Subgroups — C₃₁×#35094 #21491853

Order 7936.

2434 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2849	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2623	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2617	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2479	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2477	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2475	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2471	C₂	1	4	yes	maximal, complemented
13	C₃₁×#2321	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₃₁×#123	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#539	—	2	8	no	—
18	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
19	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
20	C₂×C₃₁×#123	C₂²	1	2	yes	—
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#120	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₃₁×#117	—	2	8	no	—
29	C₂×C₃₁×#117	C₂²	1	4	yes	—
30	C₂×C₃₁×#117	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#400	C₂²	1	4	yes	complemented
38	C₃₁×#399	C₂²	1	2	yes	—
39	C₃₁×#399	C₂²	1	4	yes	complemented
40	C₃₁×#398	C₂²	1	4	yes	complemented
41	C₃₁×#397	C₂²	1	2	yes	—
42	C₃₁×#397	C₂²	1	4	yes	complemented
43	C₃₁×#396	C₂²	1	4	yes	—
44	C₃₁×#394	C₂²	1	4	yes	—
45	C₃₁×#393	C₂²	1	2	yes	—
46	C₃₁×#392	C₂²	1	2	yes	—
47	C₃₁×#391	C₂²	1	2	yes	complemented
48	C₃₁×#390	C₂²	1	4	yes	—
49	C₃₁×#390	C₂²	1	2	yes	complemented
50	C₃₁×#389	C₂²	1	2	yes	complemented
51	C₃₁×#389	C₂²	1	2	yes	complemented
52	C₃₁×#388	C₂²	1	4	yes	—
53	C₃₁×#388	C₂²	1	4	yes	—
54	C₃₁×#388	C₂²	1	4	yes	complemented
55	C₃₁×#388	C₂²	1	4	yes	complemented
56	C₃₁×#387	C₂²	1	4	yes	complemented
57	C₃₁×#387	C₂²	1	4	yes	complemented
58	C₃₁×#387	C₂²	1	4	yes	complemented
59	C₃₁×#387	C₂²	1	4	yes	complemented
60	C₃₁×#386	C₂²	1	2	yes	—
61	C₃₁×#386	C₂²	1	4	yes	—
62	C₃₁×#386	C₂²	1	4	yes	—
63	C₃₁×#386	C₂²	1	4	yes	—
64	C₃₁×#386	C₂²	1	2	yes	—
65	C₃₁×#385	C₂²	1	2	yes	—
66	C₃₁×#385	C₂²	1	4	yes	—
67	C₃₁×#385	C₂²	1	4	yes	—
68	C₃₁×#385	C₂²	1	2	yes	—
69	C₃₁×#381	C₂²	1	2	yes	—
70	C₃₁×#381	C₂²	1	2	yes	—
71	C₃₁×#380	C₂²	1	1	yes	characteristic
72	C₃₁×#380	C₂²	1	1	yes	characteristic
73	C₃₁×#379	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	—	2	4	no	—
83	C₂³×C₄×C₃₁	—	2	4	no	—
84	C₂³×C₄×C₃₁	—	2	4	no	—
85	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₃₁×#126	—	2	8	no	—
94	C₃₁×#125	—	2	8	no	—
95	C₃₁×#123	—	2	8	no	—
96	C₃₁×#123	—	2	8	no	—
97	C₃₁×#123	—	2	8	no	—
98	C₃₁×C₂²⋊Q₈	—	2	4	no	—
99	C₃₁×C₂²⋊Q₈	—	2	8	no	—
100	C₃₁×#121	—	2	4	no	—
101	C₃₁×#120	—	2	8	no	—
102	C₄×D₄×C₃₁	—	2	8	no	—
103	C₃₁×#117	—	2	16	no	—
104	C₃₁×#117	—	2	16	no	—
105	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₃₁	—	2	4	no	—
140	C₂×C₄²×C₃₁	—	2	4	no	—
