Subgroups — C₂×C₃₁×#3061 #21517208

Order 7936.

2806 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3061	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#468	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#466	C₂	1	2	yes	maximal, complemented
8	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#417	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₃₁	C₂²	1	2	yes	—
11	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#135	—	2	8	no	—
13	C₂×C₃₁×#135	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
16	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#131	—	2	8	no	—
18	C₂×C₃₁×#131	C₂²	1	8	yes	complemented
19	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
21	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
22	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#537	—	2	8	no	—
24	C₃₁×#537	C₂²	1	16	yes	complemented
25	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₃₁×#121	—	2	2	no	—
28	C₂×C₃₁×#121	—	2	4	no	—
29	C₂×C₃₁×#121	C₂²	1	4	yes	—
30	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#468	C₂²	1	32	yes	complemented
32	C₃₁×#467	C₂²	1	16	yes	complemented
33	C₃₁×#466	C₂²	1	16	yes	complemented
34	C₂×C₃₁×#107	C₂²	1	2	yes	—
35	C₂×C₃₁×#107	C₂²	1	2	yes	—
36	C₂×C₃₁×#107	C₂²	1	8	yes	complemented
37	C₃₁×#417	C₂²	1	16	yes	complemented
38	C₂×C₃₁×#103	C₂²	1	4	yes	—
39	C₂×C₃₁×#102	C₂²	1	4	yes	—
40	C₂×#41×C₃₁	—	2	4	no	—
41	C₂×#41×C₃₁	—	2	4	no	—
42	C₂×#41×C₃₁	—	2	4	no	—
43	C₂×#41×C₃₁	—	2	8	no	—
44	C₂×#41×C₃₁	—	2	8	no	—
45	C₂×#41×C₃₁	D₄	1	4	yes	—
46	C₂×#41×C₃₁	C₂³	1	8	yes	—
47	C₂×#41×C₃₁	C₂³	1	4	yes	—
48	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₃₁	—	2	2	no	—
51	C₂²×D₄×C₃₁	—	2	4	no	—
52	C₂²×D₄×C₃₁	D₄	1	2	yes	—
53	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₃₁	—	2	2	no	—
56	C₂³×C₄×C₃₁	—	2	2	no	—
57	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
59	C₃₁×#135	—	2	32	no	—
60	C₂×Q₁₆×C₃₁	—	2	4	no	—
61	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
62	C₂×SD₁₆×C₃₁	—	2	8	no	—
63	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
64	C₂×D₈×C₃₁	—	2	4	no	—
65	C₂×D₈×C₃₁	C₂³	1	4	yes	—
66	C₃₁×#131	—	2	32	no	—
67	C₂×M₁₆×C₃₁	—	2	4	no	—
68	C₂×M₁₆×C₃₁	—	2	8	no	—
69	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
70	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
71	C₂²×C₈×C₃₁	—	2	8	no	—
72	C₂²×C₈×C₃₁	D₄	1	8	yes	complemented
73	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
74	C₂²×C₈×C₃₁	C₂³	1	8	yes	—
75	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
78	C₃₁×C₂²⋊Q₈	—	2	16	no	—
79	C₃₁×C₂²⋊Q₈	—	2	8	no	—
80	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
81	C₃₁×#121	—	2	16	no	—
82	C₃₁×#121	—	2	32	no	—
83	C₃₁×#121	—	2	8	no	—
84	C₃₁×#121	C₂³	1	16	yes	—
85	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
88	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
92	C₃₁×#107	C₂³	1	8	yes	—
93	C₃₁×#107	C₂³	1	8	yes	—
94	C₃₁×#103	C₂³	1	16	yes	—
95	C₃₁×#102	C₂³	1	16	yes	—
96	C₂⁴×C₃₁	—	2	2	no	—
97	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
98	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
99	#41×C₃₁	—	2	16	no	—
100	#41×C₃₁	—	2	8	no	—
101	#41×C₃₁	—	2	8	no	—
102	#41×C₃₁	—	2	16	no	—
103	#41×C₃₁	—	2	16	no	—
104	#41×C₃₁	—	4	16	no	—
105	C₂×Q₈×C₃₁	—	2	4	no	—
106	C₂×Q₈×C₃₁	—	2	2	no	—
107	C₂×Q₈×C₃₁	—	2	4	no	—
108	C₂×Q₈×C₃₁	—	2	4	no	—
109	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
111	C₂×D₄×C₃₁	—	2	8	no	—
112	C₂×D₄×C₃₁	—	2	8	no	—
113	C₂×D₄×C₃₁	—	2	16	no	—
114	C₂×D₄×C₃₁	—	2	4	no	—
115	C₂×D₄×C₃₁	—	2	4	no	—
116	C₂×D₄×C₃₁	—	2	2	no	—
117	C₂×D₄×C₃₁	—	2	4	no	—
118	C₂×D₄×C₃₁	—	4	8	no	—
119	C₂×D₄×C₃₁	—	8	8	no	—
