Subgroups — C₃₁×#61460 #21518219

Order 7936.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2943	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	2	yes	—
34	C₃₁×#553	—	2	2	no	—
35	C₃₁×#553	C₂²	1	2	yes	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	—	2	2	no	—
38	C₃₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#548	—	2	1	no	—
41	C₃₁×#548	C₂²	1	2	yes	—
42	C₃₁×#547	C₂²	1	2	yes	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	2	yes	—
46	C₃₁×#532	—	2	1	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#529	—	2	2	no	—
49	C₃₁×#529	—	2	1	no	—
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
58	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#500	C₂²	1	1	yes	characteristic
61	C₃₁×#497	C₂²	1	2	yes	—
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#491	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	2	yes	—
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#482	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	2	yes	—
76	C₃₁×#476	C₂²	1	2	yes	—
77	C₃₁×#475	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	1	yes	characteristic
79	C₃₁×#475	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic
90	C₃₁×#462	C₂²	1	1	yes	characteristic
91	C₃₁×#462	C₂²	1	2	yes	—
92	C₃₁×#461	C₂²	1	2	yes	—
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#452	C₂²	1	2	yes	—
98	C₃₁×#451	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#449	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic
102	C₃₁×#446	C₂²	1	1	yes	characteristic
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	—
105	C₃₁×#441	C₂²	1	2	yes	—
106	C₃₁×#441	C₂²	1	2	yes	—
107	C₃₁×#441	C₂²	1	1	yes	characteristic
108	C₃₁×#441	C₂²	1	2	yes	—
109	C₃₁×#441	C₂²	1	1	yes	characteristic
110	C₃₁×#440	C₂²	1	2	yes	—
111	C₃₁×#440	C₂²	1	1	yes	characteristic
112	C₃₁×#440	C₂²	1	2	yes	—
113	C₃₁×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×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	C₃₁×#435	C₂²	1	2	yes	—
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#432	C₂²	1	2	yes	—
126	C₃₁×#432	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	1	yes	characteristic
128	C₃₁×#427	C₂²	1	2	yes	—
129	C₃₁×#419	C₂²	1	1	yes	characteristic
130	C₃₁×#417	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₃₁×#416	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#97	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×#137	—	2	4	no	—
143	C₃₁×#135	—	2	8	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×#127	—	2	1	no	—
165	C₃₁×#127	C₂³	1	1	yes	characteristic
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	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	D₄	1	2	yes	—
241	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	D₄	1	1	yes	characteristic
256	C₃₁×#117	D₄	1	2	yes	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₃₁	—	2	1	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	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	4	no	—
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	1	no	—
321	#41×C₃₁	—	4	4	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	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	4	1	no	—
328	C₂×Q₈×C₃₁	—	4	4	no	—
329	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
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×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
361	Q₁₆×C₃₁	—	2	4	no	—
362	Q₁₆×C₃₁	—	2	2	no	—
363	Q₁₆×C₃₁	—	2	2	no	—
364	Q₁₆×C₃₁	—	4	2	no	—
365	SD₁₆×C₃₁	—	2	2	no	—
366	SD₁₆×C₃₁	—	2	4	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	#41	1	4	yes	complemented
370	D₈×C₃₁	—	2	4	no	—
371	M₁₆×C₃₁	—	2	2	no	—
372	M₁₆×C₃₁	—	4	1	no	—
373	C₂×C₈×C₃₁	—	2	4	no	—
374	C₂×C₈×C₃₁	—	4	2	no	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	C₂×D₄	1	2	yes	—
446	C₄²×C₃₁	C₂×D₄	1	2	yes	—
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₃₁	C₂⁴	1	2	yes	—
