Subgroups — C₃×#4093 #91664

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₃×#685	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#4093	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×D₅	C₂²	1	2	yes	—
7	C₃×C₅×Q₈	—	2	2	no	—
8	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₅	C₂²	1	2	yes	—
11	C₃×D₂₀	—	2	2	no	—
12	C₃×#124	—	5	1	no	maximal, Hall
13	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×D₂₀	C₂×C₃	1	1	yes	characteristic
15	#685	C₂×C₃	1	4	yes	complemented
16	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₃×D₅	—	2	2	no	—
19	C₂×C₃×D₅	—	2	4	no	—
20	C₃×C₄×C₅	—	2	2	no	—
21	C₃×C₄×C₅	D₄	1	2	yes	—
22	C₃×Dic₅	—	2	2	no	—
23	C₂×C₃×Q₈	D₅	1	1	yes	characteristic, complemented
24	C₂×C₃×D₄	—	5	1	no	—
25	C₃×C₂²⋊C₄	—	5	4	no	—
26	C₃×C₄²	—	5	1	no	—
27	C₂²×D₅	C₂²×C₃	1	2	yes	—
28	C₅×Q₈	—	2	2	no	—
29	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂×Dic₅	C₂²×C₃	1	2	yes	—
32	D₂₀	—	2	2	no	—
33	#124	—	5	1	no	Sylow
34	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×C₅	#41	1	2	yes	—
36	C₃×D₅	—	4	2	no	—
37	C₂³×C₃	—	5	2	no	—
38	C₃×Q₈	—	2	2	no	—
39	C₃×D₄	—	10	2	no	—
40	C₂×C₃×C₄	—	5	2	no	—
41	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
42	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
43	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
44	C₂×D₅	—	2	2	no	—
45	C₂×D₅	—	2	4	no	—
46	C₄×C₅	—	2	2	no	—
47	C₄×C₅	C₃×D₄	1	2	yes	—
48	Dic₅	—	2	2	no	—
49	C₂×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
50	C₂×D₄	—	5	1	no	—
51	C₂²⋊C₄	—	5	4	no	—
52	C₄²	—	5	1	no	—
53	C₃×C₅	#124	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	—	10	4	no	—
55	C₂²×C₃	—	10	2	no	—
56	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	—	10	2	no	—
59	C₃×C₄	C₂²⋊D₅	1	2	yes	—
60	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
61	C₂×C₅	C₃×#41	1	2	yes	—
62	D₅	—	4	2	no	—
63	C₂³	—	5	2	no	—
64	Q₈	—	2	2	no	—
65	D₄	—	10	2	no	—
66	C₂×C₄	—	5	2	no	—
67	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
68	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
69	C₂×C₃	—	20	2	no	—
70	C₂×C₃	#713	1	2	yes	—
71	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
72	C₅	C₃×#124	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	10	4	no	—
74	C₂²	—	10	2	no	—
75	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	10	2	no	—
78	C₄	C₃×C₂²⋊D₅	1	2	yes	—
79	C₃	#4093	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	20	2	no	—
81	C₂	C₃×#713	1	2	yes	—
82	C₂	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂×C₃×D₂₀	C₂
hypercenter	C₂×C₃×Q₈	D₅
hypocenter	C₅	C₃×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×Q₈	C₂	semidirect
3. C₃×#685	C₂	semidirect
4. C₃×C₄×Dic₅	C₂	semidirect
5. #4093	C₃	direct (N × H)
13. C₂×C₅×Q₈	C₂×C₃	semidirect
15. #685	C₂×C₃	semidirect
16. C₄×Dic₅	C₂×C₃	semidirect
23. C₂×C₃×Q₈	D₅	semidirect
49. C₂×Q₈	C₃×D₅	semidirect
53. C₃×C₅	#124	semidirect
72. C₅	C₃×#124	semidirect
79. C₃	#4093	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×C₃×C₅×Q₈	2
C₂×C₃×D₂₀	2
C₃×#685	2
C₃×C₄×Dic₅	2
#4093	3
C₃×#124	5

Subgroups — C3×#4093 #91664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4093 #91664