Subgroups — C₃₁×#61835 #21518594

Order 7936.

1800 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3380	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3234	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#559	C₂²	1	2	yes	complemented
20	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	—	2	1	no	—
23	C₃₁×#554	—	2	2	no	—
24	C₃₁×#554	C₂²	1	2	yes	—
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	4	yes	—
27	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	2	yes	complemented
29	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#547	—	2	1	no	—
32	C₃₁×#547	—	2	2	no	—
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#542	—	2	1	no	—
35	C₃₁×#532	C₂²	1	2	yes	—
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₃₁×#529	C₂²	1	1	yes	characteristic
39	C₃₁×#529	C₂²	1	2	yes	—
40	C₂×C₃₁×#125	C₂²	1	2	yes	—
41	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
43	C₃₁×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
48	C₃₁×#501	C₂²	1	4	yes	complemented
49	C₃₁×#501	C₂²	1	2	yes	complemented
50	C₃₁×#500	C₂²	1	2	yes	complemented
51	C₃₁×#499	C₂²	1	4	yes	complemented
52	C₃₁×#490	C₂²	1	4	yes	complemented
53	C₃₁×#489	C₂²	1	2	yes	complemented
54	C₃₁×#488	C₂²	1	4	yes	complemented
55	C₃₁×#486	C₂²	1	2	yes	complemented
56	C₃₁×#484	C₂²	1	1	yes	characteristic
57	C₃₁×#483	C₂²	1	2	yes	—
58	C₃₁×#481	C₂²	1	1	yes	characteristic
59	C₃₁×#481	C₂²	1	2	yes	—
60	C₃₁×#480	C₂²	1	2	yes	—
61	C₃₁×#480	C₂²	1	2	yes	—
62	C₃₁×#480	C₂²	1	2	yes	—
63	C₃₁×#479	C₂²	1	4	yes	complemented
64	C₃₁×#478	C₂²	1	2	yes	—
65	C₃₁×#478	C₂²	1	4	yes	—
66	C₃₁×#478	C₂²	1	4	yes	complemented
67	C₃₁×#478	C₂²	1	4	yes	complemented
68	C₃₁×#478	C₂²	1	4	yes	complemented
69	C₃₁×#477	C₂²	1	2	yes	complemented
70	C₃₁×#476	C₂²	1	2	yes	—
71	C₃₁×#476	C₂²	1	2	yes	complemented
72	C₃₁×#474	C₂²	1	4	yes	—
73	C₃₁×#474	C₂²	1	4	yes	complemented
74	C₃₁×#463	C₂²	1	2	yes	—
75	C₃₁×#463	C₂²	1	4	yes	—
76	C₃₁×#459	C₂²	1	4	yes	—
77	C₃₁×#459	C₂²	1	2	yes	—
78	C₃₁×#450	C₂²	1	1	yes	characteristic
79	C₃₁×#447	C₂²	1	1	yes	characteristic
80	C₃₁×#447	C₂²	1	2	yes	—
81	C₃₁×#446	C₂²	1	2	yes	complemented
82	C₃₁×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
84	C₃₁×#442	C₂²	1	4	yes	—
85	C₃₁×#442	C₂²	1	4	yes	—
86	C₃₁×#440	C₂²	1	4	yes	—
87	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
88	C₄×D₈×C₃₁	C₂²	1	4	yes	—
89	C₄×D₈×C₃₁	C₂²	1	4	yes	—
90	C₄×D₈×C₃₁	C₂²	1	2	yes	—
91	C₃₁×#432	C₂²	1	1	yes	characteristic
92	C₃₁×#432	C₂²	1	2	yes	—
93	C₃₁×#431	C₂²	1	2	yes	—
94	C₃₁×#431	C₂²	1	1	yes	characteristic
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	—	2	1	no	—
102	C₂³×C₄×C₃₁	—	2	2	no	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×D₈×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	4	yes	—
106	C₃₁×C₄⋊Q₈	—	2	1	no	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×#127	C₂³	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	2	yes	—
116	C₃₁×#126	—	2	2	no	—
117	C₃₁×#126	—	2	1	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	C₂³	1	2	yes	—
121	C₃₁×#125	C₂³	1	1	yes	characteristic
122	C₃₁×#125	C₂³	1	4	yes	—
123	C₃₁×#125	C₂³	1	4	yes	—
124	C₃₁×#124	—	2	1	no	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	2	no	—
127	C₃₁×#124	—	2	1	no	—
128	C₃₁×#124	C₂³	1	2	yes	—
129	C₃₁×#124	C₂³	1	1	yes	characteristic
