Subgroups — C₃×C₅×#168 #10597067

Order 600.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₅×#168	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃×C₅×C₈	—	5	1	no	maximal
5	C₃×#168	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₄×C₅²	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅	—	2	2	no	—
9	C₃×C₄×C₅	D₅	1	1	yes	characteristic
10	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
11	C₂×C₅²	C₃×C₄	1	1	yes	characteristic
12	C₅×C₈	—	5	1	no	—
13	#168	C₃×C₅	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₅	—	2	2	no	—
15	C₂×C₃×C₅	Dic₅	1	1	yes	characteristic
16	C₂×C₃×C₅	C₄×C₅	1	1	yes	characteristic
17	C₅²	C₃×C₈	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₈	—	5	1	no	Hall
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	C₃×D₅	1	1	yes	characteristic
21	C₄×C₅	C₂×C₃×C₅	1	1	yes	characteristic
22	C₃×C₅	—	2	2	no	—
23	C₃×C₅	#168	1	1	yes	characteristic, direct product factor
24	C₃×C₅	C₅×C₈	1	1	yes	characteristic, complemented
25	C₃×C₄	C₅×D₅	1	1	yes	characteristic
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	C₃×Dic₅	1	1	yes	characteristic
28	C₂×C₅	C₃×C₄×C₅	1	1	yes	characteristic
29	C₈	—	5	1	no	Sylow
30	C₂×C₃	C₅×Dic₅	1	1	yes	characteristic
31	C₅	—	2	2	no	—
32	C₅	C₃×#168	1	1	yes	characteristic, direct product factor
33	C₅	C₃×C₅×C₈	1	1	yes	characteristic, complemented
34	C₄	C₃×C₅×D₅	1	1	yes	characteristic
35	C₃	C₅×#168	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	C₃×C₅×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₅	D₅
commutator, hypocenter	C₅	C₃×C₅×C₈
Frattini	C₄	C₃×C₅×D₅
Fitting	C₃×C₄×C₅²	C₂
socle, prime radical	C₂×C₃×C₅²	C₄
cosocle	C₄×C₅	C₂×C₃×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#168	C₃	direct (N × H)
5. C₃×#168	C₅	direct (N × H)
7. C₃×C₅²	C₈	semidirect
13. #168	C₃×C₅	direct (N × H)
17. C₅²	C₃×C₈	semidirect
23. C₃×C₅	#168	direct (N × H)
24. C₃×C₅	C₅×C₈	semidirect
32. C₅	C₃×#168	direct (N × H)
33. C₅	C₃×C₅×C₈	semidirect
35. C₃	C₅×#168	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×C₄×C₅²	2
C₅×#168	3
C₃×C₅×C₈	5
C₃×#168	5

Subgroups — C3×C5×#168 #10597067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#168 #10597067