Subgroups — C₃₁×#60822 #21517581

Order 7936.

2194 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3224	C₂	1	8	yes	maximal, complemented
4	C₃₁×#3210	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3208	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3207	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3205	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3045	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3012	C₂	1	4	yes	maximal, complemented
14	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
18	C₃₁×#556	—	2	1	no	—
19	C₃₁×#555	—	2	1	no	—
20	C₃₁×#554	—	2	1	no	—
21	C₃₁×#553	—	2	2	no	—
22	C₃₁×#550	—	2	1	no	—
23	C₃₁×#550	—	2	1	no	—
24	C₃₁×#548	—	2	2	no	—
25	C₃₁×#547	—	2	1	no	—
26	D₄²×C₃₁	—	2	1	no	—
27	D₄²×C₃₁	—	2	2	no	—
28	D₄²×C₃₁	—	2	2	no	—
29	D₄²×C₃₁	—	2	1	no	—
30	C₃₁×#542	C₂²	1	4	yes	complemented
31	C₃₁×#537	C₂²	1	2	yes	—
32	C₃₁×#535	C₂²	1	4	yes	—
33	C₃₁×#535	C₂²	1	2	yes	—
34	C₃₁×#533	C₂²	1	2	yes	complemented
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	2	yes	—
37	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#532	C₂²	1	2	yes	complemented
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#127	C₂²	1	2	yes	—
42	C₃₁×#520	C₂²	1	2	yes	complemented
43	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#496	C₂²	1	4	yes	complemented
45	C₃₁×#495	C₂²	1	4	yes	complemented
46	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#493	C₂²	1	2	yes	complemented
49	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#492	C₂²	1	2	yes	complemented
52	C₃₁×#489	C₂²	1	4	yes	complemented
53	C₃₁×#487	C₂²	1	2	yes	complemented
54	C₃₁×#486	C₂²	1	2	yes	complemented
55	C₃₁×#486	C₂²	1	2	yes	complemented
56	C₃₁×#486	C₂²	1	4	yes	complemented
57	C₃₁×#486	C₂²	1	2	yes	complemented
58	C₃₁×#464	C₂²	1	8	yes	complemented
59	C₃₁×#463	C₂²	1	8	yes	complemented
60	C₃₁×#460	C₂²	1	8	yes	complemented
61	C₃₁×#459	C₂²	1	8	yes	complemented
62	C₃₁×#452	C₂²	1	8	yes	complemented
63	C₃₁×#450	C₂²	1	8	yes	complemented
64	C₃₁×#449	C₂²	1	8	yes	complemented
65	C₃₁×#447	C₂²	1	8	yes	complemented
66	C₃₁×#433	C₂²	1	4	yes	complemented
67	C₃₁×#431	C₂²	1	2	yes	complemented
68	C₃₁×#431	C₂²	1	2	yes	complemented
69	C₃₁×#424	C₂²	1	2	yes	complemented
70	C₃₁×#417	C₂²	1	4	yes	complemented
71	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
72	C₃₁×#408	C₂²	1	2	yes	—
73	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×H(5,𝔽₂)	—	4	8	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	2	no	—
78	C₂×#41×C₃₁	C₂³	1	2	yes	—
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	C₂²×Q₈×C₃₁	—	2	1	no	—
83	C₂²×D₄×C₃₁	—	2	4	no	—
84	C₂²×D₄×C₃₁	—	2	2	no	—
85	C₂²×D₄×C₃₁	—	2	1	no	—
86	C₂²×D₄×C₃₁	—	2	2	no	—
87	C₂²×D₄×C₃₁	—	2	1	no	—
88	C₂²×D₄×C₃₁	—	2	2	no	—
89	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
91	C₃₁×AGL(1,ℤ/8)	—	4	8	no	—
92	C₃₁×#135	—	4	8	no	—
93	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
97	C₂×D₈×C₃₁	C₂³	1	4	yes	—
98	C₂×D₈×C₃₁	C₂³	1	8	yes	—
99	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
101	C₃₁×C₄⋊Q₈	—	2	1	no	—
102	C₃₁×C₄⋊Q₈	—	2	1	no	—
103	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₃₁×#127	—	2	2	no	—
108	C₃₁×#127	—	2	1	no	—
109	C₃₁×#127	—	2	1	no	—
110	C₃₁×#127	—	2	2	no	—
111	C₃₁×#127	C₂³	1	4	yes	—
112	C₃₁×#127	C₂³	1	2	yes	—
113	C₃₁×#127	C₂³	1	1	yes	characteristic
114	C₃₁×#127	C₂³	1	2	yes	—
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#125	—	2	2	no	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#124	—	2	2	no	—