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
146	C₃₁×#95	C₂³	1	4	yes	—
147	C₃₁×#95	C₂³	1	4	yes	—
148	C₃₁×#95	C₂³	1	2	yes	—
149	C₃₁×#95	C₂³	1	4	yes	—
150	C₃₁×#95	C₂³	1	4	yes	—
151	C₃₁×#95	C₂³	1	4	yes	—
152	C₃₁×#95	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	4	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₂⁴×C₃₁	—	2	2	no	—
158	C₂⁴×C₃₁	—	2	2	no	—
159	C₂⁴×C₃₁	—	4	2	no	—
160	C₂⁴×C₃₁	—	4	2	no	—
161	C₂⁴×C₃₁	#41	1	4	yes	—
162	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
163	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₃₁	—	2	2	no	—
166	C₂×Q₈×C₃₁	—	4	2	no	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	4	no	—
169	C₂×D₄×C₃₁	—	2	4	no	—
170	C₂×D₄×C₃₁	—	2	8	no	—
171	C₂×D₄×C₃₁	—	2	2	no	—
172	C₂×D₄×C₃₁	—	4	2	no	—
173	C₂×D₄×C₃₁	—	4	4	no	—
174	C₂×D₄×C₃₁	—	4	4	no	—
175	C₂²×C₄×C₃₁	—	2	32	no	—
176	C₂²×C₄×C₃₁	—	2	2	no	—
177	C₂²×C₄×C₃₁	—	2	8	no	—
178	C₂²×C₄×C₃₁	—	2	2	no	—
179	C₂²×C₄×C₃₁	—	2	2	no	—
180	C₂²×C₄×C₃₁	—	2	2	no	—
181	C₂²×C₄×C₃₁	—	2	8	no	—
182	C₂²×C₄×C₃₁	—	2	8	no	—
183	C₂²×C₄×C₃₁	—	2	2	no	—
184	C₂²×C₄×C₃₁	—	2	2	no	—
185	C₂²×C₄×C₃₁	—	2	4	no	—
186	C₂²×C₄×C₃₁	—	4	2	no	—
187	C₂²×C₄×C₃₁	—	4	2	no	—
188	C₂²×C₄×C₃₁	—	4	2	no	—
189	C₂²×C₄×C₃₁	—	4	2	no	—
190	C₂²×C₄×C₃₁	—	4	4	no	—
191	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₃₁	#41	1	4	yes	—
195	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
207	C₄⋊C₄×C₃₁	—	2	8	no	—
208	C₄⋊C₄×C₃₁	—	2	4	no	—
209	C₄⋊C₄×C₃₁	—	2	2	no	—
210	C₄⋊C₄×C₃₁	—	2	4	no	—
211	C₄⋊C₄×C₃₁	—	2	4	no	—
212	C₄⋊C₄×C₃₁	—	2	2	no	—
213	C₄⋊C₄×C₃₁	—	2	4	no	—
214	C₄⋊C₄×C₃₁	—	2	8	no	—
215	C₄⋊C₄×C₃₁	—	4	2	no	—
216	C₄⋊C₄×C₃₁	—	4	2	no	—
217	C₄⋊C₄×C₃₁	—	4	4	no	—
218	C₄⋊C₄×C₃₁	—	4	4	no	—
219	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
220	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
221	C₂²⋊C₄×C₃₁	—	2	4	no	—
222	C₂²⋊C₄×C₃₁	—	2	8	no	—
223	C₂²⋊C₄×C₃₁	—	2	4	no	—
224	C₂²⋊C₄×C₃₁	—	2	4	no	—
225	C₂²⋊C₄×C₃₁	—	2	8	no	—
226	C₂²⋊C₄×C₃₁	—	2	4	no	—
227	C₂²⋊C₄×C₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₃₁	—	2	4	no	—
229	C₂²⋊C₄×C₃₁	—	2	4	no	—
230	C₂²⋊C₄×C₃₁	—	2	4	no	—
231	C₂²⋊C₄×C₃₁	—	2	4	no	—
232	C₂²⋊C₄×C₃₁	—	2	8	no	—
233	C₂²⋊C₄×C₃₁	—	4	4	no	—
234	C₂²⋊C₄×C₃₁	—	4	4	no	—
235	C₂²⋊C₄×C₃₁	—	4	4	no	—
236	C₂²⋊C₄×C₃₁	—	4	4	no	—
237	C₄²×C₃₁	—	2	8	no	—
238	C₄²×C₃₁	—	2	4	no	—
239	C₄²×C₃₁	—	2	4	no	—
240	C₄²×C₃₁	—	2	4	no	—
241	C₄²×C₃₁	—	4	4	no	—
242	#35094	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₃₁	—	2	2	no	—
244	C₂³×C₃₁	—	2	2	no	—
245	C₂³×C₃₁	—	2	8	no	—
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	—	2	2	no	—
248	C₂³×C₃₁	—	2	4	no	—
249	C₂³×C₃₁	—	2	4	no	—
250	C₂³×C₃₁	—	2	2	no	—
251	C₂³×C₃₁	—	2	2	no	—
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	4	no	—
254	C₂³×C₃₁	—	2	4	no	—
