Subgroups — C₃₁×#61479 #21518238

Order 7936.

1880 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3309	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3287	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3119	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2951	C₂	1	2	yes	maximal, complemented
17	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#135	C₂²	1	2	yes	—
20	C₃₁×#557	C₂²	1	2	yes	—
21	C₃₁×#553	—	2	4	no	—
22	C₃₁×#553	C₂²	1	4	yes	—
23	C₃₁×#550	—	2	2	no	—
24	C₃₁×#550	C₂²	1	2	yes	—
25	C₃₁×#550	C₂²	1	4	yes	—
26	C₃₁×#550	C₂²	1	2	yes	—
27	C₃₁×#547	—	2	2	no	—
28	C₃₁×#547	C₂²	1	2	yes	—
29	C₃₁×#540	—	2	4	no	—
30	C₃₁×#540	C₂²	1	4	yes	—
31	C₃₁×#532	—	2	2	no	—
32	C₃₁×#532	C₂²	1	2	yes	—
33	C₃₁×#529	—	2	2	no	—
34	C₃₁×#529	C₂²	1	1	yes	characteristic
35	C₃₁×#520	C₂²	1	4	yes	—
36	C₄×#41×C₃₁	C₂²	1	2	yes	—
37	C₃₁×#500	C₂²	1	1	yes	characteristic
38	C₃₁×#499	C₂²	1	2	yes	—
39	C₃₁×#493	C₂²	1	1	yes	characteristic
40	C₃₁×#493	C₂²	1	2	yes	—
41	C₃₁×#490	C₂²	1	4	yes	—
42	C₃₁×#486	C₂²	1	2	yes	—
43	C₃₁×#482	C₂²	1	4	yes	—
44	C₃₁×#481	C₂²	1	4	yes	—
45	C₃₁×#480	C₂²	1	4	yes	—
46	C₃₁×#479	C₂²	1	4	yes	—
47	C₃₁×#478	C₂²	1	4	yes	—
48	C₃₁×#475	C₂²	1	2	yes	—
49	C₃₁×#474	C₂²	1	2	yes	—
50	C₃₁×#469	C₂²	1	4	yes	—
51	C₃₁×#466	C₂²	1	2	yes	—
52	C₃₁×#466	C₂²	1	2	yes	—
53	C₃₁×#466	C₂²	1	2	yes	—
54	C₃₁×#466	C₂²	1	2	yes	—
55	C₃₁×#460	C₂²	1	2	yes	—
56	C₃₁×#460	C₂²	1	4	yes	—
57	C₃₁×#459	C₂²	1	2	yes	—
58	C₃₁×#459	C₂²	1	4	yes	—
59	C₃₁×#449	C₂²	1	4	yes	—
60	C₃₁×#449	C₂²	1	4	yes	—
61	C₃₁×#449	C₂²	1	4	yes	—
62	C₃₁×#446	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
64	C₃₁×#442	C₂²	1	4	yes	—
65	C₃₁×#440	C₂²	1	4	yes	—
66	C₃₁×#440	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
69	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
72	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×D₈×C₃₁	C₂²	1	2	yes	—
74	C₄×D₈×C₃₁	C₂²	1	2	yes	—
75	C₄×D₈×C₃₁	C₂²	1	2	yes	—
76	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#436	C₂²	1	1	yes	characteristic
78	C₃₁×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₃₁	C₂²	1	2	yes	—
81	C₃₁×#433	C₂²	1	2	yes	—
82	C₃₁×#432	C₂²	1	1	yes	characteristic
83	C₃₁×#427	C₂²	1	1	yes	characteristic
84	C₂×C₃₁×#107	C₂²	1	2	yes	—
85	C₃₁×#417	C₂²	1	4	yes	—
86	C₃₁×#416	C₂²	1	2	yes	—
87	C₃₁×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	—	2	2	no	—
91	C₂×#41×C₃₁	—	2	2	no	—
92	C₂×#41×C₃₁	C₂³	1	2	yes	—
93	C₂×#41×C₃₁	C₂³	1	4	yes	—
94	C₃₁×#135	—	2	4	no	—
95	C₃₁×#135	—	2	8	no	—
96	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×D₈×C₃₁	C₂³	1	2	yes	—
101	C₂×D₈×C₃₁	C₂³	1	2	yes	—
102	C₂×D₈×C₃₁	C₂³	1	4	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×#127	—	2	2	no	—
110	C₃₁×#127	—	2	4	no	—
111	C₃₁×#127	C₂³	1	2	yes	—
112	C₃₁×#127	C₂³	1	4	yes	—
113	C₃₁×#126	—	2	4	no	—
114	C₃₁×#126	D₄	1	2	yes	—
115	C₃₁×#125	—	2	4	no	—
116	C₃₁×#125	D₄	1	1	yes	characteristic
117	C₃₁×#125	C₂³	1	4	yes	—
118	C₃₁×#124	—	2	2	no	—
119	C₃₁×#124	D₄	1	1	yes	characteristic
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	D₄	1	2	yes	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₃₁×#121	—	2	4	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	2	no	—
