Subgroups — C₃₁×#61261 #21518020

Order 7936.

1782 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3493	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3350	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3348	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3342	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3093	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#556	—	2	2	no	—
22	C₃₁×#556	C₂²	1	4	yes	—
23	C₃₁×#555	—	2	2	no	—
24	C₃₁×#555	C₂²	1	4	yes	—
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#553	C₂²	1	4	yes	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	4	yes	—
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#538	—	2	4	no	—
31	C₃₁×#537	C₂²	1	2	yes	—
32	C₃₁×#529	—	2	4	no	—
33	C₃₁×#525	C₂²	1	2	yes	—
34	C₃₁×#525	C₂²	1	1	yes	characteristic
35	C₃₁×#520	C₂²	1	2	yes	—
36	C₃₁×#520	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	C₂²	1	2	yes	—
38	C₃₁×#501	C₂²	1	4	yes	complemented
39	C₃₁×#500	C₂²	1	2	yes	complemented
40	C₃₁×#499	C₂²	1	2	yes	complemented
41	C₃₁×#485	C₂²	1	4	yes	—
42	C₃₁×#485	C₂²	1	4	yes	—
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#483	C₂²	1	4	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	—
46	C₃₁×#482	C₂²	1	4	yes	—
47	C₃₁×#482	C₂²	1	4	yes	complemented
48	C₃₁×#481	C₂²	1	4	yes	complemented
49	C₃₁×#479	C₂²	1	4	yes	complemented
50	C₃₁×#478	C₂²	1	4	yes	complemented
51	C₃₁×#476	C₂²	1	4	yes	complemented
52	C₃₁×#475	C₂²	1	4	yes	complemented
53	C₃₁×#468	C₂²	1	4	yes	complemented
54	C₃₁×#467	C₂²	1	1	yes	characteristic
55	C₃₁×#467	C₂²	1	1	yes	characteristic
56	C₃₁×#467	C₂²	1	2	yes	complemented
57	C₃₁×#466	C₂²	1	1	yes	characteristic
58	C₃₁×#466	C₂²	1	1	yes	characteristic
59	C₃₁×#466	C₂²	1	2	yes	complemented
60	C₃₁×#465	C₂²	1	2	yes	—
61	C₃₁×#465	C₂²	1	2	yes	—
62	C₃₁×#440	C₂²	1	4	yes	complemented
63	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
64	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
65	C₃₁×#435	C₂²	1	2	yes	—
66	C₃₁×#435	C₂²	1	2	yes	—
67	C₈×D₄×C₃₁	C₂²	1	2	yes	—
68	C₈×D₄×C₃₁	C₂²	1	2	yes	—
69	C₃₁×#428	C₂²	1	2	yes	—
70	C₃₁×#428	C₂²	1	2	yes	—
71	C₃₁×#428	C₂²	1	4	yes	complemented
72	C₃₁×#427	C₂²	1	2	yes	—
73	C₃₁×#427	C₂²	1	2	yes	—
74	C₃₁×#427	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	2	yes	—
76	C₃₁×#427	C₂²	1	1	yes	characteristic
77	C₃₁×#427	C₂²	1	2	yes	complemented
78	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
79	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
80	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
81	C₂×C₃₁×#106	C₂²	1	2	yes	—
82	C₃₁×#424	C₂²	1	1	yes	characteristic
83	C₃₁×#417	C₂²	1	2	yes	—
84	C₃₁×#417	C₂²	1	2	yes	—
85	C₃₁×#416	C₂²	1	2	yes	—
86	C₃₁×#408	C₂²	1	1	yes	characteristic
87	C₃₁×#407	C₂²	1	1	yes	characteristic
88	C₃₁×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₃₁×#135	—	2	4	no	—
93	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
95	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×#131	—	2	4	no	—
97	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂²×C₈×C₃₁	—	2	4	no	—
101	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#126	—	2	4	no	—
114	C₃₁×#125	—	2	4	no	—
115	C₃₁×#125	—	2	2	no	—
116	C₃₁×#125	C₂³	1	4	yes	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#124	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	2	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	D₄	1	2	yes	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	D₄	1	1	yes	characteristic
136	C₃₁×#121	D₄	1	1	yes	characteristic
137	C₃₁×#121	C₂³	1	2	yes	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#120	—	2	2	no	—
141	C₃₁×#120	D₄	1	2	yes	—
142	C₄×Q₈×C₃₁	—	2	2	no	—
143	C₄×Q₈×C₃₁	—	2	4	no	—
