Subgroups — C₃₁×#61808 #21518567

Order 7936.

1788 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	C₃₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3345	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3332	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3307	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3198	C₂	1	4	yes	maximal, complemented
12	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3099	C₂	1	4	yes	maximal, complemented
15	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#562	—	2	2	no	—
17	C₃₁×#559	—	2	2	no	—
18	C₃₁×#556	—	2	1	no	—
19	C₃₁×#555	C₂²	1	2	yes	—
20	C₃₁×#554	—	2	1	no	—
21	C₃₁×#554	C₂²	1	2	yes	complemented
22	C₃₁×#553	C₂²	1	4	yes	—
23	C₃₁×#550	—	2	1	no	—
24	C₃₁×#550	—	2	1	no	—
25	C₃₁×#550	C₂²	1	2	yes	complemented
26	C₃₁×#547	C₂²	1	2	yes	—
27	C₃₁×#547	C₂²	1	2	yes	complemented
28	C₃₁×#547	C₂²	1	2	yes	complemented
29	C₃₁×#540	—	2	2	no	—
30	C₃₁×#538	—	2	2	no	—
31	C₃₁×#537	—	2	2	no	—
32	C₃₁×#537	C₂²	1	4	yes	—
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×#532	C₂²	1	1	yes	characteristic
38	C₃₁×#525	—	2	2	no	—
39	C₃₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#501	C₂²	1	2	yes	complemented
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#491	C₂²	1	2	yes	complemented
45	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#485	C₂²	1	4	yes	—
48	C₃₁×#485	C₂²	1	4	yes	complemented
49	C₃₁×#483	C₂²	1	2	yes	—
50	C₃₁×#483	C₂²	1	4	yes	complemented
51	C₃₁×#482	C₂²	1	4	yes	—
52	C₃₁×#482	C₂²	1	4	yes	complemented
53	C₃₁×#481	C₂²	1	4	yes	—
54	C₃₁×#481	C₂²	1	2	yes	—
55	C₃₁×#481	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	4	yes	—
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	2	yes	complemented
59	C₃₁×#476	C₂²	1	2	yes	—
60	C₃₁×#476	C₂²	1	2	yes	—
61	C₃₁×#475	C₂²	1	2	yes	complemented
62	C₃₁×#469	C₂²	1	4	yes	—
63	C₃₁×#468	C₂²	1	4	yes	—
64	C₃₁×#466	C₂²	1	4	yes	—
65	C₃₁×#465	C₂²	1	4	yes	—
66	C₃₁×#461	C₂²	1	2	yes	—
67	C₃₁×#459	C₂²	1	2	yes	—
68	C₃₁×#450	C₂²	1	2	yes	—
69	C₃₁×#449	C₂²	1	4	yes	—
70	C₃₁×#449	C₂²	1	4	yes	—
71	C₃₁×#447	C₂²	1	2	yes	—
72	C₃₁×#442	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
75	C₃₁×#436	C₂²	1	2	yes	complemented
76	C₃₁×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
78	C₃₁×#432	C₂²	1	1	yes	characteristic
79	C₃₁×#431	C₂²	1	1	yes	characteristic
80	C₃₁×#428	C₂²	1	4	yes	complemented
81	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
82	C₃₁×#417	C₂²	1	4	yes	complemented
83	C₃₁×#416	C₂²	1	4	yes	complemented
84	C₃₁×#408	C₂²	1	4	yes	—
85	C₂×#41×C₃₁	—	2	2	no	—
86	C₂×#41×C₃₁	—	2	2	no	—
87	C₂×#41×C₃₁	—	2	1	no	—
88	C₂×#41×C₃₁	C₂³	1	4	yes	—
89	C₂×#41×C₃₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	—	2	1	no	—
92	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
94	C₂×D₈×C₃₁	C₂³	1	4	yes	—
95	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
96	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
97	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×#127	—	2	2	no	—
104	C₃₁×#127	—	2	2	no	—
105	C₃₁×#127	D₄	1	1	yes	characteristic
106	C₃₁×#127	C₂³	1	1	yes	characteristic
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#125	—	2	2	no	—
109	C₃₁×#125	—	2	1	no	—
110	C₃₁×#125	C₂³	1	2	yes	—
111	C₃₁×#124	—	2	2	no	—
112	C₃₁×#124	—	2	4	no	—
113	C₃₁×#124	—	2	1	no	—
114	C₃₁×#124	D₄	1	2	yes	—
115	C₃₁×#123	—	2	4	no	—
116	C₃₁×#123	—	2	4	no	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×C₂²⋊Q₈	—	2	1	no	—
121	C₃₁×C₂²⋊Q₈	—	2	1	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	2	no	—
