Subgroups — C₃₁×#61937 #21518696

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3396	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3362	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3358	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3224	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3118	C₂	1	4	yes	maximal, complemented
15	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#563	—	2	2	no	—
19	C₃₁×#559	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	2	yes	—
21	C₃₁×#559	C₂²	1	2	yes	complemented
22	Q₈²×C₃₁	C₂²	1	2	yes	complemented
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	C₂²	1	2	yes	complemented
25	C₃₁×#550	C₂²	1	2	yes	—
26	C₃₁×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₃₁	—	2	1	no	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#546	—	2	2	no	—
30	C₃₁×#546	—	2	2	no	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#542	C₂²	1	4	yes	—
33	C₃₁×#540	—	2	2	no	—
34	C₃₁×#536	—	2	2	no	—
35	C₃₁×#535	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	—	2	1	no	—
40	C₃₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
42	C₃₁×#518	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#496	C₂²	1	4	yes	complemented
45	C₃₁×#495	C₂²	1	4	yes	complemented
46	C₃₁×#493	C₂²	1	2	yes	—
47	C₃₁×#492	C₂²	1	2	yes	—
48	C₃₁×#489	C₂²	1	4	yes	complemented
49	C₃₁×#486	C₂²	1	2	yes	—
50	C₃₁×#486	C₂²	1	2	yes	—
51	C₃₁×#486	C₂²	1	4	yes	complemented
52	C₃₁×#485	C₂²	1	2	yes	—
53	C₃₁×#482	C₂²	1	2	yes	—
54	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#476	C₂²	1	4	yes	complemented
57	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#474	C₂²	1	4	yes	complemented
60	C₃₁×#464	C₂²	1	4	yes	complemented
61	C₃₁×#463	C₂²	1	4	yes	complemented
62	C₃₁×#463	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#460	C₂²	1	2	yes	—
67	C₃₁×#460	C₂²	1	2	yes	—
68	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#460	C₂²	1	4	yes	complemented
70	C₃₁×#459	C₂²	1	2	yes	—
71	C₃₁×#459	C₂²	1	2	yes	—
72	C₃₁×#459	C₂²	1	4	yes	complemented
73	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#452	C₂²	1	2	yes	—
75	C₃₁×#450	C₂²	1	4	yes	—
76	C₃₁×#449	C₂²	1	2	yes	—
77	C₃₁×#447	C₂²	1	4	yes	—
78	C₃₁×#446	C₂²	1	2	yes	complemented
79	C₃₁×#446	C₂²	1	2	yes	complemented
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
81	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
82	C₃₁×#442	C₂²	1	4	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
87	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
88	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
89	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
90	C₃₁×#433	C₂²	1	4	yes	—
91	C₃₁×#431	C₂²	1	1	yes	characteristic
92	C₃₁×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	—	2	2	no	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	—	2	2	no	—
98	C₂²×D₄×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂×D₈×C₃₁	C₂³	1	2	yes	—
108	C₂×D₈×C₃₁	C₂³	1	4	yes	—
109	C₃₁×C₄⋊Q₈	—	2	4	no	—
110	C₃₁×C₄⋊Q₈	—	2	2	no	—
111	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃₁×#127	—	2	1	no	—
118	C₃₁×#127	—	2	1	no	—
119	C₃₁×#127	C₂³	1	2	yes	—
120	C₃₁×#127	C₂³	1	4	yes	—
121	C₃₁×#127	C₂³	1	1	yes	characteristic
122	C₃₁×#127	C₂³	1	2	yes	—
