Subgroups — C₃₁×#61017 #21517776

Order 7936.

1792 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×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3257	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3235	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3217	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3213	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3199	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3180	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3118	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#559	—	2	2	no	—
17	C₃₁×#559	—	2	2	no	—
18	C₃₁×#556	—	2	2	no	—
19	C₃₁×#551	—	2	2	no	—
20	C₃₁×#551	—	2	2	no	—
21	C₃₁×#550	—	2	2	no	—
22	C₃₁×#546	—	2	2	no	—
23	C₃₁×#546	—	2	2	no	—
24	C₃₁×#542	C₂²	1	2	yes	—
25	C₃₁×#542	C₂²	1	2	yes	complemented
26	C₃₁×#540	C₂²	1	2	yes	—
27	C₃₁×#540	C₂²	1	2	yes	complemented
28	C₃₁×#536	C₂²	1	1	yes	characteristic
29	C₃₁×#535	C₂²	1	1	yes	characteristic
30	C₃₁×#535	C₂²	1	2	yes	—
31	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#532	C₂²	1	2	yes	—
34	C₃₁×#532	C₂²	1	2	yes	complemented
35	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#518	C₂²	1	2	yes	complemented
41	C₃₁×#518	C₂²	1	1	yes	characteristic, complemented
42	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#501	C₂²	1	2	yes	complemented
44	C₃₁×#501	C₂²	1	2	yes	complemented
45	C₃₁×#496	C₂²	1	2	yes	—
46	C₃₁×#496	C₂²	1	2	yes	—
47	C₃₁×#490	C₂²	1	2	yes	complemented
48	C₃₁×#490	C₂²	1	2	yes	complemented
49	C₃₁×#489	C₂²	1	2	yes	complemented
50	C₃₁×#489	C₂²	1	2	yes	complemented
51	C₃₁×#485	C₂²	1	4	yes	complemented
52	C₃₁×#482	C₂²	1	4	yes	—
53	C₃₁×#482	C₂²	1	4	yes	complemented
54	C₃₁×#482	C₂²	1	4	yes	complemented
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	complemented
57	C₃₁×#476	C₂²	1	4	yes	complemented
58	C₃₁×#474	C₂²	1	4	yes	complemented
59	C₃₁×#469	C₂²	1	4	yes	complemented
60	C₃₁×#468	C₂²	1	4	yes	complemented
61	C₃₁×#466	C₂²	1	4	yes	complemented
62	C₃₁×#465	C₂²	1	4	yes	complemented
63	C₃₁×#463	C₂²	1	4	yes	complemented
64	C₃₁×#463	C₂²	1	4	yes	complemented
65	C₃₁×#460	C₂²	1	4	yes	complemented
66	C₃₁×#459	C₂²	1	4	yes	—
67	C₃₁×#450	C₂²	1	4	yes	complemented
68	C₃₁×#448	C₂²	1	4	yes	complemented
69	C₃₁×#447	C₂²	1	4	yes	—
70	C₃₁×#447	C₂²	1	4	yes	complemented
71	C₃₁×#442	C₂²	1	4	yes	complemented
72	C₃₁×#440	C₂²	1	4	yes	complemented
73	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
74	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
75	C₃₁×#433	C₂²	1	2	yes	complemented
76	C₃₁×#433	C₂²	1	2	yes	complemented
77	C₃₁×#432	C₂²	1	2	yes	complemented
78	C₃₁×#432	C₂²	1	2	yes	complemented
79	C₃₁×#424	C₂²	1	2	yes	complemented
80	C₃₁×#408	C₂²	1	2	yes	—
81	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
83	C₂×#41×C₃₁	—	2	2	no	—
84	C₂×#41×C₃₁	—	2	2	no	—
85	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂×D₈×C₃₁	C₂³	1	4	yes	—
