Subgroups — C₃₁×#62535 #21519294

Order 7936.

2098 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3366	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3325	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3318	C₂	1	8	yes	maximal, complemented
6	C₃₁×#3228	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3205	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3184	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3138	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
16	C₃₁×#556	—	2	1	no	—
17	C₃₁×#555	C₂²	1	2	yes	complemented
18	C₃₁×#554	C₂²	1	2	yes	complemented
19	C₃₁×#553	C₂²	1	4	yes	complemented
20	C₃₁×#550	—	2	1	no	—
21	C₃₁×#550	C₂²	1	2	yes	—
22	C₃₁×#548	—	2	2	no	—
23	C₃₁×#547	—	2	1	no	—
24	D₄²×C₃₁	—	2	1	no	—
25	D₄²×C₃₁	—	2	2	no	—
26	D₄²×C₃₁	C₂²	1	4	yes	—
27	D₄²×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#542	—	2	2	no	—
29	C₃₁×#537	—	2	1	no	—
30	C₃₁×#535	—	2	1	no	—
31	C₃₁×#535	—	2	2	no	—
32	C₃₁×#533	C₂²	1	2	yes	complemented
33	C₃₁×#532	C₂²	1	1	yes	characteristic
34	C₃₁×#532	C₂²	1	2	yes	—
35	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#532	C₂²	1	2	yes	complemented
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#127	C₂²	1	2	yes	—
40	C₃₁×#520	—	2	1	no	—
41	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	2	yes	complemented
44	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#493	C₂²	1	2	yes	complemented
46	C₃₁×#490	C₂²	1	8	yes	complemented
47	C₃₁×#486	C₂²	1	4	yes	complemented
48	C₃₁×#486	C₂²	1	2	yes	complemented
49	C₃₁×#486	C₂²	1	2	yes	complemented
50	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#486	C₂²	1	2	yes	complemented
52	C₃₁×#486	C₂²	1	2	yes	complemented
53	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#482	C₂²	1	8	yes	complemented
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	8	yes	complemented
57	C₃₁×#476	C₂²	1	4	yes	complemented
58	C₃₁×#469	C₂²	1	8	yes	complemented
59	C₃₁×#466	C₂²	1	4	yes	complemented
60	C₃₁×#459	C₂²	1	8	yes	complemented
61	C₃₁×#459	C₂²	1	4	yes	complemented
62	C₃₁×#447	C₂²	1	4	yes	complemented
63	C₃₁×#447	C₂²	1	8	yes	complemented
64	C₃₁×#446	C₂²	1	2	yes	complemented
65	C₃₁×#442	C₂²	1	8	yes	complemented
66	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	2	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#431	C₂²	1	2	yes	complemented
71	C₃₁×#418	C₂²	1	8	yes	complemented
72	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
73	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×H(5,𝔽₂)	—	4	8	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	1	no	—
78	C₂×#41×C₃₁	—	2	2	no	—
79	C₂×#41×C₃₁	—	2	1	no	—
80	C₂×#41×C₃₁	—	2	2	no	—
81	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
82	C₂²×Q₈×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	—	2	4	no	—
84	C₂²×D₄×C₃₁	—	2	2	no	—
85	C₂²×D₄×C₃₁	—	2	2	no	—
86	C₂²×D₄×C₃₁	—	2	1	no	—
87	C₂²×D₄×C₃₁	—	2	1	no	—
88	C₂²×D₄×C₃₁	—	2	2	no	—
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₂×D₈×C₃₁	C₂³	1	4	yes	—
92	C₂×D₈×C₃₁	C₂³	1	8	yes	—
93	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
95	C₃₁×C₄⋊Q₈	—	2	1	no	—
96	C₃₁×C₄⋊Q₈	—	2	1	no	—
97	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×#127	—	2	2	no	—
102	C₃₁×#127	—	2	1	no	—
103	C₃₁×#127	—	2	1	no	—
104	C₃₁×#127	—	2	2	no	—
105	C₃₁×#127	C₂³	1	2	yes	—
106	C₃₁×#127	C₂³	1	4	yes	—
107	C₃₁×#127	C₂³	1	2	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#127	C₂³	1	1	yes	characteristic
