Subgroups — C₃₁×#34238 #21490997

Order 7936.

2742 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2374	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2359	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2345	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2342	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal
8	C₃₁×#2335	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#123	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2273	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#123	C₄	1	16	yes	complemented
19	C₂×C₃₁×#123	C₂²	1	2	yes	—
20	C₂×C₃₁×#123	C₂²	1	2	yes	—
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
24	C₂×C₃₁×#117	C₂²	1	2	yes	—
25	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#390	C₂²	1	4	yes	—
35	C₃₁×#389	C₂²	1	4	yes	complemented
36	C₃₁×#388	C₂²	1	4	yes	complemented
37	C₃₁×#388	C₂²	1	4	yes	complemented
38	C₃₁×#388	C₂²	1	4	yes	complemented
39	C₃₁×#388	C₂²	1	4	yes	complemented
40	C₃₁×#388	C₂²	1	4	yes	complemented
41	C₃₁×#388	C₂²	1	4	yes	complemented
42	C₃₁×#387	C₂²	1	4	yes	complemented
43	C₃₁×#387	C₂²	1	4	yes	complemented
44	C₃₁×#387	C₂²	1	4	yes	complemented
45	C₃₁×#387	C₂²	1	4	yes	complemented
46	C₃₁×#386	C₂²	1	4	yes	—
47	C₃₁×#386	C₂²	1	4	yes	—
48	C₃₁×#385	C₂²	1	4	yes	complemented
49	C₃₁×#385	C₂²	1	4	yes	complemented
50	C₃₁×#381	C₂²	1	2	yes	—
51	C₃₁×#381	C₂²	1	2	yes	complemented
52	C₃₁×#380	C₂²	1	2	yes	—
53	C₃₁×#380	C₂²	1	2	yes	—
54	C₃₁×#380	C₂²	1	2	yes	—
55	C₃₁×#380	C₂²	1	2	yes	complemented
56	C₃₁×#379	C₂²	1	2	yes	—
57	C₃₁×#379	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
59	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
60	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
70	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
71	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
75	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₃₁	—	4	4	no	—
79	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₃₁	—	4	4	no	—
83	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
84	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₃₁×#123	C₂×C₄	1	16	yes	complemented
96	C₃₁×#123	C₂×C₄	1	16	yes	complemented
97	C₃₁×#123	C₂×C₄	1	16	yes	complemented
98	C₃₁×#123	C₂×C₄	1	16	yes	complemented
99	C₄×D₄×C₃₁	—	4	8	no	—
100	C₃₁×#117	—	2	8	no	—
101	C₃₁×#117	—	4	4	no	—
102	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
103	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
113	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
114	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
115	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
116	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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×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×C₄²×C₃₁	—	4	4	no	—
134	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₃₁×#95	C₂³	1	2	yes	—
143	C₃₁×#95	C₂³	1	4	yes	—
144	C₃₁×#95	C₂³	1	2	yes	—
145	C₃₁×#95	C₂³	1	2	yes	—
146	C₃₁×#95	C₂³	1	4	yes	—
147	C₃₁×#95	C₂³	1	2	yes	—
148	C₃₁×#95	C₂³	1	4	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	4	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₂⁴×C₃₁	—	2	4	no	—
155	C₂⁴×C₃₁	—	2	4	no	—
156	C₂⁴×C₃₁	—	2	4	no	—
157	C₂⁴×C₃₁	—	4	2	no	—
158	C₂⁴×C₃₁	—	4	2	no	—
159	C₂⁴×C₃₁	—	4	2	no	—
160	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
161	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
162	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
166	C₂×D₄×C₃₁	—	2	8	no	—
167	C₂×D₄×C₃₁	—	4	4	no	—
168	C₂×D₄×C₃₁	—	4	16	no	—
169	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
171	C₂²×C₄×C₃₁	—	2	4	no	—
172	C₂²×C₄×C₃₁	—	2	4	no	—
173	C₂²×C₄×C₃₁	—	2	4	no	—
174	C₂²×C₄×C₃₁	—	2	8	no	—
175	C₂²×C₄×C₃₁	—	2	8	no	—
176	C₂²×C₄×C₃₁	—	2	8	no	—
177	C₂²×C₄×C₃₁	—	4	16	no	—
178	C₂²×C₄×C₃₁	—	4	2	no	—
179	C₂²×C₄×C₃₁	—	4	2	no	—
180	C₂²×C₄×C₃₁	—	4	2	no	—
