Subgroups — C₂×C₃₁×#3352 #21518004

Order 7936.

1834 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#552	C₂	1	2	yes	maximal
2	C₃₁×#3352	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#470	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃₁×#428	C₂	1	2	yes	maximal, complemented
11	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
13	C₃₁×#552	—	2	8	no	—
14	C₃₁×#552	C₂²	1	16	yes	—
15	C₂×C₃₁×#126	—	2	2	no	—
16	C₂×C₃₁×#125	—	2	2	no	—
17	C₂×C₃₁×#125	C₂²	1	2	yes	—
18	C₂×C₃₁×#123	—	2	2	no	—
19	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#117	—	2	2	no	—
24	C₂×C₃₁×#117	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#499	C₂²	1	8	yes	complemented
27	C₃₁×#485	C₂²	1	16	yes	complemented
28	C₃₁×#484	C₂²	1	16	yes	complemented
29	C₃₁×#479	C₂²	1	16	yes	complemented
30	C₃₁×#470	C₂²	1	16	yes	complemented
31	C₄×Q₁₆×C₃₁	C₂²	1	8	yes	complemented
32	C₃₁×#436	C₂²	1	8	yes	—
33	C₃₁×#428	C₂²	1	16	yes	complemented
34	C₂×C₃₁×#107	C₂²	1	2	yes	—
35	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#106	C₂²	1	2	yes	—
39	C₂×C₃₁×#106	C₂²	1	2	yes	—
40	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#103	C₂²	1	2	yes	—
42	C₂×C₃₁×#103	C₂²	1	2	yes	—
43	C₂×C₃₁×#103	C₂²	1	2	yes	—
44	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	—	2	2	no	—
49	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₃₁	—	2	4	no	—
51	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
52	C₂×M₁₆×C₃₁	—	2	8	no	—
53	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×#126	—	2	16	no	—
58	C₃₁×#125	—	2	16	no	—
59	C₃₁×#125	—	2	4	no	—
60	C₃₁×#125	C₂³	1	8	yes	—
61	C₃₁×#123	—	2	16	no	—
62	C₃₁×C₂²⋊Q₈	—	2	4	no	—
63	C₃₁×C₂²⋊Q₈	—	2	4	no	—
64	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
65	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₄×Q₈×C₃₁	—	2	4	no	—
67	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
68	C₄×D₄×C₃₁	D₄	1	4	yes	—
69	C₄×D₄×C₃₁	C₂³	1	4	yes	—
70	C₃₁×#117	—	2	4	no	—
71	C₃₁×#117	—	2	16	no	—
72	C₃₁×#117	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
75	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
89	C₂×C₄²×C₃₁	—	2	2	no	—
90	C₂×C₄²×C₃₁	—	2	2	no	—
91	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
92	C₃₁×#107	C₂³	1	4	yes	—
93	C₃₁×#107	C₂³	1	8	yes	—
94	C₃₁×#107	C₂³	1	4	yes	—
95	C₃₁×#107	C₂³	1	4	yes	—
96	C₃₁×#106	C₂³	1	8	yes	—
97	C₃₁×#106	C₂³	1	8	yes	—
98	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
99	C₃₁×#103	C₂³	1	8	yes	—
100	C₃₁×#103	C₂³	1	8	yes	—
101	C₃₁×#103	C₂³	1	8	yes	—
102	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
103	C₄×C₈×C₃₁	C₂³	1	4	yes	—
104	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₃₁	—	2	2	no	—
106	C₂×Q₈×C₃₁	—	2	4	no	—
107	C₂×Q₈×C₃₁	—	2	4	no	—
108	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
109	C₂×D₄×C₃₁	—	4	2	no	—
110	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₃₁	—	2	4	no	—
112	C₂²×C₄×C₃₁	—	2	4	no	—
113	C₂²×C₄×C₃₁	—	2	8	no	—
114	C₂²×C₄×C₃₁	—	2	2	no	—
115	C₂²×C₄×C₃₁	—	2	2	no	—
116	C₂²×C₄×C₃₁	—	2	2	no	—
117	C₂²×C₄×C₃₁	—	2	2	no	—
118	C₂²×C₄×C₃₁	—	4	8	no	—
119	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₃₁	—	2	8	no	—
126	M₁₆×C₃₁	—	2	16	no	—
127	C₂×C₈×C₃₁	—	2	4	no	—
128	C₂×C₈×C₃₁	—	2	2	no	—
129	C₂×C₈×C₃₁	#41	1	4	yes	—
130	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
131	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
132	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₄⋊C₄×C₃₁	—	2	8	no	—
136	C₄⋊C₄×C₃₁	—	2	8	no	—
137	C₄⋊C₄×C₃₁	—	2	8	no	—
138	C₄⋊C₄×C₃₁	—	2	8	no	—
139	C₄⋊C₄×C₃₁	—	2	8	no	—
140	C₄⋊C₄×C₃₁	—	2	8	no	—
141	C₄⋊C₄×C₃₁	—	2	2	no	—
142	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
143	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
144	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
