Subgroups — C₂×C₃₁×#2613 #21491312

Order 7936.

7946 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#120	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2613	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#394	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#392	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#379	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₃₁	C₂²	1	2	yes	—
10	C₂³×D₄×C₃₁	—	2	16	no	—
11	C₂³×D₄×C₃₁	—	2	8	no	—
12	C₂³×D₄×C₃₁	C₂²	1	4	yes	—
13	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₃₁	C₂²	1	8	yes	complemented
15	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#123	—	2	8	no	—
18	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
19	C₂×C₃₁×#120	—	2	16	no	—
20	C₂×C₃₁×#120	C₂²	1	16	yes	complemented
21	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
27	C₃₁×#394	C₂²	1	32	yes	complemented
28	C₃₁×#392	C₂²	1	32	yes	complemented
29	C₃₁×#381	C₂²	1	8	yes	complemented
30	C₃₁×#379	C₂²	1	16	yes	complemented
31	C₂×C₃₁×#95	C₂²	1	4	yes	complemented
32	C₂⁵×C₃₁	—	2	8	no	—
33	C₂⁵×C₃₁	—	2	8	no	—
34	C₂⁵×C₃₁	—	4	16	no	—
35	C₂⁵×C₃₁	D₄	1	16	yes	complemented
36	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
37	C₂⁵×C₃₁	C₂³	1	4	yes	—
38	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
39	C₂⁵×C₃₁	C₂³	1	8	yes	—
40	C₂²×D₄×C₃₁	—	2	128	no	—
41	C₂²×D₄×C₃₁	—	2	32	no	—
42	C₂²×D₄×C₃₁	—	2	64	no	—
43	C₂²×D₄×C₃₁	—	2	8	no	—
44	C₂²×D₄×C₃₁	—	2	16	no	—
45	C₂²×D₄×C₃₁	—	2	4	no	—
46	C₂²×D₄×C₃₁	—	2	16	no	—
47	C₂²×D₄×C₃₁	—	2	32	no	—
48	C₂²×D₄×C₃₁	—	4	16	no	—
49	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
50	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
51	C₂²×D₄×C₃₁	C₂³	1	16	yes	complemented
52	C₂³×C₄×C₃₁	—	2	8	no	—
53	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
54	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
59	C₃₁×#123	—	2	32	no	—
60	C₃₁×#120	—	2	64	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
63	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₃₁	—	4	16	no	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
71	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
72	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	complemented
73	C₃₁×#95	C₂³	1	16	yes	complemented
74	C₂⁴×C₃₁	—	2	8	no	—
75	C₂⁴×C₃₁	—	2	64	no	—
76	C₂⁴×C₃₁	—	2	8	no	—
77	C₂⁴×C₃₁	—	2	8	no	—
78	C₂⁴×C₃₁	—	2	16	no	—
79	C₂⁴×C₃₁	—	2	16	no	—
80	C₂⁴×C₃₁	—	2	16	no	—
81	C₂⁴×C₃₁	—	2	16	no	—
82	C₂⁴×C₃₁	—	2	2	no	—
83	C₂⁴×C₃₁	—	2	4	no	—
84	C₂⁴×C₃₁	—	2	8	no	—
85	C₂⁴×C₃₁	—	4	64	no	—
86	C₂⁴×C₃₁	—	4	32	no	—
87	C₂⁴×C₃₁	—	4	64	no	—
88	C₂⁴×C₃₁	—	4	64	no	—
89	C₂⁴×C₃₁	C₂×D₄	1	16	yes	—
90	C₂⁴×C₃₁	C₂×D₄	1	8	yes	—
91	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
92	C₂⁴×C₃₁	C₂×D₄	1	32	yes	complemented
93	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
94	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
95	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
96	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
97	C₂×D₄×C₃₁	—	2	128	no	—
98	C₂×D₄×C₃₁	—	2	256	no	—
99	C₂×D₄×C₃₁	—	2	64	no	—
100	C₂×D₄×C₃₁	—	2	16	no	—
101	C₂×D₄×C₃₁	—	2	32	no	—
102	C₂×D₄×C₃₁	—	2	8	no	—
103	C₂×D₄×C₃₁	—	2	32	no	—
104	C₂×D₄×C₃₁	—	4	32	no	—
105	C₂×D₄×C₃₁	—	4	64	no	—
106	C₂×D₄×C₃₁	—	4	16	no	—
107	C₂²×C₄×C₃₁	—	2	32	no	—
108	C₂²×C₄×C₃₁	—	2	8	no	—
109	C₂²×C₄×C₃₁	—	2	16	no	—
110	C₂²×C₄×C₃₁	—	2	4	no	—
111	C₂²×C₄×C₃₁	—	2	4	no	—
112	C₂²×C₄×C₃₁	—	2	8	no	—
113	C₂²×C₄×C₃₁	—	2	2	no	—
114	C₂²×C₄×C₃₁	—	2	8	no	—
115	C₂²×C₄×C₃₁	—	2	16	no	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	complemented
118	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₄⋊C₄×C₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₃₁	—	2	16	no	—