144	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	C₂³	1	2	yes	—
154	C₃₁×#117	—	2	2	no	—
155	C₃₁×#117	—	2	2	no	—
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	—	2	4	no	—
159	C₃₁×#117	C₂³	1	2	yes	—
160	C₃₁×#117	C₂³	1	4	yes	—
161	C₃₁×#117	C₂³	1	4	yes	—
162	C₃₁×#117	C₂³	1	4	yes	—
163	C₃₁×#117	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
169	C₂×C₄²×C₃₁	—	2	2	no	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	1	yes	characteristic
175	C₃₁×#107	C₂³	1	4	yes	—
176	C₃₁×#107	C₂³	1	1	yes	characteristic
177	C₃₁×#107	C₂³	1	4	yes	—
178	C₃₁×#106	C₂³	1	4	yes	—
179	C₃₁×#106	C₂³	1	4	yes	—
180	C₃₁×#106	C₂³	1	2	yes	—
181	C₃₁×#106	C₂³	1	4	yes	—
182	C₃₁×#106	C₂³	1	4	yes	—
183	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
184	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	2	yes	—
186	C₃₁×#103	C₂³	1	2	yes	—
187	C₃₁×#103	C₂³	1	4	yes	—
188	C₃₁×#103	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	2	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₃₁	C₂³	1	2	yes	—
199	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
200	#41×C₃₁	—	2	2	no	—
201	#41×C₃₁	—	2	2	no	—
202	#41×C₃₁	—	2	4	no	—
203	#41×C₃₁	—	2	4	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	4	no	—
223	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₃₁	—	2	2	no	—
231	SD₁₆×C₃₁	—	2	4	no	—
232	D₈×C₃₁	—	2	2	no	—
233	M₁₆×C₃₁	—	2	2	no	—
234	M₁₆×C₃₁	—	2	2	no	—
235	M₁₆×C₃₁	—	2	4	no	—
236	C₂×C₈×C₃₁	—	2	2	no	—
237	C₂×C₈×C₃₁	—	2	2	no	—
238	C₂×C₈×C₃₁	—	2	2	no	—
239	C₂×C₈×C₃₁	—	2	2	no	—
240	C₂×C₈×C₃₁	—	2	2	no	—
241	C₂×C₈×C₃₁	—	2	4	no	—
242	C₂×C₈×C₃₁	#41	1	4	yes	—
243	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	yes	characteristic
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	2	no	—
252	C₄⋊C₄×C₃₁	—	2	4	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	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	2	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₄²×C₃₁	—	2	4	no	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	4	no	—
286	C₄²×C₃₁	—	2	4	no	—
287	C₄²×C₃₁	—	2	2	no	—
288	C₄²×C₃₁	C₂⁴	1	2	yes	—
289	#61261	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	4	1	no	—
293	C₂³×C₃₁	—	4	1	no	—
294	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
296	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
297	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₃₁	—	2	2	no	—
299	Q₈×C₃₁	—	2	2	no	—
300	Q₈×C₃₁	—	2	2	no	—
301	Q₈×C₃₁	—	8	4	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	2	2	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	4	2	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	8	2	no	—
310	D₄×C₃₁	—	8	4	no	—
311	D₄×C₃₁	—	8	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	1	no	—
316	C₂×C₄×C₃₁	—	2	1	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	1	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	—	8	2	no	—
329	C₂×C₄×C₃₁	—	8	4	no	—
330	C₂×C₄×C₃₁	—	8	2	no	—
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	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
338	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
339	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
340	C₈×C₃₁	—	2	1	no	—
341	C₈×C₃₁	—	2	1	no	—
342	C₈×C₃₁	—	2	2	no	—
343	C₈×C₃₁	—	2	2	no	—
344	C₈×C₃₁	C₂×#41	1	2	yes	—
345	C₈×C₃₁	C₂×#41	1	2	yes	—
346	#3493	C₂×C₃₁	1	2	yes	complemented
347	#3350	C₂×C₃₁	1	4	yes	complemented
348	#3348	C₂×C₃₁	1	4	yes	complemented
349	#3342	C₂×C₃₁	1	2	yes	complemented
350	#3341	C₂×C₃₁	1	2	yes	complemented
351	#3339	C₂×C₃₁	1	2	yes	complemented
352	#3336	C₂×C₃₁	1	2	yes	complemented
353	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3099	C₂×C₃₁	1	2	yes	complemented
355	#3093	C₂×C₃₁	1	2	yes	complemented
356	#3084	C₂×C₃₁	1	2	yes	complemented
