Subgroups — C₃×#3954 #91024

Order 480.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#681	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	#3954	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×C₈	—	2	1	no	—
7	C₃×#168	—	2	1	no	—
8	C₃×#168	C₄	1	2	yes	—
9	C₃×#108	—	5	1	no	maximal, Hall
10	C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
11	#681	C₂×C₃	1	1	yes	characteristic
12	C₂×#168	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
14	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₃×M₁₆	—	5	1	no	—
17	C₃×M₁₆	D₅	1	1	yes	characteristic
18	C₂×C₃×C₈	—	5	1	no	—
19	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
20	C₅×C₈	—	2	1	no	—
21	#168	—	2	1	no	—
22	#168	C₃×C₄	1	2	yes	—
23	#108	—	5	1	no	Sylow
24	C₂×C₃×C₅	—	2	1	no	—
25	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
27	C₃×C₈	—	2	1	no	—
28	C₃×C₈	—	5	2	no	—
29	C₃×C₈	—	10	1	no	—
30	C₂²×C₅	C₃×Q₈	1	1	yes	characteristic
31	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
32	C₄×C₅	C₃×D₄	1	1	yes	characteristic
33	M₁₆	—	5	1	no	—
34	M₁₆	C₃×D₅	1	1	yes	characteristic
35	C₂×C₈	—	5	1	no	—
36	C₃×C₅	#108	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃	Dic₁₀	1	1	yes	characteristic
38	C₃×C₄	C₄×D₅	1	1	yes	characteristic
39	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
40	C₂×C₅	—	2	1	no	—
41	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	5	2	no	—
45	C₈	—	10	1	no	—
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	#683	1	1	yes	characteristic
48	C₅	C₃×#108	1	1	yes	characteristic, complemented, Sylow
49	C₂²	C₃×Dic₁₀	1	1	yes	characteristic
50	C₄	C₃×C₄×D₅	1	1	yes	characteristic
51	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
52	C₃	#3954	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	2	1	no	—
54	C₂	C₃×#683	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₃×C₅×M₁₆	C₂
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂²×C₃×C₅	Q₈
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₃×M₁₆	D₅
hypocenter	C₅	C₃×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. #3954	C₃	direct (N × H)
36. C₃×C₅	#108	semidirect
48. C₅	C₃×#108	semidirect
52. C₃	#3954	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×C₅×M₁₆	2
C₃×#681	2
C₂×C₃×#168	2
#3954	3
C₃×#108	5

Subgroups — C3×#3954 #91024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3954 #91024