Subgroups — #47977151

Order 35300.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₁₇₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#20296560	—	5	1	no	maximal
4	#20296559	—	5	1	no	maximal
5	D₁₇₆₅	—	5	1	no	—
6	D₁₇₆₅	—	5	1	no	—
7	D₁₇₆₅	—	10	2	no	—
8	C₅×C₃₅₃	—	2	2	no	—
9	C₅×C₃₅₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
10	C₅×C₃₅₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	#13083443	—	25	1	no	Hall
12	D₃₅₃	—	25	1	no	—
13	C₃₅₃	#1044	1	1	yes	characteristic, complemented, Sylow
14	#1044	—	353	1	no	maximal, Hall
15	C₅⋊D₅	—	353	1	no	—
16	C₅²	#13083443	1	1	yes	characteristic, complemented, Sylow
17	AGL(1,𝔽₅)	—	1765	1	no	—
18	AGL(1,𝔽₅)	—	1765	1	no	—
19	D₅	—	3530	2	no	—
20	D₅	—	1765	1	no	—
21	D₅	—	1765	1	no	—
22	C₅	—	2	2	no	—
23	C₅	#20296559	1	1	yes	characteristic, complemented
24	C₅	#20296560	1	1	yes	characteristic, complemented
25	C₄	—	8825	1	no	Sylow
26	C₂	—	8825	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₃₅₃	C₄
prime radical, cosocle	C₅⋊D₁₇₆₅	C₂
LCS	G ▷ C₅²×C₃₅₃
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.