Subgroups — C₃₁×#61633 #21518392

Order 7936.

2146 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3320	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3301	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₃₁	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3265	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3188	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3010	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#448	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
17	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
18	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#560	—	2	2	no	—
20	C₃₁×#553	C₂²	1	4	yes	—
21	D₄×Q₈×C₃₁	—	2	2	no	—
22	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
23	C₃₁×#548	—	2	2	no	—
24	C₃₁×#548	C₂²	1	4	yes	complemented
25	D₄²×C₃₁	—	2	2	no	—
26	D₄²×C₃₁	C₂²	1	4	yes	—
27	C₃₁×#540	C₂²	1	2	yes	—
28	C₃₁×#538	—	2	2	no	—
29	C₃₁×#536	—	2	2	no	—
30	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#535	C₂²	1	2	yes	—
33	C₃₁×#534	—	2	2	no	—
34	C₃₁×#525	—	2	2	no	—
35	C₃₁×#525	C₂²	1	1	yes	characteristic
36	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃₁×#121	C₂²	1	2	yes	—
38	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#496	C₂²	1	2	yes	complemented
40	C₃₁×#492	C₂²	1	2	yes	complemented
41	C₃₁×#491	C₂²	1	2	yes	complemented
42	C₃₁×#488	C₂²	1	2	yes	complemented
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#484	C₂²	1	2	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#481	C₂²	1	2	yes	complemented
47	C₃₁×#479	C₂²	1	4	yes	complemented
48	C₃₁×#468	C₂²	1	4	yes	complemented
49	C₃₁×#466	C₂²	1	4	yes	complemented
50	C₃₁×#465	C₂²	1	4	yes	complemented
51	C₃₁×#465	C₂²	1	4	yes	complemented
52	C₃₁×#463	C₂²	1	4	yes	complemented
53	C₃₁×#461	C₂²	1	4	yes	complemented
54	C₃₁×#460	C₂²	1	4	yes	complemented
55	C₃₁×#450	C₂²	1	2	yes	complemented
56	C₃₁×#450	C₂²	1	4	yes	complemented
57	C₃₁×#449	C₂²	1	4	yes	complemented
58	C₃₁×#449	C₂²	1	4	yes	complemented
59	C₃₁×#448	C₂²	1	4	yes	complemented
60	C₃₁×#448	C₂²	1	4	yes	complemented
61	C₃₁×#448	C₂²	1	4	yes	complemented
62	C₃₁×#448	C₂²	1	4	yes	complemented
63	C₃₁×#448	C₂²	1	4	yes	complemented
64	C₃₁×#447	C₂²	1	2	yes	complemented
65	C₃₁×#440	C₂²	1	4	yes	complemented
66	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#435	C₂²	1	4	yes	complemented
68	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
69	C₃₁×#433	C₂²	1	2	yes	complemented
70	C₃₁×#419	C₂²	1	2	yes	complemented
71	C₃₁×#416	C₂²	1	2	yes	complemented
72	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
73	C₃₁×#408	C₂²	1	2	yes	complemented
74	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
75	C₃₁×2₋¹⁺⁴	—	4	4	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	1	no	—
78	C₂×#41×C₃₁	C₂³	1	2	yes	—
79	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₃₁	—	2	1	no	—
82	C₂²×Q₈×C₃₁	—	2	1	no	—
83	C₂²×Q₈×C₃₁	—	2	2	no	—
84	C₂²×Q₈×C₃₁	—	4	4	no	—
85	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
87	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	—	2	4	no	—
91	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	—	2	1	no	—
94	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
95	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
96	C₂×SD₁₆×C₃₁	—	4	4	no	—
97	C₂×SD₁₆×C₃₁	—	4	8	no	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×D₈×C₃₁	C₂³	1	4	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	4	no	—
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×#127	—	2	2	no	—
111	C₃₁×#127	C₂³	1	2	yes	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#125	C₂³	1	2	yes	—
