Subgroups — C₂×C₃₁×#1683 #21475868

Order 7936.

726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1683	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₃₁	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#487	—	2	2	no	—
14	C₃₁×#487	C₂²	1	4	yes	complemented
15	C₃₁×#476	—	2	2	no	—
16	C₃₁×#476	C₂²	1	4	yes	—
17	C₃₁×#474	—	2	2	no	—
18	C₃₁×#474	C₂²	1	4	yes	—
19	C₈×D₄×C₃₁	—	2	2	no	—
20	C₈×D₄×C₃₁	C₂²	1	4	yes	—
21	C₂×C₃₁×#107	—	2	1	no	—
22	C₂×C₃₁×#106	—	2	1	no	—
23	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#103	—	2	1	no	—
27	C₂×C₃₁×#103	—	2	1	no	—
28	C₂×C₃₁×#102	—	2	1	no	—
29	C₂×C₃₁×#102	—	2	1	no	—
30	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	4	yes	complemented
33	C₃₁×#333	C₂²	1	4	yes	complemented
34	C₃₁×#332	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	1	no	—
39	C₂²×C₈×C₃₁	—	2	1	no	—
40	C₂²×C₈×C₃₁	—	2	1	no	—
41	C₂²×C₈×C₃₁	—	2	1	no	—
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	—	4	4	no	—
44	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
46	C₃₁×C₄⋊Q₈	—	2	1	no	—
47	C₃₁×C₄⋊Q₈	—	2	1	no	—
48	C₃₁×C₄⋊Q₈	—	2	1	no	—
49	C₃₁×C₄⋊Q₈	—	2	1	no	—
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₄×D₄×C₃₁	—	2	1	no	—
55	C₄×D₄×C₃₁	—	2	1	no	—
56	C₄×D₄×C₃₁	D₄	1	2	yes	—
57	C₄×D₄×C₃₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#107	—	2	4	no	—
66	C₃₁×#106	—	2	4	no	—
67	C₃₁×C₄⋊C₈	—	2	1	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×#103	—	2	4	no	—
74	C₃₁×#103	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×C₂²⋊C₈	—	2	4	no	—
78	C₄×C₈×C₃₁	D₄	1	2	yes	—
79	C₄×C₈×C₃₁	C₂³	1	2	yes	—
80	C₂⁴×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×Q₈×C₃₁	—	4	1	no	—
84	C₂×Q₈×C₃₁	—	4	1	no	—
85	C₂×Q₈×C₃₁	—	4	2	no	—
86	C₂×Q₈×C₃₁	—	4	2	no	—
87	C₂×Q₈×C₃₁	—	8	2	no	—
88	C₂×D₄×C₃₁	—	2	1	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	Q₁₆	1	4	yes	—
91	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	—	4	1	no	—
98	C₂²×C₄×C₃₁	—	4	1	no	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	4	8	no	—
108	C₂×C₈×C₃₁	—	4	2	no	—
109	C₂×C₈×C₃₁	—	4	2	no	—
110	C₂×C₈×C₃₁	—	4	2	no	—
111	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₃₁	—	2	1	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	4	1	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	4	1	no	—
121	C₄⋊C₄×C₃₁	—	4	1	no	—
122	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₃₁	—	2	2	no	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₃₁	#41	1	1	yes	characteristic
128	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
129	C₂×#1683	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	4	no	—
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	#121	1	1	yes	characteristic
135	Q₈×C₃₁	—	4	2	no	—
136	Q₈×C₃₁	—	4	2	no	—
137	Q₈×C₃₁	—	8	2	no	—
138	Q₈×C₃₁	—	8	2	no	—
139	Q₈×C₃₁	—	8	2	no	—
140	D₄×C₃₁	—	2	2	no	—
141	D₄×C₃₁	—	2	4	no	—
142	D₄×C₃₁	C₂×Q₁₆	1	4	yes	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	4	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	8	2	no	—
152	C₂×C₄×C₃₁	—	8	2	no	—
153	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
157	C₂×C₄×C₃₁	#135	1	2	yes	—
158	C₂×C₄×C₃₁	#135	1	2	yes	—
159	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
163	C₈×C₃₁	—	2	2	no	—
164	C₈×C₃₁	—	2	2	no	—
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	—	4	2	no	—
167	C₈×C₃₁	—	4	2	no	—
168	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂×#476	C₂×C₃₁	1	1	yes	characteristic
170	C₂×#474	C₂×C₃₁	1	1	yes	characteristic
171	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
172	#1683	C₂×C₃₁	1	8	yes	direct product factor
173	C₂×#335	C₂×C₃₁	1	1	yes	characteristic, complemented
174	C₂×#333	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
176	C₂²×C₃₁	—	2	4	no	—
177	C₂²×C₃₁	—	4	8	no	—
178	C₂²×C₃₁	—	4	2	no	—
179	C₂²×C₃₁	—	4	2	no	—
180	C₂²×C₃₁	#463	1	2	yes	—
181	C₂²×C₃₁	#467	1	2	yes	—
182	C₂²×C₃₁	#471	1	2	yes	—
183	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	2	no	—
189	C₄×C₃₁	#463	1	2	yes	—
190	C₄×C₃₁	#467	1	2	yes	—
191	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
192	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
