Subgroups — C₂×C₃₁×#2494 #21491544

Order 7936.

2182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2494	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃₁×#401	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#397	C₂	1	2	yes	maximal
4	C₂×C₃₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#388	C₂	1	2	yes	maximal
7	C₂×C₃₁×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#401	C₂²	1	16	yes	complemented
28	C₃₁×#397	C₂²	1	16	yes	—
29	C₃₁×#389	C₂²	1	8	yes	complemented
30	C₃₁×#389	C₂²	1	8	yes	complemented
31	C₃₁×#388	C₂²	1	16	yes	—
32	C₃₁×#387	C₂²	1	16	yes	complemented
33	C₃₁×#382	C₂²	1	8	yes	complemented
34	C₃₁×#380	C₂²	1	8	yes	—
35	C₃₁×#380	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₃₁	C₂²	1	8	yes	complemented
37	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
38	C₂×C₃₁×#95	C₂²	1	2	yes	—
39	C₂×C₃₁×#95	C₂²	1	2	yes	—
40	C₂×C₃₁×#95	C₂²	1	2	yes	—
41	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#95	C₂²	1	2	yes	—
43	C₂×C₃₁×#95	C₂²	1	2	yes	—
44	C₂×C₃₁×#95	C₂²	1	2	yes	—
45	C₂×C₃₁×#95	C₂²	1	2	yes	—
46	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
47	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	—	2	4	no	—
49	C₂³×C₄×C₃₁	—	2	4	no	—
50	C₂³×C₄×C₃₁	—	2	4	no	—
51	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
78	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
81	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
82	C₂×C₄²×C₃₁	—	2	4	no	—
83	C₂×C₄²×C₃₁	—	2	4	no	—
84	C₂×C₄²×C₃₁	—	4	4	no	—
85	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
86	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
87	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
88	C₃₁×#95	C₂³	1	8	yes	—
89	C₃₁×#95	C₂³	1	8	yes	—
90	C₃₁×#95	C₂³	1	8	yes	—
91	C₃₁×#95	C₂³	1	4	yes	—
92	C₃₁×#95	C₂³	1	8	yes	—
93	C₃₁×#95	C₂³	1	8	yes	—
94	C₃₁×#95	C₂³	1	8	yes	—
95	C₃₁×#95	C₂³	1	8	yes	—
96	C₃₁×#95	C₂³	1	4	yes	—
97	C₂⁴×C₃₁	—	2	2	no	—
98	C₂⁴×C₃₁	—	2	2	no	—
99	C₂⁴×C₃₁	—	2	2	no	—
100	C₂⁴×C₃₁	—	2	2	no	—
101	C₂⁴×C₃₁	—	2	2	no	—
102	C₂⁴×C₃₁	—	2	2	no	—
103	C₂⁴×C₃₁	#41	1	4	yes	—
104	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
105	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	—	2	2	no	—
109	C₂²×C₄×C₃₁	—	2	2	no	—
110	C₂²×C₄×C₃₁	—	2	2	no	—
111	C₂²×C₄×C₃₁	—	2	4	no	—
112	C₂²×C₄×C₃₁	—	2	2	no	—
113	C₂²×C₄×C₃₁	—	2	2	no	—
114	C₂²×C₄×C₃₁	—	2	4	no	—
115	C₂²×C₄×C₃₁	—	2	2	no	—
116	C₂²×C₄×C₃₁	—	2	4	no	—
117	C₂²×C₄×C₃₁	—	2	4	no	—
118	C₂²×C₄×C₃₁	—	2	4	no	—
119	C₂²×C₄×C₃₁	—	2	4	no	—
120	C₂²×C₄×C₃₁	—	2	4	no	—
121	C₂²×C₄×C₃₁	—	2	4	no	—
122	C₂²×C₄×C₃₁	—	2	2	no	—
123	C₂²×C₄×C₃₁	—	2	2	no	—
124	C₂²×C₄×C₃₁	—	2	2	no	—
125	C₂²×C₄×C₃₁	—	2	4	no	—
126	C₂²×C₄×C₃₁	—	2	4	no	—
127	C₂²×C₄×C₃₁	—	2	4	no	—
128	C₂²×C₄×C₃₁	—	2	2	no	—
129	C₂²×C₄×C₃₁	—	2	4	no	—
130	C₂²×C₄×C₃₁	—	2	2	no	—
131	C₂²×C₄×C₃₁	—	2	2	no	—
132	C₂²×C₄×C₃₁	—	2	8	no	—
133	C₂²×C₄×C₃₁	—	2	8	no	—
134	C₂²×C₄×C₃₁	—	2	8	no	—
135	C₂²×C₄×C₃₁	—	4	16	no	—
136	C₂²×C₄×C₃₁	#41	1	4	yes	—
137	C₂²×C₄×C₃₁	#41	1	4	yes	—
138	C₂²×C₄×C₃₁	#41	1	4	yes	—
139	C₂²×C₄×C₃₁	#41	1	4	yes	—
140	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₃₁	—	2	16	no	—
151	C₄⋊C₄×C₃₁	—	2	8	no	—
152	C₄⋊C₄×C₃₁	—	2	8	no	—
153	C₄⋊C₄×C₃₁	—	2	8	no	—
154	C₄⋊C₄×C₃₁	—	2	8	no	—
155	C₄⋊C₄×C₃₁	—	4	8	no	—
156	C₂²⋊C₄×C₃₁	—	2	8	no	—
157	C₂²⋊C₄×C₃₁	—	2	16	no	—
