Subgroups — C₃×C₅×#108 #91135

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	2	yes	maximal
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#108	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₅×C₈	—	2	2	no	—
6	C₃×C₅×C₈	C₄	1	2	yes	—
7	C₃×#108	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×M₁₆	C₂×C₃	1	2	yes	—
9	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
10	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	D₄	1	1	yes	characteristic
13	C₃×M₁₆	C₂×C₅	1	2	yes	—
14	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
16	C₅×C₈	—	2	2	no	—
17	C₅×C₈	C₃×C₄	1	2	yes	—
18	#108	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃×C₅	—	2	1	no	—
20	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
22	C₃×C₈	—	2	2	no	—
23	C₃×C₈	C₄×C₅	1	2	yes	—
24	C₂²×C₅	C₃×Q₈	1	1	yes	characteristic
25	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
26	C₄×C₅	C₃×D₄	1	1	yes	characteristic
27	M₁₆	C₂×C₃×C₅	1	2	yes	—
28	C₂×C₈	C₂×C₃×C₅	1	1	yes	characteristic
29	C₃×C₅	#108	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₃	C₅×Q₈	1	1	yes	characteristic
31	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
32	C₃×C₄	C₅×D₄	1	1	yes	characteristic
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
36	C₈	—	2	2	no	—
37	C₈	C₃×C₄×C₅	1	2	yes	—
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
40	C₅	C₃×#108	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₃×C₅×Q₈	1	1	yes	characteristic
42	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
43	C₄	C₃×C₅×D₄	1	1	yes	characteristic
44	C₃	C₅×#108	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	D₄
commutator	C₄	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂²×C₃×C₅	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#108	C₃	direct (N × H)
7. C₃×#108	C₅	direct (N × H)
18. #108	C₃×C₅	direct (N × H)
29. C₃×C₅	#108	direct (N × H)
40. C₅	C₃×#108	direct (N × H)
44. C₃	C₅×#108	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
C₂×C₃×C₅×C₈	2
C₅×#108	3
C₃×#108	5

Subgroups — C3×C5×#108 #91135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#108 #91135