Subgroups — C₃₁×#10953 #21467712

Order 7936.

1018 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#418	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁×#100	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
15	C₃₁×#418	—	2	2	no	—
16	C₃₁×#418	—	2	2	no	—
17	C₃₁×#418	—	2	2	no	—
18	C₃₁×#418	C₄	1	4	yes	complemented
19	C₂×C₃₁×#102	—	2	2	no	—
20	C₂×C₃₁×#102	C₄	1	4	yes	complemented
21	C₂×C₃₁×#100	—	2	2	no	—
22	C₂×C₃₁×#100	—	2	2	no	—
23	C₂×C₃₁×#100	C₄	1	4	yes	complemented
24	C₃₁×#405	—	2	2	no	—
25	C₃₁×#405	—	2	2	no	—
26	C₄×M₁₆×C₃₁	—	2	2	no	—
27	C₃₁×#344	—	2	2	no	—
28	C₃₁×#339	—	2	2	no	—
29	C₃₁×#338	—	2	2	no	—
30	C₂⁵×C₃₁	—	2	1	no	—
31	C₂²×D₄×C₃₁	—	2	1	no	—
32	C₂²×D₄×C₃₁	—	2	1	no	—
33	C₂²×D₄×C₃₁	—	2	1	no	—
34	C₂²×D₄×C₃₁	—	2	1	no	—
35	C₂²×D₄×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂²×D₄×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	—	2	1	no	—
42	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
44	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₃₁	—	2	1	no	—
47	C₂×M₁₆×C₃₁	—	2	1	no	—
48	C₂×M₁₆×C₃₁	—	2	1	no	—
49	C₂×M₁₆×C₃₁	—	2	1	no	—
50	C₂×M₁₆×C₃₁	—	2	1	no	—
51	C₂×M₁₆×C₃₁	—	2	1	no	—
52	C₂×M₁₆×C₃₁	—	2	1	no	—
53	C₂×M₁₆×C₃₁	—	2	1	no	—
54	C₂×M₁₆×C₃₁	—	2	1	no	—
55	C₂×M₁₆×C₃₁	—	2	1	no	—
56	C₂×M₁₆×C₃₁	—	2	1	no	—
57	C₂×M₁₆×C₃₁	—	2	1	no	—
58	C₂×M₁₆×C₃₁	—	2	1	no	—
59	C₂×M₁₆×C₃₁	—	2	1	no	—
60	C₂×M₁₆×C₃₁	—	2	1	no	—
61	C₂×M₁₆×C₃₁	—	2	1	no	—
62	C₂×M₁₆×C₃₁	—	2	1	no	—
63	C₂×M₁₆×C₃₁	—	2	1	no	—
64	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
66	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
68	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
69	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
70	C₂²×C₈×C₃₁	—	2	1	no	—
71	C₂²×C₈×C₃₁	—	2	1	no	—
72	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₃₁	D₄	1	2	yes	—
74	C₃₁×#117	—	2	1	no	—
75	C₃₁×#117	—	2	1	no	—
76	C₃₁×#117	—	2	1	no	—
77	C₃₁×#117	—	2	1	no	—
78	C₃₁×#117	—	2	1	no	—
79	C₃₁×#117	C₂×C₄	1	2	yes	—
80	C₃₁×#117	D₄	1	2	yes	—
81	C₃₁×#117	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
86	C₂×C₄²×C₃₁	—	2	1	no	—
87	C₂×C₄²×C₃₁	—	2	1	no	—
88	C₃₁×#102	—	2	8	no	—
89	C₃₁×#102	—	2	8	no	—
90	C₃₁×#100	—	2	8	no	—
91	C₃₁×#97	—	2	4	no	—
92	C₄×C₈×C₃₁	—	2	4	no	—
93	C₂⁴×C₃₁	—	2	2	no	—
94	C₂⁴×C₃₁	—	2	2	no	—
95	C₂⁴×C₃₁	—	2	2	no	—
96	C₂⁴×C₃₁	—	4	1	no	—
97	C₂⁴×C₃₁	—	4	1	no	—
98	C₂⁴×C₃₁	—	4	1	no	—
99	C₂⁴×C₃₁	—	4	1	no	—
100	C₂⁴×C₃₁	—	8	4	no	—
101	C₂⁴×C₃₁	#41	1	1	yes	characteristic
102	C₂×D₄×C₃₁	—	2	2	no	—
103	C₂×D₄×C₃₁	—	2	2	no	—
104	C₂×D₄×C₃₁	—	2	2	no	—
105	C₂×D₄×C₃₁	—	2	2	no	—
106	C₂×D₄×C₃₁	—	2	2	no	—
107	C₂×D₄×C₃₁	—	2	2	no	—
108	C₂×D₄×C₃₁	—	2	2	no	—
109	C₂×D₄×C₃₁	—	2	2	no	—
110	C₂×D₄×C₃₁	—	2	2	no	—
111	C₂×D₄×C₃₁	—	2	2	no	—
112	C₂×D₄×C₃₁	—	2	2	no	—
113	C₂×D₄×C₃₁	—	2	2	no	—
114	C₂×D₄×C₃₁	—	2	2	no	—
115	C₂×D₄×C₃₁	—	2	2	no	—
116	C₂×D₄×C₃₁	—	2	2	no	—
117	C₂×D₄×C₃₁	—	4	1	no	—
