Subgroups — C₅×C₅⋊#11716326 #34093029

Order 19950.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊#11716326	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#11716326	—	5	1	no	maximal
5	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₅×D₅×C₁₉⋊C₃	—	7	1	no	maximal, Hall
7	C₅×#87705	—	2	2	no	—
8	C₅×#87705	D₅	1	1	yes	characteristic, complemented
9	C₅×#87705	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅²×C₁₉⋊C₃	—	7	1	no	Hall
11	C₁₉×D₃₅	C₃×C₅	1	1	yes	characteristic, complemented
12	C₅×D₇×C₁₉	—	5	1	no	—
13	C₅×C₅⋊AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
14	C₅×D₅×C₁₉	—	21	1	no	Hall
15	#11716326	—	5	1	no	Hall
16	C₅×C₇×C₁₉	—	2	2	no	—
17	C₅×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₅×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₂×C₅×C₁₉⋊C₃	—	35	1	no	—
20	D₅×C₁₉⋊C₃	—	7	1	no	—
21	C₅²×ΓL(1,𝔽₈)	—	19	1	no	Hall
22	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
23	#87705	C₅×D₅	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₅×C₁₉⋊C₃	—	7	1	no	—
26	C₅×C₁₉⋊C₃	—	7	1	no	—
27	C₅×C₁₉⋊C₃	—	14	2	no	—
28	D₇×C₁₉	—	5	1	no	Hall
29	C₅⋊AGL(1,𝔽₇)	—	19	1	no	—
30	C₅×AGL(1,𝔽₇)	—	95	1	no	—
31	C₂×C₅×C₁₉	—	105	1	no	—
32	D₅×C₁₉	—	7	1	no	—
33	C₅²×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×D₅	—	133	1	no	Hall
35	C₇×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₉⋊C₃	—	35	1	no	Hall
37	C₅×ΓL(1,𝔽₈)	—	19	1	no	—
38	C₅×ΓL(1,𝔽₈)	—	19	1	no	—
39	C₅×ΓL(1,𝔽₈)	—	38	2	no	—
40	C₅×C₁₉	—	2	2	no	—
41	C₅×C₁₉	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
43	C₃×C₅²	—	133	1	no	Hall
44	D₃₅	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
45	C₅×D₇	—	5	1	no	—
46	C₁₉⋊C₃	—	7	1	no	Hall
47	C₅×D₅	—	21	1	no	Hall
48	AGL(1,𝔽₇)	—	95	1	no	Hall
49	C₂×C₁₉	—	105	1	no	Hall
50	C₅×C₇	—	2	2	no	—
51	C₅×C₇	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
52	C₅×C₇	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅	—	665	1	no	—
54	C₃×D₅	—	133	1	no	—
55	C₅²	#11716326	1	1	yes	characteristic, complemented, Sylow
56	ΓL(1,𝔽₈)	—	19	1	no	Hall
57	C₁₉	C₅×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₅	—	266	2	no	—
59	C₃×C₅	—	133	1	no	—
60	C₃×C₅	—	133	1	no	—
61	D₇	—	5	1	no	Hall
62	C₂×C₅	—	35	1	no	—
63	D₅	—	21	1	no	—
64	C₇	C₅×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	665	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×#11716326	1	1	yes	characteristic, complemented
68	C₅	C₅⋊#11716326	1	1	yes	characteristic, direct product factor
69	C₃	—	133	1	no	Sylow
70	C₂	—	105	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₅⋊#11716326
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×#87705	C₂	semidirect
2. C₅×C₁₉×D₃₅	C₃	semidirect
3. C₅⋊#11716326	C₅	direct (N × H)
5. C₅²×C₇×C₁₉	C₂×C₃	semidirect
8. C₅×#87705	D₅	semidirect
9. C₅×#87705	C₂×C₅	semidirect
11. C₁₉×D₃₅	C₃×C₅	semidirect
17. C₅×C₇×C₁₉	C₃×D₅	semidirect
18. C₅×C₇×C₁₉	C₂×C₃×C₅	semidirect
22. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
23. #87705	C₅×D₅	semidirect
24. C₅×D₃₅	C₁₉⋊C₃	semidirect
33. C₅²×C₇	C₂×C₁₉⋊C₃	semidirect
35. C₇×C₁₉	C₃×C₅×D₅	semidirect
41. C₅×C₁₉	C₅×AGL(1,𝔽₇)	semidirect
42. C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
44. D₃₅	C₅×C₁₉⋊C₃	semidirect
51. C₅×C₇	D₅×C₁₉⋊C₃	semidirect
52. C₅×C₇	C₂×C₅×C₁₉⋊C₃	semidirect
55. C₅²	#11716326	semidirect
57. C₁₉	C₅×C₅⋊AGL(1,𝔽₇)	semidirect
64. C₇	C₅×D₅×C₁₉⋊C₃	semidirect
67. C₅	C₅×#11716326	semidirect
68. C₅	C₅⋊#11716326	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×#87705	2
C₅×C₁₉×D₃₅	3
C₅⋊#11716326	5
C₅×#11716326	5
C₅×D₅×C₁₉⋊C₃	7
C₅×C₅⋊AGL(1,𝔽₇)	19

Subgroups — C5×C5⋊#11716326 #34093029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₅⋊#11716326 #34093029