Subgroups — C₃₁×#35144 #21491903

Order 7936.

2402 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2852	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2634	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2632	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2599	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2599	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2598	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2598	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2564	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2543	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2498	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2430	C₂	1	2	yes	maximal, complemented
16	C₃₁×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×C₃₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#529	—	2	8	no	—
20	C₂×C₃₁×#126	C₂²	1	2	yes	—
21	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#123	C₂²	1	2	yes	—
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#121	C₂²	1	4	yes	—
26	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
27	C₄×#41×C₃₁	—	2	8	no	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	2	yes	—
38	C₂×C₃₁×#117	C₂²	1	2	yes	—
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
41	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#400	C₂²	1	2	yes	—
43	C₃₁×#400	C₂²	1	2	yes	—
44	C₃₁×#399	C₂²	1	2	yes	—
45	C₃₁×#399	C₂²	1	2	yes	—
46	C₃₁×#398	C₂²	1	2	yes	—
47	C₃₁×#398	C₂²	1	2	yes	—
48	C₃₁×#397	C₂²	1	2	yes	—
49	C₃₁×#397	C₂²	1	2	yes	—
50	C₃₁×#395	C₂²	1	2	yes	—
51	C₃₁×#395	C₂²	1	2	yes	—
52	C₃₁×#394	C₂²	1	2	yes	—
53	C₃₁×#394	C₂²	1	2	yes	—
54	C₃₁×#393	C₂²	1	2	yes	—
55	C₃₁×#393	C₂²	1	2	yes	—
56	C₃₁×#392	C₂²	1	2	yes	—
57	C₃₁×#392	C₂²	1	2	yes	—
58	C₃₁×#388	C₂²	1	4	yes	—
59	C₃₁×#388	C₂²	1	4	yes	—
60	C₃₁×#388	C₂²	1	4	yes	—
61	C₃₁×#388	C₂²	1	4	yes	—
62	C₃₁×#387	C₂²	1	4	yes	—
63	C₃₁×#387	C₂²	1	4	yes	—
64	C₃₁×#387	C₂²	1	4	yes	—
65	C₃₁×#387	C₂²	1	4	yes	—
66	C₃₁×#386	C₂²	1	4	yes	—
67	C₃₁×#386	C₂²	1	4	yes	—
68	C₃₁×#386	C₂²	1	4	yes	—
69	C₃₁×#386	C₂²	1	4	yes	—
70	C₃₁×#386	C₂²	1	4	yes	—
71	C₃₁×#386	C₂²	1	4	yes	—
72	C₃₁×#385	C₂²	1	4	yes	—
73	C₃₁×#385	C₂²	1	4	yes	—
74	C₃₁×#385	C₂²	1	4	yes	—
75	C₃₁×#385	C₂²	1	4	yes	—
76	C₃₁×#383	C₂²	1	2	yes	—
77	C₃₁×#383	C₂²	1	2	yes	—
78	C₃₁×#383	C₂²	1	2	yes	—
79	C₃₁×#383	C₂²	1	1	yes	characteristic
80	C₃₁×#383	C₂²	1	1	yes	characteristic
81	C₃₁×#380	C₂²	1	4	yes	—
82	C₂×C₃₁×#95	C₂²	1	2	yes	—
83	C₂×C₃₁×#95	C₂²	1	2	yes	—
84	C₂×C₃₁×#95	C₂²	1	2	yes	—
85	C₂×#41×C₃₁	—	2	8	no	—
86	C₂×#41×C₃₁	—	2	4	no	—
87	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
98	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
99	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
102	C₃₁×#126	—	2	8	no	—
103	C₃₁×#125	—	2	4	no	—
104	C₃₁×#124	—	2	4	no	—
105	C₃₁×#123	—	2	8	no	—
106	C₃₁×C₂²⋊Q₈	—	2	4	no	—
107	C₃₁×#121	—	2	16	no	—
108	C₃₁×#121	—	2	4	no	—
109	C₄×Q₈×C₃₁	—	2	4	no	—
110	C₄×Q₈×C₃₁	—	2	4	no	—
111	C₄×Q₈×C₃₁	—	2	4	no	—
112	C₄×D₄×C₃₁	—	2	8	no	—
113	C₄×D₄×C₃₁	—	2	8	no	—
114	C₄×D₄×C₃₁	—	2	8	no	—
115	C₄×D₄×C₃₁	—	2	4	no	—
116	C₄×D₄×C₃₁	—	2	4	no	—
117	C₄×D₄×C₃₁	—	2	4	no	—
118	C₃₁×#117	—	2	4	no	—