130	C₃₁×#123	—	2	1	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	4	no	—
138	C₃₁×C₂²⋊Q₈	—	2	1	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	no	—
140	C₃₁×C₂²⋊Q₈	—	2	4	no	—
141	C₃₁×C₂²⋊Q₈	—	2	4	no	—
142	C₃₁×C₂²⋊Q₈	—	2	4	no	—
143	C₃₁×C₂²⋊Q₈	—	2	4	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	C₂³	1	1	yes	characteristic
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	—	2	1	no	—
151	C₃₁×#121	—	2	2	no	—
152	C₃₁×#121	C₂³	1	1	yes	characteristic
153	C₃₁×#121	C₂³	1	2	yes	—
154	C₄×Q₈×C₃₁	—	2	1	no	—
155	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
156	C₄×Q₈×C₃₁	D₄	1	2	yes	—
157	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	—	2	1	no	—
164	C₄×D₄×C₃₁	—	2	2	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	2	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	2	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	C₂³	1	4	yes	—
174	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₃₁	C₂³	1	2	yes	—
176	C₄×D₄×C₃₁	C₂³	1	2	yes	—
177	C₄×D₄×C₃₁	C₂³	1	2	yes	—
178	C₄×D₄×C₃₁	C₂³	1	4	yes	—
179	C₄×D₄×C₃₁	C₂³	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	2	yes	—
182	C₃₁×#117	—	2	2	no	—
183	C₃₁×#117	—	2	1	no	—
184	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
185	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
186	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
187	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
188	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
189	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
190	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
200	C₃₁×#107	C₂³	1	4	yes	—
201	C₃₁×#107	C₂³	1	4	yes	—
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#106	C₂³	1	2	yes	—
205	C₃₁×#106	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#102	C₂³	1	2	yes	—
214	C₃₁×#102	C₂³	1	4	yes	—
215	C₃₁×#102	C₂³	1	2	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	4	yes	—
218	C₃₁×#102	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	4	yes	—
225	C₃₁×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₃₁	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	C₂⁴×C₃₁	—	2	1	no	—
229	#41×C₃₁	—	4	4	no	—
230	#41×C₃₁	—	8	4	no	—
231	#41×C₃₁	—	8	2	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	1	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	4	2	no	—
237	C₂×Q₈×C₃₁	—	8	2	no	—
238	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
241	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	1	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	1	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₃₁	—	2	1	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	2	no	—
257	C₂²×C₄×C₃₁	—	2	2	no	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	4	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	2	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	4	4	no	—
265	C₂²×C₄×C₃₁	—	8	4	no	—
266	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
271	SD₁₆×C₃₁	—	2	4	no	—
272	D₈×C₃₁	—	2	4	no	—
273	D₈×C₃₁	—	2	8	no	—
274	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	—	2	4	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	1	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	4	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	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²⋊C₄×C₃₁	—	2	1	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	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	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	1	no	—
