Subgroups — C₃₁×#61018 #21517777

Order 7936.

1672 conjugacy classes of subgroups.

The subgroup lattice has 738 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
2	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3258	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3240	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3237	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3218	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3202	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3200	C₂	1	2	yes	maximal
10	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3172	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3121	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#559	—	2	2	no	—
17	C₃₁×#557	—	2	2	no	—
18	C₃₁×#556	—	2	2	no	—
19	C₃₁×#556	—	2	2	no	—
20	C₃₁×#552	—	2	2	no	—
21	C₃₁×#552	—	2	2	no	—
22	C₃₁×#551	—	2	2	no	—
23	C₃₁×#551	—	2	2	no	—
24	C₃₁×#542	C₂²	1	2	yes	—
25	C₃₁×#542	C₂²	1	2	yes	—
26	C₃₁×#541	C₂²	1	2	yes	—
27	C₃₁×#541	C₂²	1	2	yes	complemented
28	C₃₁×#536	C₂²	1	2	yes	—
29	C₃₁×#536	C₂²	1	1	yes	characteristic
30	C₃₁×#535	C₂²	1	1	yes	characteristic
31	C₃₁×#533	C₂²	1	2	yes	—
32	C₃₁×#533	C₂²	1	1	yes	characteristic
33	C₃₁×#533	C₂²	1	2	yes	complemented
34	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#529	C₂²	1	2	yes	—
37	C₃₁×#529	C₂²	1	2	yes	—
38	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
39	C₃₁×#519	C₂²	1	1	yes	characteristic
40	C₃₁×#519	C₂²	1	2	yes	complemented
41	C₃₁×#518	C₂²	1	1	yes	characteristic
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×#497	C₂²	1	2	yes	—
46	C₃₁×#497	C₂²	1	2	yes	—
47	C₃₁×#491	C₂²	1	2	yes	complemented
48	C₃₁×#491	C₂²	1	2	yes	complemented
49	C₃₁×#489	C₂²	1	2	yes	—
50	C₃₁×#489	C₂²	1	2	yes	—
51	C₃₁×#485	C₂²	1	4	yes	—
52	C₃₁×#485	C₂²	1	4	yes	—
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#482	C₂²	1	4	yes	—
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#478	C₂²	1	4	yes	—
57	C₃₁×#477	C₂²	1	4	yes	complemented
58	C₃₁×#475	C₂²	1	4	yes	complemented
59	C₃₁×#470	C₂²	1	4	yes	complemented
60	C₃₁×#468	C₂²	1	4	yes	—
61	C₃₁×#467	C₂²	1	4	yes	complemented
62	C₃₁×#465	C₂²	1	4	yes	—
63	C₃₁×#464	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	—
65	C₃₁×#462	C₂²	1	4	yes	complemented
66	C₃₁×#461	C₂²	1	4	yes	—
67	C₃₁×#451	C₂²	1	4	yes	—
68	C₃₁×#451	C₂²	1	4	yes	complemented
69	C₃₁×#450	C₂²	1	4	yes	—
70	C₃₁×#448	C₂²	1	4	yes	—
71	C₃₁×#441	C₂²	1	4	yes	complemented
72	C₃₁×#440	C₂²	1	4	yes	—
73	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
74	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
75	C₃₁×#433	C₂²	1	2	yes	—
76	C₃₁×#433	C₂²	1	2	yes	complemented
77	C₃₁×#432	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
85	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₃₁×C₄⋊Q₈	—	2	1	no	—
94	C₃₁×C₄⋊Q₈	—	2	2	no	—
95	C₃₁×C₄⋊Q₈	—	2	2	no	—
96	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₃₁×#127	—	2	1	no	—
101	C₃₁×#126	—	2	2	no	—
102	C₃₁×#126	—	2	2	no	—
103	C₃₁×#126	—	2	4	no	—
104	C₃₁×#126	—	2	4	no	—
105	C₃₁×#126	—	2	2	no	—
106	C₃₁×#126	—	2	2	no	—
107	C₃₁×#125	—	2	4	no	—
108	C₃₁×#125	—	2	4	no	—
109	C₃₁×#125	—	2	2	no	—
110	C₃₁×#125	—	2	2	no	—
111	C₃₁×#125	C₂³	1	2	yes	—
112	C₃₁×#125	C₂³	1	2	yes	—
113	C₃₁×#124	—	2	1	no	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	2	no	—
118	C₃₁×#124	—	2	2	no	—
119	C₃₁×#124	C₂³	1	2	yes	—
120	C₃₁×#124	C₂³	1	2	yes	—
121	C₃₁×#123	—	2	1	no	—
122	C₃₁×#123	—	2	1	no	—
123	C₃₁×#123	—	2	2	no	—
124	C₃₁×#123	—	2	2	no	—
125	C₃₁×#123	—	2	2	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	2	no	—
