Subgroups — C₃₁×#23029 #21479788

Order 7936.

1138 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1926	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1874	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1864	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#121	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₃₁	—	2	2	no	—
16	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₃₁×#466	C₄	1	8	yes	complemented
19	C₃₁×#442	—	2	4	no	—
20	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#106	—	2	4	no	—
22	C₂×C₃₁×#106	C₂²	1	2	yes	—
23	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	2	yes	—
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	2	yes	—
28	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
31	C₃₁×#390	C₂²	1	2	yes	—
32	C₃₁×#389	C₂²	1	2	yes	—
33	C₃₁×#388	—	2	2	no	—
34	C₃₁×#386	—	2	2	no	—
35	C₃₁×#385	—	2	2	no	—
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#336	C₂²	1	1	yes	characteristic
41	C₃₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	2	no	—
43	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₃₁	—	2	2	no	—
45	C₂³×C₄×C₃₁	—	2	2	no	—
46	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₃₁	—	2	2	no	—
48	C₂×D₈×C₃₁	—	2	2	no	—
49	C₂×D₈×C₃₁	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	—	2	2	no	—
52	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×#121	—	2	4	no	—
58	C₃₁×#121	C₂×C₄	1	8	yes	complemented
59	C₄×D₄×C₃₁	—	2	4	no	—
60	C₄×D₄×C₃₁	—	4	2	no	—
61	C₄×D₄×C₃₁	—	4	8	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
74	C₂×C₄²×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
77	C₃₁×#107	C₂×C₄	1	4	yes	complemented
78	C₃₁×#106	—	2	2	no	—
79	C₃₁×#106	—	2	4	no	—
80	C₃₁×#106	D₄	1	4	yes	complemented
81	C₃₁×#102	—	2	4	no	—
82	C₃₁×#102	—	4	2	no	—
83	C₃₁×#102	C₂×C₄	1	8	yes	complemented
84	C₃₁×C₂²⋊C₈	—	2	2	no	—
85	C₃₁×#97	—	2	2	no	—
86	C₃₁×#97	—	2	2	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	—	2	2	no	—
89	C₃₁×#95	D₄	1	2	yes	—
90	C₂⁴×C₃₁	—	2	2	no	—
91	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₃₁	—	2	8	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	2	2	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	2	2	no	—
98	C₂×D₄×C₃₁	—	4	4	no	—
99	C₂×D₄×C₃₁	—	4	4	no	—
100	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	—	4	4	no	—
109	C₂²×C₄×C₃₁	—	4	4	no	—
110	C₂²×C₄×C₃₁	—	4	4	no	—
111	C₂²×C₄×C₃₁	—	4	4	no	—
112	C₂²×C₄×C₃₁	—	8	2	no	—
113	C₂²×C₄×C₃₁	—	8	2	no	—
114	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	#41	1	2	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
120	D₈×C₃₁	—	2	8	no	—
121	C₂×C₈×C₃₁	—	2	1	no	—
122	C₂×C₈×C₃₁	—	2	1	no	—
123	C₂×C₈×C₃₁	—	2	8	no	—
124	C₂×C₈×C₃₁	—	2	1	no	—
125	C₂×C₈×C₃₁	—	2	1	no	—
126	C₂×C₈×C₃₁	—	2	1	no	—
127	C₂×C₈×C₃₁	—	2	1	no	—
128	C₂×C₈×C₃₁	—	2	1	no	—
129	C₂×C₈×C₃₁	—	2	1	no	—
130	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₃₁	#41	1	2	yes	—
