Subgroups — C₃₁×#61873 #21518632

Order 7936.

1666 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3386	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3118	C₂	1	2	yes	maximal
17	C₃₁×#3114	C₂	1	1	yes	maximal, characteristic
18	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
23	C₃₁×#557	C₂²	1	2	yes	complemented
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#556	C₂²	1	2	yes	complemented
26	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#554	—	2	1	no	—
28	C₃₁×#554	—	2	2	no	—
29	C₃₁×#554	C₂²	1	2	yes	—
30	C₃₁×#554	C₂²	1	2	yes	—
31	C₃₁×#554	C₂²	1	2	yes	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#552	—	2	1	no	—
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	C₂²	1	2	yes	—
38	C₃₁×#543	—	2	1	no	—
39	C₃₁×#543	—	2	1	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#541	—	2	1	no	—
42	C₃₁×#541	—	2	2	no	—
43	C₃₁×#541	C₂²	1	2	yes	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
49	C₃₁×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#501	C₂²	1	2	yes	complemented
53	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#501	C₂²	1	2	yes	complemented
55	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#500	C₂²	1	2	yes	complemented
57	C₃₁×#499	C₂²	1	2	yes	complemented
58	C₃₁×#491	C₂²	1	2	yes	complemented
59	C₃₁×#491	C₂²	1	2	yes	complemented
60	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	complemented
62	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#487	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	1	yes	characteristic
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#480	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#477	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	2	yes	complemented
84	C₃₁×#476	C₂²	1	2	yes	—
85	C₃₁×#475	C₂²	1	2	yes	complemented
86	C₃₁×#475	C₂²	1	2	yes	complemented
87	C₃₁×#474	C₂²	1	2	yes	—
88	C₃₁×#474	C₂²	1	2	yes	—
89	C₃₁×#474	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#461	C₂²	1	2	yes	—
94	C₃₁×#461	C₂²	1	2	yes	—
95	C₃₁×#461	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#450	C₂²	1	1	yes	characteristic
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	2	yes	—
110	C₃₁×#440	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₃₁×#433	C₂²	1	2	yes	—
116	C₃₁×#433	C₂²	1	2	yes	—
117	C₃₁×#432	C₂²	1	1	yes	characteristic
118	C₃₁×#432	C₂²	1	1	yes	characteristic
119	C₂²×Q₈×C₃₁	—	2	2	no	—
120	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	—	2	1	no	—
122	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×D₈×C₃₁	C₂³	1	2	yes	—
126	C₃₁×C₄⋊Q₈	—	2	2	no	—
127	C₃₁×C₄⋊Q₈	—	2	2	no	—
128	C₃₁×C₄⋊Q₈	—	2	1	no	—
129	C₃₁×C₄⋊Q₈	—	2	2	no	—
130	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
131	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
132	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	1	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	1	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	1	no	—
155	C₃₁×#125	D₄	1	2	yes	—
156	C₃₁×#125	C₂³	1	2	yes	—
157	C₃₁×#125	C₂³	1	1	yes	characteristic
158	C₃₁×#125	C₂³	1	2	yes	—
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	2	yes	—
161	C₃₁×#124	—	2	2	no	—
162	C₃₁×#124	C₂³	1	2	yes	—
163	C₃₁×#124	C₂³	1	1	yes	characteristic
164	C₃₁×#123	—	2	1	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	1	no	—
168	C₃₁×C₂²⋊Q₈	—	2	1	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	1	no	—
173	C₃₁×C₂²⋊Q₈	—	2	1	no	—
174	C₃₁×C₂²⋊Q₈	—	2	1	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
190	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×#121	C₂³	1	1	yes	characteristic
194	C₄×Q₈×C₃₁	—	2	1	no	—