181	C₂²×C₄×C₃₁	—	4	2	no	—
182	C₂²×C₄×C₃₁	—	4	2	no	—
183	C₂²×C₄×C₃₁	—	4	4	no	—
184	C₂²×C₄×C₃₁	—	4	2	no	—
185	C₂²×C₄×C₃₁	—	4	4	no	—
186	C₂²×C₄×C₃₁	—	4	4	no	—
187	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₃₁	—	2	8	no	—
208	C₄⋊C₄×C₃₁	—	4	4	no	—
209	C₄⋊C₄×C₃₁	—	4	4	no	—
210	C₄⋊C₄×C₃₁	—	4	4	no	—
211	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₃₁	—	2	4	no	—
216	C₂²⋊C₄×C₃₁	—	2	4	no	—
217	C₂²⋊C₄×C₃₁	—	2	4	no	—
218	C₂²⋊C₄×C₃₁	—	2	8	no	—
219	C₂²⋊C₄×C₃₁	—	2	8	no	—
220	C₂²⋊C₄×C₃₁	—	2	8	no	—
221	C₂²⋊C₄×C₃₁	—	4	4	no	—
222	C₂²⋊C₄×C₃₁	—	4	4	no	—
223	C₂²⋊C₄×C₃₁	—	4	4	no	—
224	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₃₁	#41	1	8	yes	—
231	C₄²×C₃₁	—	2	8	no	—
232	C₄²×C₃₁	—	4	2	no	—
233	C₄²×C₃₁	—	4	4	no	—
234	C₄²×C₃₁	—	4	2	no	—
235	C₄²×C₃₁	—	4	4	no	—
236	C₄²×C₃₁	—	4	2	no	—
237	C₄²×C₃₁	—	4	2	no	—
238	C₄²×C₃₁	—	4	4	no	—
239	#34238	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₃₁	—	2	2	no	—
241	C₂³×C₃₁	—	2	2	no	—
242	C₂³×C₃₁	—	2	2	no	—
243	C₂³×C₃₁	—	2	2	no	—
244	C₂³×C₃₁	—	2	8	no	—
245	C₂³×C₃₁	—	2	8	no	—
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	—	2	2	no	—
248	C₂³×C₃₁	—	2	2	no	—
249	C₂³×C₃₁	—	2	4	no	—
250	C₂³×C₃₁	—	2	2	no	—
251	C₂³×C₃₁	—	2	2	no	—
252	C₂³×C₃₁	—	2	4	no	—
253	C₂³×C₃₁	—	2	8	no	—
254	C₂³×C₃₁	—	4	4	no	—
255	C₂³×C₃₁	—	4	4	no	—
256	C₂³×C₃₁	—	4	4	no	—
257	C₂³×C₃₁	—	4	16	no	—
258	C₂³×C₃₁	—	8	8	no	—
259	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
260	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
261	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
262	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
263	C₂³×C₃₁	C₂×#41	1	4	yes	—
264	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
265	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
266	D₄×C₃₁	—	2	16	no	—
267	D₄×C₃₁	—	4	8	no	—
268	C₂×C₄×C₃₁	—	2	8	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	4	no	—
274	C₂×C₄×C₃₁	—	2	2	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	4	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	4	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	2	4	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	—	4	4	no	—
291	C₂×C₄×C₃₁	—	4	4	no	—
292	C₂×C₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	4	4	no	—
294	C₂×C₄×C₃₁	—	4	4	no	—
295	C₂×C₄×C₃₁	—	4	4	no	—
296	C₂×C₄×C₃₁	—	4	16	no	—
297	C₂×C₄×C₃₁	—	8	8	no	—
298	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
306	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic
307	#2374	C₂×C₃₁	1	4	yes	complemented
308	#2359	C₂×C₃₁	1	4	yes	complemented
309	#2345	C₂×C₃₁	1	2	yes	complemented
310	#2342	C₂×C₃₁	1	2	yes	complemented
311	#2342	C₂×C₃₁	1	2	yes	complemented
312	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	—
313	#2335	C₂×C₃₁	1	4	yes	complemented
314	#2313	C₂×C₃₁	1	1	yes	characteristic, complemented
315	#2312	C₂×C₃₁	1	1	yes	characteristic, complemented
316	C₄×#123	C₂×C₃₁	1	4	yes	complemented
317	#2280	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#2274	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#2273	C₂×C₃₁	1	1	yes	characteristic, complemented
320	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
321	C₂²×C₃₁	—	2	2	no	—
322	C₂²×C₃₁	—	2	2	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	2	no	—
325	C₂²×C₃₁	—	2	8	no	—
326	C₂²×C₃₁	—	2	8	no	—
327	C₂²×C₃₁	—	2	2	no	—
328	C₂²×C₃₁	—	2	4	no	—
329	C₂²×C₃₁	—	2	2	no	—
330	C₂²×C₃₁	—	2	4	no	—
331	C₂²×C₃₁	—	2	2	no	—
332	C₂²×C₃₁	—	2	4	no	—
333	C₂²×C₃₁	—	4	16	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	—	4	4	no	—
336	C₂²×C₃₁	—	4	4	no	—
337	C₂²×C₃₁	—	8	8	no	—
338	C₂²×C₃₁	C₄×#41	1	4	yes	—
339	C₂²×C₃₁	#518	1	4	yes	—
340	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
341	C₂²×C₃₁	C₂²×#41	1	2	yes	—
342	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
343	C₂²×C₃₁	#585	1	2	yes	—
344	C₄×C₃₁	—	2	4	no	—
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	2	2	no	—
