Subgroups — #28358303

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#14584033	—	5	1	no	maximal, Hall
4	D₆₉₇	—	5	1	no	—
5	#11717962	—	17	1	no	maximal, Hall
6	C₁₇×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₂₀₅	—	17	1	no	—
8	#66775	—	41	1	no	maximal, Hall
9	C₅×C₄₁	#595	1	1	yes	characteristic, complemented, Hall
10	D₈₅	—	41	1	no	—
11	#4223	—	85	1	no	Hall
12	C₅×C₁₇	#4223	1	1	yes	characteristic, complemented, Hall
13	D₄₁	—	85	1	no	—
14	#595	—	205	1	no	Hall
15	C₄₁	#66775	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	205	1	no	—
17	AGL(1,𝔽₅)	—	697	1	no	Hall
18	C₁₇	#11717962	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	697	1	no	—
20	C₅	#14584033	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	3485	1	no	Sylow
22	C₂	—	3485	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₄₁	C₄
prime radical, cosocle	D₃₄₈₅	C₂
LCS	G ▷ C₅×C₁₇×C₄₁
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.