Subgroups — C₃₁×#61332 #21518091

Order 7936.

1862 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3373	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3366	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3041	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#559	C₂²	1	4	yes	complemented
19	C₃₁×#556	C₂²	1	2	yes	complemented
20	C₃₁×#555	—	2	1	no	—
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	—	2	2	no	—
23	C₃₁×#554	C₂²	1	4	yes	complemented
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	—	2	2	no	—
26	C₃₁×#550	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₃₁	—	2	1	no	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#544	C₂²	1	2	yes	—
31	C₃₁×#543	—	2	2	no	—
32	C₃₁×#538	—	2	2	no	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₃₁×#525	—	2	2	no	—
38	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	—
40	C₃₁×#518	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#491	C₂²	1	2	yes	complemented
44	C₃₁×#490	C₂²	1	2	yes	complemented
45	C₃₁×#490	C₂²	1	4	yes	complemented
46	C₃₁×#489	C₂²	1	2	yes	complemented
47	C₃₁×#489	C₂²	1	2	yes	complemented
48	C₃₁×#489	C₂²	1	4	yes	complemented
49	C₃₁×#488	C₂²	1	4	yes	complemented
50	C₃₁×#486	C₂²	1	4	yes	complemented
51	C₃₁×#479	C₂²	1	4	yes	complemented
52	C₃₁×#478	C₂²	1	4	yes	complemented
53	C₃₁×#478	C₂²	1	4	yes	complemented
54	C₃₁×#476	C₂²	1	2	yes	complemented
55	C₃₁×#476	C₂²	1	4	yes	complemented
56	C₃₁×#475	C₂²	1	4	yes	complemented
57	C₃₁×#474	C₂²	1	2	yes	complemented
58	C₃₁×#463	C₂²	1	4	yes	—
59	C₃₁×#463	C₂²	1	4	yes	—
60	C₃₁×#463	C₂²	1	4	yes	complemented
61	C₃₁×#461	C₂²	1	2	yes	complemented
62	C₃₁×#459	C₂²	1	4	yes	—
63	C₃₁×#459	C₂²	1	4	yes	—
64	C₃₁×#459	C₂²	1	2	yes	complemented
65	C₃₁×#446	C₂²	1	4	yes	complemented
66	C₃₁×#446	C₂²	1	4	yes	complemented
67	C₃₁×#442	C₂²	1	4	yes	—
68	C₃₁×#442	C₂²	1	4	yes	—
69	C₃₁×#442	C₂²	1	4	yes	complemented
70	C₃₁×#440	C₂²	1	4	yes	complemented
71	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
72	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
73	C₃₁×#428	C₂²	1	2	yes	—
74	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
75	C₃₁×#424	C₂²	1	2	yes	—
76	C₃₁×#423	C₂²	1	1	yes	characteristic
77	C₃₁×#418	C₂²	1	2	yes	—
78	C₃₁×#417	C₂²	1	2	yes	—
79	C₃₁×#416	C₂²	1	2	yes	—
80	C₃₁×#416	C₂²	1	2	yes	—
81	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
82	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
83	C₃₁×#405	C₂²	1	2	yes	—
84	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₃₁	—	2	1	no	—
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
93	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×D₈×C₃₁	—	2	4	no	—
95	C₂×D₈×C₃₁	C₂³	1	4	yes	—
96	C₂×D₈×C₃₁	C₂³	1	4	yes	—
97	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
98	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	—	2	2	no	—
101	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×#127	C₂³	1	4	yes	—
108	C₃₁×#127	C₂³	1	1	yes	characteristic
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#125	—	2	2	no	—
111	C₃₁×#125	D₄	1	2	yes	—
112	C₃₁×#125	C₂³	1	2	yes	—
113	C₃₁×#125	C₂³	1	4	yes	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#124	C₂³	1	4	yes	—
116	C₃₁×#124	C₂³	1	2	yes	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	2	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	1	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
