Subgroups — C₇×#1043⋊C₃ #14523607

Order 2100.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₇×#1043	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	#1043⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅²×C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	(C₅⋊D₅)⋊C₃	C₂×C₇	1	1	yes	characteristic
8	C₇×AGL(1,𝔽₅)	—	15	2	no	—
9	#1043	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₄×C₇	—	25	1	no	maximal, Hall
11	C₅²⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₅	—	15	2	no	—
13	C₅⋊D₅	C₂×C₃×C₇	1	1	yes	characteristic
14	C₂×C₃×C₇	—	25	1	no	—
15	C₅×C₇	—	3	2	no	—
16	C₄×C₇	—	25	1	no	Hall
17	C₅²	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₇	—	25	1	no	Hall
19	AGL(1,𝔽₅)	—	15	2	no	—
20	C₂×C₇	—	25	1	no	—
21	C₃×C₄	—	25	1	no	Hall
22	D₅	—	15	2	no	—
23	C₇	#1043⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	25	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.