Subgroups — C₃₁×#35078 #21491837

Order 7936.

3230 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2856	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2850	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2661	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2543	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2500	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2435	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2431	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2410	C₂	1	4	yes	maximal, complemented
14	C₃₁×#2321	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
18	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
22	C₃₁×#525	—	2	8	no	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#121	—	2	8	no	—
27	C₂×C₃₁×#121	C₂²	1	2	yes	—
28	C₂×C₃₁×#121	C₂²	1	2	yes	—
29	C₂×C₃₁×#121	C₂²	1	2	yes	—
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
34	C₂×C₃₁×#120	C₂²	1	4	yes	—
35	C₂×C₃₁×#120	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
42	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
43	C₃₁×#398	C₂²	1	4	yes	complemented
44	C₃₁×#397	C₂²	1	4	yes	complemented
45	C₃₁×#394	C₂²	1	8	yes	complemented
46	C₃₁×#394	C₂²	1	4	yes	complemented
47	C₃₁×#392	C₂²	1	8	yes	complemented
48	C₃₁×#392	C₂²	1	4	yes	complemented
49	C₃₁×#391	C₂²	1	2	yes	complemented
50	C₃₁×#390	C₂²	1	8	yes	complemented
51	C₃₁×#390	C₂²	1	2	yes	complemented
52	C₃₁×#390	C₂²	1	2	yes	complemented
53	C₃₁×#390	C₂²	1	2	yes	complemented
54	C₃₁×#388	C₂²	1	8	yes	complemented
55	C₃₁×#388	C₂²	1	8	yes	complemented
56	C₃₁×#386	C₂²	1	4	yes	—
57	C₃₁×#386	C₂²	1	8	yes	complemented
58	C₃₁×#386	C₂²	1	8	yes	complemented
59	C₃₁×#385	C₂²	1	4	yes	—
60	C₃₁×#384	C₂²	1	2	yes	complemented
61	C₃₁×#382	C₂²	1	2	yes	complemented
62	C₃₁×#379	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
68	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
69	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
70	C₂⁵×C₃₁	C₂³	1	2	yes	—
71	C₂×#41×C₃₁	—	2	4	no	—
72	C₂×#41×C₃₁	—	4	4	no	—
73	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₃₁	—	2	8	no	—
75	C₂²×D₄×C₃₁	—	2	4	no	—
76	C₂²×D₄×C₃₁	—	4	4	no	—
77	C₂²×D₄×C₃₁	—	4	8	no	—
78	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
82	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
84	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂³×C₄×C₃₁	—	4	4	no	—
88	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
89	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
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	2	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
98	C₃₁×#127	—	4	4	no	—
99	C₃₁×#124	—	4	4	no	—
100	C₃₁×#123	—	2	8	no	—
101	C₃₁×C₂²⋊Q₈	—	2	4	no	—
102	C₃₁×C₂²⋊Q₈	—	2	4	no	—
103	C₃₁×#121	—	2	8	no	—
104	C₃₁×#121	—	2	8	no	—
105	C₃₁×#121	—	2	8	no	—
106	C₃₁×#121	—	2	8	no	—
107	C₃₁×#121	—	2	4	no	—
108	C₃₁×#121	—	2	4	no	—
109	C₃₁×#121	—	4	16	no	—
110	C₃₁×#120	—	2	8	no	—
111	C₃₁×#120	—	2	16	no	—
112	C₄×D₄×C₃₁	—	2	8	no	—
113	C₄×D₄×C₃₁	—	2	8	no	—
114	C₃₁×#117	—	2	4	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
124	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	8	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	—	4	4	no	—
140	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
144	C₃₁×#95	C₂³	1	2	yes	—
145	C₃₁×#95	C₂³	1	8	yes	—
146	C₃₁×#95	C₂³	1	2	yes	—
147	C₃₁×#95	C₂³	1	8	yes	—