120	C₃₁×#124	C₂³	1	4	yes	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#124	C₂³	1	2	yes	—
123	C₃₁×#123	—	2	4	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	1	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	1	no	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	1	no	—
135	C₃₁×#121	—	2	1	no	—
136	C₃₁×#121	—	2	2	no	—
137	C₃₁×#121	—	2	2	no	—
138	C₃₁×#121	—	2	2	no	—
139	C₃₁×#121	—	2	4	no	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	C₂³	1	4	yes	—
142	C₃₁×#120	—	2	4	no	—
143	C₃₁×#120	—	2	4	no	—
144	C₃₁×#120	—	2	4	no	—
145	C₄×Q₈×C₃₁	—	2	2	no	—
146	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	1	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	—	2	2	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	2	no	—
156	C₄×D₄×C₃₁	—	2	1	no	—
157	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
158	C₄×D₄×C₃₁	D₄	1	2	yes	—
159	C₄×D₄×C₃₁	D₄	1	2	yes	—
160	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
161	C₄×D₄×C₃₁	C₂³	1	4	yes	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	—	2	2	no	—
164	C₃₁×#117	C₂³	1	1	yes	characteristic
165	C₃₁×#117	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
171	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
172	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
173	C₃₁×#103	C₂³	1	8	yes	—
174	C₃₁×#102	C₂³	1	8	yes	—
175	C₃₁×#102	C₂³	1	8	yes	—
176	C₃₁×#102	C₂³	1	8	yes	—
177	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₃₁×#97	C₂³	1	2	yes	—
180	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₃₁	C₂³	1	2	yes	—
183	C₄×C₈×C₃₁	C₂³	1	2	yes	—
184	C₂⁴×C₃₁	—	2	4	no	—
185	C₂⁴×C₃₁	—	2	2	no	—
186	#41×C₃₁	—	2	4	no	—
187	#41×C₃₁	—	2	8	no	—
188	#41×C₃₁	—	2	8	no	—
189	#41×C₃₁	—	4	8	no	—
190	#41×C₃₁	—	4	8	no	—
191	#41×C₃₁	—	8	4	no	—
192	C₂×Q₈×C₃₁	—	2	2	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	8	2	no	—
195	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
196	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	4	no	—
200	C₂×D₄×C₃₁	—	2	2	no	—
201	C₂×D₄×C₃₁	—	2	4	no	—
202	C₂×D₄×C₃₁	—	2	1	no	—
203	C₂×D₄×C₃₁	—	2	1	no	—
204	C₂×D₄×C₃₁	—	2	1	no	—
205	C₂×D₄×C₃₁	—	2	2	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	1	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	2	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	8	no	—
215	C₂×D₄×C₃₁	—	4	8	no	—
216	C₂×D₄×C₃₁	—	4	16	no	—
217	C₂×D₄×C₃₁	—	4	8	no	—
218	C₂×D₄×C₃₁	—	8	2	no	—
219	C₂×D₄×C₃₁	—	8	4	no	—
220	C₂×D₄×C₃₁	—	8	2	no	—
221	C₂×D₄×C₃₁	—	8	4	no	—
222	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
224	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
225	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	—	2	2	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	4	no	—
232	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	Q₁₆×C₃₁	—	4	4	no	—
239	SD₁₆×C₃₁	—	4	4	no	—
240	SD₁₆×C₃₁	—	4	4	no	—
241	SD₁₆×C₃₁	—	4	8	no	—
242	D₈×C₃₁	—	4	4	no	—
243	D₈×C₃₁	—	4	8	no	—
244	M₁₆×C₃₁	—	2	4	no	—
245	C₂×C₈×C₃₁	—	2	4	no	—
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
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	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	4	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	C₂×D₄	1	2	yes	—
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₃₁	C₂×D₄	1	2	yes	—
280	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₄²×C₃₁	C₂⁴	1	2	yes	—
283	#60822	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	2	4	no	—
286	C₂³×C₃₁	—	2	2	no	—
287	C₂³×C₃₁	—	4	8	no	—
288	C₂³×C₃₁	—	4	4	no	—
289	C₂³×C₃₁	—	8	2	no	—
