Subgroups — C₃×#3992 #91196

Order 480.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	#3992	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
6	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₃×#170	C₄	1	2	yes	complemented
8	C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
9	C₃×#168	C₄	1	1	yes	characteristic, complemented
10	C₃×#97	—	5	1	no	maximal, Hall
11	C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
12	D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
13	C₈×D₅	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×D₅	C₂×C₄	1	1	yes	characteristic
15	C₃×AGL(1,𝔽₅)	—	2	2	no	—
16	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₈	—	5	1	no	—
19	C₂×C₃×C₈	—	5	1	no	—
20	C₃×C₄²	—	5	1	no	—
21	C₂×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
22	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
23	#170	C₃×C₄	1	2	yes	complemented
24	C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
25	#168	C₃×C₄	1	1	yes	characteristic, complemented
26	#97	—	5	1	no	Sylow
27	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
28	C₃×D₅	M₁₆	1	2	yes	—
29	C₂×C₃×C₄	—	5	1	no	—
30	C₂×C₃×C₄	—	5	2	no	—
31	C₃×C₈	—	5	2	no	—
32	C₃×C₈	—	5	1	no	—
33	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
34	C₂×D₅	C₂×C₃×C₄	1	1	yes	characteristic
35	AGL(1,𝔽₅)	—	2	2	no	—
36	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
37	Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂×C₈	—	5	1	no	—
39	C₂×C₈	—	5	1	no	—
40	C₄²	—	5	1	no	—
41	C₃×C₅	#97	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃	—	5	1	no	—
43	C₃×C₄	—	5	1	no	—
44	C₃×C₄	—	10	2	no	—
45	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
46	C₂×C₅	C₃×C₄²	1	1	yes	characteristic
47	D₅	C₃×M₁₆	1	2	yes	—
48	C₂×C₄	—	5	1	no	—
49	C₂×C₄	—	5	2	no	—
50	C₈	—	5	2	no	—
51	C₈	—	5	1	no	—
52	C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
53	C₂×C₃	—	5	2	no	—
54	C₂×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₅	C₃×#97	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	5	1	no	—
57	C₄	—	5	1	no	—
58	C₄	—	10	2	no	—
59	C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
60	C₃	#3992	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	5	2	no	—
62	C₂	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₃×C₄²
Frattini	C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄²
prime radical	C₂×C₃×D₅	C₂×C₄
cosocle	C₄×D₅	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#97
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
4. #3992	C₃	direct (N × H)
7. C₃×#170	C₄	semidirect
8. C₃×C₅×C₈	C₄	semidirect
9. C₃×#168	C₄	semidirect
23. #170	C₃×C₄	semidirect
24. C₅×C₈	C₃×C₄	semidirect
25. #168	C₃×C₄	semidirect
33. C₃×C₈	AGL(1,𝔽₅)	semidirect
41. C₃×C₅	#97	semidirect
52. C₈	C₃×AGL(1,𝔽₅)	semidirect
55. C₅	C₃×#97	semidirect
60. C₃	#3992	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×C₄×AGL(1,𝔽₅)	2
C₃×D₅⋊C₈	2
C₃×C₈×D₅	2
#3992	3
C₃×#97	5

Subgroups — C3×#3992 #91196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3992 #91196