195	C₄×Q₈×C₃₁	—	2	1	no	—
196	C₄×Q₈×C₃₁	—	2	2	no	—
197	C₄×Q₈×C₃₁	—	2	1	no	—
198	C₄×Q₈×C₃₁	—	2	1	no	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	2	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	1	no	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	2	no	—
223	C₃₁×#117	—	2	1	no	—
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
234	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
235	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#107	C₂³	1	2	yes	—
237	C₃₁×#107	C₂³	1	2	yes	—
238	C₃₁×#107	C₂³	1	2	yes	—
239	C₃₁×#107	C₂³	1	2	yes	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
251	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×#97	C₂³	1	1	yes	characteristic
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂×Q₈×C₃₁	—	2	1	no	—
282	C₂×Q₈×C₃₁	—	2	1	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	8	4	no	—
288	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
291	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₃₁	—	2	4	no	—
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	2	1	no	—
296	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
297	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₃₁	—	2	1	no	—
299	C₂²×C₄×C₃₁	—	2	1	no	—
300	C₂²×C₄×C₃₁	—	2	2	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	2	no	—
305	C₂²×C₄×C₃₁	—	2	2	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	—	8	2	no	—
308	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	SD₁₆×C₃₁	—	2	4	no	—
312	SD₁₆×C₃₁	—	2	4	no	—
313	SD₁₆×C₃₁	—	2	4	no	—
314	D₈×C₃₁	—	2	4	no	—
315	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
316	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
317	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₃₁	—	2	2	no	—
320	C₄⋊C₄×C₃₁	—	2	1	no	—
321	C₄⋊C₄×C₃₁	—	2	1	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	2	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	2	no	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	1	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	1	no	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	1	no	—
372	C₂²⋊C₄×C₃₁	—	2	1	no	—
373	C₂²⋊C₄×C₃₁	—	2	1	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₄²×C₃₁	—	2	2	no	—
381	C₄²×C₃₁	—	2	1	no	—
382	C₄²×C₃₁	—	2	2	no	—
383	C₄²×C₃₁	—	2	2	no	—
384	C₄²×C₃₁	—	2	2	no	—
385	C₄²×C₃₁	—	2	2	no	—
386	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₃₁	C₂⁴	1	2	yes	—
389	C₄²×C₃₁	C₂⁴	1	2	yes	—
390	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
392	#61873	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂³×C₃₁	—	2	4	no	—
394	C₂³×C₃₁	—	2	2	no	—
395	C₂³×C₃₁	—	2	1	no	—
396	C₂³×C₃₁	—	8	1	no	—
397	C₂³×C₃₁	—	8	1	no	—
398	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
399	Q₈×C₃₁	—	2	2	no	—
400	Q₈×C₃₁	—	2	2	no	—
401	Q₈×C₃₁	—	2	2	no	—
402	Q₈×C₃₁	—	4	2	no	—
403	Q₈×C₃₁	—	4	1	no	—
404	Q₈×C₃₁	—	4	1	no	—
405	Q₈×C₃₁	—	4	2	no	—
406	Q₈×C₃₁	—	8	1	no	—
407	Q₈×C₃₁	—	8	2	no	—
408	Q₈×C₃₁	—	8	1	no	—
409	Q₈×C₃₁	—	8	2	no	—
410	Q₈×C₃₁	—	8	2	no	—
411	D₄×C₃₁	—	2	4	no	—
412	D₄×C₃₁	—	2	2	no	—
413	D₄×C₃₁	—	2	2	no	—
414	D₄×C₃₁	—	8	1	no	—
415	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	1	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	1	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	4	1	no	—
426	C₂×C₄×C₃₁	—	4	1	no	—
427	C₂×C₄×C₃₁	—	4	2	no	—
428	C₂×C₄×C₃₁	—	4	4	no	—
429	C₂×C₄×C₃₁	—	8	2	no	—
430	C₂×C₄×C₃₁	—	8	2	no	—
431	C₂×C₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	8	2	no	—
434	C₂×C₄×C₃₁	—	8	2	no	—
435	C₂×C₄×C₃₁	—	8	1	no	—
436	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
446	C₈×C₃₁	—	2	2	no	—
447	C₈×C₃₁	—	2	2	no	—