130	C₃₁×#121	—	2	4	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	D₄	1	1	yes	characteristic
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
142	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	4	no	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	4	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	2	yes	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
159	C₃₁×#117	—	2	4	no	—
160	C₃₁×#117	—	2	2	no	—
161	C₃₁×#117	C₂³	1	2	yes	—
162	C₃₁×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
165	C₂×C₄²×C₃₁	—	2	2	no	—
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	2	yes	—
169	C₃₁×#107	C₂³	1	4	yes	—
170	C₃₁×#107	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#106	C₂³	1	2	yes	—
173	C₃₁×#106	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×#103	C₂³	1	2	yes	—
179	C₃₁×#103	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	4	yes	—
181	C₃₁×#102	C₂³	1	2	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×#97	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	#41×C₃₁	—	2	4	no	—
199	#41×C₃₁	—	2	8	no	—
200	#41×C₃₁	—	4	2	no	—
201	#41×C₃₁	—	4	4	no	—
202	#41×C₃₁	—	8	4	no	—
203	#41×C₃₁	—	8	4	no	—
204	#41×C₃₁	—	8	4	no	—
205	C₂×Q₈×C₃₁	—	2	2	no	—
206	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	2	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
232	Q₁₆×C₃₁	#41	1	4	yes	complemented
233	SD₁₆×C₃₁	—	2	4	no	—
234	SD₁₆×C₃₁	—	2	8	no	—
235	D₈×C₃₁	—	2	2	no	—
236	D₈×C₃₁	—	2	4	no	—
237	D₈×C₃₁	—	4	2	no	—
238	D₈×C₃₁	—	4	4	no	—
239	M₁₆×C₃₁	—	4	2	no	—
240	C₂×C₈×C₃₁	—	2	2	no	—
241	C₂×C₈×C₃₁	—	2	4	no	—
242	C₂×C₈×C₃₁	—	4	1	no	—
243	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	2	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	2	yes	—
287	#61479	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	4	no	—
290	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
291	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
292	Q₈×C₃₁	—	2	2	no	—
293	Q₈×C₃₁	—	2	2	no	—
294	Q₈×C₃₁	—	4	4	no	—
295	Q₈×C₃₁	C₂×#41	1	4	yes	—
296	D₄×C₃₁	—	2	2	no	—
297	D₄×C₃₁	—	2	2	no	—
298	D₄×C₃₁	—	2	4	no	—
299	D₄×C₃₁	—	2	4	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	4	2	no	—
302	D₄×C₃₁	—	4	4	no	—
303	D₄×C₃₁	—	4	8	no	—
304	D₄×C₃₁	—	4	4	no	—
305	D₄×C₃₁	—	8	2	no	—
306	D₄×C₃₁	—	8	4	no	—
307	D₄×C₃₁	—	8	4	no	—
308	D₄×C₃₁	—	8	4	no	—
309	D₄×C₃₁	—	8	4	no	—
310	D₄×C₃₁	—	8	4	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	1	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	1	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	4	1	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	4	8	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	8	2	no	—
325	C₂×C₄×C₃₁	—	8	4	no	—
326	C₂×C₄×C₃₁	—	8	4	no	—
327	C₂×C₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	1	no	—
338	C₈×C₃₁	—	2	2	no	—
339	C₈×C₃₁	—	2	1	no	—
340	C₈×C₃₁	—	2	1	no	—
341	C₈×C₃₁	—	2	2	no	—
342	C₈×C₃₁	C₂×#41	1	2	yes	—
343	#3517	C₂×C₃₁	1	2	yes	complemented
344	#3391	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3368	C₂×C₃₁	1	2	yes	complemented