290	C₂³×C₃₁	—	8	2	no	—
291	C₂³×C₃₁	—	8	4	no	—
292	C₂³×C₃₁	—	8	4	no	—
293	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
294	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	4	no	—
297	Q₈×C₃₁	—	2	4	no	—
298	Q₈×C₃₁	—	4	4	no	—
299	Q₈×C₃₁	—	8	2	no	—
300	D₄×C₃₁	—	2	4	no	—
301	D₄×C₃₁	—	2	2	no	—
302	D₄×C₃₁	—	2	4	no	—
303	D₄×C₃₁	—	2	8	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	4	8	no	—
306	D₄×C₃₁	—	4	8	no	—
307	D₄×C₃₁	—	4	4	no	—
308	D₄×C₃₁	—	4	4	no	—
309	D₄×C₃₁	—	4	4	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	2	no	—
312	D₄×C₃₁	—	4	2	no	—
313	D₄×C₃₁	—	4	2	no	—
314	D₄×C₃₁	—	4	4	no	—
315	D₄×C₃₁	—	4	2	no	—
316	D₄×C₃₁	—	8	4	no	—
317	D₄×C₃₁	—	8	2	no	—
318	D₄×C₃₁	—	8	4	no	—
319	D₄×C₃₁	—	8	2	no	—
320	D₄×C₃₁	—	8	4	no	—
321	C₂×C₄×C₃₁	—	2	2	no	—
322	C₂×C₄×C₃₁	—	2	4	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	4	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	4	no	—
328	C₂×C₄×C₃₁	—	2	2	no	—
329	C₂×C₄×C₃₁	—	4	8	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	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
343	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
344	C₈×C₃₁	—	2	2	no	—
345	C₈×C₃₁	—	2	2	no	—
346	C₈×C₃₁	—	2	4	no	—
347	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#3224	C₂×C₃₁	1	8	yes	complemented
350	#3210	C₂×C₃₁	1	2	yes	complemented
351	#3208	C₂×C₃₁	1	2	yes	complemented
352	#3207	C₂×C₃₁	1	2	yes	complemented
353	#3205	C₂×C₃₁	1	2	yes	complemented
354	#3151	C₂×C₃₁	1	1	yes	characteristic, complemented
355	#3147	C₂×C₃₁	1	1	yes	characteristic, complemented
356	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
357	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3045	C₂×C₃₁	1	4	yes	complemented
359	#3012	C₂×C₃₁	1	4	yes	complemented
360	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
361	C₂²×C₃₁	—	2	1	no	—
362	C₂²×C₃₁	—	2	1	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	2	no	—
365	C₂²×C₃₁	—	2	2	no	—
366	C₂²×C₃₁	—	4	4	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	4	no	—
371	C₂²×C₃₁	—	4	2	no	—
372	C₂²×C₃₁	—	4	4	no	—
373	C₂²×C₃₁	—	4	2	no	—
374	C₂²×C₃₁	—	4	2	no	—
375	C₂²×C₃₁	—	16	4	no	—
376	C₂²×C₃₁	—	16	8	no	—
377	C₂²×C₃₁	#535	1	2	yes	—
378	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₃₁	—	2	2	no	—
380	C₄×C₃₁	—	2	2	no	—
381	C₄×C₃₁	—	2	1	no	—
382	C₄×C₃₁	—	2	2	no	—
383	C₄×C₃₁	—	2	1	no	—
384	C₄×C₃₁	—	4	2	no	—
385	C₄×C₃₁	—	4	2	no	—
386	C₄×C₃₁	—	4	4	no	—
387	C₄×C₃₁	#535	1	2	yes	—
388	C₄×C₃₁	#576	1	2	yes	—
389	C₄×C₃₁	#577	1	2	yes	—
390	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
391	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
392	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
393	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
394	#556	—	2	1	no	—
395	#555	—	2	1	no	—
396	#554	—	2	1	no	—
397	#553	—	2	2	no	—
398	#550	—	2	1	no	—
399	#550	—	2	1	no	—
400	#548	—	2	2	no	—
401	#547	—	2	1	no	—
402	D₄²	—	2	1	no	—
403	D₄²	—	2	2	no	—
404	D₄²	—	2	2	no	—
405	D₄²	—	2	1	no	—
406	#542	C₂²×C₃₁	1	4	yes	complemented
407	#537	C₂²×C₃₁	1	2	yes	—
408	#535	C₂²×C₃₁	1	4	yes	—
409	#535	C₂²×C₃₁	1	2	yes	—
410	#533	C₂²×C₃₁	1	2	yes	complemented
411	#532	C₂²×C₃₁	1	1	yes	characteristic
412	#532	C₂²×C₃₁	1	2	yes	—
413	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	#532	C₂²×C₃₁	1	2	yes	complemented
415	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
417	C₂×#127	C₂²×C₃₁	1	2	yes	—
418	#520	C₂²×C₃₁	1	2	yes	complemented
419	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
