Subgroups — C₃₁×#61316 #21518075

Order 7936.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3135	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₃₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2943	C₂	1	2	yes	maximal, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	C₃₁×#559	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#557	C₂²	1	1	yes	characteristic
31	C₃₁×#557	C₂²	1	2	yes	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	2	yes	—
34	C₃₁×#554	—	2	1	no	—
35	C₃₁×#554	—	2	2	no	—
36	C₃₁×#554	C₂²	1	1	yes	characteristic
37	C₃₁×#554	C₂²	1	2	yes	—
38	C₃₁×#553	—	2	1	no	—
39	C₃₁×#553	—	2	2	no	—
40	C₃₁×#550	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₃₁	—	2	1	no	—
42	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#548	—	2	1	no	—
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	—	2	2	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	2	yes	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	2	yes	—
50	C₃₁×#529	—	2	1	no	—
51	C₃₁×#529	—	2	2	no	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	2	yes	—
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
58	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#491	C₂²	1	2	yes	—
60	C₃₁×#491	C₂²	1	2	yes	—
61	C₃₁×#490	C₂²	1	2	yes	—
62	C₃₁×#490	C₂²	1	2	yes	—
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#489	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#488	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#487	C₂²	1	1	yes	characteristic
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	—
80	C₃₁×#477	C₂²	1	1	yes	characteristic
81	C₃₁×#476	C₂²	1	1	yes	characteristic
82	C₃₁×#476	C₂²	1	2	yes	—
83	C₃₁×#475	C₂²	1	2	yes	—
84	C₃₁×#475	C₂²	1	1	yes	characteristic
85	C₃₁×#474	C₂²	1	1	yes	characteristic
86	C₃₁×#474	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#462	C₂²	1	1	yes	characteristic
94	C₃₁×#462	C₂²	1	2	yes	—
95	C₃₁×#461	C₂²	1	1	yes	characteristic
96	C₃₁×#461	C₂²	1	2	yes	—
97	C₃₁×#460	C₂²	1	2	yes	—
98	C₃₁×#460	C₂²	1	1	yes	characteristic
99	C₃₁×#459	C₂²	1	2	yes	—
100	C₃₁×#459	C₂²	1	1	yes	characteristic
101	C₃₁×#446	C₂²	1	1	yes	characteristic
102	C₃₁×#446	C₂²	1	1	yes	characteristic
103	C₃₁×#446	C₂²	1	1	yes	characteristic
104	C₃₁×#446	C₂²	1	1	yes	characteristic
105	C₃₁×#446	C₂²	1	2	yes	—
106	C₃₁×#446	C₂²	1	2	yes	—
107	C₃₁×#442	C₂²	1	2	yes	—
108	C₃₁×#442	C₂²	1	2	yes	—
109	C₃₁×#441	C₂²	1	2	yes	—
110	C₃₁×#441	C₂²	1	2	yes	—
111	C₃₁×#440	C₂²	1	2	yes	—
112	C₃₁×#440	C₂²	1	2	yes	—
113	C₃₁×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
123	C₃₁×#427	C₂²	1	1	yes	characteristic
124	C₃₁×#427	C₂²	1	2	yes	—
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
127	C₃₁×#416	C₂²	1	2	yes	—
128	C₃₁×#416	C₂²	1	2	yes	—
129	C₃₁×#416	C₂²	1	2	yes	—
130	C₃₁×#416	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#416	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
141	C₃₁×#135	—	2	4	no	—
142	C₃₁×#135	—	2	8	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	1	no	—
207	C₄×Q₈×C₃₁	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	D₄	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	—	2	2	no	—
263	C₂×C₄²×C₃₁	—	2	1	no	—
264	C₂×C₄²×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	2	4	no	—
318	#41×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	4	4	no	—
320	#41×C₃₁	#41	1	4	yes	complemented
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	—	4	4	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	Q₁₆×C₃₁	—	2	2	no	—
360	Q₁₆×C₃₁	—	2	4	no	—
361	SD₁₆×C₃₁	—	2	2	no	—
362	SD₁₆×C₃₁	—	2	4	no	—
363	SD₁₆×C₃₁	—	2	2	no	—
364	SD₁₆×C₃₁	—	2	4	no	—
365	D₈×C₃₁	—	2	2	no	—
366	D₈×C₃₁	—	2	4	no	—
367	C₂×C₈×C₃₁	—	2	2	no	—
368	C₂×C₈×C₃₁	—	2	4	no	—
369	C₂×C₈×C₃₁	—	2	2	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	C₂×D₄	1	2	yes	—
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	#61316	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	—	2	2	no	—
