Subgroups — #44528166

Order 31140.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#20262015	—	5	1	no	maximal, Hall
4	D₁₅×C₁₇₃	—	6	2	no	—
5	#16812339	—	9	1	no	maximal, Hall
6	C₃⋊D₃×C₁₇₃	—	5	1	no	—
7	C₃×C₅×C₁₇₃	—	2	2	no	—
8	D₅×C₁₇₃	—	9	1	no	—
9	C₃²×C₁₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₇₃	—	30	2	no	—
11	C₅×C₁₇₃	#157	1	1	yes	characteristic, complemented, Hall
12	Dic₁₇₃	—	45	1	no	Hall
13	C₃×C₁₇₃	—	2	2	no	—
14	C₂×C₁₇₃	—	45	1	no	—
15	#4380	—	173	1	no	maximal, Hall
16	C₁₇₃	#4380	1	1	yes	characteristic, complemented, Sylow
17	C₃⋊D₁₅	D₁₇₃	1	1	yes	characteristic
18	C₃²×C₅	Dic₁₇₃	1	1	yes	characteristic, complemented, Hall
19	#157	—	865	1	no	Hall
20	D₁₅	—	6	2	no	—
21	AGL(1,𝔽₅)	—	1557	1	no	Hall
22	C₃⋊D₃	—	5	1	no	—
23	C₃×C₅	—	2	2	no	—
24	D₅	—	9	1	no	—
25	C₃²	#16812339	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	30	2	no	—
27	C₅	#20262015	1	1	yes	characteristic, complemented, Sylow
28	C₄	—	7785	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₇₃	C₄
prime radical, cosocle	C₃⋊D₁₅×C₁₇₃	C₂
LCS	G ▷ C₃²×C₅×C₁₇₃
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.