Subgroups — C₃×#23758769 #44475889

Order 30300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14579005	C₂	1	1	yes	maximal, characteristic
2	#23758769	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×#14579005	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₁₀₁⋊C₅	C₅	1	1	yes	maximal, characteristic
5	C₂×#14579005	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₀₁⋊C₅	C₂×C₅	1	1	yes	characteristic
7	#14579005	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₁₀₁⋊C₅	C₃×C₅	1	1	yes	characteristic
9	C₃×C₁₀₁⋊C₅	C₄×C₅	1	1	yes	characteristic
10	C₃×Dic₁₀₁	C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₀₁⋊C₅	C₂×C₃×C₅	1	1	yes	characteristic
12	C₂×C₃×C₁₀₁	C₂×C₂₅	1	1	yes	characteristic
13	C₁₀₁⋊C₅	C₃×C₄×C₅	1	1	yes	characteristic
14	Dic₁₀₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₀₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₂₅	—	101	1	no	maximal, Hall
17	C₂×C₁₀₁	C₂×C₃×C₂₅	1	1	yes	characteristic
18	C₂×C₃×C₂₅	—	101	1	no	—
19	C₁₀₁	C₃×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₄×C₂₅	—	101	1	no	Hall
21	C₃×C₂₅	—	101	1	no	Hall
22	C₃×C₄×C₅	—	101	1	no	—
23	C₂×C₂₅	—	101	1	no	—
24	C₂×C₃×C₅	—	101	1	no	—
25	C₂₅	—	101	1	no	Sylow
26	C₄×C₅	—	101	1	no	—
27	C₃×C₅	—	101	1	no	—
28	C₃×C₄	—	2525	1	no	Hall
29	C₂×C₅	—	101	1	no	—
30	C₂×C₃	#14579005⋊C₂	1	1	yes	characteristic
31	C₅	—	101	1	no	—
32	C₄	—	2525	1	no	Sylow
33	C₃	#23758769	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×#14579005⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#14579005⋊C₂
commutator, hypocenter	C₁₀₁	C₃×C₄×C₂₅
Frattini	C₂	C₃×#14579005⋊C₂
Fitting, socle	C₂×C₃×C₁₀₁	C₂×C₂₅
prime radical	C₂×C₃×C₁₀₁⋊C₅	C₂×C₅
cosocle	C₂×C₁₀₁⋊C₅	C₂×C₃×C₅
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #23758769	C₃	direct (N × H)
3. C₃×#14579005	C₄	semidirect
7. #14579005	C₃×C₄	semidirect
10. C₃×Dic₁₀₁	C₂₅	semidirect
14. Dic₁₀₁	C₃×C₂₅	semidirect
15. C₃×C₁₀₁	C₄×C₂₅	semidirect
19. C₁₀₁	C₃×C₄×C₂₅	semidirect
33. C₃	#23758769	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×#14579005	2
#23758769	3
C₃×Dic₁₀₁⋊C₅	5
C₃×C₄×C₂₅	101

Subgroups — C3×#23758769 #44475889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23758769 #44475889