Subgroups — C₃₁×#61648 #21518407

Order 7936.

2170 conjugacy classes of subgroups.

The subgroup lattice has 760 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×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3322	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3307	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3272	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3264	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×#3194	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3008	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3006	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
18	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#560	—	2	2	no	—
20	C₃₁×#553	C₂²	1	4	yes	complemented
21	C₃₁×#547	—	2	2	no	—
22	C₃₁×#547	C₂²	1	4	yes	complemented
23	C₃₁×#546	—	2	2	no	—
24	C₃₁×#546	C₂²	1	4	yes	complemented
25	D₄²×C₃₁	—	2	2	no	—
26	D₄²×C₃₁	C₂²	1	4	yes	complemented
27	C₃₁×#540	C₂²	1	2	yes	complemented
28	C₃₁×#538	—	2	2	no	—
29	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#535	C₂²	1	2	yes	—
32	C₃₁×#534	—	2	2	no	—
33	C₃₁×#534	—	2	2	no	—
34	C₃₁×#525	C₂²	1	1	yes	characteristic
35	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃₁×#123	—	2	2	no	—
37	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
38	C₃₁×#518	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×#483	C₂²	1	2	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#480	C₂²	1	2	yes	complemented
47	C₃₁×#478	C₂²	1	4	yes	complemented
48	C₃₁×#469	C₂²	1	4	yes	complemented
49	C₃₁×#468	C₂²	1	4	yes	complemented
50	C₃₁×#468	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×#459	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×#449	C₂²	1	4	yes	complemented
60	C₃₁×#449	C₂²	1	4	yes	complemented
61	C₃₁×#448	C₂²	1	4	yes	complemented
62	C₃₁×#447	C₂²	1	4	yes	complemented
63	C₃₁×#447	C₂²	1	2	yes	complemented
64	C₃₁×#447	C₂²	1	4	yes	complemented
65	C₃₁×#442	C₂²	1	4	yes	complemented
66	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	4	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	complemented
69	C₃₁×#433	C₂²	1	2	yes	complemented
70	C₃₁×#418	C₂²	1	2	yes	complemented
71	C₃₁×#417	C₂²	1	4	yes	complemented
72	C₃₁×#416	C₂²	1	2	yes	complemented
73	C₃₁×#408	C₂²	1	2	yes	complemented
74	C₃₁×#407	C₂²	1	2	yes	complemented
75	C₃₁×H(5,𝔽₂)	—	4	4	no	—
76	C₂×#41×C₃₁	—	2	1	no	—
77	C₂×#41×C₃₁	—	2	2	no	—
78	C₂×#41×C₃₁	—	4	4	no	—
79	C₂×#41×C₃₁	C₂³	1	2	yes	—
80	C₂×#41×C₃₁	C₂³	1	4	yes	—
81	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
82	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₃₁	—	2	1	no	—
85	C₂²×D₄×C₃₁	—	2	2	no	—
86	C₂²×D₄×C₃₁	—	2	2	no	—
87	C₂²×D₄×C₃₁	—	2	1	no	—
88	C₂²×D₄×C₃₁	—	2	4	no	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
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	8	no	—
96	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
100	C₂×D₈×C₃₁	—	4	4	no	—
101	C₂×D₈×C₃₁	C₂³	1	4	yes	—
102	C₂×D₈×C₃₁	C₂³	1	4	yes	—
103	C₂×D₈×C₃₁	C₂³	1	4	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×#127	—	2	2	no	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#125	C₂³	1	2	yes	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	1	no	—
115	C₃₁×#124	C₂³	1	2	yes	—
116	C₃₁×#123	—	2	2	no	—
117	C₃₁×#123	—	2	1	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	2	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×#123	D₄	1	2	yes	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
