Subgroups — C₃₁×#34227 #21490986

Order 7936.

2186 conjugacy classes of subgroups.

The subgroup lattice has 670 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
2	C₃₁×#2374	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2373	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2357	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2353	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2347	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2343	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2324	C₂	1	2	yes	maximal
9	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2320	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₃₁×#125	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×#124	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#529	C₄	1	16	yes	complemented
19	C₂×C₃₁×#126	C₂²	1	2	yes	—
20	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₃₁×#117	C₂²	1	2	yes	—
31	C₂×C₃₁×#117	C₂²	1	2	yes	—
32	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#391	C₂²	1	2	yes	—
34	C₃₁×#390	C₂²	1	2	yes	—
35	C₃₁×#390	C₂²	1	4	yes	—
36	C₃₁×#389	C₂²	1	2	yes	—
37	C₃₁×#389	C₂²	1	2	yes	—
38	C₃₁×#389	C₂²	1	4	yes	—
39	C₃₁×#388	C₂²	1	4	yes	—
40	C₃₁×#388	C₂²	1	4	yes	—
41	C₃₁×#388	C₂²	1	4	yes	—
42	C₃₁×#388	C₂²	1	4	yes	—
43	C₃₁×#388	C₂²	1	4	yes	—
44	C₃₁×#388	C₂²	1	4	yes	—
45	C₃₁×#387	C₂²	1	4	yes	—
46	C₃₁×#387	C₂²	1	4	yes	—
47	C₃₁×#387	C₂²	1	4	yes	—
48	C₃₁×#387	C₂²	1	4	yes	—
49	C₃₁×#386	C₂²	1	4	yes	—
50	C₃₁×#385	C₂²	1	4	yes	—
51	C₃₁×#383	C₂²	1	2	yes	—
52	C₃₁×#383	C₂²	1	2	yes	—
53	C₃₁×#382	C₂²	1	2	yes	—
54	C₃₁×#382	C₂²	1	2	yes	—
55	C₃₁×#381	C₂²	1	2	yes	—
56	C₃₁×#381	C₂²	1	2	yes	—
57	C₃₁×#380	C₂²	1	2	yes	—
58	C₃₁×#380	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
61	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
78	C₃₁×#376	C₂²	1	1	yes	characteristic
79	C₃₁×#376	C₂²	1	2	yes	—
80	C₃₁×#376	C₂²	1	2	yes	—
81	C₃₁×#376	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#95	C₂²	1	2	yes	—
83	C₄³×C₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
92	C₃₁×#126	C₂×C₄	1	16	yes	complemented
93	C₃₁×#125	C₂×C₄	1	8	yes	complemented
94	C₃₁×#124	C₂×C₄	1	8	yes	—
95	C₃₁×#123	C₂×C₄	1	16	yes	complemented
96	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₃₁×#121	C₂×C₄	1	8	yes	—
98	C₄×Q₈×C₃₁	—	2	8	no	—
99	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
100	C₄×D₄×C₃₁	—	2	8	no	—
101	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
102	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
103	C₃₁×#117	—	2	8	no	—
104	C₃₁×#117	C₂×C₄	1	16	yes	complemented
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
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	1	yes	characteristic
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	2	yes	—
129	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	complemented
130	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
146	C₃₁×#95	C₂³	1	1	yes	characteristic
147	C₃₁×#95	C₂³	1	2	yes	—
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₃₁×#95	C₂³	1	1	yes	characteristic
150	C₃₁×#95	C₂³	1	2	yes	—
151	C₃₁×#95	C₂³	1	1	yes	characteristic
152	C₃₁×#95	C₂³	1	1	yes	characteristic
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	2	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₃₁	—	2	4	no	—
166	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	4	2	no	—
169	C₂×D₄×C₃₁	—	4	2	no	—