146	C₂²⋊C₄×C₃₁	—	2	8	no	—
147	C₂²⋊C₄×C₃₁	—	2	8	no	—
148	C₂²⋊C₄×C₃₁	—	2	8	no	—
149	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
150	C₄²×C₃₁	—	2	8	no	—
151	C₄²×C₃₁	—	2	8	no	—
152	C₄²×C₃₁	C₂×D₄	1	2	yes	—
153	C₄²×C₃₁	C₂⁴	1	2	yes	—
154	C₂×#3352	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₃₁	—	2	4	no	—
156	C₂³×C₃₁	—	2	4	no	—
157	C₂³×C₃₁	—	2	4	no	—
158	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
159	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₃₁	—	2	4	no	—
161	Q₈×C₃₁	—	2	4	no	—
162	Q₈×C₃₁	—	4	4	no	—
163	D₄×C₃₁	—	4	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	8	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	4	no	—
173	C₂×C₄×C₃₁	—	2	4	no	—
174	C₂×C₄×C₃₁	—	4	16	no	—
175	C₂×C₄×C₃₁	—	4	4	no	—
176	C₂×C₄×C₃₁	—	4	4	no	—
177	C₂×C₄×C₃₁	—	4	4	no	—
178	C₂×C₄×C₃₁	—	4	4	no	—
179	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
184	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
185	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
186	C₈×C₃₁	—	2	4	no	—
187	C₈×C₃₁	—	2	2	no	—
188	C₈×C₃₁	C₂×#41	1	4	yes	—
189	C₂×#552	C₂×C₃₁	1	2	yes	—
190	#3352	C₂×C₃₁	1	16	yes	direct product factor
191	C₂×#499	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#484	C₂×C₃₁	1	2	yes	complemented
193	C₂×#485	C₂×C₃₁	1	2	yes	complemented
194	C₂×#479	C₂×C₃₁	1	2	yes	complemented
195	C₂×#470	C₂×C₃₁	1	2	yes	complemented
196	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
197	C₂×#436	C₂×C₃₁	1	1	yes	characteristic
198	C₂×#428	C₂×C₃₁	1	2	yes	complemented
199	C₂²×C₃₁	—	2	4	no	—
200	C₂²×C₃₁	—	2	4	no	—
201	C₂²×C₃₁	—	2	4	no	—
202	C₂²×C₃₁	—	4	8	no	—
203	C₂²×C₃₁	#547	1	2	yes	—
204	C₂²×C₃₁	#575	1	2	yes	—
205	C₂²×C₃₁	#578	1	2	yes	—
206	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
207	C₄×C₃₁	—	2	4	no	—
208	C₄×C₃₁	—	2	2	no	—
209	C₄×C₃₁	—	2	2	no	—
210	C₄×C₃₁	—	4	4	no	—
211	C₄×C₃₁	—	4	4	no	—
212	C₄×C₃₁	—	4	4	no	—
213	C₄×C₃₁	—	4	4	no	—
214	C₄×C₃₁	#547	1	2	yes	—
215	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
216	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
219	#552	—	2	8	no	—
220	#552	C₂²×C₃₁	1	16	yes	—
221	C₂×#126	—	2	2	no	—
222	C₂×#125	—	2	2	no	—
223	C₂×#125	C₂²×C₃₁	1	2	yes	—
224	C₂×#123	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×#117	—	2	2	no	—
230	C₂×#117	C₂²×C₃₁	1	2	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
232	#499	C₂²×C₃₁	1	8	yes	complemented
233	#485	C₂²×C₃₁	1	16	yes	complemented
234	#484	C₂²×C₃₁	1	16	yes	complemented
235	#479	C₂²×C₃₁	1	16	yes	complemented
236	#470	C₂²×C₃₁	1	16	yes	complemented
237	C₄×Q₁₆	C₂²×C₃₁	1	8	yes	complemented
238	#436	C₂²×C₃₁	1	8	yes	—
239	#428	C₂²×C₃₁	1	16	yes	complemented
240	C₂×#107	C₂²×C₃₁	1	2	yes	—
241	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
243	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×#106	C₂²×C₃₁	1	2	yes	—
245	C₂×#106	C₂²×C₃₁	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×#103	C₂²×C₃₁	1	2	yes	—
248	C₂×#103	C₂²×C₃₁	1	2	yes	—
249	C₂×#103	C₂²×C₃₁	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
252	C₂×C₃₁	—	4	4	no	—
253	C₂×C₃₁	#3352	1	4	yes	direct product factor
254	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
255	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
256	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
258	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
263	C₂×M₁₆	—	2	8	no	—
264	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
265	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
266	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
268	#126	—	2	16	no	—
269	#125	—	2	16	no	—
270	#125	—	2	4	no	—
271	#125	C₂³×C₃₁	1	8	yes	—
272	#123	—	2	16	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
