Subgroups — SL(2,𝔽₂₅) #72209729

Order 15600.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6033⋊C₃	—	26	1	no	maximal
2	#1039⋊C₃	—	26	1	no	—
3	#6728	—	65	2	no	maximal
4	#6033	—	26	1	no	—
5	C₂×C₅²⋊C₃	—	26	1	no	—
6	SL(2,𝔽₅)	—	65	2	no	—
7	#1039	—	26	1	no	—
8	C₅²⋊C₃	—	26	1	no	Hall
9	Dic₁₃	—	300	1	no	maximal
10	C₂×C₅²	—	26	1	no	—
11	#226	—	325	2	no	Hall
12	Dic₁₂	—	325	1	no	maximal, Hall
13	#170	—	390	2	no	—
14	C₂×C₁₃	—	300	1	no	—
15	C₅²	—	26	1	no	Sylow
16	Dic₆	—	325	2	no	—
17	SL(2,𝔽₃)	—	325	2	no	—
18	C₃×C₈	—	325	1	no	—
19	Dic₅	—	390	2	no	—
20	Q₁₆	—	975	1	no	Sylow
21	C₁₃	—	300	1	no	Sylow
22	C₃×C₄	—	325	1	no	—
23	Dic₃	—	650	2	no	—
24	C₂×C₅	—	78	2	no	—
25	Q₈	—	325	2	no	—
26	C₈	—	325	1	no	—
27	C₂×C₃	—	325	1	no	—
28	C₅	—	78	2	no	—
29	C₄	—	325	1	no	—
30	C₃	—	325	1	no	Sylow
31	C₂	PSL(2,𝔽₂₅)	1	1	yes	maximal normal, characteristic

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

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