Subgroups — C₃×C₅×M₃₂ #91137

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₆	C₂	1	2	yes	maximal, complemented
3	C₅×M₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃×M₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
9	C₅×C₁₆	C₂×C₃	1	2	yes	complemented
10	C₂²×C₃×C₅	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₈	1	1	yes	characteristic
12	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic
14	C₃×C₁₆	C₂×C₅	1	2	yes	complemented
15	C₂×C₄×C₅	C₃×C₄	1	1	yes	characteristic
16	C₅×C₈	C₃×C₄	1	1	yes	characteristic
17	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
18	M₃₂	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃×C₅	—	2	1	no	—
20	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃×C₄	C₄×C₅	1	1	yes	characteristic
22	C₃×C₈	C₄×C₅	1	1	yes	characteristic
23	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
24	C₂²×C₅	C₃×C₈	1	1	yes	characteristic
25	C₄×C₅	C₃×C₈	1	1	yes	characteristic
26	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂×C₈	C₂×C₃×C₅	1	1	yes	characteristic
28	C₁₆	C₂×C₃×C₅	1	2	yes	complemented
29	C₃×C₅	M₃₂	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₃	C₅×C₈	1	1	yes	characteristic
31	C₃×C₄	C₅×C₈	1	1	yes	characteristic
32	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	C₂×C₃×C₈	1	1	yes	characteristic
35	C₂×C₄	C₃×C₄×C₅	1	1	yes	characteristic
36	C₈	C₃×C₄×C₅	1	1	yes	characteristic
37	C₈	C₂²×C₃×C₅	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₂×C₅×C₈	1	1	yes	characteristic
40	C₅	C₃×M₃₂	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₃×C₅×C₈	1	1	yes	characteristic
42	C₄	C₃×C₅×C₈	1	1	yes	characteristic
43	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
44	C₃	C₅×M₃₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₃×C₅×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₅×C₈	C₂²
commutator	C₂	C₂×C₃×C₅×C₈
Frattini, cosocle	C₈	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂²×C₃×C₅	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₁₆	C₂	semidirect
3. C₅×M₃₂	C₃	direct (N × H)
7. C₃×M₃₂	C₅	direct (N × H)
9. C₅×C₁₆	C₂×C₃	semidirect
14. C₃×C₁₆	C₂×C₅	semidirect
18. M₃₂	C₃×C₅	direct (N × H)
28. C₁₆	C₂×C₃×C₅	semidirect
29. C₃×C₅	M₃₂	direct (N × H)
40. C₅	C₃×M₃₂	direct (N × H)
44. C₃	C₅×M₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₈	2
C₃×C₅×C₁₆	2
C₅×M₃₂	3
C₃×M₃₂	5

Subgroups — C3×C5×M32 #91137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×M₃₂ #91137