120	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
121	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₃₁	—	2	4	no	—
124	C₂²×C₄×C₃₁	—	2	4	no	—
125	C₂²×C₄×C₃₁	—	2	4	no	—
126	C₂²×C₄×C₃₁	—	2	2	no	—
127	C₂²×C₄×C₃₁	—	2	8	no	—
128	C₂²×C₄×C₃₁	—	2	8	no	—
129	C₂²×C₄×C₃₁	—	4	8	no	—
130	C₂²×C₄×C₃₁	—	8	4	no	—
131	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₃₁	#41	1	4	yes	—
137	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₃₁	—	2	8	no	—
141	SD₁₆×C₃₁	—	2	16	no	—
142	D₈×C₃₁	—	2	8	no	—
143	M₁₆×C₃₁	—	2	8	no	—
144	M₁₆×C₃₁	—	2	16	no	—
145	C₂×C₈×C₃₁	—	2	4	no	—
146	C₂×C₈×C₃₁	—	2	16	no	—
147	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
149	C₂×C₈×C₃₁	C₂×D₄	1	16	yes	complemented
150	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
151	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
152	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
153	C₄⋊C₄×C₃₁	—	2	8	no	—
154	C₄⋊C₄×C₃₁	—	2	4	no	—
155	C₄⋊C₄×C₃₁	—	2	16	no	—
156	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
157	C₂²⋊C₄×C₃₁	—	2	16	no	—
158	C₂²⋊C₄×C₃₁	—	2	16	no	—
159	C₂×#3061	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₃₁	—	2	2	no	—
161	C₂³×C₃₁	—	2	2	no	—
162	C₂³×C₃₁	—	2	4	no	—
163	C₂³×C₃₁	—	2	4	no	—
164	C₂³×C₃₁	—	2	4	no	—
165	C₂³×C₃₁	—	2	4	no	—
166	C₂³×C₃₁	—	4	4	no	—
167	C₂³×C₃₁	—	4	4	no	—
168	C₂³×C₃₁	—	4	4	no	—
169	C₂³×C₃₁	#121	1	4	yes	—
170	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
171	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
172	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₃₁	—	2	8	no	—
174	Q₈×C₃₁	—	2	4	no	—
175	Q₈×C₃₁	—	2	4	no	—
176	Q₈×C₃₁	—	4	4	no	—
177	D₄×C₃₁	—	2	16	no	—
178	D₄×C₃₁	—	2	8	no	—
179	D₄×C₃₁	—	2	4	no	—
180	D₄×C₃₁	—	2	4	no	—
181	D₄×C₃₁	—	4	16	no	—
182	D₄×C₃₁	—	4	4	no	—
183	D₄×C₃₁	—	8	16	no	—
184	C₂×C₄×C₃₁	—	2	4	no	—
185	C₂×C₄×C₃₁	—	2	8	no	—
186	C₂×C₄×C₃₁	—	2	4	no	—
187	C₂×C₄×C₃₁	—	2	4	no	—
188	C₂×C₄×C₃₁	—	2	8	no	—
189	C₂×C₄×C₃₁	—	2	4	no	—
190	C₂×C₄×C₃₁	—	4	4	no	—
191	C₂×C₄×C₃₁	—	4	8	no	—
192	C₂×C₄×C₃₁	—	4	16	no	—
193	C₂×C₄×C₃₁	—	8	8	no	—
194	C₂×C₄×C₃₁	#121	1	4	yes	—
195	C₂×C₄×C₃₁	#121	1	8	yes	—
196	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
202	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
203	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
204	C₈×C₃₁	—	2	4	no	—
205	C₈×C₃₁	C₂²×D₄	1	4	yes	—
206	C₈×C₃₁	C₂²×D₄	1	4	yes	—
207	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
208	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
209	C₂×#537	C₂×C₃₁	1	2	yes	complemented
210	#3061	C₂×C₃₁	1	16	yes	direct product factor
211	C₂×#468	C₂×C₃₁	1	4	yes	complemented
212	C₂×#467	C₂×C₃₁	1	2	yes	complemented
213	C₂×#466	C₂×C₃₁	1	2	yes	complemented
214	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic, complemented
215	C₂×#417	C₂×C₃₁	1	2	yes	complemented
216	C₂²×C₃₁	—	2	8	no	—
217	C₂²×C₃₁	—	2	2	no	—
218	C₂²×C₃₁	—	2	2	no	—
219	C₂²×C₃₁	—	2	4	no	—
220	C₂²×C₃₁	—	2	4	no	—
221	C₂²×C₃₁	—	2	4	no	—
222	C₂²×C₃₁	—	4	8	no	—
223	C₂²×C₃₁	—	4	4	no	—
224	C₂²×C₃₁	—	4	4	no	—
225	C₂²×C₃₁	—	4	4	no	—
226	C₂²×C₃₁	—	8	8	no	—
227	C₂²×C₃₁	C₂×#121	1	4	yes	—
228	C₂²×C₃₁	C₂×#121	1	2	yes	—
229	C₂²×C₃₁	#576	1	2	yes	—
230	C₂²×C₃₁	#578	1	2	yes	—
231	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
232	C₄×C₃₁	—	2	4	no	—
233	C₄×C₃₁	—	4	4	no	—
234	C₄×C₃₁	—	4	8	no	—
235	C₄×C₃₁	C₂×#121	1	2	yes	—
236	C₄×C₃₁	C₂×#121	1	4	yes	—
237	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
238	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
239	C₂²×#41	C₂²×C₃₁	1	2	yes	—
240	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
241	C₂×#135	—	2	8	no	—
242	C₂×#135	C₂²×C₃₁	1	8	yes	complemented
243	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