452	#61460	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	4	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	C₂×#41	1	2	yes	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	4	4	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	4	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	8	1	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	C₂×#41	1	2	yes	—
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	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	1	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	4	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	4	4	no	—
507	C₂×C₄×C₃₁	—	4	4	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	—	8	1	no	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	2	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	C₂×#41	1	2	yes	—
526	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3350	C₂×C₃₁	1	2	yes	complemented
533	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3313	C₂×C₃₁	1	2	yes	complemented
535	#3307	C₂×C₃₁	1	2	yes	complemented
536	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3269	C₂×C₃₁	1	2	yes	complemented
540	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3181	C₂×C₃₁	1	2	yes	complemented
542	#3116	C₂×C₃₁	1	2	yes	complemented
543	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3111	C₂×C₃₁	1	2	yes	complemented
546	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
547	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#2943	C₂×C₃₁	1	2	yes	complemented
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	2	1	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	2	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	2	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	#575	1	2	yes	—
580	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
581	C₄×C₃₁	#585	1	1	yes	characteristic
582	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
583	C₂×#135	C₂²×C₃₁	1	2	yes	—
584	#559	—	2	1	no	—
585	#559	C₂²×C₃₁	1	1	yes	characteristic
586	#557	C₂²×C₃₁	1	1	yes	characteristic
587	#557	C₂²×C₃₁	1	1	yes	characteristic
588	#556	—	2	1	no	—
589	#556	C₂²×C₃₁	1	1	yes	characteristic
590	#556	C₂²×C₃₁	1	1	yes	characteristic
591	#556	C₂²×C₃₁	1	2	yes	—
592	#553	—	2	2	no	—
593	#553	C₂²×C₃₁	1	2	yes	—
594	#552	—	2	1	no	—
595	#552	—	2	2	no	—
596	#550	C₂²×C₃₁	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
598	#548	—	2	1	no	—
599	#548	C₂²×C₃₁	1	2	yes	—
600	#547	C₂²×C₃₁	1	2	yes	—
601	#547	C₂²×C₃₁	1	1	yes	characteristic
602	#533	C₂²×C₃₁	1	1	yes	characteristic
603	#533	C₂²×C₃₁	1	2	yes	—
604	#532	—	2	1	no	—
605	#532	C₂²×C₃₁	1	1	yes	characteristic
606	#529	—	2	2	no	—
607	#529	—	2	1	no	—
608	#529	—	2	2	no	—
609	#529	C₂²×C₃₁	1	2	yes	—
610	C₄×#41	—	2	1	no	—
611	C₄×#41	C₂²×C₃₁	1	2	yes	—
612	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
613	C₄×#41	C₂²×C₃₁	1	2	yes	—
614	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
615	C₂×C₄×Q₈	—	2	1	no	—
616	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
617	#501	C₂²×C₃₁	1	2	yes	—
618	#500	C₂²×C₃₁	1	1	yes	characteristic
619	#497	C₂²×C₃₁	1	2	yes	—
620	#492	C₂²×C₃₁	1	1	yes	characteristic
621	#491	C₂²×C₃₁	1	2	yes	—
622	#489	C₂²×C₃₁	1	2	yes	—
623	#487	C₂²×C₃₁	1	1	yes	characteristic
624	#486	C₂²×C₃₁	1	1	yes	characteristic
625	#485	C₂²×C₃₁	1	2	yes	—
626	#485	C₂²×C₃₁	1	2	yes	—
627	#485	C₂²×C₃₁	1	2	yes	—
628	#483	C₂²×C₃₁	1	2	yes	—
629	#482	C₂²×C₃₁	1	2	yes	—
630	#482	C₂²×C₃₁	1	2	yes	—
631	#479	C₂²×C₃₁	1	2	yes	—
632	#478	C₂²×C₃₁	1	2	yes	—
633	#477	C₂²×C₃₁	1	2	yes	—
634	#476	C₂²×C₃₁	1	2	yes	—
635	#475	C₂²×C₃₁	1	1	yes	characteristic
636	#475	C₂²×C₃₁	1	1	yes	characteristic
637	#475	C₂²×C₃₁	1	1	yes	characteristic
638	#474	C₂²×C₃₁	1	1	yes	characteristic
639	#468	C₂²×C₃₁	1	2	yes	—
640	#468	C₂²×C₃₁	1	2	yes	—
641	#467	C₂²×C₃₁	1	2	yes	—
642	#467	C₂²×C₃₁	1	2	yes	—
643	#465	C₂²×C₃₁	1	2	yes	—
644	#465	C₂²×C₃₁	1	2	yes	—
645	#464	C₂²×C₃₁	1	2	yes	—
646	#463	C₂²×C₃₁	1	2	yes	—
