Subgroups — C₂×C₃₁×#2482 #21491563

Order 7936.

4166 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2482	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#379	C₂	1	2	yes	maximal
10	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#117	—	2	8	no	—
14	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
18	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
19	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
26	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
27	C₃₁×#399	C₂²	1	16	yes	complemented
28	C₃₁×#397	C₂²	1	16	yes	complemented
29	C₃₁×#388	C₂²	1	32	yes	complemented
30	C₃₁×#385	C₂²	1	16	yes	complemented
31	C₃₁×#381	C₂²	1	8	yes	complemented
32	C₃₁×#379	C₂²	1	16	yes	—
33	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
34	C₂×C₃₁×#95	C₂²	1	4	yes	complemented
35	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
36	C₂⁵×C₃₁	—	2	4	no	—
37	C₂⁵×C₃₁	—	2	8	no	—
38	C₂⁵×C₃₁	—	2	8	no	—
39	C₂⁵×C₃₁	—	4	4	no	—
40	C₂⁵×C₃₁	C₂³	1	2	yes	—
41	C₂⁵×C₃₁	C₂³	1	4	yes	—
42	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₃₁	—	2	8	no	—
44	C₂³×C₄×C₃₁	—	2	4	no	—
45	C₂³×C₄×C₃₁	—	4	4	no	—
46	C₂³×C₄×C₃₁	D₄	1	8	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
55	C₃₁×#117	—	2	32	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
62	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	32	no	—
68	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
71	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
75	C₂×C₄²×C₃₁	—	2	8	no	—
76	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
77	C₃₁×#95	C₂³	1	8	yes	complemented
78	C₃₁×#95	C₂³	1	16	yes	complemented
79	C₃₁×#95	C₂³	1	8	yes	complemented
80	C₂⁴×C₃₁	—	2	4	no	—
81	C₂⁴×C₃₁	—	2	4	no	—
82	C₂⁴×C₃₁	—	2	32	no	—
83	C₂⁴×C₃₁	—	2	8	no	—
84	C₂⁴×C₃₁	—	2	4	no	—
85	C₂⁴×C₃₁	—	2	16	no	—
86	C₂⁴×C₃₁	—	2	4	no	—
87	C₂⁴×C₃₁	—	2	8	no	—
88	C₂⁴×C₃₁	—	2	8	no	—
89	C₂⁴×C₃₁	—	2	16	no	—
90	C₂⁴×C₃₁	—	4	8	no	—
91	C₂⁴×C₃₁	—	4	64	no	—
92	C₂⁴×C₃₁	—	4	16	no	—
93	C₂⁴×C₃₁	—	4	16	no	—
94	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
95	C₂⁴×C₃₁	#41	1	8	yes	—
96	C₂⁴×C₃₁	#41	1	8	yes	—
97	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
98	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
99	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	—	2	32	no	—
101	C₂²×C₄×C₃₁	—	2	16	no	—
102	C₂²×C₄×C₃₁	—	2	4	no	—
103	C₂²×C₄×C₃₁	—	2	4	no	—
104	C₂²×C₄×C₃₁	—	2	4	no	—
105	C₂²×C₄×C₃₁	—	2	4	no	—
106	C₂²×C₄×C₃₁	—	2	8	no	—
107	C₂²×C₄×C₃₁	—	2	4	no	—
108	C₂²×C₄×C₃₁	—	2	8	no	—
109	C₂²×C₄×C₃₁	—	2	8	no	—
110	C₂²×C₄×C₃₁	—	2	8	no	—
111	C₂²×C₄×C₃₁	—	2	8	no	—
112	C₂²×C₄×C₃₁	—	2	8	no	—
113	C₂²×C₄×C₃₁	—	2	8	no	—
114	C₂²×C₄×C₃₁	—	4	8	no	—
115	C₂²×C₄×C₃₁	—	4	16	no	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
125	C₄⋊C₄×C₃₁	—	2	8	no	—
126	C₄⋊C₄×C₃₁	—	2	8	no	—
127	C₄⋊C₄×C₃₁	—	4	16	no	—
128	C₂²⋊C₄×C₃₁	—	2	16	no	—
129	C₂²⋊C₄×C₃₁	—	2	32	no	—
130	C₂²⋊C₄×C₃₁	—	2	16	no	—
131	C₂²⋊C₄×C₃₁	—	2	16	no	—
132	C₂²⋊C₄×C₃₁	—	2	16	no	—
133	C₂²⋊C₄×C₃₁	—	4	16	no	—
134	C₄²×C₃₁	—	2	16	no	—
135	C₂×#2482	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₃₁	—	2	8	no	—
137	C₂³×C₃₁	—	2	8	no	—
138	C₂³×C₃₁	—	2	32	no	—
139	C₂³×C₃₁	—	2	4	no	—
140	C₂³×C₃₁	—	2	4	no	—
141	C₂³×C₃₁	—	2	32	no	—
142	C₂³×C₃₁	—	2	16	no	—
143	C₂³×C₃₁	—	2	32	no	—
144	C₂³×C₃₁	—	2	4	no	—
145	C₂³×C₃₁	—	2	4	no	—
