Subgroups — C₃₁×#61913 #21518672

Order 7936.

1760 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3373	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3362	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3224	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3125	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#563	—	2	2	no	—
17	C₃₁×#559	C₂²	1	4	yes	—
18	C₃₁×#559	C₂²	1	2	yes	complemented
19	Q₈²×C₃₁	C₂²	1	2	yes	complemented
20	C₃₁×#556	—	2	1	no	—
21	C₃₁×#556	C₂²	1	2	yes	—
22	C₃₁×#556	C₂²	1	2	yes	complemented
23	C₃₁×#555	—	2	1	no	—
24	C₃₁×#553	—	2	2	no	—
25	C₃₁×#550	C₂²	1	2	yes	—
26	D₄×Q₈×C₃₁	—	2	1	no	—
27	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
28	C₃₁×#547	—	2	1	no	—
29	C₃₁×#542	—	2	2	no	—
30	C₃₁×#542	C₂²	1	4	yes	—
31	C₃₁×#538	—	2	2	no	—
32	C₃₁×#536	—	2	2	no	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	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	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#497	C₂²	1	2	yes	complemented
42	C₃₁×#496	C₂²	1	4	yes	—
43	C₃₁×#495	C₂²	1	4	yes	—
44	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#489	C₂²	1	4	yes	—
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#486	C₂²	1	4	yes	—
50	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#483	C₂²	1	2	yes	—
52	C₃₁×#481	C₂²	1	2	yes	—
53	C₃₁×#476	C₂²	1	2	yes	—
54	C₃₁×#476	C₂²	1	2	yes	—
55	C₃₁×#476	C₂²	1	4	yes	complemented
56	C₃₁×#475	C₂²	1	4	yes	complemented
57	C₃₁×#464	C₂²	1	4	yes	—
58	C₃₁×#464	C₂²	1	4	yes	complemented
59	C₃₁×#463	C₂²	1	4	yes	—
60	C₃₁×#463	C₂²	1	4	yes	complemented
61	C₃₁×#463	C₂²	1	4	yes	complemented
62	C₃₁×#462	C₂²	1	2	yes	complemented
63	C₃₁×#461	C₂²	1	2	yes	—
64	C₃₁×#460	C₂²	1	4	yes	—
65	C₃₁×#460	C₂²	1	2	yes	complemented
66	C₃₁×#459	C₂²	1	2	yes	—
67	C₃₁×#459	C₂²	1	4	yes	—
68	C₃₁×#452	C₂²	1	4	yes	—
69	C₃₁×#450	C₂²	1	2	yes	—
70	C₃₁×#449	C₂²	1	4	yes	—
71	C₃₁×#447	C₂²	1	2	yes	—
72	C₃₁×#446	C₂²	1	2	yes	complemented
73	C₃₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#442	C₂²	1	4	yes	—
76	C₃₁×#442	C₂²	1	4	yes	complemented
77	C₃₁×#441	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
82	C₃₁×#433	C₂²	1	4	yes	—
83	C₃₁×#432	C₂²	1	1	yes	characteristic
84	C₃₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	1	no	—
87	C₂×#41×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	—	2	2	no	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	—	2	1	no	—
91	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂×D₈×C₃₁	C₂³	1	4	yes	—
97	C₂×D₈×C₃₁	C₂³	1	4	yes	—
98	C₃₁×C₄⋊Q₈	—	2	4	no	—
99	C₃₁×C₄⋊Q₈	—	2	2	no	—
100	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×#127	C₂³	1	1	yes	characteristic
108	C₃₁×#127	C₂³	1	4	yes	—
109	C₃₁×#127	C₂³	1	1	yes	characteristic
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#125	—	2	1	no	—
114	C₃₁×#125	D₄	1	2	yes	—
115	C₃₁×#124	—	2	4	no	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	1	no	—
119	C₃₁×#124	C₂³	1	4	yes	—
120	C₃₁×#124	C₂³	1	2	yes	—
121	C₃₁×#124	C₂³	1	4	yes	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	—	2	4	no	—
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	—	2	2	no	—
127	C₃₁×C₂²⋊Q₈	—	2	2	no	—
128	C₃₁×C₂²⋊Q₈	—	2	1	no	—
129	C₃₁×C₂²⋊Q₈	—	2	2	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₃₁×#121	—	2	1	no	—
136	C₃₁×#121	—	2	1	no	—
137	C₃₁×#121	—	2	1	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	C₂³	1	2	yes	—
143	C₃₁×#120	—	2	4	no	—
144	C₄×Q₈×C₃₁	—	2	2	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
