Subgroups — C₄₁×C₃⋊#1043 #27134297

Order 12300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₁×ΓL(1,𝔽₁₆)	—	5	6	no	maximal
5	C₄₁×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₄₁	—	5	6	no	—
7	C₅²×C₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₄₁	—	15	6	no	—
9	C₃×C₅×C₄₁	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₃×C₄₁	—	25	1	no	Hall
11	D₅×C₄₁	—	5	6	no	—
12	C₃⋊#1043	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄₁	—	25	1	no	—
14	C₅×C₄₁	ΓL(1,𝔽₁₆)	1	6	yes	complemented
15	C₄×C₄₁	—	75	1	no	Hall
16	C₃×C₅⋊D₅	C₂×C₄₁	1	1	yes	characteristic
17	C₃×C₄₁	#1043	1	1	yes	characteristic, complemented, Hall
18	#1043	—	3	1	no	Hall
19	C₂×C₄₁	—	25	1	no	—
20	C₃×C₅²	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
21	ΓL(1,𝔽₁₆)	—	5	6	no	—
22	C₅⋊D₅	D₃×C₄₁	1	1	yes	characteristic
23	C₄₁	C₃⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	15	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₄₁	1	6	yes	complemented
28	Dic₃	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₄₁×ΓL(1,𝔽₁₆)	1	6	yes	complemented
32	C₄	—	75	1	no	Sylow
33	C₃	C₄₁×#1043	1	1	yes	characteristic, complemented, Sylow
34	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.