Subgroups — C₂×C₃₁×#3342 #21517992

Order 7936.

1854 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#556	C₂	1	2	yes	maximal
2	C₃₁×#3342	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#485	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#475	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃₁×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
12	C₃₁×#556	—	2	8	no	—
13	C₃₁×#556	C₂²	1	16	yes	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃₁×#126	—	2	4	no	—
16	C₂×C₃₁×#124	—	2	2	no	—
17	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₃₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#117	C₂²	1	4	yes	—
22	C₃₁×#500	C₂²	1	8	yes	complemented
23	C₃₁×#485	C₂²	1	32	yes	complemented
24	C₃₁×#475	C₂²	1	16	yes	complemented
25	C₃₁×#467	C₂²	1	16	yes	complemented
26	C₄×Q₁₆×C₃₁	C₂²	1	8	yes	complemented
27	C₈×D₄×C₃₁	C₂²	1	8	yes	—
28	C₃₁×#427	C₂²	1	16	yes	complemented
29	C₂×C₃₁×#107	C₂²	1	2	yes	—
30	C₂×C₃₁×#107	C₂²	1	2	yes	—
31	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#106	C₂²	1	4	yes	—
33	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#103	C₂²	1	2	yes	—
35	C₂×C₃₁×#103	C₂²	1	4	yes	—
36	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₃₁	—	2	2	no	—
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
42	C₂×Q₁₆×C₃₁	—	2	4	no	—
43	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
44	C₂²×C₈×C₃₁	—	2	8	no	—
45	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₃₁	C₂³	1	8	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₃₁×C₄⋊Q₈	—	2	4	no	—
50	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
51	C₃₁×#126	—	2	32	no	—
52	C₃₁×#124	—	2	16	no	—
53	C₃₁×C₂²⋊Q₈	—	2	8	no	—
54	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
55	C₄×Q₈×C₃₁	—	2	16	no	—
56	C₄×Q₈×C₃₁	—	2	4	no	—
57	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
58	C₄×D₄×C₃₁	D₄	1	4	yes	—
59	C₄×D₄×C₃₁	C₂³	1	4	yes	—
60	C₃₁×#117	—	2	8	no	—
61	C₃₁×#117	C₂³	1	16	yes	—
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	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
71	C₂×C₄²×C₃₁	—	2	4	no	—
72	C₂×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×#107	C₂³	1	4	yes	—
75	C₃₁×#107	C₂³	1	8	yes	—
76	C₃₁×#107	C₂³	1	8	yes	—
77	C₃₁×#106	C₂³	1	16	yes	—
78	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
79	C₃₁×#103	C₂³	1	8	yes	—
80	C₃₁×#103	C₂³	1	16	yes	—
81	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₃₁	C₂³	1	4	yes	—
83	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
84	C₂×Q₈×C₃₁	—	2	2	no	—
85	C₂×Q₈×C₃₁	—	2	8	no	—
86	C₂×Q₈×C₃₁	—	2	4	no	—
87	C₂×Q₈×C₃₁	—	2	4	no	—
88	C₂×Q₈×C₃₁	—	4	8	no	—
89	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
90	C₂×D₄×C₃₁	—	2	4	no	—
91	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	2	4	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
103	Q₁₆×C₃₁	—	2	8	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	16	no	—
107	C₂×C₈×C₃₁	#41	1	4	yes	—
108	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
109	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
110	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₃₁	—	2	16	no	—
112	C₄⋊C₄×C₃₁	—	2	8	no	—
113	C₄⋊C₄×C₃₁	—	2	8	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	4	no	—
116	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
117	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
118	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
119	C₂²⋊C₄×C₃₁	—	2	16	no	—
120	C₂²⋊C₄×C₃₁	—	2	16	no	—
121	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
122	C₄²×C₃₁	—	2	16	no	—
123	C₄²×C₃₁	—	2	8	no	—
124	C₄²×C₃₁	C₂×D₄	1	2	yes	—
125	C₄²×C₃₁	C₂⁴	1	2	yes	—
126	C₂×#3342	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₃₁	—	2	4	no	—
