Subgroups — C₅⋊(C₅⋊#11716322) #34093049

Order 19950.

128 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	C₇×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊#11716322	—	5	4	no	maximal
4	C₅⋊#11716322	—	5	1	no	maximal
5	C₅⋊#11716322	—	5	1	no	maximal
6	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
7	C₅⋊(C₅⋊(D₁₉⋊C₃))	—	7	1	no	maximal, Hall
8	C₅×#87705	D₅	1	4	yes	complemented
9	C₅×#87705	D₅	1	1	yes	characteristic, complemented
10	C₅×#87705	D₅	1	1	yes	characteristic, complemented
11	C₅²×C₁₉⋊C₃	—	7	1	no	Hall
12	C₇×D₉₅	—	5	4	no	—
13	C₇×D₉₅	—	5	1	no	—
14	C₇×D₉₅	—	5	1	no	—
15	ΓL(1,𝔽₈)×C₅⋊D₅	—	19	1	no	maximal, Hall
16	C₅⋊D₉₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
17	#11716322	—	25	1	no	Hall
18	C₅×C₇×C₁₉	C₃×D₅	1	4	yes	complemented
19	C₅×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
20	C₅×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
21	C₅⋊(D₁₉⋊C₃)	—	35	4	no	—
22	C₅⋊(D₁₉⋊C₃)	—	35	1	no	—
23	C₅⋊(D₁₉⋊C₃)	—	35	1	no	—
24	C₅²×ΓL(1,𝔽₈)	—	19	1	no	Hall
25	C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
26	#87705	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₇×C₅⋊D₅	—	57	1	no	Hall
28	C₅×C₁₉⋊C₃	—	7	4	no	—
29	C₅×C₁₉⋊C₃	—	7	1	no	—
30	C₅×C₁₉⋊C₃	—	7	1	no	—
31	C₇×D₁₉	—	25	1	no	Hall
32	D₅×ΓL(1,𝔽₈)	—	95	4	no	—
33	D₅×ΓL(1,𝔽₈)	—	95	1	no	—
34	D₅×ΓL(1,𝔽₈)	—	95	1	no	—
35	D₉₅	—	5	4	no	—
36	D₉₅	—	5	1	no	—
37	D₉₅	—	5	1	no	—
38	C₅²×C₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅⋊D₅	—	133	1	no	Hall
40	C₇×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
41	D₁₉⋊C₃	—	175	1	no	Hall
42	C₅×ΓL(1,𝔽₈)	—	19	4	no	—
43	C₅×ΓL(1,𝔽₈)	—	19	1	no	—
44	C₅×ΓL(1,𝔽₈)	—	19	1	no	—
45	C₅×C₁₉	D₅×ΓL(1,𝔽₈)	1	4	yes	complemented
46	C₅×C₁₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
47	C₅×C₁₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
48	C₃×C₅²	—	133	1	no	Hall
49	C₇×D₅	—	285	4	no	—
50	C₇×D₅	—	285	1	no	—
51	C₇×D₅	—	95	1	no	—
52	C₁₉⋊C₃	—	7	1	no	Hall
53	C₅⋊D₅	—	57	1	no	Hall
54	C₂×ΓL(1,𝔽₈)	—	475	1	no	Hall
55	D₁₉	—	25	1	no	Hall
56	C₅×C₇	C₅⋊(D₁₉⋊C₃)	1	4	yes	complemented
57	C₅×C₇	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
58	C₅×C₇	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
59	C₃×D₅	—	665	4	no	—
60	C₃×D₅	—	665	1	no	—
61	C₃×D₅	—	665	1	no	—
62	C₅²	#11716322	1	1	yes	characteristic, complemented, Sylow
63	ΓL(1,𝔽₈)	—	19	1	no	Hall
64	C₁₉	ΓL(1,𝔽₈)×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	133	4	no	—
66	C₃×C₅	—	133	1	no	—
67	C₃×C₅	—	133	1	no	—
68	C₂×C₇	—	1425	1	no	Hall
69	D₅	—	285	4	no	—
70	D₅	—	285	1	no	—
71	D₅	—	95	1	no	—
72	C₇	C₅⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3325	1	no	Hall
74	C₅	C₅⋊#11716322	1	4	yes	complemented
75	C₅	C₅⋊#11716322	1	1	yes	characteristic, complemented
76	C₅	C₅⋊#11716322	1	1	yes	characteristic, complemented
77	C₃	—	133	1	no	Sylow
78	C₂	—	1425	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅²×#87705	C₂	semidirect
2. C₇×C₅⋊D₉₅	C₃	semidirect
6. C₅²×C₇×C₁₉	C₂×C₃	semidirect
8. C₅×#87705	D₅	semidirect
9. C₅×#87705	D₅	semidirect
10. C₅×#87705	D₅	semidirect
16. C₅⋊D₉₅	ΓL(1,𝔽₈)	semidirect
18. C₅×C₇×C₁₉	C₃×D₅	semidirect
19. C₅×C₇×C₁₉	C₃×D₅	semidirect
20. C₅×C₇×C₁₉	C₃×D₅	semidirect
25. C₅²×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
26. #87705	C₅⋊D₅	semidirect
38. C₅²×C₇	D₁₉⋊C₃	semidirect
40. C₇×C₁₉	C₃×C₅⋊D₅	semidirect
45. C₅×C₁₉	D₅×ΓL(1,𝔽₈)	semidirect
46. C₅×C₁₉	D₅×ΓL(1,𝔽₈)	semidirect
47. C₅×C₁₉	D₅×ΓL(1,𝔽₈)	semidirect
56. C₅×C₇	C₅⋊(D₁₉⋊C₃)	semidirect
57. C₅×C₇	C₅⋊(D₁₉⋊C₃)	semidirect
58. C₅×C₇	C₅⋊(D₁₉⋊C₃)	semidirect
62. C₅²	#11716322	semidirect
64. C₁₉	ΓL(1,𝔽₈)×C₅⋊D₅	semidirect
72. C₇	C₅⋊(C₅⋊(D₁₉⋊C₃))	semidirect
74. C₅	C₅⋊#11716322	semidirect
75. C₅	C₅⋊#11716322	semidirect
76. C₅	C₅⋊#11716322	semidirect

Maximal subgroups

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

subgroup	index
C₅²×#87705	2
C₇×C₅⋊D₉₅	3
C₅⋊#11716322	5
C₅⋊(C₅⋊(D₁₉⋊C₃))	7
ΓL(1,𝔽₈)×C₅⋊D₅	19

Subgroups — C5⋊(C5⋊#11716322) #34093049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₅⋊#11716322) #34093049