158	C₂²⋊C₄×C₃₁	—	2	8	no	—
159	C₂²⋊C₄×C₃₁	—	4	8	no	—
160	C₄²×C₃₁	—	2	8	no	—
161	C₄²×C₃₁	—	2	8	no	—
162	C₄²×C₃₁	—	4	8	no	—
163	C₂×#2494	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₃₁	—	2	8	no	—
165	C₂³×C₃₁	—	2	8	no	—
166	C₂³×C₃₁	—	2	8	no	—
167	C₂³×C₃₁	—	2	2	no	—
168	C₂³×C₃₁	—	2	2	no	—
169	C₂³×C₃₁	—	2	2	no	—
170	C₂³×C₃₁	—	2	2	no	—
171	C₂³×C₃₁	—	2	2	no	—
172	C₂³×C₃₁	—	2	2	no	—
173	C₂³×C₃₁	—	4	4	no	—
174	C₂³×C₃₁	—	4	4	no	—
175	C₂³×C₃₁	—	4	4	no	—
176	C₂³×C₃₁	—	4	4	no	—
177	C₂³×C₃₁	C₂×#41	1	4	yes	—
178	C₂³×C₃₁	C₂×#41	1	2	yes	—
179	C₂³×C₃₁	C₂×#41	1	2	yes	—
180	C₂³×C₃₁	C₂×#41	1	2	yes	—
181	C₂³×C₃₁	C₂×#41	1	2	yes	—
182	C₂³×C₃₁	C₂×#41	1	2	yes	—
183	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
184	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
185	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
186	C₂×C₄×C₃₁	—	2	8	no	—
187	C₂×C₄×C₃₁	—	2	2	no	—
188	C₂×C₄×C₃₁	—	2	2	no	—
189	C₂×C₄×C₃₁	—	2	2	no	—
190	C₂×C₄×C₃₁	—	2	2	no	—
191	C₂×C₄×C₃₁	—	2	2	no	—
192	C₂×C₄×C₃₁	—	2	4	no	—
193	C₂×C₄×C₃₁	—	2	2	no	—
194	C₂×C₄×C₃₁	—	2	2	no	—
195	C₂×C₄×C₃₁	—	2	4	no	—
196	C₂×C₄×C₃₁	—	2	2	no	—
197	C₂×C₄×C₃₁	—	2	4	no	—
198	C₂×C₄×C₃₁	—	2	4	no	—
199	C₂×C₄×C₃₁	—	2	4	no	—
200	C₂×C₄×C₃₁	—	2	4	no	—
201	C₂×C₄×C₃₁	—	2	4	no	—
202	C₂×C₄×C₃₁	—	2	4	no	—
203	C₂×C₄×C₃₁	—	2	2	no	—
204	C₂×C₄×C₃₁	—	2	2	no	—
205	C₂×C₄×C₃₁	—	2	2	no	—
206	C₂×C₄×C₃₁	—	2	4	no	—
207	C₂×C₄×C₃₁	—	2	4	no	—
208	C₂×C₄×C₃₁	—	2	4	no	—
209	C₂×C₄×C₃₁	—	2	2	no	—
210	C₂×C₄×C₃₁	—	2	4	no	—
211	C₂×C₄×C₃₁	—	2	2	no	—
212	C₂×C₄×C₃₁	—	2	2	no	—
213	C₂×C₄×C₃₁	—	4	4	no	—
214	C₂×C₄×C₃₁	—	4	8	no	—
215	C₂×C₄×C₃₁	—	4	8	no	—
216	C₂×C₄×C₃₁	—	4	4	no	—
217	C₂×C₄×C₃₁	—	4	8	no	—
218	C₂×C₄×C₃₁	—	4	4	no	—
219	C₂×C₄×C₃₁	—	4	8	no	—
220	C₂×C₄×C₃₁	—	4	4	no	—
221	C₂×C₄×C₃₁	—	4	16	no	—
222	C₂×C₄×C₃₁	#126	1	16	yes	—
223	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
224	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
225	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
226	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
227	#2494	C₂×C₃₁	1	16	yes	direct product factor
228	C₂×#401	C₂×C₃₁	1	2	yes	complemented
229	C₂×#397	C₂×C₃₁	1	2	yes	—
230	C₂×#389	C₂×C₃₁	1	1	yes	characteristic, complemented
231	C₂×#389	C₂×C₃₁	1	1	yes	characteristic, complemented
232	C₂×#388	C₂×C₃₁	1	2	yes	—
233	C₂×#387	C₂×C₃₁	1	2	yes	complemented
234	C₂×#382	C₂×C₃₁	1	1	yes	characteristic, complemented
235	C₂×#380	C₂×C₃₁	1	1	yes	characteristic
236	C₂×#380	C₂×C₃₁	1	1	yes	characteristic
237	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
238	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
239	C₂²×C₃₁	—	2	4	no	—
240	C₂²×C₃₁	—	2	4	no	—
241	C₂²×C₃₁	—	2	4	no	—
242	C₂²×C₃₁	—	4	2	no	—
243	C₂²×C₃₁	—	4	2	no	—
244	C₂²×C₃₁	—	4	2	no	—
245	C₂²×C₃₁	—	4	2	no	—
246	C₂²×C₃₁	—	4	16	no	—
247	C₂²×C₃₁	C₂×#126	1	4	yes	—
248	C₂²×C₃₁	#529	1	4	yes	—
249	C₂²×C₃₁	#542	1	4	yes	—
250	C₂²×C₃₁	#552	1	4	yes	—
251	C₂²×C₃₁	#553	1	4	yes	—
252	C₂²×C₃₁	#553	1	4	yes	—
253	C₂²×C₃₁	#556	1	4	yes	—
254	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
255	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
256	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
257	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
258	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