93	C₂×D₈×C₃₁	C₂³	1	4	yes	—
94	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
95	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
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×#127	—	2	2	no	—
100	C₃₁×#127	—	2	1	no	—
101	C₃₁×#127	—	2	2	no	—
102	C₃₁×#127	C₂³	1	2	yes	—
103	C₃₁×#127	C₂³	1	2	yes	—
104	C₃₁×#126	—	2	2	no	—
105	C₃₁×#126	—	2	2	no	—
106	C₃₁×#126	—	2	2	no	—
107	C₃₁×#126	—	2	2	no	—
108	C₃₁×#125	C₂³	1	2	yes	—
109	C₃₁×#125	C₂³	1	2	yes	—
110	C₃₁×#124	—	2	1	no	—
111	C₃₁×#124	—	2	2	no	—
112	C₃₁×#124	—	2	1	no	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	2	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	C₂³	1	2	yes	—
119	C₃₁×#124	C₂³	1	2	yes	—
120	C₃₁×#123	—	2	1	no	—
121	C₃₁×#123	—	2	1	no	—
122	C₃₁×#123	—	2	2	no	—
123	C₃₁×#123	—	2	2	no	—
124	C₃₁×#123	—	2	4	no	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	2	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#121	C₂³	1	4	yes	—
141	C₃₁×#121	C₂³	1	2	yes	—
142	C₃₁×#120	—	2	2	no	—
143	C₃₁×#120	—	2	2	no	—
144	C₃₁×#120	—	2	1	no	—
145	C₃₁×#120	—	2	1	no	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	D₄	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	4	no	—
155	C₄×D₄×C₃₁	—	2	2	no	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	—	2	2	no	—
158	C₄×D₄×C₃₁	D₄	1	2	yes	—
159	C₄×D₄×C₃₁	D₄	1	2	yes	—
160	C₄×D₄×C₃₁	D₄	1	2	yes	—
161	C₄×D₄×C₃₁	C₂³	1	2	yes	—
162	C₄×D₄×C₃₁	C₂³	1	4	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₄×D₄×C₃₁	C₂³	1	4	yes	—
165	C₃₁×#117	—	2	2	no	—
166	C₃₁×#117	—	2	2	no	—
167	C₃₁×#117	—	2	2	no	—
168	C₃₁×#117	C₂³	1	2	yes	—
169	C₃₁×#117	C₂³	1	1	yes	characteristic
170	C₃₁×#117	C₂³	1	1	yes	characteristic
171	C₃₁×#117	C₂³	1	1	yes	characteristic
172	C₃₁×#117	C₂³	1	1	yes	characteristic
173	C₃₁×#117	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
176	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
177	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
180	C₃₁×#107	C₂³	1	4	yes	—
181	C₃₁×#107	C₂³	1	4	yes	—
182	C₃₁×#106	C₂³	1	4	yes	—
183	C₃₁×#106	C₂³	1	4	yes	—
184	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
185	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
186	C₃₁×#103	C₂³	1	4	yes	—
187	C₃₁×#103	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
195	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₃₁×#97	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	2	yes	—
198	C₃₁×#97	C₂³	1	2	yes	—
199	C₄×C₈×C₃₁	C₂³	1	2	yes	—
200	C₂⁴×C₃₁	—	2	1	no	—
201	C₂⁴×C₃₁	—	2	2	no	—
202	#41×C₃₁	—	4	2	no	—
203	#41×C₃₁	—	8	4	no	—
204	#41×C₃₁	—	8	4	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	2	2	no	—
207	C₂×Q₈×C₃₁	—	2	2	no	—
208	C₂×Q₈×C₃₁	—	4	2	no	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	4	no	—
215	C₂×D₄×C₃₁	—	2	1	no	—
216	C₂×D₄×C₃₁	—	2	2	no	—
217	C₂×D₄×C₃₁	—	2	2	no	—