127	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	4	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	D₄	1	2	yes	—
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#121	C₂³	1	2	yes	—
140	C₃₁×#121	C₂³	1	4	yes	—
141	C₃₁×#120	—	2	1	no	—
142	C₃₁×#120	—	2	2	no	—
143	C₃₁×#120	—	2	4	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×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	4	no	—
151	C₄×D₄×C₃₁	C₂³	1	4	yes	—
152	C₄×D₄×C₃₁	C₂³	1	4	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₃₁×#117	C₂³	1	2	yes	—
155	C₃₁×#117	C₂³	1	1	yes	characteristic
156	C₃₁×#117	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
158	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	4	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×#102	C₂³	1	4	yes	—
169	C₃₁×#102	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	1	no	—
180	C₂⁴×C₃₁	—	2	2	no	—
181	C₂⁴×C₃₁	—	2	2	no	—
182	C₂⁴×C₃₁	—	2	2	no	—
183	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
184	#41×C₃₁	—	2	8	no	—
185	#41×C₃₁	—	2	4	no	—
186	#41×C₃₁	—	4	2	no	—
187	#41×C₃₁	—	4	4	no	—
188	#41×C₃₁	—	4	2	no	—
189	#41×C₃₁	—	4	2	no	—
190	#41×C₃₁	—	4	8	no	—
191	#41×C₃₁	—	4	4	no	—
192	C₂×Q₈×C₃₁	—	2	1	no	—
193	C₂×Q₈×C₃₁	—	4	2	no	—
194	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
197	C₂×D₄×C₃₁	—	2	4	no	—
198	C₂×D₄×C₃₁	—	2	4	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	1	no	—
202	C₂×D₄×C₃₁	—	2	2	no	—
203	C₂×D₄×C₃₁	—	2	2	no	—
204	C₂×D₄×C₃₁	—	2	4	no	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	1	no	—
207	C₂×D₄×C₃₁	—	2	2	no	—
208	C₂×D₄×C₃₁	—	2	2	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	4	2	no	—
212	C₂×D₄×C₃₁	—	4	2	no	—
213	C₂×D₄×C₃₁	—	4	4	no	—
214	C₂×D₄×C₃₁	—	4	2	no	—
215	C₂×D₄×C₃₁	—	4	4	no	—
216	C₂×D₄×C₃₁	—	4	4	no	—
217	C₂×D₄×C₃₁	—	4	8	no	—
218	C₂×D₄×C₃₁	—	8	8	no	—
219	C₂×D₄×C₃₁	—	8	4	no	—
220	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
225	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₃₁	—	2	1	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	4	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	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	4	2	no	—
234	C₂²×C₄×C₃₁	—	4	4	no	—
235	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
240	SD₁₆×C₃₁	—	4	4	no	—
241	SD₁₆×C₃₁	—	4	4	no	—
242	SD₁₆×C₃₁	—	4	4	no	—
243	D₈×C₃₁	—	2	8	no	—
244	D₈×C₃₁	—	2	8	no	—
245	D₈×C₃₁	—	4	4	no	—
246	M₁₆×C₃₁	—	4	4	no	—
247	M₁₆×C₃₁	—	4	2	no	—
248	C₂×C₈×C₃₁	—	4	2	no	—
249	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
250	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	4	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	2	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	4	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	2	no	—
264	C₂²⋊C₄×C₃₁	—	2	2	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	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
274	C₄²×C₃₁	—	2	1	no	—
275	C₄²×C₃₁	—	2	2	no	—
276	C₄²×C₃₁	C₂⁴	1	2	yes	—
277	#61648	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₃₁	—	2	4	no	—
279	C₂³×C₃₁	—	2	2	no	—
280	C₂³×C₃₁	—	2	1	no	—
281	C₂³×C₃₁	—	2	4	no	—
282	C₂³×C₃₁	—	4	1	no	—
283	C₂³×C₃₁	—	4	2	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	—	4	4	no	—
286	C₂³×C₃₁	—	8	2	no	—
287	C₂³×C₃₁	—	8	2	no	—
288	C₂³×C₃₁	—	8	2	no	—
289	C₂³×C₃₁	—	8	2	no	—
290	C₂³×C₃₁	—	8	4	no	—
291	C₂³×C₃₁	—	8	4	no	—
292	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
293	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
294	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₃₁	—	2	4	no	—