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₂⁴×C₃₁	—	2	4	no	—
150	C₂⁴×C₃₁	—	2	4	no	—
151	C₂⁴×C₃₁	—	2	4	no	—
152	C₂⁴×C₃₁	—	2	8	no	—
153	C₂⁴×C₃₁	—	4	2	no	—
154	C₂⁴×C₃₁	—	4	4	no	—
155	C₂⁴×C₃₁	—	4	4	no	—
156	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
157	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
158	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
159	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
162	#41×C₃₁	—	4	16	no	—
163	C₂×Q₈×C₃₁	—	2	2	no	—
164	C₂×Q₈×C₃₁	—	2	4	no	—
165	C₂×D₄×C₃₁	—	2	4	no	—
166	C₂×D₄×C₃₁	—	2	4	no	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	8	no	—
169	C₂×D₄×C₃₁	—	2	8	no	—
170	C₂×D₄×C₃₁	—	2	8	no	—
171	C₂×D₄×C₃₁	—	2	8	no	—
172	C₂×D₄×C₃₁	—	2	16	no	—
173	C₂×D₄×C₃₁	—	2	4	no	—
174	C₂×D₄×C₃₁	—	2	4	no	—
175	C₂×D₄×C₃₁	—	2	2	no	—
176	C₂×D₄×C₃₁	—	2	16	no	—
177	C₂×D₄×C₃₁	—	2	4	no	—
178	C₂×D₄×C₃₁	—	2	4	no	—
179	C₂×D₄×C₃₁	—	2	4	no	—
180	C₂×D₄×C₃₁	—	4	4	no	—
181	C₂×D₄×C₃₁	—	4	8	no	—
182	C₂×D₄×C₃₁	—	4	4	no	—
183	C₂×D₄×C₃₁	—	4	16	no	—
184	C₂×D₄×C₃₁	—	4	8	no	—
185	C₂×D₄×C₃₁	—	4	8	no	—
186	C₂×D₄×C₃₁	—	4	32	no	—
187	C₂²×C₄×C₃₁	—	2	4	no	—
188	C₂²×C₄×C₃₁	—	2	4	no	—
189	C₂²×C₄×C₃₁	—	2	4	no	—
190	C₂²×C₄×C₃₁	—	2	4	no	—
191	C₂²×C₄×C₃₁	—	2	8	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	8	no	—
194	C₂²×C₄×C₃₁	—	4	16	no	—
195	C₂²×C₄×C₃₁	—	4	4	no	—
196	C₂²×C₄×C₃₁	—	4	2	no	—
197	C₂²×C₄×C₃₁	—	4	2	no	—
198	C₂²×C₄×C₃₁	—	4	2	no	—
199	C₂²×C₄×C₃₁	—	4	4	no	—
200	C₂²×C₄×C₃₁	—	4	4	no	—
201	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₃₁	—	2	4	no	—
218	C₄⋊C₄×C₃₁	—	2	4	no	—
219	C₄⋊C₄×C₃₁	—	2	2	no	—
220	C₄⋊C₄×C₃₁	—	2	2	no	—
221	C₄⋊C₄×C₃₁	—	2	4	no	—
222	C₄⋊C₄×C₃₁	—	2	4	no	—
223	C₄⋊C₄×C₃₁	—	4	8	no	—
224	C₂²⋊C₄×C₃₁	—	2	4	no	—
225	C₂²⋊C₄×C₃₁	—	2	4	no	—
226	C₂²⋊C₄×C₃₁	—	2	4	no	—
227	C₂²⋊C₄×C₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₃₁	—	2	8	no	—
229	C₂²⋊C₄×C₃₁	—	2	8	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	—	2	16	no	—
234	C₂²⋊C₄×C₃₁	—	4	8	no	—
235	C₂²⋊C₄×C₃₁	—	4	8	no	—
236	C₂²⋊C₄×C₃₁	—	4	8	no	—
237	C₂²⋊C₄×C₃₁	#41	1	8	yes	complemented
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	#35078	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	2	no	—
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	—	2	8	no	—
248	C₂³×C₃₁	—	2	8	no	—
249	C₂³×C₃₁	—	2	2	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	8	no	—
255	C₂³×C₃₁	—	2	4	no	—
256	C₂³×C₃₁	—	2	4	no	—
257	C₂³×C₃₁	—	2	4	no	—
258	C₂³×C₃₁	—	2	8	no	—
259	C₂³×C₃₁	—	2	4	no	—
260	C₂³×C₃₁	—	2	4	no	—
261	C₂³×C₃₁	—	4	4	no	—
262	C₂³×C₃₁	—	4	16	no	—
263	C₂³×C₃₁	—	4	8	no	—
264	C₂³×C₃₁	—	4	8	no	—
265	C₂³×C₃₁	—	4	8	no	—
266	C₂³×C₃₁	—	8	16	no	—
267	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
268	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
269	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
270	C₂³×C₃₁	C₂×#41	1	4	yes	—
271	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
272	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
273	Q₈×C₃₁	—	4	4	no	—
274	D₄×C₃₁	—	4	8	no	—
275	D₄×C₃₁	—	4	16	no	—
276	D₄×C₃₁	—	4	8	no	—
277	D₄×C₃₁	—	4	8	no	—
278	D₄×C₃₁	—	4	8	no	—
279	D₄×C₃₁	—	4	16	no	—
280	D₄×C₃₁	—	4	8	no	—
281	D₄×C₃₁	—	4	4	no	—
282	D₄×C₃₁	—	8	16	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	2	no	—
288	C₂×C₄×C₃₁	—	2	8	no	—
289	C₂×C₄×C₃₁	—	2	8	no	—
290	C₂×C₄×C₃₁	—	2	8	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	4	no	—
294	C₂×C₄×C₃₁	—	2	2	no	—
