Subgroups — #41032913

Order 27380.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₃₇⋊D₃₇)	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	#19129959	—	5	1	no	maximal, Hall
4	C₃₇⋊D₃₇	—	5	1	no	—
5	C₃₇²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	#10625192	—	37	1	no	maximal
7	#10625191	—	37	1	no	maximal
8	D₁₈₅	—	37	1	no	—
9	D₁₈₅	—	37	1	no	—
10	D₁₈₅	—	74	18	no	—
11	C₅×C₃₇	—	2	18	no	—
12	C₅×C₃₇	#3866	1	1	yes	characteristic, complemented
13	C₅×C₃₇	#3866	1	1	yes	characteristic, complemented
14	#3866	—	185	1	no	—
15	#3866	—	185	1	no	—
16	D₃₇	—	370	18	no	—
17	D₃₇	—	185	1	no	—
18	D₃₇	—	185	1	no	—
19	C₃₇	—	2	18	no	—
20	C₃₇	#10625191	1	1	yes	characteristic, complemented
21	C₃₇	#10625192	1	1	yes	characteristic, complemented
22	AGL(1,𝔽₅)	—	1369	1	no	Hall
23	D₅	—	1369	1	no	—
24	C₅	#19129959	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	6845	1	no	Sylow
26	C₂	—	6845	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₃₇²	C₄
prime radical, cosocle	C₅⋊(C₃₇⋊D₃₇)	C₂
LCS	G ▷ C₅×C₃₇²
UCS	C₁

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.