124	C₂²⋊C₄×C₃₁	—	2	8	no	—
125	C₂²⋊C₄×C₃₁	—	2	32	no	—
126	C₂²⋊C₄×C₃₁	—	2	16	no	—
127	C₂²⋊C₄×C₃₁	—	4	32	no	—
128	C₂×#2613	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	2	32	no	—
130	C₂³×C₃₁	—	2	16	no	—
131	C₂³×C₃₁	—	2	8	no	—
132	C₂³×C₃₁	—	2	32	no	—
133	C₂³×C₃₁	—	2	64	no	—
134	C₂³×C₃₁	—	2	32	no	—
135	C₂³×C₃₁	—	2	32	no	—
136	C₂³×C₃₁	—	2	8	no	—
137	C₂³×C₃₁	—	2	8	no	—
138	C₂³×C₃₁	—	2	16	no	—
139	C₂³×C₃₁	—	2	16	no	—
140	C₂³×C₃₁	—	2	2	no	—
141	C₂³×C₃₁	—	2	4	no	—
142	C₂³×C₃₁	—	2	8	no	—
143	C₂³×C₃₁	—	4	64	no	—
144	C₂³×C₃₁	—	4	256	no	—
145	C₂³×C₃₁	—	4	64	no	—
146	C₂³×C₃₁	—	4	64	no	—
147	C₂³×C₃₁	—	4	32	no	—
148	C₂³×C₃₁	—	4	32	no	—
149	C₂³×C₃₁	—	4	4	no	—
150	C₂³×C₃₁	—	4	16	no	—
151	C₂³×C₃₁	—	4	8	no	—
152	C₂³×C₃₁	#120	1	16	yes	—
153	C₂³×C₃₁	C₂²×D₄	1	16	yes	—
154	C₂³×C₃₁	C₂²×D₄	1	8	yes	—
155	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
156	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
157	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
158	C₂³×C₃₁	H(5,𝔽₂)	1	8	yes	—
159	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
160	D₄×C₃₁	—	2	128	no	—
161	D₄×C₃₁	—	4	64	no	—
162	D₄×C₃₁	—	4	16	no	—
163	C₂×C₄×C₃₁	—	2	16	no	—
164	C₂×C₄×C₃₁	—	2	32	no	—
165	C₂×C₄×C₃₁	—	2	8	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	8	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	8	no	—
171	C₂×C₄×C₃₁	—	2	16	no	—
172	C₂×C₄×C₃₁	—	4	4	no	—
173	C₂×C₄×C₃₁	—	4	16	no	—
174	C₂×C₄×C₃₁	—	4	8	no	—
175	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
176	C₂⁴×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂²×#120	C₂×C₃₁	1	2	yes	complemented
179	#2613	C₂×C₃₁	1	16	yes	direct product factor
180	C₂×#394	C₂×C₃₁	1	4	yes	complemented
181	C₂×#392	C₂×C₃₁	1	4	yes	complemented
182	C₂×#381	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂×#379	C₂×C₃₁	1	2	yes	complemented
184	C₂²×C₃₁	—	2	32	no	—
185	C₂²×C₃₁	—	2	16	no	—
186	C₂²×C₃₁	—	2	8	no	—
187	C₂²×C₃₁	—	2	16	no	—
188	C₂²×C₃₁	—	2	16	no	—
189	C₂²×C₃₁	—	2	16	no	—
190	C₂²×C₃₁	—	4	128	no	—
191	C₂²×C₃₁	—	4	64	no	—
192	C₂²×C₃₁	—	4	16	no	—
193	C₂²×C₃₁	—	4	16	no	—
194	C₂²×C₃₁	—	4	2	no	—
195	C₂²×C₃₁	—	4	8	no	—
196	C₂²×C₃₁	—	4	4	no	—
197	C₂²×C₃₁	—	8	8	no	—
198	C₂²×C₃₁	C₂×#120	1	8	yes	—
199	C₂²×C₃₁	C₂×#120	1	4	yes	—
200	C₂²×C₃₁	#534	1	16	yes	—
201	C₂²×C₃₁	#535	1	8	yes	—
202	C₂²×C₃₁	C₂³×D₄	1	2	yes	—
203	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
204	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
205	C₄×C₃₁	—	2	8	no	—
206	C₄×C₃₁	—	4	2	no	—
207	C₄×C₃₁	—	4	8	no	—
208	C₄×C₃₁	—	4	4	no	—
209	C₂⁶	C₂²×C₃₁	1	2	yes	—
210	C₂³×D₄	—	2	16	no	—
211	C₂³×D₄	—	2	8	no	—
212	C₂³×D₄	C₂²×C₃₁	1	4	yes	—
213	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₂³×D₄	C₂²×C₃₁	1	8	yes	complemented
215	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
216	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×#123	—	2	8	no	—
218	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
219	C₂×#120	—	2	16	no	—
220	C₂×#120	C₂²×C₃₁	1	16	yes	complemented
221	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
222	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
225	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
226	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
227	#394	C₂²×C₃₁	1	32	yes	complemented
228	#392	C₂²×C₃₁	1	32	yes	complemented
229	#381	C₂²×C₃₁	1	8	yes	complemented
230	#379	C₂²×C₃₁	1	16	yes	complemented
231	C₂×#95	C₂²×C₃₁	1	4	yes	complemented
232	C₂×C₃₁	—	2	8	no	—
233	C₂×C₃₁	—	4	16	no	—
234	C₂×C₃₁	—	8	2	no	—
235	C₂×C₃₁	#2613	1	8	yes	direct product factor
236	C₂×C₃₁	C₂²×#120	1	1	yes	characteristic
237	C₂×C₃₁	C₂×#534	1	4	yes	—
238	C₂×C₃₁	C₂×#535	1	2	yes	—
