Subgroups — C₃₁×#61802 #21518561

Order 7936.

1860 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3347	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3318	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3199	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3096	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×H(3,𝔽₄)	—	2	2	no	—
17	C₃₁×#559	—	2	2	no	—
18	C₃₁×#556	—	2	1	no	—
19	C₃₁×#555	—	2	1	no	—
20	C₃₁×#555	C₂²	1	2	yes	complemented
21	C₃₁×#555	C₂²	1	2	yes	complemented
22	C₃₁×#555	C₂²	1	2	yes	complemented
23	C₃₁×#553	C₂²	1	4	yes	complemented
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#547	C₂²	1	2	yes	complemented
26	D₄²×C₃₁	—	2	1	no	—
27	D₄²×C₃₁	C₂²	1	2	yes	complemented
28	D₄²×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#538	—	2	2	no	—
30	C₃₁×#535	—	2	2	no	—
31	C₃₁×#535	—	2	2	no	—
32	C₃₁×#535	C₂²	1	4	yes	—
33	C₃₁×#535	C₂²	1	2	yes	complemented
34	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#525	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#501	C₂²	1	2	yes	complemented
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#490	C₂²	1	2	yes	complemented
45	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#482	C₂²	1	4	yes	complemented
48	C₃₁×#482	C₂²	1	4	yes	complemented
49	C₃₁×#482	C₂²	1	4	yes	complemented
50	C₃₁×#482	C₂²	1	4	yes	complemented
51	C₃₁×#482	C₂²	1	4	yes	complemented
52	C₃₁×#482	C₂²	1	4	yes	complemented
53	C₃₁×#481	C₂²	1	2	yes	complemented
54	C₃₁×#481	C₂²	1	4	yes	complemented
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	2	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#476	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	complemented
60	C₃₁×#474	C₂²	1	2	yes	complemented
61	C₃₁×#474	C₂²	1	2	yes	complemented
62	C₃₁×#469	C₂²	1	4	yes	complemented
63	C₃₁×#469	C₂²	1	4	yes	complemented
64	C₃₁×#466	C₂²	1	4	yes	complemented
65	C₃₁×#466	C₂²	1	4	yes	complemented
66	C₃₁×#459	C₂²	1	2	yes	—
67	C₃₁×#459	C₂²	1	2	yes	—
68	C₃₁×#447	C₂²	1	2	yes	complemented
69	C₃₁×#447	C₂²	1	2	yes	complemented
70	C₃₁×#447	C₂²	1	4	yes	complemented
71	C₃₁×#447	C₂²	1	4	yes	complemented
72	C₃₁×#442	C₂²	1	4	yes	complemented
73	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#428	C₂²	1	4	yes	complemented
81	C₃₁×#427	C₂²	1	4	yes	complemented
82	C₃₁×#418	C₂²	1	4	yes	complemented
83	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
84	C₃₁×#408	C₂²	1	4	yes	complemented
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	1	no	—
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂×#41×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	—	2	2	no	—
91	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	—	2	1	no	—
94	C₂×D₈×C₃₁	C₂³	1	2	yes	—
95	C₂×D₈×C₃₁	C₂³	1	2	yes	—
96	C₂×D₈×C₃₁	C₂³	1	4	yes	—
97	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
99	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×#127	—	2	4	no	—
105	C₃₁×#127	—	2	2	no	—
106	C₃₁×#127	D₄	1	1	yes	characteristic
107	C₃₁×#127	C₂³	1	1	yes	characteristic
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#125	C₂³	1	2	yes	—
111	C₃₁×#124	—	2	4	no	—
112	C₃₁×#124	—	2	2	no	—
113	C₃₁×#124	—	2	4	no	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#124	—	2	4	no	—
116	C₃₁×#124	—	2	1	no	—
117	C₃₁×#124	—	2	1	no	—
118	C₃₁×#124	D₄	1	2	yes	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×C₂²⋊Q₈	—	2	1	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×#121	—	2	2	no	—