357	#3061	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
359	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
361	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
363	C₂²×C₃₁	—	2	1	no	—
364	C₂²×C₃₁	—	2	1	no	—
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	2	1	no	—
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	2	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	2	1	no	—
372	C₂²×C₃₁	—	2	1	no	—
373	C₂²×C₃₁	—	2	2	no	—
374	C₂²×C₃₁	—	4	4	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	#547	1	2	yes	—
379	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₃₁	—	2	2	no	—
381	C₄×C₃₁	—	2	2	no	—
382	C₄×C₃₁	—	2	1	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	2	2	no	—
385	C₄×C₃₁	—	4	4	no	—
386	C₄×C₃₁	—	4	2	no	—
387	C₄×C₃₁	—	4	4	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	#547	1	2	yes	—
391	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
392	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
394	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
395	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
396	#556	—	2	2	no	—
397	#556	C₂²×C₃₁	1	4	yes	—
398	#555	—	2	2	no	—
399	#555	C₂²×C₃₁	1	4	yes	—
400	#553	—	2	2	no	—
401	#553	C₂²×C₃₁	1	4	yes	—
402	#552	—	2	2	no	—
403	#552	C₂²×C₃₁	1	4	yes	—
404	#544	C₂²×C₃₁	1	2	yes	—
405	#538	—	2	4	no	—
406	#537	C₂²×C₃₁	1	2	yes	—
407	#529	—	2	4	no	—
408	#525	C₂²×C₃₁	1	2	yes	—
409	#525	C₂²×C₃₁	1	1	yes	characteristic
410	#520	C₂²×C₃₁	1	2	yes	—
411	#520	C₂²×C₃₁	1	2	yes	—
412	C₂×#117	C₂²×C₃₁	1	2	yes	—
413	#501	C₂²×C₃₁	1	4	yes	complemented
414	#500	C₂²×C₃₁	1	2	yes	complemented
415	#499	C₂²×C₃₁	1	2	yes	complemented
416	#485	C₂²×C₃₁	1	4	yes	—
417	#485	C₂²×C₃₁	1	4	yes	—
418	#485	C₂²×C₃₁	1	4	yes	complemented
419	#483	C₂²×C₃₁	1	4	yes	complemented
420	#482	C₂²×C₃₁	1	4	yes	—
421	#482	C₂²×C₃₁	1	4	yes	—
422	#482	C₂²×C₃₁	1	4	yes	complemented
423	#481	C₂²×C₃₁	1	4	yes	complemented
424	#479	C₂²×C₃₁	1	4	yes	complemented
425	#478	C₂²×C₃₁	1	4	yes	complemented
426	#476	C₂²×C₃₁	1	4	yes	complemented
427	#475	C₂²×C₃₁	1	4	yes	complemented
428	#468	C₂²×C₃₁	1	4	yes	complemented
429	#467	C₂²×C₃₁	1	1	yes	characteristic
430	#467	C₂²×C₃₁	1	1	yes	characteristic
431	#467	C₂²×C₃₁	1	2	yes	complemented
432	#466	C₂²×C₃₁	1	1	yes	characteristic
433	#466	C₂²×C₃₁	1	1	yes	characteristic
434	#466	C₂²×C₃₁	1	2	yes	complemented
435	#465	C₂²×C₃₁	1	2	yes	—
436	#465	C₂²×C₃₁	1	2	yes	—
437	#440	C₂²×C₃₁	1	4	yes	complemented
438	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
439	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
440	#435	C₂²×C₃₁	1	2	yes	—
441	#435	C₂²×C₃₁	1	2	yes	—
442	C₈×D₄	C₂²×C₃₁	1	2	yes	—
443	C₈×D₄	C₂²×C₃₁	1	2	yes	—
444	#428	C₂²×C₃₁	1	2	yes	—
445	#428	C₂²×C₃₁	1	2	yes	—
446	#428	C₂²×C₃₁	1	4	yes	complemented
447	#427	C₂²×C₃₁	1	2	yes	—
448	#427	C₂²×C₃₁	1	2	yes	—
449	#427	C₂²×C₃₁	1	2	yes	—
450	#427	C₂²×C₃₁	1	2	yes	—
451	#427	C₂²×C₃₁	1	1	yes	characteristic
452	#427	C₂²×C₃₁	1	2	yes	complemented
453	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
454	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
455	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
456	C₂×#106	C₂²×C₃₁	1	2	yes	—
457	#424	C₂²×C₃₁	1	1	yes	characteristic
458	#417	C₂²×C₃₁	1	2	yes	—
459	#417	C₂²×C₃₁	1	2	yes	—
460	#416	C₂²×C₃₁	1	2	yes	—
461	#408	C₂²×C₃₁	1	1	yes	characteristic
462	#407	C₂²×C₃₁	1	1	yes	characteristic
463	#405	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×C₃₁	—	2	2	no	—
465	C₂×C₃₁	—	4	2	no	—
466	C₂×C₃₁	—	4	1	no	—
467	C₂×C₃₁	—	4	1	no	—
468	C₂×C₃₁	—	8	2	no	—
469	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
470	C₂×C₃₁	#3584	1	1	yes	characteristic
471	C₂×C₃₁	#3584	1	1	yes	characteristic
472	C₂×#41	C₂³×C₃₁	1	2	yes	—