147	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
149	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	—	2	4	no	—
152	C₄×D₄×C₃₁	—	2	2	no	—
153	C₄×D₄×C₃₁	—	2	4	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	—	2	1	no	—
158	C₄×D₄×C₃₁	—	2	1	no	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	4	yes	—
161	C₄×D₄×C₃₁	C₂³	1	4	yes	—
162	C₄×D₄×C₃₁	C₂³	1	2	yes	—
163	C₄×D₄×C₃₁	C₂³	1	2	yes	—
164	C₃₁×#117	—	2	1	no	—
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	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₃₁×#106	C₂³	1	2	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#103	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	2	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#103	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	2	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	4	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×#97	C₂³	1	2	yes	—
193	C₃₁×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	4	yes	—
197	C₂⁴×C₃₁	—	2	1	no	—
198	#41×C₃₁	—	4	4	no	—
199	#41×C₃₁	—	8	2	no	—
200	#41×C₃₁	—	8	4	no	—
201	C₂×Q₈×C₃₁	—	2	1	no	—
202	C₂×Q₈×C₃₁	—	2	4	no	—
203	C₂×Q₈×C₃₁	—	2	1	no	—
204	C₂×Q₈×C₃₁	—	8	4	no	—
205	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	1	no	—
212	C₂×D₄×C₃₁	—	2	1	no	—
213	C₂×D₄×C₃₁	—	2	1	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	2	1	no	—
216	C₂×D₄×C₃₁	—	2	4	no	—
217	C₂×D₄×C₃₁	—	2	1	no	—
218	C₂×D₄×C₃₁	—	4	2	no	—
219	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
220	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₃₁	—	2	1	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	2	no	—
225	C₂²×C₄×C₃₁	—	2	2	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	4	no	—
229	C₂²×C₄×C₃₁	—	8	2	no	—
230	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₃₁	—	4	4	no	—
234	SD₁₆×C₃₁	—	4	2	no	—
235	SD₁₆×C₃₁	—	4	4	no	—
236	SD₁₆×C₃₁	—	4	4	no	—
237	SD₁₆×C₃₁	—	4	2	no	—
238	D₈×C₃₁	—	4	4	no	—
239	D₈×C₃₁	—	4	4	no	—
240	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
242	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	4	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	4	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	C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	2	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
278	C₄²×C₃₁	—	2	4	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	4	yes	—
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	#61913	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	4	2	no	—
291	C₂³×C₃₁	—	8	1	no	—
292	C₂³×C₃₁	—	8	1	no	—
293	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₃₁	—	2	4	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	2	no	—
297	Q₈×C₃₁	—	2	4	no	—
298	Q₈×C₃₁	—	4	2	no	—
299	Q₈×C₃₁	—	4	2	no	—
300	Q₈×C₃₁	—	8	4	no	—
301	Q₈×C₃₁	—	8	1	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	2	2	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	1	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	1	no	—
313	D₄×C₃₁	—	8	4	no	—
314	D₄×C₃₁	—	8	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	4	1	no	—
323	C₂×C₄×C₃₁	—	4	4	no	—
324	C₂×C₄×C₃₁	—	4	4	no	—
325	C₂×C₄×C₃₁	—	4	4	no	—
326	C₂×C₄×C₃₁	—	8	2	no	—
327	C₂×C₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	—	8	4	no	—
329	C₂×C₄×C₃₁	—	8	1	no	—
330	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	4	no	—
340	C₈×C₃₁	—	2	2	no	—
341	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#3401	C₂×C₃₁	1	4	yes	complemented
