Subgroups — C₂×C₃₁×#3126 #21517314

Order 7936.

2122 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3126	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#479	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#460	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#448	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#440	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#540	—	2	4	no	—
15	C₃₁×#540	C₂²	1	8	yes	—
16	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#123	—	2	2	no	—
19	C₂×C₃₁×#121	—	2	2	no	—
20	C₂×C₃₁×#121	C₂²	1	2	yes	—
21	C₃₁×#519	—	2	4	no	—
22	C₃₁×#519	C₂²	1	8	yes	complemented
23	C₂×C₄×Q₈×C₃₁	—	2	2	no	—
24	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
27	C₂×C₃₁×#117	—	2	2	no	—
28	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
30	C₃₁×#482	C₂²	1	16	yes	complemented
31	C₃₁×#479	C₂²	1	16	yes	complemented
32	C₃₁×#460	C₂²	1	16	yes	complemented
33	C₃₁×#448	C₂²	1	16	yes	complemented
34	C₃₁×#440	C₂²	1	16	yes	complemented
35	C₄×SD₁₆×C₃₁	C₂²	1	16	yes	complemented
36	C₃₁×#433	C₂²	1	8	yes	complemented
37	C₂×C₃₁×#107	C₂²	1	2	yes	—
38	C₂×C₃₁×#106	C₂²	1	2	yes	—
39	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₃₁×#103	C₂²	1	2	yes	—
41	C₂×C₃₁×#103	C₂²	1	2	yes	—
42	C₂×C₃₁×#102	C₂²	1	2	yes	—
43	C₂×C₃₁×#102	C₂²	1	2	yes	—
44	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₃₁	—	2	8	no	—
48	C₂²×Q₈×C₃₁	—	2	1	no	—
49	C₂²×Q₈×C₃₁	—	2	2	no	—
50	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
51	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
52	C₂²×D₄×C₃₁	—	2	2	no	—
53	C₂²×D₄×C₃₁	—	2	2	no	—
54	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₃₁	—	2	1	no	—
56	C₂³×C₄×C₃₁	—	2	2	no	—
57	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₃₁	—	2	8	no	—
59	C₂×SD₁₆×C₃₁	—	2	8	no	—
60	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
61	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
62	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
64	C₃₁×#127	—	2	2	no	—
65	C₃₁×#127	C₂³	1	4	yes	—
66	C₃₁×#125	—	2	2	no	—
67	C₃₁×#125	C₂³	1	4	yes	—
68	C₃₁×#123	—	2	16	no	—
69	C₃₁×#121	—	2	4	no	—
70	C₃₁×#121	—	2	16	no	—
71	C₃₁×#121	C₂³	1	8	yes	—
72	C₄×Q₈×C₃₁	—	2	16	no	—
73	C₄×Q₈×C₃₁	—	2	4	no	—
74	C₄×Q₈×C₃₁	—	2	4	no	—
75	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
76	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
77	C₄×D₄×C₃₁	—	2	4	no	—
78	C₄×D₄×C₃₁	C₂³	1	8	yes	—
79	C₃₁×#117	—	2	2	no	—
80	C₃₁×#117	—	2	16	no	—
81	C₃₁×#117	D₄	1	4	yes	—
82	C₃₁×#117	C₂³	1	4	yes	—
83	C₃₁×#117	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
94	C₂×C₄²×C₃₁	—	2	2	no	—
95	C₂×C₄²×C₃₁	—	2	2	no	—
96	C₂×C₄²×C₃₁	—	2	1	no	—
97	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
99	C₃₁×#107	C₂³	1	8	yes	—
100	C₃₁×#106	C₂³	1	8	yes	—
101	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
102	C₃₁×#103	C₂³	1	8	yes	—
103	C₃₁×#103	C₂³	1	8	yes	—
104	C₃₁×#102	C₂³	1	8	yes	—
105	C₃₁×#102	C₂³	1	8	yes	—
106	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₃₁×#97	C₂³	1	4	yes	—
108	C₄×C₈×C₃₁	C₂³	1	4	yes	—
109	C₂⁴×C₃₁	—	2	2	no	—
110	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₃₁	—	2	16	no	—
