Subgroups — C₂×C₃⋊(D₅₄₁⋊C₅) #44570200

Order 32460.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(D₅₄₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₄₁⋊C₅	—	3	1	no	maximal, Hall
4	C₃×C₅₄₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₆₂₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₅₄₁⋊C₅	D₃	1	1	yes	characteristic, complemented
7	D₅₄₁⋊C₅	—	3	2	no	—
8	C₂×C₃×C₅₄₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₁₆₂₃	C₂×C₅	1	2	yes	complemented
10	C₅₄₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₄₁	—	3	1	no	Hall
12	C₃×C₅₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₄₁	C₅×D₃	1	1	yes	characteristic, complemented
14	D₅₄₁	—	3	2	no	—
15	C₅₄₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×D₃	—	541	1	no	maximal, Hall
17	C₂×C₃×C₅	—	541	1	no	—
18	C₅×D₃	—	541	2	no	—
19	C₂²×C₅	—	1623	1	no	Hall
20	C₃×C₅	—	541	1	no	Hall
21	C₂×D₃	—	541	1	no	Hall
22	C₂×C₅	—	541	1	no	—
23	C₂×C₅	—	1623	2	no	—
24	C₂×C₃	D₅₄₁⋊C₅	1	1	yes	characteristic, complemented
25	D₃	—	541	2	no	—
26	C₅	—	541	1	no	Sylow
27	C₂²	—	1623	1	no	Sylow
28	C₃	C₂×D₅₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	1623	2	no	—
30	C₂	C₃⋊(D₅₄₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(D₅₄₁⋊C₅)
commutator, cosocle, hypocenter	C₃×C₅₄₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅₄₁	C₂×C₅
LCS	G ▷ C₃×C₅₄₁
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.