347	#3339	C₂×C₃₁	1	2	yes	complemented
348	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#3332	C₂×C₃₁	1	2	yes	complemented
350	#3309	C₂×C₃₁	1	4	yes	complemented
351	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3287	C₂×C₃₁	1	2	yes	complemented
353	#3176	C₂×C₃₁	1	2	yes	complemented
354	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3119	C₂×C₃₁	1	4	yes	complemented
356	#3115	C₂×C₃₁	1	2	yes	complemented
357	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#2951	C₂×C₃₁	1	2	yes	complemented
359	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	1	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	1	no	—
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	4	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	4	no	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	2	no	—
376	C₄×C₃₁	—	2	1	no	—
377	C₄×C₃₁	—	2	2	no	—
378	C₄×C₃₁	—	2	4	no	—
379	C₄×C₃₁	—	2	1	no	—
380	C₄×C₃₁	—	2	2	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	2	no	—
383	C₄×C₃₁	—	4	4	no	—
384	C₄×C₃₁	#576	1	2	yes	—
385	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
386	C₄×C₃₁	#585	1	1	yes	characteristic
387	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
388	C₂×#135	C₂²×C₃₁	1	2	yes	—
389	#557	C₂²×C₃₁	1	2	yes	—
390	#553	—	2	4	no	—
391	#553	C₂²×C₃₁	1	4	yes	—
392	#550	—	2	2	no	—
393	#550	C₂²×C₃₁	1	2	yes	—
394	#550	C₂²×C₃₁	1	4	yes	—
395	#550	C₂²×C₃₁	1	2	yes	—
396	#547	—	2	2	no	—
397	#547	C₂²×C₃₁	1	2	yes	—
398	#540	—	2	4	no	—
399	#540	C₂²×C₃₁	1	4	yes	—
400	#532	—	2	2	no	—
401	#532	C₂²×C₃₁	1	2	yes	—
402	#529	—	2	2	no	—
403	#529	C₂²×C₃₁	1	1	yes	characteristic
404	#520	C₂²×C₃₁	1	4	yes	—
405	C₄×#41	C₂²×C₃₁	1	2	yes	—
406	#500	C₂²×C₃₁	1	1	yes	characteristic
407	#499	C₂²×C₃₁	1	2	yes	—
408	#493	C₂²×C₃₁	1	1	yes	characteristic
409	#493	C₂²×C₃₁	1	2	yes	—
410	#490	C₂²×C₃₁	1	4	yes	—
411	#486	C₂²×C₃₁	1	2	yes	—
412	#482	C₂²×C₃₁	1	4	yes	—
413	#481	C₂²×C₃₁	1	4	yes	—
414	#480	C₂²×C₃₁	1	4	yes	—
415	#479	C₂²×C₃₁	1	4	yes	—
416	#478	C₂²×C₃₁	1	4	yes	—
417	#475	C₂²×C₃₁	1	2	yes	—
418	#474	C₂²×C₃₁	1	2	yes	—
419	#469	C₂²×C₃₁	1	4	yes	—
420	#466	C₂²×C₃₁	1	2	yes	—
421	#466	C₂²×C₃₁	1	2	yes	—
422	#466	C₂²×C₃₁	1	2	yes	—
423	#466	C₂²×C₃₁	1	2	yes	—
424	#460	C₂²×C₃₁	1	2	yes	—
425	#460	C₂²×C₃₁	1	4	yes	—
426	#459	C₂²×C₃₁	1	2	yes	—
427	#459	C₂²×C₃₁	1	4	yes	—
428	#449	C₂²×C₃₁	1	4	yes	—
429	#449	C₂²×C₃₁	1	4	yes	—
430	#449	C₂²×C₃₁	1	4	yes	—
431	#446	C₂²×C₃₁	1	1	yes	characteristic
432	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
433	#442	C₂²×C₃₁	1	4	yes	—
434	#440	C₂²×C₃₁	1	4	yes	—
435	#440	C₂²×C₃₁	1	4	yes	—
436	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
437	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
438	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
439	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
440	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
441	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
442	C₄×D₈	C₂²×C₃₁	1	2	yes	—
443	C₄×D₈	C₂²×C₃₁	1	2	yes	—
444	C₄×D₈	C₂²×C₃₁	1	2	yes	—
445	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