255	C₂³×C₃₁	—	4	8	no	—
256	C₂³×C₃₁	—	4	8	no	—
257	C₂³×C₃₁	—	4	4	no	—
258	C₂³×C₃₁	—	4	4	no	—
259	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
260	C₂³×C₃₁	C₂×#41	1	4	yes	—
261	C₂³×C₃₁	C₂×#41	1	2	yes	—
262	C₂³×C₃₁	C₂×#41	1	2	yes	—
263	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
264	Q₈×C₃₁	—	8	2	no	—
265	D₄×C₃₁	—	4	8	no	—
266	D₄×C₃₁	—	8	2	no	—
267	D₄×C₃₁	—	8	8	no	—
268	C₂×C₄×C₃₁	—	2	32	no	—
269	C₂×C₄×C₃₁	—	2	8	no	—
270	C₂×C₄×C₃₁	—	2	8	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	2	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	2	no	—
275	C₂×C₄×C₃₁	—	2	4	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	2	2	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	2	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	4	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	2	4	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	4	no	—
292	C₂×C₄×C₃₁	—	2	4	no	—
293	C₂×C₄×C₃₁	—	2	4	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	4	4	no	—
297	C₂×C₄×C₃₁	—	4	4	no	—
298	C₂×C₄×C₃₁	—	4	4	no	—
299	C₂×C₄×C₃₁	—	4	4	no	—
300	C₂×C₄×C₃₁	—	8	4	no	—
301	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
306	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
307	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
308	#2855	C₂×C₃₁	1	1	yes	characteristic, complemented
309	#2854	C₂×C₃₁	1	1	yes	characteristic, complemented
310	#2849	C₂×C₃₁	1	2	yes	complemented
311	#2626	C₂×C₃₁	1	1	yes	characteristic, complemented
312	#2623	C₂×C₃₁	1	2	yes	complemented
313	#2617	C₂×C₃₁	1	1	yes	characteristic
314	#2479	C₂×C₃₁	1	4	yes	complemented
315	#2477	C₂×C₃₁	1	4	yes	complemented
316	#2475	C₂×C₃₁	1	4	yes	complemented
317	#2471	C₂×C₃₁	1	4	yes	complemented
318	#2321	C₂×C₃₁	1	2	yes	complemented
319	#2313	C₂×C₃₁	1	1	yes	characteristic, complemented
320	C₄×#123	C₂×C₃₁	1	2	yes	complemented
321	C₂²×C₃₁	—	2	4	no	—
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	4	no	—
325	C₂²×C₃₁	—	2	4	no	—
326	C₂²×C₃₁	—	2	8	no	—
327	C₂²×C₃₁	—	4	16	no	—
328	C₂²×C₃₁	—	4	4	no	—
329	C₂²×C₃₁	—	4	2	no	—
330	C₂²×C₃₁	—	4	2	no	—
331	C₂²×C₃₁	—	4	2	no	—
332	C₂²×C₃₁	—	4	4	no	—
333	C₂²×C₃₁	—	4	2	no	—
334	C₂²×C₃₁	—	4	2	no	—
335	C₂²×C₃₁	—	4	4	no	—
336	C₂²×C₃₁	#525	1	4	yes	—
337	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
338	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₃₁	#585	1	2	yes	—
341	C₂²×C₃₁	#585	1	2	yes	—
342	C₄×C₃₁	—	2	4	no	—
343	C₄×C₃₁	—	2	4	no	—
344	C₄×C₃₁	—	2	4	no	—
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	4	2	no	—
348	C₄×C₃₁	—	4	4	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	—	4	2	no	—
351	C₄×C₃₁	—	4	2	no	—
352	C₄×C₃₁	—	4	2	no	—
353	C₄×C₃₁	—	4	4	no	—
354	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