146	C₂³×C₃₁	—	2	8	no	—
147	C₂³×C₃₁	—	2	8	no	—
148	C₂³×C₃₁	—	4	64	no	—
149	C₂³×C₃₁	—	4	16	no	—
150	C₂³×C₃₁	—	4	128	no	—
151	C₂³×C₃₁	—	4	16	no	—
152	C₂³×C₃₁	—	4	8	no	—
153	C₂³×C₃₁	—	4	8	no	—
154	C₂³×C₃₁	—	4	16	no	—
155	C₂³×C₃₁	#123	1	16	yes	—
156	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
157	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
158	C₂³×C₃₁	C₂×#41	1	8	yes	—
159	C₂³×C₃₁	C₂×#41	1	8	yes	—
160	C₂³×C₃₁	C₂×#41	1	4	yes	—
161	C₂³×C₃₁	C₂×#41	1	4	yes	—
162	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
163	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
164	C₂×C₄×C₃₁	—	2	32	no	—
165	C₂×C₄×C₃₁	—	2	8	no	—
166	C₂×C₄×C₃₁	—	2	8	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	4	no	—
169	C₂×C₄×C₃₁	—	2	4	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	4	no	—
172	C₂×C₄×C₃₁	—	2	8	no	—
173	C₂×C₄×C₃₁	—	2	8	no	—
174	C₂×C₄×C₃₁	—	2	8	no	—
175	C₂×C₄×C₃₁	—	2	8	no	—
176	C₂×C₄×C₃₁	—	2	8	no	—
177	C₂×C₄×C₃₁	—	2	8	no	—
178	C₂×C₄×C₃₁	—	4	16	no	—
179	C₂×C₄×C₃₁	—	4	8	no	—
180	C₂×C₄×C₃₁	—	4	8	no	—
181	C₂×C₄×C₃₁	—	4	8	no	—
182	C₂×C₄×C₃₁	—	4	16	no	—
183	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
185	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
187	#2482	C₂×C₃₁	1	16	yes	direct product factor
188	C₂×#399	C₂×C₃₁	1	2	yes	complemented
189	C₂×#397	C₂×C₃₁	1	2	yes	complemented
190	C₂×#388	C₂×C₃₁	1	4	yes	complemented
191	C₂×#385	C₂×C₃₁	1	2	yes	complemented
192	C₂×#381	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂×#379	C₂×C₃₁	1	2	yes	—
194	C₂²×C₃₁	—	2	4	no	—
195	C₂²×C₃₁	—	2	4	no	—
196	C₂²×C₃₁	—	2	16	no	—
197	C₂²×C₃₁	—	2	32	no	—
198	C₂²×C₃₁	—	2	8	no	—
199	C₂²×C₃₁	—	2	16	no	—
200	C₂²×C₃₁	—	4	64	no	—
201	C₂²×C₃₁	—	4	4	no	—
202	C₂²×C₃₁	—	4	4	no	—
203	C₂²×C₃₁	—	4	8	no	—
204	C₂²×C₃₁	—	4	32	no	—
205	C₂²×C₃₁	C₂×#123	1	8	yes	—
206	C₂²×C₃₁	C₂×#123	1	4	yes	—
207	C₂²×C₃₁	#525	1	4	yes	—
208	C₂²×C₃₁	#535	1	4	yes	—
209	C₂²×C₃₁	#551	1	16	yes	—
210	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
211	C₂²×C₃₁	C₂²×#41	1	2	yes	—
212	C₂²×C₃₁	C₂²×#41	1	2	yes	—
213	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
214	C₄×C₃₁	—	2	4	no	—
215	C₄×C₃₁	—	2	4	no	—
216	C₄×C₃₁	—	4	4	no	—
217	C₄×C₃₁	—	4	4	no	—
218	C₄×C₃₁	—	4	4	no	—
219	C₄×C₃₁	—	4	8	no	—
220	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
221	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
222	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×#117	—	2	8	no	—
224	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
225	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
226	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
227	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
228	C₂²×C₂²⋊C₄	—	2	8	no	—
229	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
236	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
237	#399	C₂²×C₃₁	1	16	yes	complemented
238	#397	C₂²×C₃₁	1	16	yes	complemented
239	#388	C₂²×C₃₁	1	32	yes	complemented
240	#385	C₂²×C₃₁	1	16	yes	complemented
241	#381	C₂²×C₃₁	1	8	yes	complemented
242	#379	C₂²×C₃₁	1	16	yes	—
243	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
244	C₂×#95	C₂²×C₃₁	1	4	yes	complemented
245	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
246	C₂×C₃₁	—	2	8	no	—
247	C₂×C₃₁	—	4	8	no	—
248	C₂×C₃₁	#2482	1	8	yes	direct product factor
