Subgroups — C₃₁×#36719 #21493478

Order 7936.

2490 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2847	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2704	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2702	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2683	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2681	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2618	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2534	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2413	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2411	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2409	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2316	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#539	—	2	8	no	—
19	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
20	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#123	C₂²	1	2	yes	—
22	C₂×C₃₁×#123	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
24	C₂×C₃₁×C₂²⋊Q₈	—	2	8	no	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
31	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#121	C₂²	1	2	yes	—
33	C₂×C₃₁×#120	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₃₁×#117	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#400	C₂²	1	2	yes	complemented
42	C₃₁×#398	C₂²	1	2	yes	complemented
43	C₃₁×#398	C₂²	1	4	yes	complemented
44	C₃₁×#398	C₂²	1	4	yes	complemented
45	C₃₁×#396	C₂²	1	4	yes	—
46	C₃₁×#396	C₂²	1	4	yes	—
47	C₃₁×#396	C₂²	1	4	yes	complemented
48	C₃₁×#396	C₂²	1	4	yes	complemented
49	C₃₁×#395	C₂²	1	2	yes	complemented
50	C₃₁×#395	C₂²	1	4	yes	complemented
51	C₃₁×#394	C₂²	1	4	yes	—
52	C₃₁×#394	C₂²	1	4	yes	—
53	C₃₁×#394	C₂²	1	2	yes	complemented
54	C₃₁×#393	C₂²	1	4	yes	complemented
55	C₃₁×#391	C₂²	1	4	yes	complemented
56	C₃₁×#390	C₂²	1	4	yes	—
57	C₃₁×#389	C₂²	1	4	yes	complemented
58	C₃₁×#389	C₂²	1	4	yes	complemented
59	C₃₁×#389	C₂²	1	4	yes	complemented
60	C₃₁×#388	C₂²	1	4	yes	—
61	C₃₁×#388	C₂²	1	4	yes	—
62	C₃₁×#388	C₂²	1	4	yes	complemented
63	C₃₁×#386	C₂²	1	2	yes	—
64	C₃₁×#386	C₂²	1	4	yes	—
65	C₃₁×#386	C₂²	1	2	yes	—
66	C₃₁×#386	C₂²	1	4	yes	—
67	C₃₁×#385	C₂²	1	2	yes	—
68	C₃₁×#385	C₂²	1	4	yes	—
69	C₃₁×#385	C₂²	1	2	yes	—
70	C₃₁×#381	C₂²	1	2	yes	—
71	C₃₁×#380	C₂²	1	1	yes	characteristic
72	C₃₁×#380	C₂²	1	1	yes	characteristic
73	C₃₁×#380	C₂²	1	2	yes	—
74	C₃₁×#380	C₂²	1	2	yes	—
75	C₃₁×#380	C₂²	1	2	yes	—
76	C₃₁×#379	C₂²	1	2	yes	—
77	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₃₁	—	2	4	no	—
79	C₂²×Q₈×C₃₁	—	4	4	no	—
80	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
81	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
84	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₃₁	—	2	4	no	—
86	C₂³×C₄×C₃₁	—	4	4	no	—
87	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₃₁×#126	—	2	8	no	—
97	C₃₁×#125	—	2	8	no	—
98	C₃₁×#123	—	2	8	no	—
99	C₃₁×#123	—	2	8	no	—
100	C₃₁×#123	—	4	4	no	—
101	C₃₁×C₂²⋊Q₈	—	2	4	no	—
102	C₃₁×C₂²⋊Q₈	—	2	16	no	—
103	C₃₁×C₂²⋊Q₈	—	2	16	no	—
104	C₃₁×C₂²⋊Q₈	—	2	8	no	—
105	C₃₁×C₂²⋊Q₈	—	4	8	no	—
106	C₃₁×C₂²⋊Q₈	—	4	4	no	—
107	C₃₁×#121	—	2	4	no	—
108	C₃₁×#121	—	4	4	no	—
109	C₃₁×#120	—	4	4	no	—
110	C₄×D₄×C₃₁	—	2	8	no	—
111	C₃₁×#117	—	4	4	no	—
112	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
133	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
144	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
150	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
152	C₃₁×#95	C₂³	1	4	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	4	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	2	yes	—
161	C₂⁴×C₃₁	—	2	2	no	—
162	C₂⁴×C₃₁	—	2	4	no	—
163	C₂⁴×C₃₁	—	2	2	no	—
164	C₂⁴×C₃₁	—	2	2	no	—