119	C₃₁×#117	—	2	8	no	—
120	C₃₁×#117	—	2	8	no	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₄²×C₃₁	—	2	8	no	—
149	C₂×C₄²×C₃₁	D₄	1	8	yes	complemented
150	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
153	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
154	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
158	C₃₁×#95	C₂³	1	2	yes	—
159	C₃₁×#95	C₂³	1	2	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	2	yes	—
165	C₃₁×#95	C₂³	1	2	yes	—
166	C₃₁×#95	C₂³	1	4	yes	—
167	C₃₁×#95	C₂³	1	4	yes	—
168	C₃₁×#95	C₂³	1	2	yes	—
169	C₃₁×#95	C₂³	1	4	yes	—
170	C₃₁×#95	C₂³	1	4	yes	—
171	C₃₁×#95	C₂³	1	4	yes	—
172	C₃₁×#95	C₂³	1	2	yes	—
173	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
174	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
175	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
176	#41×C₃₁	—	2	32	no	—
177	C₂×Q₈×C₃₁	—	2	2	no	—
178	C₂×Q₈×C₃₁	—	2	2	no	—
179	C₂×Q₈×C₃₁	—	2	4	no	—
180	C₂×Q₈×C₃₁	—	4	2	no	—
181	C₂×D₄×C₃₁	—	2	4	no	—
182	C₂×D₄×C₃₁	—	2	4	no	—
183	C₂×D₄×C₃₁	—	2	4	no	—
184	C₂×D₄×C₃₁	—	2	4	no	—
185	C₂×D₄×C₃₁	—	2	8	no	—
186	C₂×D₄×C₃₁	—	2	8	no	—
187	C₂×D₄×C₃₁	—	2	2	no	—
188	C₂×D₄×C₃₁	—	2	2	no	—
189	C₂×D₄×C₃₁	—	4	2	no	—
190	C₂×D₄×C₃₁	—	4	4	no	—
191	C₂×D₄×C₃₁	—	4	4	no	—
192	C₂×D₄×C₃₁	#41	1	8	yes	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	4	no	—
197	C₂²×C₄×C₃₁	—	2	8	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	4	2	no	—
202	C₂²×C₄×C₃₁	—	4	2	no	—
203	C₂²×C₄×C₃₁	—	4	2	no	—
204	C₂²×C₄×C₃₁	—	4	4	no	—
205	C₂²×C₄×C₃₁	—	4	4	no	—
206	C₂²×C₄×C₃₁	—	4	2	no	—
207	C₂²×C₄×C₃₁	—	4	4	no	—
208	C₂²×C₄×C₃₁	—	4	4	no	—
209	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	4	no	—
228	C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	2	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	4	no	—
236	C₄⋊C₄×C₃₁	—	2	8	no	—
237	C₄⋊C₄×C₃₁	—	4	4	no	—
238	C₄⋊C₄×C₃₁	—	4	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	8	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	2	8	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	—	4	4	no	—
251	C₂²⋊C₄×C₃₁	—	4	4	no	—
252	C₂²⋊C₄×C₃₁	—	4	4	no	—
253	C₄²×C₃₁	—	2	4	no	—
254	C₄²×C₃₁	—	2	4	no	—
255	C₄²×C₃₁	—	2	4	no	—
256	C₄²×C₃₁	—	2	4	no	—
257	C₄²×C₃₁	C₂×D₄	1	4	yes	—
258	C₄²×C₃₁	C₂×D₄	1	4	yes	—
259	C₄²×C₃₁	C₂×D₄	1	4	yes	—
260	C₄²×C₃₁	C₂×D₄	1	4	yes	—
261	#35144	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂³×C₃₁	—	2	2	no	—
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	2	2	no	—
265	C₂³×C₃₁	—	2	2	no	—
266	C₂³×C₃₁	—	2	4	no	—
267	C₂³×C₃₁	—	2	4	no	—
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	4	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	4	no	—
272	C₂³×C₃₁	—	2	2	no	—
273	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
274	C₂³×C₃₁	C₂×#41	1	4	yes	—
275	C₂³×C₃₁	C₂×#41	1	4	yes	—
276	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
277	Q₈×C₃₁	—	2	8	no	—
278	Q₈×C₃₁	—	4	4	no	—
279	D₄×C₃₁	—	2	8	no	—
280	D₄×C₃₁	—	2	16	no	—
281	D₄×C₃₁	—	4	4	no	—
282	D₄×C₃₁	—	4	8	no	—
283	D₄×C₃₁	—	8	8	no	—
284	C₂×C₄×C₃₁	—	2	16	no	—
285	C₂×C₄×C₃₁	—	2	8	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	2	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	2	no	—