118	C₂×D₄×C₃₁	—	4	1	no	—
119	C₂×D₄×C₃₁	—	4	1	no	—
120	C₂×D₄×C₃₁	—	4	1	no	—
121	C₂×D₄×C₃₁	—	4	1	no	—
122	C₂×D₄×C₃₁	—	4	1	no	—
123	C₂×D₄×C₃₁	—	4	1	no	—
124	C₂×D₄×C₃₁	—	4	1	no	—
125	C₂×D₄×C₃₁	—	4	1	no	—
126	C₂×D₄×C₃₁	—	4	1	no	—
127	C₂×D₄×C₃₁	—	4	1	no	—
128	C₂×D₄×C₃₁	—	4	1	no	—
129	C₂×D₄×C₃₁	C₄²	1	4	yes	—
130	C₂²×C₄×C₃₁	—	2	2	no	—
131	C₂²×C₄×C₃₁	—	4	1	no	—
132	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
142	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
143	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
144	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
145	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
146	M₁₆×C₃₁	—	2	2	no	—
147	M₁₆×C₃₁	—	2	2	no	—
148	M₁₆×C₃₁	—	2	2	no	—
149	M₁₆×C₃₁	—	2	2	no	—
150	M₁₆×C₃₁	—	2	2	no	—
151	M₁₆×C₃₁	—	2	2	no	—
152	M₁₆×C₃₁	—	2	2	no	—
153	M₁₆×C₃₁	—	2	2	no	—
154	M₁₆×C₃₁	—	2	2	no	—
155	M₁₆×C₃₁	—	4	1	no	—
156	M₁₆×C₃₁	—	4	1	no	—
157	M₁₆×C₃₁	—	4	1	no	—
158	M₁₆×C₃₁	—	4	1	no	—
159	M₁₆×C₃₁	—	4	1	no	—
160	M₁₆×C₃₁	—	4	1	no	—
161	M₁₆×C₃₁	C₂²⋊C₄	1	4	yes	—
162	C₂×C₈×C₃₁	—	2	2	no	—
163	C₂×C₈×C₃₁	—	2	2	no	—
164	C₂×C₈×C₃₁	—	2	2	no	—
165	C₂×C₈×C₃₁	—	2	2	no	—
166	C₂×C₈×C₃₁	—	2	2	no	—
167	C₂×C₈×C₃₁	—	2	2	no	—
168	C₂×C₈×C₃₁	—	2	2	no	—
169	C₂×C₈×C₃₁	—	2	2	no	—
170	C₂×C₈×C₃₁	—	2	2	no	—
171	C₂×C₈×C₃₁	—	4	1	no	—
172	C₂×C₈×C₃₁	—	4	1	no	—
173	C₂×C₈×C₃₁	C₂²⋊C₄	1	4	yes	—
174	C₄⋊C₄×C₃₁	—	2	2	no	—
175	C₄⋊C₄×C₃₁	—	2	2	no	—
176	C₄⋊C₄×C₃₁	—	4	1	no	—
177	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
178	C₂²⋊C₄×C₃₁	—	2	2	no	—
179	C₂²⋊C₄×C₃₁	—	2	2	no	—
180	C₂²⋊C₄×C₃₁	—	2	2	no	—
181	C₂²⋊C₄×C₃₁	—	4	1	no	—
182	C₄²×C₃₁	—	2	2	no	—
183	C₄²×C₃₁	—	2	2	no	—
184	C₄²×C₃₁	—	2	2	no	—
185	C₄²×C₃₁	—	4	1	no	—
186	#10953	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₃₁	—	2	4	no	—
188	C₂³×C₃₁	—	4	2	no	—
189	C₂³×C₃₁	—	4	2	no	—
190	C₂³×C₃₁	—	4	2	no	—
191	C₂³×C₃₁	—	4	2	no	—
192	C₂³×C₃₁	—	4	2	no	—
193	C₂³×C₃₁	—	4	2	no	—
194	C₂³×C₃₁	—	4	2	no	—
195	C₂³×C₃₁	—	8	4	no	—
196	C₂³×C₃₁	—	8	4	no	—
197	C₂³×C₃₁	—	8	4	no	—
198	C₂³×C₃₁	—	8	4	no	—
199	C₂³×C₃₁	—	8	4	no	—
200	C₂³×C₃₁	—	8	4	no	—
201	C₂³×C₃₁	—	8	4	no	—
202	C₂³×C₃₁	#117	1	1	yes	characteristic
203	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
204	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
205	C₂³×C₃₁	#121	1	1	yes	characteristic
206	C₂³×C₃₁	#123	1	1	yes	characteristic
207	C₂³×C₃₁	#124	1	1	yes	characteristic
208	C₂³×C₃₁	#126	1	1	yes	characteristic
209	D₄×C₃₁	—	2	4	no	—
210	D₄×C₃₁	—	2	4	no	—
211	D₄×C₃₁	—	4	2	no	—
212	D₄×C₃₁	—	4	2	no	—
213	D₄×C₃₁	—	4	2	no	—
214	D₄×C₃₁	—	4	2	no	—
215	D₄×C₃₁	—	4	2	no	—
216	D₄×C₃₁	—	4	2	no	—
217	C₂×C₄×C₃₁	—	2	4	no	—
218	C₂×C₄×C₃₁	—	4	2	no	—
219	C₂×C₄×C₃₁	—	8	2	no	—
220	C₂×C₄×C₃₁	—	8	2	no	—
221	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
226	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
227	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
