Subgroups — C₃₁×#60460 #21517219

Order 7936.

2734 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3063	C₂	1	3	yes	maximal, complemented
6	C₃₁×#3062	C₂	1	3	yes	maximal, complemented
7	C₃₁×#3061	C₂	1	3	yes	maximal, complemented
8	C₃₁×#3057	C₂	1	3	yes	maximal, complemented
9	C₃₁×#3056	C₂	1	3	yes	maximal, complemented
10	C₃₁×#3055	C₂	1	3	yes	maximal, complemented
11	C₃₁×#3054	C₂	1	3	yes	maximal, complemented
12	C₂×C₃₁×#468	C₂	1	3	yes	maximal, complemented
13	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#577	—	2	8	no	—
20	C₂×C₃₁×#137	C₂²	1	3	yes	complemented
21	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
22	C₂×C₃₁×#135	C₂²	1	3	yes	complemented
23	C₂²×SD₁₆×C₃₁	C₂²	1	3	yes	complemented
24	C₃₁×#568	—	2	8	no	—
25	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#131	C₂²	1	3	yes	complemented
28	C₂×C₃₁×#131	C₂²	1	3	yes	complemented
29	C₂²×M₁₆×C₃₁	C₂²	1	3	yes	complemented
30	C₂²×M₁₆×C₃₁	C₂²	1	3	yes	complemented
31	C₃₁×#550	—	2	1	no	—
32	D₄×Q₈×C₃₁	—	2	1	no	—
33	C₃₁×#548	—	2	1	no	—
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	3	no	—
36	C₃₁×#546	—	2	3	no	—
37	C₃₁×#546	—	2	3	no	—
38	D₄²×C₃₁	—	2	3	no	—
39	C₃₁×#537	C₂²	1	3	yes	—
40	C₃₁×#537	C₂²	1	3	yes	complemented
41	C₃₁×#536	C₂²	1	3	yes	complemented
42	C₃₁×#535	C₂²	1	3	yes	—
43	C₃₁×#525	C₂²	1	3	yes	—
44	C₃₁×#525	C₂²	1	3	yes	complemented
45	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	3	yes	complemented
46	C₂×C₃₁×#121	C₂²	1	3	yes	—
47	C₃₁×#520	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic
49	C₃₁×#470	C₂²	1	3	yes	complemented
50	C₃₁×#470	C₂²	1	3	yes	complemented
51	C₃₁×#469	C₂²	1	3	yes	complemented
52	C₃₁×#469	C₂²	1	3	yes	complemented
53	C₃₁×#468	C₂²	1	3	yes	complemented
54	C₃₁×#468	C₂²	1	6	yes	complemented
55	C₃₁×#468	C₂²	1	6	yes	complemented
56	C₃₁×#468	C₂²	1	6	yes	complemented
57	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#468	C₂²	1	3	yes	complemented
59	C₃₁×#468	C₂²	1	3	yes	complemented
60	C₃₁×#467	C₂²	1	6	yes	complemented
61	C₃₁×#466	C₂²	1	6	yes	complemented
62	C₃₁×#465	C₂²	1	6	yes	complemented
63	C₃₁×#465	C₂²	1	6	yes	complemented
64	C₃₁×#428	C₂²	1	3	yes	complemented
65	C₃₁×#428	C₂²	1	3	yes	complemented
66	C₃₁×#427	C₂²	1	3	yes	complemented
67	C₂×C₃₁×#107	C₂²	1	3	yes	complemented
68	C₃₁×#419	C₂²	1	3	yes	complemented
69	C₃₁×#418	C₂²	1	3	yes	complemented
70	C₃₁×#417	C₂²	1	3	yes	complemented
71	C₃₁×#417	C₂²	1	3	yes	complemented
72	C₃₁×#416	C₂²	1	3	yes	complemented
73	C₃₁×#416	C₂²	1	3	yes	complemented
74	C₂×C₃₁×#103	C₂²	1	3	yes	complemented
75	C₂×C₃₁×#102	C₂²	1	3	yes	complemented
76	C₃₁×2₋¹⁺⁴	—	2	4	no	—
77	C₃₁×2₋¹⁺⁴	—	2	4	no	—
78	C₃₁×H(5,𝔽₂)	—	2	4	no	—
79	C₃₁×H(5,𝔽₂)	—	2	4	no	—
80	C₂×#41×C₃₁	—	2	4	no	—
81	C₂×#41×C₃₁	—	2	4	no	—
82	C₂×#41×C₃₁	—	2	1	no	—
83	C₂×#41×C₃₁	—	2	3	no	—
84	C₂×#41×C₃₁	D₄	1	3	yes	—
85	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
86	C₂×#41×C₃₁	C₂³	1	3	yes	—
87	C₂×#41×C₃₁	C₂³	1	3	yes	—
88	C₂×#41×C₃₁	C₂³	1	3	yes	—
89	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₃₁	—	2	1	no	—
91	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
93	C₂²×D₄×C₃₁	—	2	3	no	—
94	C₂²×D₄×C₃₁	—	2	3	no	—
95	C₂²×D₄×C₃₁	D₄	1	3	yes	—
96	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
97	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
