Subgroups — #37590404

Order 24660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₄₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#19096903	—	5	1	no	maximal, Hall
4	C₅×D₄₁₁	—	6	2	no	—
5	#14582306	—	9	1	no	maximal, Hall
6	C₃⋊D₄₁₁	D₅	1	1	yes	characteristic
7	C₃×C₅×C₁₃₇	—	2	2	no	—
8	C₅×D₁₃₇	—	9	1	no	—
9	C₃²×C₁₃₇	Dic₅	1	1	yes	characteristic, complemented, Hall
10	D₄₁₁	—	6	2	no	—
11	C₅×C₁₃₇	#157	1	1	yes	characteristic, complemented, Hall
12	#10587739	—	45	1	no	Hall
13	C₃×C₁₃₇	—	2	2	no	—
14	D₁₃₇	—	9	1	no	—
15	#4379	—	137	1	no	maximal, Hall
16	C₁₃₇	#4379	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₃⋊D₃	—	137	1	no	—
18	C₃²×C₅	#10587739	1	1	yes	characteristic, complemented, Hall
19	#157	—	685	1	no	Hall
20	C₅×D₃	—	822	2	no	—
21	Dic₅	—	1233	1	no	Hall
22	C₃⋊D₃	—	137	1	no	—
23	C₃×C₅	—	2	2	no	—
24	C₂×C₅	—	1233	1	no	—
25	C₃²	#14582306	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	822	2	no	—
27	C₅	#19096903	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	6165	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	1233	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₃₇	C₄
prime radical, cosocle	C₅×C₃⋊D₄₁₁	C₂
LCS	G ▷ C₃²×C₅×C₁₃₇
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.