131	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₃₁×#121	—	2	1	no	—
133	C₃₁×#121	—	2	1	no	—
134	C₃₁×#121	—	2	2	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	4	no	—
138	C₃₁×#120	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	1	no	—
140	C₄×Q₈×C₃₁	—	2	1	no	—
141	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
142	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	—	2	4	no	—
148	C₄×D₄×C₃₁	—	2	1	no	—
149	C₄×D₄×C₃₁	—	2	1	no	—
150	C₄×D₄×C₃₁	—	2	1	no	—
151	C₄×D₄×C₃₁	—	2	1	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	C₂³	1	4	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₄×D₄×C₃₁	C₂³	1	2	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₄×D₄×C₃₁	C₂³	1	2	yes	—
160	C₄×D₄×C₃₁	C₂³	1	2	yes	—
161	C₃₁×#117	—	2	2	no	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	C₂³	1	2	yes	—
164	C₃₁×#117	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
166	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
167	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
171	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
173	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
174	C₃₁×#107	C₂³	1	4	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
180	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	2	yes	—
182	C₃₁×#103	C₂³	1	2	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	2	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	2	yes	—
190	C₃₁×#102	C₂³	1	2	yes	—
191	C₃₁×#102	C₂³	1	2	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×#102	C₂³	1	4	yes	—
194	C₃₁×#102	C₂³	1	4	yes	—
195	C₃₁×#97	C₂³	1	2	yes	—
196	C₃₁×#97	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₃₁	C₂³	1	4	yes	—
199	C₂⁴×C₃₁	—	2	1	no	—
200	C₂⁴×C₃₁	—	2	1	no	—
201	#41×C₃₁	—	2	4	no	—
202	#41×C₃₁	—	2	4	no	—
203	#41×C₃₁	—	8	4	no	—
204	C₂×Q₈×C₃₁	—	2	1	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	2	4	no	—
207	C₂×Q₈×C₃₁	—	8	4	no	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	1	no	—
213	C₂×D₄×C₃₁	—	2	1	no	—
214	C₂×D₄×C₃₁	—	2	1	no	—
215	C₂×D₄×C₃₁	—	2	4	no	—
216	C₂×D₄×C₃₁	—	2	1	no	—
217	C₂×D₄×C₃₁	—	2	4	no	—
218	C₂×D₄×C₃₁	—	2	2	no	—
219	C₂×D₄×C₃₁	—	2	2	no	—
220	C₂×D₄×C₃₁	—	2	2	no	—
221	C₂×D₄×C₃₁	#41	1	4	yes	complemented
222	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₃₁	—	2	1	no	—
226	C₂²×C₄×C₃₁	—	2	1	no	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	2	no	—
230	C₂²×C₄×C₃₁	—	2	4	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	—	2	2	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	—	2	2	no	—
235	C₂²×C₄×C₃₁	—	8	2	no	—
236	C₂²×C₄×C₃₁	—	8	2	no	—
237	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	SD₁₆×C₃₁	—	2	8	no	—
241	D₈×C₃₁	—	2	8	no	—
242	D₈×C₃₁	—	2	8	no	—
243	M₁₆×C₃₁	—	2	4	no	—
244	C₂×C₈×C₃₁	—	2	2	no	—
245	C₂×C₈×C₃₁	—	2	2	no	—
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	1	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	4	no	—
256	C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	2	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂²⋊C₄×C₃₁	—	2	2	no	—
277	C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	—	2	4	no	—
280	C₂²⋊C₄×C₃₁	—	2	2	no	—
281	C₂²⋊C₄×C₃₁	—	2	4	no	—