124	C₃₁×C₂²⋊Q₈	—	2	2	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
127	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₃₁×#121	—	2	2	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	4	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	4	no	—
133	C₃₁×#121	—	2	4	no	—
134	C₃₁×#121	—	2	1	no	—
135	C₃₁×#121	—	2	4	no	—
136	C₃₁×#121	D₄	1	2	yes	—
137	C₃₁×#121	D₄	1	2	yes	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₃₁×#121	C₂³	1	4	yes	—
140	C₃₁×#121	C₂³	1	4	yes	—
141	C₃₁×#121	C₂³	1	4	yes	—
142	C₃₁×#120	—	2	4	no	—
143	C₄×Q₈×C₃₁	—	2	2	no	—
144	C₄×Q₈×C₃₁	—	2	1	no	—
145	C₄×Q₈×C₃₁	—	2	1	no	—
146	C₄×Q₈×C₃₁	—	2	1	no	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×D₄×C₃₁	—	2	4	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	—	2	1	no	—
154	C₄×D₄×C₃₁	—	2	1	no	—
155	C₄×D₄×C₃₁	—	2	1	no	—
156	C₄×D₄×C₃₁	C₂³	1	2	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	1	no	—
162	C₃₁×#117	—	2	2	no	—
163	C₃₁×#117	C₂³	1	4	yes	—
164	C₃₁×#117	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
170	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	4	yes	—
173	C₃₁×#106	C₂³	1	2	yes	—
174	C₃₁×#106	C₂³	1	4	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×#106	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
180	C₃₁×#103	C₂³	1	2	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	2	yes	—
183	C₃₁×#103	C₂³	1	4	yes	—
184	C₃₁×#102	C₂³	1	4	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	2	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
194	C₃₁×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₂⁴×C₃₁	—	2	1	no	—
198	#41×C₃₁	—	4	4	no	—
199	#41×C₃₁	—	4	4	no	—
200	#41×C₃₁	—	4	4	no	—
201	#41×C₃₁	—	8	2	no	—
202	#41×C₃₁	—	8	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	1	no	—
207	C₂×Q₈×C₃₁	—	2	1	no	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	2	1	no	—
216	C₂×D₄×C₃₁	—	2	1	no	—
217	C₂×D₄×C₃₁	—	2	1	no	—
218	C₂×D₄×C₃₁	—	4	2	no	—
219	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₃₁	C₂×D₄	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	4	no	—
227	C₂²×C₄×C₃₁	—	2	4	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	2	no	—
232	C₂²×C₄×C₃₁	—	8	2	no	—
233	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
237	SD₁₆×C₃₁	—	4	2	no	—
238	SD₁₆×C₃₁	—	4	2	no	—
239	D₈×C₃₁	—	4	4	no	—
240	M₁₆×C₃₁	—	4	4	no	—
241	C₂×C₈×C₃₁	—	4	4	no	—
242	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
243	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₄⋊C₄×C₃₁	—	2	1	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	—	2	4	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	C₂×D₄	1	4	yes	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
279	C₄²×C₃₁	—	2	4	no	—
280	C₄²×C₃₁	—	2	2	no	—
281	C₄²×C₃₁	—	2	2	no	—
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	#61808	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₃₁	—	2	2	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	4	2	no	—
290	C₂³×C₃₁	—	8	1	no	—
291	C₂³×C₃₁	—	8	1	no	—
292	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
294	Q₈×C₃₁	—	2	2	no	—
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	4	2	no	—
297	Q₈×C₃₁	—	4	2	no	—
298	Q₈×C₃₁	—	4	2	no	—
299	Q₈×C₃₁	—	8	1	no	—
300	Q₈×C₃₁	—	8	1	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	2	no	—
307	D₄×C₃₁	—	4	2	no	—
308	D₄×C₃₁	—	4	2	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	8	1	no	—
311	D₄×C₃₁	—	8	4	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	2	no	—
314	D₄×C₃₁	—	8	4	no	—
315	D₄×C₃₁	—	8	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	2	no	—