295	C₂×C₄×C₃₁	—	2	4	no	—
296	C₂×C₄×C₃₁	—	2	4	no	—
297	C₂×C₄×C₃₁	—	2	4	no	—
298	C₂×C₄×C₃₁	—	2	4	no	—
299	C₂×C₄×C₃₁	—	2	4	no	—
300	C₂×C₄×C₃₁	—	2	4	no	—
301	C₂×C₄×C₃₁	—	2	8	no	—
302	C₂×C₄×C₃₁	—	4	4	no	—
303	C₂×C₄×C₃₁	—	4	4	no	—
304	C₂×C₄×C₃₁	—	4	4	no	—
305	C₂×C₄×C₃₁	—	4	16	no	—
306	C₂×C₄×C₃₁	—	4	8	no	—
307	C₂×C₄×C₃₁	—	4	8	no	—
308	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
313	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
314	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
315	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
316	#2856	C₂×C₃₁	1	2	yes	complemented
317	#2850	C₂×C₃₁	1	2	yes	complemented
318	#2661	C₂×C₃₁	1	4	yes	complemented
319	#2543	C₂×C₃₁	1	4	yes	complemented
320	#2504	C₂×C₃₁	1	1	yes	characteristic, complemented
321	#2502	C₂×C₃₁	1	1	yes	characteristic, complemented
322	#2500	C₂×C₃₁	1	2	yes	complemented
323	#2435	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#2433	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#2431	C₂×C₃₁	1	2	yes	complemented
326	#2410	C₂×C₃₁	1	4	yes	complemented
327	#2321	C₂×C₃₁	1	4	yes	complemented
328	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
329	C₂²×C₃₁	—	2	2	no	—
330	C₂²×C₃₁	—	2	2	no	—
331	C₂²×C₃₁	—	2	2	no	—
332	C₂²×C₃₁	—	2	2	no	—
333	C₂²×C₃₁	—	2	8	no	—
334	C₂²×C₃₁	—	2	8	no	—
335	C₂²×C₃₁	—	2	2	no	—
336	C₂²×C₃₁	—	2	2	no	—
337	C₂²×C₃₁	—	2	2	no	—
338	C₂²×C₃₁	—	4	16	no	—
339	C₂²×C₃₁	—	4	4	no	—
340	C₂²×C₃₁	—	4	2	no	—
341	C₂²×C₃₁	—	4	4	no	—
342	C₂²×C₃₁	—	4	2	no	—
343	C₂²×C₃₁	—	4	4	no	—
344	C₂²×C₃₁	—	4	4	no	—
345	C₂²×C₃₁	—	4	2	no	—
346	C₂²×C₃₁	—	4	8	no	—
347	C₂²×C₃₁	—	4	8	no	—
348	C₂²×C₃₁	—	4	8	no	—
349	C₂²×C₃₁	—	8	16	no	—
350	C₂²×C₃₁	#532	1	4	yes	—
351	C₂²×C₃₁	#535	1	4	yes	—
352	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₃₁	C₂²×#41	1	2	yes	—
354	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
355	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₄×C₃₁	—	2	2	no	—
357	C₄×C₃₁	—	2	2	no	—
358	C₄×C₃₁	—	2	2	no	—
359	C₄×C₃₁	—	2	8	no	—
360	C₄×C₃₁	—	4	2	no	—
361	C₄×C₃₁	—	4	2	no	—
362	C₄×C₃₁	—	4	4	no	—
363	C₄×C₃₁	—	4	2	no	—
364	C₄×C₃₁	—	4	4	no	—
365	C₄×C₃₁	#534	1	4	yes	—
366	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
367	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
368	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
370	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
371	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
372	#525	—	2	8	no	—
373	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
374	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
375	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
376	C₂×#121	—	2	8	no	—
377	C₂×#121	C₂²×C₃₁	1	2	yes	—
378	C₂×#121	C₂²×C₃₁	1	2	yes	—
379	C₂×#121	C₂²×C₃₁	1	2	yes	—
380	C₂×#121	C₂²×C₃₁	1	2	yes	—
381	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
382	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
383	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
384	C₂×#120	C₂²×C₃₁	1	4	yes	—
385	C₂×#120	C₂²×C₃₁	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
388	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
389	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
391	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
392	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
393	#398	C₂²×C₃₁	1	4	yes	complemented
394	#397	C₂²×C₃₁	1	4	yes	complemented
