Subgroups — D₂₉₇₄₅ #72293708

Order 59490.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₉₉₁₅	—	3	1	no	maximal
3	D₅₉₄₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₆₆₁	D₃	1	1	yes	characteristic
5	D₃₃₀₅	—	9	1	no	Hall
6	C₉×C₆₆₁	D₅	1	1	yes	characteristic, complemented, Hall
7	D₁₉₈₃	—	15	1	no	—
8	C₅×C₆₆₁	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₆₆₁	D₁₅	1	1	yes	characteristic
10	D₆₆₁	—	45	1	no	Hall
11	C₆₆₁	D₄₅	1	1	yes	characteristic, complemented, Sylow
12	D₄₅	—	661	1	no	maximal, Hall
13	C₅×C₉	D₆₆₁	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	1983	1	no	—
15	D₉	—	3305	1	no	Hall
16	C₃×C₅	D₁₉₈₃	1	1	yes	characteristic
17	D₅	—	5949	1	no	Hall
18	C₉	D₃₃₀₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	9915	1	no	—
20	C₅	D₅₉₄₉	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₉₉₁₅	1	1	yes	characteristic
22	C₂	—	29745	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₆₆₁	C₂
Frattini	C₃	D₉₉₁₅
socle	C₃×C₅×C₆₆₁	D₃
LCS	G ▷ C₅×C₉×C₆₆₁
UCS	C₁

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.