Subgroups — C₃₁×#61965 #21518724

Order 7936.

1888 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3314	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3216	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3112	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3037	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#559	C₂²	1	2	yes	—
22	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#554	—	2	2	no	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#550	—	2	1	no	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	4	yes	—
35	C₃₁×#540	—	2	2	no	—
36	C₃₁×#535	—	2	1	no	—
37	C₃₁×#533	—	2	1	no	—
38	C₃₁×#533	—	2	2	no	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic
40	C₃₁×#533	C₂²	1	1	yes	characteristic
41	C₃₁×#533	C₂²	1	2	yes	complemented
42	C₃₁×#532	C₂²	1	2	yes	—
43	C₃₁×#532	C₂²	1	2	yes	—
44	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
45	C₃₁×#518	—	2	1	no	—
46	C₄×#41×C₃₁	—	2	1	no	—
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#497	C₂²	1	4	yes	complemented
51	C₃₁×#492	C₂²	1	2	yes	—
52	C₃₁×#489	C₂²	1	4	yes	complemented
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	2	yes	—
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#477	C₂²	1	2	yes	complemented
57	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#477	C₂²	1	2	yes	complemented
60	C₃₁×#474	C₂²	1	4	yes	complemented
61	C₃₁×#468	C₂²	1	4	yes	complemented
62	C₃₁×#468	C₂²	1	4	yes	complemented
63	C₃₁×#467	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	complemented
65	C₃₁×#464	C₂²	1	4	yes	complemented
66	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#462	C₂²	1	2	yes	complemented
69	C₃₁×#462	C₂²	1	2	yes	complemented
70	C₃₁×#461	C₂²	1	4	yes	complemented
71	C₃₁×#460	C₂²	1	2	yes	—
72	C₃₁×#460	C₂²	1	2	yes	—
73	C₃₁×#460	C₂²	1	2	yes	—
74	C₃₁×#460	C₂²	1	2	yes	—
75	C₃₁×#460	C₂²	1	2	yes	—
76	C₃₁×#460	C₂²	1	2	yes	—
77	C₃₁×#452	C₂²	1	4	yes	complemented
78	C₃₁×#452	C₂²	1	4	yes	complemented
79	C₃₁×#451	C₂²	1	2	yes	—
80	C₃₁×#450	C₂²	1	4	yes	—
81	C₃₁×#448	C₂²	1	4	yes	complemented
82	C₃₁×#446	C₂²	1	2	yes	complemented
83	C₃₁×#440	C₂²	1	4	yes	complemented
84	C₃₁×#440	C₂²	1	4	yes	complemented
85	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
86	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
87	C₃₁×#436	C₂²	1	2	yes	complemented
88	C₃₁×#435	C₂²	1	4	yes	—
89	C₃₁×#432	C₂²	1	2	yes	complemented
90	C₃₁×#431	C₂²	1	1	yes	characteristic
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₃₁×#417	C₂²	1	4	yes	complemented
94	C₂×C₃₁×#102	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	2	no	—
96	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	4	yes	—
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₃₁×#137	—	4	8	no	—
104	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₃₁	—	4	4	no	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
112	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
113	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	—	2	2	no	—
115	C₃₁×C₄⋊Q₈	—	2	1	no	—
116	C₃₁×C₄⋊Q₈	—	2	1	no	—
117	C₃₁×C₄⋊Q₈	—	2	2	no	—