249	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
250	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
251	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
252	C₂×C₃₁	C₂×#551	1	4	yes	—
253	C₂⁵	—	2	4	no	—
254	C₂⁵	—	2	8	no	—
255	C₂⁵	—	2	8	no	—
256	C₂⁵	—	4	4	no	—
257	C₂⁵	C₂³×C₃₁	1	2	yes	—
258	C₂⁵	C₂³×C₃₁	1	4	yes	—
259	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
260	C₂³×C₄	—	2	8	no	—
261	C₂³×C₄	—	2	4	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	D₄×C₃₁	1	8	yes	—
264	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
265	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
266	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
267	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
268	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
270	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
272	#117	—	2	32	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	4	8	no	—
276	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	complemented
277	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	complemented
278	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	16	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	2	32	no	—
285	C₂×C₂²⋊C₄	—	4	8	no	—
286	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
292	C₂×C₄²	—	2	8	no	—
293	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
294	#95	C₂³×C₃₁	1	8	yes	complemented
295	#95	C₂³×C₃₁	1	8	yes	complemented
296	#95	C₂³×C₃₁	1	16	yes	complemented
297	C₃₁	C₂×#2482	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	32	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	16	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	—	2	16	no	—
308	C₂⁴	—	4	8	no	—
309	C₂⁴	—	4	64	no	—
310	C₂⁴	—	4	16	no	—
311	C₂⁴	—	4	16	no	—
312	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
313	C₂⁴	#41×C₃₁	1	8	yes	—
314	C₂⁴	#41×C₃₁	1	8	yes	—
315	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
316	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
317	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
318	C₂²×C₄	—	2	32	no	—
319	C₂²×C₄	—	2	16	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	16	no	—
334	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	—
337	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
338	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	4	16	no	—
346	C₂²⋊C₄	—	2	16	no	—
347	C₂²⋊C₄	—	2	32	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	2	16	no	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	—	4	16	no	—
352	C₄²	—	2	16	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	32	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	32	no	—
359	C₂³	—	2	16	no	—
360	C₂³	—	2	32	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	4	64	no	—
366	C₂³	—	4	16	no	—
367	C₂³	—	4	128	no	—
368	C₂³	—	4	16	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	16	no	—
372	C₂³	C₃₁×#123	1	16	yes	—
373	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
374	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
375	C₂³	C₂×#41×C₃₁	1	8	yes	—
376	C₂³	C₂×#41×C₃₁	1	8	yes	—
377	C₂³	C₂×#41×C₃₁	1	4	yes	—
378	C₂³	C₂×#41×C₃₁	1	4	yes	—
379	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
380	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
381	C₂×C₄	—	2	32	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	16	no	—