98	C₃₁×#137	—	2	12	no	—
99	C₃₁×AGL(1,ℤ/8)	—	2	12	no	—
100	C₃₁×#135	—	2	12	no	—
101	C₂×Q₁₆×C₃₁	C₂³	1	3	yes	—
102	C₂×SD₁₆×C₃₁	—	2	12	no	—
103	C₂×SD₁₆×C₃₁	C₂³	1	6	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	3	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
106	C₂×D₈×C₃₁	C₂³	1	3	yes	—
107	C₃₁×#131	—	2	4	no	—
108	C₃₁×#131	—	2	12	no	—
109	C₃₁×#131	—	2	12	no	—
110	C₃₁×#131	D₄	1	8	yes	complemented
111	C₂×M₁₆×C₃₁	—	2	12	no	—
112	C₂×M₁₆×C₃₁	—	2	12	no	—
113	C₂×M₁₆×C₃₁	C₂³	1	3	yes	—
114	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₃₁	C₂³	1	3	yes	—
116	C₂×M₁₆×C₃₁	C₂³	1	3	yes	—
117	C₂×M₁₆×C₃₁	C₂³	1	3	yes	—
118	C₂×M₁₆×C₃₁	C₂³	1	3	yes	—
119	C₂²×C₈×C₃₁	C₂³	1	3	yes	—
120	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
121	C₂²×C₈×C₃₁	C₂³	1	3	yes	—
122	C₃₁×C₄⋊Q₈	—	2	3	no	—
123	C₃₁×#127	—	2	3	no	—
124	C₃₁×#124	—	2	3	no	—
125	C₃₁×#124	—	2	3	no	—
126	C₃₁×#123	—	2	6	no	—
127	C₃₁×#123	—	2	3	no	—
128	C₃₁×#123	—	2	3	no	—
129	C₃₁×C₂²⋊Q₈	—	2	3	no	—
130	C₃₁×C₂²⋊Q₈	—	2	3	no	—
131	C₃₁×C₂²⋊Q₈	—	2	3	no	—
132	C₃₁×C₂²⋊Q₈	—	2	3	no	—
133	C₃₁×C₂²⋊Q₈	C₂³	1	3	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	6	yes	—
135	C₃₁×C₂²⋊Q₈	C₂³	1	3	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	3	yes	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×#121	—	2	6	no	—
139	C₃₁×#121	—	2	3	no	—
140	C₃₁×#121	—	2	6	no	—
141	C₃₁×#121	—	2	3	no	—
142	C₃₁×#121	—	2	3	no	—
143	C₃₁×#121	—	2	3	no	—
144	C₃₁×#121	C₂³	1	3	yes	—
145	C₃₁×#121	C₂³	1	6	yes	—
146	C₃₁×#121	C₂³	1	3	yes	—
147	C₃₁×#121	C₂³	1	3	yes	—
148	C₃₁×#121	C₂³	1	1	yes	characteristic
149	C₃₁×#120	—	2	3	no	—
150	C₃₁×#120	—	2	3	no	—
151	C₃₁×#120	—	2	6	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	—	2	3	no	—
155	C₄×D₄×C₃₁	—	2	3	no	—
156	C₄×D₄×C₃₁	—	2	3	no	—
157	C₄×D₄×C₃₁	—	2	3	no	—
158	C₄×D₄×C₃₁	—	2	3	no	—
159	C₄×D₄×C₃₁	—	2	3	no	—
160	C₃₁×#117	C₂³	1	3	yes	—
161	C₃₁×#117	C₂³	1	3	yes	—
162	C₂×C₄⋊C₄×C₃₁	—	2	3	no	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
165	C₂×C₂²⋊C₄×C₃₁	—	2	3	no	—
166	C₂×C₂²⋊C₄×C₃₁	—	2	3	no	—
167	C₃₁×#107	C₂³	1	3	yes	—
168	C₃₁×#107	C₂³	1	6	yes	—
169	C₃₁×#107	C₂³	1	1	yes	characteristic
170	C₃₁×#106	C₂³	1	3	yes	—
171	C₃₁×#106	C₂³	1	3	yes	—
172	C₃₁×#103	C₂³	1	3	yes	—
173	C₃₁×#103	C₂³	1	6	yes	—
174	C₃₁×#103	C₂³	1	1	yes	characteristic
175	C₃₁×#103	C₂³	1	3	yes	—
176	C₃₁×#103	C₂³	1	3	yes	—
177	C₃₁×#102	C₂³	1	3	yes	—
178	C₃₁×#102	C₂³	1	6	yes	—
179	C₃₁×#102	C₂³	1	1	yes	characteristic
180	C₃₁×#102	C₂³	1	3	yes	—
181	C₃₁×#102	C₂³	1	3	yes	—
182	C₂⁴×C₃₁	—	2	3	no	—
183	C₂⁴×C₃₁	C₂×D₄	1	3	yes	—
184	#41×C₃₁	—	2	4	no	—
185	#41×C₃₁	—	2	12	no	—
186	#41×C₃₁	—	2	6	no	—
187	#41×C₃₁	—	2	6	no	—
188	#41×C₃₁	—	2	6	no	—
189	#41×C₃₁	—	2	6	no	—
190	#41×C₃₁	—	2	6	no	—
191	#41×C₃₁	—	2	6	no	—
192	#41×C₃₁	—	4	4	no	—
193	#41×C₃₁	—	4	12	no	—
194	#41×C₃₁	C₂×D₄	1	4	yes	—
195	#41×C₃₁	#41	1	4	yes	—
196	C₂×Q₈×C₃₁	—	2	4	no	—
197	C₂×Q₈×C₃₁	—	2	3	no	—
198	C₂×Q₈×C₃₁	—	2	6	no	—
199	C₂×Q₈×C₃₁	—	2	6	no	—
200	C₂×Q₈×C₃₁	—	4	4	no	—
201	C₂×Q₈×C₃₁	C₂×D₄	1	3	yes	—
202	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
203	C₂×Q₈×C₃₁	C₂⁴	1	3	yes	—
204	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
205	C₂×D₄×C₃₁	—	2	12	no	—
206	C₂×D₄×C₃₁	—	2	1	no	—
207	C₂×D₄×C₃₁	—	2	3	no	—
208	C₂×D₄×C₃₁	—	2	3	no	—
