Subgroups — Sp(2,𝔽₂₉) #72209938

Order 24360.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉⋊C₇	—	30	1	no	maximal
2	C₂×C₂₉⋊C₇	—	30	1	no	—
3	C₂₉⋊C₇	—	30	1	no	Hall
4	SL(2,𝔽₅)	—	203	2	no	maximal, Hall
5	Dic₂₉	—	30	1	no	—
6	Dic₁₅	—	406	1	no	maximal
7	C₂×C₂₉	—	30	1	no	—
8	Dic₁₄	—	435	1	no	maximal, Hall
9	C₂×C₃×C₅	—	406	1	no	—
10	C₂₉	—	30	1	no	Sylow
11	C₄×C₇	—	435	1	no	—
12	Dic₇	—	435	2	no	—
13	SL(2,𝔽₃)	—	1015	1	no	Hall
14	Dic₅	—	1218	1	no	—
15	C₃×C₅	—	406	1	no	Hall
16	C₂×C₇	—	435	1	no	—
17	Dic₃	—	2030	1	no	—
18	C₂×C₅	—	406	1	no	—
19	Q₈	—	1015	1	no	Sylow
20	C₇	—	435	1	no	Sylow
21	C₂×C₃	—	406	1	no	—
22	C₅	—	406	1	no	Sylow
23	C₄	—	435	1	no	—
24	C₃	—	406	1	no	Sylow
25	C₂	PSL(2,𝔽₂₉)	1	1	yes	maximal normal, characteristic

	subgroup	G/H
center, Frattini, Fitting, socle, cosocle, hypercenter	C₂	PSL(2,𝔽₂₉)
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.