Subgroups — C₃×C₅×#2183 #14275217

Order 1920.

252 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₄⋊C₁₆	C₂	1	2	yes	maximal
3	C₃×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#346	C₂	1	2	yes	maximal
5	C₃×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₅×#2183	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×C₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₄⋊C₈	C₄	1	2	yes	—
12	C₃×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
15	C₃×#2183	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
17	C₅×C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic
18	C₅×C₄⋊C₁₆	C₂×C₃	1	2	yes	—
19	C₅×#346	C₂×C₃	1	2	yes	—
20	C₄×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₈	C₈	1	1	yes	characteristic
22	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	C₈	1	2	yes	—
26	C₃×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
27	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
29	C₃×C₅×C₁₆	—	2	1	no	—
30	C₃×C₅×C₁₆	—	2	2	no	—
31	C₃×C₅×C₁₆	Q₈	1	2	yes	complemented
32	C₃×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
33	C₃×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic
34	C₃×C₄⋊C₁₆	C₂×C₅	1	2	yes	—
35	C₃×#346	C₂×C₅	1	2	yes	—
36	C₃×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
37	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic
38	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₅×C₁₆	C₂²×C₃	1	2	yes	—
40	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
41	C₅×C₄⋊C₈	C₃×C₄	1	2	yes	—
42	C₅×C₄⋊C₈	C₃×C₄	1	1	yes	characteristic
43	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
44	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
45	#2183	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
48	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
49	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
50	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
52	C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₈	—	2	2	no	—
54	C₃×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
55	C₃×C₅×C₈	#41	1	1	yes	characteristic
56	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
57	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
58	C₂×C₃×C₁₆	C₂²×C₅	1	2	yes	—
59	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
60	C₃×C₄⋊C₈	C₄×C₅	1	2	yes	—
61	C₃×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
62	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
63	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
64	C₂×C₅×Q₈	C₃×C₈	1	1	yes	characteristic
65	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
66	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
67	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
68	C₅×C₄⋊C₄	C₃×C₈	1	2	yes	—
69	C₅×C₄⋊C₄	C₃×C₈	1	1	yes	characteristic
70	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
71	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
72	C₅×C₁₆	—	2	1	no	—
73	C₅×C₁₆	—	2	2	no	—
74	C₅×C₁₆	C₃×Q₈	1	2	yes	complemented
75	C₈×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
76	C₄⋊C₁₆	C₂×C₃×C₅	1	1	yes	characteristic
77	C₄⋊C₁₆	C₂×C₃×C₅	1	2	yes	—
78	#346	C₂×C₃×C₅	1	2	yes	—
79	C₄×C₁₆	C₂×C₃×C₅	1	1	yes	characteristic
80	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
81	C₃×C₄×C₅	—	2	2	no	—
82	C₃×C₄×C₅	—	2	2	no	—
83	C₃×C₄×C₅	—	2	1	no	—
84	C₃×C₄×C₅	M₃₂	1	2	yes	—
85	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
86	C₃×C₄×C₅	#131	1	1	yes	characteristic
87	C₂×C₃×Q₈	C₅×C₈	1	1	yes	characteristic
88	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
89	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
90	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
91	C₃×C₄⋊C₄	C₅×C₈	1	2	yes	—
92	C₃×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
93	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
94	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
95	C₃×C₁₆	—	2	1	no	—
96	C₃×C₁₆	—	2	2	no	—
97	C₃×C₁₆	C₅×Q₈	1	2	yes	complemented
98	C₅×Q₈	—	2	2	no	—
99	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
100	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