238	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
239	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
240	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
241	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
242	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
243	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
244	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
245	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
246	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
247	C₂×C₄×C₃₁	#126	1	1	yes	characteristic
248	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
249	C₈×C₃₁	—	2	4	no	—
250	C₈×C₃₁	—	2	4	no	—
251	C₈×C₃₁	—	4	2	no	—
252	C₈×C₃₁	—	4	2	no	—
253	C₂×#418	C₂×C₃₁	1	1	yes	characteristic
254	C₂×#418	C₂×C₃₁	1	1	yes	characteristic
255	C₂²×#100	C₂×C₃₁	1	1	yes	characteristic
256	#2873	C₂×C₃₁	1	1	yes	characteristic, complemented
257	C₂×#344	C₂×C₃₁	1	1	yes	characteristic, complemented
258	#1733	C₂×C₃₁	1	1	yes	characteristic, complemented
259	C₂×#338	C₂×C₃₁	1	1	yes	characteristic, complemented
260	C₂²×C₃₁	—	2	2	no	—
261	C₂²×C₃₁	—	2	2	no	—
262	C₂²×C₃₁	—	2	2	no	—
263	C₂²×C₃₁	—	4	1	no	—
264	C₂²×C₃₁	—	4	1	no	—
265	C₂²×C₃₁	—	4	1	no	—
266	C₂²×C₃₁	—	4	1	no	—
267	C₂²×C₃₁	—	4	4	no	—
268	C₂²×C₃₁	—	8	4	no	—
269	C₂²×C₃₁	—	8	4	no	—
270	C₂²×C₃₁	—	8	4	no	—
271	C₂²×C₃₁	—	8	4	no	—
272	C₂²×C₃₁	—	8	4	no	—
273	C₂²×C₃₁	—	8	4	no	—
274	C₂²×C₃₁	—	8	4	no	—
275	C₂²×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₃₁	#386	1	1	yes	characteristic
277	C₂²×C₃₁	#388	1	1	yes	characteristic
278	C₂²×C₃₁	#388	1	1	yes	characteristic
279	C₂²×C₃₁	#388	1	1	yes	characteristic
280	C₂²×C₃₁	#388	1	1	yes	characteristic
281	C₂²×C₃₁	#390	1	1	yes	characteristic
282	C₄×C₃₁	—	4	4	no	—
283	C₄×C₃₁	—	8	2	no	—
284	C₄×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₃₁	#386	1	1	yes	characteristic
287	C₄×C₃₁	#386	1	1	yes	characteristic
288	C₄×C₃₁	#388	1	1	yes	characteristic
289	C₄×C₃₁	#388	1	1	yes	characteristic
290	C₄×C₃₁	#390	1	1	yes	characteristic
291	C₄×C₃₁	#390	1	1	yes	characteristic
292	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
293	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
294	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
296	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
297	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
298	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
299	#418	—	2	2	no	—
300	#418	—	2	2	no	—
301	#418	—	2	2	no	—
302	#418	C₄×C₃₁	1	4	yes	complemented
303	C₂×#102	—	2	2	no	—
304	C₂×#102	C₄×C₃₁	1	4	yes	complemented
305	C₂×#100	—	2	2	no	—
306	C₂×#100	—	2	2	no	—
307	C₂×#100	C₄×C₃₁	1	4	yes	complemented
308	#405	—	2	2	no	—
309	#405	—	2	2	no	—
310	C₄×M₁₆	—	2	2	no	—
311	#344	—	2	2	no	—
312	#339	—	2	2	no	—
313	#338	—	2	2	no	—
314	C₂×C₃₁	—	2	1	no	—
315	C₂×C₃₁	—	2	1	no	—
316	C₂×C₃₁	—	2	1	no	—