239	C₂⁵	—	2	8	no	—
240	C₂⁵	—	2	8	no	—
241	C₂⁵	—	4	16	no	—
242	C₂⁵	D₄×C₃₁	1	16	yes	complemented
243	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
244	C₂⁵	C₂³×C₃₁	1	4	yes	—
245	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
246	C₂⁵	C₂³×C₃₁	1	8	yes	—
247	C₂²×D₄	—	2	128	no	—
248	C₂²×D₄	—	2	32	no	—
249	C₂²×D₄	—	2	64	no	—
250	C₂²×D₄	—	2	8	no	—
251	C₂²×D₄	—	2	16	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	16	no	—
254	C₂²×D₄	—	2	32	no	—
255	C₂²×D₄	—	4	16	no	—
256	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
257	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
258	C₂²×D₄	C₂³×C₃₁	1	16	yes	complemented
259	C₂³×C₄	—	2	8	no	—
260	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
261	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
262	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
263	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
265	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
266	#123	—	2	32	no	—
267	#120	—	2	64	no	—
268	C₂×C₄⋊C₄	—	2	8	no	—
269	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	16	no	—
273	C₂×C₂²⋊C₄	—	2	8	no	—
274	C₂×C₂²⋊C₄	—	4	16	no	—
275	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
278	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
279	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	complemented
280	#95	C₂³×C₃₁	1	16	yes	complemented
281	C₃₁	C₂×#2613	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	64	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	16	no	—
287	C₂⁴	—	2	16	no	—
288	C₂⁴	—	2	16	no	—
289	C₂⁴	—	2	16	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	4	64	no	—
294	C₂⁴	—	4	32	no	—
295	C₂⁴	—	4	64	no	—
296	C₂⁴	—	4	64	no	—
297	C₂⁴	C₂×D₄×C₃₁	1	16	yes	—
298	C₂⁴	C₂×D₄×C₃₁	1	8	yes	—
299	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
300	C₂⁴	C₂×D₄×C₃₁	1	32	yes	complemented
301	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
302	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
303	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
304	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
305	C₂×D₄	—	2	128	no	—
306	C₂×D₄	—	2	256	no	—
307	C₂×D₄	—	2	64	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	32	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	32	no	—
312	C₂×D₄	—	4	32	no	—
313	C₂×D₄	—	4	64	no	—
314	C₂×D₄	—	4	16	no	—
315	C₂²×C₄	—	2	32	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	16	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
325	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	complemented
326	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
327	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
330	C₄⋊C₄	—	2	16	no	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	32	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	4	32	no	—
336	C₂³	—	2	32	no	—
337	C₂³	—	2	16	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	32	no	—
340	C₂³	—	2	64	no	—
341	C₂³	—	2	32	no	—
342	C₂³	—	2	32	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	16	no	—
346	C₂³	—	2	16	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	4	64	no	—
351	C₂³	—	4	256	no	—
352	C₂³	—	4	64	no	—
353	C₂³	—	4	64	no	—
354	C₂³	—	4	32	no	—
355	C₂³	—	4	32	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	8	no	—
359	C₂³	C₃₁×#120	1	16	yes	—
360	C₂³	C₂²×D₄×C₃₁	1	16	yes	—
361	C₂³	C₂²×D₄×C₃₁	1	8	yes	—
362	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
363	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
364	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
365	C₂³	C₃₁×H(5,𝔽₂)	1	8	yes	—
366	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
367	D₄	—	2	128	no	—
368	D₄	—	4	64	no	—