448	C₈×C₃₁	—	2	2	no	—
449	C₈×C₃₁	—	2	2	no	—
450	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
451	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#3389	C₂×C₃₁	1	2	yes	complemented
453	#3388	C₂×C₃₁	1	2	yes	complemented
454	#3386	C₂×C₃₁	1	2	yes	complemented
455	#3385	C₂×C₃₁	1	2	yes	complemented
456	#3376	C₂×C₃₁	1	2	yes	complemented
457	#3376	C₂×C₃₁	1	2	yes	complemented
458	#3372	C₂×C₃₁	1	2	yes	complemented
459	#3367	C₂×C₃₁	1	2	yes	complemented
460	#3243	C₂×C₃₁	1	2	yes	complemented
461	#3242	C₂×C₃₁	1	2	yes	complemented
462	#3240	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
464	#3123	C₂×C₃₁	1	2	yes	complemented
465	#3118	C₂×C₃₁	1	2	yes	—
466	#3114	C₂×C₃₁	1	1	yes	characteristic
467	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
469	C₂²×C₃₁	—	2	1	no	—
470	C₂²×C₃₁	—	2	1	no	—
471	C₂²×C₃₁	—	2	1	no	—
472	C₂²×C₃₁	—	2	4	no	—
473	C₂²×C₃₁	—	4	2	no	—
474	C₂²×C₃₁	—	4	2	no	—
475	C₂²×C₃₁	—	4	1	no	—
476	C₂²×C₃₁	—	4	1	no	—
477	C₂²×C₃₁	—	4	1	no	—
478	C₂²×C₃₁	—	8	4	no	—
479	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₃₁	—	2	1	no	—
481	C₄×C₃₁	—	2	1	no	—
482	C₄×C₃₁	—	2	2	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	1	no	—
485	C₄×C₃₁	—	2	1	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	1	no	—
489	C₄×C₃₁	—	4	2	no	—
490	C₄×C₃₁	—	4	2	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	1	no	—
493	C₄×C₃₁	—	4	1	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
498	#563	—	2	2	no	—
499	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
500	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#557	C₂²×C₃₁	1	2	yes	complemented
502	#556	—	2	1	no	—
503	#556	C₂²×C₃₁	1	2	yes	complemented
504	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
505	#554	—	2	1	no	—
506	#554	—	2	2	no	—
507	#554	C₂²×C₃₁	1	2	yes	—
508	#554	C₂²×C₃₁	1	2	yes	—
509	#554	C₂²×C₃₁	1	2	yes	—
510	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	#552	—	2	1	no	—
512	D₄×Q₈	—	2	1	no	—
513	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
514	#544	—	2	1	no	—
515	#544	C₂²×C₃₁	1	2	yes	—
516	#543	—	2	1	no	—
517	#543	—	2	1	no	—
518	#542	C₂²×C₃₁	1	2	yes	—
519	#541	—	2	1	no	—
520	#541	—	2	2	no	—
521	#541	C₂²×C₃₁	1	2	yes	—
522	#533	C₂²×C₃₁	1	1	yes	characteristic
523	#533	C₂²×C₃₁	1	1	yes	characteristic
524	#533	C₂²×C₃₁	1	1	yes	characteristic
525	#529	C₂²×C₃₁	1	1	yes	characteristic
526	C₂×C₂²⋊Q₈	—	2	2	no	—
527	#518	C₂²×C₃₁	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
529	#501	C₂²×C₃₁	1	2	yes	complemented
530	#501	C₂²×C₃₁	1	2	yes	complemented
531	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#501	C₂²×C₃₁	1	2	yes	complemented
533	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
534	#500	C₂²×C₃₁	1	2	yes	complemented
535	#499	C₂²×C₃₁	1	2	yes	complemented
536	#491	C₂²×C₃₁	1	2	yes	complemented
537	#491	C₂²×C₃₁	1	2	yes	complemented
538	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
539	#489	C₂²×C₃₁	1	2	yes	complemented
540	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
541	#488	C₂²×C₃₁	1	2	yes	complemented
542	#487	C₂²×C₃₁	1	2	yes	complemented
543	#485	C₂²×C₃₁	1	2	yes	—
544	#485	C₂²×C₃₁	1	2	yes	—
545	#485	C₂²×C₃₁	1	2	yes	—
546	#484	C₂²×C₃₁	1	2	yes	—
547	#483	C₂²×C₃₁	1	1	yes	characteristic
548	#482	C₂²×C₃₁	1	2	yes	—
549	#480	C₂²×C₃₁	1	1	yes	characteristic
550	#479	C₂²×C₃₁	1	2	yes	complemented
551	#479	C₂²×C₃₁	1	2	yes	complemented
552	#479	C₂²×C₃₁	1	2	yes	complemented
553	#479	C₂²×C₃₁	1	2	yes	complemented
554	#478	C₂²×C₃₁	1	2	yes	—
555	#478	C₂²×C₃₁	1	2	yes	—
556	#478	C₂²×C₃₁	1	2	yes	—
557	#478	C₂²×C₃₁	1	2	yes	complemented
558	#478	C₂²×C₃₁	1	2	yes	complemented