420	#496	C₂²×C₃₁	1	4	yes	complemented
421	#495	C₂²×C₃₁	1	4	yes	complemented
422	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
423	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
424	#493	C₂²×C₃₁	1	2	yes	complemented
425	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
426	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
427	#492	C₂²×C₃₁	1	2	yes	complemented
428	#489	C₂²×C₃₁	1	4	yes	complemented
429	#487	C₂²×C₃₁	1	2	yes	complemented
430	#486	C₂²×C₃₁	1	2	yes	complemented
431	#486	C₂²×C₃₁	1	2	yes	complemented
432	#486	C₂²×C₃₁	1	4	yes	complemented
433	#486	C₂²×C₃₁	1	2	yes	complemented
434	#464	C₂²×C₃₁	1	8	yes	complemented
435	#463	C₂²×C₃₁	1	8	yes	complemented
436	#460	C₂²×C₃₁	1	8	yes	complemented
437	#459	C₂²×C₃₁	1	8	yes	complemented
438	#452	C₂²×C₃₁	1	8	yes	complemented
439	#450	C₂²×C₃₁	1	8	yes	complemented
440	#449	C₂²×C₃₁	1	8	yes	complemented
441	#447	C₂²×C₃₁	1	8	yes	complemented
442	#433	C₂²×C₃₁	1	4	yes	complemented
443	#431	C₂²×C₃₁	1	2	yes	complemented
444	#431	C₂²×C₃₁	1	2	yes	complemented
445	#424	C₂²×C₃₁	1	2	yes	complemented
446	#417	C₂²×C₃₁	1	4	yes	complemented
447	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
448	#408	C₂²×C₃₁	1	2	yes	—
449	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
451	C₂×C₃₁	—	2	2	no	—
452	C₂×C₃₁	—	4	2	no	—
453	C₂×C₃₁	—	8	2	no	—
454	C₂×C₃₁	—	8	4	no	—
455	C₂×C₃₁	—	8	2	no	—
456	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
457	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
458	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
459	H(5,𝔽₂)	—	4	8	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	C₂³×C₃₁	1	2	yes	—
463	C₂×#41	C₂³×C₃₁	1	2	yes	—
464	C₂×#41	C₂³×C₃₁	1	4	yes	—
465	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
466	C₂²×Q₈	—	2	1	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
474	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
475	AGL(1,ℤ/8)	—	4	8	no	—
476	#135	—	4	8	no	—
477	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
479	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
480	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
481	C₂×D₈	C₂³×C₃₁	1	4	yes	—
482	C₂×D₈	C₂³×C₃₁	1	8	yes	—
483	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
484	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
485	C₄⋊Q₈	—	2	1	no	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
490	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
491	#127	—	2	2	no	—
492	#127	—	2	1	no	—
493	#127	—	2	1	no	—
494	#127	—	2	2	no	—
495	#127	C₂³×C₃₁	1	2	yes	—
496	#127	C₂³×C₃₁	1	1	yes	characteristic
497	#127	C₂³×C₃₁	1	4	yes	—
498	#127	C₂³×C₃₁	1	2	yes	—
499	#127	C₂³×C₃₁	1	1	yes	characteristic
500	#126	—	2	4	no	—
501	#125	—	2	2	no	—
502	#124	—	2	4	no	—
503	#124	—	2	2	no	—
504	#124	C₂³×C₃₁	1	4	yes	—
505	#124	C₂³×C₃₁	1	2	yes	—
506	#124	C₂³×C₃₁	1	2	yes	—
507	#123	—	2	4	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
512	#121	—	2	2	no	—
513	#121	—	2	4	no	—
514	#121	—	2	1	no	—
515	#121	—	2	2	no	—
516	#121	—	2	1	no	—
517	#121	—	2	2	no	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	4	no	—
524	#121	—	2	4	no	—
525	#121	C₂³×C₃₁	1	4	yes	—
526	#120	—	2	4	no	—
527	#120	—	2	4	no	—
528	#120	—	2	4	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
531	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
532	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
533	C₄×D₄	—	2	4	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
542	C₄×D₄	D₄×C₃₁	1	2	yes	—
543	C₄×D₄	D₄×C₃₁	1	2	yes	—