218	C₂×D₄×C₃₁	—	2	2	no	—
219	C₂×D₄×C₃₁	—	2	4	no	—
220	C₂×D₄×C₃₁	—	4	2	no	—
221	C₂×D₄×C₃₁	—	4	2	no	—
222	C₂×D₄×C₃₁	—	4	2	no	—
223	C₂×D₄×C₃₁	—	8	4	no	—
224	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
227	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₃₁	—	2	1	no	—
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₃₁	—	4	4	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	D₈×C₃₁	—	4	4	no	—
243	D₈×C₃₁	—	4	4	no	—
244	M₁₆×C₃₁	—	4	2	no	—
245	C₂×C₈×C₃₁	—	4	2	no	—
246	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
248	C₄⋊C₄×C₃₁	—	2	2	no	—
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	1	no	—
265	C₂²⋊C₄×C₃₁	—	2	1	no	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	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	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	2	no	—
284	C₄²×C₃₁	—	2	2	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	—	2	1	no	—
287	C₄²×C₃₁	—	2	1	no	—
288	C₄²×C₃₁	C₂×D₄	1	2	yes	—
289	C₄²×C₃₁	C₂×D₄	1	2	yes	—
290	C₄²×C₃₁	C₂×D₄	1	2	yes	—
291	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
292	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
295	#61017	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₃₁	—	2	2	no	—
297	C₂³×C₃₁	—	2	4	no	—
298	C₂³×C₃₁	—	4	2	no	—
299	C₂³×C₃₁	—	4	4	no	—
300	C₂³×C₃₁	—	8	4	no	—
301	C₂³×C₃₁	—	8	2	no	—
302	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
303	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
304	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₃₁	—	2	4	no	—
306	Q₈×C₃₁	—	4	1	no	—
307	Q₈×C₃₁	—	4	2	no	—
308	Q₈×C₃₁	—	4	4	no	—
309	Q₈×C₃₁	—	8	2	no	—
310	D₄×C₃₁	—	2	4	no	—
311	D₄×C₃₁	—	2	4	no	—
312	D₄×C₃₁	—	2	4	no	—
313	D₄×C₃₁	—	4	1	no	—
314	D₄×C₃₁	—	4	1	no	—
315	D₄×C₃₁	—	4	1	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	2	no	—
318	D₄×C₃₁	—	4	4	no	—
319	D₄×C₃₁	—	4	4	no	—
320	D₄×C₃₁	—	8	4	no	—
321	D₄×C₃₁	—	8	2	no	—
322	D₄×C₃₁	—	8	2	no	—
323	D₄×C₃₁	—	8	4	no	—
324	D₄×C₃₁	—	8	4	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	2	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	4	2	no	—
333	C₂×C₄×C₃₁	—	4	2	no	—
334	C₂×C₄×C₃₁	—	4	2	no	—
335	C₂×C₄×C₃₁	—	4	2	no	—
336	C₂×C₄×C₃₁	—	8	2	no	—
337	C₂×C₄×C₃₁	—	8	2	no	—
338	C₂×C₄×C₃₁	—	8	4	no	—
339	C₂×C₄×C₃₁	—	8	4	no	—
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
348	C₈×C₃₁	—	2	4	no	—
349	C₈×C₃₁	—	2	4	no	—
350	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3257	C₂×C₃₁	1	4	yes	complemented
353	#3240	C₂×C₃₁	1	2	yes	complemented
354	#3235	C₂×C₃₁	1	2	yes	complemented
355	#3217	C₂×C₃₁	1	2	yes	complemented
356	#3213	C₂×C₃₁	1	2	yes	complemented
357	#3200	C₂×C₃₁	1	2	yes	complemented
358	#3199	C₂×C₃₁	1	2	yes	complemented
359	#3180	C₂×C₃₁	1	2	yes	complemented
360	#3171	C₂×C₃₁	1	2	yes	complemented
361	#3126	C₂×C₃₁	1	2	yes	complemented
362	#3122	C₂×C₃₁	1	2	yes	complemented
363	#3118	C₂×C₃₁	1	4	yes	complemented