647	#462	C₂²×C₃₁	1	1	yes	characteristic
648	#462	C₂²×C₃₁	1	1	yes	characteristic
649	#462	C₂²×C₃₁	1	2	yes	—
650	#461	C₂²×C₃₁	1	2	yes	—
651	#460	C₂²×C₃₁	1	1	yes	characteristic
652	#459	C₂²×C₃₁	1	1	yes	characteristic
653	#452	C₂²×C₃₁	1	2	yes	—
654	#452	C₂²×C₃₁	1	2	yes	—
655	#452	C₂²×C₃₁	1	2	yes	—
656	#451	C₂²×C₃₁	1	2	yes	—
657	#449	C₂²×C₃₁	1	2	yes	—
658	#449	C₂²×C₃₁	1	2	yes	—
659	#446	C₂²×C₃₁	1	1	yes	characteristic
660	#446	C₂²×C₃₁	1	1	yes	characteristic
661	#442	C₂²×C₃₁	1	2	yes	—
662	#442	C₂²×C₃₁	1	2	yes	—
663	#441	C₂²×C₃₁	1	2	yes	—
664	#441	C₂²×C₃₁	1	2	yes	—
665	#441	C₂²×C₃₁	1	1	yes	characteristic
666	#441	C₂²×C₃₁	1	2	yes	—
667	#441	C₂²×C₃₁	1	1	yes	characteristic
668	#440	C₂²×C₃₁	1	2	yes	—
669	#440	C₂²×C₃₁	1	1	yes	characteristic
670	#440	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	—
672	#440	C₂²×C₃₁	1	2	yes	—
673	#440	C₂²×C₃₁	1	2	yes	—
674	#440	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	#435	C₂²×C₃₁	1	2	yes	—
680	#435	C₂²×C₃₁	1	2	yes	—
681	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
682	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
683	#432	C₂²×C₃₁	1	2	yes	—
684	#432	C₂²×C₃₁	1	1	yes	characteristic
685	#428	C₂²×C₃₁	1	1	yes	characteristic
686	#427	C₂²×C₃₁	1	2	yes	—
687	#419	C₂²×C₃₁	1	1	yes	characteristic
688	#417	C₂²×C₃₁	1	1	yes	characteristic
689	#416	C₂²×C₃₁	1	2	yes	—
690	#416	C₂²×C₃₁	1	2	yes	—
691	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
692	C₂×#97	C₂²×C₃₁	1	2	yes	—
693	C₂×C₃₁	—	4	1	no	—
694	C₂×C₃₁	—	4	2	no	—
695	C₂×C₃₁	—	4	2	no	—
696	C₂×C₃₁	—	8	2	no	—
697	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
698	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
699	C₂×C₃₁	#3586	1	1	yes	characteristic
700	C₂×#41	—	2	1	no	—
701	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
702	C₂×#41	C₂³×C₃₁	1	2	yes	—
703	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×#41	C₂³×C₃₁	1	2	yes	—
705	C₂²×Q₈	—	2	1	no	—
706	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	#137	—	2	4	no	—
708	#135	—	2	8	no	—
709	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₃₁	1	2	yes	—
719	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
722	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	#127	—	2	1	no	—
730	#127	C₂³×C₃₁	1	1	yes	characteristic
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	—	2	2	no	—
741	#125	—	2	1	no	—
742	#125	C₂³×C₃₁	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	—	2	2	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	C₂³×C₃₁	1	2	yes	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	1	no	—
770	#121	—	2	2	no	—
771	#121	C₂³×C₃₁	1	2	yes	—
772	#121	C₂³×C₃₁	1	2	yes	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	D₄×C₃₁	1	2	yes	—
806	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	2	yes	—
809	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	D₄×C₃₁	1	1	yes	characteristic
821	#117	D₄×C₃₁	1	2	yes	—
822	#117	C₂³×C₃₁	1	2	yes	—
823	#117	C₂³×C₃₁	1	2	yes	—
824	#117	C₂³×C₃₁	1	1	yes	characteristic
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	—	2	2	no	—
828	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₂×C₄²	—	2	1	no	—
830	C₂×C₄²	—	2	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	2	2	no	—
833	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
834	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
835	#107	C₂³×C₃₁	1	1	yes	characteristic
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	2	yes	—
839	#107	C₂³×C₃₁	1	2	yes	—
840	#106	C₂³×C₃₁	1	2	yes	—
841	#106	C₂³×C₃₁	1	2	yes	—
842	#106	C₂³×C₃₁	1	1	yes	characteristic
843	#106	C₂³×C₃₁	1	1	yes	characteristic
844	#106	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	1	yes	characteristic
854	#103	C₂³×C₃₁	1	1	yes	characteristic
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	1	yes	characteristic
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	2	yes	—
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
