Subgroups — C₃₇×C₃⋊#1043 #26012902

Order 11100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×ΓL(1,𝔽₁₆)	—	5	6	no	maximal
5	C₃₇×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃×D₅×C₃₇	—	5	6	no	—
7	C₅²×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₃₇	—	15	6	no	—
9	C₃×C₅×C₃₇	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₃×C₃₇	—	25	1	no	Hall
11	D₅×C₃₇	—	5	6	no	—
12	C₃⋊#1043	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₃₇	—	25	1	no	—
14	C₅×C₃₇	ΓL(1,𝔽₁₆)	1	6	yes	complemented
15	C₃×C₅⋊D₅	C₂×C₃₇	1	1	yes	characteristic
16	C₄×C₃₇	—	75	1	no	Hall
17	C₃×C₃₇	#1043	1	1	yes	characteristic, complemented, Hall
18	#1043	—	3	1	no	Hall
19	C₃×C₅²	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₇	—	25	1	no	—
21	ΓL(1,𝔽₁₆)	—	5	6	no	—
22	C₅⋊D₅	D₃×C₃₇	1	1	yes	characteristic
23	C₃₇	C₃⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	15	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₃₇	1	6	yes	complemented
28	Dic₃	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃₇×ΓL(1,𝔽₁₆)	1	6	yes	complemented
32	C₄	—	75	1	no	Sylow
33	C₃	C₃₇×#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.