395	#394	C₂²×C₃₁	1	8	yes	complemented
396	#394	C₂²×C₃₁	1	4	yes	complemented
397	#392	C₂²×C₃₁	1	8	yes	complemented
398	#392	C₂²×C₃₁	1	4	yes	complemented
399	#391	C₂²×C₃₁	1	2	yes	complemented
400	#390	C₂²×C₃₁	1	8	yes	complemented
401	#390	C₂²×C₃₁	1	2	yes	complemented
402	#390	C₂²×C₃₁	1	2	yes	complemented
403	#390	C₂²×C₃₁	1	2	yes	complemented
404	#388	C₂²×C₃₁	1	8	yes	complemented
405	#388	C₂²×C₃₁	1	8	yes	complemented
406	#386	C₂²×C₃₁	1	4	yes	—
407	#386	C₂²×C₃₁	1	8	yes	complemented
408	#386	C₂²×C₃₁	1	8	yes	complemented
409	#385	C₂²×C₃₁	1	4	yes	—
410	#384	C₂²×C₃₁	1	2	yes	complemented
411	#382	C₂²×C₃₁	1	2	yes	complemented
412	#379	C₂²×C₃₁	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
415	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
417	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
418	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
419	C₂×C₃₁	—	2	4	no	—
420	C₂×C₃₁	—	2	4	no	—
421	C₂×C₃₁	—	4	2	no	—
422	C₂×C₃₁	—	8	2	no	—
423	C₂×C₃₁	—	8	4	no	—
424	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
425	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
426	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
427	C₂×C₃₁	#3519	1	4	yes	—
428	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
429	C₂⁵	C₂³×C₃₁	1	2	yes	—
430	C₂×#41	—	2	4	no	—
431	C₂×#41	—	4	4	no	—
432	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
433	C₂²×D₄	—	2	8	no	—
434	C₂²×D₄	—	2	4	no	—
435	C₂²×D₄	—	4	4	no	—
436	C₂²×D₄	—	4	8	no	—
437	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
438	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
439	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
440	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
441	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
443	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
444	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
445	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
446	C₂³×C₄	—	4	4	no	—
447	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
448	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
449	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
453	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
454	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
457	#127	—	4	4	no	—
458	#124	—	4	4	no	—
459	#123	—	2	8	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	—	2	4	no	—
462	#121	—	2	8	no	—
463	#121	—	2	8	no	—
464	#121	—	2	8	no	—
465	#121	—	2	8	no	—
466	#121	—	2	4	no	—
467	#121	—	2	4	no	—
468	#121	—	4	16	no	—
469	#120	—	2	8	no	—
470	#120	—	2	16	no	—
471	C₄×D₄	—	2	8	no	—
472	C₄×D₄	—	2	8	no	—
473	#117	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	4	no	—
475	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
482	C₂×C₂²⋊C₄	—	2	8	no	—
483	C₂×C₂²⋊C₄	—	2	8	no	—
484	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
498	C₂×C₄²	—	4	4	no	—
499	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
500	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
501	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
502	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
503	#95	C₂³×C₃₁	1	4	yes	—
504	#95	C₂³×C₃₁	1	2	yes	—
505	#95	C₂³×C₃₁	1	2	yes	—
506	#95	C₂³×C₃₁	1	8	yes	—
507	#95	C₂³×C₃₁	1	8	yes	—
508	C₃₁	#35078	1	1	yes	characteristic, direct product factor, Sylow
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	2	8	no	—
513	C₂⁴	—	4	2	no	—