209	C₂×D₄×C₃₁	—	2	3	no	—
210	C₂×D₄×C₃₁	—	2	3	no	—
211	C₂×D₄×C₃₁	—	2	3	no	—
212	C₂×D₄×C₃₁	—	2	6	no	—
213	C₂×D₄×C₃₁	—	2	6	no	—
214	C₂×D₄×C₃₁	—	2	3	no	—
215	C₂×D₄×C₃₁	—	2	6	no	—
216	C₂×D₄×C₃₁	—	4	12	no	—
217	C₂×D₄×C₃₁	—	8	6	no	—
218	C₂×D₄×C₃₁	C₂×D₄	1	6	yes	—
219	C₂×D₄×C₃₁	C₂×D₄	1	3	yes	—
220	C₂×D₄×C₃₁	C₂×D₄	1	3	yes	—
221	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂×D₄×C₃₁	C₂⁴	1	3	yes	—
223	C₂²×C₄×C₃₁	—	2	6	no	—
224	C₂²×C₄×C₃₁	—	2	6	no	—
225	C₂²×C₄×C₃₁	—	2	3	no	—
226	C₂²×C₄×C₃₁	—	2	3	no	—
227	C₂²×C₄×C₃₁	—	2	3	no	—
228	C₂²×C₄×C₃₁	—	2	3	no	—
229	C₂²×C₄×C₃₁	—	2	3	no	—
230	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
231	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
233	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
234	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
236	Q₁₆×C₃₁	—	2	6	no	—
237	SD₁₆×C₃₁	—	2	6	no	—
238	SD₁₆×C₃₁	—	2	12	no	—
239	SD₁₆×C₃₁	—	2	2	no	—
240	D₈×C₃₁	—	2	6	no	—
241	M₁₆×C₃₁	—	2	6	no	—
242	M₁₆×C₃₁	—	2	6	no	—
243	M₁₆×C₃₁	—	2	2	no	—
244	M₁₆×C₃₁	—	2	6	no	—
245	M₁₆×C₃₁	—	2	6	no	—
246	M₁₆×C₃₁	C₂×D₄	1	12	yes	complemented
247	C₂×C₈×C₃₁	—	2	6	no	—
248	C₂×C₈×C₃₁	—	2	12	no	—
249	C₂×C₈×C₃₁	C₂×D₄	1	12	yes	complemented
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	3	yes	—
252	C₂×C₈×C₃₁	C₂⁴	1	3	yes	—
253	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₃₁	—	2	3	no	—
255	C₄⋊C₄×C₃₁	—	2	6	no	—
256	C₄⋊C₄×C₃₁	—	2	3	no	—
257	C₄⋊C₄×C₃₁	—	2	3	no	—
258	C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₄⋊C₄×C₃₁	—	2	3	no	—
260	C₄⋊C₄×C₃₁	—	2	3	no	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
264	C₄⋊C₄×C₃₁	C₂⁴	1	3	yes	—
265	C₂²⋊C₄×C₃₁	—	2	3	no	—
266	C₂²⋊C₄×C₃₁	—	2	6	no	—
267	C₂²⋊C₄×C₃₁	—	2	3	no	—
268	C₂²⋊C₄×C₃₁	—	2	3	no	—
269	C₂²⋊C₄×C₃₁	—	2	1	no	—
270	C₂²⋊C₄×C₃₁	—	2	3	no	—
271	C₂²⋊C₄×C₃₁	—	2	3	no	—
272	C₂²⋊C₄×C₃₁	—	2	3	no	—
273	C₂²⋊C₄×C₃₁	—	2	6	no	—
274	C₂²⋊C₄×C₃₁	—	2	1	no	—
275	C₂²⋊C₄×C₃₁	—	2	3	no	—
276	C₂²⋊C₄×C₃₁	—	2	3	no	—
277	C₄²×C₃₁	—	2	3	no	—
278	C₄²×C₃₁	—	2	3	no	—
279	#60460	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₃₁	—	2	6	no	—
281	C₂³×C₃₁	—	2	1	no	—
282	C₂³×C₃₁	—	2	3	no	—
283	C₂³×C₃₁	—	4	3	no	—
284	C₂³×C₃₁	—	4	3	no	—
285	C₂³×C₃₁	—	4	6	no	—
286	C₂³×C₃₁	—	8	3	no	—
287	C₂³×C₃₁	—	8	3	no	—
288	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₃₁	C₂²×D₄	1	3	yes	—
290	C₂³×C₃₁	C₂²×D₄	1	3	yes	—
291	Q₈×C₃₁	—	2	6	no	—
292	Q₈×C₃₁	—	2	3	no	—
293	Q₈×C₃₁	—	2	1	no	—
294	Q₈×C₃₁	—	2	3	no	—
295	Q₈×C₃₁	—	2	1	no	—
296	Q₈×C₃₁	—	4	6	no	—
297	Q₈×C₃₁	#121	1	4	yes	—
298	D₄×C₃₁	—	2	12	no	—
299	D₄×C₃₁	—	2	6	no	—
300	D₄×C₃₁	—	2	1	no	—
301	D₄×C₃₁	—	2	3	no	—
302	D₄×C₃₁	—	2	3	no	—
303	D₄×C₃₁	—	2	1	no	—
304	D₄×C₃₁	—	4	2	no	—
305	D₄×C₃₁	—	4	6	no	—
306	D₄×C₃₁	—	4	6	no	—
307	D₄×C₃₁	—	4	6	no	—
308	D₄×C₃₁	—	4	6	no	—
309	D₄×C₃₁	—	8	3	no	—
310	D₄×C₃₁	—	8	3	no	—
311	D₄×C₃₁	—	8	6	no	—
312	D₄×C₃₁	#121	1	12	yes	—
313	C₂×C₄×C₃₁	—	2	6	no	—
314	C₂×C₄×C₃₁	—	2	6	no	—
315	C₂×C₄×C₃₁	—	2	6	no	—
316	C₂×C₄×C₃₁	—	2	3	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	3	no	—
320	C₂×C₄×C₃₁	—	2	1	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	3	no	—
323	C₂×C₄×C₃₁	—	2	3	no	—
324	C₂×C₄×C₃₁	—	2	1	no	—
325	C₂×C₄×C₃₁	—	2	3	no	—
326	C₂×C₄×C₃₁	—	4	6	no	—
327	C₂×C₄×C₃₁	—	4	6	no	—
328	C₂×C₄×C₃₁	—	4	6	no	—
329	C₂×C₄×C₃₁	—	8	3	no	—
