Subgroups — C₂×C₃₁×#3336 #21517986

Order 7936.

1866 conjugacy classes of subgroups.

The subgroup lattice has 500 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×#3336	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#485	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#483	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#552	—	2	8	no	—
17	C₃₁×#552	C₂²	1	16	yes	—
18	C₂×C₃₁×#126	—	2	2	no	—
19	C₂×C₃₁×#125	—	2	2	no	—
20	C₂×C₃₁×#125	C₂²	1	2	yes	—
21	C₂×C₃₁×#123	—	2	2	no	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#117	—	2	2	no	—
27	C₂×C₃₁×#117	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#499	C₂²	1	8	yes	complemented
30	C₃₁×#485	C₂²	1	16	yes	complemented
31	C₃₁×#483	C₂²	1	16	yes	complemented
32	C₃₁×#479	C₂²	1	16	yes	complemented
33	C₃₁×#467	C₂²	1	8	yes	complemented
34	C₃₁×#467	C₂²	1	8	yes	complemented
35	C₄×Q₁₆×C₃₁	C₂²	1	8	yes	complemented
36	C₈×D₄×C₃₁	C₂²	1	8	yes	—
37	C₃₁×#427	C₂²	1	8	yes	complemented
38	C₂×C₃₁×#107	C₂²	1	2	yes	—
39	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#107	C₂²	1	8	yes	complemented
43	C₂×C₃₁×#106	C₂²	1	2	yes	—
44	C₂×C₃₁×#106	C₂²	1	2	yes	—
45	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#103	C₂²	1	2	yes	—
47	C₂×C₃₁×#103	C₂²	1	2	yes	—
48	C₂×C₃₁×#103	C₂²	1	2	yes	—
49	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₃₁	—	2	2	no	—
55	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×Q₁₆×C₃₁	—	2	4	no	—
58	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
59	C₂²×C₈×C₃₁	—	2	4	no	—
60	C₂²×C₈×C₃₁	—	2	4	no	—
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
65	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
66	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#126	—	2	16	no	—
68	C₃₁×#125	—	2	16	no	—
69	C₃₁×#125	—	2	4	no	—
70	C₃₁×#125	C₂³	1	8	yes	—
71	C₃₁×#123	—	2	16	no	—
72	C₃₁×C₂²⋊Q₈	—	2	4	no	—
73	C₃₁×C₂²⋊Q₈	—	2	4	no	—
74	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₄×Q₈×C₃₁	—	2	4	no	—
77	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
78	C₄×D₄×C₃₁	D₄	1	4	yes	—
79	C₄×D₄×C₃₁	C₂³	1	4	yes	—
80	C₃₁×#117	—	2	4	no	—
81	C₃₁×#117	—	2	16	no	—
82	C₃₁×#117	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
85	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₃₁	—	2	2	no	—
101	C₂×C₄²×C₃₁	—	2	2	no	—
102	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
103	C₃₁×#107	C₂³	1	4	yes	—
104	C₃₁×#107	C₂³	1	4	yes	—
105	C₃₁×#107	C₂³	1	8	yes	—
106	C₃₁×#107	C₂³	1	4	yes	—
107	C₃₁×#106	C₂³	1	8	yes	—
108	C₃₁×#106	C₂³	1	8	yes	—
109	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
110	C₃₁×#103	C₂³	1	8	yes	—
111	C₃₁×#103	C₂³	1	8	yes	—
112	C₃₁×#103	C₂³	1	8	yes	—
113	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
115	C₄×C₈×C₃₁	C₂³	1	4	yes	—
116	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₃₁	—	2	2	no	—
119	C₂×Q₈×C₃₁	—	2	4	no	—
120	C₂×Q₈×C₃₁	—	2	4	no	—
121	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
122	C₂×D₄×C₃₁	—	2	4	no	—
123	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₃₁	—	2	2	no	—
125	C₂²×C₄×C₃₁	—	2	2	no	—
126	C₂²×C₄×C₃₁	—	2	2	no	—
127	C₂²×C₄×C₃₁	—	2	2	no	—
128	C₂²×C₄×C₃₁	—	2	8	no	—
129	C₂²×C₄×C₃₁	—	2	2	no	—
130	C₂²×C₄×C₃₁	—	2	2	no	—
131	C₂²×C₄×C₃₁	—	2	2	no	—
132	C₂²×C₄×C₃₁	—	2	2	no	—
133	C₂²×C₄×C₃₁	—	4	8	no	—
134	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₃₁	—	2	8	no	—
144	C₂×C₈×C₃₁	—	2	2	no	—
145	C₂×C₈×C₃₁	—	2	2	no	—
146	C₂×C₈×C₃₁	—	2	2	no	—
147	C₂×C₈×C₃₁	—	2	8	no	—