446	#436	C₂²×C₃₁	1	1	yes	characteristic
447	#435	C₂²×C₃₁	1	2	yes	—
448	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
449	C₈×D₄	C₂²×C₃₁	1	2	yes	—
450	#433	C₂²×C₃₁	1	2	yes	—
451	#432	C₂²×C₃₁	1	1	yes	characteristic
452	#427	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#107	C₂²×C₃₁	1	2	yes	—
454	#417	C₂²×C₃₁	1	4	yes	—
455	#416	C₂²×C₃₁	1	2	yes	—
456	#405	C₂²×C₃₁	1	2	yes	—
457	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₃₁	—	4	1	no	—
459	C₂×C₃₁	—	4	2	no	—
460	C₂×C₃₁	—	8	2	no	—
461	C₂×C₃₁	—	8	4	no	—
462	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
463	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
464	C₂×C₃₁	#3584	1	1	yes	characteristic
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	C₂³×C₃₁	1	2	yes	—
469	C₂×#41	C₂³×C₃₁	1	4	yes	—
470	#135	—	2	4	no	—
471	#135	—	2	8	no	—
472	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×D₈	C₂³×C₃₁	1	2	yes	—
477	C₂×D₈	C₂³×C₃₁	1	2	yes	—
478	C₂×D₈	C₂³×C₃₁	1	4	yes	—
479	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
480	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
482	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
485	#127	—	2	2	no	—
486	#127	—	2	4	no	—
487	#127	C₂³×C₃₁	1	2	yes	—
488	#127	C₂³×C₃₁	1	4	yes	—
489	#126	—	2	4	no	—
490	#126	D₄×C₃₁	1	2	yes	—
491	#125	—	2	4	no	—
492	#125	D₄×C₃₁	1	1	yes	characteristic
493	#125	C₂³×C₃₁	1	4	yes	—
494	#124	—	2	2	no	—
495	#124	D₄×C₃₁	1	1	yes	characteristic
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	D₄×C₃₁	1	2	yes	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
503	#121	—	2	4	no	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	D₄×C₃₁	1	1	yes	characteristic
513	#121	C₂³×C₃₁	1	4	yes	—
514	#121	C₂³×C₃₁	1	4	yes	—
515	#121	C₂³×C₃₁	1	4	yes	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
518	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
520	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	C₂³×C₃₁	1	2	yes	—
530	C₄×D₄	C₂³×C₃₁	1	2	yes	—
531	C₄×D₄	C₂³×C₃₁	1	4	yes	—
532	C₄×D₄	C₂³×C₃₁	1	4	yes	—
533	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	#117	—	2	4	no	—
536	#117	—	2	2	no	—
537	#117	C₂³×C₃₁	1	2	yes	—
538	#117	C₂³×C₃₁	1	2	yes	—
539	C₂×C₄⋊C₄	—	2	4	no	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
541	C₂×C₄²	—	2	2	no	—
542	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
543	#107	C₂³×C₃₁	1	1	yes	characteristic
544	#107	C₂³×C₃₁	1	2	yes	—
545	#107	C₂³×C₃₁	1	4	yes	—
546	#107	C₂³×C₃₁	1	1	yes	characteristic
547	#107	C₂³×C₃₁	1	2	yes	—
548	#106	C₂³×C₃₁	1	2	yes	—
549	#106	C₂³×C₃₁	1	4	yes	—
550	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
554	#103	C₂³×C₃₁	1	2	yes	—
555	#103	C₂³×C₃₁	1	2	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#102	C₂³×C₃₁	1	2	yes	—
558	#102	C₂³×C₃₁	1	2	yes	—
559	#102	C₂³×C₃₁	1	4	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
567	#97	C₂³×C₃₁	1	2	yes	—
568	#97	C₂³×C₃₁	1	2	yes	—
569	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₃₁	1	2	yes	—
574	C₃₁	#61479	1	1	yes	characteristic, direct product factor, Sylow
575	#41	—	2	4	no	—
576	#41	—	2	8	no	—