355	#539	—	2	8	no	—
356	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
357	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
358	C₂×#123	C₂²×C₃₁	1	2	yes	—
359	C₂×#123	C₂²×C₃₁	1	2	yes	—
360	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
361	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
362	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
363	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
364	C₂×#120	C₂²×C₃₁	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
366	C₂×#117	—	2	8	no	—
367	C₂×#117	C₂²×C₃₁	1	4	yes	—
368	C₂×#117	C₂²×C₃₁	1	4	yes	—
369	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
374	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
375	#400	C₂²×C₃₁	1	4	yes	complemented
376	#399	C₂²×C₃₁	1	2	yes	—
377	#399	C₂²×C₃₁	1	4	yes	complemented
378	#398	C₂²×C₃₁	1	4	yes	complemented
379	#397	C₂²×C₃₁	1	2	yes	—
380	#397	C₂²×C₃₁	1	4	yes	complemented
381	#396	C₂²×C₃₁	1	4	yes	—
382	#394	C₂²×C₃₁	1	4	yes	—
383	#393	C₂²×C₃₁	1	2	yes	—
384	#392	C₂²×C₃₁	1	2	yes	—
385	#391	C₂²×C₃₁	1	2	yes	complemented
386	#390	C₂²×C₃₁	1	4	yes	—
387	#390	C₂²×C₃₁	1	2	yes	complemented
388	#389	C₂²×C₃₁	1	2	yes	complemented
389	#389	C₂²×C₃₁	1	2	yes	complemented
390	#388	C₂²×C₃₁	1	4	yes	—
391	#388	C₂²×C₃₁	1	4	yes	—
392	#388	C₂²×C₃₁	1	4	yes	complemented
393	#388	C₂²×C₃₁	1	4	yes	complemented
394	#387	C₂²×C₃₁	1	4	yes	complemented
395	#387	C₂²×C₃₁	1	4	yes	complemented
396	#387	C₂²×C₃₁	1	4	yes	complemented
397	#387	C₂²×C₃₁	1	4	yes	complemented
398	#386	C₂²×C₃₁	1	2	yes	—
399	#386	C₂²×C₃₁	1	4	yes	—
400	#386	C₂²×C₃₁	1	4	yes	—
401	#386	C₂²×C₃₁	1	4	yes	—
402	#386	C₂²×C₃₁	1	2	yes	—
403	#385	C₂²×C₃₁	1	2	yes	—
404	#385	C₂²×C₃₁	1	4	yes	—
405	#385	C₂²×C₃₁	1	4	yes	—
406	#385	C₂²×C₃₁	1	2	yes	—
407	#381	C₂²×C₃₁	1	2	yes	—
408	#381	C₂²×C₃₁	1	2	yes	—
409	#380	C₂²×C₃₁	1	1	yes	characteristic
410	#380	C₂²×C₃₁	1	1	yes	characteristic
411	#379	C₂²×C₃₁	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
415	C₂×C₃₁	—	2	4	no	—
416	C₂×C₃₁	—	4	4	no	—
417	C₂×C₃₁	—	8	2	no	—
418	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
419	C₂×C₃₁	#3455	1	2	yes	—
420	C₂×C₃₁	#3485	1	1	yes	characteristic
421	C₂×C₃₁	#3487	1	1	yes	characteristic
422	C₂×C₃₁	#3491	1	2	yes	—
423	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
426	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
427	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
428	C₂³×C₄	—	2	4	no	—
429	C₂³×C₄	—	2	4	no	—
430	C₂³×C₄	—	2	4	no	—
431	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
432	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
437	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
439	#126	—	2	8	no	—
440	#125	—	2	8	no	—
441	#123	—	2	8	no	—
442	#123	—	2	8	no	—