324	C₄²×C₃₁	C₂×D₄	1	2	yes	—
325	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₃₁	C₂⁴	1	2	yes	—
329	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₄²×C₃₁	C₂⁴	1	2	yes	—
332	#61835	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂³×C₃₁	—	2	4	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	4	2	no	—
338	C₂³×C₃₁	—	4	2	no	—
339	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	2	no	—
343	Q₈×C₃₁	—	4	2	no	—
344	Q₈×C₃₁	—	8	2	no	—
345	Q₈×C₃₁	—	8	2	no	—
346	Q₈×C₃₁	—	8	2	no	—
347	Q₈×C₃₁	—	8	1	no	—
348	D₄×C₃₁	—	2	4	no	—
349	D₄×C₃₁	—	2	2	no	—
350	D₄×C₃₁	—	2	2	no	—
351	D₄×C₃₁	—	2	4	no	—
352	D₄×C₃₁	—	4	4	no	—
353	D₄×C₃₁	—	4	2	no	—
354	D₄×C₃₁	—	4	4	no	—
355	D₄×C₃₁	—	4	2	no	—
356	D₄×C₃₁	—	8	2	no	—
357	D₄×C₃₁	—	8	1	no	—
358	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
359	C₂×C₄×C₃₁	—	2	4	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	1	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	4	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	4	4	no	—
371	C₂×C₄×C₃₁	—	4	4	no	—
372	C₂×C₄×C₃₁	—	4	2	no	—
373	C₂×C₄×C₃₁	—	4	4	no	—
374	C₂×C₄×C₃₁	—	4	4	no	—
375	C₂×C₄×C₃₁	—	4	2	no	—
376	C₂×C₄×C₃₁	—	8	4	no	—
377	C₂×C₄×C₃₁	—	8	4	no	—
378	C₂×C₄×C₃₁	—	8	2	no	—
379	C₂×C₄×C₃₁	—	8	2	no	—
380	C₂×C₄×C₃₁	—	8	2	no	—
381	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
391	C₈×C₃₁	—	2	2	no	—
392	C₈×C₃₁	—	2	4	no	—
393	C₈×C₃₁	—	2	2	no	—
394	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
395	C₂×#554	C₂×C₃₁	1	1	yes	characteristic, complemented
396	#3389	C₂×C₃₁	1	4	yes	complemented
397	#3385	C₂×C₃₁	1	2	yes	complemented
398	#3380	C₂×C₃₁	1	2	yes	complemented
399	#3370	C₂×C₃₁	1	4	yes	complemented
400	#3366	C₂×C₃₁	1	2	yes	complemented
401	#3361	C₂×C₃₁	1	2	yes	complemented
402	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#3234	C₂×C₃₁	1	2	yes	complemented
404	#3232	C₂×C₃₁	1	2	yes	complemented
405	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
406	#3114	C₂×C₃₁	1	2	yes	complemented
407	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3100	C₂×C₃₁	1	2	yes	complemented
410	#2984	C₂×C₃₁	1	1	yes	characteristic, complemented
411	C₂²×C₃₁	—	2	1	no	—
412	C₂²×C₃₁	—	2	1	no	—
413	C₂²×C₃₁	—	2	4	no	—
414	C₂²×C₃₁	—	4	8	no	—
415	C₂²×C₃₁	—	4	2	no	—
416	C₂²×C₃₁	—	4	2	no	—
417	C₂²×C₃₁	—	4	2	no	—
418	C₂²×C₃₁	—	4	1	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	1	no	—
421	C₂²×C₃₁	—	4	1	no	—
422	C₂²×C₃₁	—	4	2	no	—
423	C₂²×C₃₁	#576	1	2	yes	—
424	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₃₁	—	2	1	no	—
426	C₄×C₃₁	—	2	1	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	2	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	2	1	no	—
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	4	1	no	—
434	C₄×C₃₁	—	4	1	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	4	no	—
437	C₄×C₃₁	—	4	1	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	#575	1	2	yes	—
440	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
441	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
442	#559	C₂²×C₃₁	1	2	yes	complemented
443	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	#554	—	2	1	no	—
445	#554	—	2	1	no	—
446	#554	—	2	2	no	—
447	#554	C₂²×C₃₁	1	2	yes	—