112	C₂×Q₈×C₃₁	—	2	8	no	—
113	C₂×Q₈×C₃₁	—	2	16	no	—
114	C₂×Q₈×C₃₁	—	2	4	no	—
115	C₂×Q₈×C₃₁	—	2	2	no	—
116	C₂×Q₈×C₃₁	—	2	4	no	—
117	C₂×Q₈×C₃₁	#41	1	8	yes	—
118	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
119	C₂×D₄×C₃₁	—	2	8	no	—
120	C₂×D₄×C₃₁	—	2	2	no	—
121	C₂×D₄×C₃₁	—	2	8	no	—
122	C₂×D₄×C₃₁	—	2	4	no	—
123	C₂×D₄×C₃₁	—	2	4	no	—
124	C₂×D₄×C₃₁	—	8	4	no	—
125	C₂×D₄×C₃₁	—	8	4	no	—
126	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₃₁	—	2	8	no	—
128	C₂²×C₄×C₃₁	—	2	4	no	—
129	C₂²×C₄×C₃₁	—	2	2	no	—
130	C₂²×C₄×C₃₁	—	2	4	no	—
131	C₂²×C₄×C₃₁	—	2	2	no	—
132	C₂²×C₄×C₃₁	—	2	2	no	—
133	C₂²×C₄×C₃₁	—	2	8	no	—
134	C₂²×C₄×C₃₁	—	8	4	no	—
135	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
141	SD₁₆×C₃₁	—	2	16	no	—
142	SD₁₆×C₃₁	—	2	16	no	—
143	C₂×C₈×C₃₁	—	2	4	no	—
144	C₂×C₈×C₃₁	—	2	4	no	—
145	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
146	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
147	C₄⋊C₄×C₃₁	—	2	8	no	—
148	C₄⋊C₄×C₃₁	—	2	8	no	—
149	C₄⋊C₄×C₃₁	—	2	8	no	—
150	C₄⋊C₄×C₃₁	—	2	2	no	—
151	C₄⋊C₄×C₃₁	—	2	2	no	—
152	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
153	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₃₁	—	2	4	no	—
156	C₂²⋊C₄×C₃₁	—	2	8	no	—
157	C₂²⋊C₄×C₃₁	—	2	8	no	—
158	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
159	C₄²×C₃₁	—	2	8	no	—
160	C₄²×C₃₁	—	2	8	no	—
161	C₄²×C₃₁	—	2	4	no	—
162	C₄²×C₃₁	C₂×D₄	1	2	yes	—
163	C₄²×C₃₁	C₂×D₄	1	2	yes	—
164	C₄²×C₃₁	C₂⁴	1	2	yes	—
165	C₄²×C₃₁	C₂⁴	1	2	yes	—
166	C₂×#3126	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₃₁	—	2	2	no	—
168	C₂³×C₃₁	—	2	4	no	—
169	C₂³×C₃₁	—	2	4	no	—
170	C₂³×C₃₁	—	4	4	no	—
171	C₂³×C₃₁	—	4	4	no	—
172	C₂³×C₃₁	—	4	4	no	—
173	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
174	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₃₁	—	2	16	no	—
176	Q₈×C₃₁	—	2	8	no	—
177	Q₈×C₃₁	—	2	4	no	—
178	Q₈×C₃₁	C₂×#41	1	8	yes	—
179	D₄×C₃₁	—	2	4	no	—
180	D₄×C₃₁	—	2	4	no	—
181	D₄×C₃₁	—	4	4	no	—
182	D₄×C₃₁	—	8	8	no	—
183	D₄×C₃₁	—	8	8	no	—
184	C₂×C₄×C₃₁	—	2	16	no	—
185	C₂×C₄×C₃₁	—	2	8	no	—
186	C₂×C₄×C₃₁	—	2	2	no	—
187	C₂×C₄×C₃₁	—	2	4	no	—
188	C₂×C₄×C₃₁	—	2	4	no	—
189	C₂×C₄×C₃₁	—	2	4	no	—
190	C₂×C₄×C₃₁	—	2	4	no	—
191	C₂×C₄×C₃₁	—	2	4	no	—
192	C₂×C₄×C₃₁	—	2	4	no	—
193	C₂×C₄×C₃₁	—	2	4	no	—
194	C₂×C₄×C₃₁	—	4	4	no	—
195	C₂×C₄×C₃₁	—	4	4	no	—
196	C₂×C₄×C₃₁	—	8	8	no	—
197	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
202	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
203	C₈×C₃₁	—	2	4	no	—
204	C₈×C₃₁	—	2	4	no	—
205	C₂×#540	C₂×C₃₁	1	1	yes	characteristic
206	C₂×#519	C₂×C₃₁	1	1	yes	characteristic, complemented
207	#3126	C₂×C₃₁	1	16	yes	direct product factor
208	C₂×#482	C₂×C₃₁	1	2	yes	complemented
209	C₂×#479	C₂×C₃₁	1	2	yes	complemented
210	C₂×#460	C₂×C₃₁	1	2	yes	complemented
211	C₂×#448	C₂×C₃₁	1	2	yes	complemented
212	C₂×#440	C₂×C₃₁	1	2	yes	complemented
213	C₂×C₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
214	C₂×#433	C₂×C₃₁	1	1	yes	characteristic, complemented
215	C₂²×C₃₁	—	2	2	no	—
216	C₂²×C₃₁	—	2	4	no	—
217	C₂²×C₃₁	—	4	4	no	—
218	C₂²×C₃₁	—	4	4	no	—
219	C₂²×C₃₁	—	4	4	no	—
220	C₂²×C₃₁	—	4	4	no	—
221	C₂²×C₃₁	—	8	8	no	—