125	C₃₁×#121	—	2	2	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	4	no	—
128	C₃₁×#121	—	2	1	no	—
129	C₃₁×#121	—	2	1	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	D₄	1	2	yes	—
133	C₃₁×#121	D₄	1	2	yes	—
134	C₃₁×#121	C₂³	1	4	yes	—
135	C₃₁×#121	C₂³	1	4	yes	—
136	C₃₁×#121	C₂³	1	2	yes	—
137	C₃₁×#121	C₂³	1	2	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#120	—	2	4	no	—
141	C₃₁×#120	—	2	4	no	—
142	C₃₁×#120	—	2	4	no	—
143	C₃₁×#120	—	2	4	no	—
144	C₃₁×#120	—	2	4	no	—
145	C₄×Q₈×C₃₁	—	2	2	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	—	2	1	no	—
148	C₄×D₄×C₃₁	—	2	4	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	1	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	C₂³	1	2	yes	—
156	C₄×D₄×C₃₁	C₂³	1	2	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₃₁×#117	—	2	2	no	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	C₂³	1	4	yes	—
165	C₃₁×#117	C₂³	1	4	yes	—
166	C₃₁×#117	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#107	C₂³	1	4	yes	—
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#107	C₂³	1	4	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×#106	C₂³	1	4	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
180	C₃₁×#102	C₂³	1	2	yes	—
181	C₃₁×#102	C₂³	1	4	yes	—
182	C₃₁×#102	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₂⁴×C₃₁	—	2	1	no	—
198	C₂⁴×C₃₁	—	2	4	no	—
199	#41×C₃₁	—	4	4	no	—
200	#41×C₃₁	—	8	2	no	—
201	#41×C₃₁	—	8	2	no	—
202	#41×C₃₁	—	8	4	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	2	1	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	2	1	no	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	1	no	—
215	C₂×D₄×C₃₁	—	2	1	no	—
216	C₂×D₄×C₃₁	—	2	1	no	—
217	C₂×D₄×C₃₁	—	2	1	no	—
218	C₂×D₄×C₃₁	—	2	1	no	—
219	C₂×D₄×C₃₁	—	2	4	no	—
220	C₂×D₄×C₃₁	—	4	2	no	—
221	C₂×D₄×C₃₁	—	4	4	no	—
222	C₂×D₄×C₃₁	—	4	4	no	—
223	C₂×D₄×C₃₁	—	8	4	no	—
224	C₂×D₄×C₃₁	—	8	4	no	—
225	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
229	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
230	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
231	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₃₁	—	2	1	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	—	2	2	no	—
236	C₂²×C₄×C₃₁	—	2	2	no	—
237	C₂²×C₄×C₃₁	—	2	2	no	—
238	C₂²×C₄×C₃₁	—	8	2	no	—
239	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
243	D₈×C₃₁	—	4	2	no	—
244	D₈×C₃₁	—	4	4	no	—
245	D₈×C₃₁	—	4	2	no	—
246	M₁₆×C₃₁	—	4	4	no	—
247	C₂×C₈×C₃₁	—	4	4	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	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	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂²⋊C₄×C₃₁	—	2	2	no	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
280	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	4	no	—
283	C₄²×C₃₁	—	2	2	no	—
284	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
288	#61802	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	2	2	no	—
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	4	2	no	—
293	C₂³×C₃₁	—	8	1	no	—
294	C₂³×C₃₁	—	8	1	no	—
295	C₂³×C₃₁	—	8	4	no	—
296	C₂³×C₃₁	—	8	4	no	—
297	C₂³×C₃₁	—	8	4	no	—
298	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
299	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₃₁	—	4	2	no	—
301	Q₈×C₃₁	—	4	2	no	—