148	C₂×C₈×C₃₁	—	2	8	no	—
149	C₂×C₈×C₃₁	#41	1	4	yes	—
150	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
151	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
152	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
153	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₃₁	—	2	2	no	—
155	C₄⋊C₄×C₃₁	—	2	2	no	—
156	C₄⋊C₄×C₃₁	—	2	8	no	—
157	C₄⋊C₄×C₃₁	—	2	8	no	—
158	C₄⋊C₄×C₃₁	—	2	8	no	—
159	C₄⋊C₄×C₃₁	—	2	8	no	—
160	C₄⋊C₄×C₃₁	—	2	8	no	—
161	C₄⋊C₄×C₃₁	—	2	8	no	—
162	C₄⋊C₄×C₃₁	—	2	2	no	—
163	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
164	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
165	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
166	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
167	C₂²⋊C₄×C₃₁	—	2	8	no	—
168	C₂²⋊C₄×C₃₁	—	2	8	no	—
169	C₂²⋊C₄×C₃₁	—	2	8	no	—
170	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
171	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
172	C₄²×C₃₁	—	2	8	no	—
173	C₄²×C₃₁	—	2	8	no	—
174	C₄²×C₃₁	C₂×D₄	1	2	yes	—
175	C₄²×C₃₁	C₂⁴	1	2	yes	—
176	C₂×#3336	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₃₁	—	2	2	no	—
178	C₂³×C₃₁	—	2	2	no	—
179	C₂³×C₃₁	—	2	2	no	—
180	C₂³×C₃₁	—	2	2	no	—
181	C₂³×C₃₁	—	2	2	no	—
182	C₂³×C₃₁	#135	1	4	yes	—
183	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
184	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
185	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₃₁	—	2	4	no	—
187	Q₈×C₃₁	—	2	4	no	—
188	Q₈×C₃₁	—	4	4	no	—
189	D₄×C₃₁	—	2	8	no	—
190	C₂×C₄×C₃₁	—	2	2	no	—
191	C₂×C₄×C₃₁	—	2	2	no	—
192	C₂×C₄×C₃₁	—	2	2	no	—
193	C₂×C₄×C₃₁	—	2	2	no	—
194	C₂×C₄×C₃₁	—	2	4	no	—
195	C₂×C₄×C₃₁	—	2	4	no	—
196	C₂×C₄×C₃₁	—	2	2	no	—
197	C₂×C₄×C₃₁	—	2	2	no	—
198	C₂×C₄×C₃₁	—	2	2	no	—
199	C₂×C₄×C₃₁	—	2	2	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	4	no	—
204	C₂×C₄×C₃₁	—	4	4	no	—
205	C₂×C₄×C₃₁	—	4	16	no	—
206	C₂×C₄×C₃₁	—	4	4	no	—
207	C₂×C₄×C₃₁	—	4	4	no	—
208	C₂×C₄×C₃₁	—	4	4	no	—
209	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
215	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
216	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
217	C₈×C₃₁	—	2	2	no	—
218	C₈×C₃₁	—	2	2	no	—
219	C₈×C₃₁	—	2	2	no	—
220	C₈×C₃₁	C₂×#41	1	4	yes	—
221	C₂×#552	C₂×C₃₁	1	2	yes	—
222	#3336	C₂×C₃₁	1	16	yes	direct product factor
223	C₂×#499	C₂×C₃₁	1	1	yes	characteristic, complemented
224	C₂×#485	C₂×C₃₁	1	2	yes	complemented
225	C₂×#483	C₂×C₃₁	1	2	yes	complemented
226	C₂×#479	C₂×C₃₁	1	2	yes	complemented
227	C₂×#467	C₂×C₃₁	1	1	yes	characteristic, complemented
228	C₂×#467	C₂×C₃₁	1	1	yes	characteristic, complemented
229	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
230	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
231	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
232	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic, complemented
233	C₂²×C₃₁	—	2	8	no	—
234	C₂²×C₃₁	—	2	2	no	—
235	C₂²×C₃₁	—	2	2	no	—
236	C₂²×C₃₁	—	2	2	no	—
237	C₂²×C₃₁	—	2	2	no	—
238	C₂²×C₃₁	—	2	2	no	—
239	C₂²×C₃₁	—	4	4	no	—
240	C₂²×C₃₁	#547	1	2	yes	—
241	C₂²×C₃₁	C₂×#135	1	4	yes	—
242	C₂²×C₃₁	C₂×#135	1	2	yes	—
243	C₂²×C₃₁	#578	1	2	yes	—
244	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₃₁	—	2	2	no	—
246	C₄×C₃₁	—	2	2	no	—
247	C₄×C₃₁	—	2	2	no	—
248	C₄×C₃₁	—	2	2	no	—
249	C₄×C₃₁	—	4	4	no	—
250	C₄×C₃₁	—	4	4	no	—
251	C₄×C₃₁	—	4	4	no	—
252	C₄×C₃₁	—	4	4	no	—
253	C₄×C₃₁	#547	1	2	yes	—
254	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