330	C₂×C₄×C₃₁	—	8	3	no	—
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
335	C₂×C₄×C₃₁	C₂×#41	1	6	yes	—
336	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
337	C₈×C₃₁	—	2	1	no	—
338	C₈×C₃₁	—	2	3	no	—
339	C₈×C₃₁	C₂²×D₄	1	6	yes	—
340	C₈×C₃₁	C₂²×D₄	1	2	yes	—
341	C₂×#577	C₂×C₃₁	1	1	yes	characteristic, complemented
342	C₂×#568	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
344	#3488	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3063	C₂×C₃₁	1	3	yes	complemented
346	#3062	C₂×C₃₁	1	3	yes	complemented
347	#3061	C₂×C₃₁	1	3	yes	complemented
348	#3057	C₂×C₃₁	1	3	yes	complemented
349	#3056	C₂×C₃₁	1	3	yes	complemented
350	#3055	C₂×C₃₁	1	3	yes	complemented
351	#3054	C₂×C₃₁	1	3	yes	complemented
352	C₂×#468	C₂×C₃₁	1	3	yes	complemented
353	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#2898	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#2897	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂²×C₃₁	—	2	3	no	—
357	C₂²×C₃₁	—	2	3	no	—
358	C₂²×C₃₁	—	2	1	no	—
359	C₂²×C₃₁	—	2	3	no	—
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	3	no	—
362	C₂²×C₃₁	—	2	1	no	—
363	C₂²×C₃₁	—	2	3	no	—
364	C₂²×C₃₁	—	4	3	no	—
365	C₂²×C₃₁	—	4	1	no	—
366	C₂²×C₃₁	—	4	1	no	—
367	C₂²×C₃₁	—	4	3	no	—
368	C₂²×C₃₁	—	4	1	no	—
369	C₂²×C₃₁	—	4	3	no	—
370	C₂²×C₃₁	—	8	6	no	—
371	C₂²×C₃₁	—	16	6	no	—
372	C₂²×C₃₁	C₂×#121	1	6	yes	—
373	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	3	no	—
376	C₄×C₃₁	—	4	3	no	—
377	C₄×C₃₁	—	4	3	no	—
378	C₄×C₃₁	—	4	1	no	—
379	C₄×C₃₁	—	4	1	no	—
380	C₄×C₃₁	—	4	1	no	—
381	C₄×C₃₁	—	4	3	no	—
382	C₄×C₃₁	C₂×#121	1	6	yes	—
383	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
385	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
386	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
387	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
388	#577	—	2	8	no	—
389	C₂×#137	C₂²×C₃₁	1	3	yes	complemented
390	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	3	yes	complemented
391	C₂×#135	C₂²×C₃₁	1	3	yes	complemented
392	C₂²×SD₁₆	C₂²×C₃₁	1	3	yes	complemented
393	#568	—	2	8	no	—
394	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
395	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×#131	C₂²×C₃₁	1	3	yes	complemented
397	C₂×#131	C₂²×C₃₁	1	3	yes	complemented
398	C₂²×M₁₆	C₂²×C₃₁	1	3	yes	complemented
399	C₂²×M₁₆	C₂²×C₃₁	1	3	yes	complemented
400	#550	—	2	1	no	—
401	D₄×Q₈	—	2	1	no	—
402	#548	—	2	1	no	—
403	#548	—	2	1	no	—
404	#547	—	2	3	no	—
405	#546	—	2	3	no	—
406	#546	—	2	3	no	—
407	D₄²	—	2	3	no	—
408	#537	C₂²×C₃₁	1	3	yes	—
409	#537	C₂²×C₃₁	1	3	yes	complemented
410	#536	C₂²×C₃₁	1	3	yes	complemented
411	#535	C₂²×C₃₁	1	3	yes	—
412	#525	C₂²×C₃₁	1	3	yes	—
413	#525	C₂²×C₃₁	1	3	yes	complemented
414	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
415	C₂×#121	C₂²×C₃₁	1	3	yes	—
416	#520	C₂²×C₃₁	1	1	yes	characteristic
417	#520	C₂²×C₃₁	1	1	yes	characteristic
418	#470	C₂²×C₃₁	1	3	yes	complemented
419	#470	C₂²×C₃₁	1	3	yes	complemented
420	#469	C₂²×C₃₁	1	3	yes	complemented
421	#469	C₂²×C₃₁	1	3	yes	complemented
422	#468	C₂²×C₃₁	1	3	yes	complemented
423	#468	C₂²×C₃₁	1	6	yes	complemented
424	#468	C₂²×C₃₁	1	6	yes	complemented
425	#468	C₂²×C₃₁	1	6	yes	complemented
