Subgroups — C₂×C₅⋊#11716325 #22547686

Order 7980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#11716325	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#87704	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#87704	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#11716325	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₉×D₃₅	C₂×C₃	1	2	yes	complemented
8	C₂×D₅×C₁₉⋊C₃	—	7	1	no	maximal, Hall
9	C₂×#87704	D₅	1	1	yes	characteristic, complemented
10	#11716325	—	5	2	no	—
11	C₅×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₁₉⋊C₃	—	7	1	no	—
13	D₅×C₁₉⋊C₃	—	7	2	no	—
14	C₂×D₇×C₁₉	—	5	1	no	Hall
15	C₂×C₅⋊AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
16	#87704	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×D₅×C₁₉	—	7	1	no	Hall
18	C₅×C₁₉⋊C₃	—	7	1	no	Hall
19	C₂×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
20	D₇×C₁₉	—	5	2	no	—
21	C₂²×C₁₉⋊C₃	—	35	1	no	Hall
22	C₂×C₅×ΓL(1,𝔽₈)	—	19	1	no	—
23	C₅⋊AGL(1,𝔽₇)	—	19	2	no	—
24	C₂×C₅×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	D₅×C₁₉	—	7	2	no	—
26	C₂×D₃₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₉⋊C₃	—	7	1	no	—
29	C₂×C₁₉⋊C₃	—	35	2	no	—
30	C₅×ΓL(1,𝔽₈)	—	19	1	no	Hall
31	C₅×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
32	C₂×AGL(1,𝔽₇)	—	95	1	no	Hall
33	C₂²×C₁₉	—	35	1	no	Hall
34	C₂×C₅×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	D₃₅	C₂×C₁₉⋊C₃	1	2	yes	complemented
36	C₂×C₃×D₅	—	133	1	no	Hall
37	C₁₉⋊C₃	—	7	1	no	Hall
38	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
39	AGL(1,𝔽₇)	—	95	2	no	—
40	C₂×C₁₉	—	35	2	no	—
41	C₂×C₁₉	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₅×C₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	—	133	1	no	—
44	C₃×D₅	—	133	2	no	—
45	C₂×D₇	—	5	1	no	Hall
46	ΓL(1,𝔽₈)	—	19	1	no	Hall
47	C₂×D₅	—	7	1	no	Hall
48	C₁₉	C₂×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
49	C₃×C₅	—	133	1	no	Hall
50	C₂×C₇	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
51	D₇	—	5	2	no	—
52	C₂²×C₃	—	665	1	no	Hall
53	C₂×C₅	#11716325	1	1	yes	characteristic, complemented
54	D₅	—	7	2	no	—
55	C₇	C₂×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	133	1	no	—
57	C₂×C₃	—	665	2	no	—
58	C₅	C₂×#11716325	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	35	1	no	Sylow
60	C₃	—	133	1	no	Sylow
61	C₂	—	35	2	no	—
62	C₂	C₅⋊#11716325	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#11716325
commutator, hypocenter	C₅×C₇×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊#11716325	C₂	direct (N × H)
2. C₂×C₅×#87704	C₂	semidirect
3. C₂×C₁₉×D₃₅	C₃	semidirect
4. C₅×#87704	C₂²	semidirect
6. C₂×C₅×C₇×C₁₉	C₂×C₃	semidirect
7. C₁₉×D₃₅	C₂×C₃	semidirect
9. C₂×#87704	D₅	semidirect
11. C₅×C₇×C₁₉	C₂²×C₃	semidirect
16. #87704	C₂×D₅	semidirect
19. C₂×C₇×C₁₉	C₃×D₅	semidirect
24. C₂×C₅×C₁₉	AGL(1,𝔽₇)	semidirect
26. C₂×D₃₅	C₁₉⋊C₃	semidirect
27. C₇×C₁₉	C₂×C₃×D₅	semidirect
31. C₅×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
34. C₂×C₅×C₇	C₂×C₁₉⋊C₃	semidirect
35. D₃₅	C₂×C₁₉⋊C₃	semidirect
41. C₂×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
42. C₅×C₇	C₂²×C₁₉⋊C₃	semidirect
48. C₁₉	C₂×C₅⋊AGL(1,𝔽₇)	semidirect
50. C₂×C₇	D₅×C₁₉⋊C₃	semidirect
53. C₂×C₅	#11716325	semidirect
55. C₇	C₂×D₅×C₁₉⋊C₃	semidirect
58. C₅	C₂×#11716325	semidirect
62. C₂	C₅⋊#11716325	direct (N × H)

Subgroups — C2×C5⋊#11716325 #22547686

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊#11716325 #22547686