Subgroups — #72224461

Order 15600.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSL(2,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	#10597167	—	26	1	no	maximal
3	#1043⋊C₃	—	26	1	no	—
4	#6053	—	78	1	no	—
5	(C₅⋊D₅)⋊C₃	—	26	1	no	—
6	S₅	—	130	1	no	—
7	#1043	—	26	1	no	—
8	C₅²⋊C₃	—	26	1	no	Hall
9	A₅	—	130	1	no	—
10	#261	—	300	1	no	maximal
11	C₅⋊D₅	—	26	1	no	—
12	#215	—	325	1	no	maximal, Hall
13	D₁₃	—	300	1	no	—
14	C₅²	—	26	1	no	Sylow
15	S₄	—	650	1	no	—
16	C₃×Q₈	—	325	1	no	—
17	D₁₂	—	325	1	no	—
18	C₃⋊C₈	—	325	1	no	—
19	AGL(1,𝔽₅)	—	780	1	no	—
20	SD₁₆	—	975	1	no	Sylow
21	C₁₃	—	300	1	no	Sylow
22	C₂×D₃	—	650	1	no	—
23	A₄	—	650	1	no	—
24	C₃×C₄	—	325	1	no	—
25	C₃×C₄	—	650	1	no	—
26	D₅	—	780	1	no	—
27	Q₈	—	325	1	no	—
28	D₄	—	975	1	no	—
29	C₈	—	975	1	no	—
30	C₂×C₃	—	325	1	no	—
31	D₃	—	1300	1	no	—
32	C₅	—	156	1	no	—
33	C₂²	—	650	1	no	—
34	C₄	—	325	1	no	—
35	C₄	—	650	1	no	—
36	C₃	—	325	1	no	Sylow
37	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, prime radical, cosocle, hypocenter	PSL(2,𝔽₂₅)	C₂
LCS	G ▷ PSL(2,𝔽₂₅)
UCS	C₁

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