123	C₃₁×#126	—	2	4	no	—
124	C₃₁×#126	—	2	4	no	—
125	C₃₁×#125	—	2	1	no	—
126	C₃₁×#125	D₄	1	2	yes	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	—	2	2	no	—
130	C₃₁×#124	—	2	4	no	—
131	C₃₁×#124	—	2	1	no	—
132	C₃₁×#124	C₂³	1	4	yes	—
133	C₃₁×#124	C₂³	1	4	yes	—
134	C₃₁×#123	—	2	4	no	—
135	C₃₁×#123	—	2	4	no	—
136	C₃₁×#123	—	2	4	no	—
137	C₃₁×#123	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	1	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×#121	—	2	1	no	—
147	C₃₁×#121	—	2	2	no	—
148	C₃₁×#121	—	2	2	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	2	no	—
151	C₃₁×#121	—	2	4	no	—
152	C₃₁×#121	—	2	4	no	—
153	C₃₁×#121	C₂³	1	2	yes	—
154	C₃₁×#120	—	2	4	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
159	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	2	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	2	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₃₁	C₂³	1	2	yes	—
173	C₄×D₄×C₃₁	C₂³	1	4	yes	—
174	C₄×D₄×C₃₁	C₂³	1	4	yes	—
175	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	C₂³	1	4	yes	—
177	C₃₁×#117	—	2	1	no	—
178	C₃₁×#117	—	2	2	no	—
179	C₃₁×#117	—	2	1	no	—
180	C₃₁×#117	C₂³	1	1	yes	characteristic
181	C₃₁×#117	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
183	C₂×C₄²×C₃₁	—	2	1	no	—
184	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
185	C₃₁×#107	C₂³	1	2	yes	—
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#106	C₂³	1	2	yes	—
188	C₃₁×#106	C₂³	1	2	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
194	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃₁×#103	C₂³	1	2	yes	—
196	C₃₁×#103	C₂³	1	2	yes	—
197	C₃₁×#103	C₂³	1	2	yes	—
198	C₃₁×#103	C₂³	1	2	yes	—
199	C₃₁×#102	C₂³	1	2	yes	—
200	C₃₁×#102	C₂³	1	2	yes	—
201	C₃₁×#102	C₂³	1	4	yes	—
202	C₃₁×#102	C₂³	1	2	yes	—
203	C₃₁×#102	C₂³	1	4	yes	—
204	C₃₁×#102	C₂³	1	2	yes	—
205	C₃₁×#102	C₂³	1	4	yes	—
206	C₃₁×#102	C₂³	1	4	yes	—
207	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₃₁×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₃₁	C₂³	1	2	yes	—
211	C₄×C₈×C₃₁	C₂³	1	2	yes	—
212	C₄×C₈×C₃₁	C₂³	1	4	yes	—
213	C₂⁴×C₃₁	—	2	2	no	—
214	#41×C₃₁	—	4	1	no	—
215	#41×C₃₁	—	4	1	no	—
216	#41×C₃₁	—	8	2	no	—
217	#41×C₃₁	—	8	4	no	—
218	#41×C₃₁	—	8	4	no	—
219	C₂×Q₈×C₃₁	—	2	1	no	—
220	C₂×Q₈×C₃₁	—	2	4	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	8	4	no	—
223	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
227	C₂×D₄×C₃₁	—	2	1	no	—
228	C₂×D₄×C₃₁	—	2	2	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	2	no	—
231	C₂×D₄×C₃₁	—	2	2	no	—
232	C₂×D₄×C₃₁	—	2	2	no	—
233	C₂×D₄×C₃₁	—	2	4	no	—
234	C₂×D₄×C₃₁	—	2	4	no	—
235	C₂×D₄×C₃₁	—	2	2	no	—
236	C₂×D₄×C₃₁	—	2	2	no	—
237	C₂×D₄×C₃₁	—	2	1	no	—
238	C₂×D₄×C₃₁	—	4	2	no	—
239	C₂×D₄×C₃₁	—	4	2	no	—
240	C₂×D₄×C₃₁	—	8	2	no	—
241	C₂×D₄×C₃₁	—	8	2	no	—
242	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₃₁	—	2	1	no	—
246	C₂²×C₄×C₃₁	—	2	1	no	—
247	C₂²×C₄×C₃₁	—	2	1	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	4	no	—
250	C₂²×C₄×C₃₁	—	2	4	no	—
251	C₂²×C₄×C₃₁	—	2	4	no	—
252	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	Q₁₆×C₃₁	—	4	2	no	—
256	SD₁₆×C₃₁	—	4	2	no	—
257	SD₁₆×C₃₁	—	4	4	no	—
258	SD₁₆×C₃₁	—	4	2	no	—
259	SD₁₆×C₃₁	—	4	4	no	—
260	D₈×C₃₁	—	4	4	no	—
261	D₈×C₃₁	—	4	4	no	—