514	C₂⁴	—	4	4	no	—
515	C₂⁴	—	4	4	no	—
516	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
517	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
518	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
519	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
520	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
521	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
522	#41	—	4	16	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	16	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	16	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	8	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	16	no	—
544	C₂×D₄	—	4	8	no	—
545	C₂×D₄	—	4	8	no	—
546	C₂×D₄	—	4	32	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	8	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	8	no	—
554	C₂²×C₄	—	4	16	no	—
555	C₂²×C₄	—	4	4	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
562	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
563	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
564	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
565	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
566	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	4	8	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	16	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₂²⋊C₄	—	4	8	no	—
596	C₂²⋊C₄	—	4	8	no	—
597	C₂²⋊C₄	#41×C₃₁	1	8	yes	complemented
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	4	4	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	8	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	16	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	8	16	no	—
626	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
627	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
628	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
629	C₂³	C₂×#41×C₃₁	1	4	yes	—
630	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
631	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
632	Q₈	—	4	4	no	—
633	D₄	—	4	8	no	—
634	D₄	—	4	16	no	—
635	D₄	—	4	8	no	—
636	D₄	—	4	8	no	—
637	D₄	—	4	8	no	—
638	D₄	—	4	16	no	—
639	D₄	—	4	8	no	—
640	D₄	—	4	4	no	—
641	D₄	—	8	16	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
670	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
671	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
672	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	8	no	—
678	C₂²	—	2	8	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	4	16	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	4	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	8	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	8	no	—
693	C₂²	—	8	16	no	—
694	C₂²	C₃₁×#532	1	4	yes	—
695	C₂²	C₃₁×#535	1	4	yes	—
696	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₃₁	1	2	yes	—
698	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
699	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	8	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	4	no	—
709	C₄	C₃₁×#534	1	4	yes	—
710	C₂	—	2	4	no	—
711	C₂	—	2	4	no	—
712	C₂	—	4	2	no	—
713	C₂	—	8	4	no	—
714	C₂	—	8	2	no	—
715	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
716	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
717	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
718	C₂	C₃₁×#3519	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×#525	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₃₁×#2856	C₂	semidirect