255	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
256	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
259	#552	—	2	8	no	—
260	#552	C₂²×C₃₁	1	16	yes	—
261	C₂×#126	—	2	2	no	—
262	C₂×#125	—	2	2	no	—
263	C₂×#125	C₂²×C₃₁	1	2	yes	—
264	C₂×#123	—	2	2	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
266	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
267	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
268	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
269	C₂×#117	—	2	2	no	—
270	C₂×#117	C₂²×C₃₁	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
272	#499	C₂²×C₃₁	1	8	yes	complemented
273	#485	C₂²×C₃₁	1	16	yes	complemented
274	#483	C₂²×C₃₁	1	16	yes	complemented
275	#479	C₂²×C₃₁	1	16	yes	complemented
276	#467	C₂²×C₃₁	1	8	yes	complemented
277	#467	C₂²×C₃₁	1	8	yes	complemented
278	C₄×Q₁₆	C₂²×C₃₁	1	8	yes	complemented
279	C₈×D₄	C₂²×C₃₁	1	8	yes	—
280	#427	C₂²×C₃₁	1	8	yes	complemented
281	C₂×#107	C₂²×C₃₁	1	2	yes	—
282	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
283	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
284	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
285	C₂×#107	C₂²×C₃₁	1	8	yes	complemented
286	C₂×#106	C₂²×C₃₁	1	2	yes	—
287	C₂×#106	C₂²×C₃₁	1	2	yes	—
288	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
289	C₂×#103	C₂²×C₃₁	1	2	yes	—
290	C₂×#103	C₂²×C₃₁	1	2	yes	—
291	C₂×#103	C₂²×C₃₁	1	2	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
295	C₂×C₃₁	—	2	4	no	—
296	C₂×C₃₁	—	4	2	no	—
297	C₂×C₃₁	#3336	1	4	yes	direct product factor
298	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
299	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
300	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
301	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
302	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
306	C₂×Q₁₆	—	2	4	no	—
307	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
308	C₂²×C₈	—	2	4	no	—
309	C₂²×C₈	—	2	4	no	—
310	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
313	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
314	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
316	#126	—	2	16	no	—
317	#125	—	2	16	no	—
318	#125	—	2	4	no	—
319	#125	C₂³×C₃₁	1	8	yes	—
320	#123	—	2	16	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
324	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
325	C₄×Q₈	—	2	4	no	—
326	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
327	C₄×D₄	D₄×C₃₁	1	4	yes	—
328	C₄×D₄	C₂³×C₃₁	1	4	yes	—
329	#117	—	2	4	no	—
330	#117	—	2	16	no	—
331	#117	C₂³×C₃₁	1	8	yes	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
352	#107	C₂³×C₃₁	1	4	yes	—
353	#107	C₂³×C₃₁	1	4	yes	—
354	#107	C₂³×C₃₁	1	8	yes	—
355	#107	C₂³×C₃₁	1	4	yes	—
356	#106	C₂³×C₃₁	1	8	yes	—
357	#106	C₂³×C₃₁	1	8	yes	—
358	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
359	#103	C₂³×C₃₁	1	8	yes	—
360	#103	C₂³×C₃₁	1	8	yes	—
361	#103	C₂³×C₃₁	1	8	yes	—
362	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
363	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
364	C₄×C₈	C₂³×C₃₁	1	4	yes	—
365	C₃₁	C₂×#3336	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
367	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
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	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	4	8	no	—
384	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