577	#41	—	4	2	no	—
578	#41	—	4	4	no	—
579	#41	—	8	4	no	—
580	#41	—	8	4	no	—
581	#41	—	8	4	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
584	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
597	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
609	Q₁₆	#41×C₃₁	1	4	yes	complemented
610	SD₁₆	—	2	4	no	—
611	SD₁₆	—	2	8	no	—
612	D₈	—	2	2	no	—
613	D₈	—	2	4	no	—
614	D₈	—	4	2	no	—
615	D₈	—	4	4	no	—
616	M₁₆	—	4	2	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	4	no	—
619	C₂×C₈	—	4	1	no	—
620	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
624	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
625	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₄²	C₂⁴×C₃₁	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
667	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
668	Q₈	—	2	2	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	4	4	no	—
671	Q₈	C₂×#41×C₃₁	1	4	yes	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	8	no	—
680	D₄	—	4	4	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	4	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
713	C₈	—	2	1	no	—
714	C₈	—	2	2	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	2	no	—
718	C₈	C₂×#41×C₃₁	1	2	yes	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	2	no	—
743	C₄	C₃₁×#576	1	2	yes	—
744	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
745	C₄	C₃₁×#585	1	1	yes	characteristic
746	C₂	—	4	1	no	—
747	C₂	—	4	2	no	—
748	C₂	—	8	2	no	—
749	C₂	—	8	4	no	—
750	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
751	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
752	C₂	C₃₁×#3584	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3391	C₂	semidirect
3. C₃₁×#3383	C₂	semidirect
4. C₃₁×#3368	C₂	semidirect
5. C₃₁×#3339	C₂	semidirect
6. C₃₁×#3334	C₂	semidirect
7. C₃₁×#3332	C₂	semidirect
8. C₃₁×#3309	C₂	semidirect
9. C₃₁×#3287	C₂	semidirect
10. C₃₁×#3287	C₂	semidirect
11. C₃₁×#3176	C₂	semidirect
12. C₃₁×#3169	C₂	semidirect
13. C₃₁×#3119	C₂	semidirect
14. C₃₁×#3115	C₂	semidirect
15. C₃₁×#2966	C₂	semidirect
16. C₃₁×#2951	C₂	semidirect
17. C₄×C₃₁×#135	C₂	semidirect
232. Q₁₆×C₃₁	#41	semidirect
287. #61479	C₃₁	direct (N × H)
343. #3517	C₂×C₃₁	semidirect
344. #3391	C₂×C₃₁	semidirect
345. #3383	C₂×C₃₁	semidirect
346. #3368	C₂×C₃₁	semidirect
347. #3339	C₂×C₃₁	semidirect
348. #3334	C₂×C₃₁	semidirect
349. #3332	C₂×C₃₁	semidirect
350. #3309	C₂×C₃₁	semidirect
351. #3287	C₂×C₃₁	semidirect
352. #3287	C₂×C₃₁	semidirect
353. #3176	C₂×C₃₁	semidirect
354. #3169	C₂×C₃₁	semidirect
355. #3119	C₂×C₃₁	semidirect
356. #3115	C₂×C₃₁	semidirect
357. #2966	C₂×C₃₁	semidirect
358. #2951	C₂×C₃₁	semidirect
359. C₄×#135	C₂×C₃₁	semidirect
574. C₃₁	#61479	direct (N × H)
609. Q₁₆	#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×#3517	2
C₃₁×#3391	2
C₃₁×#3383	2
C₃₁×#3368	2
C₃₁×#3339	2
C₃₁×#3334	2
C₃₁×#3332	2
C₃₁×#3309	2
C₃₁×#3287	2
C₃₁×#3176	2
C₃₁×#3169	2
C₃₁×#3119	2
C₃₁×#3115	2
C₃₁×#2966	2
C₃₁×#2951	2
C₄×C₃₁×#135	2
#61479	31

Subgroups — C31×#61479 #21518238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61479 #21518238