302	Q₈×C₃₁	—	8	1	no	—
303	Q₈×C₃₁	—	8	1	no	—
304	Q₈×C₃₁	—	8	1	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	2	2	no	—
308	D₄×C₃₁	—	2	2	no	—
309	D₄×C₃₁	—	2	4	no	—
310	D₄×C₃₁	—	2	2	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	4	2	no	—
313	D₄×C₃₁	—	4	4	no	—
314	D₄×C₃₁	—	4	2	no	—
315	D₄×C₃₁	—	4	2	no	—
316	D₄×C₃₁	—	4	2	no	—
317	D₄×C₃₁	—	8	4	no	—
318	D₄×C₃₁	—	8	1	no	—
319	D₄×C₃₁	—	8	1	no	—
320	D₄×C₃₁	—	8	4	no	—
321	D₄×C₃₁	—	8	4	no	—
322	D₄×C₃₁	—	8	4	no	—
323	D₄×C₃₁	—	8	2	no	—
324	D₄×C₃₁	—	8	2	no	—
325	D₄×C₃₁	—	8	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	4	no	—
328	C₂×C₄×C₃₁	—	2	4	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	2	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	4	1	no	—
336	C₂×C₄×C₃₁	—	4	4	no	—
337	C₂×C₄×C₃₁	—	4	4	no	—
338	C₂×C₄×C₃₁	—	4	4	no	—
339	C₂×C₄×C₃₁	—	8	2	no	—
340	C₂×C₄×C₃₁	—	8	1	no	—
341	C₂×C₄×C₃₁	—	8	4	no	—
342	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
349	C₈×C₃₁	—	2	2	no	—
350	C₈×C₃₁	—	2	4	no	—
351	C₈×C₃₁	—	2	2	no	—
352	#3549	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3354	C₂×C₃₁	1	2	yes	complemented
355	#3347	C₂×C₃₁	1	4	yes	complemented
356	#3341	C₂×C₃₁	1	2	yes	complemented
357	#3325	C₂×C₃₁	1	2	yes	complemented
358	#3318	C₂×C₃₁	1	4	yes	complemented
359	#3294	C₂×C₃₁	1	2	yes	complemented
360	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
361	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3199	C₂×C₃₁	1	4	yes	complemented
363	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#3096	C₂×C₃₁	1	4	yes	complemented
366	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	4	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	4	no	—
371	C₂²×C₃₁	—	2	1	no	—
372	C₂²×C₃₁	—	2	4	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	4	2	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	2	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	—	8	4	no	—
383	C₂²×C₃₁	—	16	8	no	—
384	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	4	no	—
389	C₄×C₃₁	—	2	1	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	#576	1	2	yes	—
396	C₄×C₃₁	#585	1	2	yes	—
397	H(3,𝔽₄)	—	2	2	no	—
398	#559	—	2	2	no	—
399	#556	—	2	1	no	—
400	#555	—	2	1	no	—
401	#555	C₂²×C₃₁	1	2	yes	complemented
402	#555	C₂²×C₃₁	1	2	yes	complemented
403	#555	C₂²×C₃₁	1	2	yes	complemented
404	#553	C₂²×C₃₁	1	4	yes	complemented
405	#550	—	2	1	no	—
406	#547	C₂²×C₃₁	1	2	yes	complemented
407	D₄²	—	2	1	no	—
408	D₄²	C₂²×C₃₁	1	2	yes	complemented
409	D₄²	C₂²×C₃₁	1	2	yes	complemented
410	#538	—	2	2	no	—
411	#535	—	2	2	no	—
412	#535	—	2	2	no	—
413	#535	C₂²×C₃₁	1	4	yes	—
414	#535	C₂²×C₃₁	1	2	yes	complemented
415	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	#532	C₂²×C₃₁	1	1	yes	characteristic
417	#532	C₂²×C₃₁	1	1	yes	characteristic
418	#532	C₂²×C₃₁	1	1	yes	characteristic
419	#525	—	2	2	no	—
420	#520	C₂²×C₃₁	1	2	yes	complemented
421	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
422	#501	C₂²×C₃₁	1	2	yes	complemented
423	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
425	#490	C₂²×C₃₁	1	2	yes	complemented
426	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	#482	C₂²×C₃₁	1	4	yes	complemented
429	#482	C₂²×C₃₁	1	4	yes	complemented
430	#482	C₂²×C₃₁	1	4	yes	complemented
431	#482	C₂²×C₃₁	1	4	yes	complemented
432	#482	C₂²×C₃₁	1	4	yes	complemented
433	#482	C₂²×C₃₁	1	4	yes	complemented
