Subgroups — C₃×C₈₃⋊#1039 #38735233

Order 24900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₈₃⋊#1039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₄₁₅	—	5	6	no	maximal
5	C₂×C₅²×C₈₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₈₃	D₅	1	6	yes	—
7	C₅²×C₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₄₁₅	—	5	6	no	—
9	C₃×C₅×C₈₃	Dic₅	1	6	yes	complemented
10	C₃×Dic₈₃	—	25	1	no	Hall
11	C₂×C₅×C₈₃	C₃×D₅	1	6	yes	—
12	C₂×C₃×C₈₃	C₅⋊D₅	1	1	yes	characteristic
13	C₅×C₈₃	C₃×Dic₅	1	6	yes	complemented
14	Dic₈₃	—	25	1	no	Hall
15	C₃×#1039	—	83	1	no	maximal, Hall
16	C₃×C₈₃	#1039	1	1	yes	characteristic, complemented, Hall
17	C₂×C₈₃	C₃×C₅⋊D₅	1	1	yes	characteristic
18	C₂×C₃×C₅²	D₈₃	1	1	yes	characteristic
19	#1039	—	83	1	no	Hall
20	C₈₃	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₅²	Dic₈₃	1	1	yes	characteristic, complemented, Hall
22	C₃×Dic₅	—	415	6	no	—
23	C₂×C₅²	C₃×D₈₃	1	1	yes	characteristic
24	C₂×C₃×C₅	D₄₁₅	1	6	yes	—
25	C₅²	C₃×Dic₈₃	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	415	6	no	—
27	C₃×C₅	Dic₄₁₅	1	6	yes	complemented
28	C₃×C₄	—	2075	1	no	Hall
29	C₂×C₅	C₃×D₄₁₅	1	6	yes	—
30	C₂×C₃	C₅⋊D₄₁₅	1	1	yes	characteristic
31	C₅	C₃×Dic₄₁₅	1	6	yes	complemented
32	C₄	—	2075	1	no	Sylow
33	C₃	C₈₃⋊#1039	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅⋊D₄₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₄₁₅
commutator, hypocenter	C₅²×C₈₃	C₃×C₄
Frattini	C₂	C₃×C₅⋊D₄₁₅
Fitting, socle, prime radical	C₂×C₃×C₅²×C₈₃	C₂
cosocle	C₂×C₅²×C₈₃	C₂×C₃
LCS	G ▷ C₅²×C₈₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₈₃⋊#1039	C₃	direct (N × H)
3. C₃×C₅²×C₈₃	C₄	semidirect
7. C₅²×C₈₃	C₃×C₄	semidirect
9. C₃×C₅×C₈₃	Dic₅	semidirect
13. C₅×C₈₃	C₃×Dic₅	semidirect
16. C₃×C₈₃	#1039	semidirect
20. C₈₃	C₃×#1039	semidirect
21. C₃×C₅²	Dic₈₃	semidirect
25. C₅²	C₃×Dic₈₃	semidirect
27. C₃×C₅	Dic₄₁₅	semidirect
31. C₅	C₃×Dic₄₁₅	semidirect
33. C₃	C₈₃⋊#1039	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×C₅²×C₈₃	2
C₈₃⋊#1039	3
C₃×Dic₄₁₅	5
C₃×#1039	83

Subgroups — C3×C83⋊#1039 #38735233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈₃⋊#1039 #38735233