282	C₂²⋊C₄×C₃₁	—	2	2	no	—
283	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
284	C₄²×C₃₁	—	2	4	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₃₁	C₂⁴	1	4	yes	—
289	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
291	#61332	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	4	no	—
294	C₂³×C₃₁	—	2	2	no	—
295	C₂³×C₃₁	—	2	2	no	—
296	C₂³×C₃₁	—	4	2	no	—
297	C₂³×C₃₁	—	8	1	no	—
298	C₂³×C₃₁	—	8	1	no	—
299	C₂³×C₃₁	—	8	1	no	—
300	C₂³×C₃₁	—	8	1	no	—
301	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₃₁	—	2	2	no	—
303	Q₈×C₃₁	—	2	2	no	—
304	Q₈×C₃₁	—	4	2	no	—
305	Q₈×C₃₁	—	4	2	no	—
306	Q₈×C₃₁	—	4	2	no	—
307	Q₈×C₃₁	—	8	1	no	—
308	Q₈×C₃₁	—	8	4	no	—
309	D₄×C₃₁	—	2	4	no	—
310	D₄×C₃₁	—	2	2	no	—
311	D₄×C₃₁	—	2	2	no	—
312	D₄×C₃₁	—	2	2	no	—
313	D₄×C₃₁	—	2	2	no	—
314	D₄×C₃₁	—	2	2	no	—
315	D₄×C₃₁	—	4	2	no	—
316	D₄×C₃₁	—	4	4	no	—
317	D₄×C₃₁	—	4	2	no	—
318	D₄×C₃₁	—	8	1	no	—
319	D₄×C₃₁	—	8	4	no	—
320	D₄×C₃₁	—	8	4	no	—
321	D₄×C₃₁	C₂×#41	1	4	yes	—
322	C₂×C₄×C₃₁	—	2	2	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	4	1	no	—
328	C₂×C₄×C₃₁	—	4	1	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	4	4	no	—
332	C₂×C₄×C₃₁	—	8	4	no	—
333	C₂×C₄×C₃₁	—	8	2	no	—
334	C₂×C₄×C₃₁	—	8	2	no	—
335	C₂×C₄×C₃₁	—	8	4	no	—
336	C₂×C₄×C₃₁	—	8	4	no	—
337	C₂×C₄×C₃₁	—	8	1	no	—
338	C₂×C₄×C₃₁	—	8	1	no	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
347	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
348	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
349	C₈×C₃₁	—	2	2	no	—
350	C₈×C₃₁	—	2	4	no	—
351	C₈×C₃₁	—	2	2	no	—
352	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3376	C₂×C₃₁	1	4	yes	complemented
355	#3373	C₂×C₃₁	1	4	yes	complemented
356	#3370	C₂×C₃₁	1	4	yes	complemented
357	#3366	C₂×C₃₁	1	4	yes	complemented
358	#3136	C₂×C₃₁	1	2	yes	complemented
359	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
360	#3084	C₂×C₃₁	1	2	yes	complemented
361	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
362	#3041	C₂×C₃₁	1	2	yes	complemented
363	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#2946	C₂×C₃₁	1	2	yes	complemented
366	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	2	4	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	2	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	4	2	no	—
376	C₂²×C₃₁	—	4	2	no	—
377	C₂²×C₃₁	—	4	2	no	—
378	C₂²×C₃₁	—	8	4	no	—
379	C₂²×C₃₁	—	8	4	no	—
380	C₂²×C₃₁	#548	1	2	yes	—
381	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₃₁	—	2	1	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	2	1	no	—
385	C₄×C₃₁	—	2	1	no	—
386	C₄×C₃₁	—	2	4	no	—
387	C₄×C₃₁	—	2	4	no	—
388	C₄×C₃₁	—	4	2	no	—
389	C₄×C₃₁	—	4	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	#548	1	2	yes	—
394	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
395	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
396	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
397	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
398	#559	C₂²×C₃₁	1	4	yes	complemented
399	#556	C₂²×C₃₁	1	2	yes	complemented
400	#555	—	2	1	no	—
401	#554	—	2	1	no	—
402	#554	—	2	2	no	—
403	#554	C₂²×C₃₁	1	4	yes	complemented
404	#554	C₂²×C₃₁	1	2	yes	complemented
405	#553	—	2	2	no	—
406	#550	C₂²×C₃₁	1	2	yes	complemented
407	D₄×Q₈	—	2	1	no	—
