Subgroups — D₇×C₇⋊(C₅²⋊C₃) #20301307

Order 7350.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₇×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇⋊(C₅²⋊C₃)	—	7	1	no	maximal
5	D₇×C₅²⋊C₃	—	7	1	no	maximal
6	C₇⋊(C₅²⋊C₃)	D₇	1	1	yes	characteristic, direct product factor
7	C₇×C₅²⋊C₃	—	7	1	no	—
8	C₅×C₇×D₇	—	3	2	no	—
9	C₂×C₅²×C₇	—	7	1	no	—
10	C₅²×D₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	D₇×ΓL(1,𝔽₈)	—	25	1	no	maximal, Hall
12	C₅×C₇²	—	3	2	no	—
13	C₅²×C₇	—	6	1	no	—
14	C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
16	C₂×C₅²⋊C₃	—	49	1	no	Hall
17	C₇×ΓL(1,𝔽₈)	—	25	1	no	Hall
18	C₇×D₇	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₅²⋊C₃	—	7	1	no	Hall
20	C₂×C₅×C₇	—	21	2	no	—
21	C₅×D₇	—	3	2	no	—
22	C₂×C₅²	—	7	1	no	Hall
23	C₇²	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₇	—	175	1	no	—
25	C₂×ΓL(1,𝔽₈)	—	175	1	no	—
26	C₅×C₇	—	3	2	no	—
27	C₅×C₇	—	3	2	no	—
28	C₅×C₇	—	6	6	no	—
29	C₅²	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₇	—	175	1	no	—
31	ΓL(1,𝔽₈)	—	25	1	no	—
32	C₂×C₇	—	7	1	no	—
33	D₇	C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
34	C₂×C₅	—	21	2	no	—
35	C₇	—	6	1	no	—
36	C₇	D₇×C₅²⋊C₃	1	1	yes	characteristic, complemented
37	C₇	C₂×C₇⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
38	C₂×C₃	—	1225	1	no	Hall
39	C₅	—	3	2	no	—
40	C₃	—	175	1	no	Sylow
41	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₇⋊(C₅²⋊C₃)	C₂	semidirect
2. C₅²×C₇×D₇	C₃	semidirect
3. C₅²×C₇²	C₂×C₃	semidirect
6. C₇⋊(C₅²⋊C₃)	D₇	direct (N × H)
10. C₅²×D₇	ΓL(1,𝔽₈)	semidirect
14. C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
15. C₅²×C₇	C₃×D₇	semidirect
18. C₇×D₇	C₅²⋊C₃	semidirect
23. C₇²	C₂×C₅²⋊C₃	semidirect
29. C₅²	D₇×ΓL(1,𝔽₈)	semidirect
33. D₇	C₇⋊(C₅²⋊C₃)	direct (N × H)
36. C₇	D₇×C₅²⋊C₃	semidirect
37. C₇	C₂×C₇⋊(C₅²⋊C₃)	semidirect

Subgroups — D7×C7⋊(C52⋊C3) #20301307

Conjugacy classes of subgroups

Complements

Subgroups — D₇×C₇⋊(C₅²⋊C₃) #20301307