Subgroups — C₄₁×#64480 #27134243

Order 12300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1044	—	3	1	no	maximal, Hall
3	C₄₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₁×C₅⋊D₅	D₃	1	1	yes	characteristic
5	C₅²×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	AGL(1,𝔽₅)×C₄₁	—	15	2	no	—
7	Dic₃×C₄₁	—	25	1	no	maximal, Hall
8	D₅×C₄₁	—	15	2	no	—
9	#64480	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₄₁	—	25	1	no	—
11	C₅×C₄₁	—	3	2	no	—
12	C₄×C₄₁	—	75	1	no	Hall
13	(C₅⋊D₅)⋊C₃	C₂×C₄₁	1	1	yes	characteristic
14	C₃×C₄₁	—	25	1	no	Hall
15	#1044	—	3	1	no	Hall
16	C₂×C₄₁	—	25	1	no	—
17	C₅²⋊C₃	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
18	C₅⋊D₅	D₃×C₄₁	1	1	yes	characteristic
19	C₄₁	#64480	1	1	yes	characteristic, direct product factor, Sylow
20	C₅²	Dic₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₅)	—	15	2	no	—
22	Dic₃	—	25	1	no	Hall
23	D₅	—	15	2	no	—
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	75	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	—	25	1	no	—

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.