165	C₂⁴×C₃₁	—	4	2	no	—
166	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
167	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
168	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
169	C₂×Q₈×C₃₁	—	2	8	no	—
170	C₂×Q₈×C₃₁	—	2	2	no	—
171	C₂×Q₈×C₃₁	—	2	8	no	—
172	C₂×Q₈×C₃₁	—	4	4	no	—
173	C₂×Q₈×C₃₁	—	4	2	no	—
174	C₂×Q₈×C₃₁	—	4	16	no	—
175	C₂×D₄×C₃₁	—	2	4	no	—
176	C₂×D₄×C₃₁	—	2	4	no	—
177	C₂×D₄×C₃₁	—	2	4	no	—
178	C₂×D₄×C₃₁	—	2	8	no	—
179	C₂×D₄×C₃₁	—	2	2	no	—
180	C₂×D₄×C₃₁	—	4	4	no	—
181	C₂×D₄×C₃₁	—	4	2	no	—
182	C₂×D₄×C₃₁	—	4	4	no	—
183	C₂²×C₄×C₃₁	—	2	2	no	—
184	C₂²×C₄×C₃₁	—	2	2	no	—
185	C₂²×C₄×C₃₁	—	2	2	no	—
186	C₂²×C₄×C₃₁	—	2	4	no	—
187	C₂²×C₄×C₃₁	—	2	2	no	—
188	C₂²×C₄×C₃₁	—	2	2	no	—
189	C₂²×C₄×C₃₁	—	2	2	no	—
190	C₂²×C₄×C₃₁	—	2	2	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
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	—	4	2	no	—
197	C₂²×C₄×C₃₁	—	4	2	no	—
198	C₂²×C₄×C₃₁	—	4	2	no	—
199	C₂²×C₄×C₃₁	—	4	2	no	—
200	C₂²×C₄×C₃₁	—	4	2	no	—
201	C₂²×C₄×C₃₁	—	4	4	no	—
202	C₂²×C₄×C₃₁	—	4	16	no	—
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	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
218	C₄⋊C₄×C₃₁	—	2	8	no	—
219	C₄⋊C₄×C₃₁	—	2	4	no	—
220	C₄⋊C₄×C₃₁	—	2	4	no	—
221	C₄⋊C₄×C₃₁	—	2	4	no	—
222	C₄⋊C₄×C₃₁	—	2	2	no	—
223	C₄⋊C₄×C₃₁	—	2	4	no	—
224	C₄⋊C₄×C₃₁	—	2	4	no	—
225	C₄⋊C₄×C₃₁	—	2	2	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	8	no	—
228	C₄⋊C₄×C₃₁	—	4	4	no	—
229	C₄⋊C₄×C₃₁	—	4	2	no	—
230	C₄⋊C₄×C₃₁	—	4	2	no	—
231	C₄⋊C₄×C₃₁	—	4	4	no	—
232	C₄⋊C₄×C₃₁	—	4	4	no	—
233	C₄⋊C₄×C₃₁	—	4	4	no	—
234	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
235	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
236	C₂²⋊C₄×C₃₁	—	2	4	no	—
237	C₂²⋊C₄×C₃₁	—	2	4	no	—
238	C₂²⋊C₄×C₃₁	—	2	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	8	no	—
240	C₂²⋊C₄×C₃₁	—	2	8	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	8	no	—
247	C₂²⋊C₄×C₃₁	—	4	4	no	—
248	C₂²⋊C₄×C₃₁	—	4	4	no	—
249	C₂²⋊C₄×C₃₁	—	4	4	no	—
250	C₂²⋊C₄×C₃₁	—	4	4	no	—
251	C₄²×C₃₁	—	2	4	no	—
252	C₄²×C₃₁	—	4	4	no	—
253	#36719	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₃₁	—	2	2	no	—
255	C₂³×C₃₁	—	2	2	no	—
256	C₂³×C₃₁	—	2	8	no	—
257	C₂³×C₃₁	—	2	2	no	—
258	C₂³×C₃₁	—	2	2	no	—
259	C₂³×C₃₁	—	2	2	no	—
260	C₂³×C₃₁	—	2	2	no	—
261	C₂³×C₃₁	—	2	2	no	—
262	C₂³×C₃₁	—	2	2	no	—
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	2	4	no	—
265	C₂³×C₃₁	—	2	2	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	4	no	—
268	C₂³×C₃₁	—	4	8	no	—
269	C₂³×C₃₁	—	4	8	no	—
270	C₂³×C₃₁	—	4	4	no	—
271	C₂³×C₃₁	—	4	4	no	—
272	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
273	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
274	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
275	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
276	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
277	Q₈×C₃₁	—	4	16	no	—
278	Q₈×C₃₁	—	8	2	no	—
279	D₄×C₃₁	—	4	8	no	—
280	D₄×C₃₁	—	8	2	no	—
281	D₄×C₃₁	—	8	8	no	—
282	C₂×C₄×C₃₁	—	2	8	no	—
283	C₂×C₄×C₃₁	—	2	8	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	2	no	—
288	C₂×C₄×C₃₁	—	2	4	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	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	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	4	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	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	4	no	—
309	C₂×C₄×C₃₁	—	4	4	no	—
310	C₂×C₄×C₃₁	—	4	4	no	—
311	C₂×C₄×C₃₁	—	4	8	no	—
312	C₂×C₄×C₃₁	—	4	8	no	—
313	C₂×C₄×C₃₁	—	4	4	no	—
314	C₂×C₄×C₃₁	—	4	4	no	—
315	C₂×C₄×C₃₁	—	8	4	no	—
316	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
321	C₂×#539	C₂×C₃₁	1	1	yes	characteristic, complemented