320	C₂×C₄×C₃₁	—	2	2	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	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	4	1	no	—
327	C₂×C₄×C₃₁	—	4	4	no	—
328	C₂×C₄×C₃₁	—	4	4	no	—
329	C₂×C₄×C₃₁	—	8	2	no	—
330	C₂×C₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	8	1	no	—
332	C₂×C₄×C₃₁	—	8	4	no	—
333	C₂×C₄×C₃₁	—	8	4	no	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	4	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	1	yes	characteristic
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
341	C₈×C₃₁	—	2	2	no	—
342	C₈×C₃₁	—	2	4	no	—
343	C₈×C₃₁	—	2	2	no	—
344	#3548	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3357	C₂×C₃₁	1	2	yes	complemented
347	#3345	C₂×C₃₁	1	4	yes	complemented
348	#3335	C₂×C₃₁	1	2	yes	complemented
349	#3332	C₂×C₃₁	1	2	yes	complemented
350	#3307	C₂×C₃₁	1	4	yes	complemented
351	#3305	C₂×C₃₁	1	2	yes	complemented
352	#3237	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3198	C₂×C₃₁	1	4	yes	complemented
355	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
356	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#3099	C₂×C₃₁	1	4	yes	complemented
358	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	2	1	no	—
362	C₂²×C₃₁	—	2	4	no	—
363	C₂²×C₃₁	—	2	1	no	—
364	C₂²×C₃₁	—	2	4	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	4	2	no	—
371	C₂²×C₃₁	—	8	4	no	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	1	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	4	no	—
376	C₄×C₃₁	—	2	1	no	—
377	C₄×C₃₁	—	2	1	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	2	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	2	no	—
383	C₄×C₃₁	—	4	2	no	—
384	C₄×C₃₁	#577	1	2	yes	—
385	C₄×C₃₁	#585	1	2	yes	—
386	#562	—	2	2	no	—
387	#559	—	2	2	no	—
388	#556	—	2	1	no	—
389	#555	C₂²×C₃₁	1	2	yes	—
390	#554	—	2	1	no	—
391	#554	C₂²×C₃₁	1	2	yes	complemented
392	#553	C₂²×C₃₁	1	4	yes	—
393	#550	—	2	1	no	—
394	#550	—	2	1	no	—
395	#550	C₂²×C₃₁	1	2	yes	complemented
396	#547	C₂²×C₃₁	1	2	yes	—
397	#547	C₂²×C₃₁	1	2	yes	complemented
398	#547	C₂²×C₃₁	1	2	yes	complemented
399	#540	—	2	2	no	—
400	#538	—	2	2	no	—
401	#537	—	2	2	no	—
402	#537	C₂²×C₃₁	1	4	yes	—
403	#535	C₂²×C₃₁	1	2	yes	—
404	#533	C₂²×C₃₁	1	1	yes	characteristic
405	#533	C₂²×C₃₁	1	1	yes	characteristic
406	#532	C₂²×C₃₁	1	1	yes	characteristic
407	#532	C₂²×C₃₁	1	1	yes	characteristic
408	#525	—	2	2	no	—
409	#520	C₂²×C₃₁	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
411	#501	C₂²×C₃₁	1	2	yes	complemented
412	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	#491	C₂²×C₃₁	1	2	yes	complemented
415	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
416	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
417	#485	C₂²×C₃₁	1	4	yes	—
418	#485	C₂²×C₃₁	1	4	yes	complemented
419	#483	C₂²×C₃₁	1	2	yes	—
420	#483	C₂²×C₃₁	1	4	yes	complemented
421	#482	C₂²×C₃₁	1	4	yes	—
422	#482	C₂²×C₃₁	1	4	yes	complemented
423	#481	C₂²×C₃₁	1	4	yes	—
424	#481	C₂²×C₃₁	1	2	yes	—
425	#481	C₂²×C₃₁	1	4	yes	complemented
426	#480	C₂²×C₃₁	1	4	yes	—
427	#478	C₂²×C₃₁	1	4	yes	complemented
428	#477	C₂²×C₃₁	1	2	yes	complemented
429	#476	C₂²×C₃₁	1	2	yes	—
430	#476	C₂²×C₃₁	1	2	yes	—
431	#475	C₂²×C₃₁	1	2	yes	complemented
432	#469	C₂²×C₃₁	1	4	yes	—
433	#468	C₂²×C₃₁	1	4	yes	—
434	#466	C₂²×C₃₁	1	4	yes	—
435	#465	C₂²×C₃₁	1	4	yes	—
436	#461	C₂²×C₃₁	1	2	yes	—
437	#459	C₂²×C₃₁	1	2	yes	—
438	#450	C₂²×C₃₁	1	2	yes	—
439	#449	C₂²×C₃₁	1	4	yes	—
440	#449	C₂²×C₃₁	1	4	yes	—
441	#447	C₂²×C₃₁	1	2	yes	—
442	#442	C₂²×C₃₁	1	4	yes	—
