Subgroups — C₃₁×#61221 #21517980

Order 7936.

2018 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3497	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3317	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3316	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3313	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3312	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2898	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂×C₃₁×#137	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#556	—	2	2	no	—
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#554	C₂²	1	2	yes	—
25	C₃₁×#552	C₂²	1	4	yes	—
26	C₃₁×#550	—	2	1	no	—
27	C₃₁×#550	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	—	2	1	no	—
29	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#548	—	2	2	no	—
31	C₃₁×#548	C₂²	1	4	yes	—
32	C₃₁×#539	—	2	2	no	—
33	C₃₁×#537	—	2	2	no	—
34	C₃₁×#537	C₂²	1	2	yes	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#532	—	2	2	no	—
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₃₁×#529	—	2	2	no	—
41	C₃₁×#520	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#491	C₂²	1	2	yes	—
45	C₃₁×#490	C₂²	1	2	yes	—
46	C₃₁×#489	C₂²	1	2	yes	—
47	C₃₁×#489	C₂²	1	2	yes	—
48	C₃₁×#485	C₂²	1	4	yes	—
49	C₃₁×#483	C₂²	1	4	yes	—
50	C₃₁×#482	C₂²	1	4	yes	—
51	C₃₁×#481	C₂²	1	4	yes	—
52	C₃₁×#479	C₂²	1	4	yes	—
53	C₃₁×#477	C₂²	1	2	yes	—
54	C₃₁×#475	C₂²	1	2	yes	—
55	C₃₁×#470	C₂²	1	4	yes	—
56	C₃₁×#468	C₂²	1	4	yes	—
57	C₃₁×#467	C₂²	1	4	yes	—
58	C₃₁×#465	C₂²	1	4	yes	—
59	C₃₁×#464	C₂²	1	4	yes	—
60	C₃₁×#462	C₂²	1	2	yes	—
61	C₃₁×#460	C₂²	1	2	yes	—
62	C₃₁×#452	C₂²	1	4	yes	—
63	C₃₁×#452	C₂²	1	4	yes	—
64	C₃₁×#451	C₂²	1	4	yes	—
65	C₃₁×#451	C₂²	1	4	yes	—
66	C₃₁×#441	C₂²	1	4	yes	—
67	C₃₁×#441	C₂²	1	4	yes	—
68	C₃₁×#435	C₂²	1	4	yes	—
69	C₃₁×#435	C₂²	1	4	yes	—
70	C₃₁×#428	C₂²	1	2	yes	—
71	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
72	C₃₁×#423	C₂²	1	1	yes	characteristic
73	C₃₁×#419	C₂²	1	2	yes	—
74	C₃₁×#419	C₂²	1	4	yes	—
75	C₃₁×#417	C₂²	1	2	yes	—
76	C₃₁×#417	C₂²	1	4	yes	—
77	C₃₁×#416	C₂²	1	2	yes	—
78	C₃₁×#416	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	4	yes	—
80	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
81	C₂×C₃₁×#103	C₂²	1	4	yes	—
82	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
83	C₃₁×#408	C₂²	1	2	yes	—
84	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
85	C₃₁×2₋¹⁺⁴	—	2	8	no	—
86	C₃₁×2₋¹⁺⁴	—	4	4	no	—
87	C₂×#41×C₃₁	—	2	4	no	—
88	C₂×#41×C₃₁	—	2	2	no	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂×#41×C₃₁	C₂³	1	2	yes	—
92	C₂²×Q₈×C₃₁	—	2	2	no	—
93	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×#137	—	4	4	no	—
97	C₂×Q₁₆×C₃₁	—	2	4	no	—
98	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₃₁×#131	—	4	4	no	—
102	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×#127	—	2	2	no	—
114	C₃₁×#127	D₄	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#125	—	2	2	no	—
119	C₃₁×#125	—	2	4	no	—
120	C₃₁×#125	C₂³	1	2	yes	—
121	C₃₁×#124	—	2	2	no	—
122	C₃₁×#124	—	2	2	no	—
123	C₃₁×#124	—	2	4	no	—
124	C₃₁×#124	D₄	1	2	yes	—
125	C₃₁×#124	C₂³	1	2	yes	—
126	C₃₁×#123	—	2	4	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	1	no	—
130	C₃₁×C₂²⋊Q₈	—	2	1	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#121	—	2	4	no	—
139	C₃₁×#121	—	2	2	no	—
140	C₃₁×#121	—	2	1	no	—
141	C₃₁×#121	—	2	1	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	D₄	1	2	yes	—
144	C₃₁×#121	D₄	1	2	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	1	no	—