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₃₁×#127	—	2	2	no	—
125	C₃₁×#127	—	2	1	no	—
126	C₃₁×#127	—	2	1	no	—
127	C₃₁×#127	C₂³	1	2	yes	—
128	C₃₁×#127	C₂³	1	2	yes	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	2	no	—
132	C₃₁×#125	—	2	1	no	—
133	C₃₁×#125	—	2	1	no	—
134	C₃₁×#125	—	2	1	no	—
135	C₃₁×#125	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	—	2	2	no	—
138	C₃₁×#124	C₂³	1	4	yes	—
139	C₃₁×#123	—	2	4	no	—
140	C₃₁×#123	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	1	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	—	2	2	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#121	—	2	2	no	—
155	C₃₁×#121	—	2	2	no	—
156	C₃₁×#121	—	2	2	no	—
157	C₃₁×#121	—	2	4	no	—
158	C₃₁×#121	—	2	4	no	—
159	C₃₁×#121	C₂³	1	4	yes	—
160	C₃₁×#120	—	2	4	no	—
161	C₄×Q₈×C₃₁	—	2	1	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	1	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	—	2	2	no	—
166	C₄×Q₈×C₃₁	—	2	2	no	—
167	C₄×Q₈×C₃₁	—	2	1	no	—
168	C₄×Q₈×C₃₁	—	2	2	no	—
169	C₄×Q₈×C₃₁	—	2	1	no	—
170	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
174	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
175	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
176	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
179	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	—	2	2	no	—
183	C₄×D₄×C₃₁	—	2	1	no	—
184	C₄×D₄×C₃₁	—	2	2	no	—
185	C₄×D₄×C₃₁	—	2	2	no	—
186	C₄×D₄×C₃₁	—	2	2	no	—
187	C₄×D₄×C₃₁	—	2	2	no	—
188	C₄×D₄×C₃₁	—	2	2	no	—
189	C₄×D₄×C₃₁	D₄	1	2	yes	—
190	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
191	C₄×D₄×C₃₁	C₂³	1	4	yes	—
192	C₄×D₄×C₃₁	C₂³	1	2	yes	—
193	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₃₁×#117	—	2	1	no	—
195	C₃₁×#117	—	2	2	no	—
196	C₃₁×#117	—	2	1	no	—
197	C₃₁×#117	D₄	1	1	yes	characteristic
198	C₃₁×#117	D₄	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂×C₄²×C₃₁	—	2	1	no	—
205	C₂×C₄²×C₃₁	—	2	2	no	—
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
208	C₃₁×#107	C₂³	1	2	yes	—
209	C₃₁×#107	C₂³	1	2	yes	—
210	C₃₁×#107	C₂³	1	4	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
215	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#103	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃₁×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₃₁	C₂³	1	2	yes	—
230	C₂⁴×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	4	4	no	—
234	#41×C₃₁	—	8	4	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	2	1	no	—
240	C₂×Q₈×C₃₁	—	2	2	no	—
241	C₂×Q₈×C₃₁	—	2	4	no	—
242	C₂×Q₈×C₃₁	—	4	1	no	—
243	C₂×Q₈×C₃₁	—	4	2	no	—
244	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₃₁	—	2	4	no	—
250	C₂×D₄×C₃₁	—	2	4	no	—
251	C₂×D₄×C₃₁	—	2	2	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	2	no	—
254	C₂×D₄×C₃₁	—	2	2	no	—
255	C₂×D₄×C₃₁	—	2	2	no	—
256	C₂×D₄×C₃₁	—	4	2	no	—
257	C₂×D₄×C₃₁	—	4	2	no	—
258	C₂×D₄×C₃₁	—	4	4	no	—
259	C₂×D₄×C₃₁	—	8	2	no	—
260	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	1	no	—
267	C₂²×C₄×C₃₁	—	2	4	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	Q₁₆×C₃₁	—	2	4	no	—
276	Q₁₆×C₃₁	—	4	2	no	—
277	Q₁₆×C₃₁	—	4	4	no	—
278	SD₁₆×C₃₁	—	2	8	no	—
