Subgroups — C₃×#3994 #91198

Order 480.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#3994	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
5	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
7	C₃×#168	C₄	1	1	yes	characteristic, complemented
8	C₃×#107	—	5	1	no	maximal, Hall
9	C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
10	C₈×D₅	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃×D₅	D₄	1	1	yes	characteristic
12	C₃×AGL(1,𝔽₅)	—	4	2	no	—
13	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃×Dic₅	Q₈	1	1	yes	characteristic
15	C₂×C₃×C₈	—	5	1	no	—
16	C₃×C₄⋊C₄	—	5	2	no	—
17	C₂×AGL(1,𝔽₅)	—	2	2	no	—
18	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
19	C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
20	#168	C₃×C₄	1	1	yes	characteristic, complemented
21	#107	—	5	1	no	Sylow
22	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
23	C₃×D₅	D₈	1	1	yes	characteristic
24	C₃×D₅	Q₁₆	1	1	yes	characteristic
25	C₂×C₃×C₄	—	5	1	no	—
26	C₂×C₃×C₄	—	10	2	no	—
27	C₃×C₈	—	5	1	no	—
28	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
29	C₂×D₅	C₃×D₄	1	1	yes	characteristic
30	AGL(1,𝔽₅)	—	4	2	no	—
31	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
32	Dic₅	C₃×Q₈	1	1	yes	characteristic
33	C₂×C₈	—	5	1	no	—
34	C₄⋊C₄	—	5	2	no	—
35	C₃×C₅	#107	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	—	5	1	no	—
37	C₃×C₄	—	5	1	no	—
38	C₃×C₄	—	20	2	no	—
39	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
41	D₅	C₃×D₈	1	1	yes	characteristic
42	D₅	C₃×Q₁₆	1	1	yes	characteristic
43	C₂×C₄	—	5	1	no	—
44	C₂×C₄	—	10	2	no	—
45	C₈	—	5	1	no	—
46	C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
47	C₂×C₃	—	5	1	no	—
48	C₂×C₃	—	5	1	no	—
49	C₂×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
50	C₅	C₃×#107	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	5	1	no	—
52	C₄	—	5	1	no	—
53	C₄	—	20	2	no	—
54	C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₃	#3994	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	5	1	no	—
57	C₂	—	5	1	no	—
58	C₂	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂×C₃×D₅	D₄
cosocle	C₄×D₅	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#107
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
3. #3994	C₃	direct (N × H)
6. C₃×C₅×C₈	C₄	semidirect
7. C₃×#168	C₄	semidirect
19. C₅×C₈	C₃×C₄	semidirect
20. #168	C₃×C₄	semidirect
28. C₃×C₈	AGL(1,𝔽₅)	semidirect
35. C₃×C₅	#107	semidirect
46. C₈	C₃×AGL(1,𝔽₅)	semidirect
50. C₅	C₃×#107	semidirect
55. C₃	#3994	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×C₈×D₅	2
#3994	3
C₃×#107	5

Subgroups — C3×#3994 #91198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3994 #91198