294	C₂×C₄×C₃₁	—	2	2	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	2	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	4	no	—
300	C₂×C₄×C₃₁	—	2	4	no	—
301	C₂×C₄×C₃₁	—	2	4	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	4	no	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	4	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	2	4	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	4	4	no	—
312	C₂×C₄×C₃₁	—	4	4	no	—
313	C₂×C₄×C₃₁	—	4	8	no	—
314	C₂×C₄×C₃₁	—	4	8	no	—
315	C₂×C₄×C₃₁	—	4	8	no	—
316	C₂×C₄×C₃₁	—	8	8	no	—
317	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
324	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
325	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#2852	C₂×C₃₁	1	4	yes	complemented
327	#2634	C₂×C₃₁	1	1	yes	characteristic, complemented
328	#2633	C₂×C₃₁	1	1	yes	characteristic, complemented
329	#2632	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#2631	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#2599	C₂×C₃₁	1	2	yes	complemented
332	#2599	C₂×C₃₁	1	2	yes	complemented
333	#2598	C₂×C₃₁	1	2	yes	complemented
334	#2598	C₂×C₃₁	1	2	yes	complemented
335	#2564	C₂×C₃₁	1	2	yes	complemented
336	#2543	C₂×C₃₁	1	2	yes	complemented
337	#2498	C₂×C₃₁	1	2	yes	complemented
338	#2430	C₂×C₃₁	1	2	yes	complemented
339	#2325	C₂×C₃₁	1	4	yes	complemented
340	C₂×#383	C₂×C₃₁	1	1	yes	characteristic, complemented
341	C₂²×C₃₁	—	2	2	no	—
342	C₂²×C₃₁	—	2	2	no	—
343	C₂²×C₃₁	—	2	8	no	—
344	C₂²×C₃₁	—	2	4	no	—
345	C₂²×C₃₁	—	2	8	no	—
346	C₂²×C₃₁	—	4	2	no	—
347	C₂²×C₃₁	—	4	2	no	—
348	C₂²×C₃₁	—	4	4	no	—
349	C₂²×C₃₁	—	4	2	no	—
350	C₂²×C₃₁	—	4	2	no	—
351	C₂²×C₃₁	—	4	2	no	—
352	C₂²×C₃₁	—	4	4	no	—
353	C₂²×C₃₁	—	4	4	no	—
354	C₂²×C₃₁	#525	1	4	yes	—
355	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₃₁	C₂²×#41	1	2	yes	—
357	C₂²×C₃₁	#585	1	2	yes	—
358	C₂²×C₃₁	#585	1	2	yes	—
359	C₄×C₃₁	—	2	2	no	—
360	C₄×C₃₁	—	2	2	no	—
361	C₄×C₃₁	—	2	4	no	—
362	C₄×C₃₁	—	2	2	no	—
363	C₄×C₃₁	—	2	2	no	—
364	C₄×C₃₁	—	2	2	no	—
365	C₄×C₃₁	—	2	2	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	—	4	2	no	—
371	C₄×C₃₁	—	4	4	no	—
372	C₄×C₃₁	—	4	4	no	—
373	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
374	#529	—	2	8	no	—
375	C₂×#126	C₂²×C₃₁	1	2	yes	—
376	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
377	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
378	C₂×#123	C₂²×C₃₁	1	2	yes	—
379	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
380	C₂×#121	C₂²×C₃₁	1	4	yes	—
381	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
382	C₄×#41	—	2	8	no	—
383	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
388	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
392	C₂×#117	C₂²×C₃₁	1	2	yes	—
393	C₂×#117	C₂²×C₃₁	1	2	yes	—
394	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
396	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
397	#400	C₂²×C₃₁	1	2	yes	—
398	#400	C₂²×C₃₁	1	2	yes	—
399	#399	C₂²×C₃₁	1	2	yes	—
400	#399	C₂²×C₃₁	1	2	yes	—
401	#398	C₂²×C₃₁	1	2	yes	—
402	#398	C₂²×C₃₁	1	2	yes	—
403	#397	C₂²×C₃₁	1	2	yes	—
404	#397	C₂²×C₃₁	1	2	yes	—
405	#395	C₂²×C₃₁	1	2	yes	—
