Subgroups — D₇⋊((C₅⋊D₅)⋊C₃) #14523613

Order 2100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760386	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇⋊(C₅²⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×(C₅⋊D₅)⋊C₃	—	7	1	no	maximal, Hall
10	C₅²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅²⋊C₃	—	7	1	no	—
12	(C₅⋊D₅)⋊C₃	—	7	1	no	—
13	(C₅⋊D₅)⋊C₃	—	7	1	no	—
14	D₅×D₇	—	15	2	no	—
15	C₂×C₅⋊D₅	—	7	1	no	Hall
16	C₂×AGL(1,𝔽₇)	—	25	1	no	maximal, Hall
17	C₅²⋊C₃	—	7	1	no	Hall
18	D₃₅	—	15	2	no	—
19	C₅×D₇	—	3	2	no	—
20	C₇×D₅	—	15	2	no	—
21	C₂×C₅²	—	7	1	no	—
22	C₅⋊D₅	—	7	1	no	—
23	C₅⋊D₅	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₂×ΓL(1,𝔽₈)	—	25	1	no	—
25	AGL(1,𝔽₇)	—	25	1	no	—
26	AGL(1,𝔽₇)	—	25	1	no	—
27	C₅×C₇	—	3	2	no	—
28	C₂×D₇	—	25	1	no	Hall
29	C₅²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
30	ΓL(1,𝔽₈)	—	25	1	no	Hall
31	C₂×D₅	—	105	2	no	—
32	C₂×C₇	—	25	1	no	—
33	D₇	—	25	1	no	—
34	D₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
35	C₂²×C₃	—	175	1	no	Hall
36	C₂×C₅	—	21	2	no	—
37	D₅	—	15	2	no	—
38	D₅	—	105	2	no	—
39	C₇	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	—	175	1	no	—
41	C₂×C₃	—	175	1	no	—
42	C₂×C₃	—	175	1	no	—
43	C₅	—	3	2	no	—
44	C₂²	—	175	1	no	Sylow
45	C₃	—	175	1	no	Sylow
46	C₂	—	7	1	no	—
47	C₂	—	25	1	no	—
48	C₂	—	175	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. #11760386	C₂	semidirect
2. (C₅⋊D₅)⋊ΓL(1,𝔽₈)	C₂	semidirect
3. D₇⋊(C₅²⋊C₃)	C₂	semidirect
4. D₇×C₅⋊D₅	C₃	semidirect
5. C₇⋊(C₅²⋊C₃)	C₂²	semidirect
6. C₅⋊D₃₅	C₂×C₃	semidirect
7. C₇×C₅⋊D₅	C₂×C₃	semidirect
8. C₅²×D₇	C₂×C₃	semidirect
10. C₅²×C₇	C₂²×C₃	semidirect
23. C₅⋊D₅	AGL(1,𝔽₇)	semidirect
29. C₅²	C₂×AGL(1,𝔽₇)	semidirect
34. D₇	(C₅⋊D₅)⋊C₃	semidirect
39. C₇	C₂×(C₅⋊D₅)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#11760386	2
(C₅⋊D₅)⋊ΓL(1,𝔽₈)	2
D₇⋊(C₅²⋊C₃)	2
D₇×C₅⋊D₅	3
C₂×(C₅⋊D₅)⋊C₃	7
C₂×AGL(1,𝔽₇)	25

Subgroups — D7⋊((C5⋊D5)⋊C3) #14523613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇⋊((C₅⋊D₅)⋊C₃) #14523613