Subgroups — #37558086

Order 23780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#18011702	—	5	1	no	maximal, Hall
4	C₄₁×D₂₉	—	5	1	no	—
5	C₂₉×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	#11717963	—	29	1	no	maximal, Hall
7	#10596814	—	41	1	no	maximal, Hall
8	D₅×C₄₁	—	29	1	no	—
9	D₁₄₅	D₄₁	1	1	yes	characteristic
10	C₅×C₄₁	#1181	1	1	yes	characteristic, complemented, Hall
11	Dic₄₁	—	145	1	no	Hall
12	C₅×C₂₉	Dic₄₁	1	1	yes	characteristic, complemented, Hall
13	#1181	—	205	1	no	Hall
14	C₂×C₄₁	—	145	1	no	—
15	D₂₉	—	5	1	no	—
16	C₄₁	#10596814	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	#11717963	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	1189	1	no	Hall
19	D₅	—	29	1	no	—
20	C₅	#18011702	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5945	1	no	Sylow
22	C₂	—	145	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₂₉×C₄₁	C₄
prime radical, cosocle	C₄₁×D₁₄₅	C₂
LCS	G ▷ C₅×C₂₉×C₄₁
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.