426	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#468	C₂²×C₃₁	1	3	yes	complemented
428	#468	C₂²×C₃₁	1	3	yes	complemented
429	#467	C₂²×C₃₁	1	6	yes	complemented
430	#466	C₂²×C₃₁	1	6	yes	complemented
431	#465	C₂²×C₃₁	1	6	yes	complemented
432	#465	C₂²×C₃₁	1	6	yes	complemented
433	#428	C₂²×C₃₁	1	3	yes	complemented
434	#428	C₂²×C₃₁	1	3	yes	complemented
435	#427	C₂²×C₃₁	1	3	yes	complemented
436	C₂×#107	C₂²×C₃₁	1	3	yes	complemented
437	#419	C₂²×C₃₁	1	3	yes	complemented
438	#418	C₂²×C₃₁	1	3	yes	complemented
439	#417	C₂²×C₃₁	1	3	yes	complemented
440	#417	C₂²×C₃₁	1	3	yes	complemented
441	#416	C₂²×C₃₁	1	3	yes	complemented
442	#416	C₂²×C₃₁	1	3	yes	complemented
443	C₂×#103	C₂²×C₃₁	1	3	yes	complemented
444	C₂×#102	C₂²×C₃₁	1	3	yes	complemented
445	C₂×C₃₁	—	2	6	no	—
446	C₂×C₃₁	—	4	3	no	—
447	C₂×C₃₁	—	4	1	no	—
448	C₂×C₃₁	—	8	1	no	—
449	C₂×C₃₁	—	8	3	no	—
450	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
451	C₂×C₃₁	#3585	1	1	yes	characteristic
452	C₂×C₃₁	#3586	1	1	yes	characteristic
453	2₋¹⁺⁴	—	2	4	no	—
454	2₋¹⁺⁴	—	2	4	no	—
455	H(5,𝔽₂)	—	2	4	no	—
456	H(5,𝔽₂)	—	2	4	no	—
457	C₂×#41	—	2	4	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	3	no	—
461	C₂×#41	D₄×C₃₁	1	3	yes	—
462	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
463	C₂×#41	C₂³×C₃₁	1	3	yes	—
464	C₂×#41	C₂³×C₃₁	1	3	yes	—
465	C₂×#41	C₂³×C₃₁	1	3	yes	—
466	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
467	C₂²×Q₈	—	2	1	no	—
468	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
470	C₂²×D₄	—	2	3	no	—
471	C₂²×D₄	—	2	3	no	—
472	C₂²×D₄	D₄×C₃₁	1	3	yes	—
473	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
474	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
475	#137	—	2	12	no	—
476	AGL(1,ℤ/8)	—	2	12	no	—
477	#135	—	2	12	no	—
478	C₂×Q₁₆	C₂³×C₃₁	1	3	yes	—
479	C₂×SD₁₆	—	2	12	no	—
480	C₂×SD₁₆	C₂³×C₃₁	1	3	yes	—
481	C₂×SD₁₆	C₂³×C₃₁	1	6	yes	—
482	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
483	C₂×D₈	C₂³×C₃₁	1	3	yes	—
484	#131	—	2	4	no	—
485	#131	—	2	12	no	—
486	#131	—	2	12	no	—
487	#131	D₄×C₃₁	1	8	yes	complemented
488	C₂×M₁₆	—	2	12	no	—
489	C₂×M₁₆	—	2	12	no	—
490	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×M₁₆	C₂³×C₃₁	1	3	yes	—
492	C₂×M₁₆	C₂³×C₃₁	1	3	yes	—
493	C₂×M₁₆	C₂³×C₃₁	1	3	yes	—
494	C₂×M₁₆	C₂³×C₃₁	1	3	yes	—
495	C₂×M₁₆	C₂³×C₃₁	1	3	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	3	yes	—
497	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
498	C₂²×C₈	C₂³×C₃₁	1	3	yes	—
499	C₄⋊Q₈	—	2	3	no	—
500	#127	—	2	3	no	—
501	#124	—	2	3	no	—
502	#124	—	2	3	no	—
503	#123	—	2	6	no	—
504	#123	—	2	3	no	—
505	#123	—	2	3	no	—
506	C₂²⋊Q₈	—	2	3	no	—
507	C₂²⋊Q₈	—	2	3	no	—
508	C₂²⋊Q₈	—	2	3	no	—
509	C₂²⋊Q₈	—	2	3	no	—
510	C₂²⋊Q₈	C₂³×C₃₁	1	3	yes	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	6	yes	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
513	C₂²⋊Q₈	C₂³×C₃₁	1	3	yes	—
514	C₂²⋊Q₈	C₂³×C₃₁	1	3	yes	—
515	#121	—	2	6	no	—
516	#121	—	2	3	no	—
517	#121	—	2	6	no	—
518	#121	—	2	3	no	—
519	#121	—	2	3	no	—
520	#121	—	2	3	no	—
521	#121	C₂³×C₃₁	1	3	yes	—
522	#121	C₂³×C₃₁	1	6	yes	—
523	#121	C₂³×C₃₁	1	3	yes	—
524	#121	C₂³×C₃₁	1	1	yes	characteristic
525	#121	C₂³×C₃₁	1	3	yes	—
526	#120	—	2	3	no	—
527	#120	—	2	3	no	—
528	#120	—	2	6	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×D₄	—	2	3	no	—