559	#477	C₂²×C₃₁	1	2	yes	complemented
560	#477	C₂²×C₃₁	1	2	yes	complemented
561	#477	C₂²×C₃₁	1	2	yes	complemented
562	#476	C₂²×C₃₁	1	2	yes	—
563	#475	C₂²×C₃₁	1	2	yes	complemented
564	#475	C₂²×C₃₁	1	2	yes	complemented
565	#474	C₂²×C₃₁	1	2	yes	—
566	#474	C₂²×C₃₁	1	2	yes	—
567	#474	C₂²×C₃₁	1	2	yes	complemented
568	#463	C₂²×C₃₁	1	2	yes	—
569	#463	C₂²×C₃₁	1	2	yes	—
570	#463	C₂²×C₃₁	1	2	yes	—
571	#461	C₂²×C₃₁	1	2	yes	—
572	#461	C₂²×C₃₁	1	2	yes	—
573	#461	C₂²×C₃₁	1	2	yes	—
574	#450	C₂²×C₃₁	1	2	yes	—
575	#450	C₂²×C₃₁	1	1	yes	characteristic
576	#447	C₂²×C₃₁	1	1	yes	characteristic
577	#446	C₂²×C₃₁	1	2	yes	complemented
578	#446	C₂²×C₃₁	1	2	yes	complemented
579	#446	C₂²×C₃₁	1	2	yes	complemented
580	#446	C₂²×C₃₁	1	2	yes	complemented
581	#442	C₂²×C₃₁	1	2	yes	—
582	#442	C₂²×C₃₁	1	2	yes	—
583	#440	C₂²×C₃₁	1	2	yes	—
584	#440	C₂²×C₃₁	1	2	yes	—
585	#440	C₂²×C₃₁	1	2	yes	—
586	#440	C₂²×C₃₁	1	2	yes	—
587	#440	C₂²×C₃₁	1	2	yes	—
588	#440	C₂²×C₃₁	1	2	yes	—
589	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
590	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
591	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
592	C₄×D₈	C₂²×C₃₁	1	2	yes	—
593	#433	C₂²×C₃₁	1	2	yes	—
594	#433	C₂²×C₃₁	1	2	yes	—
595	#432	C₂²×C₃₁	1	1	yes	characteristic
596	#432	C₂²×C₃₁	1	1	yes	characteristic
597	C₂×C₃₁	—	4	1	no	—
598	C₂×C₃₁	—	4	4	no	—
599	C₂×C₃₁	—	8	1	no	—
600	C₂×C₃₁	#3486	1	1	yes	characteristic
601	C₂×C₃₁	#3585	1	1	yes	characteristic
602	C₂×C₃₁	#3586	1	1	yes	characteristic
603	C₂²×Q₈	—	2	2	no	—
604	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
605	C₂³×C₄	—	2	1	no	—
606	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
609	C₂×D₈	C₂³×C₃₁	1	2	yes	—
610	C₄⋊Q₈	—	2	2	no	—
611	C₄⋊Q₈	—	2	2	no	—
612	C₄⋊Q₈	—	2	1	no	—
613	C₄⋊Q₈	—	2	2	no	—
614	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
615	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
618	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
619	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
620	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
622	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
623	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	1	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	—	2	2	no	—
638	#125	—	2	1	no	—
639	#125	D₄×C₃₁	1	2	yes	—
640	#125	C₂³×C₃₁	1	1	yes	characteristic
641	#125	C₂³×C₃₁	1	2	yes	—
642	#125	C₂³×C₃₁	1	2	yes	—
643	#125	C₂³×C₃₁	1	2	yes	—
644	#125	C₂³×C₃₁	1	2	yes	—
645	#124	—	2	2	no	—
646	#124	C₂³×C₃₁	1	1	yes	characteristic
647	#124	C₂³×C₃₁	1	2	yes	—
648	#123	—	2	1	no	—
649	#123	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	—	2	1	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
673	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
674	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
675	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
676	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
677	#121	C₂³×C₃₁	1	1	yes	characteristic
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
686	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
687	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
688	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
689	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	C₂³×C₃₁	1	2	yes	—
698	C₄×D₄	C₂³×C₃₁	1	2	yes	—
699	C₄×D₄	C₂³×C₃₁	1	2	yes	—
700	C₄×D₄	C₂³×C₃₁	1	2	yes	—
701	C₄×D₄	C₂³×C₃₁	1	2	yes	—
702	C₄×D₄	C₂³×C₃₁	1	2	yes	—
703	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
704	C₄×D₄	C₂³×C₃₁	1	2	yes	—
705	#117	—	2	1	no	—
706	#117	—	2	2	no	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	C₂³×C₃₁	1	2	yes	—
