Subgroups — C₂×C₃₁×#2943 #21516914

Order 7936.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 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
2	C₂×C₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2943	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#442	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#441	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#440	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#416	C₂	1	2	yes	maximal, complemented
9	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×#135	C₄	1	16	yes	complemented
12	C₂×C₃₁×#135	C₂²	1	8	yes	—
13	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
15	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₄×#41×C₃₁	—	2	8	no	—
19	C₄×#41×C₃₁	C₂²	1	16	yes	complemented
20	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₃₁	—	2	4	no	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
23	C₂×C₃₁×#117	—	2	2	no	—
24	C₂×C₃₁×#117	C₂²	1	2	yes	—
25	C₂²×C₄²×C₃₁	—	2	2	no	—
26	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#442	C₂²	1	16	yes	complemented
28	C₃₁×#441	C₂²	1	16	yes	complemented
29	C₃₁×#440	C₂²	1	32	yes	complemented
30	C₃₁×#427	C₂²	1	8	yes	complemented
31	C₂×C₃₁×#107	C₂²	1	2	yes	—
32	C₂×C₃₁×#106	C₂²	1	2	yes	—
33	C₃₁×#416	C₂²	1	16	yes	complemented
34	C₂×C₃₁×#103	C₂²	1	4	yes	—
35	C₂×C₃₁×#102	C₂²	1	4	yes	—
36	C₂×C₃₁×#97	C₂²	1	2	yes	—
37	C₂×C₃₁×#97	C₂²	1	2	yes	—
38	C₂×C₃₁×#97	C₂²	1	8	yes	complemented
39	C₂×#41×C₃₁	—	2	4	no	—
40	C₂×#41×C₃₁	—	2	8	no	—
41	C₂×#41×C₃₁	C₂×C₄	1	16	yes	complemented
42	C₂×#41×C₃₁	C₂³	1	8	yes	—
43	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₃₁	—	2	2	no	—
45	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₁	—	2	2	no	—
47	C₂³×C₄×C₃₁	—	2	4	no	—
48	C₂³×C₄×C₃₁	D₄	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×#135	C₂×C₄	1	64	yes	complemented
51	C₂×Q₁₆×C₃₁	C₂×C₄	1	8	yes	complemented
52	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
53	C₂×SD₁₆×C₃₁	C₂×C₄	1	16	yes	complemented
54	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
55	C₂×D₈×C₃₁	C₂×C₄	1	8	yes	complemented
56	C₂×D₈×C₃₁	C₂³	1	4	yes	—
57	C₂²×C₈×C₃₁	—	2	4	no	—
58	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	complemented
59	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
61	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
64	C₄×Q₈×C₃₁	—	2	8	no	—
65	C₄×Q₈×C₃₁	C₂³	1	16	yes	—
66	C₄×D₄×C₃₁	—	2	32	no	—
67	C₄×D₄×C₃₁	—	2	8	no	—
68	C₄×D₄×C₃₁	C₂³	1	16	yes	—
69	C₃₁×#117	—	2	4	no	—
70	C₃₁×#117	—	2	16	no	—
71	C₃₁×#117	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
74	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
76	C₂×C₄²×C₃₁	—	2	4	no	—
77	C₂×C₄²×C₃₁	—	2	2	no	—
78	C₂×C₄²×C₃₁	—	2	16	no	—
79	C₂×C₄²×C₃₁	D₄	1	4	yes	—
80	C₂×C₄²×C₃₁	D₄	1	2	yes	—
81	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
83	C₃₁×#107	C₂³	1	8	yes	—
84	C₃₁×#106	C₂³	1	8	yes	—
85	C₃₁×#103	C₂³	1	16	yes	—
86	C₃₁×#102	C₂³	1	16	yes	—
87	C₃₁×#97	C₂³	1	8	yes	—
88	C₃₁×#97	C₂³	1	8	yes	—
89	C₂⁴×C₃₁	—	2	2	no	—
90	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
91	#41×C₃₁	—	2	32	no	—
92	#41×C₃₁	—	2	16	no	—
93	#41×C₃₁	C₂²×C₄	1	32	yes	complemented
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	4	no	—
96	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
97	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
98	C₂×D₄×C₃₁	—	2	16	no	—
99	C₂×D₄×C₃₁	—	2	8	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	—	2	4	no	—
102	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