532	C₄×D₄	—	2	3	no	—
533	C₄×D₄	—	2	3	no	—
534	C₄×D₄	—	2	3	no	—
535	C₄×D₄	—	2	3	no	—
536	C₄×D₄	—	2	3	no	—
537	#117	C₂³×C₃₁	1	3	yes	—
538	#117	C₂³×C₃₁	1	3	yes	—
539	C₂×C₄⋊C₄	—	2	3	no	—
540	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
542	C₂×C₂²⋊C₄	—	2	3	no	—
543	C₂×C₂²⋊C₄	—	2	3	no	—
544	#107	C₂³×C₃₁	1	3	yes	—
545	#107	C₂³×C₃₁	1	6	yes	—
546	#107	C₂³×C₃₁	1	1	yes	characteristic
547	#106	C₂³×C₃₁	1	3	yes	—
548	#106	C₂³×C₃₁	1	3	yes	—
549	#103	C₂³×C₃₁	1	3	yes	—
550	#103	C₂³×C₃₁	1	6	yes	—
551	#103	C₂³×C₃₁	1	1	yes	characteristic
552	#103	C₂³×C₃₁	1	3	yes	—
553	#103	C₂³×C₃₁	1	3	yes	—
554	#102	C₂³×C₃₁	1	3	yes	—
555	#102	C₂³×C₃₁	1	6	yes	—
556	#102	C₂³×C₃₁	1	1	yes	characteristic
557	#102	C₂³×C₃₁	1	3	yes	—
558	#102	C₂³×C₃₁	1	3	yes	—
559	C₃₁	#60460	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	—	2	3	no	—
561	C₂⁴	C₂×D₄×C₃₁	1	3	yes	—
562	#41	—	2	4	no	—
563	#41	—	2	12	no	—
564	#41	—	2	6	no	—
565	#41	—	2	6	no	—
566	#41	—	2	6	no	—
567	#41	—	2	6	no	—
568	#41	—	2	6	no	—
569	#41	—	2	6	no	—
570	#41	—	4	4	no	—
571	#41	—	4	12	no	—
572	#41	C₂×D₄×C₃₁	1	4	yes	—
573	#41	#41×C₃₁	1	4	yes	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	3	no	—
576	C₂×Q₈	—	2	6	no	—
577	C₂×Q₈	—	2	6	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	C₂×D₄×C₃₁	1	3	yes	—
580	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₃₁	1	3	yes	—
582	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
583	C₂×D₄	—	2	12	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	3	no	—
586	C₂×D₄	—	2	3	no	—
587	C₂×D₄	—	2	3	no	—
588	C₂×D₄	—	2	3	no	—
589	C₂×D₄	—	2	3	no	—
590	C₂×D₄	—	2	6	no	—
591	C₂×D₄	—	2	6	no	—
592	C₂×D₄	—	2	3	no	—
593	C₂×D₄	—	2	6	no	—
594	C₂×D₄	—	4	12	no	—
595	C₂×D₄	—	8	6	no	—
596	C₂×D₄	C₂×D₄×C₃₁	1	6	yes	—
597	C₂×D₄	C₂×D₄×C₃₁	1	3	yes	—
598	C₂×D₄	C₂×D₄×C₃₁	1	3	yes	—
599	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
600	C₂×D₄	C₂⁴×C₃₁	1	3	yes	—
601	C₂²×C₄	—	2	6	no	—
602	C₂²×C₄	—	2	6	no	—
603	C₂²×C₄	—	2	3	no	—
604	C₂²×C₄	—	2	3	no	—
605	C₂²×C₄	—	2	3	no	—
606	C₂²×C₄	—	2	3	no	—
607	C₂²×C₄	—	2	3	no	—
608	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
609	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
610	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
611	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
612	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
614	Q₁₆	—	2	6	no	—
615	SD₁₆	—	2	6	no	—
616	SD₁₆	—	2	12	no	—
617	SD₁₆	—	2	2	no	—
618	D₈	—	2	6	no	—
619	M₁₆	—	2	6	no	—
620	M₁₆	—	2	6	no	—
621	M₁₆	—	2	2	no	—
622	M₁₆	—	2	6	no	—
623	M₁₆	—	2	6	no	—
624	M₁₆	C₂×D₄×C₃₁	1	12	yes	complemented
625	C₂×C₈	—	2	6	no	—
626	C₂×C₈	—	2	12	no	—
627	C₂×C₈	C₂×D₄×C₃₁	1	12	yes	complemented
628	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₃₁	1	3	yes	—
630	C₂×C₈	C₂⁴×C₃₁	1	3	yes	—
631	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
632	C₄⋊C₄	—	2	3	no	—
633	C₄⋊C₄	—	2	6	no	—
634	C₄⋊C₄	—	2	3	no	—
635	C₄⋊C₄	—	2	3	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	3	no	—
638	C₄⋊C₄	—	2	3	no	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₄⋊C₄	C₂⁴×C₃₁	1	3	yes	—
643	C₂²⋊C₄	—	2	3	no	—
644	C₂²⋊C₄	—	2	6	no	—
645	C₂²⋊C₄	—	2	3	no	—
646	C₂²⋊C₄	—	2	3	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	3	no	—
649	C₂²⋊C₄	—	2	3	no	—
650	C₂²⋊C₄	—	2	3	no	—