128	C₂³×C₃₁	—	2	4	no	—
129	C₂³×C₃₁	—	2	4	no	—
130	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
131	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	2	4	no	—
133	Q₈×C₃₁	—	2	4	no	—
134	Q₈×C₃₁	—	4	4	no	—
135	Q₈×C₃₁	—	4	16	no	—
136	D₄×C₃₁	—	2	8	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	8	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	4	8	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	#135	1	4	yes	—
149	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
154	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
155	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
156	C₈×C₃₁	—	2	4	no	—
157	C₈×C₃₁	—	2	2	no	—
158	C₈×C₃₁	C₂×#41	1	4	yes	—
159	C₂×#556	C₂×C₃₁	1	2	yes	—
160	#3342	C₂×C₃₁	1	16	yes	direct product factor
161	C₂×#500	C₂×C₃₁	1	1	yes	characteristic, complemented
162	C₂×#485	C₂×C₃₁	1	4	yes	complemented
163	C₂×#475	C₂×C₃₁	1	2	yes	complemented
164	C₂×#467	C₂×C₃₁	1	2	yes	complemented
165	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
167	C₂×#427	C₂×C₃₁	1	2	yes	complemented
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	2	4	no	—
170	C₂²×C₃₁	—	2	4	no	—
171	C₂²×C₃₁	—	4	8	no	—
172	C₂²×C₃₁	#547	1	2	yes	—
173	C₂²×C₃₁	C₂×#135	1	2	yes	—
174	C₂²×C₃₁	#578	1	2	yes	—
175	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
176	C₄×C₃₁	—	2	4	no	—
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	4	4	no	—
179	C₄×C₃₁	—	4	8	no	—
180	C₄×C₃₁	—	4	4	no	—
181	C₄×C₃₁	#547	1	2	yes	—
182	C₄×C₃₁	C₂×#135	1	4	yes	—
183	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
184	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
187	#556	—	2	8	no	—
188	#556	C₂²×C₃₁	1	16	yes	—
189	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
190	C₂×#126	—	2	4	no	—
191	C₂×#124	—	2	2	no	—
192	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
193	C₂×C₄×Q₈	—	2	2	no	—
194	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
195	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#117	C₂²×C₃₁	1	4	yes	—
197	#500	C₂²×C₃₁	1	8	yes	complemented
198	#485	C₂²×C₃₁	1	32	yes	complemented
199	#475	C₂²×C₃₁	1	16	yes	complemented
200	#467	C₂²×C₃₁	1	16	yes	complemented
201	C₄×Q₁₆	C₂²×C₃₁	1	8	yes	complemented
202	C₈×D₄	C₂²×C₃₁	1	8	yes	—
203	#427	C₂²×C₃₁	1	16	yes	complemented
204	C₂×#107	C₂²×C₃₁	1	2	yes	—
205	C₂×#107	C₂²×C₃₁	1	2	yes	—
206	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#106	C₂²×C₃₁	1	4	yes	—
208	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×#103	C₂²×C₃₁	1	4	yes	—
210	C₂×#103	C₂²×C₃₁	1	2	yes	—
211	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₃₁	—	4	4	no	—
214	C₂×C₃₁	#3342	1	4	yes	direct product factor
215	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
216	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
217	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
220	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
222	C₂×Q₁₆	—	2	4	no	—
223	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
224	C₂²×C₈	—	2	8	no	—
225	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₃₁	1	8	yes	—
227	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	4	no	—
230	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
231	#126	—	2	32	no	—
232	#124	—	2	16	no	—
233	C₂²⋊Q₈	—	2	8	no	—
234	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
235	C₄×Q₈	—	2	16	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
238	C₄×D₄	D₄×C₃₁	1	4	yes	—
239	C₄×D₄	C₂³×C₃₁	1	4	yes	—
240	#117	—	2	8	no	—
241	#117	C₂³×C₃₁	1	16	yes	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
251	C₂×C₄²	—	2	4	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
254	#107	C₂³×C₃₁	1	4	yes	—
255	#107	C₂³×C₃₁	1	8	yes	—
256	#107	C₂³×C₃₁	1	8	yes	—