103	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	16	no	—
106	C₂²×C₄×C₃₁	—	2	8	no	—
107	C₂²×C₄×C₃₁	—	2	4	no	—
108	C₂²×C₄×C₃₁	—	2	16	no	—
109	C₂²×C₄×C₃₁	—	4	4	no	—
110	C₂²×C₄×C₃₁	—	4	16	no	—
111	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₁	#41	1	4	yes	—
117	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
119	Q₁₆×C₃₁	C₂²×C₄	1	16	yes	complemented
120	SD₁₆×C₃₁	C₂²×C₄	1	32	yes	complemented
121	D₈×C₃₁	C₂²×C₄	1	16	yes	complemented
122	C₂×C₈×C₃₁	—	2	4	no	—
123	C₂×C₈×C₃₁	—	2	8	no	—
124	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₃₁	C₂²×C₄	1	16	yes	complemented
127	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
128	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
129	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
130	C₄⋊C₄×C₃₁	—	2	16	no	—
131	C₄⋊C₄×C₃₁	—	2	4	no	—
132	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
133	C₂²⋊C₄×C₃₁	—	2	8	no	—
134	C₂²⋊C₄×C₃₁	—	2	16	no	—
135	C₄²×C₃₁	—	2	8	no	—
136	C₄²×C₃₁	—	2	16	no	—
137	C₄²×C₃₁	C₂×D₄	1	8	yes	—
138	C₄²×C₃₁	C₂×D₄	1	4	yes	—
139	C₄²×C₃₁	C₂⁴	1	4	yes	—
140	C₂×#2943	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	2	4	no	—
142	C₂³×C₃₁	—	2	8	no	—
143	C₂³×C₃₁	—	2	4	no	—
144	C₂³×C₃₁	—	4	8	no	—
145	C₂³×C₃₁	C₄×D₄	1	4	yes	—
146	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₁	—	2	8	no	—
149	Q₈×C₃₁	—	2	4	no	—
150	Q₈×C₃₁	C₂³×C₄	1	8	yes	—
151	D₄×C₃₁	—	2	32	no	—
152	D₄×C₃₁	—	2	8	no	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	C₂³×C₄	1	8	yes	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	8	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	2	32	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	4	8	no	—
161	C₂×C₄×C₃₁	—	4	32	no	—
162	C₂×C₄×C₃₁	—	4	8	no	—
163	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₃₁	C₄×D₄	1	8	yes	—
165	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
166	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
167	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
172	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
173	C₈×C₃₁	—	2	4	no	—
174	C₈×C₃₁	C₂³×C₄	1	4	yes	—
175	C₈×C₃₁	C₂³×C₄	1	4	yes	—
176	C₂²×#135	C₂×C₃₁	1	1	yes	characteristic
177	C₂×C₄×#41	C₂×C₃₁	1	2	yes	complemented
178	#2943	C₂×C₃₁	1	16	yes	direct product factor
179	C₂×#442	C₂×C₃₁	1	2	yes	complemented
180	C₂×#441	C₂×C₃₁	1	2	yes	complemented
181	C₂×#440	C₂×C₃₁	1	4	yes	complemented
182	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂×#416	C₂×C₃₁	1	2	yes	complemented
184	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
185	C₂²×C₃₁	—	2	8	no	—
186	C₂²×C₃₁	—	2	4	no	—
187	C₂²×C₃₁	—	2	8	no	—
188	C₂²×C₃₁	—	4	16	no	—
189	C₂²×C₃₁	—	4	8	no	—
190	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
191	C₂²×C₃₁	C₂×C₄×D₄	1	2	yes	—
192	C₂²×C₃₁	#575	1	4	yes	—
193	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
194	C₄×C₃₁	—	2	8	no	—
195	C₄×C₃₁	—	2	8	no	—
196	C₄×C₃₁	—	4	8	no	—
197	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
198	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
199	C₄×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
200	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
201	C₂²×#41	C₂²×C₃₁	1	2	yes	—
202	C₂×#135	C₄×C₃₁	1	16	yes	complemented
203	C₂×#135	C₂²×C₃₁	1	8	yes	—
204	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
206	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₄×#41	—	2	8	no	—
210	C₄×#41	C₂²×C₃₁	1	16	yes	complemented
211	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	—
212	C₂×C₄×D₄	—	2	4	no	—
213	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
