Subgroups — C₂×C₃×C₅×#382 #14275315

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
2	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#382	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#95	C₂	1	4	yes	maximal
5	C₂×C₅×#382	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×C₄⋊C₄	—	2	8	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
11	C₂×C₃×C₄²×C₅	C₄	1	8	yes	complemented
12	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
13	C₃×C₅×#95	C₂²	1	16	yes	—
14	C₂×C₃×#382	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
16	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
17	C₅×#382	C₂×C₃	1	8	yes	direct product factor
18	C₂×C₅×#95	C₂×C₃	1	4	yes	—
19	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	—	2	8	no	—
21	C₂²×C₃×C₄×C₅	—	2	8	no	—
22	C₂²×C₃×C₄×C₅	—	2	16	no	—
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
24	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
25	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
26	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
27	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
28	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
29	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
30	C₃×C₅×C₄⋊C₄	—	2	16	no	—
31	C₃×C₄²×C₅	C₂×C₄	1	16	yes	complemented
32	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	2	yes	—
33	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
34	C₃×#382	C₂×C₅	1	8	yes	direct product factor
35	C₂×C₃×#95	C₂×C₅	1	4	yes	—
36	C₂³×C₄×C₅	C₂²×C₃	1	4	yes	—
37	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
38	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₄	—	2	8	no	—
40	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
41	C₂×C₄²×C₅	C₃×C₄	1	8	yes	complemented
42	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
43	C₅×#95	C₂²×C₃	1	16	yes	—
44	C₂×#382	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
46	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
47	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
48	C₂³×C₃×C₅	#41	1	8	yes	—
49	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	—	2	16	no	—
51	C₂×C₃×C₄×C₅	—	2	8	no	—
52	C₂×C₃×C₄×C₅	—	2	8	no	—
53	C₂×C₃×C₄×C₅	—	2	16	no	—
54	C₂×C₃×C₄×C₅	—	4	16	no	—
55	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	—
56	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
57	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
58	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
59	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
60	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	—
61	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
62	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
63	C₂×C₃×C₄⋊C₄	—	2	8	no	—
64	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
65	C₂×C₃×C₄²	C₄×C₅	1	8	yes	complemented
66	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
67	C₃×#95	C₂²×C₅	1	16	yes	—
68	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
69	C₂²×C₄×C₅	—	2	8	no	—
70	C₂²×C₄×C₅	—	2	8	no	—
71	C₂²×C₄×C₅	—	2	16	no	—
72	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
73	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
74	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
75	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
76	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
77	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
78	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
79	C₅×C₄⋊C₄	—	2	16	no	—
80	C₄²×C₅	C₂×C₃×C₄	1	16	yes	complemented
81	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
82	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
83	#382	C₂×C₃×C₅	1	8	yes	direct product factor
84	C₂×#95	C₂×C₃×C₅	1	4	yes	—
85	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
86	C₂²×C₃×C₅	#117	1	8	yes	—
87	C₂²×C₃×C₅	#124	1	8	yes	—
88	C₂²×C₃×C₅	#125	1	8	yes	—
89	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
90	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
91	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
92	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
93	C₃×C₄×C₅	—	2	8	no	—
94	C₃×C₄×C₅	—	4	8	no	—
95	C₃×C₄×C₅	C₂×C₄⋊C₄	1	8	yes	—
96	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
97	C₂²×C₃×C₄	—	2	8	no	—
98	C₂²×C₃×C₄	—	2	8	no	—
99	C₂²×C₃×C₄	—	2	16	no	—
100	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
101	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
102	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
103	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
104	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
105	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
106	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
107	C₃×C₄⋊C₄	—	2	16	no	—
108	C₃×C₄²	C₂×C₄×C₅	1	16	yes	complemented
109	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
110	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
111	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
112	C₂³×C₅	C₃×#41	1	8	yes	—
113	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
114	C₂×C₄×C₅	—	2	16	no	—
115	C₂×C₄×C₅	—	2	8	no	—
116	C₂×C₄×C₅	—	2	8	no	—
117	C₂×C₄×C₅	—	2	16	no	—
118	C₂×C₄×C₅	—	4	16	no	—
119	C₂×C₄×C₅	C₃×C₄⋊C₄	1	16	yes	—
120	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
121	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
122	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
123	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
124	C₂³×C₄	C₂²×C₃×C₅	1	4	yes	—