102	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
103	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
104	C₅×C₈	—	2	1	no	—
105	C₅×C₈	—	2	2	no	—
106	C₅×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
107	C₅×C₈	C₃×#41	1	1	yes	characteristic
108	C₄×Q₈	C₃×C₄×C₅	1	1	yes	characteristic
109	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
110	C₂×C₁₆	C₂²×C₃×C₅	1	2	yes	—
111	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
112	C₄⋊C₈	C₃×C₄×C₅	1	2	yes	—
113	C₄⋊C₈	C₃×C₄×C₅	1	1	yes	characteristic
114	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
115	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
116	C₂×C₃×C₅	C₈×Q₈	1	1	yes	characteristic
117	C₂×C₃×C₅	C₂×M₃₂	1	1	yes	characteristic
118	C₂×C₃×C₅	#504	1	1	yes	characteristic
119	C₃×Q₈	—	2	2	no	—
120	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
121	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
122	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
123	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
124	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
125	C₃×C₈	—	2	1	no	—
126	C₃×C₈	—	2	2	no	—
127	C₃×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
128	C₃×C₈	C₅×#41	1	1	yes	characteristic
129	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
130	C₄×C₅	—	2	2	no	—
131	C₄×C₅	—	2	2	no	—
132	C₄×C₅	—	2	1	no	—
133	C₄×C₅	C₃×M₃₂	1	2	yes	—
134	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
135	C₄×C₅	C₃×#131	1	1	yes	characteristic
136	C₂×Q₈	C₃×C₅×C₈	1	1	yes	characteristic
137	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
138	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
139	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
140	C₄⋊C₄	C₃×C₅×C₈	1	2	yes	—
141	C₄⋊C₄	C₃×C₅×C₈	1	1	yes	characteristic
142	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
143	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
144	C₁₆	—	2	1	no	—
145	C₁₆	—	2	2	no	—
146	C₁₆	C₃×C₅×Q₈	1	2	yes	complemented
147	C₃×C₅	#2183	1	1	yes	characteristic, direct product factor, Hall
148	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
149	C₃×C₄	—	2	2	no	—
150	C₃×C₄	—	2	2	no	—
151	C₃×C₄	—	2	1	no	—
152	C₃×C₄	C₅×M₃₂	1	2	yes	—
153	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
154	C₃×C₄	C₅×#131	1	1	yes	characteristic
155	C₂×C₅	C₃×C₈×Q₈	1	1	yes	characteristic
156	C₂×C₅	C₂×C₃×M₃₂	1	1	yes	characteristic
157	C₂×C₅	C₃×#504	1	1	yes	characteristic
158	Q₈	—	2	2	no	—
159	C₂×C₄	C₂×C₃×C₅×C₈	1	2	yes	—
160	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
161	C₂×C₄	C₂×C₃×C₅×C₈	1	2	yes	—
162	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
163	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
164	C₈	—	2	1	no	—
165	C₈	—	2	2	no	—
166	C₈	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
167	C₈	C₃×C₅×#41	1	1	yes	characteristic
168	C₂×C₃	C₅×C₈×Q₈	1	1	yes	characteristic
169	C₂×C₃	C₂×C₅×M₃₂	1	1	yes	characteristic
170	C₂×C₃	C₅×#504	1	1	yes	characteristic
171	C₅	C₃×#2183	1	1	yes	characteristic, direct product factor, Sylow
172	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
173	C₄	—	2	2	no	—
174	C₄	—	2	2	no	—
175	C₄	—	2	1	no	—
176	C₄	C₃×C₅×M₃₂	1	2	yes	—
177	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
178	C₄	C₃×C₅×#131	1	1	yes	characteristic
179	C₃	C₅×#2183	1	1	yes	characteristic, direct product factor, Sylow
180	C₂	C₃×C₅×C₈×Q₈	1	1	yes	characteristic
181	C₂	C₂×C₃×C₅×M₃₂	1	1	yes	characteristic
182	C₂	C₃×C₅×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₅×C₈	C₂³
commutator	C₂²	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2183	C₃	direct (N × H)
15. C₃×#2183	C₅	direct (N × H)
31. C₃×C₅×C₁₆	Q₈	semidirect
45. #2183	C₃×C₅	direct (N × H)
74. C₅×C₁₆	C₃×Q₈	semidirect
97. C₃×C₁₆	C₅×Q₈	semidirect
146. C₁₆	C₃×C₅×Q₈	semidirect
147. C₃×C₅	#2183	direct (N × H)
171. C₅	C₃×#2183	direct (N × H)
179. C₃	C₅×#2183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₈×Q₈	2
C₃×C₅×C₄⋊C₁₆	2
C₃×C₅×#346	2
C₃×C₄×C₅×C₁₆	2
C₅×#2183	3
C₃×#2183	5

Subgroups — C3×C5×#2183 #14275217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2183 #14275217