279	SD₁₆×C₃₁	—	4	4	no	—
280	SD₁₆×C₃₁	—	4	4	no	—
281	SD₁₆×C₃₁	—	4	4	no	—
282	M₁₆×C₃₁	—	4	4	no	—
283	C₂×C₈×C₃₁	—	4	2	no	—
284	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
285	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	1	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	—	2	2	no	—
301	C₄⋊C₄×C₃₁	—	2	1	no	—
302	C₄⋊C₄×C₃₁	—	2	1	no	—
303	C₄⋊C₄×C₃₁	—	2	2	no	—
304	C₄⋊C₄×C₃₁	—	2	2	no	—
305	C₄⋊C₄×C₃₁	—	2	1	no	—
306	C₄⋊C₄×C₃₁	—	2	2	no	—
307	C₄⋊C₄×C₃₁	—	2	2	no	—
308	C₄⋊C₄×C₃₁	—	2	2	no	—
309	C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₂²⋊C₄×C₃₁	—	2	4	no	—
323	C₂²⋊C₄×C₃₁	—	2	4	no	—
324	C₂²⋊C₄×C₃₁	—	2	4	no	—
325	C₂²⋊C₄×C₃₁	—	2	4	no	—
326	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	—	2	1	no	—
330	C₄²×C₃₁	—	2	1	no	—
331	C₄²×C₃₁	—	2	2	no	—
332	C₄²×C₃₁	—	2	2	no	—
333	C₄²×C₃₁	—	2	1	no	—
334	C₄²×C₃₁	—	2	2	no	—
335	C₄²×C₃₁	—	2	1	no	—
336	C₄²×C₃₁	—	2	2	no	—
337	C₄²×C₃₁	C₂×D₄	1	2	yes	—
338	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₃₁	C₂×D₄	1	2	yes	—
340	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₄²×C₃₁	C₂⁴	1	2	yes	—
343	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
344	#61965	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂³×C₃₁	—	2	4	no	—
346	C₂³×C₃₁	—	4	4	no	—
347	C₂³×C₃₁	—	8	2	no	—
348	C₂³×C₃₁	—	8	2	no	—
349	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
350	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	Q₈×C₃₁	—	2	2	no	—
352	Q₈×C₃₁	—	2	1	no	—
353	Q₈×C₃₁	—	2	1	no	—
354	Q₈×C₃₁	—	2	2	no	—
355	Q₈×C₃₁	—	2	2	no	—
356	Q₈×C₃₁	—	2	2	no	—
357	Q₈×C₃₁	—	2	1	no	—
358	Q₈×C₃₁	—	2	2	no	—
359	Q₈×C₃₁	—	4	4	no	—
360	Q₈×C₃₁	—	4	2	no	—
361	Q₈×C₃₁	—	4	2	no	—
362	Q₈×C₃₁	—	8	2	no	—
363	Q₈×C₃₁	—	8	1	no	—
364	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
365	D₄×C₃₁	—	2	4	no	—
366	D₄×C₃₁	—	2	2	no	—
367	D₄×C₃₁	—	2	4	no	—
368	D₄×C₃₁	—	2	4	no	—
369	D₄×C₃₁	—	4	4	no	—
370	D₄×C₃₁	—	4	4	no	—
371	D₄×C₃₁	—	4	4	no	—
372	D₄×C₃₁	—	8	2	no	—
373	D₄×C₃₁	—	8	2	no	—
374	D₄×C₃₁	—	8	4	no	—
375	D₄×C₃₁	—	8	4	no	—
376	C₂×C₄×C₃₁	—	2	1	no	—
377	C₂×C₄×C₃₁	—	2	4	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	2	no	—
380	C₂×C₄×C₃₁	—	2	1	no	—
381	C₂×C₄×C₃₁	—	2	2	no	—
382	C₂×C₄×C₃₁	—	2	1	no	—
383	C₂×C₄×C₃₁	—	2	1	no	—
384	C₂×C₄×C₃₁	—	2	2	no	—
385	C₂×C₄×C₃₁	—	2	1	no	—
386	C₂×C₄×C₃₁	—	2	2	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	2	no	—
389	C₂×C₄×C₃₁	—	4	1	no	—
390	C₂×C₄×C₃₁	—	4	2	no	—
391	C₂×C₄×C₃₁	—	4	2	no	—
392	C₂×C₄×C₃₁	—	4	4	no	—
393	C₂×C₄×C₃₁	—	8	4	no	—
394	C₂×C₄×C₃₁	—	8	4	no	—
395	C₂×C₄×C₃₁	—	8	1	no	—
396	C₂×C₄×C₃₁	—	8	2	no	—
397	C₂×C₄×C₃₁	#137	1	4	yes	complemented
398	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
407	C₈×C₃₁	—	2	4	no	—
408	C₈×C₃₁	—	2	2	no	—
409	C₈×C₃₁	—	2	2	no	—
410	#3508	C₂×C₃₁	1	1	yes	characteristic
411	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3400	C₂×C₃₁	1	2	yes	complemented
413	#3375	C₂×C₃₁	1	2	yes	complemented
414	#3333	C₂×C₃₁	1	2	yes	complemented
415	#3314	C₂×C₃₁	1	4	yes	complemented
416	#3278	C₂×C₃₁	1	2	yes	complemented
417	#3266	C₂×C₃₁	1	4	yes	complemented
418	#3254	C₂×C₃₁	1	2	yes	complemented