149	C₄×Q₈×C₃₁	—	2	1	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	—	2	4	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	2	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	4	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	2	yes	—
167	C₄×D₄×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#117	—	2	4	no	—
169	C₃₁×#117	C₂³	1	2	yes	—
170	C₃₁×#117	C₂³	1	4	yes	—
171	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₃₁	—	2	1	no	—
177	C₂×C₄²×C₃₁	—	2	1	no	—
178	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
179	C₃₁×#107	C₂³	1	4	yes	—
180	C₃₁×#106	C₂³	1	4	yes	—
181	C₃₁×#106	C₂³	1	4	yes	—
182	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
183	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	4	yes	—
185	C₃₁×#103	C₂³	1	2	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	2	yes	—
191	C₃₁×#103	C₂³	1	2	yes	—
192	C₃₁×#103	C₂³	1	2	yes	—
193	C₃₁×#102	C₂³	1	2	yes	—
194	C₃₁×#102	C₂³	1	4	yes	—
195	C₃₁×#102	C₂³	1	2	yes	—
196	C₃₁×#102	C₂³	1	2	yes	—
197	C₃₁×#102	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₃₁×#97	C₂³	1	2	yes	—
201	C₃₁×#97	C₂³	1	2	yes	—
202	#41×C₃₁	—	2	4	no	—
203	#41×C₃₁	—	2	4	no	—
204	#41×C₃₁	—	2	8	no	—
205	#41×C₃₁	—	2	4	no	—
206	#41×C₃₁	—	2	4	no	—
207	#41×C₃₁	—	4	4	no	—
208	#41×C₃₁	—	4	16	no	—
209	#41×C₃₁	—	4	8	no	—
210	C₂×Q₈×C₃₁	—	2	1	no	—
211	C₂×Q₈×C₃₁	—	2	1	no	—
212	C₂×Q₈×C₃₁	—	2	1	no	—
213	C₂×Q₈×C₃₁	—	2	4	no	—
214	C₂×Q₈×C₃₁	—	2	1	no	—
215	C₂×Q₈×C₃₁	—	2	2	no	—
216	C₂×Q₈×C₃₁	—	2	8	no	—
217	C₂×Q₈×C₃₁	—	2	2	no	—
218	C₂×Q₈×C₃₁	—	2	2	no	—
219	C₂×Q₈×C₃₁	—	4	4	no	—
220	C₂×Q₈×C₃₁	—	4	8	no	—
221	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₃₁	#41	1	4	yes	—
223	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₃₁	—	2	2	no	—
227	C₂×D₄×C₃₁	—	2	4	no	—
228	C₂×D₄×C₃₁	—	2	4	no	—
229	C₂×D₄×C₃₁	—	2	1	no	—
230	C₂×D₄×C₃₁	—	2	1	no	—
231	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₃₁	—	2	1	no	—
237	C₂²×C₄×C₃₁	—	2	1	no	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	1	no	—
241	C₂²×C₄×C₃₁	—	2	4	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	2	no	—
244	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₃₁	—	2	8	no	—
249	Q₁₆×C₃₁	—	4	4	no	—
250	SD₁₆×C₃₁	—	4	4	no	—
251	M₁₆×C₃₁	—	2	4	no	—
252	M₁₆×C₃₁	—	4	4	no	—
253	C₂×C₈×C₃₁	—	2	2	no	—
254	C₂×C₈×C₃₁	—	2	2	no	—
255	C₂×C₈×C₃₁	—	4	4	no	—
256	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
257	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₄⋊C₄×C₃₁	—	2	4	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	2	no	—
283	C₂²⋊C₄×C₃₁	—	2	4	no	—
284	C₂²⋊C₄×C₃₁	—	2	4	no	—
285	C₂²⋊C₄×C₃₁	—	2	4	no	—
286	C₂²⋊C₄×C₃₁	—	2	2	no	—
287	C₂²⋊C₄×C₃₁	—	2	2	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
291	C₄²×C₃₁	—	2	2	no	—
292	C₄²×C₃₁	—	2	2	no	—
293	C₄²×C₃₁	—	2	2	no	—
294	C₄²×C₃₁	—	2	2	no	—
295	C₄²×C₃₁	—	2	4	no	—
296	C₄²×C₃₁	—	2	2	no	—
297	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
301	#61221	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂³×C₃₁	—	2	2	no	—
303	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
304	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₃₁	—	2	4	no	—
306	Q₈×C₃₁	—	2	4	no	—
307	Q₈×C₃₁	—	2	2	no	—
308	Q₈×C₃₁	—	2	2	no	—
309	Q₈×C₃₁	—	2	2	no	—
310	Q₈×C₃₁	—	2	2	no	—
311	Q₈×C₃₁	—	2	2	no	—
312	Q₈×C₃₁	—	4	8	no	—
313	Q₈×C₃₁	—	4	2	no	—
314	Q₈×C₃₁	—	4	2	no	—
315	Q₈×C₃₁	—	8	1	no	—
316	Q₈×C₃₁	C₂×#41	1	4	yes	—
317	D₄×C₃₁	—	2	8	no	—
318	D₄×C₃₁	—	2	4	no	—
319	D₄×C₃₁	—	2	2	no	—
