Subgroups — D₄₅×C₃₅₃ #44540926

Order 31770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅×C₃₅₃	—	3	1	no	maximal
3	D₉×C₃₅₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₅₃	D₃	1	1	yes	characteristic
5	D₅×C₃₅₃	—	9	1	no	Hall
6	C₉×C₃₅₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₃₅₃	—	15	1	no	—
8	C₅×C₃₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	D₁₅	1	1	yes	characteristic
10	C₂×C₃₅₃	—	45	1	no	Hall
11	C₃₅₃	D₄₅	1	1	yes	characteristic, direct product factor, Sylow
12	D₄₅	C₃₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₉	C₂×C₃₅₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	3	1	no	—
15	D₉	—	5	1	no	Hall
16	C₃×C₅	D₃×C₃₅₃	1	1	yes	characteristic
17	D₅	—	9	1	no	Hall
18	C₉	D₅×C₃₅₃	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	15	1	no	—
20	C₅	D₉×C₃₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₁₅×C₃₅₃	1	1	yes	characteristic
22	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₅₃	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₃₅₃
Frattini	C₃	D₁₅×C₃₅₃
Fitting	C₅×C₉×C₃₅₃	C₂
socle	C₃×C₅×C₃₅₃	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₃₅₃

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.