262	D₈×C₃₁	—	4	2	no	—
263	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
264	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
265	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
266	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	4	no	—
276	C₄⋊C₄×C₃₁	—	2	2	no	—
277	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²⋊C₄×C₃₁	—	2	1	no	—
288	C₂²⋊C₄×C₃₁	—	2	2	no	—
289	C₂²⋊C₄×C₃₁	—	2	4	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	1	no	—
292	C₂²⋊C₄×C₃₁	—	2	1	no	—
293	C₂²⋊C₄×C₃₁	—	2	4	no	—
294	C₂²⋊C₄×C₃₁	—	2	4	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	—	2	2	no	—
297	C₂²⋊C₄×C₃₁	—	2	4	no	—
298	C₂²⋊C₄×C₃₁	—	2	2	no	—
299	C₂²⋊C₄×C₃₁	—	2	4	no	—
300	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
301	C₄²×C₃₁	—	2	1	no	—
302	C₄²×C₃₁	—	2	1	no	—
303	C₄²×C₃₁	—	2	1	no	—
304	C₄²×C₃₁	—	2	2	no	—
305	C₄²×C₃₁	—	2	4	no	—
306	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₃₁	C₂⁴	1	4	yes	—
311	#61937	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂³×C₃₁	—	2	2	no	—
313	C₂³×C₃₁	—	2	4	no	—
314	C₂³×C₃₁	—	2	1	no	—
315	C₂³×C₃₁	—	4	4	no	—
316	C₂³×C₃₁	—	8	2	no	—
317	C₂³×C₃₁	—	8	2	no	—
318	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₃₁	—	2	4	no	—
320	Q₈×C₃₁	—	2	4	no	—
321	Q₈×C₃₁	—	2	2	no	—
322	Q₈×C₃₁	—	2	2	no	—
323	Q₈×C₃₁	—	2	1	no	—
324	Q₈×C₃₁	—	2	1	no	—
325	Q₈×C₃₁	—	4	2	no	—
326	Q₈×C₃₁	—	8	4	no	—
327	Q₈×C₃₁	—	8	1	no	—
328	D₄×C₃₁	—	2	2	no	—
329	D₄×C₃₁	—	2	2	no	—
330	D₄×C₃₁	—	2	1	no	—
331	D₄×C₃₁	—	2	4	no	—
332	D₄×C₃₁	—	2	4	no	—
333	D₄×C₃₁	—	2	1	no	—
334	D₄×C₃₁	—	4	4	no	—
335	D₄×C₃₁	—	4	2	no	—
336	D₄×C₃₁	—	4	4	no	—
337	D₄×C₃₁	—	4	2	no	—
338	D₄×C₃₁	—	4	4	no	—
339	D₄×C₃₁	—	8	2	no	—
340	D₄×C₃₁	—	8	2	no	—
341	D₄×C₃₁	—	8	1	no	—
342	D₄×C₃₁	—	8	4	no	—
343	D₄×C₃₁	—	8	4	no	—
344	D₄×C₃₁	—	8	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	2	no	—
347	C₂×C₄×C₃₁	—	2	1	no	—
348	C₂×C₄×C₃₁	—	2	1	no	—
349	C₂×C₄×C₃₁	—	2	2	no	—
350	C₂×C₄×C₃₁	—	2	1	no	—
351	C₂×C₄×C₃₁	—	2	1	no	—
352	C₂×C₄×C₃₁	—	2	1	no	—
353	C₂×C₄×C₃₁	—	2	2	no	—
354	C₂×C₄×C₃₁	—	2	2	no	—
355	C₂×C₄×C₃₁	—	4	2	no	—
356	C₂×C₄×C₃₁	—	4	4	no	—
357	C₂×C₄×C₃₁	—	4	2	no	—
358	C₂×C₄×C₃₁	—	4	2	no	—
359	C₂×C₄×C₃₁	—	8	4	no	—
360	C₂×C₄×C₃₁	—	8	4	no	—
361	C₂×C₄×C₃₁	—	8	4	no	—
362	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
370	C₈×C₃₁	—	2	2	no	—
371	C₈×C₃₁	—	2	2	no	—
372	C₈×C₃₁	—	2	2	no	—
373	C₈×C₃₁	—	2	2	no	—
374	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
375	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
376	#3399	C₂×C₃₁	1	2	yes	complemented
377	#3397	C₂×C₃₁	1	2	yes	complemented
378	#3396	C₂×C₃₁	1	2	yes	complemented
379	#3394	C₂×C₃₁	1	2	yes	complemented
380	#3375	C₂×C₃₁	1	2	yes	complemented
381	#3373	C₂×C₃₁	1	2	yes	complemented
382	#3362	C₂×C₃₁	1	2	yes	complemented
383	#3358	C₂×C₃₁	1	2	yes	complemented
384	#3224	C₂×C₃₁	1	4	yes	complemented
385	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
386	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
387	#3118	C₂×C₃₁	1	4	yes	complemented
388	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
389	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
390	#2986	C₂×C₃₁	1	1	yes	characteristic, complemented
391	C₂²×C₃₁	—	2	1	no	—
392	C₂²×C₃₁	—	2	1	no	—