419	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#3216	C₂×C₃₁	1	2	yes	complemented
421	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3112	C₂×C₃₁	1	2	yes	complemented
423	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
424	#3037	C₂×C₃₁	1	2	yes	complemented
425	C₂×#460	C₂×C₃₁	1	1	yes	characteristic, complemented
426	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	2	2	no	—
432	C₂²×C₃₁	—	4	4	no	—
433	C₂²×C₃₁	—	4	4	no	—
434	C₂²×C₃₁	—	4	4	no	—
435	C₂²×C₃₁	—	16	4	no	—
436	C₂²×C₃₁	C₂×#137	1	2	yes	—
437	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
443	C₄×C₃₁	—	2	2	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	4	1	no	—
446	C₄×C₃₁	—	4	2	no	—
447	C₄×C₃₁	—	4	1	no	—
448	C₄×C₃₁	—	4	2	no	—
449	C₄×C₃₁	—	4	1	no	—
450	C₄×C₃₁	—	4	2	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	C₂×#137	1	2	yes	—
453	C₄×C₃₁	C₂×#137	1	2	yes	—
454	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₄×C₃₁	#585	1	1	yes	characteristic
456	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
457	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
458	#559	—	2	1	no	—
459	#559	C₂²×C₃₁	1	2	yes	—
460	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	#557	—	2	1	no	—
462	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	#554	—	2	2	no	—
464	#554	—	2	1	no	—
465	#554	C₂²×C₃₁	1	2	yes	—
466	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
467	#550	—	2	1	no	—
468	#550	C₂²×C₃₁	1	2	yes	—
469	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
470	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
471	#546	—	2	2	no	—
472	#546	C₂²×C₃₁	1	4	yes	—
473	#540	—	2	2	no	—
474	#535	—	2	1	no	—
475	#533	—	2	1	no	—
476	#533	—	2	2	no	—
477	#533	C₂²×C₃₁	1	1	yes	characteristic
478	#533	C₂²×C₃₁	1	1	yes	characteristic
479	#533	C₂²×C₃₁	1	2	yes	complemented
480	#532	C₂²×C₃₁	1	2	yes	—
481	#532	C₂²×C₃₁	1	2	yes	—
482	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
483	#518	—	2	1	no	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
486	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
488	#497	C₂²×C₃₁	1	4	yes	complemented
489	#492	C₂²×C₃₁	1	2	yes	—
490	#489	C₂²×C₃₁	1	4	yes	complemented
491	#486	C₂²×C₃₁	1	2	yes	—
492	#484	C₂²×C₃₁	1	2	yes	—
493	#480	C₂²×C₃₁	1	4	yes	complemented
494	#477	C₂²×C₃₁	1	2	yes	complemented
495	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	#477	C₂²×C₃₁	1	2	yes	complemented
498	#474	C₂²×C₃₁	1	4	yes	complemented
499	#468	C₂²×C₃₁	1	4	yes	complemented
500	#468	C₂²×C₃₁	1	4	yes	complemented
501	#467	C₂²×C₃₁	1	4	yes	—
502	#464	C₂²×C₃₁	1	4	yes	complemented
503	#464	C₂²×C₃₁	1	4	yes	complemented
504	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
505	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
506	#462	C₂²×C₃₁	1	2	yes	complemented
507	#462	C₂²×C₃₁	1	2	yes	complemented
508	#461	C₂²×C₃₁	1	4	yes	complemented
509	#460	C₂²×C₃₁	1	2	yes	—
510	#460	C₂²×C₃₁	1	2	yes	—
511	#460	C₂²×C₃₁	1	2	yes	—
512	#460	C₂²×C₃₁	1	2	yes	—
513	#460	C₂²×C₃₁	1	2	yes	—
514	#460	C₂²×C₃₁	1	2	yes	—
515	#452	C₂²×C₃₁	1	4	yes	complemented
516	#452	C₂²×C₃₁	1	4	yes	complemented