170	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₃₁	—	2	4	no	—
173	C₂²×C₄×C₃₁	—	2	8	no	—
174	C₂²×C₄×C₃₁	—	4	1	no	—
175	C₂²×C₄×C₃₁	—	4	1	no	—
176	C₂²×C₄×C₃₁	—	4	2	no	—
177	C₂²×C₄×C₃₁	—	4	4	no	—
178	C₂²×C₄×C₃₁	—	4	4	no	—
179	C₂²×C₄×C₃₁	—	4	4	no	—
180	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₃₁	—	2	4	no	—
200	C₄⋊C₄×C₃₁	—	2	4	no	—
201	C₄⋊C₄×C₃₁	—	2	4	no	—
202	C₄⋊C₄×C₃₁	—	2	8	no	—
203	C₄⋊C₄×C₃₁	—	2	4	no	—
204	C₄⋊C₄×C₃₁	—	4	4	no	—
205	C₄⋊C₄×C₃₁	—	4	4	no	—
206	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
207	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
208	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
210	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
211	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
212	C₂²⋊C₄×C₃₁	—	2	4	no	—
213	C₂²⋊C₄×C₃₁	—	2	4	no	—
214	C₂²⋊C₄×C₃₁	—	2	8	no	—
215	C₂²⋊C₄×C₃₁	—	4	4	no	—
216	C₂²⋊C₄×C₃₁	—	4	4	no	—
217	C₂²⋊C₄×C₃₁	—	4	4	no	—
218	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
219	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
220	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
223	C₄²×C₃₁	—	2	4	no	—
224	C₄²×C₃₁	—	2	8	no	—
225	C₄²×C₃₁	—	4	2	no	—
226	C₄²×C₃₁	—	4	2	no	—
227	C₄²×C₃₁	—	4	4	no	—
228	C₄²×C₃₁	—	4	4	no	—
229	C₄²×C₃₁	—	4	2	no	—
230	C₄²×C₃₁	—	4	2	no	—
231	C₄²×C₃₁	—	4	2	no	—
232	C₄²×C₃₁	—	4	2	no	—
233	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
234	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
235	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
236	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
237	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
238	C₄²×C₃₁	#41	1	8	yes	—
239	#34227	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₃₁	—	2	2	no	—
241	C₂³×C₃₁	—	2	4	no	—
242	C₂³×C₃₁	—	2	2	no	—
243	C₂³×C₃₁	—	2	2	no	—
244	C₂³×C₃₁	—	2	4	no	—
245	C₂³×C₃₁	—	2	2	no	—
246	C₂³×C₃₁	—	2	1	no	—
247	C₂³×C₃₁	—	2	1	no	—
248	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
249	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
250	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
251	Q₈×C₃₁	—	2	8	no	—
252	D₄×C₃₁	—	2	8	no	—
253	D₄×C₃₁	—	4	8	no	—
254	C₂×C₄×C₃₁	—	2	4	no	—
255	C₂×C₄×C₃₁	—	2	2	no	—
256	C₂×C₄×C₃₁	—	2	2	no	—
257	C₂×C₄×C₃₁	—	2	2	no	—
258	C₂×C₄×C₃₁	—	2	1	no	—
259	C₂×C₄×C₃₁	—	2	1	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	1	no	—
262	C₂×C₄×C₃₁	—	2	1	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	4	no	—
265	C₂×C₄×C₃₁	—	2	2	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	2	8	no	—
270	C₂×C₄×C₃₁	—	2	2	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	4	no	—
273	C₂×C₄×C₃₁	—	2	4	no	—
274	C₂×C₄×C₃₁	—	2	4	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	2	4	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	4	4	no	—
283	C₂×C₄×C₃₁	—	4	8	no	—
284	C₂×C₄×C₃₁	—	4	4	no	—
285	C₂×C₄×C₃₁	—	8	8	no	—
286	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
296	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
297	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
298	C₂×#529	C₂×C₃₁	1	1	yes	characteristic
299	#2374	C₂×C₃₁	1	4	yes	complemented
300	#2373	C₂×C₃₁	1	4	yes	complemented
301	#2357	C₂×C₃₁	1	2	yes	complemented
302	#2353	C₂×C₃₁	1	2	yes	complemented
303	#2347	C₂×C₃₁	1	2	yes	complemented
304	#2343	C₂×C₃₁	1	2	yes	complemented
305	#2324	C₂×C₃₁	1	2	yes	—
306	#2323	C₂×C₃₁	1	2	yes	complemented