128	C₃₁×#123	—	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	—	2	2	no	—
133	C₃₁×C₂²⋊Q₈	—	2	2	no	—
134	C₃₁×C₂²⋊Q₈	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	2	yes	—
140	C₃₁×#121	C₂³	1	2	yes	—
141	C₃₁×#120	—	2	1	no	—
142	C₃₁×#120	—	2	1	no	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	4	no	—
145	C₄×Q₈×C₃₁	—	2	2	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	4	yes	—
151	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	—	2	2	no	—
155	C₄×D₄×C₃₁	—	2	2	no	—
156	C₄×D₄×C₃₁	—	2	2	no	—
157	C₄×D₄×C₃₁	D₄	1	2	yes	—
158	C₄×D₄×C₃₁	D₄	1	2	yes	—
159	C₄×D₄×C₃₁	D₄	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₄×D₄×C₃₁	C₂³	1	2	yes	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	—	2	2	no	—
165	C₃₁×#117	—	2	4	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×C₄⋊C₄×C₃₁	—	2	2	no	—
175	C₂×C₂²⋊C₄×C₃₁	—	2	2	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×#103	C₂³	1	4	yes	—
189	C₃₁×#103	C₂³	1	4	yes	—
190	C₃₁×#103	C₂³	1	4	yes	—
191	C₃₁×#103	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	#41×C₃₁	—	4	2	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	2	2	no	—
205	C₂×Q₈×C₃₁	—	2	2	no	—
206	C₂×Q₈×C₃₁	—	4	2	no	—
207	C₂×Q₈×C₃₁	—	4	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×Q₈×C₃₁	C₂⁴	1	4	yes	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	2	1	no	—
215	C₂×D₄×C₃₁	—	4	2	no	—
216	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₃₁	—	2	1	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂×D₄	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	—	4	4	no	—
231	Q₁₆×C₃₁	—	4	4	no	—
232	SD₁₆×C₃₁	—	4	4	no	—
233	SD₁₆×C₃₁	—	4	4	no	—
234	M₁₆×C₃₁	—	4	2	no	—
235	C₂×C₈×C₃₁	—	4	2	no	—
236	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
237	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₄⋊C₄×C₃₁	—	2	2	no	—
240	C₄⋊C₄×C₃₁	—	2	4	no	—
241	C₄⋊C₄×C₃₁	—	2	2	no	—
242	C₄⋊C₄×C₃₁	—	2	2	no	—
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	4	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
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	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂²⋊C₄×C₃₁	—	2	1	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	—	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	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	—	2	1	no	—
283	C₄²×C₃₁	—	2	1	no	—
284	C₄²×C₃₁	—	2	2	no	—
285	C₄²×C₃₁	C₂×D₄	1	2	yes	—
286	C₄²×C₃₁	C₂×D₄	1	2	yes	—
287	C₄²×C₃₁	C₂×D₄	1	2	yes	—
288	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
292	#61018	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₃₁	—	2	2	no	—
294	C₂³×C₃₁	—	4	2	no	—
295	C₂³×C₃₁	—	8	2	no	—
296	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₃₁	—	2	4	no	—
300	Q₈×C₃₁	—	2	4	no	—
301	Q₈×C₃₁	—	2	4	no	—
302	Q₈×C₃₁	—	4	1	no	—
303	Q₈×C₃₁	—	4	4	no	—
304	Q₈×C₃₁	—	4	2	no	—
305	Q₈×C₃₁	—	4	4	no	—
306	Q₈×C₃₁	—	8	2	no	—
307	D₄×C₃₁	—	2	4	no	—
308	D₄×C₃₁	—	4	1	no	—
309	D₄×C₃₁	—	4	1	no	—
310	D₄×C₃₁	—	4	1	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	8	2	no	—
313	D₄×C₃₁	—	8	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	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	2	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	4	2	no	—
323	C₂×C₄×C₃₁	—	4	2	no	—
324	C₂×C₄×C₃₁	—	4	2	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	4	2	no	—
327	C₂×C₄×C₃₁	—	8	2	no	—
328	C₂×C₄×C₃₁	—	8	2	no	—
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	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	4	no	—
338	C₈×C₃₁	—	2	4	no	—