710	#117	C₂³×C₃₁	1	2	yes	—
711	C₂×C₄⋊C₄	—	2	2	no	—
712	C₂×C₄⋊C₄	—	2	2	no	—
713	C₂×C₄⋊C₄	—	2	2	no	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	—	2	1	no	—
717	C₂×C₂²⋊C₄	—	2	2	no	—
718	C₂×C₂²⋊C₄	—	2	2	no	—
719	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
720	#107	C₂³×C₃₁	1	2	yes	—
721	#107	C₂³×C₃₁	1	2	yes	—
722	#107	C₂³×C₃₁	1	2	yes	—
723	#107	C₂³×C₃₁	1	2	yes	—
724	#107	C₂³×C₃₁	1	2	yes	—
725	#107	C₂³×C₃₁	1	2	yes	—
726	#107	C₂³×C₃₁	1	2	yes	—
727	#106	C₂³×C₃₁	1	2	yes	—
728	#106	C₂³×C₃₁	1	2	yes	—
729	#106	C₂³×C₃₁	1	2	yes	—
730	#106	C₂³×C₃₁	1	2	yes	—
731	#106	C₂³×C₃₁	1	2	yes	—
732	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
733	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
737	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
738	#103	C₂³×C₃₁	1	2	yes	—
739	#103	C₂³×C₃₁	1	2	yes	—
740	#103	C₂³×C₃₁	1	2	yes	—
741	#103	C₂³×C₃₁	1	2	yes	—
742	#103	C₂³×C₃₁	1	2	yes	—
743	#103	C₂³×C₃₁	1	2	yes	—
744	#103	C₂³×C₃₁	1	2	yes	—
745	#103	C₂³×C₃₁	1	2	yes	—
746	#103	C₂³×C₃₁	1	2	yes	—
747	#102	C₂³×C₃₁	1	2	yes	—
748	#102	C₂³×C₃₁	1	2	yes	—
749	#102	C₂³×C₃₁	1	2	yes	—
750	#102	C₂³×C₃₁	1	2	yes	—
751	#102	C₂³×C₃₁	1	2	yes	—
752	#102	C₂³×C₃₁	1	2	yes	—
753	#102	C₂³×C₃₁	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
757	#97	C₂³×C₃₁	1	1	yes	characteristic
758	#97	C₂³×C₃₁	1	1	yes	characteristic
759	#97	C₂³×C₃₁	1	2	yes	—
760	#97	C₂³×C₃₁	1	2	yes	—
761	#97	C₂³×C₃₁	1	2	yes	—
762	C₄×C₈	C₂³×C₃₁	1	2	yes	—
763	C₄×C₈	C₂³×C₃₁	1	2	yes	—
764	C₃₁	#61873	1	1	yes	characteristic, direct product factor, Sylow
765	C₂⁴	—	2	1	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	8	4	no	—
773	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
774	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
775	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
776	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
777	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	8	2	no	—
793	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
796	SD₁₆	—	2	4	no	—
797	SD₁₆	—	2	4	no	—
798	SD₁₆	—	2	4	no	—
799	D₈	—	2	4	no	—
800	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
801	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
802	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
833	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
834	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
836	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
837	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
840	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
842	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
864	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	1	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₄²	C₂⁴×C₃₁	1	2	yes	—
874	C₄²	C₂⁴×C₃₁	1	2	yes	—
875	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
876	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
877	C₂³	—	2	4	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	8	1	no	—
881	C₂³	—	8	1	no	—
882	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
883	Q₈	—	2	2	no	—
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	4	2	no	—
887	Q₈	—	4	1	no	—
888	Q₈	—	4	1	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	8	1	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	1	no	—
893	Q₈	—	8	2	no	—
894	Q₈	—	8	2	no	—
895	D₄	—	2	4	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	8	1	no	—
899	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	2	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	—	8	2	no	—
915	C₂×C₄	—	8	2	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	1	no	—