364	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	2	2	no	—
367	C₂²×C₃₁	—	2	2	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	4	4	no	—
372	C₂²×C₃₁	—	4	4	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	4	no	—
377	C₂²×C₃₁	—	16	2	no	—
378	C₂²×C₃₁	—	16	4	no	—
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	2	no	—
383	C₄×C₃₁	—	2	2	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	4	4	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	#585	1	2	yes	—
392	#559	—	2	2	no	—
393	#559	—	2	2	no	—
394	#556	—	2	2	no	—
395	#551	—	2	2	no	—
396	#551	—	2	2	no	—
397	#550	—	2	2	no	—
398	#546	—	2	2	no	—
399	#546	—	2	2	no	—
400	#542	C₂²×C₃₁	1	2	yes	—
401	#542	C₂²×C₃₁	1	2	yes	complemented
402	#540	C₂²×C₃₁	1	2	yes	—
403	#540	C₂²×C₃₁	1	2	yes	complemented
404	#536	C₂²×C₃₁	1	1	yes	characteristic
405	#535	C₂²×C₃₁	1	1	yes	characteristic
406	#535	C₂²×C₃₁	1	2	yes	—
407	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
409	#532	C₂²×C₃₁	1	2	yes	—
410	#532	C₂²×C₃₁	1	2	yes	complemented
411	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	#529	C₂²×C₃₁	1	2	yes	—
413	#529	C₂²×C₃₁	1	2	yes	complemented
414	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
415	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	#518	C₂²×C₃₁	1	2	yes	complemented
417	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
419	#501	C₂²×C₃₁	1	2	yes	complemented
420	#501	C₂²×C₃₁	1	2	yes	complemented
421	#496	C₂²×C₃₁	1	2	yes	—
422	#496	C₂²×C₃₁	1	2	yes	—
423	#490	C₂²×C₃₁	1	2	yes	complemented
424	#490	C₂²×C₃₁	1	2	yes	complemented
425	#489	C₂²×C₃₁	1	2	yes	complemented
426	#489	C₂²×C₃₁	1	2	yes	complemented
427	#485	C₂²×C₃₁	1	4	yes	complemented
428	#482	C₂²×C₃₁	1	4	yes	—
429	#482	C₂²×C₃₁	1	4	yes	complemented
430	#482	C₂²×C₃₁	1	4	yes	complemented
431	#479	C₂²×C₃₁	1	4	yes	complemented
432	#478	C₂²×C₃₁	1	4	yes	complemented
433	#476	C₂²×C₃₁	1	4	yes	complemented
434	#474	C₂²×C₃₁	1	4	yes	complemented
435	#469	C₂²×C₃₁	1	4	yes	complemented
436	#468	C₂²×C₃₁	1	4	yes	complemented
437	#466	C₂²×C₃₁	1	4	yes	complemented
438	#465	C₂²×C₃₁	1	4	yes	complemented
439	#463	C₂²×C₃₁	1	4	yes	complemented
440	#463	C₂²×C₃₁	1	4	yes	complemented
441	#460	C₂²×C₃₁	1	4	yes	complemented
442	#459	C₂²×C₃₁	1	4	yes	—
443	#450	C₂²×C₃₁	1	4	yes	complemented
444	#448	C₂²×C₃₁	1	4	yes	complemented
445	#447	C₂²×C₃₁	1	4	yes	—
446	#447	C₂²×C₃₁	1	4	yes	complemented
447	#442	C₂²×C₃₁	1	4	yes	complemented
448	#440	C₂²×C₃₁	1	4	yes	complemented
449	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
450	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
451	#433	C₂²×C₃₁	1	2	yes	complemented
452	#433	C₂²×C₃₁	1	2	yes	complemented
453	#432	C₂²×C₃₁	1	2	yes	complemented
454	#432	C₂²×C₃₁	1	2	yes	complemented
455	#424	C₂²×C₃₁	1	2	yes	complemented
456	#408	C₂²×C₃₁	1	2	yes	—
457	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