448	#554	C₂²×C₃₁	1	2	yes	—
449	#554	C₂²×C₃₁	1	4	yes	—
450	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	#554	C₂²×C₃₁	1	2	yes	complemented
452	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	#548	—	2	1	no	—
454	#547	—	2	1	no	—
455	#547	—	2	2	no	—
456	#542	—	2	2	no	—
457	#542	—	2	1	no	—
458	#532	C₂²×C₃₁	1	2	yes	—
459	#532	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
461	#529	C₂²×C₃₁	1	1	yes	characteristic
462	#529	C₂²×C₃₁	1	2	yes	—
463	C₂×#125	C₂²×C₃₁	1	2	yes	—
464	C₂×C₂²⋊Q₈	—	2	1	no	—
465	C₂×C₂²⋊Q₈	—	2	2	no	—
466	#520	—	2	1	no	—
467	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
470	C₂²×C₄⋊C₄	—	2	1	no	—
471	#501	C₂²×C₃₁	1	4	yes	complemented
472	#501	C₂²×C₃₁	1	2	yes	complemented
473	#500	C₂²×C₃₁	1	2	yes	complemented
474	#499	C₂²×C₃₁	1	4	yes	complemented
475	#490	C₂²×C₃₁	1	4	yes	complemented
476	#489	C₂²×C₃₁	1	2	yes	complemented
477	#488	C₂²×C₃₁	1	4	yes	complemented
478	#486	C₂²×C₃₁	1	2	yes	complemented
479	#484	C₂²×C₃₁	1	1	yes	characteristic
480	#483	C₂²×C₃₁	1	2	yes	—
481	#481	C₂²×C₃₁	1	1	yes	characteristic
482	#481	C₂²×C₃₁	1	2	yes	—
483	#480	C₂²×C₃₁	1	2	yes	—
484	#480	C₂²×C₃₁	1	2	yes	—
485	#480	C₂²×C₃₁	1	2	yes	—
486	#479	C₂²×C₃₁	1	4	yes	complemented
487	#478	C₂²×C₃₁	1	2	yes	—
488	#478	C₂²×C₃₁	1	4	yes	—
489	#478	C₂²×C₃₁	1	4	yes	complemented
490	#478	C₂²×C₃₁	1	4	yes	complemented
491	#478	C₂²×C₃₁	1	4	yes	complemented
492	#477	C₂²×C₃₁	1	2	yes	complemented
493	#476	C₂²×C₃₁	1	2	yes	—
494	#476	C₂²×C₃₁	1	2	yes	complemented
495	#474	C₂²×C₃₁	1	4	yes	—
496	#474	C₂²×C₃₁	1	4	yes	complemented
497	#463	C₂²×C₃₁	1	2	yes	—
498	#463	C₂²×C₃₁	1	4	yes	—
499	#459	C₂²×C₃₁	1	4	yes	—
500	#459	C₂²×C₃₁	1	2	yes	—
501	#450	C₂²×C₃₁	1	1	yes	characteristic
502	#447	C₂²×C₃₁	1	1	yes	characteristic
503	#447	C₂²×C₃₁	1	2	yes	—
504	#446	C₂²×C₃₁	1	2	yes	complemented
505	#446	C₂²×C₃₁	1	4	yes	complemented
506	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
507	#442	C₂²×C₃₁	1	4	yes	—
508	#442	C₂²×C₃₁	1	4	yes	—
509	#440	C₂²×C₃₁	1	4	yes	—
510	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
511	C₄×D₈	C₂²×C₃₁	1	4	yes	—
512	C₄×D₈	C₂²×C₃₁	1	4	yes	—
513	C₄×D₈	C₂²×C₃₁	1	2	yes	—
514	#432	C₂²×C₃₁	1	1	yes	characteristic
515	#432	C₂²×C₃₁	1	2	yes	—
516	#431	C₂²×C₃₁	1	2	yes	—
517	#431	C₂²×C₃₁	1	1	yes	characteristic
518	C₂×C₃₁	—	2	2	no	—
519	C₂×C₃₁	—	4	4	no	—
520	C₂×C₃₁	—	8	2	no	—
521	C₂×C₃₁	—	8	1	no	—
522	C₂×C₃₁	#3486	1	1	yes	characteristic
523	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
524	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	2	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	2	no	—
533	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
534	C₂×D₈	C₂³×C₃₁	1	2	yes	—
535	C₂×D₈	C₂³×C₃₁	1	4	yes	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
544	#127	C₂³×C₃₁	1	1	yes	characteristic
545	#127	C₂³×C₃₁	1	2	yes	—
546	#126	—	2	2	no	—
547	#126	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	C₂³×C₃₁	1	4	yes	—
551	#125	C₂³×C₃₁	1	4	yes	—
552	#125	C₂³×C₃₁	1	2	yes	—
553	#125	C₂³×C₃₁	1	1	yes	characteristic
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	1	no	—
558	#124	C₂³×C₃₁	1	2	yes	—
559	#124	C₂³×C₃₁	1	1	yes	characteristic
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	#123	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	2	no	—