322	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
323	#2848	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#2847	C₂×C₃₁	1	1	yes	characteristic
325	#2704	C₂×C₃₁	1	4	yes	complemented
326	#2702	C₂×C₃₁	1	4	yes	complemented
327	#2683	C₂×C₃₁	1	4	yes	complemented
328	#2681	C₂×C₃₁	1	4	yes	complemented
329	#2627	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#2618	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#2534	C₂×C₃₁	1	2	yes	complemented
332	#2413	C₂×C₃₁	1	2	yes	complemented
333	#2411	C₂×C₃₁	1	2	yes	complemented
334	#2409	C₂×C₃₁	1	2	yes	complemented
335	#2316	C₂×C₃₁	1	1	yes	characteristic, complemented
336	C₂²×C₃₁	—	2	2	no	—
337	C₂²×C₃₁	—	2	2	no	—
338	C₂²×C₃₁	—	2	4	no	—
339	C₂²×C₃₁	—	2	4	no	—
340	C₂²×C₃₁	—	2	4	no	—
341	C₂²×C₃₁	—	2	4	no	—
342	C₂²×C₃₁	—	2	4	no	—
343	C₂²×C₃₁	—	4	16	no	—
344	C₂²×C₃₁	—	4	2	no	—
345	C₂²×C₃₁	—	4	2	no	—
346	C₂²×C₃₁	—	4	2	no	—
347	C₂²×C₃₁	—	4	2	no	—
348	C₂²×C₃₁	—	4	2	no	—
349	C₂²×C₃₁	—	4	2	no	—
350	C₂²×C₃₁	—	4	2	no	—
351	C₂²×C₃₁	—	4	4	no	—
352	C₂²×C₃₁	—	4	4	no	—
353	C₂²×C₃₁	#537	1	4	yes	—
354	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
355	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
357	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
358	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
359	C₄×C₃₁	—	2	4	no	—
360	C₄×C₃₁	—	2	4	no	—
361	C₄×C₃₁	—	2	2	no	—
362	C₄×C₃₁	—	2	2	no	—
363	C₄×C₃₁	—	2	4	no	—
364	C₄×C₃₁	—	4	2	no	—
365	C₄×C₃₁	—	4	2	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	4	no	—
370	C₄×C₃₁	—	4	4	no	—
371	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
372	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
373	#539	—	2	8	no	—
374	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
375	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
376	C₂×#123	C₂²×C₃₁	1	2	yes	—
377	C₂×#123	C₂²×C₃₁	1	2	yes	—
378	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
379	C₂×C₂²⋊Q₈	—	2	8	no	—
380	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
382	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
383	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
384	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
385	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
386	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
387	C₂×#121	C₂²×C₃₁	1	2	yes	—
388	C₂×#120	C₂²×C₃₁	1	2	yes	—
389	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
390	C₂×#117	C₂²×C₃₁	1	2	yes	—
391	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
396	#400	C₂²×C₃₁	1	2	yes	complemented
397	#398	C₂²×C₃₁	1	2	yes	complemented
398	#398	C₂²×C₃₁	1	4	yes	complemented
399	#398	C₂²×C₃₁	1	4	yes	complemented
400	#396	C₂²×C₃₁	1	4	yes	—
401	#396	C₂²×C₃₁	1	4	yes	—
402	#396	C₂²×C₃₁	1	4	yes	complemented
403	#396	C₂²×C₃₁	1	4	yes	complemented
404	#395	C₂²×C₃₁	1	2	yes	complemented
405	#395	C₂²×C₃₁	1	4	yes	complemented
406	#394	C₂²×C₃₁	1	4	yes	—
407	#394	C₂²×C₃₁	1	4	yes	—
408	#394	C₂²×C₃₁	1	2	yes	complemented
409	#393	C₂²×C₃₁	1	4	yes	complemented
410	#391	C₂²×C₃₁	1	4	yes	complemented
411	#390	C₂²×C₃₁	1	4	yes	—
412	#389	C₂²×C₃₁	1	4	yes	complemented
413	#389	C₂²×C₃₁	1	4	yes	complemented
414	#389	C₂²×C₃₁	1	4	yes	complemented
415	#388	C₂²×C₃₁	1	4	yes	—
416	#388	C₂²×C₃₁	1	4	yes	—
417	#388	C₂²×C₃₁	1	4	yes	complemented
418	#386	C₂²×C₃₁	1	2	yes	—
419	#386	C₂²×C₃₁	1	4	yes	—
420	#386	C₂²×C₃₁	1	2	yes	—
421	#386	C₂²×C₃₁	1	4	yes	—
422	#385	C₂²×C₃₁	1	2	yes	—
423	#385	C₂²×C₃₁	1	4	yes	—
424	#385	C₂²×C₃₁	1	2	yes	—
425	#381	C₂²×C₃₁	1	2	yes	—
426	#380	C₂²×C₃₁	1	1	yes	characteristic
427	#380	C₂²×C₃₁	1	1	yes	characteristic
428	#380	C₂²×C₃₁	1	2	yes	—
429	#380	C₂²×C₃₁	1	2	yes	—