125	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
126	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
127	C₂×C₄⋊C₄	—	2	8	no	—
128	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
129	C₂×C₄²	C₃×C₄×C₅	1	8	yes	complemented
130	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
131	#95	C₂²×C₃×C₅	1	16	yes	—
132	C₂×C₃×C₅	#382	1	8	yes	direct product factor
133	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₃×C₅	C₂×#117	1	2	yes	—
135	C₂×C₃×C₅	C₂×#124	1	2	yes	—
136	C₂×C₃×C₅	C₂×#125	1	2	yes	—
137	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
138	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
139	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
140	C₂³×C₃	C₅×#41	1	8	yes	—
141	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄	—	2	16	no	—
143	C₂×C₃×C₄	—	2	8	no	—
144	C₂×C₃×C₄	—	2	8	no	—
145	C₂×C₃×C₄	—	2	16	no	—
146	C₂×C₃×C₄	—	4	16	no	—
147	C₂×C₃×C₄	C₅×C₄⋊C₄	1	16	yes	—
148	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
149	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
150	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
151	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
152	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
153	C₂²×C₅	C₃×#117	1	8	yes	—
154	C₂²×C₅	C₃×#124	1	8	yes	—
155	C₂²×C₅	C₃×#125	1	8	yes	—
156	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
158	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
159	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
160	C₄×C₅	—	2	8	no	—
161	C₄×C₅	—	4	8	no	—
162	C₄×C₅	C₂×C₃×C₄⋊C₄	1	8	yes	—
163	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
164	C₂²×C₄	—	2	8	no	—
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	2	16	no	—
167	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
168	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
169	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
170	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
171	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
172	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
173	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
174	C₄⋊C₄	—	2	16	no	—
175	C₄²	C₂×C₃×C₄×C₅	1	16	yes	complemented
176	C₃×C₅	C₂×#382	1	1	yes	characteristic, direct product factor, Hall
177	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
178	C₂²×C₃	C₅×#117	1	8	yes	—
179	C₂²×C₃	C₅×#124	1	8	yes	—
180	C₂²×C₃	C₅×#125	1	8	yes	—
181	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
183	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
184	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
185	C₃×C₄	—	2	8	no	—
186	C₃×C₄	—	4	8	no	—
187	C₃×C₄	C₂×C₅×C₄⋊C₄	1	8	yes	—
188	C₂×C₅	C₃×#382	1	8	yes	direct product factor
189	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₅	C₂×C₃×#117	1	2	yes	—
191	C₂×C₅	C₂×C₃×#124	1	2	yes	—
192	C₂×C₅	C₂×C₃×#125	1	2	yes	—
193	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
194	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
195	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
196	C₂³	C₃×C₅×#41	1	8	yes	—
197	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
198	C₂×C₄	—	2	16	no	—
199	C₂×C₄	—	2	8	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	2	16	no	—
202	C₂×C₄	—	4	16	no	—
203	C₂×C₄	C₃×C₅×C₄⋊C₄	1	16	yes	—
204	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
205	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
206	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
207	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
208	C₂×C₃	C₅×#382	1	8	yes	direct product factor
209	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₃	C₂×C₅×#117	1	2	yes	—
211	C₂×C₃	C₂×C₅×#124	1	2	yes	—
212	C₂×C₃	C₂×C₅×#125	1	2	yes	—
213	C₅	C₂×C₃×#382	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
215	C₂²	C₃×C₅×#117	1	8	yes	—
216	C₂²	C₃×C₅×#124	1	8	yes	—
217	C₂²	C₃×C₅×#125	1	8	yes	—
218	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
219	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
220	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
221	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
222	C₄	—	2	8	no	—
223	C₄	—	4	8	no	—
224	C₄	C₂×C₃×C₅×C₄⋊C₄	1	8	yes	—
225	C₃	C₂×C₅×#382	1	1	yes	characteristic, direct product factor, Sylow
226	C₂	C₃×C₅×#382	1	8	yes	direct product factor
227	C₂	C₂²×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
228	C₂	C₂×C₃×C₅×#117	1	2	yes	—
229	C₂	C₂×C₃×C₅×#124	1	2	yes	—
230	C₂	C₂×C₃×C₅×#125	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#382	C₂	direct (N × H)
5. C₂×C₅×#382	C₃	direct (N × H)
11. C₂×C₃×C₄²×C₅	C₄	semidirect
14. C₂×C₃×#382	C₅	direct (N × H)
17. C₅×#382	C₂×C₃	direct (N × H)
31. C₃×C₄²×C₅	C₂×C₄	semidirect
34. C₃×#382	C₂×C₅	direct (N × H)
41. C₂×C₄²×C₅	C₃×C₄	semidirect
44. C₂×#382	C₃×C₅	direct (N × H)
65. C₂×C₃×C₄²	C₄×C₅	semidirect
80. C₄²×C₅	C₂×C₃×C₄	semidirect
83. #382	C₂×C₃×C₅	direct (N × H)
108. C₃×C₄²	C₂×C₄×C₅	semidirect
129. C₂×C₄²	C₃×C₄×C₅	semidirect
132. C₂×C₃×C₅	#382	direct (N × H)
175. C₄²	C₂×C₃×C₄×C₅	semidirect
176. C₃×C₅	C₂×#382	direct (N × H)
188. C₂×C₅	C₃×#382	direct (N × H)
208. C₂×C₃	C₅×#382	direct (N × H)
213. C₅	C₂×C₃×#382	direct (N × H)
225. C₃	C₂×C₅×#382	direct (N × H)
226. C₂	C₃×C₅×#382	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×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#382	2
C₂×C₃×C₅×#95	2
C₂×C₅×#382	3
C₂×C₃×#382	5

Subgroups — C2×C3×C5×#382 #14275315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#382 #14275315