222	C₂²×C₃₁	#525	1	2	yes	—
223	C₂²×C₃₁	#577	1	4	yes	—
224	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
225	C₄×C₃₁	—	2	8	no	—
226	C₄×C₃₁	—	2	2	no	—
227	C₄×C₃₁	—	2	4	no	—
228	C₄×C₃₁	—	2	4	no	—
229	C₄×C₃₁	—	4	4	no	—
230	C₄×C₃₁	—	4	4	no	—
231	C₄×C₃₁	#525	1	2	yes	—
232	C₄×C₃₁	C₂²×#41	1	2	yes	—
233	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
235	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
236	#540	—	2	4	no	—
237	#540	C₂²×C₃₁	1	8	yes	—
238	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
239	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
240	C₂×#123	—	2	2	no	—
241	C₂×#121	—	2	2	no	—
242	C₂×#121	C₂²×C₃₁	1	2	yes	—
243	#519	—	2	4	no	—
244	#519	C₂²×C₃₁	1	8	yes	complemented
245	C₂×C₄×Q₈	—	2	2	no	—
246	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
249	C₂×#117	—	2	2	no	—
250	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
251	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
252	#482	C₂²×C₃₁	1	16	yes	complemented
253	#479	C₂²×C₃₁	1	16	yes	complemented
254	#460	C₂²×C₃₁	1	16	yes	complemented
255	#448	C₂²×C₃₁	1	16	yes	complemented
256	#440	C₂²×C₃₁	1	16	yes	complemented
257	C₄×SD₁₆	C₂²×C₃₁	1	16	yes	complemented
258	#433	C₂²×C₃₁	1	8	yes	complemented
259	C₂×#107	C₂²×C₃₁	1	2	yes	—
260	C₂×#106	C₂²×C₃₁	1	2	yes	—
261	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
262	C₂×#103	C₂²×C₃₁	1	2	yes	—
263	C₂×#103	C₂²×C₃₁	1	2	yes	—
264	C₂×#102	C₂²×C₃₁	1	2	yes	—
265	C₂×#102	C₂²×C₃₁	1	2	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
267	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
269	C₂×C₃₁	—	4	2	no	—
270	C₂×C₃₁	—	8	4	no	—
271	C₂×C₃₁	#3126	1	4	yes	direct product factor
272	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
273	C₂×C₃₁	C₂×#577	1	2	yes	—
274	C₂²×Q₈	—	2	8	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
278	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
285	C₂×SD₁₆	—	2	8	no	—
286	C₂×SD₁₆	—	2	8	no	—
287	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
288	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
289	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
290	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
291	#127	—	2	2	no	—
292	#127	C₂³×C₃₁	1	4	yes	—
293	#125	—	2	2	no	—
294	#125	C₂³×C₃₁	1	4	yes	—
295	#123	—	2	16	no	—
296	#121	—	2	4	no	—
297	#121	—	2	16	no	—
298	#121	C₂³×C₃₁	1	8	yes	—
299	C₄×Q₈	—	2	16	no	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
303	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	C₂³×C₃₁	1	8	yes	—
306	#117	—	2	2	no	—
307	#117	—	2	16	no	—
308	#117	D₄×C₃₁	1	4	yes	—
309	#117	C₂³×C₃₁	1	4	yes	—
310	#117	C₂³×C₃₁	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
326	#107	C₂³×C₃₁	1	8	yes	—
327	#106	C₂³×C₃₁	1	8	yes	—
328	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
329	#103	C₂³×C₃₁	1	8	yes	—
330	#103	C₂³×C₃₁	1	8	yes	—
331	#102	C₂³×C₃₁	1	8	yes	—
332	#102	C₂³×C₃₁	1	8	yes	—
333	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
334	#97	C₂³×C₃₁	1	4	yes	—
335	C₄×C₈	C₂³×C₃₁	1	4	yes	—
336	C₃₁	C₂×#3126	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁴	—	2	2	no	—
338	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