320	D₄×C₃₁	—	2	2	no	—
321	D₄×C₃₁	—	4	2	no	—
322	D₄×C₃₁	—	4	2	no	—
323	D₄×C₃₁	—	4	8	no	—
324	D₄×C₃₁	—	4	2	no	—
325	D₄×C₃₁	—	4	4	no	—
326	D₄×C₃₁	—	8	1	no	—
327	D₄×C₃₁	—	8	4	no	—
328	C₂×C₄×C₃₁	—	2	4	no	—
329	C₂×C₄×C₃₁	—	2	2	no	—
330	C₂×C₄×C₃₁	—	2	4	no	—
331	C₂×C₄×C₃₁	—	2	4	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	2	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	4	1	no	—
339	C₂×C₄×C₃₁	—	4	1	no	—
340	C₂×C₄×C₃₁	—	4	8	no	—
341	C₂×C₄×C₃₁	—	4	8	no	—
342	C₂×C₄×C₃₁	—	4	2	no	—
343	C₂×C₄×C₃₁	—	4	4	no	—
344	C₂×C₄×C₃₁	—	8	1	no	—
345	C₂×C₄×C₃₁	—	8	4	no	—
346	C₂×C₄×C₃₁	—	8	1	no	—
347	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
354	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
356	C₈×C₃₁	—	2	2	no	—
357	C₈×C₃₁	—	2	2	no	—
358	C₈×C₃₁	—	2	4	no	—
359	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#3497	C₂×C₃₁	1	1	yes	characteristic
361	#3317	C₂×C₃₁	1	4	yes	complemented
362	#3316	C₂×C₃₁	1	4	yes	complemented
363	#3313	C₂×C₃₁	1	4	yes	complemented
364	#3312	C₂×C₃₁	1	4	yes	complemented
365	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
366	#3099	C₂×C₃₁	1	2	yes	complemented
367	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
368	#3063	C₂×C₃₁	1	2	yes	complemented
369	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
370	#3011	C₂×C₃₁	1	2	yes	complemented
371	C₂×#441	C₂×C₃₁	1	1	yes	characteristic, complemented
372	#2932	C₂×C₃₁	1	1	yes	characteristic, complemented
373	#2898	C₂×C₃₁	1	2	yes	complemented
374	C₂²×C₃₁	—	2	1	no	—
375	C₂²×C₃₁	—	2	1	no	—
376	C₂²×C₃₁	—	2	4	no	—
377	C₂²×C₃₁	—	2	4	no	—
378	C₂²×C₃₁	—	2	4	no	—
379	C₂²×C₃₁	—	4	2	no	—
380	C₂²×C₃₁	—	4	2	no	—
381	C₂²×C₃₁	—	4	2	no	—
382	C₂²×C₃₁	#546	1	2	yes	—
383	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	4	no	—
389	C₄×C₃₁	—	2	4	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	—	4	2	no	—
395	C₄×C₃₁	—	4	2	no	—
396	C₄×C₃₁	#546	1	2	yes	—
397	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
398	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
400	C₂×#137	C₂²×C₃₁	1	2	yes	—
401	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×#131	C₂²×C₃₁	1	2	yes	—
403	#559	—	2	1	no	—
404	#557	—	2	1	no	—
405	#556	—	2	2	no	—
406	#556	C₂²×C₃₁	1	2	yes	—
407	#554	C₂²×C₃₁	1	2	yes	—
408	#552	C₂²×C₃₁	1	4	yes	—
409	#550	—	2	1	no	—
410	#550	C₂²×C₃₁	1	2	yes	—
411	D₄×Q₈	—	2	1	no	—
412	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
413	#548	—	2	2	no	—
414	#548	C₂²×C₃₁	1	4	yes	—
415	#539	—	2	2	no	—
416	#537	—	2	2	no	—
417	#537	C₂²×C₃₁	1	2	yes	—
418	#536	C₂²×C₃₁	1	2	yes	—
419	#533	C₂²×C₃₁	1	1	yes	characteristic
420	#532	—	2	2	no	—
421	#532	C₂²×C₃₁	1	1	yes	characteristic
422	#532	C₂²×C₃₁	1	1	yes	characteristic
423	#529	—	2	2	no	—
424	#520	C₂²×C₃₁	1	2	yes	—
425	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
427	#491	C₂²×C₃₁	1	2	yes	—
428	#490	C₂²×C₃₁	1	2	yes	—
429	#489	C₂²×C₃₁	1	2	yes	—
430	#489	C₂²×C₃₁	1	2	yes	—
431	#485	C₂²×C₃₁	1	4	yes	—
432	#483	C₂²×C₃₁	1	4	yes	—
433	#482	C₂²×C₃₁	1	4	yes	—
434	#481	C₂²×C₃₁	1	4	yes	—
435	#479	C₂²×C₃₁	1	4	yes	—
436	#477	C₂²×C₃₁	1	2	yes	—
437	#475	C₂²×C₃₁	1	2	yes	—
438	#470	C₂²×C₃₁	1	4	yes	—
439	#468	C₂²×C₃₁	1	4	yes	—
440	#467	C₂²×C₃₁	1	4	yes	—
441	#465	C₂²×C₃₁	1	4	yes	—
442	#464	C₂²×C₃₁	1	4	yes	—
443	#462	C₂²×C₃₁	1	2	yes	—
444	#460	C₂²×C₃₁	1	2	yes	—
445	#452	C₂²×C₃₁	1	4	yes	—
446	#452	C₂²×C₃₁	1	4	yes	—
447	#451	C₂²×C₃₁	1	4	yes	—
448	#451	C₂²×C₃₁	1	4	yes	—
449	#441	C₂²×C₃₁	1	4	yes	—
450	#441	C₂²×C₃₁	1	4	yes	—
451	#435	C₂²×C₃₁	1	4	yes	—