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#125	C₂³	1	4	yes	—
112	C₃₁×#124	—	2	4	no	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	1	no	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×C₂²⋊Q₈	—	2	2	no	—
119	C₃₁×C₂²⋊Q₈	—	2	2	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	4	no	—
122	C₃₁×#121	—	2	2	no	—
123	C₃₁×#121	—	2	4	no	—
124	C₃₁×#121	—	2	1	no	—
125	C₃₁×#121	—	2	2	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	1	no	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	2	no	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	C₂³	1	2	yes	—
133	C₃₁×#121	C₂³	1	4	yes	—
134	C₃₁×#121	C₂³	1	2	yes	—
135	C₃₁×#121	C₂³	1	4	yes	—
136	C₃₁×#120	—	2	4	no	—
137	C₃₁×#120	—	2	4	no	—
138	C₃₁×#120	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	2	no	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
142	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	1	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	—	2	1	no	—
148	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
149	C₄×D₄×C₃₁	D₄	1	2	yes	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	D₄	1	1	yes	characteristic
158	C₃₁×#117	D₄	1	2	yes	—
159	C₃₁×#117	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
161	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
165	C₃₁×#107	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	8	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
169	C₃₁×#102	C₂³	1	8	yes	—
170	C₃₁×#102	C₂³	1	8	yes	—
171	C₃₁×#102	C₂³	1	4	yes	—
172	C₃₁×#102	C₂³	1	8	yes	—
173	C₃₁×#102	C₂³	1	8	yes	—
174	C₃₁×#102	C₂³	1	4	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₃₁	C₂³	1	2	yes	—
181	C₄×C₈×C₃₁	C₂³	1	2	yes	—
182	C₂⁴×C₃₁	—	2	4	no	—
183	C₂⁴×C₃₁	—	2	2	no	—
184	#41×C₃₁	—	2	4	no	—
185	#41×C₃₁	—	4	8	no	—
186	#41×C₃₁	—	4	8	no	—
187	#41×C₃₁	—	4	4	no	—
188	#41×C₃₁	—	4	4	no	—
189	#41×C₃₁	—	8	4	no	—
190	C₂×Q₈×C₃₁	—	2	1	no	—
191	C₂×Q₈×C₃₁	—	2	2	no	—
192	C₂×Q₈×C₃₁	—	2	1	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	8	2	no	—
195	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	4	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	1	no	—
201	C₂×D₄×C₃₁	—	2	1	no	—
202	C₂×D₄×C₃₁	—	2	1	no	—
203	C₂×D₄×C₃₁	—	2	2	no	—
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	1	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	4	4	no	—
213	C₂×D₄×C₃₁	—	4	8	no	—
214	C₂×D₄×C₃₁	—	4	8	no	—
215	C₂×D₄×C₃₁	—	4	16	no	—
216	C₂×D₄×C₃₁	—	4	8	no	—
217	C₂×D₄×C₃₁	—	4	4	no	—
218	C₂×D₄×C₃₁	—	8	2	no	—
219	C₂×D₄×C₃₁	—	8	4	no	—
220	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	4	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
236	D₈×C₃₁	—	4	4	no	—
237	D₈×C₃₁	—	4	8	no	—
238	M₁₆×C₃₁	—	4	4	no	—
239	C₂×C₈×C₃₁	—	4	2	no	—
240	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
242	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
243	C₄⋊C₄×C₃₁	—	2	2	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₂²⋊C₄×C₃₁	—	2	4	no	—
258	C₂²⋊C₄×C₃₁	—	2	4	no	—
259	C₂²⋊C₄×C₃₁	—	2	4	no	—
260	C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₄²×C₃₁	—	2	4	no	—
270	C₄²×C₃₁	C₂×D₄	1	2	yes	—
271	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₃₁	C₂×D₄	1	2	yes	—
274	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₄²×C₃₁	C₂⁴	1	2	yes	—
277	#62535	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	2	no	—
279	C₂³×C₃₁	—	2	4	no	—