134	C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₄⋊C₄×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	—	2	2	no	—
138	C₄⋊C₄×C₃₁	—	4	4	no	—
139	C₄⋊C₄×C₃₁	—	4	4	no	—
140	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
141	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₃₁	—	2	4	no	—
143	C₂²⋊C₄×C₃₁	—	2	8	no	—
144	C₂²⋊C₄×C₃₁	—	4	4	no	—
145	C₂²⋊C₄×C₃₁	—	4	4	no	—
146	C₂²⋊C₄×C₃₁	—	8	2	no	—
147	C₄²×C₃₁	—	2	1	no	—
148	C₄²×C₃₁	—	2	1	no	—
149	C₄²×C₃₁	—	2	1	no	—
150	C₄²×C₃₁	—	2	1	no	—
151	C₄²×C₃₁	—	4	4	no	—
152	#23029	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂³×C₃₁	—	2	1	no	—
154	C₂³×C₃₁	—	2	1	no	—
155	C₂³×C₃₁	—	2	2	no	—
156	C₂³×C₃₁	—	2	4	no	—
157	C₂³×C₃₁	—	4	2	no	—
158	C₂³×C₃₁	—	4	2	no	—
159	C₂³×C₃₁	—	4	2	no	—
160	C₂³×C₃₁	—	4	2	no	—
161	C₂³×C₃₁	—	4	2	no	—
162	C₂³×C₃₁	—	4	2	no	—
163	C₂³×C₃₁	C₄×D₄	1	2	yes	—
164	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
165	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₃₁	—	2	4	no	—
167	D₄×C₃₁	—	2	4	no	—
168	D₄×C₃₁	—	4	16	no	—
169	D₄×C₃₁	—	4	2	no	—
170	D₄×C₃₁	—	4	2	no	—
171	C₂×C₄×C₃₁	—	2	1	no	—
172	C₂×C₄×C₃₁	—	2	1	no	—
173	C₂×C₄×C₃₁	—	2	2	no	—
174	C₂×C₄×C₃₁	—	2	2	no	—
175	C₂×C₄×C₃₁	—	2	2	no	—
176	C₂×C₄×C₃₁	—	2	2	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	2	2	no	—
179	C₂×C₄×C₃₁	—	2	4	no	—
180	C₂×C₄×C₃₁	—	2	2	no	—
181	C₂×C₄×C₃₁	—	2	2	no	—
182	C₂×C₄×C₃₁	—	2	2	no	—
183	C₂×C₄×C₃₁	—	2	2	no	—
184	C₂×C₄×C₃₁	—	2	2	no	—
185	C₂×C₄×C₃₁	—	4	2	no	—
186	C₂×C₄×C₃₁	—	4	2	no	—
187	C₂×C₄×C₃₁	—	4	2	no	—
188	C₂×C₄×C₃₁	—	4	2	no	—
189	C₂×C₄×C₃₁	—	4	2	no	—
190	C₂×C₄×C₃₁	—	4	2	no	—
191	C₂×C₄×C₃₁	—	4	2	no	—
192	C₂×C₄×C₃₁	—	8	8	no	—
193	C₂×C₄×C₃₁	—	8	8	no	—
194	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
201	C₈×C₃₁	—	2	2	no	—
202	C₈×C₃₁	—	4	1	no	—
203	C₈×C₃₁	—	4	1	no	—
204	C₈×C₃₁	C₄×D₄	1	4	yes	complemented
205	C₂×#466	C₂×C₃₁	1	1	yes	characteristic
206	C₂×#442	C₂×C₃₁	1	1	yes	characteristic, complemented
207	C₂²×#106	C₂×C₃₁	1	1	yes	characteristic, complemented
208	#2361	C₂×C₃₁	1	2	yes	complemented
209	#1972	C₂×C₃₁	1	1	yes	characteristic, complemented
210	#1943	C₂×C₃₁	1	1	yes	characteristic, complemented
211	#1926	C₂×C₃₁	1	2	yes	complemented
212	#1874	C₂×C₃₁	1	2	yes	complemented
213	#1864	C₂×C₃₁	1	2	yes	complemented
214	#1776	C₂×C₃₁	1	1	yes	characteristic, complemented
215	#1752	C₂×C₃₁	1	1	yes	characteristic, complemented
216	C₂²×C₃₁	—	2	4	no	—
217	C₂²×C₃₁	—	2	2	no	—
218	C₂²×C₃₁	—	2	2	no	—
219	C₂²×C₃₁	—	2	4	no	—
220	C₂²×C₃₁	—	4	4	no	—
221	C₂²×C₃₁	—	4	4	no	—
222	C₂²×C₃₁	—	4	4	no	—
223	C₂²×C₃₁	—	8	2	no	—
224	C₂²×C₃₁	—	8	2	no	—
225	C₂²×C₃₁	—	8	2	no	—
226	C₂²×C₃₁	—	8	2	no	—
227	C₂²×C₃₁	#442	1	4	yes	complemented
228	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₃₁	D₄²	1	1	yes	characteristic
230	C₂²×C₃₁	#547	1	1	yes	characteristic