114	C₃₁×#124	—	2	2	no	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	—	2	4	no	—
117	C₃₁×#124	C₂³	1	2	yes	—
118	C₃₁×#123	—	2	2	no	—
119	C₃₁×#123	—	2	1	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	2	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	D₄	1	2	yes	—
124	C₃₁×C₂²⋊Q₈	—	2	4	no	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₃₁×#121	—	2	4	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	D₄	1	2	yes	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#121	C₂³	1	4	yes	—
141	C₃₁×#121	C₂³	1	4	yes	—
142	C₃₁×#120	—	2	1	no	—
143	C₃₁×#120	—	2	2	no	—
144	C₃₁×#120	—	2	2	no	—
145	C₃₁×#120	—	2	4	no	—
146	C₃₁×#120	—	2	4	no	—
147	C₃₁×#120	D₄	1	2	yes	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	—	2	4	no	—
154	C₄×D₄×C₃₁	C₂³	1	4	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	C₂³	1	2	yes	—
158	C₃₁×#117	C₂³	1	1	yes	characteristic
159	C₃₁×#117	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
162	C₃₁×#107	C₂³	1	4	yes	—
163	C₃₁×#106	C₂³	1	4	yes	—
164	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
165	C₃₁×#103	C₂³	1	4	yes	—
166	C₃₁×#103	C₂³	1	4	yes	—
167	C₃₁×#103	C₂³	1	4	yes	—
168	C₃₁×#103	C₂³	1	4	yes	—
169	C₃₁×#103	C₂³	1	4	yes	—
170	C₃₁×#102	C₂³	1	4	yes	—
171	C₃₁×#102	C₂³	1	4	yes	—
172	C₃₁×#102	C₂³	1	4	yes	—
173	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₃₁×#97	C₂³	1	2	yes	—
178	C₄×C₈×C₃₁	C₂³	1	2	yes	—
179	C₂⁴×C₃₁	—	2	2	no	—
180	C₂⁴×C₃₁	—	2	2	no	—
181	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
182	#41×C₃₁	—	2	4	no	—
183	#41×C₃₁	—	4	2	no	—
184	#41×C₃₁	—	4	2	no	—
185	#41×C₃₁	—	4	2	no	—
186	#41×C₃₁	—	4	8	no	—
187	#41×C₃₁	—	4	4	no	—
188	C₂×Q₈×C₃₁	—	2	4	no	—
189	C₂×Q₈×C₃₁	—	2	1	no	—
190	C₂×Q₈×C₃₁	—	2	4	no	—
191	C₂×Q₈×C₃₁	—	2	1	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	8	no	—
194	C₂×Q₈×C₃₁	—	2	4	no	—
195	C₂×Q₈×C₃₁	—	4	4	no	—
196	C₂×Q₈×C₃₁	—	4	2	no	—
197	C₂×Q₈×C₃₁	—	4	2	no	—
198	C₂×Q₈×C₃₁	—	4	4	no	—
199	C₂×Q₈×C₃₁	—	4	8	no	—
200	C₂×Q₈×C₃₁	—	4	4	no	—
201	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
202	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	1	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	2	2	no	—
214	C₂×D₄×C₃₁	—	4	4	no	—
215	C₂×D₄×C₃₁	—	4	2	no	—
216	C₂×D₄×C₃₁	—	4	2	no	—
217	C₂×D₄×C₃₁	—	8	8	no	—
218	C₂×D₄×C₃₁	—	8	4	no	—
219	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₃₁	—	2	1	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	2	no	—
227	C₂²×C₄×C₃₁	—	2	1	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	1	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	—	4	2	no	—
233	C₂²×C₄×C₃₁	—	4	4	no	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	SD₁₆×C₃₁	—	2	8	no	—
240	SD₁₆×C₃₁	—	2	8	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	SD₁₆×C₃₁	—	4	4	no	—
243	SD₁₆×C₃₁	—	4	4	no	—
244	D₈×C₃₁	—	4	4	no	—
245	M₁₆×C₃₁	—	4	2	no	—
246	C₂×C₈×C₃₁	—	4	2	no	—
247	C₂×C₈×C₃₁	—	4	4	no	—
248	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
260	C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	—	2	4	no	—
274	C₄²×C₃₁	—	2	1	no	—
275	C₄²×C₃₁	—	2	2	no	—
276	C₄²×C₃₁	C₂⁴	1	2	yes	—
277	#61633	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	4	no	—
279	C₂³×C₃₁	—	2	1	no	—
280	C₂³×C₃₁	—	2	4	no	—
281	C₂³×C₃₁	—	4	1	no	—
282	C₂³×C₃₁	—	4	4	no	—
283	C₂³×C₃₁	—	8	2	no	—
284	C₂³×C₃₁	—	8	2	no	—
285	C₂³×C₃₁	—	8	2	no	—
286	C₂³×C₃₁	—	8	4	no	—
287	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
288	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
290	Q₈×C₃₁	—	2	4	no	—