344	#3399	C₂×C₃₁	1	2	yes	complemented
345	#3394	C₂×C₃₁	1	2	yes	complemented
346	#3373	C₂×C₃₁	1	4	yes	complemented
347	#3369	C₂×C₃₁	1	2	yes	complemented
348	#3362	C₂×C₃₁	1	2	yes	complemented
349	#3224	C₂×C₃₁	1	4	yes	complemented
350	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
352	#3125	C₂×C₃₁	1	4	yes	complemented
353	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂²×C₃₁	—	2	1	no	—
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	2	1	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	—	4	2	no	—
362	C₂²×C₃₁	—	4	2	no	—
363	C₂²×C₃₁	—	4	2	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	8	4	no	—
369	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	2	4	no	—
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	4	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	#577	1	2	yes	—
382	C₄×C₃₁	#585	1	2	yes	—
383	#563	—	2	2	no	—
384	#559	C₂²×C₃₁	1	4	yes	—
385	#559	C₂²×C₃₁	1	2	yes	complemented
386	Q₈²	C₂²×C₃₁	1	2	yes	complemented
387	#556	—	2	1	no	—
388	#556	C₂²×C₃₁	1	2	yes	—
389	#556	C₂²×C₃₁	1	2	yes	complemented
390	#555	—	2	1	no	—
391	#553	—	2	2	no	—
392	#550	C₂²×C₃₁	1	2	yes	—
393	D₄×Q₈	—	2	1	no	—
394	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
395	#547	—	2	1	no	—
396	#542	—	2	2	no	—
397	#542	C₂²×C₃₁	1	4	yes	—
398	#538	—	2	2	no	—
399	#536	—	2	2	no	—
400	#535	C₂²×C₃₁	1	2	yes	—
401	#533	C₂²×C₃₁	1	1	yes	characteristic
402	#533	C₂²×C₃₁	1	1	yes	characteristic
403	#532	C₂²×C₃₁	1	1	yes	characteristic
404	#532	C₂²×C₃₁	1	1	yes	characteristic
405	#525	—	2	2	no	—
406	#520	C₂²×C₃₁	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
408	#497	C₂²×C₃₁	1	2	yes	complemented
409	#496	C₂²×C₃₁	1	4	yes	—
410	#495	C₂²×C₃₁	1	4	yes	—
411	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	#489	C₂²×C₃₁	1	4	yes	—
414	#489	C₂²×C₃₁	1	2	yes	complemented
415	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	#486	C₂²×C₃₁	1	4	yes	—
417	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
418	#483	C₂²×C₃₁	1	2	yes	—
419	#481	C₂²×C₃₁	1	2	yes	—
420	#476	C₂²×C₃₁	1	2	yes	—
421	#476	C₂²×C₃₁	1	2	yes	—
422	#476	C₂²×C₃₁	1	4	yes	complemented
423	#475	C₂²×C₃₁	1	4	yes	complemented
424	#464	C₂²×C₃₁	1	4	yes	—
425	#464	C₂²×C₃₁	1	4	yes	complemented
426	#463	C₂²×C₃₁	1	4	yes	—
427	#463	C₂²×C₃₁	1	4	yes	complemented
428	#463	C₂²×C₃₁	1	4	yes	complemented
429	#462	C₂²×C₃₁	1	2	yes	complemented
430	#461	C₂²×C₃₁	1	2	yes	—
431	#460	C₂²×C₃₁	1	4	yes	—
432	#460	C₂²×C₃₁	1	2	yes	complemented
433	#459	C₂²×C₃₁	1	2	yes	—
434	#459	C₂²×C₃₁	1	4	yes	—
435	#452	C₂²×C₃₁	1	4	yes	—
436	#450	C₂²×C₃₁	1	2	yes	—
437	#449	C₂²×C₃₁	1	4	yes	—
438	#447	C₂²×C₃₁	1	2	yes	—
439	#446	C₂²×C₃₁	1	2	yes	complemented
440	#446	C₂²×C₃₁	1	4	yes	complemented
441	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
442	#442	C₂²×C₃₁	1	4	yes	—
443	#442	C₂²×C₃₁	1	4	yes	complemented
444	#441	C₂²×C₃₁	1	4	yes	complemented
445	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
446	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
447	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
448	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
449	#433	C₂²×C₃₁	1	4	yes	—
450	#432	C₂²×C₃₁	1	1	yes	characteristic
451	#431	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×C₃₁	—	4	1	no	—
453	C₂×C₃₁	—	8	2	no	—
454	C₂×C₃₁	—	8	2	no	—
455	C₂×C₃₁	—	8	2	no	—
456	C₂×C₃₁	#3487	1	1	yes	characteristic
457	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