296	Q₈×C₃₁	—	2	2	no	—
297	Q₈×C₃₁	—	4	1	no	—
298	Q₈×C₃₁	—	4	2	no	—
299	D₄×C₃₁	—	2	4	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	4	1	no	—
305	D₄×C₃₁	—	4	2	no	—
306	D₄×C₃₁	—	4	4	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	4	2	no	—
311	D₄×C₃₁	—	4	8	no	—
312	D₄×C₃₁	—	8	2	no	—
313	D₄×C₃₁	—	8	2	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	2	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	—	8	4	no	—
318	D₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	1	no	—
327	C₂×C₄×C₃₁	—	4	1	no	—
328	C₂×C₄×C₃₁	—	4	2	no	—
329	C₂×C₄×C₃₁	—	4	8	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	4	2	no	—
332	C₂×C₄×C₃₁	—	4	2	no	—
333	C₂×C₄×C₃₁	—	8	4	no	—
334	C₂×C₄×C₃₁	—	8	4	no	—
335	C₂×C₄×C₃₁	—	8	2	no	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
341	C₈×C₃₁	—	2	4	no	—
342	C₈×C₃₁	—	2	4	no	—
343	#3537	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3485	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3322	C₂×C₃₁	1	4	yes	complemented
346	#3307	C₂×C₃₁	1	4	yes	complemented
347	#3272	C₂×C₃₁	1	4	yes	complemented
348	#3264	C₂×C₃₁	1	4	yes	complemented
349	#3221	C₂×C₃₁	1	2	yes	complemented
350	#3200	C₂×C₃₁	1	2	yes	complemented
351	#3194	C₂×C₃₁	1	2	yes	complemented
352	#3122	C₂×C₃₁	1	2	yes	complemented
353	#3008	C₂×C₃₁	1	2	yes	complemented
354	#3006	C₂×C₃₁	1	2	yes	complemented
355	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂²×C₃₁	—	2	2	no	—
357	C₂²×C₃₁	—	2	2	no	—
358	C₂²×C₃₁	—	2	4	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	2	no	—
363	C₂²×C₃₁	—	2	4	no	—
364	C₂²×C₃₁	—	4	4	no	—
365	C₂²×C₃₁	—	4	4	no	—
366	C₂²×C₃₁	—	4	4	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	1	no	—
369	C₂²×C₃₁	—	4	4	no	—
370	C₂²×C₃₁	—	8	4	no	—
371	C₂²×C₃₁	—	8	2	no	—
372	C₂²×C₃₁	—	16	4	no	—
373	C₂²×C₃₁	—	16	4	no	—
374	C₂²×C₃₁	—	16	4	no	—
375	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₃₁	—	2	4	no	—
377	C₄×C₃₁	—	2	2	no	—
378	C₄×C₃₁	—	2	1	no	—
379	C₄×C₃₁	—	2	2	no	—
380	C₄×C₃₁	—	4	4	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	1	no	—
383	C₄×C₃₁	—	4	2	no	—
384	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
385	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic, complemented
386	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
387	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
388	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
389	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
390	#560	—	2	2	no	—
391	#553	C₂²×C₃₁	1	4	yes	complemented
392	#547	—	2	2	no	—
393	#547	C₂²×C₃₁	1	4	yes	complemented
394	#546	—	2	2	no	—
395	#546	C₂²×C₃₁	1	4	yes	complemented
396	D₄²	—	2	2	no	—
397	D₄²	C₂²×C₃₁	1	4	yes	complemented
398	#540	C₂²×C₃₁	1	2	yes	complemented
399	#538	—	2	2	no	—
400	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
401	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	#535	C₂²×C₃₁	1	2	yes	—
403	#534	—	2	2	no	—
404	#534	—	2	2	no	—
405	#525	C₂²×C₃₁	1	1	yes	characteristic
406	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	C₂×#123	—	2	2	no	—
408	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
409	#518	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	#496	C₂²×C₃₁	1	2	yes	complemented
411	#492	C₂²×C₃₁	1	2	yes	complemented
412	#491	C₂²×C₃₁	1	2	yes	complemented
413	#488	C₂²×C₃₁	1	2	yes	complemented
414	#485	C₂²×C₃₁	1	4	yes	complemented
415	#483	C₂²×C₃₁	1	2	yes	complemented
416	#482	C₂²×C₃₁	1	4	yes	complemented
417	#480	C₂²×C₃₁	1	2	yes	complemented
