Subgroups — C₂×C₈₉×(C₅⋊D₅)⋊C₃ #40998931

Order 26700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊C₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×(C₅⋊D₅)⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₅×C₈₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅²⋊C₃×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅⋊D₅×C₈₉	C₂×C₃	1	2	yes	complemented
6	C₂×C₅²×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×C₈₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅×C₈₉	—	15	2	no	—
9	C₂²×C₃×C₈₉	—	25	1	no	maximal, Hall
10	C₂×C₅×C₈₉	—	3	2	no	—
11	D₅×C₈₉	—	15	4	no	—
12	C₂×C₃×C₈₉	—	25	2	no	—
13	C₂×C₃×C₈₉	—	25	1	no	—
14	C₅×C₈₉	—	3	2	no	—
15	C₂²×C₈₉	—	25	1	no	Hall
16	C₂×(C₅⋊D₅)⋊C₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₈₉	—	25	1	no	Hall
18	C₂×C₈₉	—	25	2	no	—
19	C₂×C₈₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
20	C₂×C₅²⋊C₃	C₂×C₈₉	1	1	yes	characteristic, complemented
21	(C₅⋊D₅)⋊C₃	C₂×C₈₉	1	2	yes	direct product factor
22	C₂×C₅⋊D₅	C₃×C₈₉	1	1	yes	characteristic, complemented, Hall
23	C₈₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₅²⋊C₃	C₂²×C₈₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅²	C₂×C₃×C₈₉	1	1	yes	characteristic, complemented
26	C₅⋊D₅	C₂×C₃×C₈₉	1	2	yes	complemented
27	C₅²	C₂²×C₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×D₅	—	15	2	no	—
29	C₂²×C₃	—	25	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	15	4	no	—
32	C₂×C₃	—	25	2	no	—
33	C₂×C₃	—	25	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	25	1	no	Sylow
36	C₃	—	25	1	no	Sylow
37	C₂	—	25	2	no	—
38	C₂	C₈₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₈₉	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₈₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₈₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊C₃×C₈₉	C₂	semidirect
2. C₈₉×(C₅⋊D₅)⋊C₃	C₂	direct (N × H)
3. C₂×C₅⋊D₅×C₈₉	C₃	semidirect
4. C₅²⋊C₃×C₈₉	C₂²	semidirect
5. C₅⋊D₅×C₈₉	C₂×C₃	semidirect
6. C₂×C₅²×C₈₉	C₂×C₃	semidirect
7. C₅²×C₈₉	C₂²×C₃	semidirect
16. C₂×(C₅⋊D₅)⋊C₃	C₈₉	direct (N × H)
19. C₂×C₈₉	(C₅⋊D₅)⋊C₃	direct (N × H)
20. C₂×C₅²⋊C₃	C₂×C₈₉	semidirect
21. (C₅⋊D₅)⋊C₃	C₂×C₈₉	direct (N × H)
22. C₂×C₅⋊D₅	C₃×C₈₉	semidirect
23. C₈₉	C₂×(C₅⋊D₅)⋊C₃	direct (N × H)
24. C₅²⋊C₃	C₂²×C₈₉	semidirect
25. C₂×C₅²	C₂×C₃×C₈₉	semidirect
26. C₅⋊D₅	C₂×C₃×C₈₉	semidirect
27. C₅²	C₂²×C₃×C₈₉	semidirect
38. C₂	C₈₉×(C₅⋊D₅)⋊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
C₂×C₅²⋊C₃×C₈₉	2
C₈₉×(C₅⋊D₅)⋊C₃	2
C₂×C₅⋊D₅×C₈₉	3
C₂²×C₃×C₈₉	25
C₂×(C₅⋊D₅)⋊C₃	89

Subgroups — C2×C89×(C5⋊D5)⋊C3 #40998931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×(C₅⋊D₅)⋊C₃ #40998931