544	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₃₁	1	4	yes	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	C₂³×C₃₁	1	1	yes	characteristic
549	#117	C₂³×C₃₁	1	2	yes	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
555	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
556	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
557	#103	C₂³×C₃₁	1	8	yes	—
558	#102	C₂³×C₃₁	1	8	yes	—
559	#102	C₂³×C₃₁	1	8	yes	—
560	#102	C₂³×C₃₁	1	8	yes	—
561	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
563	#97	C₂³×C₃₁	1	2	yes	—
564	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₃₁	1	2	yes	—
567	C₄×C₈	C₂³×C₃₁	1	2	yes	—
568	C₃₁	#60822	1	1	yes	characteristic, direct product factor, Sylow
569	C₂⁴	—	2	4	no	—
570	C₂⁴	—	2	2	no	—
571	#41	—	2	4	no	—
572	#41	—	2	8	no	—
573	#41	—	2	8	no	—
574	#41	—	4	8	no	—
575	#41	—	4	8	no	—
576	#41	—	8	4	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	8	2	no	—
580	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	8	no	—
600	C₂×D₄	—	4	8	no	—
601	C₂×D₄	—	4	16	no	—
602	C₂×D₄	—	4	8	no	—
603	C₂×D₄	—	8	2	no	—
604	C₂×D₄	—	8	4	no	—
605	C₂×D₄	—	8	2	no	—
606	C₂×D₄	—	8	4	no	—
607	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
608	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
609	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
610	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
611	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
619	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
623	Q₁₆	—	4	4	no	—
624	SD₁₆	—	4	4	no	—
625	SD₁₆	—	4	4	no	—
626	SD₁₆	—	4	8	no	—
627	D₈	—	4	4	no	—
628	D₈	—	4	8	no	—
629	M₁₆	—	2	4	no	—
630	C₂×C₈	—	2	4	no	—
631	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
632	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
633	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
658	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
659	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
660	C₄²	—	2	4	no	—
661	C₄²	C₂×D₄×C₃₁	1	2	yes	—
662	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₃₁	1	2	yes	—
665	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
667	C₄²	C₂⁴×C₃₁	1	2	yes	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	8	2	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
678	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
679	Q₈	—	2	2	no	—
680	Q₈	—	2	4	no	—
681	Q₈	—	2	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	8	2	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	4	no	—
687	D₄	—	2	8	no	—
688	D₄	—	2	4	no	—
689	D₄	—	4	8	no	—
690	D₄	—	4	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	2	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	2	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	2	no	—
704	D₄	—	8	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
726	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
727	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₈	—	2	4	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	8	no	—
747	C₂²	C₃₁×#535	1	2	yes	—
748	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	4	no	—
757	C₄	C₃₁×#535	1	2	yes	—
758	C₄	C₃₁×#576	1	2	yes	—
759	C₄	C₃₁×#577	1	2	yes	—
760	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
761	C₂	—	2	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	—	8	2	no	—
766	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
767	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
768	C₂	C₂×C₃₁×#577	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3498	C₂	semidirect