408	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
409	#547	—	2	1	no	—
410	#544	C₂²×C₃₁	1	2	yes	—
411	#543	—	2	2	no	—
412	#538	—	2	2	no	—
413	#535	C₂²×C₃₁	1	2	yes	—
414	#533	C₂²×C₃₁	1	1	yes	characteristic
415	#533	C₂²×C₃₁	1	1	yes	characteristic
416	#532	C₂²×C₃₁	1	1	yes	characteristic
417	#525	—	2	2	no	—
418	C₂×C₂²⋊Q₈	—	2	2	no	—
419	#520	C₂²×C₃₁	1	2	yes	—
420	#518	C₂²×C₃₁	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
423	#491	C₂²×C₃₁	1	2	yes	complemented
424	#490	C₂²×C₃₁	1	2	yes	complemented
425	#490	C₂²×C₃₁	1	4	yes	complemented
426	#489	C₂²×C₃₁	1	2	yes	complemented
427	#489	C₂²×C₃₁	1	2	yes	complemented
428	#489	C₂²×C₃₁	1	4	yes	complemented
429	#488	C₂²×C₃₁	1	4	yes	complemented
430	#486	C₂²×C₃₁	1	4	yes	complemented
431	#479	C₂²×C₃₁	1	4	yes	complemented
432	#478	C₂²×C₃₁	1	4	yes	complemented
433	#478	C₂²×C₃₁	1	4	yes	complemented
434	#476	C₂²×C₃₁	1	2	yes	complemented
435	#476	C₂²×C₃₁	1	4	yes	complemented
436	#475	C₂²×C₃₁	1	4	yes	complemented
437	#474	C₂²×C₃₁	1	2	yes	complemented
438	#463	C₂²×C₃₁	1	4	yes	—
439	#463	C₂²×C₃₁	1	4	yes	—
440	#463	C₂²×C₃₁	1	4	yes	complemented
441	#461	C₂²×C₃₁	1	2	yes	complemented
442	#459	C₂²×C₃₁	1	4	yes	—
443	#459	C₂²×C₃₁	1	4	yes	—
444	#459	C₂²×C₃₁	1	2	yes	complemented
445	#446	C₂²×C₃₁	1	4	yes	complemented
446	#446	C₂²×C₃₁	1	4	yes	complemented
447	#442	C₂²×C₃₁	1	4	yes	—
448	#442	C₂²×C₃₁	1	4	yes	—
449	#442	C₂²×C₃₁	1	4	yes	complemented
450	#440	C₂²×C₃₁	1	4	yes	complemented
451	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
452	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
453	#428	C₂²×C₃₁	1	2	yes	—
454	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
455	#424	C₂²×C₃₁	1	2	yes	—
456	#423	C₂²×C₃₁	1	1	yes	characteristic
457	#418	C₂²×C₃₁	1	2	yes	—
458	#417	C₂²×C₃₁	1	2	yes	—
459	#416	C₂²×C₃₁	1	2	yes	—
460	#416	C₂²×C₃₁	1	2	yes	—
461	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
462	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
463	#405	C₂²×C₃₁	1	2	yes	—
464	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
465	C₂×C₃₁	—	2	2	no	—
466	C₂×C₃₁	—	4	4	no	—
467	C₂×C₃₁	—	8	2	no	—
468	C₂×C₃₁	—	8	2	no	—
469	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
470	C₂×C₃₁	#3585	1	1	yes	characteristic
471	C₂×C₃₁	#3585	1	1	yes	characteristic
472	C₂×#41	—	2	2	no	—
473	C₂×#41	C₂³×C₃₁	1	2	yes	—
474	C₂²×Q₈	—	2	2	no	—
475	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	AGL(1,ℤ/8)	—	2	8	no	—
480	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
481	C₂×D₈	—	2	4	no	—
482	C₂×D₈	C₂³×C₃₁	1	4	yes	—
483	C₂×D₈	C₂³×C₃₁	1	4	yes	—
484	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
485	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
489	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
494	#127	C₂³×C₃₁	1	1	yes	characteristic
495	#127	C₂³×C₃₁	1	4	yes	—
496	#126	—	2	4	no	—
497	#125	—	2	2	no	—
498	#125	D₄×C₃₁	1	2	yes	—
499	#125	C₂³×C₃₁	1	2	yes	—
500	#125	C₂³×C₃₁	1	4	yes	—
501	#124	—	2	4	no	—
502	#124	C₂³×C₃₁	1	2	yes	—
503	#124	C₂³×C₃₁	1	4	yes	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	4	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
518	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
519	#121	—	2	1	no	—
520	#121	—	2	1	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	4	no	—