214	C₂×#117	—	2	2	no	—
215	C₂×#117	C₂²×C₃₁	1	2	yes	—
216	C₂²×C₄²	—	2	2	no	—
217	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
218	#442	C₂²×C₃₁	1	16	yes	complemented
219	#441	C₂²×C₃₁	1	16	yes	complemented
220	#440	C₂²×C₃₁	1	32	yes	complemented
221	#427	C₂²×C₃₁	1	8	yes	complemented
222	C₂×#107	C₂²×C₃₁	1	2	yes	—
223	C₂×#106	C₂²×C₃₁	1	2	yes	—
224	#416	C₂²×C₃₁	1	16	yes	complemented
225	C₂×#103	C₂²×C₃₁	1	4	yes	—
226	C₂×#102	C₂²×C₃₁	1	4	yes	—
227	C₂×#97	C₂²×C₃₁	1	2	yes	—
228	C₂×#97	C₂²×C₃₁	1	2	yes	—
229	C₂×#97	C₂²×C₃₁	1	8	yes	complemented
230	C₂×C₃₁	—	2	4	no	—
231	C₂×C₃₁	—	4	8	no	—
232	C₂×C₃₁	#2943	1	4	yes	direct product factor
233	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#575	1	2	yes	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	—	2	8	no	—
237	C₂×#41	C₂×C₄×C₃₁	1	16	yes	complemented
238	C₂×#41	C₂³×C₃₁	1	8	yes	—
239	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	D₄×C₃₁	1	2	yes	—
245	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
246	#135	C₂×C₄×C₃₁	1	64	yes	complemented
247	C₂×Q₁₆	C₂×C₄×C₃₁	1	8	yes	complemented
248	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
249	C₂×SD₁₆	C₂×C₄×C₃₁	1	16	yes	complemented
250	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
251	C₂×D₈	C₂×C₄×C₃₁	1	8	yes	complemented
252	C₂×D₈	C₂³×C₃₁	1	4	yes	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	complemented
255	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
256	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
257	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
260	C₄×Q₈	—	2	8	no	—
261	C₄×Q₈	C₂³×C₃₁	1	16	yes	—
262	C₄×D₄	—	2	32	no	—
263	C₄×D₄	—	2	8	no	—
264	C₄×D₄	C₂³×C₃₁	1	16	yes	—
265	#117	—	2	4	no	—
266	#117	—	2	16	no	—
267	#117	C₂³×C₃₁	1	8	yes	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	—	2	16	no	—
275	C₂×C₄²	D₄×C₃₁	1	2	yes	—
276	C₂×C₄²	D₄×C₃₁	1	4	yes	—
277	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
278	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
279	#107	C₂³×C₃₁	1	8	yes	—
280	#106	C₂³×C₃₁	1	8	yes	—
281	#103	C₂³×C₃₁	1	16	yes	—
282	#102	C₂³×C₃₁	1	16	yes	—
283	#97	C₂³×C₃₁	1	8	yes	—
284	#97	C₂³×C₃₁	1	8	yes	—
285	C₃₁	C₂×#2943	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
288	#41	—	2	32	no	—
289	#41	—	2	16	no	—
290	#41	C₂²×C₄×C₃₁	1	32	yes	complemented
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
294	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
300	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	16	no	—
308	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
311	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₃₁	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
316	Q₁₆	C₂²×C₄×C₃₁	1	16	yes	complemented
317	SD₁₆	C₂²×C₄×C₃₁	1	32	yes	complemented
318	D₈	C₂²×C₄×C₃₁	1	16	yes	complemented
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
322	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
323	C₂×C₈	C₂²×C₄×C₃₁	1	16	yes	complemented
324	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
325	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
326	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
327	C₄⋊C₄	—	2	16	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₄²	—	2	8	no	—
333	C₄²	—	2	16	no	—
334	C₄²	C₂×D₄×C₃₁	1	8	yes	—
335	C₄²	C₂×D₄×C₃₁	1	4	yes	—
336	C₄²	C₂⁴×C₃₁	1	4	yes	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	C₄×D₄×C₃₁	1	4	yes	—
342	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	4	no	—
346	Q₈	C₂³×C₄×C₃₁	1	8	yes	—