434	#481	C₂²×C₃₁	1	2	yes	complemented
435	#481	C₂²×C₃₁	1	4	yes	complemented
436	#480	C₂²×C₃₁	1	4	yes	complemented
437	#480	C₂²×C₃₁	1	2	yes	complemented
438	#478	C₂²×C₃₁	1	4	yes	complemented
439	#476	C₂²×C₃₁	1	2	yes	complemented
440	#476	C₂²×C₃₁	1	2	yes	complemented
441	#474	C₂²×C₃₁	1	2	yes	complemented
442	#474	C₂²×C₃₁	1	2	yes	complemented
443	#469	C₂²×C₃₁	1	4	yes	complemented
444	#469	C₂²×C₃₁	1	4	yes	complemented
445	#466	C₂²×C₃₁	1	4	yes	complemented
446	#466	C₂²×C₃₁	1	4	yes	complemented
447	#459	C₂²×C₃₁	1	2	yes	—
448	#459	C₂²×C₃₁	1	2	yes	—
449	#447	C₂²×C₃₁	1	2	yes	complemented
450	#447	C₂²×C₃₁	1	2	yes	complemented
451	#447	C₂²×C₃₁	1	4	yes	complemented
452	#447	C₂²×C₃₁	1	4	yes	complemented
453	#442	C₂²×C₃₁	1	4	yes	complemented
454	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
455	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
456	#436	C₂²×C₃₁	1	2	yes	complemented
457	#435	C₂²×C₃₁	1	4	yes	complemented
458	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
459	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	#428	C₂²×C₃₁	1	4	yes	complemented
462	#427	C₂²×C₃₁	1	4	yes	complemented
463	#418	C₂²×C₃₁	1	4	yes	complemented
464	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
465	#408	C₂²×C₃₁	1	4	yes	complemented
466	C₂×C₃₁	—	4	1	no	—
467	C₂×C₃₁	—	4	4	no	—
468	C₂×C₃₁	—	8	2	no	—
469	C₂×C₃₁	—	8	2	no	—
470	C₂×C₃₁	—	8	2	no	—
471	C₂×C₃₁	#3485	1	1	yes	characteristic
472	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
473	C₂×C₃₁	#3585	1	1	yes	characteristic
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	1	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	C₂³×C₃₁	1	2	yes	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
482	C₂³×C₄	—	2	1	no	—
483	C₂×D₈	C₂³×C₃₁	1	2	yes	—
484	C₂×D₈	C₂³×C₃₁	1	2	yes	—
485	C₂×D₈	C₂³×C₃₁	1	4	yes	—
486	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
487	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
488	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
493	#127	—	2	4	no	—
494	#127	—	2	2	no	—
495	#127	D₄×C₃₁	1	1	yes	characteristic
496	#127	C₂³×C₃₁	1	1	yes	characteristic
497	#127	C₂³×C₃₁	1	1	yes	characteristic
498	#126	—	2	4	no	—
499	#125	C₂³×C₃₁	1	2	yes	—
500	#124	—	2	4	no	—
501	#124	—	2	2	no	—
502	#124	—	2	4	no	—
503	#124	—	2	4	no	—
504	#124	—	2	4	no	—
505	#124	—	2	1	no	—
506	#124	—	2	1	no	—
507	#124	D₄×C₃₁	1	2	yes	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	4	no	—
517	#121	—	2	1	no	—
518	#121	—	2	1	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	D₄×C₃₁	1	2	yes	—
522	#121	D₄×C₃₁	1	2	yes	—
523	#121	C₂³×C₃₁	1	2	yes	—
524	#121	C₂³×C₃₁	1	2	yes	—
525	#121	C₂³×C₃₁	1	4	yes	—
526	#121	C₂³×C₃₁	1	4	yes	—
527	#121	C₂³×C₃₁	1	4	yes	—
528	#121	C₂³×C₃₁	1	4	yes	—
529	#120	—	2	4	no	—
530	#120	—	2	4	no	—
531	#120	—	2	4	no	—
532	#120	—	2	4	no	—
533	#120	—	2	4	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	4	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	C₂³×C₃₁	1	2	yes	—
545	C₄×D₄	C₂³×C₃₁	1	2	yes	—
546	C₄×D₄	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	C₂³×C₃₁	1	2	yes	—
548	C₄×D₄	C₂³×C₃₁	1	2	yes	—
549	C₄×D₄	C₂³×C₃₁	1	2	yes	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	C₂³×C₃₁	1	2	yes	—
554	#117	C₂³×C₃₁	1	4	yes	—
555	#117	C₂³×C₃₁	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	#107	C₂³×C₃₁	1	2	yes	—