348	C₄×C₃₁	—	2	2	no	—
349	C₄×C₃₁	—	2	4	no	—
350	C₄×C₃₁	—	2	4	no	—
351	C₄×C₃₁	—	2	8	no	—
352	C₄×C₃₁	—	4	4	no	—
353	C₄×C₃₁	—	4	4	no	—
354	C₄×C₃₁	—	4	4	no	—
355	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
357	C₂×#123	C₄×C₃₁	1	16	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	—
361	C₂×#123	C₂²×C₃₁	1	2	yes	—
362	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
363	C₂×#117	C₂²×C₃₁	1	2	yes	—
364	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
365	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
368	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
369	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
373	#390	C₂²×C₃₁	1	4	yes	—
374	#389	C₂²×C₃₁	1	4	yes	complemented
375	#388	C₂²×C₃₁	1	4	yes	complemented
376	#388	C₂²×C₃₁	1	4	yes	complemented
377	#388	C₂²×C₃₁	1	4	yes	complemented
378	#388	C₂²×C₃₁	1	4	yes	complemented
379	#388	C₂²×C₃₁	1	4	yes	complemented
380	#388	C₂²×C₃₁	1	4	yes	complemented
381	#387	C₂²×C₃₁	1	4	yes	complemented
382	#387	C₂²×C₃₁	1	4	yes	complemented
383	#387	C₂²×C₃₁	1	4	yes	complemented
384	#387	C₂²×C₃₁	1	4	yes	complemented
385	#386	C₂²×C₃₁	1	4	yes	—
386	#386	C₂²×C₃₁	1	4	yes	—
387	#385	C₂²×C₃₁	1	4	yes	complemented
388	#385	C₂²×C₃₁	1	4	yes	complemented
389	#381	C₂²×C₃₁	1	2	yes	—
390	#381	C₂²×C₃₁	1	2	yes	complemented
391	#380	C₂²×C₃₁	1	2	yes	—
392	#380	C₂²×C₃₁	1	2	yes	—
393	#380	C₂²×C₃₁	1	2	yes	—
394	#380	C₂²×C₃₁	1	2	yes	complemented
395	#379	C₂²×C₃₁	1	2	yes	—
396	#379	C₂²×C₃₁	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
398	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
399	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
400	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
403	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
405	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
407	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
408	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
409	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
410	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
411	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
414	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
415	C₂×C₃₁	—	2	4	no	—
416	C₂×C₃₁	—	2	4	no	—
417	C₂×C₃₁	—	4	2	no	—
418	C₂×C₃₁	—	4	4	no	—
419	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
420	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
421	C₂×C₃₁	#3428	1	1	yes	characteristic
422	C₂×C₃₁	#3513	1	4	yes	—
423	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
424	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
427	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
428	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
429	C₂³×C₄	—	4	4	no	—
430	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
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	4	yes	—
436	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
442	#123	C₂×C₄×C₃₁	1	16	yes	complemented
443	#123	C₂×C₄×C₃₁	1	16	yes	complemented
444	#123	C₂×C₄×C₃₁	1	16	yes	complemented
445	#123	C₂×C₄×C₃₁	1	16	yes	complemented
446	C₄×D₄	—	4	8	no	—
447	#117	—	2	8	no	—
448	#117	—	4	4	no	—
449	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
450	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₂×C₂²⋊C₄	—	2	8	no	—
460	C₂×C₂²⋊C₄	—	2	8	no	—
461	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
462	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
463	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
464	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	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	2	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×C₄²	—	4	4	no	—
481	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
482	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
483	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
484	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
