Subgroups — C₃₇×#10597833 #37528882

Order 23125.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×5₋¹⁺²	C₅	1	4	yes	maximal, complemented
2	C₃₇×H(3,𝔽₅)	C₅	1	1	yes	maximal, characteristic
3	C₅×C₂₅×C₃₇	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₃₇	—	5	1	no	—
5	C₅²×C₃₇	C₅²	1	1	yes	characteristic
6	C₂₅×C₃₇	—	5	1	no	—
7	C₂₅×C₃₇	—	5	4	no	—
8	#10597833	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₅×C₃₇	—	5	1	no	—
10	C₅×C₃₇	—	25	1	no	—
11	C₅×C₃₇	H(3,𝔽₅)	1	1	yes	characteristic
12	5₋¹⁺²	C₅×C₃₇	1	4	yes	complemented
13	H(3,𝔽₅)	C₅×C₃₇	1	1	yes	characteristic
14	C₅×C₂₅	C₅×C₃₇	1	1	yes	characteristic, complemented
15	C₃₇	#10597833	1	1	yes	characteristic, direct product factor, Sylow
16	C₅²	—	5	1	no	—
17	C₅²	C₅²×C₃₇	1	1	yes	characteristic
18	C₂₅	—	5	1	no	—
19	C₂₅	—	5	4	no	—
20	C₅	—	5	1	no	—
21	C₅	—	25	1	no	—
22	C₅	C₃₇×H(3,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₅×C₃₇	H(3,𝔽₅)
commutator, Frattini, cosocle	C₅²	C₅²×C₃₇
prime radical	C₃₇×H(3,𝔽₅)	C₅
LCS	G ▷ C₅² ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅×C₃₇ ◁ C₅²×C₃₇ ◁ G

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.