Subgroups — C₃×C₅²×#6923 #32913087

Order 18300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×#6923	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×#6923	C₅	1	6	yes	maximal, direct product factor
5	C₅²×D₆₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×D₆₁	C₂×C₅	1	6	yes	—
7	C₅²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₅×#6923	C₃×C₅	1	6	yes	direct product factor
9	C₃×C₅×C₆₁	C₄×C₅	1	6	yes	complemented
10	C₃×#6923	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₆₁	C₂×C₃×C₅	1	6	yes	—
12	C₃×D₆₁	C₂×C₅²	1	1	yes	characteristic
13	C₅×C₆₁	C₃×C₄×C₅	1	6	yes	complemented
14	C₃×C₄×C₅²	—	61	1	no	maximal, Hall
15	#6923	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₆₁	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅²	—	61	1	no	—
18	D₆₁	C₂×C₃×C₅²	1	1	yes	characteristic
19	C₄×C₅²	—	61	1	no	Hall
20	C₃×C₅²	#6923	1	1	yes	characteristic, direct product factor, Hall
21	C₆₁	C₃×C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₄×C₅	—	61	6	no	—
23	C₂×C₅²	—	61	1	no	—
24	C₂×C₃×C₅	—	61	6	no	—
25	C₅²	C₃×#6923	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	—	61	6	no	—
27	C₃×C₅	C₅×#6923	1	6	yes	direct product factor
28	C₃×C₄	—	61	1	no	Hall
29	C₂×C₅	—	61	6	no	—
30	C₂×C₃	—	61	1	no	—
31	C₅	C₃×C₅×#6923	1	6	yes	direct product factor
32	C₄	—	61	1	no	Sylow
33	C₃	C₅²×#6923	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅²	#6923
commutator, hypocenter	C₆₁	C₃×C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₆₁	C₄
prime radical	C₃×C₅²×D₆₁	C₂
cosocle	D₆₁	C₂×C₃×C₅²
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₃×C₅²

Complements

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

N	H ≅ G/N	type
2. C₅²×#6923	C₃	direct (N × H)
3. C₃×C₅²×C₆₁	C₄	semidirect
4. C₃×C₅×#6923	C₅	direct (N × H)
7. C₅²×C₆₁	C₃×C₄	semidirect
8. C₅×#6923	C₃×C₅	direct (N × H)
9. C₃×C₅×C₆₁	C₄×C₅	semidirect
10. C₃×#6923	C₅²	direct (N × H)
13. C₅×C₆₁	C₃×C₄×C₅	semidirect
15. #6923	C₃×C₅²	direct (N × H)
16. C₃×C₆₁	C₄×C₅²	semidirect
20. C₃×C₅²	#6923	direct (N × H)
21. C₆₁	C₃×C₄×C₅²	semidirect
25. C₅²	C₃×#6923	direct (N × H)
27. C₃×C₅	C₅×#6923	direct (N × H)
31. C₅	C₃×C₅×#6923	direct (N × H)
33. C₃	C₅²×#6923	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×C₅²×D₆₁	2
C₅²×#6923	3
C₃×C₅×#6923	5
C₃×C₄×C₅²	61

Subgroups — C3×C52×#6923 #32913087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×#6923 #32913087