Subgroups — C₃₁×#22830 #21479589

Order 7936.

716 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1985	C₂	1	2	yes	maximal
3	C₃₁×#1917	C₂	1	2	yes	maximal
4	C₃₁×#1916	C₂	1	2	yes	maximal
5	C₃₁×#1839	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1839	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1831	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1771	C₂	1	2	yes	maximal
9	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1745	C₂	1	1	yes	maximal, characteristic
11	C₃₁×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₃₁	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₃₁	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×#97	C₂²	1	2	yes	—
18	C₂×C₃₁×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
20	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₄³×C₃₁	C₂²	1	1	yes	characteristic
30	C₄³×C₃₁	C₂²	1	1	yes	characteristic
31	C₄³×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#336	C₂²	1	1	yes	characteristic
33	C₃₁×#336	C₂²	1	1	yes	characteristic
34	C₃₁×#336	C₂²	1	2	yes	—
35	C₃₁×#336	C₂²	1	1	yes	characteristic
36	C₃₁×#336	C₂²	1	2	yes	—
37	C₃₁×#336	C₂²	1	2	yes	—
38	C₃₁×#336	C₂²	1	2	yes	—
39	C₃₁×#336	C₂²	1	2	yes	—
40	C₃₁×#336	C₂²	1	2	yes	—
41	C₃₁×#336	C₂²	1	2	yes	—
42	C₃₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₄×Q₈×C₃₁	—	2	4	no	—
49	C₄×Q₈×C₃₁	—	2	4	no	—
50	C₄×Q₈×C₃₁	—	2	2	no	—
51	C₄×Q₈×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
80	C₃₁×C₄⋊C₈	—	2	4	no	—
81	C₃₁×C₄⋊C₈	—	2	4	no	—
82	C₃₁×#97	—	2	4	no	—
83	C₃₁×#97	—	2	4	no	—
84	C₄×C₈×C₃₁	—	2	4	no	—
85	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
86	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
87	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
88	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
89	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
90	C₃₁×#95	C₂×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	#41	1	4	yes	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	2	2	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	M₁₆	1	4	yes	—
130	C₄²×C₃₁	—	2	2	no	—
131	C₄²×C₃₁	—	2	2	no	—
132	C₄²×C₃₁	—	2	2	no	—
133	C₄²×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	2	2	no	—
136	C₄²×C₃₁	—	2	2	no	—
137	C₄²×C₃₁	—	2	2	no	—
138	C₄²×C₃₁	—	2	2	no	—
139	C₄²×C₃₁	—	2	2	no	—
140	C₄²×C₃₁	—	2	2	no	—
141	C₄²×C₃₁	—	2	1	no	—
142	C₄²×C₃₁	—	2	1	no	—
143	C₄²×C₃₁	—	2	1	no	—
144	C₄²×C₃₁	—	2	1	no	—
145	C₄²×C₃₁	—	2	2	no	—
146	C₄²×C₃₁	—	4	1	no	—
147	C₄²×C₃₁	—	4	1	no	—
148	C₄²×C₃₁	—	4	1	no	—
149	C₄²×C₃₁	M₁₆	1	4	yes	—
150	C₄²×C₃₁	#41	1	2	yes	—
151	C₄²×C₃₁	#41	1	2	yes	—
152	#22830	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
154	Q₈×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	1	no	—
157	C₂×C₄×C₃₁	—	2	1	no	—
158	C₂×C₄×C₃₁	—	2	1	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	1	no	—
163	C₂×C₄×C₃₁	—	2	1	no	—
164	C₂×C₄×C₃₁	—	2	1	no	—
165	C₂×C₄×C₃₁	—	2	1	no	—
166	C₂×C₄×C₃₁	—	2	1	no	—
167	C₂×C₄×C₃₁	—	2	1	no	—
168	C₂×C₄×C₃₁	—	2	1	no	—
169	C₂×C₄×C₃₁	—	2	1	no	—
170	C₂×C₄×C₃₁	—	2	1	no	—
171	C₂×C₄×C₃₁	—	2	1	no	—
172	C₂×C₄×C₃₁	—	2	1	no	—
173	C₂×C₄×C₃₁	—	2	1	no	—
174	C₂×C₄×C₃₁	—	2	1	no	—
175	C₂×C₄×C₃₁	—	2	1	no	—
176	C₂×C₄×C₃₁	—	2	1	no	—
177	C₂×C₄×C₃₁	—	2	1	no	—
178	C₂×C₄×C₃₁	—	2	1	no	—
179	C₂×C₄×C₃₁	—	2	1	no	—
180	C₂×C₄×C₃₁	—	2	1	no	—
181	C₂×C₄×C₃₁	—	2	1	no	—
182	C₂×C₄×C₃₁	—	2	1	no	—
183	C₂×C₄×C₃₁	—	2	1	no	—
184	C₂×C₄×C₃₁	—	2	1	no	—
185	C₂×C₄×C₃₁	—	2	1	no	—
186	C₂×C₄×C₃₁	—	2	1	no	—
187	C₂×C₄×C₃₁	—	2	1	no	—
188	C₂×C₄×C₃₁	#117	1	2	yes	—
189	C₂×C₄×C₃₁	#117	1	2	yes	—
190	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₃₁	#131	1	2	yes	—
197	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₃₁	—	2	4	no	—
202	C₈×C₃₁	—	4	2	no	—
203	C₈×C₃₁	—	4	2	no	—
204	C₈×C₃₁	—	4	2	no	—
205	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic
206	#1985	C₂×C₃₁	1	2	yes	—
207	#1917	C₂×C₃₁	1	2	yes	—
208	#1916	C₂×C₃₁	1	2	yes	—
209	#1839	C₂×C₃₁	1	1	yes	characteristic
210	#1839	C₂×C₃₁	1	1	yes	characteristic
211	#1831	C₂×C₃₁	1	1	yes	characteristic
212	#1771	C₂×C₃₁	1	2	yes	—
213	#1767	C₂×C₃₁	1	1	yes	characteristic
214	#1745	C₂×C₃₁	1	1	yes	characteristic
215	#1744	C₂×C₃₁	1	1	yes	characteristic
216	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
217	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
218	C₂²×C₃₁	#519	1	1	yes	characteristic
219	C₂²×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
220	C₂²×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
221	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
222	C₂²×C₃₁	#568	1	1	yes	characteristic
223	C₄×C₃₁	—	2	2	no	—
224	C₄×C₃₁	—	2	2	no	—
