	4	no	—
434	C₂²×C₃₁	C₂×#135	1	2	yes	—
435	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
436	C₄×C₃₁	—	2	1	no	—
437	C₄×C₃₁	—	2	2	no	—
438	C₄×C₃₁	—	2	1	no	—
439	C₄×C₃₁	—	2	2	no	—
440	C₄×C₃₁	—	2	1	no	—
441	C₄×C₃₁	—	2	2	no	—
442	C₄×C₃₁	—	4	4	no	—
443	C₄×C₃₁	—	4	2	no	—
444	C₄×C₃₁	—	4	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	1	no	—
447	C₄×C₃₁	—	4	2	no	—
448	C₄×C₃₁	C₂×#135	1	2	yes	—
449	C₄×C₃₁	C₂×#135	1	2	yes	—
450	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
451	C₄×C₃₁	#585	1	1	yes	characteristic
452	#556	—	2	1	no	—
453	#556	C₂²×C₃₁	1	1	yes	characteristic
454	#555	C₂²×C₃₁	1	1	yes	characteristic
455	#555	C₂²×C₃₁	1	2	yes	complemented
456	#554	C₂²×C₃₁	1	1	yes	characteristic
457	#554	C₂²×C₃₁	1	2	yes	complemented
458	#553	—	2	1	no	—
459	#553	C₂²×C₃₁	1	4	yes	—
460	#552	—	2	1	no	—
461	#552	C₂²×C₃₁	1	2	yes	—
462	#551	—	2	2	no	—
463	#548	—	2	2	no	—
464	#547	—	2	1	no	—
465	#547	C₂²×C₃₁	1	1	yes	characteristic
466	#546	C₂²×C₃₁	1	2	yes	—
467	#542	—	2	2	no	—
468	#537	—	2	1	no	—
469	#533	C₂²×C₃₁	1	1	yes	characteristic
470	#533	C₂²×C₃₁	1	2	yes	complemented
471	#532	C₂²×C₃₁	1	1	yes	characteristic
472	#532	C₂²×C₃₁	1	2	yes	complemented
473	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
474	#529	—	2	2	no	—
475	#529	C₂²×C₃₁	1	2	yes	—
476	#525	—	2	1	no	—
477	#520	—	2	1	no	—
478	C₄×#41	C₂²×C₃₁	1	2	yes	—
479	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×#117	—	2	1	no	—
482	#500	C₂²×C₃₁	1	2	yes	complemented
483	#499	C₂²×C₃₁	1	4	yes	complemented
484	#488	C₂²×C₃₁	1	4	yes	—
485	#487	C₂²×C₃₁	1	2	yes	complemented
486	#485	C₂²×C₃₁	1	4	yes	complemented
487	#484	C₂²×C₃₁	1	4	yes	—
488	#482	C₂²×C₃₁	1	4	yes	—
489	#482	C₂²×C₃₁	1	4	yes	complemented
490	#480	C₂²×C₃₁	1	2	yes	—
491	#479	C₂²×C₃₁	1	4	yes	complemented
492	#478	C₂²×C₃₁	1	4	yes	—
493	#478	C₂²×C₃₁	1	4	yes	complemented
494	#477	C₂²×C₃₁	1	2	yes	complemented
495	#477	C₂²×C₃₁	1	2	yes	complemented
496	#476	C₂²×C₃₁	1	2	yes	—
497	#476	C₂²×C₃₁	1	2	yes	—
498	#476	C₂²×C₃₁	1	2	yes	—
499	#476	C₂²×C₃₁	1	2	yes	—
500	#476	C₂²×C₃₁	1	2	yes	complemented
501	#475	C₂²×C₃₁	1	2	yes	complemented
502	#474	C₂²×C₃₁	1	1	yes	characteristic
503	#474	C₂²×C₃₁	1	1	yes	characteristic
504	#466	C₂²×C₃₁	1	4	yes	—
505	#465	C₂²×C₃₁	1	4	yes	—
506	#465	C₂²×C₃₁	1	4	yes	complemented
507	#463	C₂²×C₃₁	1	4	yes	—
508	#461	C₂²×C₃₁	1	2	yes	complemented
509	#460	C₂²×C₃₁	1	2	yes	complemented
510	#459	C₂²×C₃₁	1	1	yes	characteristic
511	#459	C₂²×C₃₁	1	1	yes	characteristic
512	#449	C₂²×C₃₁	1	4	yes	—
513	#447	C₂²×C₃₁	1	2	yes	—
514	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
515	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
516	C₄×D₈	C₂²×C₃₁	1	2	yes	—
517	C₄×D₈	C₂²×C₃₁	1	2	yes	—
518	C₄×D₈	C₂²×C₃₁	1	4	yes	—
519	C₈×D₄	C₂²×C₃₁	1	4	yes	—
520	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
521	#431	C₂²×C₃₁	1	1	yes	characteristic
522	#431	C₂²×C₃₁	1	2	yes	complemented
523	#427	C₂²×C₃₁	1	4	yes	complemented
524	C₂×#106	C₂²×C₃₁	1	2	yes	—
525	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
527	#416	C₂²×C₃₁	1	4	yes	—
528	C₂×#102	C₂²×C₃₁	1	2	yes	—
529	C₂×C₃₁	—	2	2	no	—
530	C₂×C₃₁	—	4	2	no	—
531	C₂×C₃₁	—	4	2	no	—
532	C₂×C₃₁	—	8	2	no	—
533	C₂×C₃₁	—	8	1	no	—
534	C₂×C₃₁	#3489	1	1	yes	characteristic
535	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
536	C₂×C₃₁	#3585	1	1	yes	characteristic
537	C₂×#41	—	2	1	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
540	C₂×#41	C₂³×C₃₁	1	2	yes	—
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂³×C₄	—	2	1	no	—
544	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
545	C₂×D₈	C₂³×C₃₁	1	2	yes	—
546	C₂×D₈	C₂³×C₃₁	1	2	yes	—
547	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