406	#395	C₂²×C₃₁	1	2	yes	—
407	#394	C₂²×C₃₁	1	2	yes	—
408	#394	C₂²×C₃₁	1	2	yes	—
409	#393	C₂²×C₃₁	1	2	yes	—
410	#393	C₂²×C₃₁	1	2	yes	—
411	#392	C₂²×C₃₁	1	2	yes	—
412	#392	C₂²×C₃₁	1	2	yes	—
413	#388	C₂²×C₃₁	1	4	yes	—
414	#388	C₂²×C₃₁	1	4	yes	—
415	#388	C₂²×C₃₁	1	4	yes	—
416	#388	C₂²×C₃₁	1	4	yes	—
417	#387	C₂²×C₃₁	1	4	yes	—
418	#387	C₂²×C₃₁	1	4	yes	—
419	#387	C₂²×C₃₁	1	4	yes	—
420	#387	C₂²×C₃₁	1	4	yes	—
421	#386	C₂²×C₃₁	1	4	yes	—
422	#386	C₂²×C₃₁	1	4	yes	—
423	#386	C₂²×C₃₁	1	4	yes	—
424	#386	C₂²×C₃₁	1	4	yes	—
425	#386	C₂²×C₃₁	1	4	yes	—
426	#386	C₂²×C₃₁	1	4	yes	—
427	#385	C₂²×C₃₁	1	4	yes	—
428	#385	C₂²×C₃₁	1	4	yes	—
429	#385	C₂²×C₃₁	1	4	yes	—
430	#385	C₂²×C₃₁	1	4	yes	—
431	#383	C₂²×C₃₁	1	2	yes	—
432	#383	C₂²×C₃₁	1	2	yes	—
433	#383	C₂²×C₃₁	1	2	yes	—
434	#383	C₂²×C₃₁	1	1	yes	characteristic
435	#383	C₂²×C₃₁	1	1	yes	characteristic
436	#380	C₂²×C₃₁	1	4	yes	—
437	C₂×#95	C₂²×C₃₁	1	2	yes	—
438	C₂×#95	C₂²×C₃₁	1	2	yes	—
439	C₂×#95	C₂²×C₃₁	1	2	yes	—
440	C₂×C₃₁	—	2	4	no	—
441	C₂×C₃₁	—	4	4	no	—
442	C₂×C₃₁	—	8	2	no	—
443	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
444	C₂×C₃₁	#3449	1	1	yes	characteristic
445	C₂×C₃₁	#3449	1	1	yes	characteristic
446	C₂×C₃₁	#3521	1	4	yes	—
447	C₂×#41	—	2	8	no	—
448	C₂×#41	—	2	4	no	—
449	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
450	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
453	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
454	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
456	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
457	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
459	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
460	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
461	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
462	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
464	#126	—	2	8	no	—
465	#125	—	2	4	no	—
466	#124	—	2	4	no	—
467	#123	—	2	8	no	—
468	C₂²⋊Q₈	—	2	4	no	—
469	#121	—	2	16	no	—
470	#121	—	2	4	no	—
471	C₄×Q₈	—	2	4	no	—
472	C₄×Q₈	—	2	4	no	—
473	C₄×Q₈	—	2	4	no	—
474	C₄×D₄	—	2	8	no	—
475	C₄×D₄	—	2	8	no	—
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	#117	—	2	4	no	—
481	#117	—	2	8	no	—
482	#117	—	2	8	no	—
483	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
510	C₂×C₄²	—	2	8	no	—
511	C₂×C₄²	D₄×C₃₁	1	8	yes	complemented
512	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
513	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
514	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
515	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
516	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
520	#95	C₂³×C₃₁	1	2	yes	—
521	#95	C₂³×C₃₁	1	4	yes	—
522	#95	C₂³×C₃₁	1	4	yes	—
523	#95	C₂³×C₃₁	1	4	yes	—
524	#95	C₂³×C₃₁	1	2	yes	—
525	#95	C₂³×C₃₁	1	2	yes	—
526	#95	C₂³×C₃₁	1	2	yes	—
527	#95	C₂³×C₃₁	1	2	yes	—
528	#95	C₂³×C₃₁	1	2	yes	—
529	#95	C₂³×C₃₁	1	4	yes	—
530	#95	C₂³×C₃₁	1	4	yes	—
531	#95	C₂³×C₃₁	1	4	yes	—
532	#95	C₂³×C₃₁	1	4	yes	—
533	#95	C₂³×C₃₁	1	4	yes	—
534	#95	C₂³×C₃₁	1	4	yes	—
535	C₃₁	#35144	1	1	yes	characteristic, direct product factor, Sylow
536	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