259	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
261	C₄×C₃₁	—	2	4	no	—
262	C₄×C₃₁	—	4	2	no	—
263	C₄×C₃₁	—	4	4	no	—
264	C₄×C₃₁	—	4	4	no	—
265	C₄×C₃₁	—	4	2	no	—
266	C₄×C₃₁	—	4	4	no	—
267	C₄×C₃₁	—	4	2	no	—
268	C₄×C₃₁	—	4	4	no	—
269	C₄×C₃₁	—	4	2	no	—
270	C₄×C₃₁	C₂×#126	1	8	yes	—
271	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
280	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
282	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
283	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
284	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
285	#401	C₂²×C₃₁	1	16	yes	complemented
286	#397	C₂²×C₃₁	1	16	yes	—
287	#389	C₂²×C₃₁	1	8	yes	complemented
288	#389	C₂²×C₃₁	1	8	yes	complemented
289	#388	C₂²×C₃₁	1	16	yes	—
290	#387	C₂²×C₃₁	1	16	yes	complemented
291	#382	C₂²×C₃₁	1	8	yes	complemented
292	#380	C₂²×C₃₁	1	8	yes	—
293	#380	C₂²×C₃₁	1	8	yes	—
294	C₄×C₄⋊C₄	C₂²×C₃₁	1	8	yes	complemented
295	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
296	C₂×#95	C₂²×C₃₁	1	2	yes	—
297	C₂×#95	C₂²×C₃₁	1	2	yes	—
298	C₂×#95	C₂²×C₃₁	1	2	yes	—
299	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
300	C₂×#95	C₂²×C₃₁	1	2	yes	—
301	C₂×#95	C₂²×C₃₁	1	2	yes	—
302	C₂×#95	C₂²×C₃₁	1	2	yes	—
303	C₂×#95	C₂²×C₃₁	1	2	yes	—
304	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
305	C₂×C₃₁	—	4	4	no	—
306	C₂×C₃₁	#2494	1	8	yes	direct product factor
307	C₂×C₃₁	C₂²×#126	1	1	yes	characteristic
308	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
309	C₂×C₃₁	C₂×#542	1	1	yes	characteristic
310	C₂×C₃₁	C₂×#552	1	1	yes	characteristic
311	C₂×C₃₁	C₂×#553	1	1	yes	characteristic
312	C₂×C₃₁	C₂×#553	1	1	yes	characteristic
313	C₂×C₃₁	C₂×#556	1	1	yes	characteristic
314	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	4	no	—
318	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
319	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
320	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
322	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
323	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
327	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	4	4	no	—
335	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
341	C₂×C₂²⋊C₄	—	2	4	no	—
342	C₂×C₂²⋊C₄	—	2	8	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	4	4	no	—
345	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
349	C₂×C₄²	—	2	4	no	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	—	4	4	no	—
352	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
353	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
354	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
355	#95	C₂³×C₃₁	1	4	yes	—
356	#95	C₂³×C₃₁	1	4	yes	—
357	#95	C₂³×C₃₁	1	8	yes	—
358	#95	C₂³×C₃₁	1	8	yes	—
359	#95	C₂³×C₃₁	1	8	yes	—
360	#95	C₂³×C₃₁	1	8	yes	—
361	#95	C₂³×C₃₁	1	8	yes	—
362	#95	C₂³×C₃₁	1	8	yes	—
363	#95	C₂³×C₃₁	1	8	yes	—
364	C₃₁	C₂×#2494	1	1	yes	characteristic, direct product factor, Sylow
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	#41×C₃₁	1	4	yes	—
372	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
373	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	4	16	no	—
404	C₂²×C₄	#41×C₃₁	1	4	yes	—
405	C₂²×C₄	#41×C₃₁	1	4	yes	—
406	C₂²×C₄	#41×C₃₁	1	4	yes	—
407	C₂²×C₄	#41×C₃₁	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