193	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂³×C₈	—	2	1	no	—
196	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
199	#487	—	2	2	no	—
200	#487	C₂²×C₃₁	1	4	yes	complemented
201	#476	—	2	2	no	—
202	#476	C₂²×C₃₁	1	4	yes	—
203	#474	—	2	2	no	—
204	#474	C₂²×C₃₁	1	4	yes	—
205	C₈×D₄	—	2	2	no	—
206	C₈×D₄	C₂²×C₃₁	1	4	yes	—
207	C₂×#107	—	2	1	no	—
208	C₂×#106	—	2	1	no	—
209	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×#103	—	2	1	no	—
213	C₂×#103	—	2	1	no	—
214	C₂×#102	—	2	1	no	—
215	C₂×#102	—	2	1	no	—
216	C₂×C₂²⋊C₈	—	2	1	no	—
217	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
218	#335	C₂²×C₃₁	1	4	yes	complemented
219	#333	C₂²×C₃₁	1	4	yes	complemented
220	#332	C₂²×C₃₁	1	4	yes	complemented
221	C₂×C₃₁	—	4	4	no	—
222	C₂×C₃₁	#1683	1	4	yes	direct product factor
223	C₂×C₃₁	C₂×#463	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#467	1	1	yes	characteristic
225	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	4	4	no	—
235	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
244	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	D₄×C₃₁	1	2	yes	—
248	C₄×D₄	C₂³×C₃₁	1	2	yes	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
256	#107	—	2	4	no	—
257	#106	—	2	4	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
262	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
263	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
264	#103	—	2	4	no	—
265	#103	—	2	4	no	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₄×C₈	D₄×C₃₁	1	2	yes	—
270	C₄×C₈	C₂³×C₃₁	1	2	yes	—
271	C₃₁	C₂×#1683	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	8	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	Q₁₆×C₃₁	1	4	yes	—
283	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	8	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₄²	#41×C₃₁	1	1	yes	characteristic
320	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
321	C₂³	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	C₃₁×#121	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	2	2	no	—
333	D₄	C₂×Q₁₆×C₃₁	1	4	yes	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
345	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
346	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
347	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
348	C₂×C₄	C₃₁×#135	1	2	yes	—
349	C₂×C₄	C₃₁×#135	1	2	yes	—
350	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	2	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	C₃₁×#463	1	2	yes	—
364	C₂²	C₃₁×#467	1	2	yes	—
365	C₂²	C₃₁×#471	1	2	yes	—
366	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	C₃₁×#463	1	2	yes	—
373	C₄	C₃₁×#467	1	2	yes	—
374	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
375	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
376	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
377	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂	—	4	4	no	—
379	C₂	C₃₁×#1683	1	4	yes	direct product factor
380	C₂	C₂×C₃₁×#463	1	1	yes	characteristic
381	C₂	C₂×C₃₁×#467	1	1	yes	characteristic
382	C₂	C₂×C₃₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#487	C₂	semidirect
5. C₃₁×#1683	C₂	direct (N × H)
6. C₂×C₃₁×#335	C₂	semidirect
7. C₂×C₃₁×#333	C₂	semidirect
8. C₂×C₃₁×#332	C₂	semidirect
14. C₃₁×#487	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#333	C₂²	semidirect
34. C₃₁×#332	C₂²	semidirect
129. C₂×#1683	C₃₁	direct (N × H)
168. C₂×#487	C₂×C₃₁	semidirect
172. #1683	C₂×C₃₁	direct (N × H)
173. C₂×#335	C₂×C₃₁	semidirect
174. C₂×#333	C₂×C₃₁	semidirect
175. C₂×#332	C₂×C₃₁	semidirect
200. #487	C₂²×C₃₁	semidirect
218. #335	C₂²×C₃₁	semidirect
219. #333	C₂²×C₃₁	semidirect
220. #332	C₂²×C₃₁	semidirect
222. C₂×C₃₁	#1683	direct (N × H)
271. C₃₁	C₂×#1683	direct (N × H)
379. C₂	C₃₁×#1683	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×#487	2
C₂×C₃₁×#476	2
C₂×C₃₁×#474	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1683	2
C₂×C₃₁×#335	2
C₂×C₃₁×#333	2
C₂×C₃₁×#332	2
C₂×#1683	31

Subgroups — C2×C31×#1683 #21475868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1683 #21475868