307	#2320	C₂×C₃₁	1	1	yes	characteristic, complemented
308	#2319	C₂×C₃₁	1	1	yes	characteristic, complemented
309	C₄×#125	C₂×C₃₁	1	2	yes	complemented
310	C₄×#124	C₂×C₃₁	1	2	yes	complemented
311	#2283	C₂×C₃₁	1	1	yes	characteristic, complemented
312	#2276	C₂×C₃₁	1	1	yes	characteristic, complemented
313	#2275	C₂×C₃₁	1	1	yes	characteristic, complemented
314	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
315	C₂²×C₃₁	—	2	2	no	—
316	C₂²×C₃₁	—	2	4	no	—
317	C₂²×C₃₁	—	2	2	no	—
318	C₂²×C₃₁	—	2	2	no	—
319	C₂²×C₃₁	—	2	4	no	—
320	C₂²×C₃₁	—	2	4	no	—
321	C₂²×C₃₁	—	4	4	no	—
322	C₂²×C₃₁	—	4	2	no	—
323	C₂²×C₃₁	—	4	2	no	—
324	C₂²×C₃₁	—	4	4	no	—
325	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
326	C₂²×C₃₁	C₂²×#41	1	2	yes	—
327	C₂²×C₃₁	#585	1	1	yes	characteristic
328	C₂²×C₃₁	#585	1	2	yes	—
329	C₂²×C₃₁	#585	1	1	yes	characteristic
330	C₄×C₃₁	—	2	2	no	—
331	C₄×C₃₁	—	2	4	no	—
332	C₄×C₃₁	—	2	2	no	—
333	C₄×C₃₁	—	2	2	no	—
334	C₄×C₃₁	—	2	2	no	—
335	C₄×C₃₁	—	2	2	no	—
336	C₄×C₃₁	—	2	4	no	—
337	C₄×C₃₁	—	2	4	no	—
338	C₄×C₃₁	—	2	4	no	—
339	C₄×C₃₁	—	2	4	no	—
340	C₄×C₃₁	—	4	2	no	—
341	C₄×C₃₁	—	4	4	no	—
342	C₄×C₃₁	—	4	2	no	—
343	C₄×C₃₁	—	4	4	no	—
344	C₄×C₃₁	C₄×#41	1	4	yes	—
345	#529	C₄×C₃₁	1	16	yes	complemented
346	C₂×#126	C₂²×C₃₁	1	2	yes	—
347	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
348	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
349	C₂×#123	C₂²×C₃₁	1	2	yes	—
350	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
351	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
352	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
353	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
355	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
357	C₂×#117	C₂²×C₃₁	1	2	yes	—
358	C₂×#117	C₂²×C₃₁	1	2	yes	—
359	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
360	#391	C₂²×C₃₁	1	2	yes	—
361	#390	C₂²×C₃₁	1	2	yes	—
362	#390	C₂²×C₃₁	1	4	yes	—
363	#389	C₂²×C₃₁	1	2	yes	—
364	#389	C₂²×C₃₁	1	2	yes	—
365	#389	C₂²×C₃₁	1	4	yes	—
366	#388	C₂²×C₃₁	1	4	yes	—
367	#388	C₂²×C₃₁	1	4	yes	—
368	#388	C₂²×C₃₁	1	4	yes	—
369	#388	C₂²×C₃₁	1	4	yes	—
370	#388	C₂²×C₃₁	1	4	yes	—
371	#388	C₂²×C₃₁	1	4	yes	—
372	#387	C₂²×C₃₁	1	4	yes	—
373	#387	C₂²×C₃₁	1	4	yes	—
374	#387	C₂²×C₃₁	1	4	yes	—
375	#387	C₂²×C₃₁	1	4	yes	—
376	#386	C₂²×C₃₁	1	4	yes	—
377	#385	C₂²×C₃₁	1	4	yes	—
378	#383	C₂²×C₃₁	1	2	yes	—
379	#383	C₂²×C₃₁	1	2	yes	—
380	#382	C₂²×C₃₁	1	2	yes	—
381	#382	C₂²×C₃₁	1	2	yes	—
382	#381	C₂²×C₃₁	1	2	yes	—
383	#381	C₂²×C₃₁	1	2	yes	—
384	#380	C₂²×C₃₁	1	2	yes	—
385	#380	C₂²×C₃₁	1	2	yes	—
386	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
387	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
388	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
389	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
390	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
391	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
392	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
393	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
395	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
397	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
398	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
399	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
401	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
405	#376	C₂²×C₃₁	1	1	yes	characteristic
406	#376	C₂²×C₃₁	1	2	yes	—
407	#376	C₂²×C₃₁	1	2	yes	—