458	C₂×C₃₁	#3585	1	1	yes	characteristic
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	C₂³×C₃₁	1	2	yes	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
466	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
467	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
468	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
470	C₂×D₈	C₂³×C₃₁	1	4	yes	—
471	C₂×D₈	C₂³×C₃₁	1	4	yes	—
472	C₄⋊Q₈	—	2	4	no	—
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
475	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
481	#127	C₂³×C₃₁	1	1	yes	characteristic
482	#127	C₂³×C₃₁	1	1	yes	characteristic
483	#127	C₂³×C₃₁	1	4	yes	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#125	—	2	1	no	—
488	#125	D₄×C₃₁	1	2	yes	—
489	#124	—	2	4	no	—
490	#124	—	2	2	no	—
491	#124	—	2	4	no	—
492	#124	—	2	1	no	—
493	#124	C₂³×C₃₁	1	2	yes	—
494	#124	C₂³×C₃₁	1	4	yes	—
495	#124	C₂³×C₃₁	1	4	yes	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
507	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
508	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
509	#121	—	2	1	no	—
510	#121	—	2	1	no	—
511	#121	—	2	1	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	4	no	—
516	#121	C₂³×C₃₁	1	2	yes	—
517	#120	—	2	4	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
521	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
522	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
523	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
524	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	C₂³×C₃₁	1	2	yes	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	C₂³×C₃₁	1	4	yes	—
536	C₄×D₄	C₂³×C₃₁	1	2	yes	—
537	C₄×D₄	C₂³×C₃₁	1	4	yes	—
538	#117	—	2	1	no	—
539	#117	—	2	2	no	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	C₂³×C₃₁	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
547	#106	C₂³×C₃₁	1	2	yes	—
548	#106	C₂³×C₃₁	1	2	yes	—
549	#106	C₂³×C₃₁	1	4	yes	—
550	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
551	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
552	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
554	#103	C₂³×C₃₁	1	2	yes	—
555	#103	C₂³×C₃₁	1	2	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#103	C₂³×C₃₁	1	4	yes	—
558	#102	C₂³×C₃₁	1	2	yes	—
559	#102	C₂³×C₃₁	1	2	yes	—
560	#102	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
566	#97	C₂³×C₃₁	1	2	yes	—
567	#97	C₂³×C₃₁	1	4	yes	—
568	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₃₁	1	4	yes	—
571	C₃₁	#61913	1	1	yes	characteristic, direct product factor, Sylow
572	C₂⁴	—	2	1	no	—
573	#41	—	4	4	no	—
574	#41	—	8	2	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	8	4	no	—
580	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
581	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
583	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
595	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	8	2	no	—
605	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
608	Q₁₆	—	4	4	no	—
609	SD₁₆	—	4	2	no	—
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	4	no	—
612	SD₁₆	—	4	2	no	—
613	D₈	—	4	4	no	—
614	D₈	—	4	4	no	—
615	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
616	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
617	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
635	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₄²	C₂⁴×C₃₁	1	4	yes	—
660	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	8	1	no	—