452	#435	C₂²×C₃₁	1	4	yes	—
453	#428	C₂²×C₃₁	1	2	yes	—
454	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
455	#423	C₂²×C₃₁	1	1	yes	characteristic
456	#419	C₂²×C₃₁	1	2	yes	—
457	#419	C₂²×C₃₁	1	4	yes	—
458	#417	C₂²×C₃₁	1	2	yes	—
459	#417	C₂²×C₃₁	1	4	yes	—
460	#416	C₂²×C₃₁	1	2	yes	—
461	#416	C₂²×C₃₁	1	2	yes	—
462	#416	C₂²×C₃₁	1	4	yes	—
463	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
464	C₂×#103	C₂²×C₃₁	1	4	yes	—
465	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
466	#408	C₂²×C₃₁	1	2	yes	—
467	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
468	C₂×C₃₁	—	2	2	no	—
469	C₂×C₃₁	—	4	4	no	—
470	C₂×C₃₁	—	8	2	no	—
471	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
472	C₂×C₃₁	#3586	1	1	yes	characteristic
473	C₂×C₃₁	#3586	1	1	yes	characteristic
474	2₋¹⁺⁴	—	2	8	no	—
475	2₋¹⁺⁴	—	4	4	no	—
476	C₂×#41	—	2	4	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	C₂³×C₃₁	1	2	yes	—
479	C₂×#41	C₂³×C₃₁	1	4	yes	—
480	C₂×#41	C₂³×C₃₁	1	2	yes	—
481	C₂²×Q₈	—	2	2	no	—
482	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
484	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
485	#137	—	4	4	no	—
486	C₂×Q₁₆	—	2	4	no	—
487	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
488	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
490	#131	—	4	4	no	—
491	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
492	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
493	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
502	#127	—	2	2	no	—
503	#127	D₄×C₃₁	1	1	yes	characteristic
504	#127	C₂³×C₃₁	1	1	yes	characteristic
505	#126	—	2	4	no	—
506	#126	—	2	4	no	—
507	#125	—	2	2	no	—
508	#125	—	2	4	no	—
509	#125	C₂³×C₃₁	1	2	yes	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	—	2	4	no	—
513	#124	D₄×C₃₁	1	2	yes	—
514	#124	C₂³×C₃₁	1	2	yes	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
525	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	—	2	2	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	4	no	—
532	#121	D₄×C₃₁	1	2	yes	—
533	#121	D₄×C₃₁	1	2	yes	—
534	#121	C₂³×C₃₁	1	4	yes	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
544	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
545	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
546	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	4	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₃₁	1	2	yes	—
556	C₄×D₄	C₂³×C₃₁	1	2	yes	—
557	#117	—	2	4	no	—
558	#117	C₂³×C₃₁	1	2	yes	—
559	#117	C₂³×C₃₁	1	4	yes	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
565	C₂×C₄²	—	2	1	no	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
568	#107	C₂³×C₃₁	1	4	yes	—
569	#106	C₂³×C₃₁	1	4	yes	—
570	#106	C₂³×C₃₁	1	4	yes	—
571	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
572	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
573	#103	C₂³×C₃₁	1	4	yes	—
574	#103	C₂³×C₃₁	1	2	yes	—
575	#103	C₂³×C₃₁	1	4	yes	—
576	#103	C₂³×C₃₁	1	4	yes	—
577	#103	C₂³×C₃₁	1	4	yes	—
578	#103	C₂³×C₃₁	1	4	yes	—
579	#103	C₂³×C₃₁	1	2	yes	—
580	#103	C₂³×C₃₁	1	2	yes	—
581	#103	C₂³×C₃₁	1	2	yes	—
582	#102	C₂³×C₃₁	1	2	yes	—
583	#102	C₂³×C₃₁	1	4	yes	—
584	#102	C₂³×C₃₁	1	2	yes	—
585	#102	C₂³×C₃₁	1	2	yes	—
586	#102	C₂³×C₃₁	1	2	yes	—
587	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
589	#97	C₂³×C₃₁	1	2	yes	—
590	#97	C₂³×C₃₁	1	2	yes	—
591	C₃₁	#61221	1	1	yes	characteristic, direct product factor, Sylow
592	#41	—	2	4	no	—
593	#41	—	2	4	no	—
594	#41	—	2	8	no	—
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	16	no	—