225	C₄×C₃₁	—	2	2	no	—
226	C₄×C₃₁	—	2	2	no	—
227	C₄×C₃₁	—	2	2	no	—
228	C₄×C₃₁	—	2	2	no	—
229	C₄×C₃₁	—	2	2	no	—
230	C₄×C₃₁	—	2	2	no	—
231	C₄×C₃₁	—	2	2	no	—
232	C₄×C₃₁	—	4	1	no	—
233	C₄×C₃₁	—	4	1	no	—
234	C₄×C₃₁	—	4	1	no	—
235	C₄×C₃₁	—	4	1	no	—
236	C₄×C₃₁	—	4	1	no	—
237	C₄×C₃₁	#552	1	2	yes	—
238	C₄×C₃₁	#556	1	2	yes	—
239	C₂×C₄×Q₈	C₄×C₃₁	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
243	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
244	C₂×#97	C₂²×C₃₁	1	2	yes	—
245	C₂×#97	C₂²×C₃₁	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
247	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
256	C₄³	C₂²×C₃₁	1	1	yes	characteristic
257	C₄³	C₂²×C₃₁	1	1	yes	characteristic
258	C₄³	C₂²×C₃₁	1	1	yes	characteristic
259	#336	C₂²×C₃₁	1	1	yes	characteristic
260	#336	C₂²×C₃₁	1	1	yes	characteristic
261	#336	C₂²×C₃₁	1	2	yes	—
262	#336	C₂²×C₃₁	1	1	yes	characteristic
263	#336	C₂²×C₃₁	1	2	yes	—
264	#336	C₂²×C₃₁	1	2	yes	—
265	#336	C₂²×C₃₁	1	2	yes	—
266	#336	C₂²×C₃₁	1	2	yes	—
267	#336	C₂²×C₃₁	1	2	yes	—
268	#336	C₂²×C₃₁	1	2	yes	—
269	#336	C₂²×C₃₁	1	1	yes	characteristic
270	C₂×C₃₁	#2356	1	1	yes	characteristic
271	C₂×C₃₁	#2920	1	1	yes	characteristic
272	C₂×C₃₁	#2925	1	1	yes	characteristic
273	C₂×C₃₁	#2965	1	1	yes	characteristic
274	C₂×C₃₁	#2970	1	1	yes	characteristic
275	C₂×C₃₁	#2983	1	1	yes	characteristic
276	C₂×C₃₁	#2984	1	1	yes	characteristic
277	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
279	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
281	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
295	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
296	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
297	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
299	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
301	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
304	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
305	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
306	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
314	C₄⋊C₈	—	2	4	no	—
315	C₄⋊C₈	—	2	4	no	—
316	#97	—	2	4	no	—
317	#97	—	2	4	no	—
318	C₄×C₈	—	2	4	no	—
319	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
320	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
321	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
322	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
323	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
324	#95	C₂×C₄×C₃₁	1	1	yes	characteristic
325	C₃₁	#22830	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	#41×C₃₁	1	4	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	M₁₆×C₃₁	1	4	yes	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	M₁₆×C₃₁	1	4	yes	—
385	C₄²	#41×C₃₁	1	2	yes	—
386	C₄²	#41×C₃₁	1	2	yes	—
387	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	C₃₁×#117	1	2	yes	—
423	C₂×C₄	C₃₁×#117	1	2	yes	—
424	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
425	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
426	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
427	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
428	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
429	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
430	C₂×C₄	C₃₁×#131	1	2	yes	—
431	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
433	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
434	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
435	C₈	—	2	4	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
440	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
441	C₂²	C₃₁×#519	1	1	yes	characteristic
442	C₂²	C₂²×M₁₆×C₃₁	1	1	yes	characteristic
443	C₂²	C₂²×M₁₆×C₃₁	1	1	yes	characteristic
444	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
445	C₂²	C₃₁×#568	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	C₃₁×#552	1	2	yes	—
461	C₄	C₃₁×#556	1	2	yes	—
462	C₂	C₃₁×#2356	1	1	yes	characteristic
463	C₂	C₃₁×#2920	1	1	yes	characteristic
464	C₂	C₃₁×#2925	1	1	yes	characteristic
465	C₂	C₃₁×#2965	1	1	yes	characteristic
466	C₂	C₃₁×#2970	1	1	yes	characteristic
467	C₂	C₃₁×#2983	1	1	yes	characteristic
468	C₂	C₃₁×#2984	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle, prime radical	C₂³×C₃₁	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
152. #22830	C₃₁	direct (N × H)
325. C₃₁	#22830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₃₁	2
C₃₁×#1985	2
C₃₁×#1917	2
C₃₁×#1916	2
C₃₁×#1839	2
C₃₁×#1831	2
C₃₁×#1771	2
C₃₁×#1767	2
C₃₁×#1745	2
C₃₁×#1744	2
#22830	31

Subgroups — C31×#22830 #21479589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22830 #21479589