Subgroups — C₂×C₅×C₃⋊C₈ #6693

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊C₈	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₈	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₄	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₄×C₅	D₃	1	1	yes	characteristic
9	C₅×C₈	—	3	2	no	—
10	C₂×C₃×C₅	C₈	1	2	yes	complemented
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂×C₅	1	1	yes	characteristic
13	C₃⋊C₈	C₂×C₅	1	2	yes	direct product factor
14	C₂²×C₅	Dic₃	1	1	yes	characteristic
15	C₄×C₅	Dic₃	1	1	yes	characteristic
16	C₄×C₅	C₂×D₃	1	1	yes	characteristic
17	C₂×C₈	—	3	1	no	Sylow
18	C₃×C₅	C₂×C₈	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	C₄×C₅	1	1	yes	characteristic
20	C₃×C₄	C₄×C₅	1	1	yes	characteristic
21	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
22	C₂×C₅	C₃⋊C₈	1	2	yes	direct product factor
23	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
24	C₂×C₄	C₅×D₃	1	1	yes	characteristic
25	C₈	—	3	2	no	—
26	C₂×C₃	C₅×C₈	1	2	yes	complemented
27	C₂×C₃	C₂×C₄×C₅	1	1	yes	characteristic
28	C₅	C₂×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₅×Dic₃	1	1	yes	characteristic
30	C₄	C₅×Dic₃	1	1	yes	characteristic
31	C₄	C₂×C₅×D₃	1	1	yes	characteristic
32	C₃	C₂×C₅×C₈	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₅×C₃⋊C₈	1	2	yes	direct product factor
34	C₂	C₂×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	D₃
commutator, hypocenter	C₃	C₂×C₅×C₈
Frattini	C₄	C₂×C₅×D₃
Fitting	C₂×C₃×C₄×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₄
cosocle	C₃×C₄	C₂²×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₃⋊C₈	C₂	direct (N × H)
7. C₂×C₃⋊C₈	C₅	direct (N × H)
10. C₂×C₃×C₅	C₈	semidirect
13. C₃⋊C₈	C₂×C₅	direct (N × H)
18. C₃×C₅	C₂×C₈	semidirect
22. C₂×C₅	C₃⋊C₈	direct (N × H)
26. C₂×C₃	C₅×C₈	semidirect
28. C₅	C₂×C₃⋊C₈	direct (N × H)
32. C₃	C₂×C₅×C₈	semidirect
33. C₂	C₅×C₃⋊C₈	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×C₄×C₅	2
C₅×C₃⋊C₈	2
C₂×C₅×C₈	3
C₂×C₃⋊C₈	5

Subgroups — C2×C5×C3⋊C8 #6693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃⋊C₈ #6693