458	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₂×C₃₁	—	4	1	no	—
460	C₂×C₃₁	—	4	1	no	—
461	C₂×C₃₁	—	4	1	no	—
462	C₂×C₃₁	—	8	4	no	—
463	C₂×C₃₁	—	8	2	no	—
464	C₂×C₃₁	#3449	1	1	yes	characteristic
465	C₂×C₃₁	#3585	1	2	yes	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
473	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×D₈	C₂³×C₃₁	1	4	yes	—
476	C₂×D₈	C₂³×C₃₁	1	4	yes	—
477	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
478	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
479	C₄⋊Q₈	—	2	1	no	—
480	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
481	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
482	#127	—	2	2	no	—
483	#127	—	2	1	no	—
484	#127	—	2	2	no	—
485	#127	C₂³×C₃₁	1	2	yes	—
486	#127	C₂³×C₃₁	1	2	yes	—
487	#126	—	2	2	no	—
488	#126	—	2	2	no	—
489	#126	—	2	2	no	—
490	#126	—	2	2	no	—
491	#125	C₂³×C₃₁	1	2	yes	—
492	#125	C₂³×C₃₁	1	2	yes	—
493	#124	—	2	1	no	—
494	#124	—	2	2	no	—
495	#124	—	2	1	no	—
496	#124	—	2	2	no	—
497	#124	—	2	2	no	—
498	#124	—	2	2	no	—
499	#124	—	2	2	no	—
500	#124	—	2	2	no	—
501	#124	C₂³×C₃₁	1	2	yes	—
502	#124	C₂³×C₃₁	1	2	yes	—
503	#123	—	2	1	no	—
504	#123	—	2	1	no	—
505	#123	—	2	2	no	—
506	#123	—	2	2	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	2	no	—
510	#123	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
516	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
517	#121	—	2	2	no	—
518	#121	—	2	2	no	—
519	#121	—	2	4	no	—
520	#121	—	2	4	no	—
521	#121	C₂³×C₃₁	1	2	yes	—
522	#121	C₂³×C₃₁	1	2	yes	—
523	#121	C₂³×C₃₁	1	4	yes	—
524	#121	C₂³×C₃₁	1	4	yes	—
525	#120	—	2	2	no	—
526	#120	—	2	2	no	—
527	#120	—	2	1	no	—
528	#120	—	2	1	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	D₄×C₃₁	1	2	yes	—
533	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
534	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	D₄×C₃₁	1	2	yes	—
542	C₄×D₄	D₄×C₃₁	1	2	yes	—
543	C₄×D₄	D₄×C₃₁	1	2	yes	—
544	C₄×D₄	C₂³×C₃₁	1	2	yes	—
545	C₄×D₄	C₂³×C₃₁	1	2	yes	—
546	C₄×D₄	C₂³×C₃₁	1	4	yes	—
547	C₄×D₄	C₂³×C₃₁	1	4	yes	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	C₂³×C₃₁	1	2	yes	—
552	#117	C₂³×C₃₁	1	1	yes	characteristic
553	#117	C₂³×C₃₁	1	1	yes	characteristic
554	#117	C₂³×C₃₁	1	1	yes	characteristic
555	#117	C₂³×C₃₁	1	1	yes	characteristic
556	#117	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	2	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	2	no	—
560	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
563	#107	C₂³×C₃₁	1	4	yes	—
564	#107	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	4	yes	—
568	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
569	#103	C₂³×C₃₁	1	4	yes	—
570	#103	C₂³×C₃₁	1	4	yes	—
571	#102	C₂³×C₃₁	1	4	yes	—
572	#102	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	4	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
579	#97	C₂³×C₃₁	1	2	yes	—