485	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
486	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
487	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
489	#95	C₂³×C₃₁	1	2	yes	—
490	#95	C₂³×C₃₁	1	4	yes	—
491	#95	C₂³×C₃₁	1	2	yes	—
492	#95	C₂³×C₃₁	1	2	yes	—
493	#95	C₂³×C₃₁	1	4	yes	—
494	#95	C₂³×C₃₁	1	2	yes	—
495	#95	C₂³×C₃₁	1	4	yes	—
496	#95	C₂³×C₃₁	1	4	yes	—
497	#95	C₂³×C₃₁	1	4	yes	—
498	#95	C₂³×C₃₁	1	4	yes	—
499	#95	C₂³×C₃₁	1	4	yes	—
500	#95	C₂³×C₃₁	1	4	yes	—
501	C₃₁	#34238	1	1	yes	characteristic, direct product factor, Sylow
502	C₂⁴	—	2	4	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	4	2	no	—
506	C₂⁴	—	4	2	no	—
507	C₂⁴	—	4	2	no	—
508	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
509	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
510	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
511	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
512	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
513	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	16	no	—
517	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
518	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	8	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	4	16	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
536	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
537	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
539	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
540	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
541	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
542	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
543	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
560	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
561	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
562	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	—	4	4	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
578	C₂²⋊C₄	#41×C₃₁	1	8	yes	—
579	C₄²	—	2	8	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	4	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	4	4	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	4	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	8	no	—
592	C₂³	—	2	8	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	16	no	—
605	C₂³	—	8	8	no	—
606	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
607	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
608	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
609	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
610	C₂³	C₂×#41×C₃₁	1	4	yes	—
611	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
612	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
613	D₄	—	2	16	no	—
614	D₄	—	4	8	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	16	no	—
644	C₂×C₄	—	8	8	no	—
645	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
648	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
652	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	4	16	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	8	8	no	—
670	C₂²	C₄×#41×C₃₁	1	4	yes	—
671	C₂²	C₃₁×#518	1	4	yes	—
672	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₃₁	1	2	yes	—
674	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
675	C₂²	C₃₁×#585	1	2	yes	—
676	C₄	—	2	4	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	8	no	—
684	C₄	—	4	4	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	4	no	—
687	C₂	—	2	4	no	—
688	C₂	—	2	4	no	—
689	C₂	—	4	2	no	—
690	C₂	—	4	4	no	—
691	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
692	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
693	C₂	C₃₁×#3428	1	1	yes	characteristic
694	C₂	C₃₁×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂³×D₄×C₃₁	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×#2359	C₂	semidirect
4. C₃₁×#2345	C₂	semidirect
5. C₃₁×#2342	C₂	semidirect