517	#451	C₂²×C₃₁	1	2	yes	—
518	#450	C₂²×C₃₁	1	4	yes	—
519	#448	C₂²×C₃₁	1	4	yes	complemented
520	#446	C₂²×C₃₁	1	2	yes	complemented
521	#440	C₂²×C₃₁	1	4	yes	complemented
522	#440	C₂²×C₃₁	1	4	yes	complemented
523	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
524	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
525	#436	C₂²×C₃₁	1	2	yes	complemented
526	#435	C₂²×C₃₁	1	4	yes	—
527	#432	C₂²×C₃₁	1	2	yes	complemented
528	#431	C₂²×C₃₁	1	1	yes	characteristic
529	#423	C₂²×C₃₁	1	2	yes	complemented
530	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
531	#417	C₂²×C₃₁	1	4	yes	complemented
532	C₂×#102	C₂²×C₃₁	1	2	yes	—
533	C₂×C₃₁	—	2	2	no	—
534	C₂×C₃₁	—	4	2	no	—
535	C₂×C₃₁	—	8	4	no	—
536	C₂×C₃₁	#3488	1	1	yes	characteristic
537	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
538	C₂×C₃₁	#3585	1	1	yes	characteristic
539	C₂×#41	—	2	2	no	—
540	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
541	C₂×#41	C₂³×C₃₁	1	4	yes	—
542	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
547	#137	—	4	8	no	—
548	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
549	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
550	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
551	C₂×SD₁₆	—	4	4	no	—
552	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
556	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
557	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
558	C₄⋊Q₈	—	2	2	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
567	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
568	#127	—	2	2	no	—
569	#127	—	2	1	no	—
570	#127	—	2	1	no	—
571	#127	C₂³×C₃₁	1	2	yes	—
572	#127	C₂³×C₃₁	1	2	yes	—
573	#125	—	2	1	no	—
574	#125	—	2	2	no	—
575	#125	—	2	2	no	—
576	#125	—	2	1	no	—
577	#125	—	2	1	no	—
578	#125	—	2	1	no	—
579	#125	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₃₁	1	4	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
597	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
598	#121	—	2	2	no	—
599	#121	—	2	2	no	—
600	#121	—	2	2	no	—
601	#121	—	2	4	no	—
602	#121	—	2	4	no	—
603	#121	C₂³×C₃₁	1	4	yes	—
604	#120	—	2	4	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
620	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
621	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
622	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	D₄×C₃₁	1	2	yes	—
634	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₃₁	1	4	yes	—
636	C₄×D₄	C₂³×C₃₁	1	2	yes	—
637	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	1	no	—
641	#117	D₄×C₃₁	1	1	yes	characteristic
642	#117	D₄×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
647	C₂×C₂²⋊C₄	—	2	4	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	2	no	—
650	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
652	#107	C₂³×C₃₁	1	2	yes	—
653	#107	C₂³×C₃₁	1	2	yes	—
654	#107	C₂³×C₃₁	1	4	yes	—
655	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
656	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
658	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
660	#103	C₂³×C₃₁	1	2	yes	—
