Subgroups — C₅₃×C₅⋊D₄₅ #37558708

Order 23850.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₃×C₃⋊(C₅⋊D₅)	—	3	1	no	maximal
3	C₅₃×D₄₅	—	5	6	no	maximal
4	C₃×C₅²×C₅₃	D₃	1	1	yes	characteristic
5	C₅⋊D₅×C₅₃	—	9	1	no	Hall
6	C₅×C₉×C₅₃	D₅	1	6	yes	complemented
7	D₁₅×C₅₃	—	15	6	no	—
8	C₅²×C₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	D₉×C₅₃	—	25	1	no	Hall
10	C₃×C₅×C₅₃	D₁₅	1	6	yes	—
11	D₅×C₅₃	—	45	6	no	—
12	C₉×C₅₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
13	C₅⋊D₄₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	D₃×C₅₃	—	75	1	no	—
15	C₅×C₅₃	D₄₅	1	6	yes	complemented
16	C₅²×C₉	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
18	C₃⋊(C₅⋊D₅)	—	3	1	no	—
19	C₂×C₅₃	—	225	1	no	Hall
20	D₄₅	—	5	6	no	—
21	C₃×C₅²	D₃×C₅₃	1	1	yes	characteristic
22	C₅₃	C₅⋊D₄₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅⋊D₅	—	9	1	no	Hall
24	C₅×C₉	D₅×C₅₃	1	6	yes	complemented
25	D₁₅	—	15	6	no	—
26	C₅²	D₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	25	1	no	Hall
28	C₃×C₅	D₁₅×C₅₃	1	6	yes	—
29	D₅	—	45	6	no	—
30	C₉	C₅⋊D₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	75	1	no	—
32	C₅	C₅₃×D₄₅	1	6	yes	complemented
33	C₃	C₅₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
34	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	C₅⋊D₄₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂×C₅₃
Frattini	C₃	C₅₃×C₃⋊(C₅⋊D₅)
Fitting	C₅²×C₉×C₅₃	C₂
socle	C₃×C₅²×C₅₃	D₃
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₅₃

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.