Subgroups — C₃×#3996 #91200

Order 480.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#700	C₂	1	2	yes	maximal
2	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#3996	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
5	C₃×#170	—	2	2	no	—
6	C₃×C₅×C₈	C₄	1	1	yes	characteristic
7	C₃×#168	C₄	1	1	yes	characteristic
8	C₃×#108	—	5	1	no	maximal, Hall
9	#700	C₂×C₃	1	2	yes	—
10	C₈×D₅	C₂×C₃	1	1	yes	characteristic
11	C₂×C₃×D₅	Q₈	1	1	yes	characteristic
12	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₃×Dic₅	D₄	1	1	yes	characteristic
14	C₃×M₁₆	—	5	2	no	—
15	C₂×C₃×C₈	—	5	1	no	—
16	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
17	#170	—	2	2	no	—
18	C₅×C₈	C₃×C₄	1	1	yes	characteristic
19	#168	C₃×C₄	1	1	yes	characteristic
20	#108	—	5	1	no	Sylow
21	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
22	C₃×D₅	—	2	1	no	—
23	C₂×C₃×C₄	—	5	1	no	—
24	C₃×C₈	—	5	1	no	—
25	C₃×C₈	—	10	2	no	—
26	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₂×D₅	C₃×Q₈	1	1	yes	characteristic
28	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
29	Dic₅	C₃×D₄	1	1	yes	characteristic
30	M₁₆	—	5	2	no	—
31	C₂×C₈	—	5	1	no	—
32	C₃×C₅	#108	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃	—	5	1	no	—
34	C₃×C₄	—	5	1	no	—
35	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
37	D₅	—	2	1	no	—
38	C₂×C₄	—	5	1	no	—
39	C₈	—	5	1	no	—
40	C₈	—	10	2	no	—
41	C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₂×C₃	—	10	1	no	—
43	C₂×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₅	C₃×#108	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	5	1	no	—
46	C₄	—	5	1	no	—
47	C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₃	#3996	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	10	1	no	—
50	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	Q₈
cosocle	C₄×D₅	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#108
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. #3996	C₃	direct (N × H)
32. C₃×C₅	#108	semidirect
44. C₅	C₃×#108	semidirect
48. C₃	#3996	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×#700	2
C₃×C₈×D₅	2
#3996	3
C₃×#108	5

Subgroups — C3×#3996 #91200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3996 #91200