339	#3510	C₂×C₃₁	1	1	yes	characteristic
340	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#3258	C₂×C₃₁	1	4	yes	complemented
342	#3240	C₂×C₃₁	1	2	yes	complemented
343	#3237	C₂×C₃₁	1	2	yes	complemented
344	#3218	C₂×C₃₁	1	2	yes	complemented
345	#3215	C₂×C₃₁	1	2	yes	complemented
346	#3202	C₂×C₃₁	1	2	yes	complemented
347	#3200	C₂×C₃₁	1	2	yes	—
348	#3181	C₂×C₃₁	1	2	yes	complemented
349	#3172	C₂×C₃₁	1	2	yes	complemented
350	#3127	C₂×C₃₁	1	2	yes	complemented
351	#3123	C₂×C₃₁	1	2	yes	complemented
352	#3121	C₂×C₃₁	1	4	yes	complemented
353	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	2	no	—
356	C₂²×C₃₁	—	2	2	no	—
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	2	1	no	—
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	16	2	no	—
364	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	2	2	no	—
367	C₄×C₃₁	—	2	2	no	—
368	C₄×C₃₁	—	2	2	no	—
369	C₄×C₃₁	—	2	1	no	—
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	4	2	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	4	no	—
375	C₄×C₃₁	—	4	2	no	—
376	C₄×C₃₁	—	4	4	no	—
377	C₄×C₃₁	#585	1	2	yes	—
378	#559	—	2	2	no	—
379	#557	—	2	2	no	—
380	#556	—	2	2	no	—
381	#556	—	2	2	no	—
382	#552	—	2	2	no	—
383	#552	—	2	2	no	—
384	#551	—	2	2	no	—
385	#551	—	2	2	no	—
386	#542	C₂²×C₃₁	1	2	yes	—
387	#542	C₂²×C₃₁	1	2	yes	—
388	#541	C₂²×C₃₁	1	2	yes	—
389	#541	C₂²×C₃₁	1	2	yes	complemented
390	#536	C₂²×C₃₁	1	2	yes	—
391	#536	C₂²×C₃₁	1	1	yes	characteristic
392	#535	C₂²×C₃₁	1	1	yes	characteristic
393	#533	C₂²×C₃₁	1	2	yes	—
394	#533	C₂²×C₃₁	1	1	yes	characteristic
395	#533	C₂²×C₃₁	1	2	yes	complemented
396	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
397	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
398	#529	C₂²×C₃₁	1	2	yes	—
399	#529	C₂²×C₃₁	1	2	yes	—
400	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
401	#519	C₂²×C₃₁	1	1	yes	characteristic
402	#519	C₂²×C₃₁	1	2	yes	complemented
403	#518	C₂²×C₃₁	1	1	yes	characteristic
404	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
405	#501	C₂²×C₃₁	1	2	yes	complemented
406	#501	C₂²×C₃₁	1	2	yes	complemented
407	#497	C₂²×C₃₁	1	2	yes	—
408	#497	C₂²×C₃₁	1	2	yes	—
409	#491	C₂²×C₃₁	1	2	yes	complemented
410	#491	C₂²×C₃₁	1	2	yes	complemented
411	#489	C₂²×C₃₁	1	2	yes	—
412	#489	C₂²×C₃₁	1	2	yes	—
413	#485	C₂²×C₃₁	1	4	yes	—
414	#485	C₂²×C₃₁	1	4	yes	—
415	#485	C₂²×C₃₁	1	4	yes	complemented
416	#482	C₂²×C₃₁	1	4	yes	—
417	#479	C₂²×C₃₁	1	4	yes	complemented
418	#478	C₂²×C₃₁	1	4	yes	—
419	#477	C₂²×C₃₁	1	4	yes	complemented
420	#475	C₂²×C₃₁	1	4	yes	complemented
421	#470	C₂²×C₃₁	1	4	yes	complemented
422	#468	C₂²×C₃₁	1	4	yes	—
423	#467	C₂²×C₃₁	1	4	yes	complemented
424	#465	C₂²×C₃₁	1	4	yes	—
425	#464	C₂²×C₃₁	1	4	yes	—
426	#464	C₂²×C₃₁	1	4	yes	—
427	#462	C₂²×C₃₁	1	4	yes	complemented
428	#461	C₂²×C₃₁	1	4	yes	—
429	#451	C₂²×C₃₁	1	4	yes	—
430	#451	C₂²×C₃₁	1	4	yes	complemented
431	#450	C₂²×C₃₁	1	4	yes	—
432	#448	C₂²×C₃₁	1	4	yes	—
433	#441	C₂²×C₃₁	1	4	yes	complemented
434	#440	C₂²×C₃₁	1	4	yes	—
435	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
436	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
437	#433	C₂²×C₃₁	1	2	yes	—
438	#433	C₂²×C₃₁	1	2	yes	complemented
439	#432	C₂²×C₃₁	1	2	yes	—
440	#432	C₂²×C₃₁	1	2	yes	complemented
441	#424	C₂²×C₃₁	1	2	yes	complemented
442	#408	C₂²×C₃₁	1	2	yes	—
443	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
445	C₂×C₃₁	—	4	1	no	—
446	C₂×C₃₁	—	4	1	no	—
447	C₂×C₃₁	—	4	1	no	—
448	C₂×C₃₁	—	8	2	no	—
449	C₂×C₃₁	#3449	1	1	yes	characteristic
450	C₂×C₃₁	#3586	1	2	yes	—
451	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