280	C₂³×C₃₁	—	2	2	no	—
281	C₂³×C₃₁	—	4	8	no	—
282	C₂³×C₃₁	—	4	4	no	—
283	C₂³×C₃₁	—	8	2	no	—
284	C₂³×C₃₁	—	8	4	no	—
285	C₂³×C₃₁	—	8	2	no	—
286	C₂³×C₃₁	—	8	4	no	—
287	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
288	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₃₁	—	2	2	no	—
290	Q₈×C₃₁	—	4	2	no	—
291	Q₈×C₃₁	—	4	2	no	—
292	Q₈×C₃₁	—	4	4	no	—
293	Q₈×C₃₁	—	8	2	no	—
294	D₄×C₃₁	—	2	4	no	—
295	D₄×C₃₁	—	2	2	no	—
296	D₄×C₃₁	—	2	4	no	—
297	D₄×C₃₁	—	2	4	no	—
298	D₄×C₃₁	—	2	8	no	—
299	D₄×C₃₁	—	4	8	no	—
300	D₄×C₃₁	—	4	8	no	—
301	D₄×C₃₁	—	4	4	no	—
302	D₄×C₃₁	—	4	4	no	—
303	D₄×C₃₁	—	4	2	no	—
304	D₄×C₃₁	—	4	4	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	8	2	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	2	no	—
314	D₄×C₃₁	—	8	4	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	4	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	—	4	8	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	8	4	no	—
327	C₂×C₄×C₃₁	—	8	2	no	—
328	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
338	C₈×C₃₁	—	2	2	no	—
339	C₈×C₃₁	—	2	2	no	—
340	C₈×C₃₁	—	2	4	no	—
341	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#3366	C₂×C₃₁	1	4	yes	complemented
344	#3325	C₂×C₃₁	1	4	yes	complemented
345	#3318	C₂×C₃₁	1	8	yes	complemented
346	#3228	C₂×C₃₁	1	2	yes	complemented
347	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#3205	C₂×C₃₁	1	2	yes	complemented
350	#3184	C₂×C₃₁	1	2	yes	complemented
351	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3138	C₂×C₃₁	1	2	yes	complemented
353	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	4	4	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	4	4	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	4	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	16	4	no	—
370	C₂²×C₃₁	—	16	8	no	—
371	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	2	2	no	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	1	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	4	no	—
381	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
382	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
383	C₄×C₃₁	#576	1	2	yes	—
384	C₄×C₃₁	#585	1	2	yes	—
385	C₂×H(5,𝔽₂)	—	2	1	no	—
386	#556	—	2	1	no	—
387	#555	C₂²×C₃₁	1	2	yes	complemented
388	#554	C₂²×C₃₁	1	2	yes	complemented
389	#553	C₂²×C₃₁	1	4	yes	complemented
390	#550	—	2	1	no	—
391	#550	C₂²×C₃₁	1	2	yes	—
392	#548	—	2	2	no	—
393	#547	—	2	1	no	—
394	D₄²	—	2	1	no	—
395	D₄²	—	2	2	no	—
396	D₄²	C₂²×C₃₁	1	4	yes	—
397	D₄²	C₂²×C₃₁	1	2	yes	—
398	#542	—	2	2	no	—
399	#537	—	2	1	no	—
400	#535	—	2	1	no	—
401	#535	—	2	2	no	—
402	#533	C₂²×C₃₁	1	2	yes	complemented
403	#532	C₂²×C₃₁	1	1	yes	characteristic
404	#532	C₂²×C₃₁	1	2	yes	—
405	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	#532	C₂²×C₃₁	1	2	yes	complemented
407	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×#127	C₂²×C₃₁	1	2	yes	—
410	#520	—	2	1	no	—
411	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
412	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	#498	C₂²×C₃₁	1	2	yes	complemented
414	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
415	#493	C₂²×C₃₁	1	2	yes	complemented
416	#490	C₂²×C₃₁	1	8	yes	complemented
417	#486	C₂²×C₃₁	1	4	yes	complemented
418	#486	C₂²×C₃₁	1	2	yes	complemented
419	#486	C₂²×C₃₁	1	2	yes	complemented
420	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
421	#486	C₂²×C₃₁	1	2	yes	complemented