561	#107	C₂³×C₃₁	1	4	yes	—
562	#107	C₂³×C₃₁	1	2	yes	—
563	#107	C₂³×C₃₁	1	4	yes	—
564	#106	C₂³×C₃₁	1	4	yes	—
565	#106	C₂³×C₃₁	1	4	yes	—
566	#106	C₂³×C₃₁	1	4	yes	—
567	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
568	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
569	#102	C₂³×C₃₁	1	2	yes	—
570	#102	C₂³×C₃₁	1	4	yes	—
571	#102	C₂³×C₃₁	1	4	yes	—
572	#102	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	2	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	2	yes	—
577	#102	C₂³×C₃₁	1	2	yes	—
578	#102	C₂³×C₃₁	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
583	#97	C₂³×C₃₁	1	2	yes	—
584	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
586	C₃₁	#61802	1	1	yes	characteristic, direct product factor, Sylow
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	2	4	no	—
589	#41	—	4	4	no	—
590	#41	—	8	2	no	—
591	#41	—	8	2	no	—
592	#41	—	8	4	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	8	4	no	—
614	C₂×D₄	—	8	4	no	—
615	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
617	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
620	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
633	D₈	—	4	2	no	—
634	D₈	—	4	4	no	—
635	D₈	—	4	2	no	—
636	M₁₆	—	4	4	no	—
637	C₂×C₈	—	4	4	no	—
638	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
639	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
640	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
670	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
688	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	Q₈	—	4	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	1	no	—
692	Q₈	—	8	1	no	—
693	Q₈	—	8	1	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	1	no	—
708	D₄	—	8	1	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	D₄	—	8	2	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	2	no	—
729	C₂×C₄	—	8	1	no	—
730	C₂×C₄	—	8	4	no	—
731	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
737	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	4	no	—
740	C₈	—	2	2	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	8	4	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	C₃₁×#576	1	2	yes	—
770	C₄	C₃₁×#585	1	2	yes	—
771	C₂	—	4	1	no	—
772	C₂	—	4	4	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	C₃₁×#3485	1	1	yes	characteristic
777	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
778	C₂	C₃₁×#3585	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3549	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3354	C₂	semidirect
4. C₃₁×#3347	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3325	C₂	semidirect
7. C₃₁×#3318	C₂	semidirect
8. C₃₁×#3294	C₂	semidirect
9. C₃₁×#3235	C₂	semidirect
10. C₃₁×#3228	C₂	semidirect
11. C₃₁×#3199	C₂	semidirect
12. C₃₁×#3109	C₂	semidirect
13. C₃₁×#3100	C₂	semidirect
14. C₃₁×#3096	C₂	semidirect
15. C₃₁×#2981	C₂	semidirect
20. C₃₁×#555	C₂²	semidirect
21. C₃₁×#555	C₂²	semidirect
22. C₃₁×#555	C₂²	semidirect
23. C₃₁×#553	C₂²	semidirect
25. C₃₁×#547	C₂²	semidirect
27. D₄²×C₃₁	C₂²	semidirect
28. D₄²×C₃₁	C₂²	semidirect
33. C₃₁×#535	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
39. C₃₁×#520	C₂²	semidirect
40. C₂×C₄×D₄×C₃₁	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
44. C₃₁×#490	C₂²	semidirect
45. C₃₁×#486	C₂²	semidirect
46. C₃₁×#486	C₂²	semidirect
47. C₃₁×#482	C₂²	semidirect