454	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
456	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
459	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
460	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
461	C₄⋊Q₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	2	no	—
464	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
465	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
466	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
467	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
468	#127	—	2	1	no	—
469	#126	—	2	2	no	—
470	#126	—	2	2	no	—
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#125	—	2	4	no	—
476	#125	—	2	4	no	—
477	#125	—	2	2	no	—
478	#125	—	2	2	no	—
479	#125	C₂³×C₃₁	1	2	yes	—
480	#125	C₂³×C₃₁	1	2	yes	—
481	#124	—	2	1	no	—
482	#124	—	2	2	no	—
483	#124	—	2	1	no	—
484	#124	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	C₂³×C₃₁	1	2	yes	—
488	#124	C₂³×C₃₁	1	2	yes	—
489	#123	—	2	1	no	—
490	#123	—	2	1	no	—
491	#123	—	2	2	no	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	#123	—	2	2	no	—
495	#123	—	2	2	no	—
496	#123	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
504	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
506	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
507	#121	C₂³×C₃₁	1	2	yes	—
508	#121	C₂³×C₃₁	1	2	yes	—
509	#120	—	2	1	no	—
510	#120	—	2	1	no	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	4	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	D₄×C₃₁	1	2	yes	—
518	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
520	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
521	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	D₄×C₃₁	1	2	yes	—
526	C₄×D₄	D₄×C₃₁	1	2	yes	—
527	C₄×D₄	D₄×C₃₁	1	2	yes	—
528	C₄×D₄	C₂³×C₃₁	1	2	yes	—
529	C₄×D₄	C₂³×C₃₁	1	2	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	—	2	4	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	C₂³×C₃₁	1	1	yes	characteristic
537	#117	C₂³×C₃₁	1	1	yes	characteristic
538	#117	C₂³×C₃₁	1	2	yes	—
539	#117	C₂³×C₃₁	1	1	yes	characteristic
540	#117	C₂³×C₃₁	1	1	yes	characteristic
541	#117	C₂³×C₃₁	1	1	yes	characteristic
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₂²⋊C₄	—	2	2	no	—
544	C₂×C₂²⋊C₄	—	2	2	no	—
545	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
548	#107	C₂³×C₃₁	1	4	yes	—
549	#107	C₂³×C₃₁	1	4	yes	—
550	#106	C₂³×C₃₁	1	4	yes	—
551	#106	C₂³×C₃₁	1	4	yes	—
552	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
554	#103	C₂³×C₃₁	1	4	yes	—
555	#103	C₂³×C₃₁	1	4	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#103	C₂³×C₃₁	1	4	yes	—
558	#103	C₂³×C₃₁	1	4	yes	—
559	#103	C₂³×C₃₁	1	4	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
564	#97	C₂³×C₃₁	1	2	yes	—
565	#97	C₂³×C₃₁	1	2	yes	—
566	#97	C₂³×C₃₁	1	2	yes	—
567	C₄×C₈	C₂³×C₃₁	1	2	yes	—
568	C₃₁	#61018	1	1	yes	characteristic, direct product factor, Sylow
569	C₂⁴	—	2	1	no	—
570	#41	—	4	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
579	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
580	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
587	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
588	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
599	Q₁₆	—	4	4	no	—
600	Q₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	SD₁₆	—	4	4	no	—
603	M₁₆	—	4	2	no	—
604	C₂×C₈	—	4	2	no	—
605	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
606	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
627	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	C₂×D₄×C₃₁	1	2	yes	—