450	C₂³×C₃₁	—	2	1	no	—
451	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	4	2	no	—
460	Q₈×C₃₁	—	4	4	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	Q₈×C₃₁	—	8	1	no	—
464	Q₈×C₃₁	C₂×#41	1	2	yes	—
465	D₄×C₃₁	—	2	4	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	4	4	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	4	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	1	no	—
477	D₄×C₃₁	C₂×#41	1	2	yes	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	4	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	4	1	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	4	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	8	1	no	—
499	C₂×C₄×C₃₁	—	8	1	no	—
500	C₂×C₄×C₃₁	—	8	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
512	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
513	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	2	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
521	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3377	C₂×C₃₁	1	2	yes	complemented
523	#3376	C₂×C₃₁	1	2	yes	complemented
524	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3371	C₂×C₃₁	1	2	yes	complemented
529	#3370	C₂×C₃₁	1	2	yes	complemented
530	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3135	C₂×C₃₁	1	2	yes	complemented
535	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3076	C₂×C₃₁	1	2	yes	complemented
538	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3035	C₂×C₃₁	1	2	yes	complemented
540	C₂×#446	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2943	C₂×C₃₁	1	2	yes	complemented
542	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
543	C₂²×C₃₁	—	2	1	no	—
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	#548	1	2	yes	—
555	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	#548	1	2	yes	—
573	C₄×C₃₁	#575	1	2	yes	—
574	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
575	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
576	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
577	C₂×#135	C₂²×C₃₁	1	2	yes	—
578	#559	C₂²×C₃₁	1	2	yes	—
579	#559	C₂²×C₃₁	1	1	yes	characteristic
580	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
581	#557	C₂²×C₃₁	1	1	yes	characteristic
582	#557	C₂²×C₃₁	1	1	yes	characteristic
583	#557	C₂²×C₃₁	1	2	yes	—
584	#556	C₂²×C₃₁	1	1	yes	characteristic
585	#556	C₂²×C₃₁	1	2	yes	—
586	#554	—	2	1	no	—
587	#554	—	2	2	no	—
588	#554	C₂²×C₃₁	1	1	yes	characteristic
589	#554	C₂²×C₃₁	1	2	yes	—
590	#553	—	2	1	no	—
591	#553	—	2	2	no	—
592	#550	C₂²×C₃₁	1	1	yes	characteristic
593	D₄×Q₈	—	2	1	no	—
594	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
595	#548	—	2	1	no	—
596	#533	—	2	1	no	—
597	#533	—	2	2	no	—
598	#533	C₂²×C₃₁	1	1	yes	characteristic
599	#533	C₂²×C₃₁	1	2	yes	—
600	#532	C₂²×C₃₁	1	1	yes	characteristic
601	#532	C₂²×C₃₁	1	2	yes	—
602	#529	—	2	1	no	—
603	#529	—	2	2	no	—
604	C₄×#41	—	2	1	no	—
605	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
606	C₄×#41	C₂²×C₃₁	1	2	yes	—
607	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
608	C₄×#41	C₂²×C₃₁	1	2	yes	—
609	C₂×C₄×Q₈	—	2	1	no	—
610	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
611	#491	C₂²×C₃₁	1	2	yes	—
612	#491	C₂²×C₃₁	1	2	yes	—
613	#490	C₂²×C₃₁	1	2	yes	—
614	#490	C₂²×C₃₁	1	2	yes	—
615	#489	C₂²×C₃₁	1	2	yes	—
616	#489	C₂²×C₃₁	1	2	yes	—
617	#489	C₂²×C₃₁	1	2	yes	—
618	#489	C₂²×C₃₁	1	2	yes	—
619	#488	C₂²×C₃₁	1	2	yes	—
620	#488	C₂²×C₃₁	1	2	yes	—
621	#487	C₂²×C₃₁	1	1	yes	characteristic
622	#487	C₂²×C₃₁	1	1	yes	characteristic
623	#486	C₂²×C₃₁	1	1	yes	characteristic
624	#486	C₂²×C₃₁	1	1	yes	characteristic
625	#479	C₂²×C₃₁	1	2	yes	—
626	#479	C₂²×C₃₁	1	2	yes	—
627	#479	C₂²×C₃₁	1	2	yes	—
628	#478	C₂²×C₃₁	1	2	yes	—
629	#478	C₂²×C₃₁	1	2	yes	—
630	#478	C₂²×C₃₁	1	2	yes	—
631	#477	C₂²×C₃₁	1	2	yes	—
632	#477	C₂²×C₃₁	1	1	yes	characteristic
633	#476	C₂²×C₃₁	1	1	yes	characteristic
634	#476	C₂²×C₃₁	1	2	yes	—
635	#475	C₂²×C₃₁	1	2	yes	—