291	Q₈×C₃₁	—	2	2	no	—
292	Q₈×C₃₁	—	2	4	no	—
293	Q₈×C₃₁	—	2	2	no	—
294	Q₈×C₃₁	—	4	1	no	—
295	Q₈×C₃₁	—	4	8	no	—
296	Q₈×C₃₁	—	4	4	no	—
297	Q₈×C₃₁	—	4	2	no	—
298	Q₈×C₃₁	H(5,𝔽₂)	1	4	yes	—
299	D₄×C₃₁	—	2	8	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	4	1	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	8	no	—
309	D₄×C₃₁	—	8	2	no	—
310	D₄×C₃₁	—	8	2	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	4	no	—
314	C₂×C₄×C₃₁	—	2	4	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	1	no	—
324	C₂×C₄×C₃₁	—	4	2	no	—
325	C₂×C₄×C₃₁	—	4	1	no	—
326	C₂×C₄×C₃₁	—	4	4	no	—
327	C₂×C₄×C₃₁	—	4	8	no	—
328	C₂×C₄×C₃₁	—	4	4	no	—
329	C₂×C₄×C₃₁	—	4	2	no	—
330	C₂×C₄×C₃₁	—	4	2	no	—
331	C₂×C₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	—	8	2	no	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
338	C₈×C₃₁	—	2	4	no	—
339	C₈×C₃₁	—	2	4	no	—
340	#3537	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3320	C₂×C₃₁	1	4	yes	complemented
343	#3301	C₂×C₃₁	1	4	yes	complemented
344	D₄×SD₁₆	C₂×C₃₁	1	4	yes	complemented
345	#3265	C₂×C₃₁	1	4	yes	complemented
346	#3221	C₂×C₃₁	1	2	yes	complemented
347	#3200	C₂×C₃₁	1	2	yes	complemented
348	#3188	C₂×C₃₁	1	2	yes	complemented
349	#3126	C₂×C₃₁	1	2	yes	complemented
350	#3010	C₂×C₃₁	1	2	yes	complemented
351	C₂×#448	C₂×C₃₁	1	2	yes	complemented
352	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
353	C₂²×C₃₁	—	2	2	no	—
354	C₂²×C₃₁	—	2	2	no	—
355	C₂²×C₃₁	—	2	1	no	—
356	C₂²×C₃₁	—	2	2	no	—
357	C₂²×C₃₁	—	2	4	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	4	4	no	—
360	C₂²×C₃₁	—	4	1	no	—
361	C₂²×C₃₁	—	4	4	no	—
362	C₂²×C₃₁	—	4	4	no	—
363	C₂²×C₃₁	—	4	4	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	16	4	no	—
366	C₂²×C₃₁	—	16	4	no	—
367	C₂²×C₃₁	#577	1	4	yes	—
368	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₃₁	—	2	4	no	—
370	C₄×C₃₁	—	2	1	no	—
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	2	2	no	—
373	C₄×C₃₁	—	2	4	no	—
374	C₄×C₃₁	—	4	1	no	—
375	C₄×C₃₁	—	4	2	no	—
376	C₄×C₃₁	—	4	4	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
379	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
380	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
381	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
382	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
383	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
384	#560	—	2	2	no	—
385	#553	C₂²×C₃₁	1	4	yes	—
386	D₄×Q₈	—	2	2	no	—
387	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
388	#548	—	2	2	no	—
389	#548	C₂²×C₃₁	1	4	yes	complemented
390	D₄²	—	2	2	no	—
391	D₄²	C₂²×C₃₁	1	4	yes	—
392	#540	C₂²×C₃₁	1	2	yes	—
393	#538	—	2	2	no	—
394	#536	—	2	2	no	—
395	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
397	#535	C₂²×C₃₁	1	2	yes	—
398	#534	—	2	2	no	—
399	#525	—	2	2	no	—
400	#525	C₂²×C₃₁	1	1	yes	characteristic
401	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	C₂×#121	C₂²×C₃₁	1	2	yes	—
403	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	#496	C₂²×C₃₁	1	2	yes	complemented
405	#492	C₂²×C₃₁	1	2	yes	complemented
406	#491	C₂²×C₃₁	1	2	yes	complemented
407	#488	C₂²×C₃₁	1	2	yes	complemented
408	#485	C₂²×C₃₁	1	4	yes	complemented
409	#484	C₂²×C₃₁	1	2	yes	complemented
410	#482	C₂²×C₃₁	1	4	yes	complemented
411	#481	C₂²×C₃₁	1	2	yes	complemented
412	#479	C₂²×C₃₁	1	4	yes	complemented
413	#468	C₂²×C₃₁	1	4	yes	complemented
414	#466	C₂²×C₃₁	1	4	yes	complemented
415	#465	C₂²×C₃₁	1	4	yes	complemented
416	#465	C₂²×C₃₁	1	4	yes	complemented
417	#463	C₂²×C₃₁	1	4	yes	complemented
418	#461	C₂²×C₃₁	1	4	yes	complemented