4. C₃₁×#2850	C₂	semidirect
5. C₃₁×#2661	C₂	semidirect
6. C₃₁×#2543	C₂	semidirect
7. C₃₁×#2504	C₂	semidirect
8. C₃₁×#2502	C₂	semidirect
9. C₃₁×#2500	C₂	semidirect
10. C₃₁×#2435	C₂	semidirect
11. C₃₁×#2433	C₂	semidirect
12. C₃₁×#2431	C₂	semidirect
13. C₃₁×#2410	C₂	semidirect
14. C₃₁×#2321	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
16. C₂²×#41×C₃₁	C₂²	semidirect
20. C₂×C₃₁×#127	C₂²	semidirect
21. C₂×C₃₁×#124	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
25. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₃₁×#121	C₂²	semidirect
33. C₂×C₃₁×#121	C₂²	semidirect
37. C₂×C₄×D₄×C₃₁	C₂²	semidirect
38. C₂×C₃₁×#117	C₂²	semidirect
42. C₂²×C₄²×C₃₁	C₂²	semidirect
43. C₃₁×#398	C₂²	semidirect
44. C₃₁×#397	C₂²	semidirect
45. C₃₁×#394	C₂²	semidirect
46. C₃₁×#394	C₂²	semidirect
47. C₃₁×#392	C₂²	semidirect
48. C₃₁×#392	C₂²	semidirect
49. C₃₁×#391	C₂²	semidirect
50. C₃₁×#390	C₂²	semidirect
51. C₃₁×#390	C₂²	semidirect
52. C₃₁×#390	C₂²	semidirect
53. C₃₁×#390	C₂²	semidirect
54. C₃₁×#388	C₂²	semidirect
55. C₃₁×#388	C₂²	semidirect
57. C₃₁×#386	C₂²	semidirect
58. C₃₁×#386	C₂²	semidirect
60. C₃₁×#384	C₂²	semidirect
61. C₃₁×#382	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
67. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
68. C₂×C₃₁×#95	C₂²	semidirect
88. C₂³×C₄×C₃₁	D₄	semidirect
237. C₂²⋊C₄×C₃₁	#41	semidirect
242. #35078	C₃₁	direct (N × H)
314. C₂×#525	C₂×C₃₁	semidirect
315. C₂²×#121	C₂×C₃₁	semidirect
316. #2856	C₂×C₃₁	semidirect
317. #2850	C₂×C₃₁	semidirect
318. #2661	C₂×C₃₁	semidirect
319. #2543	C₂×C₃₁	semidirect
320. #2504	C₂×C₃₁	semidirect
321. #2502	C₂×C₃₁	semidirect
322. #2500	C₂×C₃₁	semidirect
323. #2435	C₂×C₃₁	semidirect
324. #2433	C₂×C₃₁	semidirect
325. #2431	C₂×C₃₁	semidirect
326. #2410	C₂×C₃₁	semidirect
327. #2321	C₂×C₃₁	semidirect
328. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
366. C₂²×#41	C₂²×C₃₁	semidirect
370. C₂×#127	C₂²×C₃₁	semidirect
371. C₂×#124	C₂²×C₃₁	semidirect
373. C₂×#123	C₂²×C₃₁	semidirect
375. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
382. C₂×#121	C₂²×C₃₁	semidirect
383. C₂×#121	C₂²×C₃₁	semidirect
387. C₂×C₄×D₄	C₂²×C₃₁	semidirect
388. C₂×#117	C₂²×C₃₁	semidirect
392. C₂²×C₄²	C₂²×C₃₁	semidirect
393. #398	C₂²×C₃₁	semidirect
394. #397	C₂²×C₃₁	semidirect
395. #394	C₂²×C₃₁	semidirect
396. #394	C₂²×C₃₁	semidirect
397. #392	C₂²×C₃₁	semidirect
398. #392	C₂²×C₃₁	semidirect
399. #391	C₂²×C₃₁	semidirect
400. #390	C₂²×C₃₁	semidirect
401. #390	C₂²×C₃₁	semidirect
402. #390	C₂²×C₃₁	semidirect
403. #390	C₂²×C₃₁	semidirect
404. #388	C₂²×C₃₁	semidirect
405. #388	C₂²×C₃₁	semidirect
407. #386	C₂²×C₃₁	semidirect
408. #386	C₂²×C₃₁	semidirect
410. #384	C₂²×C₃₁	semidirect
411. #382	C₂²×C₃₁	semidirect
416. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
417. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
418. C₂×#95	C₂²×C₃₁	semidirect
447. C₂³×C₄	D₄×C₃₁	semidirect
508. C₃₁	#35078	direct (N × H)
597. C₂²⋊C₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#525	2
C₂²×C₃₁×#121	2
C₃₁×#2856	2
C₃₁×#2850	2
C₃₁×#2661	2
C₃₁×#2543	2
C₃₁×#2504	2
C₃₁×#2502	2
C₃₁×#2500	2
C₃₁×#2435	2
C₃₁×#2433	2
C₃₁×#2431	2
C₃₁×#2410	2
C₃₁×#2321	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#35078	31

Subgroups — C31×#35078 #21491837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35078 #21491837