636	#475	C₂²×C₃₁	1	1	yes	characteristic
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#474	C₂²×C₃₁	1	2	yes	—
639	#464	C₂²×C₃₁	1	2	yes	—
640	#464	C₂²×C₃₁	1	2	yes	—
641	#464	C₂²×C₃₁	1	2	yes	—
642	#463	C₂²×C₃₁	1	2	yes	—
643	#463	C₂²×C₃₁	1	2	yes	—
644	#463	C₂²×C₃₁	1	2	yes	—
645	#462	C₂²×C₃₁	1	1	yes	characteristic
646	#462	C₂²×C₃₁	1	2	yes	—
647	#461	C₂²×C₃₁	1	1	yes	characteristic
648	#461	C₂²×C₃₁	1	2	yes	—
649	#460	C₂²×C₃₁	1	2	yes	—
650	#460	C₂²×C₃₁	1	1	yes	characteristic
651	#459	C₂²×C₃₁	1	2	yes	—
652	#459	C₂²×C₃₁	1	1	yes	characteristic
653	#446	C₂²×C₃₁	1	1	yes	characteristic
654	#446	C₂²×C₃₁	1	1	yes	characteristic
655	#446	C₂²×C₃₁	1	1	yes	characteristic
656	#446	C₂²×C₃₁	1	1	yes	characteristic
657	#446	C₂²×C₃₁	1	2	yes	—
658	#446	C₂²×C₃₁	1	2	yes	—
659	#442	C₂²×C₃₁	1	2	yes	—
660	#442	C₂²×C₃₁	1	2	yes	—
661	#441	C₂²×C₃₁	1	2	yes	—
662	#441	C₂²×C₃₁	1	2	yes	—
663	#440	C₂²×C₃₁	1	2	yes	—
664	#440	C₂²×C₃₁	1	2	yes	—
665	#440	C₂²×C₃₁	1	2	yes	—
666	#440	C₂²×C₃₁	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
668	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
675	#427	C₂²×C₃₁	1	1	yes	characteristic
676	#427	C₂²×C₃₁	1	2	yes	—
677	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
678	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
679	#416	C₂²×C₃₁	1	2	yes	—
680	#416	C₂²×C₃₁	1	2	yes	—
681	#416	C₂²×C₃₁	1	2	yes	—
682	#416	C₂²×C₃₁	1	2	yes	—
683	#416	C₂²×C₃₁	1	1	yes	characteristic
684	#416	C₂²×C₃₁	1	1	yes	characteristic
685	C₂×#97	C₂²×C₃₁	1	2	yes	—
686	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₃₁	—	2	2	no	—
688	C₂×C₃₁	—	4	2	no	—
689	C₂×C₃₁	—	8	2	no	—
690	C₂×C₃₁	—	8	1	no	—
691	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
692	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
693	C₂×C₃₁	#3584	1	1	yes	characteristic
694	C₂×#41	—	2	1	no	—
695	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×#41	C₂³×C₃₁	1	2	yes	—
697	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×Q₈	—	2	1	no	—
699	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
700	#135	—	2	4	no	—
701	#135	—	2	8	no	—
702	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₃₁	1	2	yes	—
710	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	#127	C₂³×C₃₁	1	1	yes	characteristic
724	#127	C₂³×C₃₁	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	C₂³×C₃₁	1	2	yes	—
734	#125	C₂³×C₃₁	1	2	yes	—
735	#125	C₂³×C₃₁	1	2	yes	—
736	#124	—	2	1	no	—
737	#124	—	2	2	no	—
738	#124	C₂³×C₃₁	1	2	yes	—
739	#124	C₂³×C₃₁	1	2	yes	—
740	#124	C₂³×C₃₁	1	2	yes	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	—	2	2	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
772	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
773	C₄×Q₈	D₄×C₃₁	1	2	yes	—
774	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
776	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	2	yes	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	—	2	1	no	—
813	#117	C₂³×C₃₁	1	1	yes	characteristic
814	#117	C₂³×C₃₁	1	1	yes	characteristic
815	#117	C₂³×C₃₁	1	2	yes	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
819	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	—	2	1	no	—
823	C₂×C₄²	—	2	2	no	—
824	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
825	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
826	#107	C₂³×C₃₁	1	1	yes	characteristic
827	#107	C₂³×C₃₁	1	1	yes	characteristic
828	#107	C₂³×C₃₁	1	2	yes	—
829	#107	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	1	yes	characteristic
831	#106	C₂³×C₃₁	1	1	yes	characteristic
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	1	yes	characteristic
844	#103	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	1	yes	characteristic
856	#102	C₂³×C₃₁	1	1	yes	characteristic
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#97	C₂³×C₃₁	1	2	yes	—
866	#97	C₂³×C₃₁	1	2	yes	—
867	#97	C₂³×C₃₁	1	2	yes	—
868	#97	C₂³×C₃₁	1	2	yes	—