525	#120	—	2	4	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
529	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
530	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	C₂³×C₃₁	1	2	yes	—
542	C₄×D₄	C₂³×C₃₁	1	2	yes	—
543	C₄×D₄	C₂³×C₃₁	1	2	yes	—
544	C₄×D₄	C₂³×C₃₁	1	2	yes	—
545	C₄×D₄	C₂³×C₃₁	1	4	yes	—
546	C₄×D₄	C₂³×C₃₁	1	4	yes	—
547	C₄×D₄	C₂³×C₃₁	1	4	yes	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	C₂³×C₃₁	1	2	yes	—
551	#117	C₂³×C₃₁	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	2	no	—
553	C₂×C₄⋊C₄	—	2	4	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	#107	C₂³×C₃₁	1	4	yes	—
562	#106	C₂³×C₃₁	1	4	yes	—
563	#106	C₂³×C₃₁	1	4	yes	—
564	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
565	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
566	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
567	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
568	#103	C₂³×C₃₁	1	2	yes	—
569	#103	C₂³×C₃₁	1	2	yes	—
570	#103	C₂³×C₃₁	1	2	yes	—
571	#103	C₂³×C₃₁	1	2	yes	—
572	#103	C₂³×C₃₁	1	4	yes	—
573	#102	C₂³×C₃₁	1	4	yes	—
574	#102	C₂³×C₃₁	1	4	yes	—
575	#102	C₂³×C₃₁	1	2	yes	—
576	#102	C₂³×C₃₁	1	2	yes	—
577	#102	C₂³×C₃₁	1	2	yes	—
578	#102	C₂³×C₃₁	1	2	yes	—
579	#102	C₂³×C₃₁	1	4	yes	—
580	#102	C₂³×C₃₁	1	4	yes	—
581	#102	C₂³×C₃₁	1	4	yes	—
582	#97	C₂³×C₃₁	1	2	yes	—
583	#97	C₂³×C₃₁	1	2	yes	—
584	#97	C₂³×C₃₁	1	4	yes	—
585	C₄×C₈	C₂³×C₃₁	1	4	yes	—
586	C₃₁	#61332	1	1	yes	characteristic, direct product factor, Sylow
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	2	1	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	8	4	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	8	4	no	—
596	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
597	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
598	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	#41×C₃₁	1	4	yes	complemented
610	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	2	no	—
624	C₂²×C₄	—	8	2	no	—
625	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
628	SD₁₆	—	2	8	no	—
629	D₈	—	2	8	no	—
630	D₈	—	2	8	no	—
631	M₁₆	—	2	4	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
635	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
636	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₄²	C₂⁴×C₃₁	1	4	yes	—
677	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
678	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	—	8	1	no	—
687	C₂³	—	8	1	no	—
688	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	2	no	—
694	Q₈	—	8	1	no	—
695	Q₈	—	8	4	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	4	no	—
704	D₄	—	4	2	no	—
705	D₄	—	8	1	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	C₂×#41×C₃₁	1	4	yes	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	1	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
734	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
735	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	4	no	—
738	C₈	—	2	2	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	8	4	no	—
751	C₂²	—	8	4	no	—
752	C₂²	C₃₁×#548	1	2	yes	—
753	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	C₃₁×#548	1	2	yes	—
766	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
767	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
768	C₂	—	2	2	no	—
