Subgroups — C₂×C₅⋊(C₂₃⋊(D₁₉⋊C₃)) #39910751

Order 26220.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₂₃⋊(D₁₉⋊C₃))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₁₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₂₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃⋊(D₁₉⋊C₃)	—	5	1	no	maximal, Hall
6	D₂₁₈₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₃⋊(D₁₉⋊C₃)	—	5	2	no	—
9	C₂×C₂₃×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₄₃₇	—	5	1	no	Hall
12	C₂×C₃×D₁₁₅	—	19	1	no	maximal, Hall
13	C₂₃×C₁₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅⋊(D₁₉⋊C₃)	—	23	1	no	maximal, Hall
15	C₂×C₁₉×C₂₃	C₃×D₅	1	1	yes	characteristic, complemented
16	D₄₃₇	—	5	2	no	—
17	C₂×C₃×C₅×C₂₃	—	38	1	no	—
18	C₃×D₁₁₅	—	19	2	no	—
19	C₂×C₅×C₁₉⋊C₃	D₂₃	1	1	yes	characteristic, complemented
20	C₅⋊(D₁₉⋊C₃)	—	23	2	no	—
21	C₂×D₁₁₅	—	19	1	no	Hall
22	C₁₉×C₂₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×D₉₅	—	23	1	no	Hall
24	C₃×C₅×C₂₃	—	38	1	no	Hall
25	C₅×C₁₉⋊C₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₂₃	—	95	1	no	Hall
27	C₂×C₅×C₂₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
28	D₁₁₅	—	19	2	no	—
29	C₂×D₁₉⋊C₃	—	115	1	no	Hall
30	C₂×C₅×C₁₉	C₃×D₂₃	1	1	yes	characteristic, complemented
31	D₉₅	—	23	2	no	—
32	C₂×C₃×C₂₃	—	38	1	no	—
33	C₃×D₂₃	—	95	2	no	—
34	C₅×C₂₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₁₉⋊C₃	D₁₁₅	1	1	yes	characteristic, complemented
36	D₁₉⋊C₃	—	115	2	no	—
37	C₅×C₁₉	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
38	C₂×D₂₃	—	95	1	no	Hall
39	C₂×D₁₉	—	115	1	no	Hall
40	C₃×C₂₃	—	38	1	no	Hall
41	C₂×C₃×D₅	—	437	1	no	Hall
42	C₁₉⋊C₃	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Hall
43	C₂×C₂₃	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
44	D₂₃	—	95	2	no	—
45	C₂×C₁₉	C₃×D₁₁₅	1	1	yes	characteristic, complemented
46	D₁₉	—	115	2	no	—
47	C₂×C₃×C₅	—	38	1	no	—
48	C₃×D₅	—	437	2	no	—
49	C₂₃	C₂×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₅	—	437	1	no	Hall
51	C₁₉	C₂×C₃×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	38	1	no	Hall
53	C₂²×C₃	—	2185	1	no	Hall
54	C₂×C₅	C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
55	D₅	—	437	2	no	—
56	C₂×C₃	—	19	1	no	—
57	C₂×C₃	—	2185	2	no	—
58	C₅	C₂×C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2185	1	no	Sylow
60	C₃	—	19	1	no	Sylow
61	C₂	—	2185	2	no	—
62	C₂	C₅⋊(C₂₃⋊(D₁₉⋊C₃))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₂₃⋊(D₁₉⋊C₃))
commutator, cosocle, hypocenter	C₅×C₁₉×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₅×C₁₉×C₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₂₃⋊(D₁₉⋊C₃))	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₁₉⋊C₃	C₂	semidirect
3. C₂×D₂₁₈₅	C₃	semidirect
4. C₅×C₂₃×C₁₉⋊C₃	C₂²	semidirect
6. D₂₁₈₅	C₂×C₃	semidirect
7. C₂×C₅×C₁₉×C₂₃	C₂×C₃	semidirect
9. C₂×C₂₃×C₁₉⋊C₃	D₅	semidirect
10. C₅×C₁₉×C₂₃	C₂²×C₃	semidirect
13. C₂₃×C₁₉⋊C₃	C₂×D₅	semidirect
15. C₂×C₁₉×C₂₃	C₃×D₅	semidirect
19. C₂×C₅×C₁₉⋊C₃	D₂₃	semidirect
22. C₁₉×C₂₃	C₂×C₃×D₅	semidirect
25. C₅×C₁₉⋊C₃	C₂×D₂₃	semidirect
27. C₂×C₅×C₂₃	D₁₉⋊C₃	semidirect
30. C₂×C₅×C₁₉	C₃×D₂₃	semidirect
34. C₅×C₂₃	C₂×D₁₉⋊C₃	semidirect
35. C₂×C₁₉⋊C₃	D₁₁₅	semidirect
37. C₅×C₁₉	C₂×C₃×D₂₃	semidirect
42. C₁₉⋊C₃	C₂×D₁₁₅	semidirect
43. C₂×C₂₃	C₅⋊(D₁₉⋊C₃)	semidirect
45. C₂×C₁₉	C₃×D₁₁₅	semidirect
49. C₂₃	C₂×C₅⋊(D₁₉⋊C₃)	semidirect
51. C₁₉	C₂×C₃×D₁₁₅	semidirect
54. C₂×C₅	C₂₃⋊(D₁₉⋊C₃)	semidirect
58. C₅	C₂×C₂₃⋊(D₁₉⋊C₃)	semidirect
62. C₂	C₅⋊(C₂₃⋊(D₁₉⋊C₃))	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊(C₂₃⋊(D₁₉⋊C₃))	2
C₂×C₅×C₂₃×C₁₉⋊C₃	2
C₂×D₂₁₈₅	3
C₂×C₂₃⋊(D₁₉⋊C₃)	5
C₂×C₃×D₁₁₅	19
C₂×C₅⋊(D₁₉⋊C₃)	23

Subgroups — C2×C5⋊(C23⋊(D19⋊C3)) #39910751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(C₂₃⋊(D₁₉⋊C₃)) #39910751