651	C₂²⋊C₄	—	2	6	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	3	no	—
654	C₂²⋊C₄	—	2	3	no	—
655	C₄²	—	2	3	no	—
656	C₄²	—	2	3	no	—
657	C₂³	—	2	6	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	3	no	—
660	C₂³	—	4	3	no	—
661	C₂³	—	4	3	no	—
662	C₂³	—	4	6	no	—
663	C₂³	—	8	3	no	—
664	C₂³	—	8	3	no	—
665	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₃₁	1	3	yes	—
667	C₂³	C₂²×D₄×C₃₁	1	3	yes	—
668	Q₈	—	2	6	no	—
669	Q₈	—	2	3	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	2	3	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	4	6	no	—
674	Q₈	C₃₁×#121	1	4	yes	—
675	D₄	—	2	12	no	—
676	D₄	—	2	6	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	3	no	—
679	D₄	—	2	3	no	—
680	D₄	—	2	1	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	6	no	—
683	D₄	—	4	6	no	—
684	D₄	—	4	6	no	—
685	D₄	—	4	6	no	—
686	D₄	—	8	3	no	—
687	D₄	—	8	3	no	—
688	D₄	—	8	6	no	—
689	D₄	C₃₁×#121	1	12	yes	—
690	C₂×C₄	—	2	6	no	—
691	C₂×C₄	—	2	6	no	—
692	C₂×C₄	—	2	6	no	—
693	C₂×C₄	—	2	3	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	3	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	3	no	—
700	C₂×C₄	—	2	3	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	3	no	—
703	C₂×C₄	—	4	6	no	—
704	C₂×C₄	—	4	6	no	—
705	C₂×C₄	—	4	6	no	—
706	C₂×C₄	—	8	3	no	—
707	C₂×C₄	—	8	3	no	—
708	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
712	C₂×C₄	C₂×#41×C₃₁	1	6	yes	—
713	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	3	no	—
716	C₈	C₂²×D₄×C₃₁	1	6	yes	—
717	C₈	C₂²×D₄×C₃₁	1	2	yes	—
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	3	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	3	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	3	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	3	no	—
728	C₂²	—	4	3	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	3	no	—
732	C₂²	—	8	6	no	—
733	C₂²	—	16	6	no	—
734	C₂²	C₂×C₃₁×#121	1	6	yes	—
735	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
736	C₄	—	2	1	no	—
737	C₄	—	2	3	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	3	no	—
740	C₄	—	4	3	no	—
741	C₄	—	4	3	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	C₂×C₃₁×#121	1	6	yes	—
745	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
746	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
747	C₂	—	2	6	no	—
748	C₂	—	4	1	no	—
749	C₂	—	4	3	no	—
750	C₂	—	8	3	no	—
751	C₂	—	8	1	no	—
752	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
753	C₂	C₃₁×#3585	1	1	yes	characteristic
754	C₂	C₃₁×#3586	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 ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#577	C₂	semidirect
2. C₂×C₃₁×#568	C₂	semidirect
3. C₃₁×#3489	C₂	semidirect
4. C₃₁×#3488	C₂	semidirect
5. C₃₁×#3063	C₂	semidirect
6. C₃₁×#3062	C₂	semidirect
7. C₃₁×#3061	C₂	semidirect
8. C₃₁×#3057	C₂	semidirect
9. C₃₁×#3056	C₂	semidirect
10. C₃₁×#3055	C₂	semidirect
11. C₃₁×#3054	C₂	semidirect
12. C₂×C₃₁×#468	C₂	semidirect
13. C₃₁×#2913	C₂	semidirect
14. C₃₁×#2898	C₂	semidirect
15. C₃₁×#2897	C₂	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
21. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₃₁×#135	C₂²	semidirect
23. C₂²×SD₁₆×C₃₁	C₂²	semidirect
27. C₂×C₃₁×#131	C₂²	semidirect
28. C₂×C₃₁×#131	C₂²	semidirect
29. C₂²×M₁₆×C₃₁	C₂²	semidirect