393	C₂²×C₃₁	—	2	1	no	—
394	C₂²×C₃₁	—	4	1	no	—
395	C₂²×C₃₁	—	4	4	no	—
396	C₂²×C₃₁	—	4	2	no	—
397	C₂²×C₃₁	—	4	2	no	—
398	C₂²×C₃₁	—	4	1	no	—
399	C₂²×C₃₁	—	4	4	no	—
400	C₂²×C₃₁	—	4	1	no	—
401	C₂²×C₃₁	—	4	4	no	—
402	C₂²×C₃₁	—	4	2	no	—
403	C₂²×C₃₁	—	16	4	no	—
404	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
405	C₄×C₃₁	—	2	1	no	—
406	C₄×C₃₁	—	2	1	no	—
407	C₄×C₃₁	—	2	4	no	—
408	C₄×C₃₁	—	2	1	no	—
409	C₄×C₃₁	—	2	4	no	—
410	C₄×C₃₁	—	4	1	no	—
411	C₄×C₃₁	—	4	2	no	—
412	C₄×C₃₁	—	4	1	no	—
413	C₄×C₃₁	—	4	2	no	—
414	C₄×C₃₁	—	4	2	no	—
415	C₄×C₃₁	—	4	1	no	—
416	C₄×C₃₁	#576	1	2	yes	—
417	C₄×C₃₁	#577	1	2	yes	—
418	C₄×C₃₁	#585	1	1	yes	characteristic
419	C₄×C₃₁	#585	1	1	yes	characteristic
420	#563	—	2	2	no	—
421	#559	C₂²×C₃₁	1	2	yes	—
422	#559	C₂²×C₃₁	1	2	yes	—
423	#559	C₂²×C₃₁	1	2	yes	complemented
424	Q₈²	C₂²×C₃₁	1	2	yes	complemented
425	#556	—	2	1	no	—
426	#556	C₂²×C₃₁	1	2	yes	complemented
427	#550	C₂²×C₃₁	1	2	yes	—
428	#550	C₂²×C₃₁	1	2	yes	—
429	D₄×Q₈	—	2	1	no	—
430	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
431	#546	—	2	2	no	—
432	#546	—	2	2	no	—
433	#542	—	2	2	no	—
434	#542	C₂²×C₃₁	1	4	yes	—
435	#540	—	2	2	no	—
436	#536	—	2	2	no	—
437	#535	C₂²×C₃₁	1	2	yes	—
438	#533	C₂²×C₃₁	1	1	yes	characteristic
439	#533	C₂²×C₃₁	1	1	yes	characteristic
440	#532	—	2	1	no	—
441	#532	—	2	1	no	—
442	#532	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
444	#518	C₂²×C₃₁	1	2	yes	—
445	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
446	#496	C₂²×C₃₁	1	4	yes	complemented
447	#495	C₂²×C₃₁	1	4	yes	complemented
448	#493	C₂²×C₃₁	1	2	yes	—
449	#492	C₂²×C₃₁	1	2	yes	—
450	#489	C₂²×C₃₁	1	4	yes	complemented
451	#486	C₂²×C₃₁	1	2	yes	—
452	#486	C₂²×C₃₁	1	2	yes	—
453	#486	C₂²×C₃₁	1	4	yes	complemented
454	#485	C₂²×C₃₁	1	2	yes	—
455	#482	C₂²×C₃₁	1	2	yes	—
456	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
457	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	#476	C₂²×C₃₁	1	4	yes	complemented
459	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	#474	C₂²×C₃₁	1	4	yes	complemented
462	#464	C₂²×C₃₁	1	4	yes	complemented
463	#463	C₂²×C₃₁	1	4	yes	complemented
464	#463	C₂²×C₃₁	1	4	yes	complemented
465	#463	C₂²×C₃₁	1	4	yes	complemented
466	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
468	#460	C₂²×C₃₁	1	2	yes	—
469	#460	C₂²×C₃₁	1	2	yes	—
470	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	#460	C₂²×C₃₁	1	4	yes	complemented
472	#459	C₂²×C₃₁	1	2	yes	—
473	#459	C₂²×C₃₁	1	2	yes	—
474	#459	C₂²×C₃₁	1	4	yes	complemented
475	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
476	#452	C₂²×C₃₁	1	2	yes	—
477	#450	C₂²×C₃₁	1	4	yes	—
478	#449	C₂²×C₃₁	1	2	yes	—
479	#447	C₂²×C₃₁	1	4	yes	—
480	#446	C₂²×C₃₁	1	2	yes	complemented
481	#446	C₂²×C₃₁	1	2	yes	complemented
482	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
483	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
484	#442	C₂²×C₃₁	1	4	yes	complemented
485	#440	C₂²×C₃₁	1	4	yes	complemented
486	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
487	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
488	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
489	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
490	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