369	D₄	—	4	16	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	32	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
383	C₂²	—	2	32	no	—
384	C₂²	—	2	16	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	2	16	no	—
387	C₂²	—	2	16	no	—
388	C₂²	—	2	16	no	—
389	C₂²	—	4	128	no	—
390	C₂²	—	4	64	no	—
391	C₂²	—	4	16	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	8	no	—
397	C₂²	C₂×C₃₁×#120	1	8	yes	—
398	C₂²	C₂×C₃₁×#120	1	4	yes	—
399	C₂²	C₃₁×#534	1	16	yes	—
400	C₂²	C₃₁×#535	1	8	yes	—
401	C₂²	C₂³×D₄×C₃₁	1	2	yes	—
402	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
403	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
404	C₄	—	2	8	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	8	no	—
407	C₄	—	4	4	no	—
408	C₂	—	2	8	no	—
409	C₂	—	4	16	no	—
410	C₂	—	8	2	no	—
411	C₂	C₃₁×#2613	1	8	yes	direct product factor
412	C₂	C₂²×C₃₁×#120	1	1	yes	characteristic
413	C₂	C₂×C₃₁×#534	1	4	yes	—
414	C₂	C₂×C₃₁×#535	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
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. C₂⁴×D₄×C₃₁	C₂	semidirect
2. C₂²×C₃₁×#123	C₂	semidirect
3. C₂²×C₃₁×#120	C₂	semidirect
4. C₃₁×#2613	C₂	direct (N × H)
5. C₂×C₃₁×#394	C₂	semidirect
6. C₂×C₃₁×#392	C₂	semidirect
7. C₂×C₃₁×#381	C₂	semidirect
8. C₂×C₃₁×#379	C₂	semidirect
14. C₂³×D₄×C₃₁	C₂²	semidirect
15. C₂³×D₄×C₃₁	C₂²	semidirect
18. C₂×C₃₁×#123	C₂²	semidirect
20. C₂×C₃₁×#120	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
26. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
27. C₃₁×#394	C₂²	semidirect
28. C₃₁×#392	C₂²	semidirect
29. C₃₁×#381	C₂²	semidirect
30. C₃₁×#379	C₂²	semidirect
31. C₂×C₃₁×#95	C₂²	semidirect
35. C₂⁵×C₃₁	D₄	semidirect
51. C₂²×D₄×C₃₁	C₂³	semidirect
53. C₂³×C₄×C₃₁	D₄	semidirect
62. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
70. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
71. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
72. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
73. C₃₁×#95	C₂³	semidirect
92. C₂⁴×C₃₁	C₂×D₄	semidirect
117. C₂²×C₄×C₃₁	C₂×D₄	semidirect
128. C₂×#2613	C₃₁	direct (N × H)
176. C₂⁴×D₄	C₂×C₃₁	semidirect
177. C₂²×#123	C₂×C₃₁	semidirect
178. C₂²×#120	C₂×C₃₁	semidirect
179. #2613	C₂×C₃₁	direct (N × H)
180. C₂×#394	C₂×C₃₁	semidirect
181. C₂×#392	C₂×C₃₁	semidirect
182. C₂×#381	C₂×C₃₁	semidirect
183. C₂×#379	C₂×C₃₁	semidirect
214. C₂³×D₄	C₂²×C₃₁	semidirect
215. C₂³×D₄	C₂²×C₃₁	semidirect
218. C₂×#123	C₂²×C₃₁	semidirect
220. C₂×#120	C₂²×C₃₁	semidirect
221. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
224. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
225. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
226. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
227. #394	C₂²×C₃₁	semidirect
228. #392	C₂²×C₃₁	semidirect
229. #381	C₂²×C₃₁	semidirect
230. #379	C₂²×C₃₁	semidirect
231. C₂×#95	C₂²×C₃₁	semidirect
235. C₂×C₃₁	#2613	direct (N × H)
242. C₂⁵	D₄×C₃₁	semidirect
258. C₂²×D₄	C₂³×C₃₁	semidirect
260. C₂³×C₄	D₄×C₃₁	semidirect
269. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
277. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
278. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
279. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
280. #95	C₂³×C₃₁	semidirect
281. C₃₁	C₂×#2613	direct (N × H)
300. C₂⁴	C₂×D₄×C₃₁	semidirect
325. C₂²×C₄	C₂×D₄×C₃₁	semidirect
411. C₂	C₃₁×#2613	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₃₁	2
C₂²×C₃₁×#123	2
C₂²×C₃₁×#120	2
C₃₁×#2613	2
C₂×C₃₁×#394	2
C₂×C₃₁×#392	2
C₂×C₃₁×#381	2
C₂×C₃₁×#379	2
C₂×#2613	31

Subgroups — C2×C31×#2613 #21491312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2613 #21491312