Subgroups — (C₅⋊D₅)⋊C₃×D₈₉ #40998917

Order 26700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉⋊((C₅⋊D₅)⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₈₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅²⋊C₃×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₄₄₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊D₅×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₈₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×C₈₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	D₅×D₈₉	—	15	2	no	—
11	C₂×C₃×D₈₉	—	25	1	no	maximal, Hall
12	D₄₄₅	—	15	2	no	—
13	C₅×D₈₉	—	3	2	no	—
14	D₅×C₈₉	—	15	2	no	—
15	C₂×C₃×C₈₉	—	25	1	no	—
16	C₃×D₈₉	—	25	1	no	—
17	C₃×D₈₉	—	50	1	no	—
18	C₅×C₈₉	—	3	2	no	—
19	C₂×D₈₉	—	25	1	no	Hall
20	C₂×(C₅⋊D₅)⋊C₃	—	89	1	no	maximal, Hall
21	C₃×C₈₉	—	50	1	no	Hall
22	C₂×C₈₉	—	25	1	no	—
23	D₈₉	—	25	1	no	—
24	D₈₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
25	C₂×C₅²⋊C₃	—	89	1	no	—
26	(C₅⋊D₅)⋊C₃	—	89	1	no	—
27	(C₅⋊D₅)⋊C₃	D₈₉	1	1	yes	characteristic, direct product factor
28	C₂×C₅⋊D₅	—	89	1	no	Hall
29	C₈₉	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₅²⋊C₃	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²	—	89	1	no	—
32	C₅⋊D₅	—	89	1	no	—
33	C₅⋊D₅	C₃×D₈₉	1	1	yes	characteristic, complemented
34	C₅²	C₂×C₃×D₈₉	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	1335	2	no	—
36	C₂²×C₃	—	2225	1	no	Hall
37	C₂×C₅	—	267	2	no	—
38	D₅	—	15	2	no	—
39	D₅	—	1335	2	no	—
40	C₂×C₃	—	25	1	no	—
41	C₂×C₃	—	4450	1	no	—
42	C₂×C₃	—	2225	1	no	—
43	C₅	—	3	2	no	—
44	C₂²	—	2225	1	no	Sylow
45	C₃	—	50	1	no	Sylow
46	C₂	—	25	1	no	—
47	C₂	—	89	1	no	—
48	C₂	—	2225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₈₉	C₂²×C₃
LCS	G ▷ C₅²×C₈₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²⋊C₃×D₈₉	C₂	semidirect
2. C₈₉⋊((C₅⋊D₅)⋊C₃)	C₂	semidirect
3. C₈₉×(C₅⋊D₅)⋊C₃	C₂	semidirect
4. C₅⋊D₅×D₈₉	C₃	semidirect
5. C₅²⋊C₃×C₈₉	C₂²	semidirect
6. C₅⋊D₄₄₅	C₂×C₃	semidirect
7. C₅⋊D₅×C₈₉	C₂×C₃	semidirect
8. C₅²×D₈₉	C₂×C₃	semidirect
9. C₅²×C₈₉	C₂²×C₃	semidirect
24. D₈₉	(C₅⋊D₅)⋊C₃	direct (N × H)
27. (C₅⋊D₅)⋊C₃	D₈₉	direct (N × H)
29. C₈₉	C₂×(C₅⋊D₅)⋊C₃	semidirect
30. C₅²⋊C₃	C₂×D₈₉	semidirect
33. C₅⋊D₅	C₃×D₈₉	semidirect
34. C₅²	C₂×C₃×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊C₃×D₈₉	2
C₈₉⋊((C₅⋊D₅)⋊C₃)	2
C₈₉×(C₅⋊D₅)⋊C₃	2
C₅⋊D₅×D₈₉	3
C₂×C₃×D₈₉	25
C₂×(C₅⋊D₅)⋊C₃	89

Subgroups — (C5⋊D5)⋊C3×D89 #40998917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊D₅)⋊C₃×D₈₉ #40998917