400	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	16	no	—
405	C₂²	—	2	32	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	16	no	—
408	C₂²	—	4	64	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	8	no	—
412	C₂²	—	4	32	no	—
413	C₂²	C₂×C₃₁×#123	1	8	yes	—
414	C₂²	C₂×C₃₁×#123	1	4	yes	—
415	C₂²	C₃₁×#525	1	4	yes	—
416	C₂²	C₃₁×#535	1	4	yes	—
417	C₂²	C₃₁×#551	1	16	yes	—
418	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
419	C₂²	C₂²×#41×C₃₁	1	2	yes	—
420	C₂²	C₂²×#41×C₃₁	1	2	yes	—
421	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	8	no	—
428	C₂	—	2	8	no	—
429	C₂	—	4	8	no	—
430	C₂	C₃₁×#2482	1	8	yes	direct product factor
431	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
432	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
433	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
434	C₂	C₂×C₃₁×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁶×C₃₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#117	C₂	semidirect
3. C₃₁×#2482	C₂	direct (N × H)
4. C₂×C₃₁×#399	C₂	semidirect
5. C₂×C₃₁×#397	C₂	semidirect
6. C₂×C₃₁×#388	C₂	semidirect
7. C₂×C₃₁×#385	C₂	semidirect
8. C₂×C₃₁×#381	C₂	semidirect
14. C₂×C₃₁×#117	C₂²	semidirect
15. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
17. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
26. C₂²×C₄²×C₃₁	C₂²	semidirect
27. C₃₁×#399	C₂²	semidirect
28. C₃₁×#397	C₂²	semidirect
29. C₃₁×#388	C₂²	semidirect
30. C₃₁×#385	C₂²	semidirect
31. C₃₁×#381	C₂²	semidirect
33. C₂×C₃₁×#95	C₂²	semidirect
34. C₂×C₃₁×#95	C₂²	semidirect
35. C₂×C₃₁×#95	C₂²	semidirect
59. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
60. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
61. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
76. C₂×C₄²×C₃₁	C₂³	semidirect
77. C₃₁×#95	C₂³	semidirect
78. C₃₁×#95	C₂³	semidirect
79. C₃₁×#95	C₂³	semidirect
135. C₂×#2482	C₃₁	direct (N × H)
185. C₂²×#117	C₂×C₃₁	semidirect
187. #2482	C₂×C₃₁	direct (N × H)
188. C₂×#399	C₂×C₃₁	semidirect
189. C₂×#397	C₂×C₃₁	semidirect
190. C₂×#388	C₂×C₃₁	semidirect
191. C₂×#385	C₂×C₃₁	semidirect
192. C₂×#381	C₂×C₃₁	semidirect
224. C₂×#117	C₂²×C₃₁	semidirect
225. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
226. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
227. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
236. C₂²×C₄²	C₂²×C₃₁	semidirect
237. #399	C₂²×C₃₁	semidirect
238. #397	C₂²×C₃₁	semidirect
239. #388	C₂²×C₃₁	semidirect
240. #385	C₂²×C₃₁	semidirect
241. #381	C₂²×C₃₁	semidirect
243. C₂×#95	C₂²×C₃₁	semidirect
244. C₂×#95	C₂²×C₃₁	semidirect
245. C₂×#95	C₂²×C₃₁	semidirect
248. C₂×C₃₁	#2482	direct (N × H)
276. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
277. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
278. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
293. C₂×C₄²	C₂³×C₃₁	semidirect
294. #95	C₂³×C₃₁	semidirect
295. #95	C₂³×C₃₁	semidirect
296. #95	C₂³×C₃₁	semidirect
297. C₃₁	C₂×#2482	direct (N × H)
430. C₂	C₃₁×#2482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#117	2
C₂³×C₂²⋊C₄×C₃₁	2
C₃₁×#2482	2
C₂×C₃₁×#399	2
C₂×C₃₁×#397	2
C₂×C₃₁×#388	2
C₂×C₃₁×#385	2
C₂×C₃₁×#381	2
C₂×C₃₁×#379	2
C₂×#2482	31

Subgroups — C2×C31×#2482 #21491563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2482 #21491563