393	Q₁₆	—	2	8	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	8	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	#41×C₃₁	1	4	yes	—
400	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
401	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
402	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
403	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
414	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
415	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
416	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
421	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
422	C₄²	—	2	8	no	—
423	C₄²	—	2	8	no	—
424	C₄²	C₂×D₄×C₃₁	1	2	yes	—
425	C₄²	C₂⁴×C₃₁	1	2	yes	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	C₃₁×#135	1	4	yes	—
432	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
433	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
434	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	4	4	no	—
438	D₄	—	2	8	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
464	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
465	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	C₂×#41×C₃₁	1	4	yes	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	C₃₁×#547	1	2	yes	—
478	C₂²	C₂×C₃₁×#135	1	4	yes	—
479	C₂²	C₂×C₃₁×#135	1	2	yes	—
480	C₂²	C₃₁×#578	1	2	yes	—
481	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	C₃₁×#547	1	2	yes	—
491	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
492	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂	—	2	4	no	—
494	C₂	—	4	2	no	—
495	C₂	C₃₁×#3336	1	4	yes	direct product factor
496	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
497	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
498	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×#3336	C₂	direct (N × H)
3. C₂×C₃₁×#499	C₂	semidirect
4. C₂×C₃₁×#485	C₂	semidirect
5. C₂×C₃₁×#483	C₂	semidirect
6. C₂×C₃₁×#479	C₂	semidirect
7. C₂×C₃₁×#467	C₂	semidirect
8. C₂×C₃₁×#467	C₂	semidirect
9. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
11. C₂×C₃₁×#427	C₂	semidirect
12. C₂²×C₃₁×#107	C₂	semidirect
29. C₃₁×#499	C₂²	semidirect
30. C₃₁×#485	C₂²	semidirect
31. C₃₁×#483	C₂²	semidirect
32. C₃₁×#479	C₂²	semidirect
33. C₃₁×#467	C₂²	semidirect
34. C₃₁×#467	C₂²	semidirect
35. C₄×Q₁₆×C₃₁	C₂²	semidirect
37. C₃₁×#427	C₂²	semidirect
42. C₂×C₃₁×#107	C₂²	semidirect
176. C₂×#3336	C₃₁	direct (N × H)
222. #3336	C₂×C₃₁	direct (N × H)
223. C₂×#499	C₂×C₃₁	semidirect
224. C₂×#485	C₂×C₃₁	semidirect
225. C₂×#483	C₂×C₃₁	semidirect
226. C₂×#479	C₂×C₃₁	semidirect
227. C₂×#467	C₂×C₃₁	semidirect
228. C₂×#467	C₂×C₃₁	semidirect
229. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
231. C₂×#427	C₂×C₃₁	semidirect
232. C₂²×#107	C₂×C₃₁	semidirect
272. #499	C₂²×C₃₁	semidirect
273. #485	C₂²×C₃₁	semidirect
274. #483	C₂²×C₃₁	semidirect
275. #479	C₂²×C₃₁	semidirect
276. #467	C₂²×C₃₁	semidirect
277. #467	C₂²×C₃₁	semidirect
278. C₄×Q₁₆	C₂²×C₃₁	semidirect
280. #427	C₂²×C₃₁	semidirect
285. C₂×#107	C₂²×C₃₁	semidirect
297. C₂×C₃₁	#3336	direct (N × H)
365. C₃₁	C₂×#3336	direct (N × H)
495. C₂	C₃₁×#3336	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×#3336	2
C₂×C₃₁×#499	2
C₂×C₃₁×#485	2
C₂×C₃₁×#483	2
C₂×C₃₁×#479	2
C₂×C₃₁×#467	2
C₂×C₄×Q₁₆×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₂×C₃₁×#427	2
C₂²×C₃₁×#107	2
C₂×#3336	31

Subgroups — C2×C31×#3336 #21517986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3336 #21517986