317	C₂×C₃₁	—	2	1	no	—
318	C₂×C₃₁	—	2	1	no	—
319	C₂×C₃₁	—	2	1	no	—
320	C₂×C₃₁	—	8	4	no	—
321	C₂×C₃₁	#1437	1	1	yes	characteristic
322	C₂×C₃₁	#1903	1	2	yes	—
323	C₂⁵	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
336	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
337	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
338	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
358	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
359	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
360	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
361	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
362	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
366	C₂²×C₈	D₄×C₃₁	1	2	yes	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	C₂×C₄×C₃₁	1	2	yes	—
373	#117	D₄×C₃₁	1	2	yes	—
374	#117	D₄×C₃₁	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	#102	—	2	8	no	—
382	#102	—	2	8	no	—
383	#100	—	2	8	no	—
384	#97	—	2	4	no	—
385	C₄×C₈	—	2	4	no	—
386	C₃₁	#10953	1	1	yes	characteristic, direct product factor, Sylow
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	4	1	no	—
391	C₂⁴	—	4	1	no	—
392	C₂⁴	—	4	1	no	—
393	C₂⁴	—	4	1	no	—
394	C₂⁴	—	8	4	no	—
395	C₂⁴	#41×C₃₁	1	1	yes	characteristic
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	C₄²×C₃₁	1	4	yes	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
435	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
436	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
437	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
438	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
439	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	4	1	no	—
450	M₁₆	—	4	1	no	—
451	M₁₆	—	4	1	no	—
452	M₁₆	—	4	1	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	C₂²⋊C₄×C₃₁	1	4	yes	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	C₂²⋊C₄×C₃₁	1	4	yes	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	4	1	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	—	8	4	no	—
494	C₂³	—	8	4	no	—
495	C₂³	C₃₁×#117	1	1	yes	characteristic
496	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
497	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
498	C₂³	C₃₁×#121	1	1	yes	characteristic
499	C₂³	C₃₁×#123	1	1	yes	characteristic
500	C₂³	C₃₁×#124	1	1	yes	characteristic
501	C₂³	C₃₁×#126	1	1	yes	characteristic
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
515	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
516	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
517	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
518	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
519	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
520	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
521	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
522	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