599	#41	—	4	8	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	8	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	4	4	no	—
610	C₂×Q₈	—	4	8	no	—
611	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
612	C₂×Q₈	#41×C₃₁	1	4	yes	—
613	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
622	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
623	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
625	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
638	Q₁₆	—	2	8	no	—
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	4	4	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	—	4	4	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	4	4	no	—
646	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
647	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
648	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
666	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
680	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂³	—	2	2	no	—
692	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
693	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
694	Q₈	—	2	4	no	—
695	Q₈	—	2	4	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	4	8	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	8	1	no	—
705	Q₈	C₂×#41×C₃₁	1	4	yes	—
706	D₄	—	2	8	no	—
707	D₄	—	2	4	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	8	1	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	1	no	—
736	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
741	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
743	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
744	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
745	C₈	—	2	2	no	—
746	C₈	—	2	2	no	—
747	C₈	—	2	4	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	C₃₁×#546	1	2	yes	—
757	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	C₃₁×#546	1	2	yes	—
771	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
772	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	4	no	—
775	C₂	—	8	2	no	—
776	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
777	C₂	C₃₁×#3586	1	1	yes	characteristic
778	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3497	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3317	C₂	semidirect
4. C₃₁×#3316	C₂	semidirect
5. C₃₁×#3313	C₂	semidirect
6. C₃₁×#3312	C₂	semidirect
7. C₃₁×#3135	C₂	semidirect
8. C₃₁×#3099	C₂	semidirect
9. C₃₁×#3078	C₂	semidirect
10. C₃₁×#3063	C₂	semidirect
11. C₃₁×#3037	C₂	semidirect
12. C₃₁×#3011	C₂	semidirect
13. C₂×C₃₁×#441	C₂	semidirect
14. C₃₁×#2932	C₂	semidirect
15. C₃₁×#2898	C₂	semidirect
301. #61221	C₃₁	direct (N × H)
359. #3507	C₂×C₃₁	semidirect
361. #3317	C₂×C₃₁	semidirect
362. #3316	C₂×C₃₁	semidirect
363. #3313	C₂×C₃₁	semidirect
364. #3312	C₂×C₃₁	semidirect
365. #3135	C₂×C₃₁	semidirect
366. #3099	C₂×C₃₁	semidirect
367. #3078	C₂×C₃₁	semidirect
368. #3063	C₂×C₃₁	semidirect
369. #3037	C₂×C₃₁	semidirect
370. #3011	C₂×C₃₁	semidirect
371. C₂×#441	C₂×C₃₁	semidirect
372. #2932	C₂×C₃₁	semidirect
373. #2898	C₂×C₃₁	semidirect
591. C₃₁	#61221	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×#3507	2
C₃₁×#3497	2
C₃₁×#3317	2
C₃₁×#3316	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3135	2
C₃₁×#3099	2
C₃₁×#3078	2
C₃₁×#3063	2
C₃₁×#3037	2
C₃₁×#3011	2
C₂×C₃₁×#441	2
C₃₁×#2932	2
C₃₁×#2898	2
#61221	31

Subgroups — C31×#61221 #21517980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61221 #21517980