430	#380	C₂²×C₃₁	1	2	yes	—
431	#379	C₂²×C₃₁	1	2	yes	—
432	C₂×C₃₁	—	2	4	no	—
433	C₂×C₃₁	—	4	4	no	—
434	C₂×C₃₁	—	8	2	no	—
435	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
436	C₂×C₃₁	#3484	1	1	yes	characteristic
437	C₂×C₃₁	#3486	1	1	yes	characteristic
438	C₂×C₃₁	#3536	1	2	yes	—
439	C₂×C₃₁	#3538	1	2	yes	—
440	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
441	C₂²×Q₈	—	2	4	no	—
442	C₂²×Q₈	—	4	4	no	—
443	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
444	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
446	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
447	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
448	C₂³×C₄	—	2	4	no	—
449	C₂³×C₄	—	4	4	no	—
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	2	yes	—
457	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
459	#126	—	2	8	no	—
460	#125	—	2	8	no	—
461	#123	—	2	8	no	—
462	#123	—	2	8	no	—
463	#123	—	4	4	no	—
464	C₂²⋊Q₈	—	2	4	no	—
465	C₂²⋊Q₈	—	2	16	no	—
466	C₂²⋊Q₈	—	2	16	no	—
467	C₂²⋊Q₈	—	2	8	no	—
468	C₂²⋊Q₈	—	4	8	no	—
469	C₂²⋊Q₈	—	4	4	no	—
470	#121	—	2	4	no	—
471	#121	—	4	4	no	—
472	#120	—	4	4	no	—
473	C₄×D₄	—	2	8	no	—
474	#117	—	4	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
478	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
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	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	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	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
496	C₂×C₂²⋊C₄	—	2	4	no	—
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	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	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
513	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
514	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
515	#95	C₂³×C₃₁	1	4	yes	—
516	#95	C₂³×C₃₁	1	2	yes	—
517	#95	C₂³×C₃₁	1	2	yes	—
518	#95	C₂³×C₃₁	1	4	yes	—
519	#95	C₂³×C₃₁	1	4	yes	—
520	#95	C₂³×C₃₁	1	4	yes	—
521	#95	C₂³×C₃₁	1	4	yes	—
522	#95	C₂³×C₃₁	1	4	yes	—
523	#95	C₂³×C₃₁	1	4	yes	—
524	C₃₁	#36719	1	1	yes	characteristic, direct product factor, Sylow
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
531	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
532	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
533	C₂×Q₈	—	2	8	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	8	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	16	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	4	no	—
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	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	16	no	—
567	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	4	4	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	4	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
599	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	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	8	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	4	4	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	8	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	4	8	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	4	4	no	—
635	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
636	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
637	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
638	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
639	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
640	Q₈	—	4	16	no	—
641	Q₈	—	8	2	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	2	no	—