443	#123	—	2	8	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	#121	—	2	4	no	—
447	#120	—	2	8	no	—
448	C₄×D₄	—	2	8	no	—
449	#117	—	2	16	no	—
450	#117	—	2	16	no	—
451	C₂×C₄⋊C₄	—	2	4	no	—
452	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
485	C₂×C₄²	—	2	4	no	—
486	C₂×C₄²	—	2	4	no	—
487	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
492	#95	C₂³×C₃₁	1	4	yes	—
493	#95	C₂³×C₃₁	1	4	yes	—
494	#95	C₂³×C₃₁	1	4	yes	—
495	#95	C₂³×C₃₁	1	4	yes	—
496	#95	C₂³×C₃₁	1	4	yes	—
497	#95	C₂³×C₃₁	1	2	yes	—
498	#95	C₂³×C₃₁	1	2	yes	—
499	#95	C₂³×C₃₁	1	4	yes	—
500	#95	C₂³×C₃₁	1	4	yes	—
501	#95	C₂³×C₃₁	1	4	yes	—
502	#95	C₂³×C₃₁	1	4	yes	—
503	C₃₁	#35094	1	1	yes	characteristic, direct product factor, Sylow
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	4	2	no	—
507	C₂⁴	—	4	2	no	—
508	C₂⁴	#41×C₃₁	1	4	yes	—
509	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
510	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
511	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	4	4	no	—
522	C₂²×C₄	—	2	32	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	8	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
539	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
540	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
541	C₂²×C₄	#41×C₃₁	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	4	2	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	4	no	—
565	C₄⋊C₄	—	4	4	no	—
566	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
567	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	8	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₄²	—	2	8	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	4	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	8	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	4	no	—
605	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
606	C₂³	C₂×#41×C₃₁	1	4	yes	—
607	C₂³	C₂×#41×C₃₁	1	2	yes	—
608	C₂³	C₂×#41×C₃₁	1	2	yes	—
609	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
610	Q₈	—	8	2	no	—
611	D₄	—	4	8	no	—
612	D₄	—	8	2	no	—
613	D₄	—	8	8	no	—
614	C₂×C₄	—	2	32	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
651	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	4	16	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	4	no	—
667	C₂²	C₃₁×#525	1	4	yes	—
668	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
669	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
670	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
671	C₂²	C₃₁×#585	1	2	yes	—
672	C₂²	C₃₁×#585	1	2	yes	—
673	C₄	—	2	4	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	4	no	—
685	C₂	—	2	4	no	—
686	C₂	—	4	4	no	—
687	C₂	—	8	2	no	—
688	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