523	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
524	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
525	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
526	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
527	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
528	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
529	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
530	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
531	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
532	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
533	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
534	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
535	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
536	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
537	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
538	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
539	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
540	C₂×C₄	C₃₁×#126	1	1	yes	characteristic
541	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	2	4	no	—
544	C₈	—	4	2	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	8	4	no	—
555	C₂²	—	8	4	no	—
556	C₂²	—	8	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
562	C₂²	C₃₁×#386	1	1	yes	characteristic
563	C₂²	C₃₁×#388	1	1	yes	characteristic
564	C₂²	C₃₁×#388	1	1	yes	characteristic
565	C₂²	C₃₁×#388	1	1	yes	characteristic
566	C₂²	C₃₁×#388	1	1	yes	characteristic
567	C₂²	C₃₁×#390	1	1	yes	characteristic
568	C₄	—	4	4	no	—
569	C₄	—	8	2	no	—
570	C₄	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
571	C₄	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
572	C₄	C₃₁×#386	1	1	yes	characteristic
573	C₄	C₃₁×#386	1	1	yes	characteristic
574	C₄	C₃₁×#388	1	1	yes	characteristic
575	C₄	C₃₁×#388	1	1	yes	characteristic
576	C₄	C₃₁×#390	1	1	yes	characteristic
577	C₄	C₃₁×#390	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	8	4	no	—
585	C₂	C₃₁×#1437	1	1	yes	characteristic
586	C₂	C₃₁×#1903	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	#386
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#2873	C₂	semidirect
5. C₂×C₃₁×#344	C₂	semidirect
6. C₃₁×#1733	C₂	semidirect
7. C₂×C₃₁×#338	C₂	semidirect
18. C₃₁×#418	C₄	semidirect
20. C₂×C₃₁×#102	C₄	semidirect
23. C₂×C₃₁×#100	C₄	semidirect
186. #10953	C₃₁	direct (N × H)
256. #2873	C₂×C₃₁	semidirect
257. C₂×#344	C₂×C₃₁	semidirect
258. #1733	C₂×C₃₁	semidirect
259. C₂×#338	C₂×C₃₁	semidirect
302. #418	C₄×C₃₁	semidirect
304. C₂×#102	C₄×C₃₁	semidirect
307. C₂×#100	C₄×C₃₁	semidirect
386. C₃₁	#10953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#418	2
C₂²×C₃₁×#100	2
C₃₁×#2873	2
C₂×C₃₁×#344	2
C₃₁×#1733	2
C₂×C₃₁×#338	2
#10953	31

Subgroups — C31×#10953 #21467712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10953 #21467712