491	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
492	#433	C₂²×C₃₁	1	4	yes	—
493	#431	C₂²×C₃₁	1	1	yes	characteristic
494	#431	C₂²×C₃₁	1	1	yes	characteristic
495	C₂×C₃₁	—	4	1	no	—
496	C₂×C₃₁	—	8	1	no	—
497	C₂×C₃₁	—	8	2	no	—
498	C₂×C₃₁	—	8	4	no	—
499	C₂×C₃₁	#3487	1	1	yes	characteristic
500	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
501	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
510	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
511	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
512	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
513	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
514	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
515	C₂×D₈	C₂³×C₃₁	1	4	yes	—
516	C₂×D₈	C₂³×C₃₁	1	2	yes	—
517	C₂×D₈	C₂³×C₃₁	1	4	yes	—
518	C₄⋊Q₈	—	2	4	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
521	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
526	#127	—	2	1	no	—
527	#127	—	2	1	no	—
528	#127	C₂³×C₃₁	1	2	yes	—
529	#127	C₂³×C₃₁	1	2	yes	—
530	#127	C₂³×C₃₁	1	1	yes	characteristic
531	#127	C₂³×C₃₁	1	4	yes	—
532	#126	—	2	4	no	—
533	#126	—	2	4	no	—
534	#125	—	2	1	no	—
535	#125	D₄×C₃₁	1	2	yes	—
536	#124	—	2	2	no	—
537	#124	—	2	2	no	—
538	#124	—	2	2	no	—
539	#124	—	2	4	no	—
540	#124	—	2	1	no	—
541	#124	C₂³×C₃₁	1	4	yes	—
542	#124	C₂³×C₃₁	1	4	yes	—
543	#123	—	2	4	no	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
553	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
554	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
555	#121	—	2	1	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	4	no	—
561	#121	—	2	4	no	—
562	#121	C₂³×C₃₁	1	2	yes	—
563	#120	—	2	4	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
567	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
568	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
569	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
570	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
571	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₃₁	1	4	yes	—
583	C₄×D₄	C₂³×C₃₁	1	4	yes	—
584	C₄×D₄	C₂³×C₃₁	1	2	yes	—
585	C₄×D₄	C₂³×C₃₁	1	4	yes	—
586	#117	—	2	1	no	—
587	#117	—	2	2	no	—
588	#117	—	2	1	no	—
589	#117	C₂³×C₃₁	1	1	yes	characteristic
590	#117	C₂³×C₃₁	1	2	yes	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
594	#107	C₂³×C₃₁	1	2	yes	—
595	#107	C₂³×C₃₁	1	2	yes	—
596	#106	C₂³×C₃₁	1	2	yes	—
597	#106	C₂³×C₃₁	1	2	yes	—
598	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
602	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
603	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
604	#103	C₂³×C₃₁	1	2	yes	—
605	#103	C₂³×C₃₁	1	2	yes	—
606	#103	C₂³×C₃₁	1	2	yes	—
607	#103	C₂³×C₃₁	1	2	yes	—
608	#102	C₂³×C₃₁	1	2	yes	—
609	#102	C₂³×C₃₁	1	2	yes	—
610	#102	C₂³×C₃₁	1	4	yes	—
611	#102	C₂³×C₃₁	1	2	yes	—
612	#102	C₂³×C₃₁	1	4	yes	—
613	#102	C₂³×C₃₁	1	2	yes	—
614	#102	C₂³×C₃₁	1	4	yes	—
615	#102	C₂³×C₃₁	1	4	yes	—
616	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
617	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
618	#97	C₂³×C₃₁	1	4	yes	—
619	C₄×C₈	C₂³×C₃₁	1	2	yes	—
620	C₄×C₈	C₂³×C₃₁	1	2	yes	—
621	C₄×C₈	C₂³×C₃₁	1	4	yes	—
622	C₃₁	#61937	1	1	yes	characteristic, direct product factor, Sylow
