Subgroups — C₃×C₇⋊#1044 #14523634

Order 2100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#1044	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇⋊AGL(1,𝔽₅)	—	5	2	no	maximal
5	C₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×#1044	—	7	1	no	maximal, Hall
7	C₃×C₇×D₅	—	5	2	no	—
8	C₃×C₇×D₅	—	10	2	no	—
9	C₅²×C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅⋊D₅	D₇	1	1	yes	characteristic
11	C₇⋊AGL(1,𝔽₅)	—	5	2	no	—
12	C₃×C₅×C₇	—	2	2	no	—
13	C₃×C₅×C₇	AGL(1,𝔽₅)	1	2	yes	complemented
14	#1044	—	7	1	no	Hall
15	C₃×Dic₇	—	25	1	no	Hall
16	C₃×C₅²	Dic₇	1	1	yes	characteristic, complemented, Hall
17	C₇×D₅	—	5	2	no	—
18	C₇×D₅	—	10	2	no	—
19	C₃×AGL(1,𝔽₅)	—	35	2	no	—
20	C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
21	C₂×C₃×C₇	—	25	1	no	—
22	C₅×C₇	—	2	2	no	—
23	C₅×C₇	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
24	C₃×D₅	—	5	2	no	—
25	C₃×D₅	—	10	2	no	—
26	Dic₇	—	25	1	no	Hall
27	C₅²	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₇	#1044	1	1	yes	characteristic, complemented, Hall
29	AGL(1,𝔽₅)	—	35	2	no	—
30	C₃×C₅	—	2	2	no	—
31	C₃×C₅	C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
32	C₂×C₇	—	25	1	no	—
33	C₃×C₄	—	175	1	no	Hall
34	D₅	—	5	2	no	—
35	D₅	—	10	2	no	—
36	C₇	C₃×#1044	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃×C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
40	C₄	—	175	1	no	Sylow
41	C₃	C₇⋊#1044	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊#1044
commutator, hypocenter	C₅²×C₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇	C₄
prime radical	C₃×C₇×C₅⋊D₅	C₂
cosocle	C₇×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇⋊#1044	C₃	direct (N × H)
3. C₃×C₅²×C₇	C₄	semidirect
9. C₅²×C₇	C₃×C₄	semidirect
13. C₃×C₅×C₇	AGL(1,𝔽₅)	semidirect
16. C₃×C₅²	Dic₇	semidirect
23. C₅×C₇	C₃×AGL(1,𝔽₅)	semidirect
27. C₅²	C₃×Dic₇	semidirect
28. C₃×C₇	#1044	semidirect
31. C₃×C₅	C₇⋊AGL(1,𝔽₅)	semidirect
36. C₇	C₃×#1044	semidirect
39. C₅	C₃×C₇⋊AGL(1,𝔽₅)	semidirect
41. C₃	C₇⋊#1044	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₅⋊D₅	2
C₇⋊#1044	3
C₃×C₇⋊AGL(1,𝔽₅)	5
C₃×#1044	7

Subgroups — C3×C7⋊#1044 #14523634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊#1044 #14523634