473	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
475	#135	—	2	4	no	—
476	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
478	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
479	#131	—	2	4	no	—
480	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
481	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
482	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×C₈	—	2	4	no	—
484	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
490	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
493	#126	—	2	4	no	—
494	#126	—	2	4	no	—
495	#126	—	2	4	no	—
496	#126	—	2	4	no	—
497	#125	—	2	4	no	—
498	#125	—	2	2	no	—
499	#125	C₂³×C₃₁	1	4	yes	—
500	#124	—	2	4	no	—
501	#124	—	2	4	no	—
502	#124	—	2	4	no	—
503	#123	—	2	4	no	—
504	#123	—	2	2	no	—
505	#123	—	2	4	no	—
506	#123	D₄×C₃₁	1	2	yes	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
510	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
511	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
513	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
514	#121	—	2	4	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#121	—	2	4	no	—
518	#121	D₄×C₃₁	1	1	yes	characteristic
519	#121	D₄×C₃₁	1	1	yes	characteristic
520	#121	C₂³×C₃₁	1	2	yes	—
521	#121	C₂³×C₃₁	1	2	yes	—
522	#121	C₂³×C₃₁	1	4	yes	—
523	#120	—	2	2	no	—
524	#120	D₄×C₃₁	1	2	yes	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	4	no	—
527	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	4	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	C₂³×C₃₁	1	4	yes	—
535	C₄×D₄	C₂³×C₃₁	1	2	yes	—
536	C₄×D₄	C₂³×C₃₁	1	2	yes	—
537	#117	—	2	2	no	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	—	2	4	no	—
541	#117	—	2	4	no	—
542	#117	C₂³×C₃₁	1	4	yes	—
543	#117	C₂³×C₃₁	1	4	yes	—
544	#117	C₂³×C₃₁	1	2	yes	—
545	#117	C₂³×C₃₁	1	4	yes	—
546	#117	C₂³×C₃₁	1	1	yes	characteristic
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₄²	—	2	2	no	—
553	#107	C₂³×C₃₁	1	2	yes	—
554	#107	C₂³×C₃₁	1	2	yes	—
555	#107	C₂³×C₃₁	1	2	yes	—
556	#107	C₂³×C₃₁	1	2	yes	—
557	#107	C₂³×C₃₁	1	1	yes	characteristic
558	#107	C₂³×C₃₁	1	4	yes	—
559	#107	C₂³×C₃₁	1	1	yes	characteristic
560	#107	C₂³×C₃₁	1	4	yes	—
561	#106	C₂³×C₃₁	1	4	yes	—
562	#106	C₂³×C₃₁	1	4	yes	—
563	#106	C₂³×C₃₁	1	2	yes	—
564	#106	C₂³×C₃₁	1	4	yes	—
565	#106	C₂³×C₃₁	1	4	yes	—
566	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
567	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
568	#103	C₂³×C₃₁	1	2	yes	—
569	#103	C₂³×C₃₁	1	2	yes	—
570	#103	C₂³×C₃₁	1	4	yes	—
571	#103	C₂³×C₃₁	1	4	yes	—
572	#102	C₂³×C₃₁	1	2	yes	—
573	#102	C₂³×C₃₁	1	2	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
580	#97	C₂³×C₃₁	1	2	yes	—
581	C₄×C₈	C₂³×C₃₁	1	2	yes	—
582	C₃₁	#61261	1	1	yes	characteristic, direct product factor, Sylow
583	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
584	#41	—	2	2	no	—
585	#41	—	2	2	no	—
586	#41	—	2	4	no	—
587	#41	—	2	4	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
590	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
596	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
599	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	SD₁₆	—	2	4	no	—
616	D₈	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	2	no	—
619	M₁₆	—	2	4	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	4	no	—
626	C₂×C₈	#41×C₃₁	1	4	yes	—
627	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
628	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
631	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
648	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
649	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
663	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
664	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