244	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
245	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
246	C₂×#131	—	2	8	no	—
247	C₂×#131	C₂²×C₃₁	1	8	yes	complemented
248	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
250	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
251	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
252	#537	—	2	8	no	—
253	#537	C₂²×C₃₁	1	16	yes	complemented
254	C₂×C₂²⋊Q₈	—	2	2	no	—
255	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
256	C₂×#121	—	2	2	no	—
257	C₂×#121	—	2	4	no	—
258	C₂×#121	C₂²×C₃₁	1	4	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
260	#468	C₂²×C₃₁	1	32	yes	complemented
261	#467	C₂²×C₃₁	1	16	yes	complemented
262	#466	C₂²×C₃₁	1	16	yes	complemented
263	C₂×#107	C₂²×C₃₁	1	2	yes	—
264	C₂×#107	C₂²×C₃₁	1	2	yes	—
265	C₂×#107	C₂²×C₃₁	1	8	yes	complemented
266	#417	C₂²×C₃₁	1	16	yes	complemented
267	C₂×#103	C₂²×C₃₁	1	4	yes	—
268	C₂×#102	C₂²×C₃₁	1	4	yes	—
269	C₂×C₃₁	—	2	4	no	—
270	C₂×C₃₁	—	4	4	no	—
271	C₂×C₃₁	—	8	4	no	—
272	C₂×C₃₁	#3061	1	4	yes	direct product factor
273	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
274	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
275	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
276	C₂×#41	—	2	4	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	8	no	—
280	C₂×#41	—	2	8	no	—
281	C₂×#41	D₄×C₃₁	1	4	yes	—
282	C₂×#41	C₂³×C₃₁	1	8	yes	—
283	C₂×#41	C₂³×C₃₁	1	4	yes	—
284	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
285	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	4	no	—
288	C₂²×D₄	D₄×C₃₁	1	2	yes	—
289	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
294	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
295	#135	—	2	32	no	—
296	C₂×Q₁₆	—	2	4	no	—
297	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
298	C₂×SD₁₆	—	2	8	no	—
299	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
300	C₂×D₈	—	2	4	no	—
301	C₂×D₈	C₂³×C₃₁	1	4	yes	—
302	#131	—	2	32	no	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	—	2	8	no	—
305	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
306	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
307	C₂²×C₈	—	2	8	no	—
308	C₂²×C₈	D₄×C₃₁	1	8	yes	complemented
309	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
310	C₂²×C₈	C₂³×C₃₁	1	8	yes	—
311	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
314	C₂²⋊Q₈	—	2	16	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
317	#121	—	2	16	no	—
318	#121	—	2	32	no	—
319	#121	—	2	8	no	—
320	#121	C₂³×C₃₁	1	16	yes	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	#107	C₂³×C₃₁	1	8	yes	—
329	#107	C₂³×C₃₁	1	8	yes	—
330	#103	C₂³×C₃₁	1	16	yes	—
331	#102	C₂³×C₃₁	1	16	yes	—
332	C₃₁	C₂×#3061	1	1	yes	characteristic, direct product factor, Sylow
333	C₂⁴	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
335	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
336	#41	—	2	16	no	—
337	#41	—	2	8	no	—
338	#41	—	2	8	no	—
339	#41	—	2	16	no	—
340	#41	—	2	16	no	—
341	#41	—	4	16	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
347	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	16	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	8	8	no	—
357	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
358	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
359	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	4	8	no	—
367	C₂²×C₄	—	8	4	no	—
368	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
373	C₂²×C₄	#41×C₃₁	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
377	Q₁₆	—	2	8	no	—
378	SD₁₆	—	2	16	no	—
379	D₈	—	2	8	no	—
380	M₁₆	—	2	8	no	—