257	#106	C₂³×C₃₁	1	16	yes	—
258	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
259	#103	C₂³×C₃₁	1	8	yes	—
260	#103	C₂³×C₃₁	1	16	yes	—
261	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
262	C₄×C₈	C₂³×C₃₁	1	4	yes	—
263	C₃₁	C₂×#3342	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	8	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	4	8	no	—
270	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
284	Q₁₆	—	2	8	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	16	no	—
288	C₂×C₈	#41×C₃₁	1	4	yes	—
289	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
290	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
291	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
292	C₄⋊C₄	—	2	16	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
298	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
299	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
303	C₄²	—	2	16	no	—
304	C₄²	—	2	8	no	—
305	C₄²	C₂×D₄×C₃₁	1	2	yes	—
306	C₄²	C₂⁴×C₃₁	1	2	yes	—
307	C₂³	—	2	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	4	no	—
310	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
311	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
312	Q₈	—	2	4	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	4	4	no	—
315	Q₈	—	4	16	no	—
316	D₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	C₃₁×#135	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
331	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
333	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
334	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
335	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
336	C₈	—	2	4	no	—
337	C₈	—	2	2	no	—
338	C₈	C₂×#41×C₃₁	1	4	yes	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	8	no	—
343	C₂²	C₃₁×#547	1	2	yes	—
344	C₂²	C₂×C₃₁×#135	1	2	yes	—
345	C₂²	C₃₁×#578	1	2	yes	—
346	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	2	2	no	—
349	C₄	—	4	4	no	—
350	C₄	—	4	8	no	—
351	C₄	—	4	4	no	—
352	C₄	C₃₁×#547	1	2	yes	—
353	C₄	C₂×C₃₁×#135	1	4	yes	—
354	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
355	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂	—	4	4	no	—
357	C₂	C₃₁×#3342	1	4	yes	direct product factor
358	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
359	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
360	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3342	C₂	direct (N × H)
3. C₂×C₃₁×#500	C₂	semidirect
4. C₂×C₃₁×#485	C₂	semidirect
5. C₂×C₃₁×#475	C₂	semidirect
6. C₂×C₃₁×#467	C₂	semidirect
7. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
9. C₂×C₃₁×#427	C₂	semidirect
22. C₃₁×#500	C₂²	semidirect
23. C₃₁×#485	C₂²	semidirect
24. C₃₁×#475	C₂²	semidirect
25. C₃₁×#467	C₂²	semidirect
26. C₄×Q₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#427	C₂²	semidirect
126. C₂×#3342	C₃₁	direct (N × H)
160. #3342	C₂×C₃₁	direct (N × H)
161. C₂×#500	C₂×C₃₁	semidirect
162. C₂×#485	C₂×C₃₁	semidirect
163. C₂×#475	C₂×C₃₁	semidirect
164. C₂×#467	C₂×C₃₁	semidirect
165. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
167. C₂×#427	C₂×C₃₁	semidirect
197. #500	C₂²×C₃₁	semidirect
198. #485	C₂²×C₃₁	semidirect
199. #475	C₂²×C₃₁	semidirect
200. #467	C₂²×C₃₁	semidirect
201. C₄×Q₁₆	C₂²×C₃₁	semidirect
203. #427	C₂²×C₃₁	semidirect
214. C₂×C₃₁	#3342	direct (N × H)
263. C₃₁	C₂×#3342	direct (N × H)
357. C₂	C₃₁×#3342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#556	2
C₃₁×#3342	2
C₂×C₃₁×#500	2
C₂×C₃₁×#485	2
C₂×C₃₁×#475	2
C₂×C₃₁×#467	2
C₂×C₄×Q₁₆×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₂×C₃₁×#427	2
C₂×#3342	31

Subgroups — C2×C31×#3342 #21517992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3342 #21517992