769	C₂	—	4	4	no	—
770	C₂	—	8	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
773	C₂	C₃₁×#3585	1	1	yes	characteristic
774	C₂	C₃₁×#3585	1	1	yes	characteristic

	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3506	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3373	C₂	semidirect
5. C₃₁×#3370	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3136	C₂	semidirect
8. C₃₁×#3135	C₂	semidirect
9. C₃₁×#3084	C₂	semidirect
10. C₃₁×#3077	C₂	semidirect
11. C₃₁×#3041	C₂	semidirect
12. C₃₁×#3036	C₂	semidirect
13. C₃₁×#2961	C₂	semidirect
14. C₃₁×#2946	C₂	semidirect
15. C₂×C₃₁×#442	C₂	semidirect
18. C₃₁×#559	C₂²	semidirect
19. C₃₁×#556	C₂²	semidirect
23. C₃₁×#554	C₂²	semidirect
24. C₃₁×#554	C₂²	semidirect
26. C₃₁×#550	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
43. C₃₁×#491	C₂²	semidirect
44. C₃₁×#490	C₂²	semidirect
45. C₃₁×#490	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#489	C₂²	semidirect
49. C₃₁×#488	C₂²	semidirect
50. C₃₁×#486	C₂²	semidirect
51. C₃₁×#479	C₂²	semidirect
52. C₃₁×#478	C₂²	semidirect
53. C₃₁×#478	C₂²	semidirect
54. C₃₁×#476	C₂²	semidirect
55. C₃₁×#476	C₂²	semidirect
56. C₃₁×#475	C₂²	semidirect
57. C₃₁×#474	C₂²	semidirect
60. C₃₁×#463	C₂²	semidirect
61. C₃₁×#461	C₂²	semidirect
64. C₃₁×#459	C₂²	semidirect
65. C₃₁×#446	C₂²	semidirect
66. C₃₁×#446	C₂²	semidirect
69. C₃₁×#442	C₂²	semidirect
70. C₃₁×#440	C₂²	semidirect
71. C₄×SD₁₆×C₃₁	C₂²	semidirect
72. C₄×D₈×C₃₁	C₂²	semidirect
221. C₂×D₄×C₃₁	#41	semidirect
291. #61332	C₃₁	direct (N × H)
352. #3506	C₂×C₃₁	semidirect
353. #3501	C₂×C₃₁	semidirect
354. #3376	C₂×C₃₁	semidirect
355. #3373	C₂×C₃₁	semidirect
356. #3370	C₂×C₃₁	semidirect
357. #3366	C₂×C₃₁	semidirect
358. #3136	C₂×C₃₁	semidirect
359. #3135	C₂×C₃₁	semidirect
360. #3084	C₂×C₃₁	semidirect
361. #3077	C₂×C₃₁	semidirect
362. #3041	C₂×C₃₁	semidirect
363. #3036	C₂×C₃₁	semidirect
364. #2961	C₂×C₃₁	semidirect
365. #2946	C₂×C₃₁	semidirect
366. C₂×#442	C₂×C₃₁	semidirect
398. #559	C₂²×C₃₁	semidirect
399. #556	C₂²×C₃₁	semidirect
403. #554	C₂²×C₃₁	semidirect
404. #554	C₂²×C₃₁	semidirect
406. #550	C₂²×C₃₁	semidirect
408. D₄×Q₈	C₂²×C₃₁	semidirect
423. #491	C₂²×C₃₁	semidirect
424. #490	C₂²×C₃₁	semidirect
425. #490	C₂²×C₃₁	semidirect
426. #489	C₂²×C₃₁	semidirect
427. #489	C₂²×C₃₁	semidirect
428. #489	C₂²×C₃₁	semidirect
429. #488	C₂²×C₃₁	semidirect
430. #486	C₂²×C₃₁	semidirect
431. #479	C₂²×C₃₁	semidirect
432. #478	C₂²×C₃₁	semidirect
433. #478	C₂²×C₃₁	semidirect
434. #476	C₂²×C₃₁	semidirect
435. #476	C₂²×C₃₁	semidirect
436. #475	C₂²×C₃₁	semidirect
437. #474	C₂²×C₃₁	semidirect
440. #463	C₂²×C₃₁	semidirect
441. #461	C₂²×C₃₁	semidirect
444. #459	C₂²×C₃₁	semidirect
445. #446	C₂²×C₃₁	semidirect
446. #446	C₂²×C₃₁	semidirect
449. #442	C₂²×C₃₁	semidirect
450. #440	C₂²×C₃₁	semidirect
451. C₄×SD₁₆	C₂²×C₃₁	semidirect
452. C₄×D₈	C₂²×C₃₁	semidirect
586. C₃₁	#61332	direct (N × H)
609. C₂×D₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3506	2
C₃₁×#3501	2
C₃₁×#3376	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3366	2
C₃₁×#3136	2
C₃₁×#3135	2
C₃₁×#3084	2
C₃₁×#3077	2
C₃₁×#3041	2
C₃₁×#3036	2
C₃₁×#2961	2
C₃₁×#2946	2
C₂×C₃₁×#442	2
#61332	31

Subgroups — C31×#61332 #21518091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61332 #21518091