418	#478	C₂²×C₃₁	1	4	yes	complemented
419	#469	C₂²×C₃₁	1	4	yes	complemented
420	#468	C₂²×C₃₁	1	4	yes	complemented
421	#468	C₂²×C₃₁	1	4	yes	complemented
422	#465	C₂²×C₃₁	1	4	yes	complemented
423	#463	C₂²×C₃₁	1	4	yes	complemented
424	#461	C₂²×C₃₁	1	4	yes	complemented
425	#459	C₂²×C₃₁	1	4	yes	complemented
426	#450	C₂²×C₃₁	1	2	yes	complemented
427	#450	C₂²×C₃₁	1	4	yes	complemented
428	#449	C₂²×C₃₁	1	4	yes	complemented
429	#449	C₂²×C₃₁	1	4	yes	complemented
430	#449	C₂²×C₃₁	1	4	yes	complemented
431	#449	C₂²×C₃₁	1	4	yes	complemented
432	#448	C₂²×C₃₁	1	4	yes	complemented
433	#447	C₂²×C₃₁	1	4	yes	complemented
434	#447	C₂²×C₃₁	1	2	yes	complemented
435	#447	C₂²×C₃₁	1	4	yes	complemented
436	#442	C₂²×C₃₁	1	4	yes	complemented
437	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
438	#436	C₂²×C₃₁	1	4	yes	complemented
439	#435	C₂²×C₃₁	1	4	yes	complemented
440	#433	C₂²×C₃₁	1	2	yes	complemented
441	#418	C₂²×C₃₁	1	2	yes	complemented
442	#417	C₂²×C₃₁	1	4	yes	complemented
443	#416	C₂²×C₃₁	1	2	yes	complemented
444	#408	C₂²×C₃₁	1	2	yes	complemented
445	#407	C₂²×C₃₁	1	2	yes	complemented
446	C₂×C₃₁	—	4	1	no	—
447	C₂×C₃₁	—	4	2	no	—
448	C₂×C₃₁	—	4	2	no	—
449	C₂×C₃₁	—	4	4	no	—
450	C₂×C₃₁	—	8	4	no	—
451	C₂×C₃₁	—	8	1	no	—
452	C₂×C₃₁	#3484	1	1	yes	characteristic
453	C₂×C₃₁	#3585	1	2	yes	—
454	H(5,𝔽₂)	—	4	4	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	4	4	no	—
458	C₂×#41	C₂³×C₃₁	1	4	yes	—
459	C₂×#41	C₂³×C₃₁	1	2	yes	—
460	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
461	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
470	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
471	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
474	AGL(1,ℤ/8)	—	4	8	no	—
475	AGL(1,ℤ/8)	—	4	4	no	—
476	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
477	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
479	C₂×D₈	—	4	4	no	—
480	C₂×D₈	C₂³×C₃₁	1	4	yes	—
481	C₂×D₈	C₂³×C₃₁	1	4	yes	—
482	C₂×D₈	C₂³×C₃₁	1	4	yes	—
483	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
484	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
485	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
488	#127	—	2	2	no	—
489	#127	C₂³×C₃₁	1	2	yes	—
490	#126	—	2	4	no	—
491	#125	C₂³×C₃₁	1	2	yes	—
492	#124	—	2	2	no	—
493	#124	—	2	1	no	—
494	#124	C₂³×C₃₁	1	2	yes	—
495	#123	—	2	2	no	—
496	#123	—	2	1	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	2	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	#123	—	2	4	no	—
503	#123	D₄×C₃₁	1	2	yes	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
506	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
507	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	D₄×C₃₁	1	2	yes	—
516	#121	C₂³×C₃₁	1	4	yes	—
517	#121	C₂³×C₃₁	1	4	yes	—
518	#121	C₂³×C₃₁	1	2	yes	—
519	#121	C₂³×C₃₁	1	4	yes	—
520	#120	—	2	1	no	—
521	#120	—	2	2	no	—
522	#120	—	2	4	no	—
523	#120	—	2	2	no	—
524	#120	—	2	4	no	—
525	#120	—	2	4	no	—
526	#120	D₄×C₃₁	1	2	yes	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	C₂³×C₃₁	1	4	yes	—
531	C₄×D₄	C₂³×C₃₁	1	4	yes	—
532	C₄×D₄	C₂³×C₃₁	1	4	yes	—
533	#117	C₂³×C₃₁	1	1	yes	characteristic
534	#117	C₂³×C₃₁	1	2	yes	—
535	#117	C₂³×C₃₁	1	1	yes	characteristic
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₂²⋊C₄	—	2	2	no	—
540	C₂×C₂²⋊C₄	—	2	4	no	—
541	#107	C₂³×C₃₁	1	4	yes	—
542	#106	C₂³×C₃₁	1	4	yes	—
543	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
544	#103	C₂³×C₃₁	1	4	yes	—
545	#103	C₂³×C₃₁	1	4	yes	—
546	#103	C₂³×C₃₁	1	4	yes	—