644	D₄	—	8	8	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	4	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	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	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	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	8	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
681	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
683	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	16	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	C₃₁×#537	1	4	yes	—
702	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
703	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
705	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
706	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	4	no	—
718	C₄	—	4	4	no	—
719	C₂	—	2	4	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
723	C₂	C₃₁×#3484	1	1	yes	characteristic
724	C₂	C₃₁×#3486	1	1	yes	characteristic
725	C₂	C₃₁×#3536	1	2	yes	—
726	C₂	C₃₁×#3538	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₃₁×#2847	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#539	C₂	semidirect
2. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
3. C₃₁×#2848	C₂	semidirect
5. C₃₁×#2704	C₂	semidirect
6. C₃₁×#2702	C₂	semidirect
7. C₃₁×#2683	C₂	semidirect
8. C₃₁×#2681	C₂	semidirect
9. C₃₁×#2627	C₂	semidirect
10. C₃₁×#2618	C₂	semidirect
11. C₃₁×#2534	C₂	semidirect
12. C₃₁×#2413	C₂	semidirect
13. C₃₁×#2411	C₂	semidirect
14. C₃₁×#2409	C₂	semidirect
15. C₃₁×#2316	C₂	semidirect
19. C₂×C₃₁×#126	C₂²	semidirect
20. C₂×C₃₁×#125	C₂²	semidirect
23. C₂×C₃₁×#123	C₂²	semidirect
29. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
30. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
41. C₃₁×#400	C₂²	semidirect
42. C₃₁×#398	C₂²	semidirect
43. C₃₁×#398	C₂²	semidirect
44. C₃₁×#398	C₂²	semidirect
47. C₃₁×#396	C₂²	semidirect
48. C₃₁×#396	C₂²	semidirect
49. C₃₁×#395	C₂²	semidirect
50. C₃₁×#395	C₂²	semidirect
53. C₃₁×#394	C₂²	semidirect
54. C₃₁×#393	C₂²	semidirect
55. C₃₁×#391	C₂²	semidirect
57. C₃₁×#389	C₂²	semidirect
58. C₃₁×#389	C₂²	semidirect
59. C₃₁×#389	C₂²	semidirect
62. C₃₁×#388	C₂²	semidirect
114. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
253. #36719	C₃₁	direct (N × H)
321. C₂×#539	C₂×C₃₁	semidirect
322. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
323. #2848	C₂×C₃₁	semidirect
325. #2704	C₂×C₃₁	semidirect
326. #2702	C₂×C₃₁	semidirect
327. #2683	C₂×C₃₁	semidirect
328. #2681	C₂×C₃₁	semidirect
329. #2627	C₂×C₃₁	semidirect
330. #2618	C₂×C₃₁	semidirect
331. #2534	C₂×C₃₁	semidirect
332. #2413	C₂×C₃₁	semidirect
333. #2411	C₂×C₃₁	semidirect
334. #2409	C₂×C₃₁	semidirect
335. #2316	C₂×C₃₁	semidirect
374. C₂×#126	C₂²×C₃₁	semidirect
375. C₂×#125	C₂²×C₃₁	semidirect
378. C₂×#123	C₂²×C₃₁	semidirect
384. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
385. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
396. #400	C₂²×C₃₁	semidirect
397. #398	C₂²×C₃₁	semidirect
398. #398	C₂²×C₃₁	semidirect
399. #398	C₂²×C₃₁	semidirect
402. #396	C₂²×C₃₁	semidirect
403. #396	C₂²×C₃₁	semidirect
404. #395	C₂²×C₃₁	semidirect
405. #395	C₂²×C₃₁	semidirect
408. #394	C₂²×C₃₁	semidirect
409. #393	C₂²×C₃₁	semidirect
410. #391	C₂²×C₃₁	semidirect
412. #389	C₂²×C₃₁	semidirect
413. #389	C₂²×C₃₁	semidirect
414. #389	C₂²×C₃₁	semidirect
417. #388	C₂²×C₃₁	semidirect
477. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
524. C₃₁	#36719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#539	2
C₂²×C₃₁×C₂²⋊Q₈	2
C₃₁×#2848	2
C₃₁×#2847	2
C₃₁×#2704	2
C₃₁×#2702	2
C₃₁×#2683	2
C₃₁×#2681	2
C₃₁×#2627	2
C₃₁×#2618	2
C₃₁×#2534	2
C₃₁×#2413	2
C₃₁×#2411	2
C₃₁×#2409	2
C₃₁×#2316	2
#36719	31

Subgroups — C31×#36719 #21493478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36719 #21493478