Subgroups — C₃⋊(C₄₃⋊#1039) #27166399

Order 12900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#1039	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₆₄₅	—	5	6	no	maximal
5	C₂×C₅²×C₄₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₄₃	D₅	1	6	yes	—
7	C₅²×C₄₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₂₁₅	—	15	6	no	—
9	C₃×C₅×C₄₃	Dic₅	1	6	yes	complemented
10	Dic₁₂₉	—	25	1	no	Hall
11	C₂×C₅×C₄₃	D₁₅	1	6	yes	—
12	C₃⋊#1039	—	43	1	no	maximal, Hall
13	C₂×C₃×C₄₃	C₅⋊D₅	1	1	yes	characteristic
14	C₅×C₄₃	Dic₁₅	1	6	yes	complemented
15	Dic₄₃	—	75	1	no	Hall
16	C₂×C₃×C₅²	D₄₃	1	1	yes	characteristic
17	C₃×C₄₃	#1039	1	1	yes	characteristic, complemented, Hall
18	#1039	—	129	1	no	Hall
19	C₂×C₄₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
20	C₃×C₅²	Dic₄₃	1	1	yes	characteristic, complemented, Hall
21	Dic₁₅	—	215	6	no	—
22	C₂×C₅²	D₁₂₉	1	1	yes	characteristic
23	C₄₃	C₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₅	D₂₁₅	1	6	yes	—
25	C₅²	Dic₁₂₉	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	645	6	no	—
27	C₃×C₅	Dic₂₁₅	1	6	yes	complemented
28	Dic₃	—	1075	1	no	Hall
29	C₂×C₅	D₆₄₅	1	6	yes	—
30	C₂×C₃	C₅⋊D₂₁₅	1	1	yes	characteristic
31	C₅	Dic₆₄₅	1	6	yes	complemented
32	C₄	—	3225	1	no	Sylow
33	C₃	C₄₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₃⋊(C₅⋊D₂₁₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₅⋊D₂₁₅)
commutator, hypocenter	C₃×C₅²×C₄₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅²×C₄₃	C₂
LCS	G ▷ C₃×C₅²×C₄₃
UCS	C₁ ◁ C₂

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.