Subgroups — C₂²×C₇⋊(C₅²⋊C₃) #14523669

Order 2100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊(C₅²⋊C₃)	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇⋊(C₅²⋊C₃)	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₇	C₂×C₃	1	3	yes	complemented
5	C₂²×C₅²⋊C₃	—	7	1	no	maximal, Hall
6	C₅²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅²⋊C₃	—	7	3	no	—
8	C₂²×C₅×C₇	—	3	2	no	—
9	C₂²×C₅²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂²×ΓL(1,𝔽₈)	—	25	1	no	maximal, Hall
11	C₅²⋊C₃	—	7	1	no	Hall
12	C₂×C₅×C₇	—	3	6	no	—
13	C₂×C₅²	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
14	C₂×ΓL(1,𝔽₈)	—	25	3	no	—
15	C₅×C₇	—	3	2	no	—
16	C₂²×C₇	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₅²	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
18	ΓL(1,𝔽₈)	—	25	1	no	Hall
19	C₂²×C₅	—	3	2	no	—
20	C₂×C₇	C₂×C₅²⋊C₃	1	3	yes	complemented
21	C₂²×C₃	—	175	1	no	Hall
22	C₂×C₅	—	3	6	no	—
23	C₇	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	175	3	no	—
25	C₅	—	3	2	no	—
26	C₂²	C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	175	1	no	Sylow
28	C₂	C₂×C₇⋊(C₅²⋊C₃)	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₇⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇	C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂²

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.