408	#376	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×#95	C₂²×C₃₁	1	2	yes	—
410	C₄³	C₂²×C₃₁	1	2	yes	—
411	C₂×C₃₁	—	4	2	no	—
412	C₂×C₃₁	—	4	4	no	—
413	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
414	C₂×C₃₁	#3428	1	1	yes	characteristic
415	C₂×C₃₁	#3428	1	1	yes	characteristic
416	C₂×C₃₁	#3510	1	2	yes	—
417	C₂×C₃₁	#3512	1	2	yes	—
418	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
421	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
423	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
424	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
426	#126	C₂×C₄×C₃₁	1	16	yes	complemented
427	#125	C₂×C₄×C₃₁	1	8	yes	complemented
428	#124	C₂×C₄×C₃₁	1	8	yes	—
429	#123	C₂×C₄×C₃₁	1	16	yes	complemented
430	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
431	#121	C₂×C₄×C₃₁	1	8	yes	—
432	C₄×Q₈	—	2	8	no	—
433	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
434	C₄×D₄	—	2	8	no	—
435	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
436	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
437	#117	—	2	8	no	—
438	#117	C₂×C₄×C₃₁	1	16	yes	complemented
439	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	complemented
464	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
465	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
466	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
467	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
468	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
469	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
470	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
471	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
472	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
473	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
474	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
476	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
480	#95	C₂³×C₃₁	1	1	yes	characteristic
481	#95	C₂³×C₃₁	1	2	yes	—
482	#95	C₂³×C₃₁	1	4	yes	—
483	#95	C₂³×C₃₁	1	1	yes	characteristic
484	#95	C₂³×C₃₁	1	2	yes	—
485	#95	C₂³×C₃₁	1	1	yes	characteristic
486	#95	C₂³×C₃₁	1	1	yes	characteristic
487	#95	C₂³×C₃₁	1	4	yes	—
488	#95	C₂³×C₃₁	1	2	yes	—
489	#95	C₂³×C₃₁	1	2	yes	—
490	#95	C₂³×C₃₁	1	4	yes	—
491	#95	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	C₃₁	#34227	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	4	2	no	—
505	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
506	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
516	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
517	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
519	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
542	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
543	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
544	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
545	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
546	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
555	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
556	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
557	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	8	no	—
560	C₄²	—	4	2	no	—
561	C₄²	—	4	2	no	—
562	C₄²	—	4	4	no	—
563	C₄²	—	4	4	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₄²	—	4	2	no	—
568	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
569	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