547	#102	C₂³×C₃₁	1	4	yes	—
548	#102	C₂³×C₃₁	1	4	yes	—
549	#102	C₂³×C₃₁	1	4	yes	—
550	#102	C₂³×C₃₁	1	4	yes	—
551	#102	C₂³×C₃₁	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
556	#97	C₂³×C₃₁	1	2	yes	—
557	C₄×C₈	C₂³×C₃₁	1	2	yes	—
558	C₃₁	#61648	1	1	yes	characteristic, direct product factor, Sylow
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	2	no	—
563	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
564	#41	—	2	8	no	—
565	#41	—	2	4	no	—
566	#41	—	4	2	no	—
567	#41	—	4	4	no	—
568	#41	—	4	2	no	—
569	#41	—	4	2	no	—
570	#41	—	4	8	no	—
571	#41	—	4	4	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	4	2	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×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	8	no	—
598	C₂×D₄	—	8	8	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
601	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
602	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
603	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
604	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
605	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	4	no	—
615	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
616	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
620	SD₁₆	—	4	4	no	—
621	SD₁₆	—	4	4	no	—
622	SD₁₆	—	4	4	no	—
623	D₈	—	2	8	no	—
624	D₈	—	2	8	no	—
625	D₈	—	4	4	no	—
626	M₁₆	—	4	4	no	—
627	M₁₆	—	4	2	no	—
628	C₂×C₈	—	4	2	no	—
629	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
630	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	2	no	—
656	C₄²	C₂⁴×C₃₁	1	2	yes	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	8	2	no	—
666	C₂³	—	8	2	no	—
667	C₂³	—	8	2	no	—
668	C₂³	—	8	2	no	—
669	C₂³	—	8	4	no	—
670	C₂³	—	8	4	no	—
671	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
672	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
673	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
674	Q₈	—	2	4	no	—
675	Q₈	—	2	2	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	8	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	8	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	2	no	—
695	D₄	—	8	4	no	—
696	D₄	—	8	4	no	—
697	D₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	2	no	—
715	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
719	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
720	C₈	—	2	4	no	—
721	C₈	—	2	4	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	8	4	no	—
737	C₂²	—	8	2	no	—
738	C₂²	—	16	4	no	—
739	C₂²	—	16	4	no	—
740	C₂²	—	16	4	no	—
741	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	2	no	—
750	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
751	C₂	—	4	1	no	—
752	C₂	—	4	2	no	—
753	C₂	—	4	2	no	—
754	C₂	—	4	4	no	—
755	C₂	—	8	1	no	—
756	C₂	—	8	4	no	—
757	C₂	C₃₁×#3484	1	1	yes	characteristic
758	C₂	C₃₁×#3585	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×#3485	C₂	semidirect
3. C₃₁×#3322	C₂	semidirect
4. C₃₁×#3307	C₂	semidirect
5. C₃₁×#3272	C₂	semidirect
6. C₃₁×#3264	C₂	semidirect
7. C₃₁×#3221	C₂	semidirect
8. C₃₁×#3200	C₂	semidirect
9. C₃₁×#3194	C₂	semidirect
10. C₃₁×#3122	C₂	semidirect
11. C₃₁×#3008	C₂	semidirect
12. C₃₁×#3006	C₂	semidirect
13. C₃₁×#2978	C₂	semidirect
14. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
15. C₂²×#41×C₃₁	C₂²	semidirect
16. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×D₈×C₃₁	C₂²	semidirect
20. C₃₁×#553	C₂²	semidirect
22. C₃₁×#547	C₂²	semidirect
24. C₃₁×#546	C₂²	semidirect