655	C₄²	C₂×D₄×C₃₁	1	2	yes	—
656	C₄²	C₂×D₄×C₃₁	1	2	yes	—
657	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
660	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	8	2	no	—
664	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
665	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
667	Q₈	—	2	4	no	—
668	Q₈	—	2	4	no	—
669	Q₈	—	2	4	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
705	C₈	—	2	4	no	—
706	C₈	—	2	4	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	16	2	no	—
717	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	4	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	C₃₁×#585	1	2	yes	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	4	1	no	—
734	C₂	—	8	2	no	—
735	C₂	C₃₁×#3449	1	1	yes	characteristic
736	C₂	C₃₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#535	C₂²
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
2. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3258	C₂	semidirect
4. C₃₁×#3240	C₂	semidirect
5. C₃₁×#3237	C₂	semidirect
6. C₃₁×#3218	C₂	semidirect
7. C₃₁×#3215	C₂	semidirect
8. C₃₁×#3202	C₂	semidirect
10. C₃₁×#3181	C₂	semidirect
11. C₃₁×#3172	C₂	semidirect
12. C₃₁×#3127	C₂	semidirect
13. C₃₁×#3123	C₂	semidirect
14. C₃₁×#3121	C₂	semidirect
15. C₃₁×#2923	C₂	semidirect
27. C₃₁×#541	C₂²	semidirect
33. C₃₁×#533	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
35. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
40. C₃₁×#519	C₂²	semidirect
43. C₃₁×#501	C₂²	semidirect
44. C₃₁×#501	C₂²	semidirect
47. C₃₁×#491	C₂²	semidirect
48. C₃₁×#491	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
57. C₃₁×#477	C₂²	semidirect
58. C₃₁×#475	C₂²	semidirect
59. C₃₁×#470	C₂²	semidirect
61. C₃₁×#467	C₂²	semidirect
65. C₃₁×#462	C₂²	semidirect
68. C₃₁×#451	C₂²	semidirect
71. C₃₁×#441	C₂²	semidirect
73. C₄×Q₁₆×C₃₁	C₂²	semidirect
76. C₃₁×#433	C₂²	semidirect
78. C₃₁×#432	C₂²	semidirect
79. C₃₁×#424	C₂²	semidirect
81. C₄×M₁₆×C₃₁	C₂²	semidirect
82. C₂×C₃₁×#97	C₂²	semidirect
292. #61018	C₃₁	direct (N × H)
340. #3509	C₂×C₃₁	semidirect
341. #3258	C₂×C₃₁	semidirect
342. #3240	C₂×C₃₁	semidirect
343. #3237	C₂×C₃₁	semidirect
344. #3218	C₂×C₃₁	semidirect
345. #3215	C₂×C₃₁	semidirect
346. #3202	C₂×C₃₁	semidirect
348. #3181	C₂×C₃₁	semidirect
349. #3172	C₂×C₃₁	semidirect
350. #3127	C₂×C₃₁	semidirect
351. #3123	C₂×C₃₁	semidirect
352. #3121	C₂×C₃₁	semidirect
353. #2923	C₂×C₃₁	semidirect
389. #541	C₂²×C₃₁	semidirect
395. #533	C₂²×C₃₁	semidirect
396. #533	C₂²×C₃₁	semidirect
397. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
402. #519	C₂²×C₃₁	semidirect
405. #501	C₂²×C₃₁	semidirect
406. #501	C₂²×C₃₁	semidirect
409. #491	C₂²×C₃₁	semidirect
410. #491	C₂²×C₃₁	semidirect
415. #485	C₂²×C₃₁	semidirect
417. #479	C₂²×C₃₁	semidirect
419. #477	C₂²×C₃₁	semidirect
420. #475	C₂²×C₃₁	semidirect
421. #470	C₂²×C₃₁	semidirect
423. #467	C₂²×C₃₁	semidirect
427. #462	C₂²×C₃₁	semidirect
430. #451	C₂²×C₃₁	semidirect
433. #441	C₂²×C₃₁	semidirect
435. C₄×Q₁₆	C₂²×C₃₁	semidirect
438. #433	C₂²×C₃₁	semidirect
440. #432	C₂²×C₃₁	semidirect
441. #424	C₂²×C₃₁	semidirect
443. C₄×M₁₆	C₂²×C₃₁	semidirect
444. C₂×#97	C₂²×C₃₁	semidirect
568. C₃₁	#61018	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×#3509	2
C₃₁×#3258	2
C₃₁×#3240	2
C₃₁×#3237	2
C₃₁×#3218	2
C₃₁×#3215	2
C₃₁×#3202	2
C₃₁×#3200	2
C₃₁×#3181	2
C₃₁×#3172	2
C₃₁×#3127	2
C₃₁×#3123	2
C₃₁×#3121	2
C₃₁×#2923	2
#61018	31

Subgroups — C31×#61018 #21517777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61018 #21517777