347	D₄	—	2	32	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	C₂³×C₄×C₃₁	1	8	yes	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	32	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	32	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
360	C₂×C₄	C₄×D₄×C₃₁	1	8	yes	—
361	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
362	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
363	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
364	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
367	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
368	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	C₂³×C₄×C₃₁	1	4	yes	—
371	C₈	C₂³×C₄×C₃₁	1	4	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	4	16	no	—
376	C₂²	—	4	8	no	—
377	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
378	C₂²	C₂×C₄×D₄×C₃₁	1	2	yes	—
379	C₂²	C₃₁×#575	1	4	yes	—
380	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
381	C₄	—	2	8	no	—
382	C₄	—	2	8	no	—
383	C₄	—	4	8	no	—
384	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
385	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
386	C₄	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
387	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
388	C₂	—	2	4	no	—
389	C₂	—	4	8	no	—
390	C₂	C₃₁×#2943	1	4	yes	direct product factor
391	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
392	C₂	C₂×C₃₁×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂²×D₄
prime radical	C₂²×C₃₁×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#2943	C₂	direct (N × H)
4. C₂×C₃₁×#442	C₂	semidirect
5. C₂×C₃₁×#441	C₂	semidirect
6. C₂×C₃₁×#440	C₂	semidirect
7. C₂×C₃₁×#427	C₂	semidirect
8. C₂×C₃₁×#416	C₂	semidirect
9. C₂²×C₃₁×#97	C₂	semidirect
11. C₂×C₃₁×#135	C₄	semidirect
19. C₄×#41×C₃₁	C₂²	semidirect
27. C₃₁×#442	C₂²	semidirect
28. C₃₁×#441	C₂²	semidirect
29. C₃₁×#440	C₂²	semidirect
30. C₃₁×#427	C₂²	semidirect
33. C₃₁×#416	C₂²	semidirect
38. C₂×C₃₁×#97	C₂²	semidirect
41. C₂×#41×C₃₁	C₂×C₄	semidirect
50. C₃₁×#135	C₂×C₄	semidirect
51. C₂×Q₁₆×C₃₁	C₂×C₄	semidirect
53. C₂×SD₁₆×C₃₁	C₂×C₄	semidirect
55. C₂×D₈×C₃₁	C₂×C₄	semidirect
58. C₂²×C₈×C₃₁	C₂×C₄	semidirect
93. #41×C₃₁	C₂²×C₄	semidirect
119. Q₁₆×C₃₁	C₂²×C₄	semidirect
120. SD₁₆×C₃₁	C₂²×C₄	semidirect
121. D₈×C₃₁	C₂²×C₄	semidirect
126. C₂×C₈×C₃₁	C₂²×C₄	semidirect
140. C₂×#2943	C₃₁	direct (N × H)
177. C₂×C₄×#41	C₂×C₃₁	semidirect
178. #2943	C₂×C₃₁	direct (N × H)
179. C₂×#442	C₂×C₃₁	semidirect
180. C₂×#441	C₂×C₃₁	semidirect
181. C₂×#440	C₂×C₃₁	semidirect
182. C₂×#427	C₂×C₃₁	semidirect
183. C₂×#416	C₂×C₃₁	semidirect
184. C₂²×#97	C₂×C₃₁	semidirect
202. C₂×#135	C₄×C₃₁	semidirect
210. C₄×#41	C₂²×C₃₁	semidirect
218. #442	C₂²×C₃₁	semidirect
219. #441	C₂²×C₃₁	semidirect
220. #440	C₂²×C₃₁	semidirect
221. #427	C₂²×C₃₁	semidirect
224. #416	C₂²×C₃₁	semidirect
229. C₂×#97	C₂²×C₃₁	semidirect
232. C₂×C₃₁	#2943	direct (N × H)
237. C₂×#41	C₂×C₄×C₃₁	semidirect
246. #135	C₂×C₄×C₃₁	semidirect
247. C₂×Q₁₆	C₂×C₄×C₃₁	semidirect
249. C₂×SD₁₆	C₂×C₄×C₃₁	semidirect
251. C₂×D₈	C₂×C₄×C₃₁	semidirect
254. C₂²×C₈	C₂×C₄×C₃₁	semidirect
285. C₃₁	C₂×#2943	direct (N × H)
290. #41	C₂²×C₄×C₃₁	semidirect
316. Q₁₆	C₂²×C₄×C₃₁	semidirect
317. SD₁₆	C₂²×C₄×C₃₁	semidirect
318. D₈	C₂²×C₄×C₃₁	semidirect
323. C₂×C₈	C₂²×C₄×C₃₁	semidirect
390. C₂	C₃₁×#2943	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
C₂×C₄×#41×C₃₁	2
C₃₁×#2943	2
C₂×C₃₁×#442	2
C₂×C₃₁×#441	2
C₂×C₃₁×#440	2
C₂×C₃₁×#427	2
C₂×C₃₁×#416	2
C₂²×C₃₁×#97	2
C₂×#2943	31

Subgroups — C2×C31×#2943 #21516914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2943 #21516914