869	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₃₁	#61316	1	1	yes	characteristic, direct product factor, Sylow
874	#41	—	2	2	no	—
875	#41	—	2	2	no	—
876	#41	—	2	4	no	—
877	#41	—	2	2	no	—
878	#41	—	2	4	no	—
879	#41	—	4	4	no	—
880	#41	#41×C₃₁	1	4	yes	complemented
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	4	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
902	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	2	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	4	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	2	4	no	—
925	D₈	—	2	2	no	—
926	D₈	—	2	4	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	2	4	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
935	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1000	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1001	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1002	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₃₁	1	2	yes	—
1006	C₄²	C₂⁴×C₃₁	1	2	yes	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	4	4	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	8	2	no	—
1022	Q₈	—	8	1	no	—
1023	Q₈	C₂×#41×C₃₁	1	2	yes	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	C₂×#41×C₃₁	1	2	yes	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1063	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1071	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1072	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	C₃₁×#548	1	2	yes	—
1091	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1092	C₄	—	2	2	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₃₁×#548	1	2	yes	—
1109	C₄	C₃₁×#575	1	2	yes	—
1110	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1111	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1112	C₂	—	2	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	2	no	—
1115	C₂	—	8	1	no	—
1116	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
1117	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1118	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3480	C₂	semidirect
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3375	C₂	semidirect
6. C₃₁×#3374	C₂	semidirect
7. C₃₁×#3373	C₂	semidirect
8. C₃₁×#3372	C₂	semidirect
9. C₃₁×#3371	C₂	semidirect
10. C₃₁×#3370	C₂	semidirect
11. C₃₁×#3369	C₂	semidirect
12. C₃₁×#3368	C₂	semidirect
13. C₃₁×#3367	C₂	semidirect
14. C₃₁×#3366	C₂	semidirect
15. C₃₁×#3135	C₂	semidirect
16. C₃₁×#3131	C₂	semidirect
17. C₃₁×#3076	C₂	semidirect
18. C₃₁×#3076	C₂	semidirect
19. C₃₁×#3035	C₂	semidirect
20. C₃₁×#3035	C₂	semidirect
21. C₂×C₃₁×#446	C₂	semidirect
22. C₃₁×#2943	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
320. #41×C₃₁	#41	semidirect
447. #61316	C₃₁	direct (N × H)
520. #3480	C₂×C₃₁	semidirect
521. Q₈×#41	C₂×C₃₁	semidirect
522. #3377	C₂×C₃₁	semidirect
523. #3376	C₂×C₃₁	semidirect
524. #3375	C₂×C₃₁	semidirect
525. #3374	C₂×C₃₁	semidirect
526. #3373	C₂×C₃₁	semidirect
527. #3372	C₂×C₃₁	semidirect
528. #3371	C₂×C₃₁	semidirect
529. #3370	C₂×C₃₁	semidirect
530. #3369	C₂×C₃₁	semidirect
531. #3368	C₂×C₃₁	semidirect
532. #3367	C₂×C₃₁	semidirect
533. #3366	C₂×C₃₁	semidirect
534. #3135	C₂×C₃₁	semidirect
535. #3131	C₂×C₃₁	semidirect
536. #3076	C₂×C₃₁	semidirect
537. #3076	C₂×C₃₁	semidirect
538. #3035	C₂×C₃₁	semidirect
539. #3035	C₂×C₃₁	semidirect
540. C₂×#446	C₂×C₃₁	semidirect
541. #2943	C₂×C₃₁	semidirect
542. C₄×#135	C₂×C₃₁	semidirect
873. C₃₁	#61316	direct (N × H)
880. #41	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3480	2
Q₈×#41×C₃₁	2
C₃₁×#3377	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3374	2
C₃₁×#3373	2
C₃₁×#3372	2
C₃₁×#3371	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3368	2
C₃₁×#3367	2
C₃₁×#3366	2
C₃₁×#3135	2
C₃₁×#3131	2
C₃₁×#3076	2
C₃₁×#3035	2
C₂×C₃₁×#446	2
C₃₁×#2943	2
C₄×C₃₁×#135	2
#61316	31

Subgroups — C31×#61316 #21518075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61316 #21518075