548	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
556	#127	C₂³×C₃₁	1	1	yes	characteristic
557	#126	—	2	2	no	—
558	#126	—	2	4	no	—
559	#126	—	2	2	no	—
560	#126	—	2	2	no	—
561	#125	—	2	2	no	—
562	#125	—	2	1	no	—
563	#125	C₂³×C₃₁	1	2	yes	—
564	#125	C₂³×C₃₁	1	4	yes	—
565	#124	—	2	2	no	—
566	#124	—	2	4	no	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	C₂³×C₃₁	1	2	yes	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	4	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
584	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
585	#121	—	2	1	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	1	no	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	C₂³×C₃₁	1	2	yes	—
593	#121	C₂³×C₃₁	1	2	yes	—
594	#121	C₂³×C₃₁	1	4	yes	—
595	#120	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
601	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	4	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
612	C₄×D₄	D₄×C₃₁	1	2	yes	—
613	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	2	yes	—
619	C₄×D₄	C₂³×C₃₁	1	4	yes	—
620	C₄×D₄	C₂³×C₃₁	1	2	yes	—
621	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₃₁	1	1	yes	characteristic
630	#117	D₄×C₃₁	1	2	yes	—
631	#117	C₂³×C₃₁	1	2	yes	—
632	#117	C₂³×C₃₁	1	4	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
644	#107	C₂³×C₃₁	1	2	yes	—
645	#107	C₂³×C₃₁	1	4	yes	—
646	#107	C₂³×C₃₁	1	2	yes	—
647	#107	C₂³×C₃₁	1	4	yes	—
648	#106	C₂³×C₃₁	1	4	yes	—
649	#106	C₂³×C₃₁	1	4	yes	—
650	#106	C₂³×C₃₁	1	4	yes	—
651	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
652	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
654	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
655	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
656	#103	C₂³×C₃₁	1	4	yes	—
657	#103	C₂³×C₃₁	1	4	yes	—
658	#103	C₂³×C₃₁	1	4	yes	—
659	#102	C₂³×C₃₁	1	4	yes	—
660	#102	C₂³×C₃₁	1	4	yes	—
661	#102	C₂³×C₃₁	1	2	yes	—
662	#102	C₂³×C₃₁	1	2	yes	—
663	#102	C₂³×C₃₁	1	2	yes	—
664	#102	C₂³×C₃₁	1	2	yes	—
665	#102	C₂³×C₃₁	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
668	C₄×C₈	C₂³×C₃₁	1	2	yes	—
669	C₄×C₈	C₂³×C₃₁	1	4	yes	—
670	C₃₁	#62098	1	1	yes	characteristic, direct product factor, Sylow
671	C₂⁴	—	2	1	no	—
672	#41	—	2	4	no	—
673	#41	—	2	4	no	—
674	#41	—	4	2	no	—
675	#41	—	4	4	no	—
676	#41	—	8	4	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	8	2	no	—
682	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
683	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
694	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
697	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	4	no	—
709	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
715	SD₁₆	—	4	4	no	—
716	D₈	—	2	4	no	—
717	D₈	—	4	2	no	—
718	C₂×C₈	—	4	4	no	—
719	C₂×C₈	—	4	2	no	—
720	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
721	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
722	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
741	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	4	no	—
771	C₄²	C₂×D₄×C₃₁	1	2	yes	—
772	C₄²	C₂×D₄×C₃₁	1	2	yes	—
773	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
776	C₄²	C₂⁴×C₃₁	1	2	yes	—
777	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	8	1	no	—
784	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
785	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	4	2	no	—
791	Q₈	—	8	1	no	—
792	Q₈	—	8	2	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	1	no	—
799	D₄	—	2	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	4	no	—
807	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	C₃₁×#135	1	4	yes	—
832	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