666	C₂³	—	8	1	no	—
667	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
668	Q₈	—	2	4	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	8	4	no	—
675	Q₈	—	8	1	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	8	1	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	1	no	—
704	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
711	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	2	4	no	—
714	C₈	—	2	2	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	4	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	C₃₁×#577	1	2	yes	—
741	C₄	C₃₁×#585	1	2	yes	—
742	C₂	—	4	1	no	—
743	C₂	—	8	2	no	—
744	C₂	—	8	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₃₁×#3487	1	1	yes	characteristic
747	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
748	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3399	C₂	semidirect
5. C₃₁×#3394	C₂	semidirect
6. C₃₁×#3373	C₂	semidirect
7. C₃₁×#3369	C₂	semidirect
8. C₃₁×#3362	C₂	semidirect
9. C₃₁×#3224	C₂	semidirect
10. C₃₁×#3216	C₂	semidirect
11. C₃₁×#3207	C₂	semidirect
12. C₃₁×#3125	C₂	semidirect
13. C₃₁×#3109	C₂	semidirect
14. C₃₁×#3101	C₂	semidirect
15. C₃₁×#2985	C₂	semidirect
18. C₃₁×#559	C₂²	semidirect
19. Q₈²×C₃₁	C₂²	semidirect
22. C₃₁×#556	C₂²	semidirect
27. D₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#497	C₂²	semidirect
44. C₃₁×#493	C₂²	semidirect
45. C₃₁×#492	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#487	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
55. C₃₁×#476	C₂²	semidirect
56. C₃₁×#475	C₂²	semidirect
58. C₃₁×#464	C₂²	semidirect
60. C₃₁×#463	C₂²	semidirect
61. C₃₁×#463	C₂²	semidirect
62. C₃₁×#462	C₂²	semidirect
65. C₃₁×#460	C₂²	semidirect
72. C₃₁×#446	C₂²	semidirect
73. C₃₁×#446	C₂²	semidirect
74. C₈×Q₈×C₃₁	C₂²	semidirect
76. C₃₁×#442	C₂²	semidirect
77. C₃₁×#441	C₂²	semidirect
80. C₄×SD₁₆×C₃₁	C₂²	semidirect
81. C₄×SD₁₆×C₃₁	C₂²	semidirect
286. #61913	C₃₁	direct (N × H)
341. #3550	C₂×C₃₁	semidirect
342. #3506	C₂×C₃₁	semidirect
343. #3401	C₂×C₃₁	semidirect
344. #3399	C₂×C₃₁	semidirect
345. #3394	C₂×C₃₁	semidirect
346. #3373	C₂×C₃₁	semidirect
347. #3369	C₂×C₃₁	semidirect
348. #3362	C₂×C₃₁	semidirect
349. #3224	C₂×C₃₁	semidirect
350. #3216	C₂×C₃₁	semidirect
351. #3207	C₂×C₃₁	semidirect
352. #3125	C₂×C₃₁	semidirect
353. #3109	C₂×C₃₁	semidirect
354. #3101	C₂×C₃₁	semidirect
355. #2985	C₂×C₃₁	semidirect
385. #559	C₂²×C₃₁	semidirect
386. Q₈²	C₂²×C₃₁	semidirect
389. #556	C₂²×C₃₁	semidirect
394. D₄×Q₈	C₂²×C₃₁	semidirect
408. #497	C₂²×C₃₁	semidirect
411. #493	C₂²×C₃₁	semidirect
412. #492	C₂²×C₃₁	semidirect
414. #489	C₂²×C₃₁	semidirect
415. #487	C₂²×C₃₁	semidirect
417. #486	C₂²×C₃₁	semidirect
422. #476	C₂²×C₃₁	semidirect
423. #475	C₂²×C₃₁	semidirect
425. #464	C₂²×C₃₁	semidirect
427. #463	C₂²×C₃₁	semidirect
428. #463	C₂²×C₃₁	semidirect
429. #462	C₂²×C₃₁	semidirect
432. #460	C₂²×C₃₁	semidirect
439. #446	C₂²×C₃₁	semidirect
440. #446	C₂²×C₃₁	semidirect
441. C₈×Q₈	C₂²×C₃₁	semidirect
443. #442	C₂²×C₃₁	semidirect
444. #441	C₂²×C₃₁	semidirect
447. C₄×SD₁₆	C₂²×C₃₁	semidirect
448. C₄×SD₁₆	C₂²×C₃₁	semidirect
571. C₃₁	#61913	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×#3550	2
C₃₁×#3506	2
C₃₁×#3401	2
C₃₁×#3399	2
C₃₁×#3394	2
C₃₁×#3373	2
C₃₁×#3369	2
C₃₁×#3362	2
C₃₁×#3224	2
C₃₁×#3216	2
C₃₁×#3207	2
C₃₁×#3125	2
C₃₁×#3109	2
C₃₁×#3101	2
C₃₁×#2985	2
#61913	31

Subgroups — C31×#61913 #21518672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61913 #21518672