Subgroups — #91165

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#168	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#674	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#674	C₂	1	1	yes	maximal, characteristic, complemented
4	#3998	—	3	1	no	maximal, Hall
5	C₄×C₅×D₃	C₄	1	1	yes	characteristic
6	C₃⋊#168	C₄	1	1	yes	characteristic
7	C₃×#168	C₂²	1	1	yes	characteristic
8	#798	—	5	1	no	maximal, Hall
9	C₂×#168	—	3	1	no	—
10	#674	—	3	1	no	—
11	#674	D₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₃	C₈	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₅×Dic₃	C₈	1	1	yes	characteristic
15	D₃×C₈	—	5	1	no	—
16	C₃×C₁₆	—	5	1	no	—
17	C₃⋊C₁₆	—	5	1	no	—
18	C₂×C₄×C₅	—	3	1	no	—
19	#168	—	3	1	no	—
20	#168	C₂×D₃	1	1	yes	characteristic
21	M₃₂	—	15	1	no	Sylow
22	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
23	C₅×D₃	—	2	1	no	—
24	C₄×D₃	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₃×C₈	—	5	1	no	—
26	C₃⋊C₈	—	5	1	no	—
27	C₂²×C₅	—	3	1	no	—
28	C₄×C₅	—	3	1	no	—
29	C₄×C₅	C₄×D₃	1	1	yes	characteristic
30	C₂×C₈	—	15	1	no	—
31	C₁₆	—	5	1	no	—
32	C₁₆	—	15	1	no	—
33	C₃×C₅	M₃₂	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃	#170	1	1	yes	characteristic
35	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	Dic₃	#170	1	1	yes	characteristic
37	C₂×C₅	—	6	1	no	—
38	C₂×C₅	D₃×C₈	1	1	yes	characteristic
39	C₂×C₄	—	3	1	no	—
40	C₈	—	5	1	no	—
41	C₈	—	15	1	no	—
42	C₂×C₃	C₂×#170	1	1	yes	characteristic
43	D₃	—	2	1	no	—
44	C₅	#798	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	3	1	no	—
46	C₄	—	3	1	no	—
47	C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₃	#3998	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	6	1	no	—
50	C₂	D₃×#170	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂×C₈
Fitting	C₃×C₄×C₅	C₂×C₄
prime radical	C₂×C₅×D₃	C₈
cosocle	C₃×#168	C₂²
hypocenter	C₃×C₅	M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊#674	C₂	semidirect
3. C₃×#674	C₂	semidirect
11. #674	D₃	semidirect
33. C₃×C₅	M₃₂	semidirect
44. C₅	#798	semidirect
48. C₃	#3998	semidirect

Maximal subgroups

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

subgroup	index
D₃×#168	2
C₃⋊#674	2
C₃×#674	2
#3998	3
#798	5