418	C₄⋊C₄	—	2	16	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	4	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	4	8	no	—
428	C₄²	—	2	8	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	4	8	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂×#41×C₃₁	1	4	yes	—
445	C₂³	C₂×#41×C₃₁	1	2	yes	—
446	C₂³	C₂×#41×C₃₁	1	2	yes	—
447	C₂³	C₂×#41×C₃₁	1	2	yes	—
448	C₂³	C₂×#41×C₃₁	1	2	yes	—
449	C₂³	C₂×#41×C₃₁	1	2	yes	—
450	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
451	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
452	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	16	no	—
489	C₂×C₄	C₃₁×#126	1	16	yes	—
490	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
491	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
492	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
493	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	16	no	—
502	C₂²	C₂×C₃₁×#126	1	4	yes	—
503	C₂²	C₃₁×#529	1	4	yes	—
504	C₂²	C₃₁×#542	1	4	yes	—
505	C₂²	C₃₁×#552	1	4	yes	—
506	C₂²	C₃₁×#553	1	4	yes	—
507	C₂²	C₃₁×#553	1	4	yes	—
508	C₂²	C₃₁×#556	1	4	yes	—
509	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
510	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
511	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
512	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
513	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
514	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	C₂×C₃₁×#126	1	8	yes	—
526	C₂	—	4	4	no	—
527	C₂	C₃₁×#2494	1	8	yes	direct product factor
528	C₂	C₂²×C₃₁×#126	1	1	yes	characteristic
529	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
530	C₂	C₂×C₃₁×#542	1	1	yes	characteristic
531	C₂	C₂×C₃₁×#552	1	1	yes	characteristic
532	C₂	C₂×C₃₁×#553	1	1	yes	characteristic
533	C₂	C₂×C₃₁×#553	1	1	yes	characteristic
534	C₂	C₂×C₃₁×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
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. C₃₁×#2494	C₂	direct (N × H)
2. C₂×C₃₁×#401	C₂	semidirect
4. C₂×C₃₁×#389	C₂	semidirect
5. C₂×C₃₁×#389	C₂	semidirect
7. C₂×C₃₁×#387	C₂	semidirect
8. C₂×C₃₁×#382	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
27. C₃₁×#401	C₂²	semidirect
29. C₃₁×#389	C₂²	semidirect
30. C₃₁×#389	C₂²	semidirect
32. C₃₁×#387	C₂²	semidirect
33. C₃₁×#382	C₂²	semidirect
36. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
163. C₂×#2494	C₃₁	direct (N × H)
227. #2494	C₂×C₃₁	direct (N × H)
228. C₂×#401	C₂×C₃₁	semidirect
230. C₂×#389	C₂×C₃₁	semidirect
231. C₂×#389	C₂×C₃₁	semidirect
233. C₂×#387	C₂×C₃₁	semidirect
234. C₂×#382	C₂×C₃₁	semidirect
237. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
285. #401	C₂²×C₃₁	semidirect
287. #389	C₂²×C₃₁	semidirect
288. #389	C₂²×C₃₁	semidirect
290. #387	C₂²×C₃₁	semidirect
291. #382	C₂²×C₃₁	semidirect
294. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
306. C₂×C₃₁	#2494	direct (N × H)
364. C₃₁	C₂×#2494	direct (N × H)
527. C₂	C₃₁×#2494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2494	2
C₂×C₃₁×#401	2
C₂×C₃₁×#397	2
C₂×C₃₁×#389	2
C₂×C₃₁×#388	2
C₂×C₃₁×#387	2
C₂×C₃₁×#382	2
C₂×C₃₁×#380	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2494	31

Subgroups — C2×C31×#2494 #21491544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2494 #21491544