30. C₂²×M₁₆×C₃₁	C₂²	semidirect
40. C₃₁×#537	C₂²	semidirect
41. C₃₁×#536	C₂²	semidirect
44. C₃₁×#525	C₂²	semidirect
45. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
49. C₃₁×#470	C₂²	semidirect
50. C₃₁×#470	C₂²	semidirect
51. C₃₁×#469	C₂²	semidirect
52. C₃₁×#469	C₂²	semidirect
53. C₃₁×#468	C₂²	semidirect
54. C₃₁×#468	C₂²	semidirect
55. C₃₁×#468	C₂²	semidirect
56. C₃₁×#468	C₂²	semidirect
57. C₃₁×#468	C₂²	semidirect
58. C₃₁×#468	C₂²	semidirect
59. C₃₁×#468	C₂²	semidirect
60. C₃₁×#467	C₂²	semidirect
61. C₃₁×#466	C₂²	semidirect
62. C₃₁×#465	C₂²	semidirect
63. C₃₁×#465	C₂²	semidirect
64. C₃₁×#428	C₂²	semidirect
65. C₃₁×#428	C₂²	semidirect
66. C₃₁×#427	C₂²	semidirect
67. C₂×C₃₁×#107	C₂²	semidirect
68. C₃₁×#419	C₂²	semidirect
69. C₃₁×#418	C₂²	semidirect
70. C₃₁×#417	C₂²	semidirect
71. C₃₁×#417	C₂²	semidirect
72. C₃₁×#416	C₂²	semidirect
73. C₃₁×#416	C₂²	semidirect
74. C₂×C₃₁×#103	C₂²	semidirect
75. C₂×C₃₁×#102	C₂²	semidirect
110. C₃₁×#131	D₄	semidirect
246. M₁₆×C₃₁	C₂×D₄	semidirect
249. C₂×C₈×C₃₁	C₂×D₄	semidirect
279. #60460	C₃₁	direct (N × H)
341. C₂×#577	C₂×C₃₁	semidirect
342. C₂×#568	C₂×C₃₁	semidirect
343. #3489	C₂×C₃₁	semidirect
344. #3488	C₂×C₃₁	semidirect
345. #3063	C₂×C₃₁	semidirect
346. #3062	C₂×C₃₁	semidirect
347. #3061	C₂×C₃₁	semidirect
348. #3057	C₂×C₃₁	semidirect
349. #3056	C₂×C₃₁	semidirect
350. #3055	C₂×C₃₁	semidirect
351. #3054	C₂×C₃₁	semidirect
352. C₂×#468	C₂×C₃₁	semidirect
353. #2913	C₂×C₃₁	semidirect
354. #2898	C₂×C₃₁	semidirect
355. #2897	C₂×C₃₁	semidirect
389. C₂×#137	C₂²×C₃₁	semidirect
390. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
391. C₂×#135	C₂²×C₃₁	semidirect
392. C₂²×SD₁₆	C₂²×C₃₁	semidirect
396. C₂×#131	C₂²×C₃₁	semidirect
397. C₂×#131	C₂²×C₃₁	semidirect
398. C₂²×M₁₆	C₂²×C₃₁	semidirect
399. C₂²×M₁₆	C₂²×C₃₁	semidirect
409. #537	C₂²×C₃₁	semidirect
410. #536	C₂²×C₃₁	semidirect
413. #525	C₂²×C₃₁	semidirect
414. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
418. #470	C₂²×C₃₁	semidirect
419. #470	C₂²×C₃₁	semidirect
420. #469	C₂²×C₃₁	semidirect
421. #469	C₂²×C₃₁	semidirect
422. #468	C₂²×C₃₁	semidirect
423. #468	C₂²×C₃₁	semidirect
424. #468	C₂²×C₃₁	semidirect
425. #468	C₂²×C₃₁	semidirect
426. #468	C₂²×C₃₁	semidirect
427. #468	C₂²×C₃₁	semidirect
428. #468	C₂²×C₃₁	semidirect
429. #467	C₂²×C₃₁	semidirect
430. #466	C₂²×C₃₁	semidirect
431. #465	C₂²×C₃₁	semidirect
432. #465	C₂²×C₃₁	semidirect
433. #428	C₂²×C₃₁	semidirect
434. #428	C₂²×C₃₁	semidirect
435. #427	C₂²×C₃₁	semidirect
436. C₂×#107	C₂²×C₃₁	semidirect
437. #419	C₂²×C₃₁	semidirect
438. #418	C₂²×C₃₁	semidirect
439. #417	C₂²×C₃₁	semidirect
440. #417	C₂²×C₃₁	semidirect
441. #416	C₂²×C₃₁	semidirect
442. #416	C₂²×C₃₁	semidirect
443. C₂×#103	C₂²×C₃₁	semidirect
444. C₂×#102	C₂²×C₃₁	semidirect
487. #131	D₄×C₃₁	semidirect
559. C₃₁	#60460	direct (N × H)
624. M₁₆	C₂×D₄×C₃₁	semidirect
627. C₂×C₈	C₂×D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#577	2
C₂×C₃₁×#568	2
C₃₁×#3489	2
C₃₁×#3488	2
C₃₁×#3063	2
C₃₁×#3062	2
C₃₁×#3061	2
C₃₁×#3057	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3054	2
C₂×C₃₁×#468	2
C₃₁×#2913	2
C₃₁×#2898	2
C₃₁×#2897	2
#60460	31

Subgroups — C31×#60460 #21517219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60460 #21517219