Subgroups — C₅²⋊C₃×Dic₄₃ #27166385

Order 12900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₄₃	—	3	2	no	—
7	C₃×Dic₄₃	—	25	1	no	maximal, Hall
8	C₂×C₅×C₄₃	—	3	2	no	—
9	C₄×C₅²⋊C₃	—	43	1	no	maximal, Hall
10	C₂×C₃×C₄₃	—	25	1	no	—
11	C₅×C₄₃	—	3	2	no	—
12	Dic₄₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅²⋊C₃	D₄₃	1	1	yes	characteristic
14	C₃×C₄₃	—	25	1	no	Hall
15	C₄×C₅²	—	43	1	no	Hall
16	C₂×C₄₃	C₂×C₅²⋊C₃	1	1	yes	characteristic
17	C₅²⋊C₃	Dic₄₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅²	C₃×D₄₃	1	1	yes	characteristic
19	C₄₃	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅²	C₃×Dic₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅	—	129	2	no	—
22	C₃×C₄	—	1075	1	no	Hall
23	C₂×C₅	—	3	2	no	—
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	43	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	C₅²⋊C₃×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅²⋊C₃×D₄₃
commutator, hypocenter	C₅²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₄₃	C₂×C₃
prime radical	C₂×C₄₃×C₅²⋊C₃	C₂
LCS	G ▷ 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.