422	#486	C₂²×C₃₁	1	2	yes	complemented
423	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	#482	C₂²×C₃₁	1	8	yes	complemented
425	#481	C₂²×C₃₁	1	4	yes	complemented
426	#478	C₂²×C₃₁	1	8	yes	complemented
427	#476	C₂²×C₃₁	1	4	yes	complemented
428	#469	C₂²×C₃₁	1	8	yes	complemented
429	#466	C₂²×C₃₁	1	4	yes	complemented
430	#459	C₂²×C₃₁	1	8	yes	complemented
431	#459	C₂²×C₃₁	1	4	yes	complemented
432	#447	C₂²×C₃₁	1	4	yes	complemented
433	#447	C₂²×C₃₁	1	8	yes	complemented
434	#446	C₂²×C₃₁	1	2	yes	complemented
435	#442	C₂²×C₃₁	1	8	yes	complemented
436	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
437	#436	C₂²×C₃₁	1	2	yes	complemented
438	#435	C₂²×C₃₁	1	4	yes	complemented
439	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	#431	C₂²×C₃₁	1	2	yes	complemented
441	#418	C₂²×C₃₁	1	8	yes	complemented
442	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
443	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
444	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	C₂×C₃₁	—	2	2	no	—
446	C₂×C₃₁	—	4	2	no	—
447	C₂×C₃₁	—	8	2	no	—
448	C₂×C₃₁	—	8	4	no	—
449	C₂×C₃₁	—	8	2	no	—
450	C₂×C₃₁	#3500	1	1	yes	characteristic
451	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
452	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
453	H(5,𝔽₂)	—	4	8	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	2	no	—
459	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
460	C₂²×Q₈	—	2	1	no	—
461	C₂²×D₄	—	2	4	no	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
468	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
469	C₂×D₈	C₂³×C₃₁	1	4	yes	—
470	C₂×D₈	C₂³×C₃₁	1	8	yes	—
471	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
472	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
473	C₄⋊Q₈	—	2	1	no	—
474	C₄⋊Q₈	—	2	1	no	—
475	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
476	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
477	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
479	#127	—	2	2	no	—
480	#127	—	2	1	no	—
481	#127	—	2	1	no	—
482	#127	—	2	2	no	—
483	#127	C₂³×C₃₁	1	2	yes	—
484	#127	C₂³×C₃₁	1	1	yes	characteristic
485	#127	C₂³×C₃₁	1	2	yes	—
486	#127	C₂³×C₃₁	1	4	yes	—
487	#127	C₂³×C₃₁	1	1	yes	characteristic
488	#126	—	2	4	no	—
489	#125	C₂³×C₃₁	1	4	yes	—
490	#124	—	2	4	no	—
491	#124	—	2	2	no	—
492	#124	—	2	1	no	—
493	#124	—	2	1	no	—
494	#124	—	2	2	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	#121	—	2	2	no	—
501	#121	—	2	4	no	—
502	#121	—	2	1	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	—	2	1	no	—
506	#121	—	2	2	no	—
507	#121	—	2	4	no	—
508	#121	—	2	2	no	—
509	#121	—	2	4	no	—
510	#121	C₂³×C₃₁	1	2	yes	—
511	#121	C₂³×C₃₁	1	4	yes	—
512	#121	C₂³×C₃₁	1	2	yes	—
513	#121	C₂³×C₃₁	1	4	yes	—
514	#120	—	2	4	no	—
515	#120	—	2	4	no	—
516	#120	—	2	4	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
520	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
527	C₄×D₄	D₄×C₃₁	1	2	yes	—
528	C₄×D₄	C₂³×C₃₁	1	2	yes	—
529	C₄×D₄	C₂³×C₃₁	1	4	yes	—
530	C₄×D₄	C₂³×C₃₁	1	4	yes	—
531	C₄×D₄	C₂³×C₃₁	1	2	yes	—
532	C₄×D₄	C₂³×C₃₁	1	2	yes	—
533	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
534	#117	—	2	2	no	—
535	#117	D₄×C₃₁	1	1	yes	characteristic
536	#117	D₄×C₃₁	1	2	yes	—
537	#117	C₂³×C₃₁	1	4	yes	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
541	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
543	#107	C₂³×C₃₁	1	4	yes	—