623	C₂⁴	—	2	2	no	—
624	#41	—	4	1	no	—
625	#41	—	4	1	no	—
626	#41	—	8	2	no	—
627	#41	—	8	4	no	—
628	#41	—	8	4	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	4	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	8	4	no	—
633	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
634	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
635	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
636	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	8	2	no	—
651	C₂×D₄	—	8	2	no	—
652	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
653	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
665	Q₁₆	—	4	2	no	—
666	SD₁₆	—	4	2	no	—
667	SD₁₆	—	4	4	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	4	no	—
670	D₈	—	4	4	no	—
671	D₈	—	4	4	no	—
672	D₈	—	4	2	no	—
673	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
674	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
675	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
676	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
688	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
691	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
692	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
693	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
696	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	4	no	—
716	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
719	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₄²	C₂⁴×C₃₁	1	4	yes	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	8	2	no	—
726	C₂³	—	8	2	no	—
727	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	Q₈	—	2	4	no	—
729	Q₈	—	2	4	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	1	no	—
733	Q₈	—	2	1	no	—
734	Q₈	—	4	2	no	—
735	Q₈	—	8	4	no	—
736	Q₈	—	8	1	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	1	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	2	1	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	8	2	no	—
749	D₄	—	8	2	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	D₄	—	8	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
776	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
778	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	—	2	2	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	4	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	16	4	no	—
796	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	4	no	—
800	C₄	—	2	1	no	—
801	C₄	—	2	4	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	1	no	—
808	C₄	C₃₁×#576	1	2	yes	—
809	C₄	C₃₁×#577	1	2	yes	—
810	C₄	C₃₁×#585	1	1	yes	characteristic
811	C₄	C₃₁×#585	1	1	yes	characteristic
812	C₂	—	4	1	no	—
813	C₂	—	8	4	no	—
814	C₂	—	8	1	no	—
815	C₂	—	8	2	no	—
816	C₂	C₃₁×#3487	1	1	yes	characteristic
817	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
818	C₂	C₂×C₃₁×#577	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 ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3397	C₂	semidirect
5. C₃₁×#3396	C₂	semidirect
6. C₃₁×#3394	C₂	semidirect
7. C₃₁×#3375	C₂	semidirect
8. C₃₁×#3373	C₂	semidirect
9. C₃₁×#3362	C₂	semidirect
10. C₃₁×#3358	C₂	semidirect
11. C₃₁×#3224	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3205	C₂	semidirect
14. C₃₁×#3118	C₂	semidirect