582	#121	C₂³×C₃₁	1	1	yes	characteristic
583	#121	C₂³×C₃₁	1	2	yes	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₃₁	1	2	yes	—
587	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	C₂³×C₃₁	1	4	yes	—
604	C₄×D₄	C₂³×C₃₁	1	2	yes	—
605	C₄×D₄	C₂³×C₃₁	1	4	yes	—
606	C₄×D₄	C₂³×C₃₁	1	2	yes	—
607	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₃₁	1	2	yes	—
609	C₄×D₄	C₂³×C₃₁	1	2	yes	—
610	C₄×D₄	C₂³×C₃₁	1	2	yes	—
611	C₄×D₄	C₂³×C₃₁	1	2	yes	—
612	#117	—	2	2	no	—
613	#117	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	4	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	2	no	—
622	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
623	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
629	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
630	#107	C₂³×C₃₁	1	4	yes	—
631	#107	C₂³×C₃₁	1	4	yes	—
632	#107	C₂³×C₃₁	1	2	yes	—
633	#107	C₂³×C₃₁	1	4	yes	—
634	#106	C₂³×C₃₁	1	2	yes	—
635	#106	C₂³×C₃₁	1	4	yes	—
636	#106	C₂³×C₃₁	1	4	yes	—
637	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
638	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
639	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
640	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
641	#103	C₂³×C₃₁	1	2	yes	—
642	#103	C₂³×C₃₁	1	4	yes	—
643	#102	C₂³×C₃₁	1	2	yes	—
644	#102	C₂³×C₃₁	1	4	yes	—
645	#102	C₂³×C₃₁	1	2	yes	—
646	#102	C₂³×C₃₁	1	4	yes	—
647	#102	C₂³×C₃₁	1	4	yes	—
648	#102	C₂³×C₃₁	1	2	yes	—
649	#102	C₂³×C₃₁	1	4	yes	—
650	#102	C₂³×C₃₁	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
652	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
654	#97	C₂³×C₃₁	1	4	yes	—
655	#97	C₂³×C₃₁	1	2	yes	—
656	C₄×C₈	C₂³×C₃₁	1	4	yes	—
657	C₄×C₈	C₂³×C₃₁	1	2	yes	—
658	C₃₁	#61835	1	1	yes	characteristic, direct product factor, Sylow
659	C₂⁴	—	2	1	no	—
660	#41	—	4	4	no	—
661	#41	—	8	4	no	—
662	#41	—	8	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	8	2	no	—
669	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
670	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
682	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	8	4	no	—
697	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
702	SD₁₆	—	2	4	no	—
703	D₈	—	2	4	no	—
704	D₈	—	2	8	no	—
705	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
706	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
707	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
730	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
734	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	1	no	—
755	C₄²	C₂×D₄×C₃₁	1	2	yes	—
756	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
757	C₄²	C₂×D₄×C₃₁	1	2	yes	—
758	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
759	C₄²	C₂⁴×C₃₁	1	2	yes	—
760	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
761	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
762	C₄²	C₂⁴×C₃₁	1	2	yes	—
763	C₂³	—	2	4	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	2	no	—
769	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	8	2	no	—
775	Q₈	—	8	2	no	—
776	Q₈	—	8	2	no	—
777	Q₈	—	8	1	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	2	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	1	no	—
788	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	4	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
820	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	4	no	—