544	#106	C₂³×C₃₁	1	8	yes	—
545	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
546	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
547	#102	C₂³×C₃₁	1	8	yes	—
548	#102	C₂³×C₃₁	1	8	yes	—
549	#102	C₂³×C₃₁	1	4	yes	—
550	#102	C₂³×C₃₁	1	8	yes	—
551	#102	C₂³×C₃₁	1	8	yes	—
552	#102	C₂³×C₃₁	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
555	#97	C₂³×C₃₁	1	4	yes	—
556	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
557	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₃₁	1	2	yes	—
559	C₄×C₈	C₂³×C₃₁	1	2	yes	—
560	C₃₁	#62535	1	1	yes	characteristic, direct product factor, Sylow
561	C₂⁴	—	2	4	no	—
562	C₂⁴	—	2	2	no	—
563	#41	—	2	4	no	—
564	#41	—	4	8	no	—
565	#41	—	4	8	no	—
566	#41	—	4	4	no	—
567	#41	—	4	4	no	—
568	#41	—	8	4	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	8	2	no	—
574	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	8	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	—	4	16	no	—
595	C₂×D₄	—	4	8	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	8	2	no	—
598	C₂×D₄	—	8	4	no	—
599	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
600	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
601	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
602	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
603	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
612	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
615	D₈	—	4	4	no	—
616	D₈	—	4	8	no	—
617	M₁₆	—	4	4	no	—
618	C₂×C₈	—	4	2	no	—
619	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
620	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
634	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
648	C₄²	—	2	4	no	—
649	C₄²	C₂×D₄×C₃₁	1	2	yes	—
650	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₄²	C₂×D₄×C₃₁	1	2	yes	—
653	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₄²	C₂⁴×C₃₁	1	2	yes	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	4	8	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	8	2	no	—
662	C₂³	—	8	4	no	—
663	C₂³	—	8	2	no	—
664	C₂³	—	8	4	no	—
665	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
666	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
667	Q₈	—	2	2	no	—
668	Q₈	—	4	2	no	—
669	Q₈	—	4	2	no	—
670	Q₈	—	4	4	no	—
671	Q₈	—	8	2	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	8	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	8	no	—
679	D₄	—	4	4	no	—
680	D₄	—	4	4	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	2	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	2	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
712	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	2	no	—
718	C₈	—	2	4	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	16	4	no	—
734	C₂²	—	16	8	no	—
735	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
736	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	1	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	4	no	—
745	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
746	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
747	C₄	C₃₁×#576	1	2	yes	—
748	C₄	C₃₁×#585	1	2	yes	—
749	C₂	—	2	2	no	—
750	C₂	—	4	2	no	—
751	C₂	—	8	4	no	—
752	C₂	—	8	2	no	—
753	C₂	—	8	2	no	—
754	C₂	C₃₁×#3500	1	1	yes	characteristic
755	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
756	C₂	C₂×C₃₁×#576	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×#3511	C₂	semidirect
2. C₃₁×#3498	C₂	semidirect