580	#97	C₂³×C₃₁	1	2	yes	—
581	#97	C₂³×C₃₁	1	2	yes	—
582	C₄×C₈	C₂³×C₃₁	1	2	yes	—
583	C₃₁	#61017	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	—	2	1	no	—
585	C₂⁴	—	2	2	no	—
586	#41	—	4	2	no	—
587	#41	—	8	4	no	—
588	#41	—	8	4	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	8	4	no	—
608	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
609	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
610	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
611	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
620	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
624	SD₁₆	—	4	4	no	—
625	SD₁₆	—	4	4	no	—
626	D₈	—	4	4	no	—
627	D₈	—	4	4	no	—
628	M₁₆	—	4	2	no	—
629	C₂×C₈	—	4	2	no	—
630	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
631	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
642	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	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	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
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	2	no	—
668	C₄²	—	2	2	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	C₂×D₄×C₃₁	1	2	yes	—
673	C₄²	C₂×D₄×C₃₁	1	2	yes	—
674	C₄²	C₂×D₄×C₃₁	1	2	yes	—
675	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	Q₈	—	2	4	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	4	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
730	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
731	C₈	—	2	4	no	—
732	C₈	—	2	4	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	4	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₃₁×#585	1	2	yes	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	C₃₁×#3449	1	1	yes	characteristic
766	C₂	C₃₁×#3585	1	2	yes	—

	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×#3510	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3257	C₂	semidirect
4. C₃₁×#3240	C₂	semidirect
5. C₃₁×#3235	C₂	semidirect
6. C₃₁×#3217	C₂	semidirect
7. C₃₁×#3213	C₂	semidirect
8. C₃₁×#3200	C₂	semidirect
9. C₃₁×#3199	C₂	semidirect
10. C₃₁×#3180	C₂	semidirect
11. C₃₁×#3171	C₂	semidirect
12. C₃₁×#3126	C₂	semidirect
13. C₃₁×#3122	C₂	semidirect
14. C₃₁×#3118	C₂	semidirect
15. C₃₁×#2923	C₂	semidirect
25. C₃₁×#542	C₂²	semidirect
27. C₃₁×#540	C₂²	semidirect
31. C₃₁×#533	C₂²	semidirect
32. C₃₁×#533	C₂²	semidirect
34. C₃₁×#532	C₂²	semidirect
35. C₂×C₃₁×#127	C₂²	semidirect
37. C₃₁×#529	C₂²	semidirect
38. C₂×C₃₁×#124	C₂²	semidirect
39. C₃₁×#519	C₂²	semidirect
40. C₃₁×#518	C₂²	semidirect
41. C₃₁×#518	C₂²	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#501	C₂²	semidirect
47. C₃₁×#490	C₂²	semidirect
48. C₃₁×#490	C₂²	semidirect
49. C₃₁×#489	C₂²	semidirect
50. C₃₁×#489	C₂²	semidirect
51. C₃₁×#485	C₂²	semidirect
53. C₃₁×#482	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
56. C₃₁×#478	C₂²	semidirect
57. C₃₁×#476	C₂²	semidirect