666	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	2	no	—
672	C₄²	C₂⁴×C₃₁	1	2	yes	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
678	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
679	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
680	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	8	4	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	4	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	—	8	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
721	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
722	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
723	C₈	—	2	1	no	—
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×#41×C₃₁	1	2	yes	—
728	C₈	C₂×#41×C₃₁	1	2	yes	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	C₃₁×#547	1	2	yes	—
745	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	—	4	2	no	—
756	C₄	C₃₁×#547	1	2	yes	—
757	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
758	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
765	C₂	C₃₁×#3584	1	1	yes	characteristic
766	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3493	C₂	semidirect
2. C₃₁×#3350	C₂	semidirect
3. C₃₁×#3348	C₂	semidirect
4. C₃₁×#3342	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3336	C₂	semidirect
8. C₃₁×#3164	C₂	semidirect
9. C₃₁×#3099	C₂	semidirect
10. C₃₁×#3093	C₂	semidirect
11. C₃₁×#3084	C₂	semidirect
12. C₃₁×#3061	C₂	semidirect
13. C₃₁×#3050	C₂	semidirect
14. C₃₁×#2951	C₂	semidirect
15. C₃₁×#2929	C₂	semidirect
16. C₃₁×#2913	C₂	semidirect
17. C₂×C₃₁×#427	C₂	semidirect
38. C₃₁×#501	C₂²	semidirect
39. C₃₁×#500	C₂²	semidirect
40. C₃₁×#499	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#483	C₂²	semidirect
47. C₃₁×#482	C₂²	semidirect
48. C₃₁×#481	C₂²	semidirect
49. C₃₁×#479	C₂²	semidirect
50. C₃₁×#478	C₂²	semidirect
51. C₃₁×#476	C₂²	semidirect
52. C₃₁×#475	C₂²	semidirect
53. C₃₁×#468	C₂²	semidirect
56. C₃₁×#467	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
62. C₃₁×#440	C₂²	semidirect
63. C₄×Q₁₆×C₃₁	C₂²	semidirect
64. C₄×D₈×C₃₁	C₂²	semidirect
71. C₃₁×#428	C₂²	semidirect
77. C₃₁×#427	C₂²	semidirect
80. C₂×C₃₁×#107	C₂²	semidirect
289. #61261	C₃₁	direct (N × H)
346. #3493	C₂×C₃₁	semidirect
347. #3350	C₂×C₃₁	semidirect
348. #3348	C₂×C₃₁	semidirect
349. #3342	C₂×C₃₁	semidirect
350. #3341	C₂×C₃₁	semidirect
351. #3339	C₂×C₃₁	semidirect
352. #3336	C₂×C₃₁	semidirect
353. #3164	C₂×C₃₁	semidirect
354. #3099	C₂×C₃₁	semidirect
355. #3093	C₂×C₃₁	semidirect
356. #3084	C₂×C₃₁	semidirect
357. #3061	C₂×C₃₁	semidirect
358. #3050	C₂×C₃₁	semidirect
359. #2951	C₂×C₃₁	semidirect
360. #2929	C₂×C₃₁	semidirect
361. #2913	C₂×C₃₁	semidirect
362. C₂×#427	C₂×C₃₁	semidirect
413. #501	C₂²×C₃₁	semidirect
414. #500	C₂²×C₃₁	semidirect
415. #499	C₂²×C₃₁	semidirect
418. #485	C₂²×C₃₁	semidirect
419. #483	C₂²×C₃₁	semidirect
422. #482	C₂²×C₃₁	semidirect
423. #481	C₂²×C₃₁	semidirect
424. #479	C₂²×C₃₁	semidirect
425. #478	C₂²×C₃₁	semidirect
426. #476	C₂²×C₃₁	semidirect
427. #475	C₂²×C₃₁	semidirect
428. #468	C₂²×C₃₁	semidirect
431. #467	C₂²×C₃₁	semidirect
434. #466	C₂²×C₃₁	semidirect
437. #440	C₂²×C₃₁	semidirect
438. C₄×Q₁₆	C₂²×C₃₁	semidirect
439. C₄×D₈	C₂²×C₃₁	semidirect
446. #428	C₂²×C₃₁	semidirect
452. #427	C₂²×C₃₁	semidirect
455. C₂×#107	C₂²×C₃₁	semidirect
582. C₃₁	#61261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3493	2
C₃₁×#3350	2
C₃₁×#3348	2
C₃₁×#3342	2
C₃₁×#3341	2
C₃₁×#3339	2
C₃₁×#3336	2
C₃₁×#3164	2
C₃₁×#3099	2
C₃₁×#3093	2
C₃₁×#3084	2
C₃₁×#3061	2
C₃₁×#3050	2
C₃₁×#2951	2
C₃₁×#2929	2
C₃₁×#2913	2
C₂×C₃₁×#427	2
#61261	31

Subgroups — C31×#61261 #21518020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61261 #21518020