3. C₃₁×#3366	C₂	semidirect
4. C₃₁×#3325	C₂	semidirect
5. C₃₁×#3318	C₂	semidirect
6. C₃₁×#3228	C₂	semidirect
7. C₃₁×#3227	C₂	semidirect
8. C₃₁×#3205	C₂	semidirect
9. C₃₁×#3205	C₂	semidirect
10. C₃₁×#3184	C₂	semidirect
11. C₃₁×#3169	C₂	semidirect
12. C₃₁×#3138	C₂	semidirect
13. C₂×C₃₁×#486	C₂	semidirect
14. C₃₁×#2965	C₂	semidirect
17. C₃₁×#555	C₂²	semidirect
18. C₃₁×#554	C₂²	semidirect
19. C₃₁×#553	C₂²	semidirect
32. C₃₁×#533	C₂²	semidirect
35. C₃₁×#532	C₂²	semidirect
36. C₃₁×#532	C₂²	semidirect
37. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
44. C₃₁×#493	C₂²	semidirect
45. C₃₁×#493	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#486	C₂²	semidirect
48. C₃₁×#486	C₂²	semidirect
49. C₃₁×#486	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#486	C₂²	semidirect
52. C₃₁×#486	C₂²	semidirect
53. C₃₁×#486	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#469	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
60. C₃₁×#459	C₂²	semidirect
61. C₃₁×#459	C₂²	semidirect
62. C₃₁×#447	C₂²	semidirect
63. C₃₁×#447	C₂²	semidirect
64. C₃₁×#446	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₄×D₈×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#431	C₂²	semidirect
70. C₃₁×#431	C₂²	semidirect
71. C₃₁×#418	C₂²	semidirect
72. C₂×C₃₁×#102	C₂²	semidirect
73. C₄×M₁₆×C₃₁	C₂²	semidirect
74. C₂×C₄×C₈×C₃₁	C₂²	semidirect
277. #62535	C₃₁	direct (N × H)
341. #3511	C₂×C₃₁	semidirect
342. #3498	C₂×C₃₁	semidirect
343. #3366	C₂×C₃₁	semidirect
344. #3325	C₂×C₃₁	semidirect
345. #3318	C₂×C₃₁	semidirect
346. #3228	C₂×C₃₁	semidirect
347. #3227	C₂×C₃₁	semidirect
348. #3205	C₂×C₃₁	semidirect
349. #3205	C₂×C₃₁	semidirect
350. #3184	C₂×C₃₁	semidirect
351. #3169	C₂×C₃₁	semidirect
352. #3138	C₂×C₃₁	semidirect
353. C₂×#486	C₂×C₃₁	semidirect
354. #2965	C₂×C₃₁	semidirect
387. #555	C₂²×C₃₁	semidirect
388. #554	C₂²×C₃₁	semidirect
389. #553	C₂²×C₃₁	semidirect
402. #533	C₂²×C₃₁	semidirect
405. #532	C₂²×C₃₁	semidirect
406. #532	C₂²×C₃₁	semidirect
407. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
412. #500	C₂²×C₃₁	semidirect
413. #498	C₂²×C₃₁	semidirect
414. #493	C₂²×C₃₁	semidirect
415. #493	C₂²×C₃₁	semidirect
416. #490	C₂²×C₃₁	semidirect
417. #486	C₂²×C₃₁	semidirect
418. #486	C₂²×C₃₁	semidirect
419. #486	C₂²×C₃₁	semidirect
420. #486	C₂²×C₃₁	semidirect
421. #486	C₂²×C₃₁	semidirect
422. #486	C₂²×C₃₁	semidirect
423. #486	C₂²×C₃₁	semidirect
424. #482	C₂²×C₃₁	semidirect
425. #481	C₂²×C₃₁	semidirect
426. #478	C₂²×C₃₁	semidirect
427. #476	C₂²×C₃₁	semidirect
428. #469	C₂²×C₃₁	semidirect
429. #466	C₂²×C₃₁	semidirect
430. #459	C₂²×C₃₁	semidirect
431. #459	C₂²×C₃₁	semidirect
432. #447	C₂²×C₃₁	semidirect
433. #447	C₂²×C₃₁	semidirect
434. #446	C₂²×C₃₁	semidirect
435. #442	C₂²×C₃₁	semidirect
436. C₄×D₈	C₂²×C₃₁	semidirect
437. #436	C₂²×C₃₁	semidirect
438. #435	C₂²×C₃₁	semidirect
439. #431	C₂²×C₃₁	semidirect
440. #431	C₂²×C₃₁	semidirect
441. #418	C₂²×C₃₁	semidirect
442. C₂×#102	C₂²×C₃₁	semidirect
443. C₄×M₁₆	C₂²×C₃₁	semidirect
444. C₂×C₄×C₈	C₂²×C₃₁	semidirect
560. C₃₁	#62535	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×#3511	2
C₃₁×#3498	2
C₃₁×#3366	2
C₃₁×#3325	2
C₃₁×#3318	2
C₃₁×#3228	2
C₃₁×#3227	2
C₃₁×#3205	2
C₃₁×#3184	2
C₃₁×#3169	2
C₃₁×#3138	2
C₂×C₃₁×#486	2
C₃₁×#2965	2
#62535	31

Subgroups — C31×#62535 #21519294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62535 #21519294