231	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
232	C₂²×C₃₁	#577	1	2	yes	—
233	C₄×C₃₁	—	2	2	no	—
234	C₄×C₃₁	—	4	2	no	—
235	C₄×C₃₁	—	4	4	no	—
236	C₄×C₃₁	—	4	2	no	—
237	C₄×C₃₁	—	4	4	no	—
238	C₄×C₃₁	—	8	2	no	—
239	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₃₁	#520	1	1	yes	characteristic
241	C₄×C₃₁	#548	1	1	yes	characteristic
242	C₄×C₃₁	#553	1	1	yes	characteristic
243	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×#121	C₂²×C₃₁	1	2	yes	—
246	C₂×C₄×D₄	—	2	2	no	—
247	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
249	#466	C₄×C₃₁	1	8	yes	complemented
250	#442	—	2	4	no	—
251	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
252	C₂×#106	—	2	4	no	—
253	C₂×#106	C₂²×C₃₁	1	2	yes	—
254	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
255	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
256	C₂×#102	C₂²×C₃₁	1	2	yes	—
257	C₂×#102	C₂²×C₃₁	1	2	yes	—
258	C₂×#102	C₂²×C₃₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
260	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
261	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
262	#390	C₂²×C₃₁	1	2	yes	—
263	#389	C₂²×C₃₁	1	2	yes	—
264	#388	—	2	2	no	—
265	#386	—	2	2	no	—
266	#385	—	2	2	no	—
267	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
269	#340	C₂²×C₃₁	1	2	yes	—
270	#340	C₂²×C₃₁	1	2	yes	—
271	#336	C₂²×C₃₁	1	1	yes	characteristic
272	#336	C₂²×C₃₁	1	1	yes	characteristic
273	C₂×C₃₁	—	2	4	no	—
274	C₂×C₃₁	—	8	4	no	—
275	C₂×C₃₁	#2361	1	1	yes	characteristic
276	C₂×C₃₁	C₂×#442	1	1	yes	characteristic
277	C₂×C₃₁	#2952	1	1	yes	characteristic
278	C₂×C₃₁	#3265	1	2	yes	—
279	C₂×C₃₁	#3345	1	2	yes	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	C₂×C₄×C₃₁	1	4	yes	complemented
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
291	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
295	#121	—	2	4	no	—
296	#121	C₂×C₄×C₃₁	1	8	yes	complemented
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	4	2	no	—
299	C₄×D₄	—	4	8	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	4	2	no	—
304	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
315	#107	C₂×C₄×C₃₁	1	4	yes	complemented
316	#106	—	2	2	no	—
317	#106	—	2	4	no	—
318	#106	D₄×C₃₁	1	4	yes	complemented
319	#102	—	2	4	no	—
320	#102	—	4	2	no	—
321	#102	C₂×C₄×C₃₁	1	8	yes	complemented
322	C₂²⋊C₈	—	2	2	no	—
323	#97	—	2	2	no	—
324	#97	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	D₄×C₃₁	1	2	yes	—
328	C₃₁	#23029	1	1	yes	characteristic, direct product factor, Sylow
329	C₂⁴	—	2	2	no	—
330	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	—	8	2	no	—
353	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
357	C₂²×C₄	#41×C₃₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
359	D₈	—	2	8	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	8	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
370	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