920	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
921	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
929	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	8	4	no	—
944	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
963	C₂	—	4	1	no	—
964	C₂	—	4	4	no	—
965	C₂	—	8	1	no	—
966	C₂	C₃₁×#3486	1	1	yes	characteristic
967	C₂	C₃₁×#3585	1	1	yes	characteristic
968	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#447	C₂²
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×#3555	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3388	C₂	semidirect
5. C₃₁×#3386	C₂	semidirect
6. C₃₁×#3385	C₂	semidirect
7. C₃₁×#3376	C₂	semidirect
8. C₃₁×#3376	C₂	semidirect
9. C₃₁×#3372	C₂	semidirect
10. C₃₁×#3367	C₂	semidirect
11. C₃₁×#3243	C₂	semidirect
12. C₃₁×#3242	C₂	semidirect
13. C₃₁×#3240	C₂	semidirect
14. C₃₁×#3237	C₂	semidirect
15. C₃₁×#3123	C₂	semidirect
18. C₃₁×#3110	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
21. Q₈²×C₃₁	C₂²	semidirect
22. C₃₁×#557	C₂²	semidirect
23. C₃₁×#557	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
32. C₃₁×#554	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#501	C₂²	semidirect
54. C₃₁×#501	C₂²	semidirect
55. C₃₁×#501	C₂²	semidirect
56. C₃₁×#500	C₂²	semidirect
57. C₃₁×#499	C₂²	semidirect
58. C₃₁×#491	C₂²	semidirect
59. C₃₁×#491	C₂²	semidirect
60. C₃₁×#489	C₂²	semidirect
61. C₃₁×#489	C₂²	semidirect
62. C₃₁×#489	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
85. C₃₁×#475	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
89. C₃₁×#474	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
392. #61873	C₃₁	direct (N × H)
450. #3555	C₂×C₃₁	semidirect
451. #3501	C₂×C₃₁	semidirect
452. #3389	C₂×C₃₁	semidirect
453. #3388	C₂×C₃₁	semidirect
454. #3386	C₂×C₃₁	semidirect
455. #3385	C₂×C₃₁	semidirect
456. #3376	C₂×C₃₁	semidirect
457. #3376	C₂×C₃₁	semidirect
458. #3372	C₂×C₃₁	semidirect
459. #3367	C₂×C₃₁	semidirect
460. #3243	C₂×C₃₁	semidirect
461. #3242	C₂×C₃₁	semidirect
462. #3240	C₂×C₃₁	semidirect
463. #3237	C₂×C₃₁	semidirect
464. #3123	C₂×C₃₁	semidirect
467. #3110	C₂×C₃₁	semidirect
468. #2987	C₂×C₃₁	semidirect
499. Q₈²	C₂²×C₃₁	semidirect
500. #557	C₂²×C₃₁	semidirect
501. #557	C₂²×C₃₁	semidirect
503. #556	C₂²×C₃₁	semidirect
504. #556	C₂²×C₃₁	semidirect
510. #554	C₂²×C₃₁	semidirect
529. #501	C₂²×C₃₁	semidirect
530. #501	C₂²×C₃₁	semidirect
531. #501	C₂²×C₃₁	semidirect
532. #501	C₂²×C₃₁	semidirect
533. #501	C₂²×C₃₁	semidirect
534. #500	C₂²×C₃₁	semidirect
535. #499	C₂²×C₃₁	semidirect
536. #491	C₂²×C₃₁	semidirect
537. #491	C₂²×C₃₁	semidirect
538. #489	C₂²×C₃₁	semidirect
539. #489	C₂²×C₃₁	semidirect
540. #489	C₂²×C₃₁	semidirect
541. #488	C₂²×C₃₁	semidirect
542. #487	C₂²×C₃₁	semidirect
550. #479	C₂²×C₃₁	semidirect
551. #479	C₂²×C₃₁	semidirect
552. #479	C₂²×C₃₁	semidirect
553. #479	C₂²×C₃₁	semidirect
557. #478	C₂²×C₃₁	semidirect
558. #478	C₂²×C₃₁	semidirect
559. #477	C₂²×C₃₁	semidirect
560. #477	C₂²×C₃₁	semidirect
561. #477	C₂²×C₃₁	semidirect
563. #475	C₂²×C₃₁	semidirect
564. #475	C₂²×C₃₁	semidirect
567. #474	C₂²×C₃₁	semidirect
577. #446	C₂²×C₃₁	semidirect
578. #446	C₂²×C₃₁	semidirect
579. #446	C₂²×C₃₁	semidirect
580. #446	C₂²×C₃₁	semidirect
764. C₃₁	#61873	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×#3555	2
C₃₁×#3501	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3386	2
C₃₁×#3385	2
C₃₁×#3376	2
C₃₁×#3372	2
C₃₁×#3367	2
C₃₁×#3243	2
C₃₁×#3242	2
C₃₁×#3240	2
C₃₁×#3237	2
C₃₁×#3123	2
C₃₁×#3118	2
C₃₁×#3114	2
C₃₁×#3110	2
C₃₁×#2987	2
#61873	31

Subgroups — C31×#61873 #21518632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61873 #21518632