570	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
571	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
572	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
573	C₄²	#41×C₃₁	1	8	yes	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
583	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
584	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
585	Q₈	—	2	8	no	—
586	D₄	—	2	8	no	—
587	D₄	—	4	8	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	8	8	no	—
620	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
621	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
622	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
625	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
626	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
629	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
630	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
631	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
643	C₂²	C₂²×#41×C₃₁	1	2	yes	—
644	C₂²	C₃₁×#585	1	1	yes	characteristic
645	C₂²	C₃₁×#585	1	2	yes	—
646	C₂²	C₃₁×#585	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	4	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	C₄×#41×C₃₁	1	4	yes	—
662	C₂	—	4	2	no	—
663	C₂	—	4	4	no	—
664	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
665	C₂	C₃₁×#3428	1	1	yes	characteristic
666	C₂	C₃₁×#3428	1	1	yes	characteristic
667	C₂	C₃₁×#3510	1	2	yes	—
668	C₂	C₃₁×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2374	C₂	semidirect
3. C₃₁×#2373	C₂	semidirect
4. C₃₁×#2357	C₂	semidirect
5. C₃₁×#2353	C₂	semidirect
6. C₃₁×#2347	C₂	semidirect
7. C₃₁×#2343	C₂	semidirect
9. C₃₁×#2323	C₂	semidirect
10. C₃₁×#2320	C₂	semidirect
11. C₃₁×#2319	C₂	semidirect
12. C₄×C₃₁×#125	C₂	semidirect
13. C₄×C₃₁×#124	C₂	semidirect
14. C₃₁×#2283	C₂	semidirect
15. C₃₁×#2276	C₂	semidirect
16. C₃₁×#2275	C₂	semidirect
17. C₄×C₃₁×#117	C₂	semidirect
18. C₃₁×#529	C₄	semidirect
92. C₃₁×#126	C₂×C₄	semidirect
93. C₃₁×#125	C₂×C₄	semidirect
95. C₃₁×#123	C₂×C₄	semidirect
96. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×Q₈×C₃₁	C₂×C₄	semidirect
102. C₄×D₄×C₃₁	C₂×C₄	semidirect
104. C₃₁×#117	C₂×C₄	semidirect
129. C₂×C₄²×C₃₁	C₂×C₄	semidirect
239. #34227	C₃₁	direct (N × H)
299. #2374	C₂×C₃₁	semidirect
300. #2373	C₂×C₃₁	semidirect
301. #2357	C₂×C₃₁	semidirect
302. #2353	C₂×C₃₁	semidirect
303. #2347	C₂×C₃₁	semidirect
304. #2343	C₂×C₃₁	semidirect
306. #2323	C₂×C₃₁	semidirect
307. #2320	C₂×C₃₁	semidirect
308. #2319	C₂×C₃₁	semidirect
309. C₄×#125	C₂×C₃₁	semidirect
310. C₄×#124	C₂×C₃₁	semidirect
311. #2283	C₂×C₃₁	semidirect
312. #2276	C₂×C₃₁	semidirect
313. #2275	C₂×C₃₁	semidirect
314. C₄×#117	C₂×C₃₁	semidirect
345. #529	C₄×C₃₁	semidirect
426. #126	C₂×C₄×C₃₁	semidirect
427. #125	C₂×C₄×C₃₁	semidirect
429. #123	C₂×C₄×C₃₁	semidirect
430. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
433. C₄×Q₈	C₂×C₄×C₃₁	semidirect
436. C₄×D₄	C₂×C₄×C₃₁	semidirect
438. #117	C₂×C₄×C₃₁	semidirect
463. C₂×C₄²	C₂×C₄×C₃₁	semidirect
497. C₃₁	#34227	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
C₃₁×#2374	2
C₃₁×#2373	2
C₃₁×#2357	2
C₃₁×#2353	2
C₃₁×#2347	2
C₃₁×#2343	2
C₃₁×#2324	2
C₃₁×#2323	2
C₃₁×#2320	2
C₃₁×#2319	2
C₄×C₃₁×#125	2
C₄×C₃₁×#124	2
C₃₁×#2283	2
C₃₁×#2276	2
C₃₁×#2275	2
C₄×C₃₁×#117	2
#34227	31

Subgroups — C31×#34227 #21490986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34227 #21490986