419	#460	C₂²×C₃₁	1	4	yes	complemented
420	#450	C₂²×C₃₁	1	2	yes	complemented
421	#450	C₂²×C₃₁	1	4	yes	complemented
422	#449	C₂²×C₃₁	1	4	yes	complemented
423	#449	C₂²×C₃₁	1	4	yes	complemented
424	#448	C₂²×C₃₁	1	4	yes	complemented
425	#448	C₂²×C₃₁	1	4	yes	complemented
426	#448	C₂²×C₃₁	1	4	yes	complemented
427	#448	C₂²×C₃₁	1	4	yes	complemented
428	#448	C₂²×C₃₁	1	4	yes	complemented
429	#447	C₂²×C₃₁	1	2	yes	complemented
430	#440	C₂²×C₃₁	1	4	yes	complemented
431	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
432	#435	C₂²×C₃₁	1	4	yes	complemented
433	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
434	#433	C₂²×C₃₁	1	2	yes	complemented
435	#419	C₂²×C₃₁	1	2	yes	complemented
436	#416	C₂²×C₃₁	1	2	yes	complemented
437	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
438	#408	C₂²×C₃₁	1	2	yes	complemented
439	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
440	C₂×C₃₁	—	2	4	no	—
441	C₂×C₃₁	—	4	1	no	—
442	C₂×C₃₁	—	4	2	no	—
443	C₂×C₃₁	—	8	1	no	—
444	C₂×C₃₁	—	8	4	no	—
445	C₂×C₃₁	#3484	1	1	yes	characteristic
446	C₂×C₃₁	C₂×#577	1	2	yes	—
447	2₋¹⁺⁴	—	4	4	no	—
448	C₂×#41	—	2	2	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	C₂³×C₃₁	1	2	yes	—
451	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
452	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	—	2	2	no	—
456	C₂²×Q₈	—	4	4	no	—
457	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
459	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
460	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
461	C₂²×D₄	—	2	2	no	—
462	C₂²×D₄	—	2	4	no	—
463	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
464	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
467	AGL(1,ℤ/8)	—	4	4	no	—
468	C₂×SD₁₆	—	4	4	no	—
469	C₂×SD₁₆	—	4	8	no	—
470	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
471	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
472	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
473	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×D₈	C₂³×C₃₁	1	4	yes	—
476	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
477	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
478	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
479	C₄⋊Q₈	—	2	1	no	—
480	C₄⋊Q₈	—	2	4	no	—
481	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
482	#127	—	2	2	no	—
483	#127	C₂³×C₃₁	1	2	yes	—
484	#126	—	2	4	no	—
485	#125	C₂³×C₃₁	1	2	yes	—
486	#124	—	2	2	no	—
487	#124	—	2	1	no	—
488	#124	—	2	4	no	—
489	#124	C₂³×C₃₁	1	2	yes	—
490	#123	—	2	2	no	—
491	#123	—	2	1	no	—
492	#123	—	2	4	no	—
493	#123	—	2	2	no	—
494	#123	—	2	4	no	—
495	#123	D₄×C₃₁	1	2	yes	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
501	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
502	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
503	#121	—	2	4	no	—
504	#121	—	2	4	no	—
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	—	2	4	no	—
508	#121	—	2	4	no	—
509	#121	D₄×C₃₁	1	2	yes	—
510	#121	C₂³×C₃₁	1	4	yes	—
511	#121	C₂³×C₃₁	1	4	yes	—
512	#121	C₂³×C₃₁	1	2	yes	—
513	#121	C₂³×C₃₁	1	4	yes	—
514	#120	—	2	1	no	—
515	#120	—	2	2	no	—
516	#120	—	2	2	no	—
517	#120	—	2	4	no	—
518	#120	—	2	4	no	—
519	#120	D₄×C₃₁	1	2	yes	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	C₂³×C₃₁	1	4	yes	—
527	C₄×D₄	C₂³×C₃₁	1	4	yes	—
528	#117	—	2	2	no	—
529	#117	C₂³×C₃₁	1	1	yes	characteristic
530	#117	C₂³×C₃₁	1	2	yes	—
531	#117	C₂³×C₃₁	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	#107	C₂³×C₃₁	1	4	yes	—
535	#106	C₂³×C₃₁	1	4	yes	—
536	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
537	#103	C₂³×C₃₁	1	4	yes	—