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	2	yes	—
663	#103	C₂³×C₃₁	1	2	yes	—
664	#103	C₂³×C₃₁	1	2	yes	—
665	#103	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	4	yes	—
667	#102	C₂³×C₃₁	1	4	yes	—
668	#102	C₂³×C₃₁	1	4	yes	—
669	#102	C₂³×C₃₁	1	4	yes	—
670	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
672	#97	C₂³×C₃₁	1	4	yes	—
673	C₄×C₈	C₂³×C₃₁	1	2	yes	—
674	C₃₁	#61965	1	1	yes	characteristic, direct product factor, Sylow
675	C₂⁴	—	2	2	no	—
676	#41	—	2	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	8	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	4	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
690	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
693	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	8	2	no	—
705	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
715	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	Q₁₆	—	2	4	no	—
721	Q₁₆	—	4	2	no	—
722	Q₁₆	—	4	4	no	—
723	SD₁₆	—	2	8	no	—
724	SD₁₆	—	4	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	M₁₆	—	4	4	no	—
728	C₂×C₈	—	4	2	no	—
729	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
730	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
759	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
762	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	2	no	—
782	C₄²	C₂×D₄×C₃₁	1	2	yes	—
783	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
784	C₄²	C₂×D₄×C₃₁	1	2	yes	—
785	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₄²	C₂⁴×C₃₁	1	2	yes	—
788	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂³	—	2	4	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	8	2	no	—
792	C₂³	—	8	2	no	—
793	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
794	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	4	no	—
804	Q₈	—	4	2	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	8	2	no	—
807	Q₈	—	8	1	no	—
808	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	D₄	—	8	4	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	C₃₁×#137	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	4	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	16	4	no	—
863	C₂²	C₂×C₃₁×#137	1	2	yes	—
864	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	C₂×C₃₁×#137	1	2	yes	—
880	C₄	C₂×C₃₁×#137	1	2	yes	—
881	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
882	C₄	C₃₁×#585	1	1	yes	characteristic
883	C₂	—	2	2	no	—
884	C₂	—	4	2	no	—
885	C₂	—	8	4	no	—
886	C₂	C₃₁×#3488	1	1	yes	characteristic
887	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
888	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3508	C₂
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
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3375	C₂	semidirect
5. C₃₁×#3333	C₂	semidirect
6. C₃₁×#3314	C₂	semidirect
7. C₃₁×#3278	C₂	semidirect
8. C₃₁×#3266	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3249	C₂	semidirect
11. C₃₁×#3216	C₂	semidirect
12. C₃₁×#3208	C₂	semidirect
13. C₃₁×#3112	C₂	semidirect
14. C₃₁×#3104	C₂	semidirect
15. C₃₁×#3037	C₂	semidirect
16. C₂×C₃₁×#460	C₂	semidirect
17. C₃₁×#2989	C₂	semidirect