372	C₂×C₈	#41×C₃₁	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
380	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	4	4	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₄×D₄×C₃₁	1	2	yes	—
402	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
403	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	8	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
437	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₈	C₄×D₄×C₃₁	1	4	yes	complemented
443	C₂²	—	2	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	C₃₁×#442	1	4	yes	complemented
455	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
456	C₂²	D₄²×C₃₁	1	1	yes	characteristic
457	C₂²	C₃₁×#547	1	1	yes	characteristic
458	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
459	C₂²	C₃₁×#577	1	2	yes	—
460	C₄	—	2	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	8	2	no	—
466	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
467	C₄	C₃₁×#520	1	1	yes	characteristic
468	C₄	C₃₁×#548	1	1	yes	characteristic
469	C₄	C₃₁×#553	1	1	yes	characteristic
470	C₂	—	2	4	no	—
471	C₂	—	8	4	no	—
472	C₂	C₃₁×#2361	1	1	yes	characteristic
473	C₂	C₂×C₃₁×#442	1	1	yes	characteristic
474	C₂	C₃₁×#2952	1	1	yes	characteristic
475	C₂	C₃₁×#3265	1	2	yes	—
476	C₂	C₃₁×#3345	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄×C₂²⋊C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#442	C₂	semidirect
3. C₂²×C₃₁×#106	C₂	semidirect
4. C₃₁×#2361	C₂	semidirect
5. C₃₁×#1972	C₂	semidirect
6. C₃₁×#1943	C₂	semidirect
7. C₃₁×#1926	C₂	semidirect
8. C₃₁×#1874	C₂	semidirect
9. C₃₁×#1864	C₂	semidirect
10. C₃₁×#1776	C₂	semidirect
11. C₃₁×#1752	C₂	semidirect
18. C₃₁×#466	C₄	semidirect
49. C₂×D₈×C₃₁	C₂×C₄	semidirect
52. C₂²×C₈×C₃₁	C₂×C₄	semidirect
58. C₃₁×#121	C₂×C₄	semidirect
77. C₃₁×#107	C₂×C₄	semidirect
80. C₃₁×#106	D₄	semidirect
83. C₃₁×#102	C₂×C₄	semidirect
152. #23029	C₃₁	direct (N × H)
204. C₈×C₃₁	C₄×D₄	semidirect
206. C₂×#442	C₂×C₃₁	semidirect
207. C₂²×#106	C₂×C₃₁	semidirect
208. #2361	C₂×C₃₁	semidirect
209. #1972	C₂×C₃₁	semidirect
210. #1943	C₂×C₃₁	semidirect
211. #1926	C₂×C₃₁	semidirect
212. #1874	C₂×C₃₁	semidirect
213. #1864	C₂×C₃₁	semidirect
214. #1776	C₂×C₃₁	semidirect
215. #1752	C₂×C₃₁	semidirect
227. C₂²×C₃₁	#442	semidirect
249. #466	C₄×C₃₁	semidirect
287. C₂×D₈	C₂×C₄×C₃₁	semidirect
290. C₂²×C₈	C₂×C₄×C₃₁	semidirect
296. #121	C₂×C₄×C₃₁	semidirect
315. #107	C₂×C₄×C₃₁	semidirect
318. #106	D₄×C₃₁	semidirect
321. #102	C₂×C₄×C₃₁	semidirect
328. C₃₁	#23029	direct (N × H)
442. C₈	C₄×D₄×C₃₁	semidirect
454. C₂²	C₃₁×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#466	2
C₂×C₃₁×#442	2
C₂²×C₃₁×#106	2
C₃₁×#2361	2
C₃₁×#1972	2
C₃₁×#1943	2
C₃₁×#1926	2
C₃₁×#1874	2
C₃₁×#1864	2
C₃₁×#1776	2
C₃₁×#1752	2
#23029	31

Subgroups — C31×#23029 #21479788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#23029 #21479788