538	#103	C₂³×C₃₁	1	4	yes	—
539	#103	C₂³×C₃₁	1	4	yes	—
540	#103	C₂³×C₃₁	1	4	yes	—
541	#103	C₂³×C₃₁	1	4	yes	—
542	#102	C₂³×C₃₁	1	4	yes	—
543	#102	C₂³×C₃₁	1	4	yes	—
544	#102	C₂³×C₃₁	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
546	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
547	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
548	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
549	#97	C₂³×C₃₁	1	2	yes	—
550	C₄×C₈	C₂³×C₃₁	1	2	yes	—
551	C₃₁	#61633	1	1	yes	characteristic, direct product factor, Sylow
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
555	#41	—	2	4	no	—
556	#41	—	4	2	no	—
557	#41	—	4	2	no	—
558	#41	—	4	2	no	—
559	#41	—	4	8	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	2	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	—	4	8	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
575	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
577	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	4	4	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	8	8	no	—
591	C₂×D₄	—	8	4	no	—
592	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
593	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
594	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
595	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
596	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
608	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
612	SD₁₆	—	2	8	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	4	4	no	—
615	SD₁₆	—	4	4	no	—
616	SD₁₆	—	4	4	no	—
617	D₈	—	4	4	no	—
618	M₁₆	—	4	2	no	—
619	C₂×C₈	—	4	2	no	—
620	C₂×C₈	—	4	4	no	—
621	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
622	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
631	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
645	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂⁴×C₃₁	1	2	yes	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	2	no	—
656	C₂³	—	8	2	no	—
657	C₂³	—	8	2	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
660	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
661	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
662	Q₈	—	2	4	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	2	4	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	8	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	2	no	—
670	Q₈	C₃₁×H(5,𝔽₂)	1	4	yes	—
671	D₄	—	2	8	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
709	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
710	C₈	—	2	4	no	—
711	C₈	—	2	4	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	16	4	no	—
725	C₂²	—	16	4	no	—
726	C₂²	C₃₁×#577	1	4	yes	—
727	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	4	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
738	C₂	—	2	4	no	—
739	C₂	—	4	1	no	—
740	C₂	—	4	2	no	—
741	C₂	—	8	4	no	—
742	C₂	—	8	1	no	—
743	C₂	C₃₁×#3484	1	1	yes	characteristic
744	C₂	C₂×C₃₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3537	C₂	semidirect
2. C₃₁×#3486	C₂	semidirect
3. C₃₁×#3320	C₂	semidirect
4. C₃₁×#3301	C₂	semidirect
5. D₄×SD₁₆×C₃₁	C₂	semidirect
6. C₃₁×#3265	C₂	semidirect
7. C₃₁×#3221	C₂	semidirect
8. C₃₁×#3200	C₂	semidirect
9. C₃₁×#3188	C₂	semidirect
10. C₃₁×#3126	C₂	semidirect
11. C₃₁×#3010	C₂	semidirect
12. C₂×C₃₁×#448	C₂	semidirect
13. C₃₁×#2977	C₂	semidirect
14. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
15. C₂³×Q₈×C₃₁	C₂²	semidirect
16. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂²×SD₁₆×C₃₁	C₂²	semidirect
18. C₂²×SD₁₆×C₃₁	C₂²	semidirect
22. D₄×Q₈×C₃₁	C₂²	semidirect