3. C₃₁×#3224	C₂	semidirect
4. C₃₁×#3210	C₂	semidirect
5. C₃₁×#3208	C₂	semidirect
6. C₃₁×#3207	C₂	semidirect
7. C₃₁×#3205	C₂	semidirect
8. C₃₁×#3151	C₂	semidirect
9. C₃₁×#3147	C₂	semidirect
10. C₃₁×#3141	C₂	semidirect
11. C₂×C₃₁×#486	C₂	semidirect
12. C₃₁×#3045	C₂	semidirect
13. C₃₁×#3012	C₂	semidirect
14. C₃₁×#2922	C₂	semidirect
16. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₃₁×#135	C₂²	semidirect
30. C₃₁×#542	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
37. C₃₁×#532	C₂²	semidirect
38. C₃₁×#532	C₂²	semidirect
39. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#520	C₂²	semidirect
44. C₃₁×#496	C₂²	semidirect
45. C₃₁×#495	C₂²	semidirect
46. C₃₁×#494	C₂²	semidirect
47. C₃₁×#493	C₂²	semidirect
48. C₃₁×#493	C₂²	semidirect
49. C₃₁×#492	C₂²	semidirect
50. C₃₁×#492	C₂²	semidirect
51. C₃₁×#492	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
53. C₃₁×#487	C₂²	semidirect
54. C₃₁×#486	C₂²	semidirect
55. C₃₁×#486	C₂²	semidirect
56. C₃₁×#486	C₂²	semidirect
57. C₃₁×#486	C₂²	semidirect
58. C₃₁×#464	C₂²	semidirect
59. C₃₁×#463	C₂²	semidirect
60. C₃₁×#460	C₂²	semidirect
61. C₃₁×#459	C₂²	semidirect
62. C₃₁×#452	C₂²	semidirect
63. C₃₁×#450	C₂²	semidirect
64. C₃₁×#449	C₂²	semidirect
65. C₃₁×#447	C₂²	semidirect
66. C₃₁×#433	C₂²	semidirect
67. C₃₁×#431	C₂²	semidirect
68. C₃₁×#431	C₂²	semidirect
69. C₃₁×#424	C₂²	semidirect
70. C₃₁×#417	C₂²	semidirect
71. C₂×C₃₁×#102	C₂²	semidirect
73. C₄×M₁₆×C₃₁	C₂²	semidirect
74. C₂×C₄×C₈×C₃₁	C₂²	semidirect
283. #60822	C₃₁	direct (N × H)
347. #3511	C₂×C₃₁	semidirect
348. #3498	C₂×C₃₁	semidirect
349. #3224	C₂×C₃₁	semidirect
350. #3210	C₂×C₃₁	semidirect
351. #3208	C₂×C₃₁	semidirect
352. #3207	C₂×C₃₁	semidirect
353. #3205	C₂×C₃₁	semidirect
354. #3151	C₂×C₃₁	semidirect
355. #3147	C₂×C₃₁	semidirect
356. #3141	C₂×C₃₁	semidirect
357. C₂×#486	C₂×C₃₁	semidirect
358. #3045	C₂×C₃₁	semidirect
359. #3012	C₂×C₃₁	semidirect
360. #2922	C₂×C₃₁	semidirect
392. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
393. C₂×#135	C₂²×C₃₁	semidirect
406. #542	C₂²×C₃₁	semidirect
410. #533	C₂²×C₃₁	semidirect
413. #532	C₂²×C₃₁	semidirect
414. #532	C₂²×C₃₁	semidirect
415. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
418. #520	C₂²×C₃₁	semidirect
420. #496	C₂²×C₃₁	semidirect
421. #495	C₂²×C₃₁	semidirect
422. #494	C₂²×C₃₁	semidirect
423. #493	C₂²×C₃₁	semidirect
424. #493	C₂²×C₃₁	semidirect
425. #492	C₂²×C₃₁	semidirect
426. #492	C₂²×C₃₁	semidirect
427. #492	C₂²×C₃₁	semidirect
428. #489	C₂²×C₃₁	semidirect
429. #487	C₂²×C₃₁	semidirect
430. #486	C₂²×C₃₁	semidirect
431. #486	C₂²×C₃₁	semidirect
432. #486	C₂²×C₃₁	semidirect
433. #486	C₂²×C₃₁	semidirect
434. #464	C₂²×C₃₁	semidirect
435. #463	C₂²×C₃₁	semidirect
436. #460	C₂²×C₃₁	semidirect
437. #459	C₂²×C₃₁	semidirect
438. #452	C₂²×C₃₁	semidirect
439. #450	C₂²×C₃₁	semidirect
440. #449	C₂²×C₃₁	semidirect
441. #447	C₂²×C₃₁	semidirect
442. #433	C₂²×C₃₁	semidirect
443. #431	C₂²×C₃₁	semidirect
444. #431	C₂²×C₃₁	semidirect
445. #424	C₂²×C₃₁	semidirect
446. #417	C₂²×C₃₁	semidirect
447. C₂×#102	C₂²×C₃₁	semidirect
449. C₄×M₁₆	C₂²×C₃₁	semidirect
450. C₂×C₄×C₈	C₂²×C₃₁	semidirect
568. C₃₁	#60822	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×#3511	2
C₃₁×#3498	2
C₃₁×#3224	2
C₃₁×#3210	2
C₃₁×#3208	2
C₃₁×#3207	2
C₃₁×#3205	2
C₃₁×#3151	2
C₃₁×#3147	2
C₃₁×#3141	2
C₂×C₃₁×#486	2
C₃₁×#3045	2
C₃₁×#3012	2
C₃₁×#2922	2
#60822	31

Subgroups — C31×#60822 #21517581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60822 #21517581