872	#97	C₂³×C₃₁	1	1	yes	characteristic
873	#97	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	#97	C₂³×C₃₁	1	2	yes	—
876	#97	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₃₁	#61460	1	1	yes	characteristic, direct product factor, Sylow
880	#41	—	2	4	no	—
881	#41	—	2	4	no	—
882	#41	—	2	2	no	—
883	#41	—	4	2	no	—
884	#41	—	4	2	no	—
885	#41	—	4	2	no	—
886	#41	—	4	1	no	—
887	#41	—	4	4	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	—	4	4	no	—
895	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
908	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
910	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
923	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
927	Q₁₆	—	2	4	no	—
928	Q₁₆	—	2	2	no	—
929	Q₁₆	—	2	2	no	—
930	Q₁₆	—	4	2	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	4	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	#41×C₃₁	1	4	yes	complemented
936	D₈	—	2	4	no	—
937	M₁₆	—	2	2	no	—
938	M₁₆	—	4	1	no	—
939	C₂×C₈	—	2	4	no	—
940	C₂×C₈	—	4	2	no	—
941	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
945	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
946	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1013	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₃₁	1	2	yes	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1021	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	4	4	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	C₂×#41×C₃₁	1	2	yes	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	D₄	C₂×#41×C₃₁	1	2	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	2	no	—
1089	C₈	—	2	1	no	—
1090	C₈	C₂×#41×C₃₁	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	C₃₁×#575	1	2	yes	—
1122	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1123	C₄	C₃₁×#585	1	1	yes	characteristic
1124	C₂	—	4	1	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	4	2	no	—
1127	C₂	—	8	2	no	—
1128	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1129	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1130	C₂	C₃₁×#3586	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3482	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3386	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3373	C₂	semidirect
7. C₃₁×#3350	C₂	semidirect
8. C₃₁×#3342	C₂	semidirect
9. C₃₁×#3313	C₂	semidirect
10. C₃₁×#3307	C₂	semidirect
11. C₃₁×#3304	C₂	semidirect
12. C₃₁×#3302	C₂	semidirect
13. C₃₁×#3284	C₂	semidirect
14. C₃₁×#3269	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3181	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3115	C₂	semidirect
19. C₃₁×#3113	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₃₁×#2943	C₂	semidirect
369. SD₁₆×C₃₁	#41	semidirect
452. #61460	C₃₁	direct (N × H)
526. #3482	C₂×C₃₁	semidirect
527. #3480	C₂×C₃₁	semidirect
528. #3400	C₂×C₃₁	semidirect
529. #3386	C₂×C₃₁	semidirect
530. #3374	C₂×C₃₁	semidirect
531. #3373	C₂×C₃₁	semidirect
532. #3350	C₂×C₃₁	semidirect
533. #3342	C₂×C₃₁	semidirect
534. #3313	C₂×C₃₁	semidirect
535. #3307	C₂×C₃₁	semidirect
536. #3304	C₂×C₃₁	semidirect
537. #3302	C₂×C₃₁	semidirect
538. #3284	C₂×C₃₁	semidirect
539. #3269	C₂×C₃₁	semidirect
540. #3182	C₂×C₃₁	semidirect
541. #3181	C₂×C₃₁	semidirect
542. #3116	C₂×C₃₁	semidirect
543. #3115	C₂×C₃₁	semidirect
544. #3113	C₂×C₃₁	semidirect
545. #3111	C₂×C₃₁	semidirect
546. #2970	C₂×C₃₁	semidirect
547. C₄×#137	C₂×C₃₁	semidirect
548. #2943	C₂×C₃₁	semidirect
879. C₃₁	#61460	direct (N × H)
935. SD₁₆	#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×#3482	2
C₃₁×#3480	2
C₃₁×#3400	2
C₃₁×#3386	2
C₃₁×#3374	2
C₃₁×#3373	2
C₃₁×#3350	2
C₃₁×#3342	2
C₃₁×#3313	2
C₃₁×#3307	2
C₃₁×#3304	2
C₃₁×#3302	2
C₃₁×#3284	2
C₃₁×#3269	2
C₃₁×#3182	2
C₃₁×#3181	2
C₃₁×#3116	2
C₃₁×#3115	2
C₃₁×#3113	2
C₃₁×#3111	2
C₃₁×#2970	2
C₄×C₃₁×#137	2
C₃₁×#2943	2
#61460	31

Subgroups — C31×#61460 #21518219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61460 #21518219