537	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
538	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
539	#41	—	2	32	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	#41×C₃₁	1	8	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
574	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	4	no	—
619	C₄²	—	2	4	no	—
620	C₄²	C₂×D₄×C₃₁	1	4	yes	—
621	C₄²	C₂×D₄×C₃₁	1	4	yes	—
622	C₄²	C₂×D₄×C₃₁	1	4	yes	—
623	C₄²	C₂×D₄×C₃₁	1	4	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	2	no	—
635	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
636	C₂³	C₂×#41×C₃₁	1	4	yes	—
637	C₂³	C₂×#41×C₃₁	1	4	yes	—
638	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
639	Q₈	—	2	8	no	—
640	Q₈	—	4	4	no	—
641	D₄	—	2	8	no	—
642	D₄	—	2	16	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	8	8	no	—
646	C₂×C₄	—	2	16	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	8	8	no	—
679	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
685	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	8	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	8	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	4	no	—
699	C₂²	C₃₁×#525	1	4	yes	—
700	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
701	C₂²	C₂²×#41×C₃₁	1	2	yes	—
702	C₂²	C₃₁×#585	1	2	yes	—
703	C₂²	C₃₁×#585	1	2	yes	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	4	no	—
718	C₂	—	2	4	no	—
719	C₂	—	4	4	no	—
720	C₂	—	8	2	no	—
721	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
722	C₂	C₃₁×#3449	1	1	yes	characteristic
723	C₂	C₃₁×#3449	1	1	yes	characteristic
724	C₂	C₃₁×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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×#529	C₂	semidirect
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#2852	C₂	semidirect
4. C₃₁×#2634	C₂	semidirect
5. C₃₁×#2633	C₂	semidirect
6. C₃₁×#2632	C₂	semidirect
7. C₃₁×#2631	C₂	semidirect
8. C₃₁×#2599	C₂	semidirect
9. C₃₁×#2599	C₂	semidirect
10. C₃₁×#2598	C₂	semidirect
11. C₃₁×#2598	C₂	semidirect
12. C₃₁×#2564	C₂	semidirect
13. C₃₁×#2543	C₂	semidirect
14. C₃₁×#2498	C₂	semidirect
15. C₃₁×#2430	C₂	semidirect
16. C₃₁×#2325	C₂	semidirect
17. C₂×C₃₁×#383	C₂	semidirect
149. C₂×C₄²×C₃₁	D₄	semidirect
261. #35144	C₃₁	direct (N × H)
324. C₂×#529	C₂×C₃₁	semidirect
325. C₂×C₄×#41	C₂×C₃₁	semidirect
326. #2852	C₂×C₃₁	semidirect
327. #2634	C₂×C₃₁	semidirect
328. #2633	C₂×C₃₁	semidirect
329. #2632	C₂×C₃₁	semidirect
330. #2631	C₂×C₃₁	semidirect
331. #2599	C₂×C₃₁	semidirect
332. #2599	C₂×C₃₁	semidirect
333. #2598	C₂×C₃₁	semidirect
334. #2598	C₂×C₃₁	semidirect
335. #2564	C₂×C₃₁	semidirect
336. #2543	C₂×C₃₁	semidirect
337. #2498	C₂×C₃₁	semidirect
338. #2430	C₂×C₃₁	semidirect
339. #2325	C₂×C₃₁	semidirect
340. C₂×#383	C₂×C₃₁	semidirect
511. C₂×C₄²	D₄×C₃₁	semidirect
535. C₃₁	#35144	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×#529	2
C₂×C₄×#41×C₃₁	2
C₃₁×#2852	2
C₃₁×#2634	2
C₃₁×#2633	2
C₃₁×#2632	2
C₃₁×#2631	2
C₃₁×#2599	2
C₃₁×#2598	2
C₃₁×#2564	2
C₃₁×#2543	2
C₃₁×#2498	2
C₃₁×#2430	2
C₃₁×#2325	2
C₂×C₃₁×#383	2
#35144	31

Subgroups — C31×#35144 #21491903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35144 #21491903