48. C₃₁×#482	C₂²	semidirect
49. C₃₁×#482	C₂²	semidirect
50. C₃₁×#482	C₂²	semidirect
51. C₃₁×#482	C₂²	semidirect
52. C₃₁×#482	C₂²	semidirect
53. C₃₁×#481	C₂²	semidirect
54. C₃₁×#481	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#476	C₂²	semidirect
59. C₃₁×#476	C₂²	semidirect
60. C₃₁×#474	C₂²	semidirect
61. C₃₁×#474	C₂²	semidirect
62. C₃₁×#469	C₂²	semidirect
63. C₃₁×#469	C₂²	semidirect
64. C₃₁×#466	C₂²	semidirect
65. C₃₁×#466	C₂²	semidirect
68. C₃₁×#447	C₂²	semidirect
69. C₃₁×#447	C₂²	semidirect
70. C₃₁×#447	C₂²	semidirect
71. C₃₁×#447	C₂²	semidirect
72. C₃₁×#442	C₂²	semidirect
73. C₄×D₈×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#435	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
78. C₃₁×#432	C₂²	semidirect
79. C₃₁×#431	C₂²	semidirect
80. C₃₁×#428	C₂²	semidirect
81. C₃₁×#427	C₂²	semidirect
82. C₃₁×#418	C₂²	semidirect
83. C₂×C₃₁×#102	C₂²	semidirect
84. C₃₁×#408	C₂²	semidirect
288. #61802	C₃₁	direct (N × H)
352. #3549	C₂×C₃₁	semidirect
353. #3506	C₂×C₃₁	semidirect
354. #3354	C₂×C₃₁	semidirect
355. #3347	C₂×C₃₁	semidirect
356. #3341	C₂×C₃₁	semidirect
357. #3325	C₂×C₃₁	semidirect
358. #3318	C₂×C₃₁	semidirect
359. #3294	C₂×C₃₁	semidirect
360. #3235	C₂×C₃₁	semidirect
361. #3228	C₂×C₃₁	semidirect
362. #3199	C₂×C₃₁	semidirect
363. #3109	C₂×C₃₁	semidirect
364. #3100	C₂×C₃₁	semidirect
365. #3096	C₂×C₃₁	semidirect
366. #2981	C₂×C₃₁	semidirect
401. #555	C₂²×C₃₁	semidirect
402. #555	C₂²×C₃₁	semidirect
403. #555	C₂²×C₃₁	semidirect
404. #553	C₂²×C₃₁	semidirect
406. #547	C₂²×C₃₁	semidirect
408. D₄²	C₂²×C₃₁	semidirect
409. D₄²	C₂²×C₃₁	semidirect
414. #535	C₂²×C₃₁	semidirect
415. #533	C₂²×C₃₁	semidirect
420. #520	C₂²×C₃₁	semidirect
421. C₂×C₄×D₄	C₂²×C₃₁	semidirect
422. #501	C₂²×C₃₁	semidirect
423. #500	C₂²×C₃₁	semidirect
424. #498	C₂²×C₃₁	semidirect
425. #490	C₂²×C₃₁	semidirect
426. #486	C₂²×C₃₁	semidirect
427. #486	C₂²×C₃₁	semidirect
428. #482	C₂²×C₃₁	semidirect
429. #482	C₂²×C₃₁	semidirect
430. #482	C₂²×C₃₁	semidirect
431. #482	C₂²×C₃₁	semidirect
432. #482	C₂²×C₃₁	semidirect
433. #482	C₂²×C₃₁	semidirect
434. #481	C₂²×C₃₁	semidirect
435. #481	C₂²×C₃₁	semidirect
436. #480	C₂²×C₃₁	semidirect
437. #480	C₂²×C₃₁	semidirect
438. #478	C₂²×C₃₁	semidirect
439. #476	C₂²×C₃₁	semidirect
440. #476	C₂²×C₃₁	semidirect
441. #474	C₂²×C₃₁	semidirect
442. #474	C₂²×C₃₁	semidirect
443. #469	C₂²×C₃₁	semidirect
444. #469	C₂²×C₃₁	semidirect
445. #466	C₂²×C₃₁	semidirect
446. #466	C₂²×C₃₁	semidirect
449. #447	C₂²×C₃₁	semidirect
450. #447	C₂²×C₃₁	semidirect
451. #447	C₂²×C₃₁	semidirect
452. #447	C₂²×C₃₁	semidirect
453. #442	C₂²×C₃₁	semidirect
454. C₄×D₈	C₂²×C₃₁	semidirect
455. C₄×D₈	C₂²×C₃₁	semidirect
456. #436	C₂²×C₃₁	semidirect
457. #435	C₂²×C₃₁	semidirect
458. C₈×D₄	C₂²×C₃₁	semidirect
459. #432	C₂²×C₃₁	semidirect
460. #431	C₂²×C₃₁	semidirect
461. #428	C₂²×C₃₁	semidirect
462. #427	C₂²×C₃₁	semidirect
463. #418	C₂²×C₃₁	semidirect
464. C₂×#102	C₂²×C₃₁	semidirect
465. #408	C₂²×C₃₁	semidirect
586. C₃₁	#61802	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×#3549	2
C₃₁×#3506	2
C₃₁×#3354	2
C₃₁×#3347	2
C₃₁×#3341	2
C₃₁×#3325	2
C₃₁×#3318	2
C₃₁×#3294	2
C₃₁×#3235	2
C₃₁×#3228	2
C₃₁×#3199	2
C₃₁×#3109	2
C₃₁×#3100	2
C₃₁×#3096	2
C₃₁×#2981	2
#61802	31

Subgroups — C31×#61802 #21518561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61802 #21518561