443	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
444	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
445	#436	C₂²×C₃₁	1	2	yes	complemented
446	#435	C₂²×C₃₁	1	4	yes	complemented
447	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
448	#432	C₂²×C₃₁	1	1	yes	characteristic
449	#431	C₂²×C₃₁	1	1	yes	characteristic
450	#428	C₂²×C₃₁	1	4	yes	complemented
451	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
452	#417	C₂²×C₃₁	1	4	yes	complemented
453	#416	C₂²×C₃₁	1	4	yes	complemented
454	#408	C₂²×C₃₁	1	4	yes	—
455	C₂×C₃₁	—	4	4	no	—
456	C₂×C₃₁	—	4	1	no	—
457	C₂×C₃₁	—	8	2	no	—
458	C₂×C₃₁	—	8	2	no	—
459	C₂×C₃₁	#3485	1	1	yes	characteristic
460	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
461	C₂×C₃₁	#3585	1	1	yes	characteristic
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	C₂³×C₃₁	1	4	yes	—
466	C₂×#41	C₂³×C₃₁	1	2	yes	—
467	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂³×C₄	—	2	1	no	—
469	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
470	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
471	C₂×D₈	C₂³×C₃₁	1	4	yes	—
472	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
473	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
474	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
480	#127	—	2	2	no	—
481	#127	—	2	2	no	—
482	#127	D₄×C₃₁	1	1	yes	characteristic
483	#127	C₂³×C₃₁	1	1	yes	characteristic
484	#126	—	2	4	no	—
485	#125	—	2	2	no	—
486	#125	—	2	1	no	—
487	#125	C₂³×C₃₁	1	2	yes	—
488	#124	—	2	2	no	—
489	#124	—	2	4	no	—
490	#124	—	2	1	no	—
491	#124	D₄×C₃₁	1	2	yes	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
504	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
505	#121	—	2	2	no	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	—	2	2	no	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	1	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₃₁	1	2	yes	—
514	#121	D₄×C₃₁	1	2	yes	—
515	#121	C₂³×C₃₁	1	2	yes	—
516	#121	C₂³×C₃₁	1	4	yes	—
517	#121	C₂³×C₃₁	1	4	yes	—
518	#121	C₂³×C₃₁	1	4	yes	—
519	#120	—	2	4	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	C₂³×C₃₁	1	2	yes	—
534	C₄×D₄	C₂³×C₃₁	1	2	yes	—
535	C₄×D₄	C₂³×C₃₁	1	2	yes	—
536	C₄×D₄	C₂³×C₃₁	1	2	yes	—
537	C₄×D₄	C₂³×C₃₁	1	2	yes	—
538	#117	—	2	1	no	—
539	#117	—	2	2	no	—
540	#117	C₂³×C₃₁	1	2	yes	—
541	#117	C₂³×C₃₁	1	4	yes	—
542	C₂×C₄⋊C₄	—	2	2	no	—
543	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
548	#107	C₂³×C₃₁	1	4	yes	—
549	#107	C₂³×C₃₁	1	4	yes	—
550	#106	C₂³×C₃₁	1	2	yes	—
551	#106	C₂³×C₃₁	1	4	yes	—
552	#106	C₂³×C₃₁	1	4	yes	—
553	#106	C₂³×C₃₁	1	4	yes	—
554	#106	C₂³×C₃₁	1	2	yes	—
555	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
556	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
557	#103	C₂³×C₃₁	1	2	yes	—
558	#103	C₂³×C₃₁	1	4	yes	—
559	#103	C₂³×C₃₁	1	2	yes	—
560	#103	C₂³×C₃₁	1	4	yes	—
561	#102	C₂³×C₃₁	1	4	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	#102	C₂³×C₃₁	1	2	yes	—
565	#102	C₂³×C₃₁	1	2	yes	—
566	#102	C₂³×C₃₁	1	4	yes	—
567	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
571	#97	C₂³×C₃₁	1	2	yes	—
572	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₃₁	#61808	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	1	no	—
576	#41	—	4	4	no	—
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	#41	—	8	2	no	—
580	#41	—	8	4	no	—
581	#41	—	8	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
599	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
600	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
601	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
