Subgroups — #27160384

Order 12580.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#14578979	—	5	1	no	maximal, Hall
4	D₆₂₉	D₅	1	1	yes	characteristic
5	#10625194	—	17	1	no	maximal, Hall
6	C₁₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₃₇	—	17	1	no	—
8	#66772	—	37	1	no	maximal, Hall
9	C₅×C₃₇	#595	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₇	—	37	1	no	—
11	#3866	—	85	1	no	Hall
12	C₅×C₁₇	#3866	1	1	yes	characteristic, complemented, Hall
13	D₃₇	—	17	1	no	—
14	#595	—	185	1	no	Hall
15	C₃₇	#66772	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	37	1	no	—
17	Dic₅	—	629	1	no	Hall
18	C₁₇	#10625194	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	629	1	no	—
20	C₅	#14578979	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	3145	1	no	Sylow
22	C₂	—	629	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₃₇	C₄
prime radical, cosocle	C₅×D₆₂₉	C₂
LCS	G ▷ C₅×C₁₇×C₃₇
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.