Subgroups — C₅×C₇×#63122 #22603268

Order 9100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#63122	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₇×#261	—	5	1	no	maximal
5	C₅×#63122	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₆₅	C₂×C₅	1	1	yes	characteristic
7	C₅×C₇×D₁₃	—	5	1	no	—
8	C₅×C₇×AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
9	C₅×D₆₅	C₂×C₇	1	1	yes	characteristic
10	C₅×C₇×C₁₃	—	4	1	no	—
11	C₅×C₇×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented
12	C₅×C₇×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
13	C₇×#261	—	5	1	no	Hall
14	C₅×C₇×D₅	—	13	1	no	—
15	C₅²×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
16	#63122	C₅×C₇	1	1	yes	characteristic, direct product factor
17	C₅×#261	—	5	1	no	—
18	C₇×D₁₃	—	5	1	no	—
19	C₅²×C₇	#261	1	1	yes	characteristic, complemented, Hall
20	C₇×AGL(1,𝔽₅)	—	13	1	no	—
21	C₄×C₅×C₇	—	65	1	no	—
22	D₆₅	C₂×C₅×C₇	1	1	yes	characteristic
23	C₅×D₁₃	—	5	1	no	—
24	C₅×AGL(1,𝔽₅)	—	13	1	no	Hall
25	C₇×C₁₃	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₇	—	65	1	no	—
27	C₇×D₅	—	13	1	no	—
28	C₅×C₁₃	—	4	1	no	—
29	C₅×C₁₃	C₄×C₅×C₇	1	1	yes	characteristic, complemented
30	C₅×C₁₃	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
31	#261	—	5	1	no	Hall
32	C₅×D₅	—	13	1	no	—
33	C₅×C₇	—	4	1	no	—
34	C₅×C₇	C₅×#261	1	1	yes	characteristic, complemented
35	C₅×C₇	#63122	1	1	yes	characteristic, direct product factor
36	C₄×C₇	—	65	1	no	Hall
37	D₁₃	—	5	1	no	—
38	C₅²	C₇×#261	1	1	yes	characteristic, complemented, Sylow
39	AGL(1,𝔽₅)	—	13	1	no	—
40	C₄×C₅	—	65	1	no	—
41	C₂×C₇	—	65	1	no	—
42	C₁₃	C₅×C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₅	—	65	1	no	—
44	D₅	—	13	1	no	—
45	C₇	C₅×#63122	1	1	yes	characteristic, direct product factor, Sylow
46	C₅	—	4	1	no	—
47	C₅	C₅×C₇×#261	1	1	yes	characteristic, complemented
48	C₅	C₇×#63122	1	1	yes	characteristic, direct product factor
49	C₄	—	65	1	no	Sylow
50	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	#63122
commutator, hypocenter	C₅×C₁₃	C₄×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₃	C₄
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₁₃	C₄	semidirect
3. C₇×#63122	C₅	direct (N × H)
5. C₅×#63122	C₇	direct (N × H)
11. C₅×C₇×C₁₃	C₄×C₅	semidirect
12. C₅×C₇×C₁₃	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₃	C₄×C₇	semidirect
16. #63122	C₅×C₇	direct (N × H)
19. C₅²×C₇	#261	semidirect
25. C₇×C₁₃	C₅×AGL(1,𝔽₅)	semidirect
29. C₅×C₁₃	C₄×C₅×C₇	semidirect
30. C₅×C₁₃	C₇×AGL(1,𝔽₅)	semidirect
34. C₅×C₇	C₅×#261	semidirect
35. C₅×C₇	#63122	direct (N × H)
38. C₅²	C₇×#261	semidirect
42. C₁₃	C₅×C₇×AGL(1,𝔽₅)	semidirect
45. C₇	C₅×#63122	direct (N × H)
47. C₅	C₅×C₇×#261	semidirect
48. C₅	C₇×#63122	direct (N × H)

Subgroups — C5×C7×#63122 #22603268

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₇×#63122 #22603268