Subgroups — C₃×C₅×2₋¹⁺⁴ #92109

Order 480.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	10	yes	maximal, complemented
2	C₂×C₃×C₅×Q₈	C₂	1	5	yes	maximal, complemented
3	C₅×2₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×Q₈	C₂²	1	10	yes	—
5	C₃×C₅×D₄	C₂²	1	10	yes	—
6	C₂×C₃×C₄×C₅	C₂²	1	15	yes	—
7	C₃×2₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#41	C₂×C₃	1	10	yes	complemented
9	C₂×C₅×Q₈	C₂×C₃	1	5	yes	complemented
10	C₂²×C₃×C₅	C₂³	1	5	yes	—
11	C₃×C₄×C₅	C₂³	1	10	yes	—
12	C₃×#41	C₂×C₅	1	10	yes	complemented
13	C₂×C₃×Q₈	C₂×C₅	1	5	yes	complemented
14	C₅×Q₈	C₂²×C₃	1	10	yes	—
15	C₅×D₄	C₂²×C₃	1	10	yes	—
16	C₂×C₄×C₅	C₂²×C₃	1	15	yes	—
17	2₋¹⁺⁴	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₅	—	2	5	no	—
19	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
20	C₃×Q₈	C₂²×C₅	1	10	yes	—
21	C₃×D₄	C₂²×C₅	1	10	yes	—
22	C₂×C₃×C₄	C₂²×C₅	1	15	yes	—
23	C₂²×C₅	C₂³×C₃	1	5	yes	—
24	C₄×C₅	C₂³×C₃	1	10	yes	—
25	#41	C₂×C₃×C₅	1	10	yes	complemented
26	C₂×Q₈	C₂×C₃×C₅	1	5	yes	complemented
27	C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₃	C₂³×C₅	1	5	yes	—
29	C₃×C₄	C₂³×C₅	1	10	yes	—
30	C₂×C₅	—	2	5	no	—
31	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
32	Q₈	C₂²×C₃×C₅	1	10	yes	—
33	D₄	C₂²×C₃×C₅	1	10	yes	—
34	C₂×C₄	C₂²×C₃×C₅	1	15	yes	—
35	C₂×C₃	—	2	5	no	—
36	C₂×C₃	C₂⁴×C₅	1	1	yes	characteristic
37	C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	C₂³×C₃×C₅	1	5	yes	—
39	C₄	C₂³×C₃×C₅	1	10	yes	—
40	C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
41	C₂	—	2	5	no	—
42	C₂	C₂⁴×C₃×C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁴×C₃×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#41	C₂	semidirect
2. C₂×C₃×C₅×Q₈	C₂	semidirect
3. C₅×2₋¹⁺⁴	C₃	direct (N × H)
7. C₃×2₋¹⁺⁴	C₅	direct (N × H)
8. C₅×#41	C₂×C₃	semidirect
9. C₂×C₅×Q₈	C₂×C₃	semidirect
12. C₃×#41	C₂×C₅	semidirect
13. C₂×C₃×Q₈	C₂×C₅	semidirect
17. 2₋¹⁺⁴	C₃×C₅	direct (N × H)
25. #41	C₂×C₃×C₅	semidirect
26. C₂×Q₈	C₂×C₃×C₅	semidirect
27. C₃×C₅	2₋¹⁺⁴	direct (N × H)
37. C₅	C₃×2₋¹⁺⁴	direct (N × H)
40. C₃	C₅×2₋¹⁺⁴	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×#41	2
C₂×C₃×C₅×Q₈	2
C₅×2₋¹⁺⁴	3
C₃×2₋¹⁺⁴	5

Subgroups — C3×C5×2−1+4 #92109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×2₋¹⁺⁴ #92109