18. C₂×C₃₁×#137	C₂²	semidirect
22. Q₈²×C₃₁	C₂²	semidirect
24. C₃₁×#557	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
32. D₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#533	C₂²	semidirect
49. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
50. C₃₁×#497	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
59. C₃₁×#477	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#468	C₂²	semidirect
62. C₃₁×#468	C₂²	semidirect
64. C₃₁×#464	C₂²	semidirect
65. C₃₁×#464	C₂²	semidirect
66. C₃₁×#462	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#462	C₂²	semidirect
69. C₃₁×#462	C₂²	semidirect
70. C₃₁×#461	C₂²	semidirect
77. C₃₁×#452	C₂²	semidirect
78. C₃₁×#452	C₂²	semidirect
81. C₃₁×#448	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₃₁×#440	C₂²	semidirect
84. C₃₁×#440	C₂²	semidirect
85. C₄×Q₁₆×C₃₁	C₂²	semidirect
86. C₄×Q₁₆×C₃₁	C₂²	semidirect
87. C₃₁×#436	C₂²	semidirect
89. C₃₁×#432	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
93. C₃₁×#417	C₂²	semidirect
344. #61965	C₃₁	direct (N × H)
397. C₂×C₄×C₃₁	#137	semidirect
411. Q₈×#41	C₂×C₃₁	semidirect
412. #3400	C₂×C₃₁	semidirect
413. #3375	C₂×C₃₁	semidirect
414. #3333	C₂×C₃₁	semidirect
415. #3314	C₂×C₃₁	semidirect
416. #3278	C₂×C₃₁	semidirect
417. #3266	C₂×C₃₁	semidirect
418. #3254	C₂×C₃₁	semidirect
419. #3249	C₂×C₃₁	semidirect
420. #3216	C₂×C₃₁	semidirect
421. #3208	C₂×C₃₁	semidirect
422. #3112	C₂×C₃₁	semidirect
423. #3104	C₂×C₃₁	semidirect
424. #3037	C₂×C₃₁	semidirect
425. C₂×#460	C₂×C₃₁	semidirect
426. #2989	C₂×C₃₁	semidirect
456. C₂×#137	C₂²×C₃₁	semidirect
460. Q₈²	C₂²×C₃₁	semidirect
462. #557	C₂²×C₃₁	semidirect
466. #554	C₂²×C₃₁	semidirect
470. D₄×Q₈	C₂²×C₃₁	semidirect
479. #533	C₂²×C₃₁	semidirect
487. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
488. #497	C₂²×C₃₁	semidirect
490. #489	C₂²×C₃₁	semidirect
493. #480	C₂²×C₃₁	semidirect
494. #477	C₂²×C₃₁	semidirect
495. #477	C₂²×C₃₁	semidirect
496. #477	C₂²×C₃₁	semidirect
497. #477	C₂²×C₃₁	semidirect
498. #474	C₂²×C₃₁	semidirect
499. #468	C₂²×C₃₁	semidirect
500. #468	C₂²×C₃₁	semidirect
502. #464	C₂²×C₃₁	semidirect
503. #464	C₂²×C₃₁	semidirect
504. #462	C₂²×C₃₁	semidirect
505. #462	C₂²×C₃₁	semidirect
506. #462	C₂²×C₃₁	semidirect
507. #462	C₂²×C₃₁	semidirect
508. #461	C₂²×C₃₁	semidirect
515. #452	C₂²×C₃₁	semidirect
516. #452	C₂²×C₃₁	semidirect
519. #448	C₂²×C₃₁	semidirect
520. #446	C₂²×C₃₁	semidirect
521. #440	C₂²×C₃₁	semidirect
522. #440	C₂²×C₃₁	semidirect
523. C₄×Q₁₆	C₂²×C₃₁	semidirect
524. C₄×Q₁₆	C₂²×C₃₁	semidirect
525. #436	C₂²×C₃₁	semidirect
527. #432	C₂²×C₃₁	semidirect
529. #423	C₂²×C₃₁	semidirect
531. #417	C₂²×C₃₁	semidirect
674. C₃₁	#61965	direct (N × H)
841. C₂×C₄	C₃₁×#137	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3508	2
Q₈×#41×C₃₁	2
C₃₁×#3400	2
C₃₁×#3375	2
C₃₁×#3333	2
C₃₁×#3314	2
C₃₁×#3278	2
C₃₁×#3266	2
C₃₁×#3254	2
C₃₁×#3249	2
C₃₁×#3216	2
C₃₁×#3208	2
C₃₁×#3112	2
C₃₁×#3104	2
C₃₁×#3037	2
C₂×C₃₁×#460	2
C₃₁×#2989	2
#61965	31

Subgroups — C31×#61965 #21518724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61965 #21518724