823	C₈	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	4	8	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	C₃₁×#576	1	2	yes	—
837	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	C₃₁×#575	1	2	yes	—
853	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
854	C₂	—	2	2	no	—
855	C₂	—	4	4	no	—
856	C₂	—	8	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₃₁×#3486	1	1	yes	characteristic
859	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
860	C₂	C₂×C₃₁×#576	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 ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3522	C₂	semidirect
2. C₂×C₃₁×#554	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3380	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3366	C₂	semidirect
8. C₃₁×#3361	C₂	semidirect
9. C₃₁×#3238	C₂	semidirect
10. C₃₁×#3234	C₂	semidirect
11. C₃₁×#3232	C₂	semidirect
12. C₃₁×#3226	C₂	semidirect
13. C₃₁×#3114	C₂	semidirect
14. C₃₁×#3109	C₂	semidirect
15. C₃₁×#3105	C₂	semidirect
16. C₃₁×#3100	C₂	semidirect
17. C₃₁×#2984	C₂	semidirect
18. C₃₁×#559	C₂²	semidirect
19. C₃₁×#559	C₂²	semidirect
20. Q₈²×C₃₁	C₂²	semidirect
27. C₃₁×#554	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#550	C₂²	semidirect
48. C₃₁×#501	C₂²	semidirect
49. C₃₁×#501	C₂²	semidirect
50. C₃₁×#500	C₂²	semidirect
51. C₃₁×#499	C₂²	semidirect
52. C₃₁×#490	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
55. C₃₁×#486	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#477	C₂²	semidirect
71. C₃₁×#476	C₂²	semidirect
73. C₃₁×#474	C₂²	semidirect
81. C₃₁×#446	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₈×Q₈×C₃₁	C₂²	semidirect
332. #61835	C₃₁	direct (N × H)
394. #3522	C₂×C₃₁	semidirect
395. C₂×#554	C₂×C₃₁	semidirect
396. #3389	C₂×C₃₁	semidirect
397. #3385	C₂×C₃₁	semidirect
398. #3380	C₂×C₃₁	semidirect
399. #3370	C₂×C₃₁	semidirect
400. #3366	C₂×C₃₁	semidirect
401. #3361	C₂×C₃₁	semidirect
402. #3238	C₂×C₃₁	semidirect
403. #3234	C₂×C₃₁	semidirect
404. #3232	C₂×C₃₁	semidirect
405. #3226	C₂×C₃₁	semidirect
406. #3114	C₂×C₃₁	semidirect
407. #3109	C₂×C₃₁	semidirect
408. #3105	C₂×C₃₁	semidirect
409. #3100	C₂×C₃₁	semidirect
410. #2984	C₂×C₃₁	semidirect
441. #559	C₂²×C₃₁	semidirect
442. #559	C₂²×C₃₁	semidirect
443. Q₈²	C₂²×C₃₁	semidirect
450. #554	C₂²×C₃₁	semidirect
451. #554	C₂²×C₃₁	semidirect
452. #550	C₂²×C₃₁	semidirect
471. #501	C₂²×C₃₁	semidirect
472. #501	C₂²×C₃₁	semidirect
473. #500	C₂²×C₃₁	semidirect
474. #499	C₂²×C₃₁	semidirect
475. #490	C₂²×C₃₁	semidirect
476. #489	C₂²×C₃₁	semidirect
477. #488	C₂²×C₃₁	semidirect
478. #486	C₂²×C₃₁	semidirect
486. #479	C₂²×C₃₁	semidirect
489. #478	C₂²×C₃₁	semidirect
490. #478	C₂²×C₃₁	semidirect
491. #478	C₂²×C₃₁	semidirect
492. #477	C₂²×C₃₁	semidirect
494. #476	C₂²×C₃₁	semidirect
496. #474	C₂²×C₃₁	semidirect
504. #446	C₂²×C₃₁	semidirect
505. #446	C₂²×C₃₁	semidirect
506. C₈×Q₈	C₂²×C₃₁	semidirect
658. C₃₁	#61835	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×#3522	2
C₂×C₃₁×#554	2
C₃₁×#3389	2
C₃₁×#3385	2
C₃₁×#3380	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3238	2
C₃₁×#3234	2
C₃₁×#3232	2
C₃₁×#3226	2
C₃₁×#3114	2
C₃₁×#3109	2
C₃₁×#3105	2
C₃₁×#3100	2
C₃₁×#2984	2
#61835	31

Subgroups — C31×#61835 #21518594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61835 #21518594