58. C₃₁×#474	C₂²	semidirect
59. C₃₁×#469	C₂²	semidirect
60. C₃₁×#468	C₂²	semidirect
61. C₃₁×#466	C₂²	semidirect
62. C₃₁×#465	C₂²	semidirect
63. C₃₁×#463	C₂²	semidirect
64. C₃₁×#463	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
67. C₃₁×#450	C₂²	semidirect
68. C₃₁×#448	C₂²	semidirect
70. C₃₁×#447	C₂²	semidirect
71. C₃₁×#442	C₂²	semidirect
72. C₃₁×#440	C₂²	semidirect
73. C₄×SD₁₆×C₃₁	C₂²	semidirect
74. C₄×D₈×C₃₁	C₂²	semidirect
75. C₃₁×#433	C₂²	semidirect
76. C₃₁×#433	C₂²	semidirect
77. C₃₁×#432	C₂²	semidirect
78. C₃₁×#432	C₂²	semidirect
79. C₃₁×#424	C₂²	semidirect
81. C₄×M₁₆×C₃₁	C₂²	semidirect
82. C₂×C₃₁×#97	C₂²	semidirect
295. #61017	C₃₁	direct (N × H)
350. #3510	C₂×C₃₁	semidirect
351. #3508	C₂×C₃₁	semidirect
352. #3257	C₂×C₃₁	semidirect
353. #3240	C₂×C₃₁	semidirect
354. #3235	C₂×C₃₁	semidirect
355. #3217	C₂×C₃₁	semidirect
356. #3213	C₂×C₃₁	semidirect
357. #3200	C₂×C₃₁	semidirect
358. #3199	C₂×C₃₁	semidirect
359. #3180	C₂×C₃₁	semidirect
360. #3171	C₂×C₃₁	semidirect
361. #3126	C₂×C₃₁	semidirect
362. #3122	C₂×C₃₁	semidirect
363. #3118	C₂×C₃₁	semidirect
364. #2923	C₂×C₃₁	semidirect
401. #542	C₂²×C₃₁	semidirect
403. #540	C₂²×C₃₁	semidirect
407. #533	C₂²×C₃₁	semidirect
408. #533	C₂²×C₃₁	semidirect
410. #532	C₂²×C₃₁	semidirect
411. C₂×#127	C₂²×C₃₁	semidirect
413. #529	C₂²×C₃₁	semidirect
414. C₂×#124	C₂²×C₃₁	semidirect
415. #519	C₂²×C₃₁	semidirect
416. #518	C₂²×C₃₁	semidirect
417. #518	C₂²×C₃₁	semidirect
419. #501	C₂²×C₃₁	semidirect
420. #501	C₂²×C₃₁	semidirect
423. #490	C₂²×C₃₁	semidirect
424. #490	C₂²×C₃₁	semidirect
425. #489	C₂²×C₃₁	semidirect
426. #489	C₂²×C₃₁	semidirect
427. #485	C₂²×C₃₁	semidirect
429. #482	C₂²×C₃₁	semidirect
430. #482	C₂²×C₃₁	semidirect
431. #479	C₂²×C₃₁	semidirect
432. #478	C₂²×C₃₁	semidirect
433. #476	C₂²×C₃₁	semidirect
434. #474	C₂²×C₃₁	semidirect
435. #469	C₂²×C₃₁	semidirect
436. #468	C₂²×C₃₁	semidirect
437. #466	C₂²×C₃₁	semidirect
438. #465	C₂²×C₃₁	semidirect
439. #463	C₂²×C₃₁	semidirect
440. #463	C₂²×C₃₁	semidirect
441. #460	C₂²×C₃₁	semidirect
443. #450	C₂²×C₃₁	semidirect
444. #448	C₂²×C₃₁	semidirect
446. #447	C₂²×C₃₁	semidirect
447. #442	C₂²×C₃₁	semidirect
448. #440	C₂²×C₃₁	semidirect
449. C₄×SD₁₆	C₂²×C₃₁	semidirect
450. C₄×D₈	C₂²×C₃₁	semidirect
451. #433	C₂²×C₃₁	semidirect
452. #433	C₂²×C₃₁	semidirect
453. #432	C₂²×C₃₁	semidirect
454. #432	C₂²×C₃₁	semidirect
455. #424	C₂²×C₃₁	semidirect
457. C₄×M₁₆	C₂²×C₃₁	semidirect
458. C₂×#97	C₂²×C₃₁	semidirect
583. C₃₁	#61017	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×#3510	2
C₃₁×#3508	2
C₃₁×#3257	2
C₃₁×#3240	2
C₃₁×#3235	2
C₃₁×#3217	2
C₃₁×#3213	2
C₃₁×#3200	2
C₃₁×#3199	2
C₃₁×#3180	2
C₃₁×#3171	2
C₃₁×#3126	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#2923	2
#61017	31

Subgroups — C31×#61017 #21517776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61017 #21517776