6. C₃₁×#2342	C₂	semidirect
8. C₃₁×#2335	C₂	semidirect
9. C₃₁×#2313	C₂	semidirect
10. C₃₁×#2312	C₂	semidirect
11. C₄×C₃₁×#123	C₂	semidirect
12. C₃₁×#2280	C₂	semidirect
13. C₃₁×#2274	C₂	semidirect
14. C₃₁×#2273	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
18. C₂×C₃₁×#123	C₄	semidirect
25. C₂×C₃₁×#117	C₂²	semidirect
33. C₂²×C₄²×C₃₁	C₂²	semidirect
35. C₃₁×#389	C₂²	semidirect
36. C₃₁×#388	C₂²	semidirect
37. C₃₁×#388	C₂²	semidirect
38. C₃₁×#388	C₂²	semidirect
39. C₃₁×#388	C₂²	semidirect
40. C₃₁×#388	C₂²	semidirect
41. C₃₁×#388	C₂²	semidirect
42. C₃₁×#387	C₂²	semidirect
43. C₃₁×#387	C₂²	semidirect
44. C₃₁×#387	C₂²	semidirect
45. C₃₁×#387	C₂²	semidirect
48. C₃₁×#385	C₂²	semidirect
49. C₃₁×#385	C₂²	semidirect
51. C₃₁×#381	C₂²	semidirect
55. C₃₁×#380	C₂²	semidirect
58. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
59. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
60. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
68. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
75. C₂×C₃₁×#95	C₂²	semidirect
83. C₂³×C₄×C₃₁	C₂×C₄	semidirect
95. C₃₁×#123	C₂×C₄	semidirect
96. C₃₁×#123	C₂×C₄	semidirect
97. C₃₁×#123	C₂×C₄	semidirect
98. C₃₁×#123	C₂×C₄	semidirect
102. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
114. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
115. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
116. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
239. #34238	C₃₁	direct (N × H)
307. #2374	C₂×C₃₁	semidirect
308. #2359	C₂×C₃₁	semidirect
309. #2345	C₂×C₃₁	semidirect
310. #2342	C₂×C₃₁	semidirect
311. #2342	C₂×C₃₁	semidirect
313. #2335	C₂×C₃₁	semidirect
314. #2313	C₂×C₃₁	semidirect
315. #2312	C₂×C₃₁	semidirect
316. C₄×#123	C₂×C₃₁	semidirect
317. #2280	C₂×C₃₁	semidirect
318. #2274	C₂×C₃₁	semidirect
319. #2273	C₂×C₃₁	semidirect
320. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
357. C₂×#123	C₄×C₃₁	semidirect
364. C₂×#117	C₂²×C₃₁	semidirect
372. C₂²×C₄²	C₂²×C₃₁	semidirect
374. #389	C₂²×C₃₁	semidirect
375. #388	C₂²×C₃₁	semidirect
376. #388	C₂²×C₃₁	semidirect
377. #388	C₂²×C₃₁	semidirect
378. #388	C₂²×C₃₁	semidirect
379. #388	C₂²×C₃₁	semidirect
380. #388	C₂²×C₃₁	semidirect
381. #387	C₂²×C₃₁	semidirect
382. #387	C₂²×C₃₁	semidirect
383. #387	C₂²×C₃₁	semidirect
384. #387	C₂²×C₃₁	semidirect
387. #385	C₂²×C₃₁	semidirect
388. #385	C₂²×C₃₁	semidirect
390. #381	C₂²×C₃₁	semidirect
394. #380	C₂²×C₃₁	semidirect
397. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
398. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
399. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
407. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
408. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
409. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
411. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
412. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
413. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
414. C₂×#95	C₂²×C₃₁	semidirect
430. C₂³×C₄	C₂×C₄×C₃₁	semidirect
442. #123	C₂×C₄×C₃₁	semidirect
443. #123	C₂×C₄×C₃₁	semidirect
444. #123	C₂×C₄×C₃₁	semidirect
445. #123	C₂×C₄×C₃₁	semidirect
449. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
450. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
461. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
462. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
463. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
501. C₃₁	#34238	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#123	2
C₃₁×#2374	2
C₃₁×#2359	2
C₃₁×#2345	2
C₃₁×#2342	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2335	2
C₃₁×#2313	2
C₃₁×#2312	2
C₄×C₃₁×#123	2
C₃₁×#2280	2
C₃₁×#2274	2
C₃₁×#2273	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#34238	31

Subgroups — C31×#34238 #21490997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34238 #21490997