26. D₄²×C₃₁	C₂²	semidirect
27. C₃₁×#540	C₂²	semidirect
29. C₃₁×#536	C₂²	semidirect
30. C₃₁×#536	C₂²	semidirect
35. C₃₁×#525	C₂²	semidirect
37. C₂×C₃₁×#121	C₂²	semidirect
38. C₃₁×#518	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×#483	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#480	C₂²	semidirect
47. C₃₁×#478	C₂²	semidirect
48. C₃₁×#469	C₂²	semidirect
49. C₃₁×#468	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
51. C₃₁×#465	C₂²	semidirect
52. C₃₁×#463	C₂²	semidirect
53. C₃₁×#461	C₂²	semidirect
54. C₃₁×#459	C₂²	semidirect
55. C₃₁×#450	C₂²	semidirect
56. C₃₁×#450	C₂²	semidirect
57. C₃₁×#449	C₂²	semidirect
58. C₃₁×#449	C₂²	semidirect
59. C₃₁×#449	C₂²	semidirect
60. C₃₁×#449	C₂²	semidirect
61. C₃₁×#448	C₂²	semidirect
62. C₃₁×#447	C₂²	semidirect
63. C₃₁×#447	C₂²	semidirect
64. C₃₁×#447	C₂²	semidirect
65. C₃₁×#442	C₂²	semidirect
66. C₄×D₈×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
68. C₃₁×#435	C₂²	semidirect
69. C₃₁×#433	C₂²	semidirect
70. C₃₁×#418	C₂²	semidirect
71. C₃₁×#417	C₂²	semidirect
72. C₃₁×#416	C₂²	semidirect
73. C₃₁×#408	C₂²	semidirect
74. C₃₁×#407	C₂²	semidirect
277. #61648	C₃₁	direct (N × H)
343. #3537	C₂×C₃₁	semidirect
344. #3485	C₂×C₃₁	semidirect
345. #3322	C₂×C₃₁	semidirect
346. #3307	C₂×C₃₁	semidirect
347. #3272	C₂×C₃₁	semidirect
348. #3264	C₂×C₃₁	semidirect
349. #3221	C₂×C₃₁	semidirect
350. #3200	C₂×C₃₁	semidirect
351. #3194	C₂×C₃₁	semidirect
352. #3122	C₂×C₃₁	semidirect
353. #3008	C₂×C₃₁	semidirect
354. #3006	C₂×C₃₁	semidirect
355. #2978	C₂×C₃₁	semidirect
385. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
386. C₂²×#41	C₂²×C₃₁	semidirect
387. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
388. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
389. C₂²×D₈	C₂²×C₃₁	semidirect
391. #553	C₂²×C₃₁	semidirect
393. #547	C₂²×C₃₁	semidirect
395. #546	C₂²×C₃₁	semidirect
397. D₄²	C₂²×C₃₁	semidirect
398. #540	C₂²×C₃₁	semidirect
400. #536	C₂²×C₃₁	semidirect
401. #536	C₂²×C₃₁	semidirect
406. #525	C₂²×C₃₁	semidirect
408. C₂×#121	C₂²×C₃₁	semidirect
409. #518	C₂²×C₃₁	semidirect
410. #496	C₂²×C₃₁	semidirect
411. #492	C₂²×C₃₁	semidirect
412. #491	C₂²×C₃₁	semidirect
413. #488	C₂²×C₃₁	semidirect
414. #485	C₂²×C₃₁	semidirect
415. #483	C₂²×C₃₁	semidirect
416. #482	C₂²×C₃₁	semidirect
417. #480	C₂²×C₃₁	semidirect
418. #478	C₂²×C₃₁	semidirect
419. #469	C₂²×C₃₁	semidirect
420. #468	C₂²×C₃₁	semidirect
421. #468	C₂²×C₃₁	semidirect
422. #465	C₂²×C₃₁	semidirect
423. #463	C₂²×C₃₁	semidirect
424. #461	C₂²×C₃₁	semidirect
425. #459	C₂²×C₃₁	semidirect
426. #450	C₂²×C₃₁	semidirect
427. #450	C₂²×C₃₁	semidirect
428. #449	C₂²×C₃₁	semidirect
429. #449	C₂²×C₃₁	semidirect
430. #449	C₂²×C₃₁	semidirect
431. #449	C₂²×C₃₁	semidirect
432. #448	C₂²×C₃₁	semidirect
433. #447	C₂²×C₃₁	semidirect
434. #447	C₂²×C₃₁	semidirect
435. #447	C₂²×C₃₁	semidirect
436. #442	C₂²×C₃₁	semidirect
437. C₄×D₈	C₂²×C₃₁	semidirect
438. #436	C₂²×C₃₁	semidirect
439. #435	C₂²×C₃₁	semidirect
440. #433	C₂²×C₃₁	semidirect
441. #418	C₂²×C₃₁	semidirect
442. #417	C₂²×C₃₁	semidirect
443. #416	C₂²×C₃₁	semidirect
444. #408	C₂²×C₃₁	semidirect
445. #407	C₂²×C₃₁	semidirect
558. C₃₁	#61648	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×#3485	2
C₃₁×#3322	2
C₃₁×#3307	2
C₃₁×#3272	2
C₃₁×#3264	2
C₃₁×#3221	2
C₃₁×#3200	2
C₃₁×#3194	2
C₃₁×#3122	2
C₃₁×#3008	2
C₃₁×#3006	2
C₃₁×#2978	2
#61648	31

Subgroups — C31×#61648 #21518407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61648 #21518407