Subgroups — C₃×C₅×SD₃₂ #91139

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×SD₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	—	2	1	no	—
6	C₃×C₅×D₄	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₃×SD₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×D₈	C₂×C₃	1	1	yes	characteristic
11	C₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₃×C₅	—	4	1	no	—
13	C₃×C₄×C₅	—	4	1	no	—
14	C₃×C₄×C₅	D₄	1	1	yes	characteristic
15	C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
16	C₃×D₈	C₂×C₅	1	1	yes	characteristic
17	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅×Q₈	—	2	1	no	—
19	C₅×D₄	—	2	1	no	—
20	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
21	SD₃₂	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃×C₅	—	8	1	no	—
23	C₂×C₃×C₅	D₈	1	1	yes	characteristic
24	C₃×Q₈	—	2	1	no	—
25	C₃×D₄	—	2	1	no	—
26	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
27	C₂²×C₅	—	4	1	no	—
28	C₄×C₅	—	4	1	no	—
29	C₄×C₅	C₃×D₄	1	1	yes	characteristic
30	Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
31	D₈	C₂×C₃×C₅	1	1	yes	characteristic
32	C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
33	C₃×C₅	SD₃₂	1	1	yes	characteristic, direct product factor, Hall
34	C₂²×C₃	—	4	1	no	—
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	C₅×D₄	1	1	yes	characteristic
37	C₂×C₅	—	8	1	no	—
38	C₂×C₅	C₃×D₈	1	1	yes	characteristic
39	Q₈	—	2	1	no	—
40	D₄	—	2	1	no	—
41	C₈	C₂²×C₃×C₅	1	1	yes	characteristic
42	C₂×C₃	—	8	1	no	—
43	C₂×C₃	C₅×D₈	1	1	yes	characteristic
44	C₅	C₃×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	—	4	1	no	—
46	C₄	—	4	1	no	—
47	C₄	C₃×C₅×D₄	1	1	yes	characteristic
48	C₃	C₅×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	8	1	no	—
50	C₂	C₃×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₃×C₅
prime radical	C₃×C₅×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₄×C₅ ◁ C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×C₅×C₁₆	C₂	semidirect
4. C₅×SD₃₂	C₃	direct (N × H)
8. C₃×SD₃₂	C₅	direct (N × H)
9. C₅×Q₁₆	C₂×C₃	semidirect
11. C₅×C₁₆	C₂×C₃	semidirect
15. C₃×Q₁₆	C₂×C₅	semidirect
17. C₃×C₁₆	C₂×C₅	semidirect
21. SD₃₂	C₃×C₅	direct (N × H)
30. Q₁₆	C₂×C₃×C₅	semidirect
32. C₁₆	C₂×C₃×C₅	semidirect
33. C₃×C₅	SD₃₂	direct (N × H)
44. C₅	C₃×SD₃₂	direct (N × H)
48. C₃	C₅×SD₃₂	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×Q₁₆	2
C₃×C₅×D₈	2
C₃×C₅×C₁₆	2
C₅×SD₃₂	3
C₃×SD₃₂	5

Subgroups — C3×C5×SD32 #91139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×SD₃₂ #91139