15. C₃₁×#3107	C₂	semidirect
16. C₃₁×#3106	C₂	semidirect
17. C₃₁×#2986	C₂	semidirect
21. C₃₁×#559	C₂²	semidirect
22. Q₈²×C₃₁	C₂²	semidirect
24. C₃₁×#556	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
44. C₃₁×#496	C₂²	semidirect
45. C₃₁×#495	C₂²	semidirect
48. C₃₁×#489	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
54. C₃₁×#477	C₂²	semidirect
55. C₃₁×#476	C₂²	semidirect
56. C₃₁×#476	C₂²	semidirect
57. C₃₁×#475	C₂²	semidirect
58. C₃₁×#474	C₂²	semidirect
59. C₃₁×#474	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#463	C₂²	semidirect
62. C₃₁×#463	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#462	C₂²	semidirect
65. C₃₁×#461	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
69. C₃₁×#460	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#459	C₂²	semidirect
78. C₃₁×#446	C₂²	semidirect
79. C₃₁×#446	C₂²	semidirect
80. C₈×Q₈×C₃₁	C₂²	semidirect
81. C₈×Q₈×C₃₁	C₂²	semidirect
82. C₃₁×#442	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₄×Q₁₆×C₃₁	C₂²	semidirect
85. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₄×SD₁₆×C₃₁	C₂²	semidirect
87. C₄×SD₁₆×C₃₁	C₂²	semidirect
88. C₄×D₈×C₃₁	C₂²	semidirect
89. C₄×D₈×C₃₁	C₂²	semidirect
311. #61937	C₃₁	direct (N × H)
374. #3550	C₂×C₃₁	semidirect
375. #3508	C₂×C₃₁	semidirect
376. #3399	C₂×C₃₁	semidirect
377. #3397	C₂×C₃₁	semidirect
378. #3396	C₂×C₃₁	semidirect
379. #3394	C₂×C₃₁	semidirect
380. #3375	C₂×C₃₁	semidirect
381. #3373	C₂×C₃₁	semidirect
382. #3362	C₂×C₃₁	semidirect
383. #3358	C₂×C₃₁	semidirect
384. #3224	C₂×C₃₁	semidirect
385. #3208	C₂×C₃₁	semidirect
386. #3205	C₂×C₃₁	semidirect
387. #3118	C₂×C₃₁	semidirect
388. #3107	C₂×C₃₁	semidirect
389. #3106	C₂×C₃₁	semidirect
390. #2986	C₂×C₃₁	semidirect
423. #559	C₂²×C₃₁	semidirect
424. Q₈²	C₂²×C₃₁	semidirect
426. #556	C₂²×C₃₁	semidirect
430. D₄×Q₈	C₂²×C₃₁	semidirect
446. #496	C₂²×C₃₁	semidirect
447. #495	C₂²×C₃₁	semidirect
450. #489	C₂²×C₃₁	semidirect
453. #486	C₂²×C₃₁	semidirect
456. #477	C₂²×C₃₁	semidirect
457. #476	C₂²×C₃₁	semidirect
458. #476	C₂²×C₃₁	semidirect
459. #475	C₂²×C₃₁	semidirect
460. #474	C₂²×C₃₁	semidirect
461. #474	C₂²×C₃₁	semidirect
462. #464	C₂²×C₃₁	semidirect
463. #463	C₂²×C₃₁	semidirect
464. #463	C₂²×C₃₁	semidirect
465. #463	C₂²×C₃₁	semidirect
466. #462	C₂²×C₃₁	semidirect
467. #461	C₂²×C₃₁	semidirect
470. #460	C₂²×C₃₁	semidirect
471. #460	C₂²×C₃₁	semidirect
474. #459	C₂²×C₃₁	semidirect
475. #459	C₂²×C₃₁	semidirect
480. #446	C₂²×C₃₁	semidirect
481. #446	C₂²×C₃₁	semidirect
482. C₈×Q₈	C₂²×C₃₁	semidirect
483. C₈×Q₈	C₂²×C₃₁	semidirect
484. #442	C₂²×C₃₁	semidirect
485. #440	C₂²×C₃₁	semidirect
486. C₄×Q₁₆	C₂²×C₃₁	semidirect
487. C₄×SD₁₆	C₂²×C₃₁	semidirect
488. C₄×SD₁₆	C₂²×C₃₁	semidirect
489. C₄×SD₁₆	C₂²×C₃₁	semidirect
490. C₄×D₈	C₂²×C₃₁	semidirect
491. C₄×D₈	C₂²×C₃₁	semidirect
622. C₃₁	#61937	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×#3550	2
C₃₁×#3508	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3396	2
C₃₁×#3394	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3362	2
C₃₁×#3358	2
C₃₁×#3224	2
C₃₁×#3208	2
C₃₁×#3205	2
C₃₁×#3118	2
C₃₁×#3107	2
C₃₁×#3106	2
C₃₁×#2986	2
#61937	31

Subgroups — C31×#61937 #21518696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61937 #21518696