24. C₃₁×#548	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
31. C₃₁×#536	C₂²	semidirect
36. C₃₁×#525	C₂²	semidirect
38. C₃₁×#519	C₂²	semidirect
39. C₃₁×#496	C₂²	semidirect
40. C₃₁×#492	C₂²	semidirect
41. C₃₁×#491	C₂²	semidirect
42. C₃₁×#488	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#484	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#481	C₂²	semidirect
47. C₃₁×#479	C₂²	semidirect
48. C₃₁×#468	C₂²	semidirect
49. C₃₁×#466	C₂²	semidirect
50. C₃₁×#465	C₂²	semidirect
51. C₃₁×#465	C₂²	semidirect
52. C₃₁×#463	C₂²	semidirect
53. C₃₁×#461	C₂²	semidirect
54. C₃₁×#460	C₂²	semidirect
55. C₃₁×#450	C₂²	semidirect
56. C₃₁×#450	C₂²	semidirect
57. C₃₁×#449	C₂²	semidirect
58. C₃₁×#449	C₂²	semidirect
59. C₃₁×#448	C₂²	semidirect
60. C₃₁×#448	C₂²	semidirect
61. C₃₁×#448	C₂²	semidirect
62. C₃₁×#448	C₂²	semidirect
63. C₃₁×#448	C₂²	semidirect
64. C₃₁×#447	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₄×SD₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#435	C₂²	semidirect
68. C₈×D₄×C₃₁	C₂²	semidirect
69. C₃₁×#433	C₂²	semidirect
70. C₃₁×#419	C₂²	semidirect
71. C₃₁×#416	C₂²	semidirect
72. C₂×C₃₁×#103	C₂²	semidirect
73. C₃₁×#408	C₂²	semidirect
74. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
277. #61633	C₃₁	direct (N × H)
340. #3537	C₂×C₃₁	semidirect
341. #3486	C₂×C₃₁	semidirect
342. #3320	C₂×C₃₁	semidirect
343. #3301	C₂×C₃₁	semidirect
344. D₄×SD₁₆	C₂×C₃₁	semidirect
345. #3265	C₂×C₃₁	semidirect
346. #3221	C₂×C₃₁	semidirect
347. #3200	C₂×C₃₁	semidirect
348. #3188	C₂×C₃₁	semidirect
349. #3126	C₂×C₃₁	semidirect
350. #3010	C₂×C₃₁	semidirect
351. C₂×#448	C₂×C₃₁	semidirect
352. #2977	C₂×C₃₁	semidirect
379. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
380. C₂³×Q₈	C₂²×C₃₁	semidirect
381. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
382. C₂²×SD₁₆	C₂²×C₃₁	semidirect
383. C₂²×SD₁₆	C₂²×C₃₁	semidirect
387. D₄×Q₈	C₂²×C₃₁	semidirect
389. #548	C₂²×C₃₁	semidirect
395. #536	C₂²×C₃₁	semidirect
396. #536	C₂²×C₃₁	semidirect
401. #525	C₂²×C₃₁	semidirect
403. #519	C₂²×C₃₁	semidirect
404. #496	C₂²×C₃₁	semidirect
405. #492	C₂²×C₃₁	semidirect
406. #491	C₂²×C₃₁	semidirect
407. #488	C₂²×C₃₁	semidirect
408. #485	C₂²×C₃₁	semidirect
409. #484	C₂²×C₃₁	semidirect
410. #482	C₂²×C₃₁	semidirect
411. #481	C₂²×C₃₁	semidirect
412. #479	C₂²×C₃₁	semidirect
413. #468	C₂²×C₃₁	semidirect
414. #466	C₂²×C₃₁	semidirect
415. #465	C₂²×C₃₁	semidirect
416. #465	C₂²×C₃₁	semidirect
417. #463	C₂²×C₃₁	semidirect
418. #461	C₂²×C₃₁	semidirect
419. #460	C₂²×C₃₁	semidirect
420. #450	C₂²×C₃₁	semidirect
421. #450	C₂²×C₃₁	semidirect
422. #449	C₂²×C₃₁	semidirect
423. #449	C₂²×C₃₁	semidirect
424. #448	C₂²×C₃₁	semidirect
425. #448	C₂²×C₃₁	semidirect
426. #448	C₂²×C₃₁	semidirect
427. #448	C₂²×C₃₁	semidirect
428. #448	C₂²×C₃₁	semidirect
429. #447	C₂²×C₃₁	semidirect
430. #440	C₂²×C₃₁	semidirect
431. C₄×SD₁₆	C₂²×C₃₁	semidirect
432. #435	C₂²×C₃₁	semidirect
433. C₈×D₄	C₂²×C₃₁	semidirect
434. #433	C₂²×C₃₁	semidirect
435. #419	C₂²×C₃₁	semidirect
436. #416	C₂²×C₃₁	semidirect
437. C₂×#103	C₂²×C₃₁	semidirect
438. #408	C₂²×C₃₁	semidirect
439. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
551. C₃₁	#61633	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3537	2
C₃₁×#3486	2
C₃₁×#3320	2
C₃₁×#3301	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3265	2
C₃₁×#3221	2
C₃₁×#3200	2
C₃₁×#3188	2
C₃₁×#3126	2
C₃₁×#3010	2
C₂×C₃₁×#448	2
C₃₁×#2977	2
#61633	31

Subgroups — C31×#61633 #21518392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61633 #21518392