689	C₂	C₃₁×#3455	1	2	yes	—
690	C₂	C₃₁×#3485	1	1	yes	characteristic
691	C₂	C₃₁×#3487	1	1	yes	characteristic
692	C₂	C₃₁×#3491	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2617	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#539	C₂	semidirect
2. C₂²×C₃₁×#117	C₂	semidirect
3. C₃₁×#2855	C₂	semidirect
4. C₃₁×#2854	C₂	semidirect
5. C₃₁×#2849	C₂	semidirect
6. C₃₁×#2626	C₂	semidirect
7. C₃₁×#2623	C₂	semidirect
9. C₃₁×#2479	C₂	semidirect
10. C₃₁×#2477	C₂	semidirect
11. C₃₁×#2475	C₂	semidirect
12. C₃₁×#2471	C₂	semidirect
13. C₃₁×#2321	C₂	semidirect
14. C₃₁×#2313	C₂	semidirect
15. C₄×C₃₁×#123	C₂	semidirect
18. C₂×C₃₁×#126	C₂²	semidirect
19. C₂×C₃₁×#125	C₂²	semidirect
22. C₂×C₃₁×#123	C₂²	semidirect
24. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₃₁×#400	C₂²	semidirect
39. C₃₁×#399	C₂²	semidirect
40. C₃₁×#398	C₂²	semidirect
42. C₃₁×#397	C₂²	semidirect
47. C₃₁×#391	C₂²	semidirect
49. C₃₁×#390	C₂²	semidirect
50. C₃₁×#389	C₂²	semidirect
51. C₃₁×#389	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#388	C₂²	semidirect
56. C₃₁×#387	C₂²	semidirect
57. C₃₁×#387	C₂²	semidirect
58. C₃₁×#387	C₂²	semidirect
59. C₃₁×#387	C₂²	semidirect
74. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
242. #35094	C₃₁	direct (N × H)
306. C₂×#539	C₂×C₃₁	semidirect
307. C₂²×#117	C₂×C₃₁	semidirect
308. #2855	C₂×C₃₁	semidirect
309. #2854	C₂×C₃₁	semidirect
310. #2849	C₂×C₃₁	semidirect
311. #2626	C₂×C₃₁	semidirect
312. #2623	C₂×C₃₁	semidirect
314. #2479	C₂×C₃₁	semidirect
315. #2477	C₂×C₃₁	semidirect
316. #2475	C₂×C₃₁	semidirect
317. #2471	C₂×C₃₁	semidirect
318. #2321	C₂×C₃₁	semidirect
319. #2313	C₂×C₃₁	semidirect
320. C₄×#123	C₂×C₃₁	semidirect
356. C₂×#126	C₂²×C₃₁	semidirect
357. C₂×#125	C₂²×C₃₁	semidirect
360. C₂×#123	C₂²×C₃₁	semidirect
362. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
375. #400	C₂²×C₃₁	semidirect
377. #399	C₂²×C₃₁	semidirect
378. #398	C₂²×C₃₁	semidirect
380. #397	C₂²×C₃₁	semidirect
385. #391	C₂²×C₃₁	semidirect
387. #390	C₂²×C₃₁	semidirect
388. #389	C₂²×C₃₁	semidirect
389. #389	C₂²×C₃₁	semidirect
392. #388	C₂²×C₃₁	semidirect
393. #388	C₂²×C₃₁	semidirect
394. #387	C₂²×C₃₁	semidirect
395. #387	C₂²×C₃₁	semidirect
396. #387	C₂²×C₃₁	semidirect
397. #387	C₂²×C₃₁	semidirect
412. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
452. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
503. C₃₁	#35094	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#539	2
C₂²×C₃₁×#117	2
C₃₁×#2855	2
C₃₁×#2854	2
C₃₁×#2849	2
C₃₁×#2626	2
C₃₁×#2623	2
C₃₁×#2617	2
C₃₁×#2479	2
C₃₁×#2477	2
C₃₁×#2475	2
C₃₁×#2471	2
C₃₁×#2321	2
C₃₁×#2313	2
C₄×C₃₁×#123	2
#35094	31

Subgroups — C31×#35094 #21491853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35094 #21491853