Subgroups — C₆₇×C₃⋊#1043 #34117287

Order 20100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₁₆)×C₆₇	—	5	6	no	maximal
5	C₅⋊D₅×C₆₇	D₃	1	1	yes	characteristic
6	C₃×D₅×C₆₇	—	5	6	no	—
7	C₅²×C₆₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₆₇	—	15	6	no	—
9	C₃×C₅×C₆₇	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₃×C₆₇	—	25	1	no	Hall
11	D₅×C₆₇	—	5	6	no	—
12	C₂×C₃×C₆₇	—	25	1	no	—
13	C₅×C₆₇	ΓL(1,𝔽₁₆)	1	6	yes	complemented
14	C₃⋊#1043	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₆₇	—	75	1	no	Hall
16	C₃×C₆₇	#1043	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅⋊D₅	C₂×C₆₇	1	1	yes	characteristic
18	C₂×C₆₇	—	25	1	no	—
19	#1043	—	3	1	no	Hall
20	C₃×C₅²	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₆₇	C₃⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
22	ΓL(1,𝔽₁₆)	—	5	6	no	—
23	C₅⋊D₅	D₃×C₆₇	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	15	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₆₇	1	6	yes	complemented
28	Dic₃	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	ΓL(1,𝔽₁₆)×C₆₇	1	6	yes	complemented
32	C₄	—	75	1	no	Sylow
33	C₃	C₆₇×#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.