381	M₁₆	—	2	16	no	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	16	no	—
384	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
385	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
386	C₂×C₈	C₂×D₄×C₃₁	1	16	yes	complemented
387	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
388	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
389	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	16	no	—
393	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
394	C₂²⋊C₄	—	2	16	no	—
395	C₂²⋊C₄	—	2	16	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	C₃₁×#121	1	4	yes	—
406	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
407	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
408	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
409	Q₈	—	2	8	no	—
410	Q₈	—	2	4	no	—
411	Q₈	—	2	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	16	no	—
414	D₄	—	2	8	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	16	no	—
418	D₄	—	4	4	no	—
419	D₄	—	8	16	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	—	8	8	no	—
430	C₂×C₄	C₃₁×#121	1	4	yes	—
431	C₂×C₄	C₃₁×#121	1	8	yes	—
432	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
437	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
438	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
439	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	C₂²×D₄×C₃₁	1	4	yes	—
442	C₈	C₂²×D₄×C₃₁	1	4	yes	—
443	C₂²	—	2	8	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	C₂×C₃₁×#121	1	4	yes	—
455	C₂²	C₂×C₃₁×#121	1	2	yes	—
456	C₂²	C₃₁×#576	1	2	yes	—
457	C₂²	C₃₁×#578	1	2	yes	—
458	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	8	no	—
462	C₄	C₂×C₃₁×#121	1	2	yes	—
463	C₄	C₂×C₃₁×#121	1	4	yes	—
464	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
465	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
466	C₂	—	2	4	no	—
467	C₂	—	4	4	no	—
468	C₂	—	8	4	no	—
469	C₂	C₃₁×#3061	1	4	yes	direct product factor
470	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
471	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
472	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#135	C₂	semidirect
2. C₂²×C₃₁×#131	C₂	semidirect
3. C₂×C₃₁×#537	C₂	semidirect
4. C₃₁×#3061	C₂	direct (N × H)
5. C₂×C₃₁×#468	C₂	semidirect
6. C₂×C₃₁×#467	C₂	semidirect
7. C₂×C₃₁×#466	C₂	semidirect
8. C₂²×C₃₁×#107	C₂	semidirect
9. C₂×C₃₁×#417	C₂	semidirect
13. C₂×C₃₁×#135	C₂²	semidirect
18. C₂×C₃₁×#131	C₂²	semidirect
24. C₃₁×#537	C₂²	semidirect
31. C₃₁×#468	C₂²	semidirect
32. C₃₁×#467	C₂²	semidirect
33. C₃₁×#466	C₂²	semidirect
36. C₂×C₃₁×#107	C₂²	semidirect
37. C₃₁×#417	C₂²	semidirect
72. C₂²×C₈×C₃₁	D₄	semidirect
149. C₂×C₈×C₃₁	C₂×D₄	semidirect
159. C₂×#3061	C₃₁	direct (N × H)
207. C₂²×#135	C₂×C₃₁	semidirect
208. C₂²×#131	C₂×C₃₁	semidirect
209. C₂×#537	C₂×C₃₁	semidirect
210. #3061	C₂×C₃₁	direct (N × H)
211. C₂×#468	C₂×C₃₁	semidirect
212. C₂×#467	C₂×C₃₁	semidirect
213. C₂×#466	C₂×C₃₁	semidirect
214. C₂²×#107	C₂×C₃₁	semidirect
215. C₂×#417	C₂×C₃₁	semidirect
242. C₂×#135	C₂²×C₃₁	semidirect
247. C₂×#131	C₂²×C₃₁	semidirect
253. #537	C₂²×C₃₁	semidirect
260. #468	C₂²×C₃₁	semidirect
261. #467	C₂²×C₃₁	semidirect
262. #466	C₂²×C₃₁	semidirect
265. C₂×#107	C₂²×C₃₁	semidirect
266. #417	C₂²×C₃₁	semidirect
272. C₂×C₃₁	#3061	direct (N × H)
308. C₂²×C₈	D₄×C₃₁	semidirect
332. C₃₁	C₂×#3061	direct (N × H)
386. C₂×C₈	C₂×D₄×C₃₁	semidirect
469. C₂	C₃₁×#3061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#135	2
C₂²×C₃₁×#131	2
C₂×C₃₁×#537	2
C₃₁×#3061	2
C₂×C₃₁×#468	2
C₂×C₃₁×#467	2
C₂×C₃₁×#466	2
C₂²×C₃₁×#107	2
C₂×C₃₁×#417	2
C₂×#3061	31

Subgroups — C2×C31×#3061 #21517208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3061 #21517208