840	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
841	C₈	—	2	2	no	—
842	C₈	—	2	2	no	—
843	C₈	—	2	4	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	8	4	no	—
859	C₂²	C₂×C₃₁×#135	1	2	yes	—
860	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
861	C₄	—	2	2	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	4	no	—
872	C₄	—	4	2	no	—
873	C₄	C₂×C₃₁×#135	1	2	yes	—
874	C₄	C₂×C₃₁×#135	1	2	yes	—
875	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
876	C₄	C₃₁×#585	1	1	yes	characteristic
877	C₂	—	2	2	no	—
878	C₂	—	4	2	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	1	no	—
881	C₂	—	8	2	no	—
882	C₂	C₃₁×#3489	1	1	yes	characteristic
883	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
884	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3380	C₂	semidirect
4. C₃₁×#3360	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3337	C₂	semidirect
7. C₃₁×#3303	C₂	semidirect
8. C₃₁×#3297	C₂	semidirect
9. C₃₁×#3247	C₂	semidirect
10. C₃₁×#3246	C₂	semidirect
11. C₃₁×#3233	C₂	semidirect
12. C₃₁×#3230	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#3076	C₂	semidirect
16. C₂×C₃₁×#476	C₂	semidirect
17. C₃₁×#2988	C₂	semidirect
21. C₃₁×#555	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
36. C₃₁×#533	C₂²	semidirect
38. C₃₁×#532	C₂²	semidirect
48. C₃₁×#500	C₂²	semidirect
49. C₃₁×#499	C₂²	semidirect
51. C₃₁×#487	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
55. C₃₁×#482	C₂²	semidirect
57. C₃₁×#479	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
60. C₃₁×#477	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
66. C₃₁×#476	C₂²	semidirect
67. C₃₁×#475	C₂²	semidirect
72. C₃₁×#465	C₂²	semidirect
74. C₃₁×#461	C₂²	semidirect
75. C₃₁×#460	C₂²	semidirect
80. C₈×Q₈×C₃₁	C₂²	semidirect
81. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₈×D₄×C₃₁	C₂²	semidirect
88. C₃₁×#431	C₂²	semidirect
89. C₃₁×#427	C₂²	semidirect
92. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
335. #62098	C₃₁	direct (N × H)
402. #3511	C₂×C₃₁	semidirect
403. #3475	C₂×C₃₁	semidirect
404. #3380	C₂×C₃₁	semidirect
405. #3360	C₂×C₃₁	semidirect
406. #3341	C₂×C₃₁	semidirect
407. #3337	C₂×C₃₁	semidirect
408. #3303	C₂×C₃₁	semidirect
409. #3297	C₂×C₃₁	semidirect
410. #3247	C₂×C₃₁	semidirect
411. #3246	C₂×C₃₁	semidirect
412. #3233	C₂×C₃₁	semidirect
413. #3230	C₂×C₃₁	semidirect
414. #3106	C₂×C₃₁	semidirect
415. #3100	C₂×C₃₁	semidirect
416. #3076	C₂×C₃₁	semidirect
417. C₂×#476	C₂×C₃₁	semidirect
418. #2988	C₂×C₃₁	semidirect
455. #555	C₂²×C₃₁	semidirect
457. #554	C₂²×C₃₁	semidirect
470. #533	C₂²×C₃₁	semidirect
472. #532	C₂²×C₃₁	semidirect
482. #500	C₂²×C₃₁	semidirect
483. #499	C₂²×C₃₁	semidirect
485. #487	C₂²×C₃₁	semidirect
486. #485	C₂²×C₃₁	semidirect
489. #482	C₂²×C₃₁	semidirect
491. #479	C₂²×C₃₁	semidirect
493. #478	C₂²×C₃₁	semidirect
494. #477	C₂²×C₃₁	semidirect
495. #477	C₂²×C₃₁	semidirect
500. #476	C₂²×C₃₁	semidirect
501. #475	C₂²×C₃₁	semidirect
506. #465	C₂²×C₃₁	semidirect
508. #461	C₂²×C₃₁	semidirect
509. #460	C₂²×C₃₁	semidirect
514. C₈×Q₈	C₂²×C₃₁	semidirect
515. C₄×SD₁₆	C₂²×C₃₁	semidirect
520. C₈×D₄	C₂²×C₃₁	semidirect
522. #431	C₂²×C₃₁	semidirect
523. #427	C₂²×C₃₁	semidirect
526. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
670. C₃₁	#62098	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3511	2
C₃₁×#3475	2
C₃₁×#3380	2
C₃₁×#3360	2
C₃₁×#3341	2
C₃₁×#3337	2
C₃₁×#3303	2
C₃₁×#3297	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3233	2
C₃₁×#3230	2
C₃₁×#3106	2
C₃₁×#3100	2
C₃₁×#3076	2
C₂×C₃₁×#476	2
C₃₁×#2988	2
#62098	31

Subgroups — C31×#62098 #21518857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62098 #21518857