Subgroups — C₃×#3990 #91194

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#674	C₂	1	2	yes	maximal, complemented
3	#3990	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×D₅	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃×#168	C₂²	1	1	yes	characteristic
7	C₃×M₃₂	—	5	1	no	maximal, Hall
8	C₈×D₅	C₂×C₃	1	1	yes	characteristic
9	#674	C₂×C₃	1	2	yes	complemented
10	C₂×C₃×D₅	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×Dic₅	C₈	1	1	yes	characteristic
13	C₂×C₃×C₈	—	5	1	no	—
14	C₃×C₁₆	—	5	2	no	—
15	C₄×D₅	C₃×C₄	1	1	yes	characteristic
16	C₅×C₈	C₃×C₄	1	1	yes	characteristic
17	#168	C₂²×C₃	1	1	yes	characteristic
18	M₃₂	—	5	1	no	Sylow
19	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
20	C₃×D₅	—	2	1	no	—
21	C₂×C₃×C₄	—	5	1	no	—
22	C₃×C₈	—	5	1	no	—
23	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₂×D₅	C₃×C₈	1	1	yes	characteristic
25	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
26	Dic₅	C₃×C₈	1	1	yes	characteristic
27	C₂×C₈	—	5	1	no	—
28	C₁₆	—	5	2	no	—
29	C₃×C₅	M₃₂	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	—	5	1	no	—
31	C₃×C₄	—	5	1	no	—
32	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₂×C₅	C₂×C₃×C₈	1	1	yes	characteristic
34	D₅	—	2	1	no	—
35	C₂×C₄	—	5	1	no	—
36	C₈	—	5	1	no	—
37	C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₂×C₃	—	10	1	no	—
39	C₂×C₃	D₅⋊C₈	1	1	yes	characteristic
40	C₅	C₃×M₃₂	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	5	1	no	—
42	C₄	—	5	1	no	—
43	C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₃	#3990	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	10	1	no	—
46	C₂	C₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₃×C₈
Frattini	C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×C₃×D₅	C₈
cosocle	#168	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×M₃₂
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
2. C₃×#674	C₂	semidirect
3. #3990	C₃	direct (N × H)
9. #674	C₂×C₃	semidirect
29. C₃×C₅	M₃₂	semidirect
40. C₅	C₃×M₃₂	semidirect
44. C₃	#3990	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×C₈×D₅	2
C₃×#674	2
#3990	3
C₃×M₃₂	5

Subgroups — C3×#3990 #91194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3990 #91194