339	C₂×Q₈	—	2	16	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	16	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	#41×C₃₁	1	8	yes	—
346	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	8	4	no	—
353	C₂×D₄	—	8	4	no	—
354	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	8	4	no	—
363	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
369	SD₁₆	—	2	16	no	—
370	SD₁₆	—	2	16	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
374	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
381	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
382	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	8	no	—
389	C₄²	—	2	4	no	—
390	C₄²	C₂×D₄×C₃₁	1	2	yes	—
391	C₄²	C₂×D₄×C₃₁	1	2	yes	—
392	C₄²	C₂⁴×C₃₁	1	2	yes	—
393	C₄²	C₂⁴×C₃₁	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
401	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
402	Q₈	—	2	16	no	—
403	Q₈	—	2	8	no	—
404	Q₈	—	2	4	no	—
405	Q₈	C₂×#41×C₃₁	1	8	yes	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	8	8	no	—
410	D₄	—	8	8	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
429	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	8	no	—
439	C₂²	C₃₁×#525	1	2	yes	—
440	C₂²	C₃₁×#577	1	4	yes	—
441	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
442	C₄	—	2	8	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	C₃₁×#525	1	2	yes	—
449	C₄	C₂²×#41×C₃₁	1	2	yes	—
450	C₂	—	4	2	no	—
451	C₂	—	8	4	no	—
452	C₂	C₃₁×#3126	1	4	yes	direct product factor
453	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
454	C₂	C₂×C₃₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#519	C₂	semidirect
3. C₃₁×#3126	C₂	direct (N × H)
4. C₂×C₃₁×#482	C₂	semidirect
5. C₂×C₃₁×#479	C₂	semidirect
6. C₂×C₃₁×#460	C₂	semidirect
7. C₂×C₃₁×#448	C₂	semidirect
8. C₂×C₃₁×#440	C₂	semidirect
9. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
10. C₂×C₃₁×#433	C₂	semidirect
22. C₃₁×#519	C₂²	semidirect
30. C₃₁×#482	C₂²	semidirect
31. C₃₁×#479	C₂²	semidirect
32. C₃₁×#460	C₂²	semidirect
33. C₃₁×#448	C₂²	semidirect
34. C₃₁×#440	C₂²	semidirect
35. C₄×SD₁₆×C₃₁	C₂²	semidirect
36. C₃₁×#433	C₂²	semidirect
166. C₂×#3126	C₃₁	direct (N × H)
206. C₂×#519	C₂×C₃₁	semidirect
207. #3126	C₂×C₃₁	direct (N × H)
208. C₂×#482	C₂×C₃₁	semidirect
209. C₂×#479	C₂×C₃₁	semidirect
210. C₂×#460	C₂×C₃₁	semidirect
211. C₂×#448	C₂×C₃₁	semidirect
212. C₂×#440	C₂×C₃₁	semidirect
213. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
214. C₂×#433	C₂×C₃₁	semidirect
244. #519	C₂²×C₃₁	semidirect
252. #482	C₂²×C₃₁	semidirect
253. #479	C₂²×C₃₁	semidirect
254. #460	C₂²×C₃₁	semidirect
255. #448	C₂²×C₃₁	semidirect
256. #440	C₂²×C₃₁	semidirect
257. C₄×SD₁₆	C₂²×C₃₁	semidirect
258. #433	C₂²×C₃₁	semidirect
271. C₂×C₃₁	#3126	direct (N × H)
336. C₃₁	C₂×#3126	direct (N × H)
452. C₂	C₃₁×#3126	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×#540	2
C₂×C₃₁×#519	2
C₃₁×#3126	2
C₂×C₃₁×#482	2
C₂×C₃₁×#479	2
C₂×C₃₁×#460	2
C₂×C₃₁×#448	2
C₂×C₃₁×#440	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₃₁×#433	2
C₂×#3126	31

Subgroups — C2×C31×#3126 #21517314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3126 #21517314