Subgroups — PSL(2,𝔽₂₅) #72209633

Order 7800.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1043⋊C₃	—	26	1	no	maximal
2	(C₅⋊D₅)⋊C₃	—	26	1	no	—
3	S₅	—	65	2	no	maximal
4	#1043	—	26	1	no	—
5	C₅²⋊C₃	—	26	1	no	Hall
6	A₅	—	65	2	no	—
7	C₅⋊D₅	—	26	1	no	—
8	D₁₃	—	300	1	no	maximal
9	C₅²	—	26	1	no	Sylow
10	S₄	—	325	2	no	Hall
11	D₁₂	—	325	1	no	maximal, Hall
12	AGL(1,𝔽₅)	—	390	2	no	—
13	C₁₃	—	300	1	no	Sylow
14	C₂×D₃	—	325	2	no	—
15	A₄	—	325	2	no	—
16	C₃×C₄	—	325	1	no	—
17	D₅	—	390	2	no	—
18	D₄	—	975	1	no	Sylow
19	C₂×C₃	—	325	1	no	—
20	D₃	—	650	2	no	—
21	C₅	—	78	2	no	—
22	C₂²	—	325	2	no	—
23	C₄	—	325	1	no	—
24	C₃	—	325	1	no	Sylow
25	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.