602	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
615	SD₁₆	—	4	2	no	—
616	SD₁₆	—	4	2	no	—
617	D₈	—	4	4	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	8	1	no	—
668	C₂³	—	8	1	no	—
669	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	8	1	no	—
677	Q₈	—	8	1	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	2	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	D₄	—	8	2	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
713	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	4	no	—
734	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
735	C₄	—	2	4	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	C₃₁×#577	1	2	yes	—
747	C₄	C₃₁×#585	1	2	yes	—
748	C₂	—	4	1	no	—
749	C₂	—	4	4	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₃₁×#3485	1	1	yes	characteristic
753	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
754	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3548	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3345	C₂	semidirect
5. C₃₁×#3335	C₂	semidirect
6. C₃₁×#3332	C₂	semidirect
7. C₃₁×#3307	C₂	semidirect
8. C₃₁×#3305	C₂	semidirect
9. C₃₁×#3237	C₂	semidirect
10. C₃₁×#3228	C₂	semidirect
11. C₃₁×#3198	C₂	semidirect
12. C₃₁×#3109	C₂	semidirect
13. C₃₁×#3101	C₂	semidirect
14. C₃₁×#3099	C₂	semidirect
15. C₃₁×#2981	C₂	semidirect
21. C₃₁×#554	C₂²	semidirect
25. C₃₁×#550	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
28. C₃₁×#547	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#498	C₂²	semidirect
44. C₃₁×#491	C₂²	semidirect
45. C₃₁×#486	C₂²	semidirect
46. C₃₁×#486	C₂²	semidirect
48. C₃₁×#485	C₂²	semidirect
50. C₃₁×#483	C₂²	semidirect
52. C₃₁×#482	C₂²	semidirect
55. C₃₁×#481	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
61. C₃₁×#475	C₂²	semidirect
75. C₃₁×#436	C₂²	semidirect
76. C₃₁×#435	C₂²	semidirect
77. C₈×D₄×C₃₁	C₂²	semidirect
80. C₃₁×#428	C₂²	semidirect
81. C₂×C₃₁×#106	C₂²	semidirect
82. C₃₁×#417	C₂²	semidirect
83. C₃₁×#416	C₂²	semidirect
286. #61808	C₃₁	direct (N × H)
344. #3548	C₂×C₃₁	semidirect
345. #3506	C₂×C₃₁	semidirect
346. #3357	C₂×C₃₁	semidirect
347. #3345	C₂×C₃₁	semidirect
348. #3335	C₂×C₃₁	semidirect
349. #3332	C₂×C₃₁	semidirect
350. #3307	C₂×C₃₁	semidirect
351. #3305	C₂×C₃₁	semidirect
352. #3237	C₂×C₃₁	semidirect
353. #3228	C₂×C₃₁	semidirect
354. #3198	C₂×C₃₁	semidirect
355. #3109	C₂×C₃₁	semidirect
356. #3101	C₂×C₃₁	semidirect
357. #3099	C₂×C₃₁	semidirect
358. #2981	C₂×C₃₁	semidirect
391. #554	C₂²×C₃₁	semidirect
395. #550	C₂²×C₃₁	semidirect
397. #547	C₂²×C₃₁	semidirect
398. #547	C₂²×C₃₁	semidirect
411. #501	C₂²×C₃₁	semidirect
412. #500	C₂²×C₃₁	semidirect
413. #498	C₂²×C₃₁	semidirect
414. #491	C₂²×C₃₁	semidirect
415. #486	C₂²×C₃₁	semidirect
416. #486	C₂²×C₃₁	semidirect
418. #485	C₂²×C₃₁	semidirect
420. #483	C₂²×C₃₁	semidirect
422. #482	C₂²×C₃₁	semidirect
425. #481	C₂²×C₃₁	semidirect
427. #478	C₂²×C₃₁	semidirect
428. #477	C₂²×C₃₁	semidirect
431. #475	C₂²×C₃₁	semidirect
445. #436	C₂²×C₃₁	semidirect
446. #435	C₂²×C₃₁	semidirect
447. C₈×D₄	C₂²×C₃₁	semidirect
450. #428	C₂²×C₃₁	semidirect
451. C₂×#106	C₂²×C₃₁	semidirect
452. #417	C₂²×C₃₁	semidirect
453. #416	C₂²×C₃₁	semidirect
574. C₃₁	#61808	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×#3548	2
C₃₁×#3506	2
C₃₁×#3357	2
C₃₁×#3345	2
C₃₁×#3335	2
C₃₁×#3332	2
C₃₁×#3307	2
C₃₁×#3305	2
C₃₁×#3237	2
C₃₁×#3228	2
C₃₁×#3198	2
C₃₁×#3109	2
C₃₁×#3101	2
C₃₁×#3099	2
C₃₁×#2981	2
#61808	31

Subgroups — C31×#61808 #21518567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61808 #21518567