276	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
279	C₄×D₄	D₄×C₃₁	1	4	yes	—
280	C₄×D₄	C₂³×C₃₁	1	4	yes	—
281	#117	—	2	4	no	—
282	#117	—	2	16	no	—
283	#117	C₂³×C₃₁	1	8	yes	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	4	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
295	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
303	#107	C₂³×C₃₁	1	4	yes	—
304	#107	C₂³×C₃₁	1	8	yes	—
305	#107	C₂³×C₃₁	1	4	yes	—
306	#107	C₂³×C₃₁	1	4	yes	—
307	#106	C₂³×C₃₁	1	8	yes	—
308	#106	C₂³×C₃₁	1	8	yes	—
309	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
310	#103	C₂³×C₃₁	1	8	yes	—
311	#103	C₂³×C₃₁	1	8	yes	—
312	#103	C₂³×C₃₁	1	8	yes	—
313	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
314	C₄×C₈	C₂³×C₃₁	1	4	yes	—
315	C₃₁	C₂×#3352	1	1	yes	characteristic, direct product factor, Sylow
316	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
337	Q₁₆	—	2	8	no	—
338	M₁₆	—	2	16	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	#41×C₃₁	1	4	yes	—
342	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
343	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
344	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
355	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
356	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
357	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	8	no	—
364	C₄²	C₂×D₄×C₃₁	1	2	yes	—
365	C₄²	C₂⁴×C₃₁	1	2	yes	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
370	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	4	no	—
374	D₄	—	4	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
392	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
395	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
397	C₈	—	2	4	no	—
398	C₈	—	2	2	no	—
399	C₈	C₂×#41×C₃₁	1	4	yes	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	C₃₁×#547	1	2	yes	—
405	C₂²	C₃₁×#575	1	2	yes	—
406	C₂²	C₃₁×#578	1	2	yes	—
407	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	4	no	—
415	C₄	C₃₁×#547	1	2	yes	—
416	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
417	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂	—	4	4	no	—
419	C₂	C₃₁×#3352	1	4	yes	direct product factor
420	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
421	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
422	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×#3352	C₂	direct (N × H)
3. C₂×C₃₁×#499	C₂	semidirect
4. C₂×C₃₁×#484	C₂	semidirect
5. C₂×C₃₁×#485	C₂	semidirect
6. C₂×C₃₁×#479	C₂	semidirect
7. C₂×C₃₁×#470	C₂	semidirect
8. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
10. C₂×C₃₁×#428	C₂	semidirect
26. C₃₁×#499	C₂²	semidirect
27. C₃₁×#485	C₂²	semidirect
28. C₃₁×#484	C₂²	semidirect
29. C₃₁×#479	C₂²	semidirect
30. C₃₁×#470	C₂²	semidirect
31. C₄×Q₁₆×C₃₁	C₂²	semidirect
33. C₃₁×#428	C₂²	semidirect
154. C₂×#3352	C₃₁	direct (N × H)
190. #3352	C₂×C₃₁	direct (N × H)
191. C₂×#499	C₂×C₃₁	semidirect
192. C₂×#484	C₂×C₃₁	semidirect
193. C₂×#485	C₂×C₃₁	semidirect
194. C₂×#479	C₂×C₃₁	semidirect
195. C₂×#470	C₂×C₃₁	semidirect
196. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
198. C₂×#428	C₂×C₃₁	semidirect
232. #499	C₂²×C₃₁	semidirect
233. #485	C₂²×C₃₁	semidirect
234. #484	C₂²×C₃₁	semidirect
235. #479	C₂²×C₃₁	semidirect
236. #470	C₂²×C₃₁	semidirect
237. C₄×Q₁₆	C₂²×C₃₁	semidirect
239. #428	C₂²×C₃₁	semidirect
253. C₂×C₃₁	#3352	direct (N × H)
315. C₃₁	C₂×#3352	direct (N × H)
419. C₂	C₃₁×#3352	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×#552	2
C₃₁×#3352	2
C₂×C₃₁×#499	2
C₂×C₃₁×#484	2
C₂×C₃₁×#485	2
C₂×C₃₁×#479	2
C₂×C₃₁×#470	2
C₂×C₄×Q₁₆×C₃₁	2
C₂×C₃₁×#436	2
C₂×C₃₁×#428	2
C₂×#3352	31

Subgroups — C2×C31×#3352 #21518004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3352 #21518004