Subgroups — (C₅⋊D₅)⋊#89204 #36347828

Order 22050.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊#89204	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic
4	(C₅⋊D₅)⋊(C₇⋊C₉)	—	7	1	no	maximal
5	(C₅⋊D₅)⋊(C₇⋊C₉)	—	7	7	no	maximal
6	C₇²×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇⋊(C₅²⋊C₉)	—	7	1	no	—
8	C₇⋊(C₅²⋊C₉)	—	7	7	no	—
9	C₃×C₇²×D₅	—	15	2	no	—
10	C₅²×C₇²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₅⋊D₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₃×C₇×C₅⋊D₅	ΓL(1,𝔽₈)	1	7	yes	—
13	C₂×#89204	—	25	1	no	maximal, Hall
14	C₃×C₅×C₇²	—	3	2	no	—
15	C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	7	yes	—
17	C₇²×D₅	—	15	2	no	—
18	(C₅⋊D₅)⋊C₉	—	49	1	no	Hall
19	#89204	—	25	1	no	Hall
20	C₇×C₅⋊D₅	C₇⋊C₉	1	1	yes	characteristic, complemented
21	C₇×C₅⋊D₅	C₇⋊C₉	1	7	yes	complemented
22	C₂×C₃×C₇²	—	75	1	no	—
23	C₅×C₇²	—	3	2	no	—
24	C₅²⋊C₉	—	49	1	no	Hall
25	C₃×C₇×D₅	—	15	2	no	—
26	C₃×C₇×D₅	—	15	14	no	—
27	C₅²×C₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
28	C₅²×C₇	C₂×C₇⋊C₉	1	7	yes	complemented
29	C₃×C₅⋊D₅	#3861	1	1	yes	characteristic
30	C₃×C₇²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
31	C₂×C₇⋊C₉	—	175	1	no	—
32	C₂×C₇⋊C₉	—	175	7	no	—
33	C₃×C₅×C₇	—	3	2	no	—
34	C₃×C₅×C₇	—	3	14	no	—
35	C₂×C₇²	—	75	1	no	Hall
36	C₃×C₅²	C₂×#3861	1	1	yes	characteristic
37	C₇×D₅	—	15	2	no	—
38	C₇×D₅	—	15	14	no	—
39	C₇⋊C₉	—	175	1	no	—
40	C₇⋊C₉	—	175	7	no	—
41	C₅⋊D₅	#89204	1	1	yes	characteristic, complemented, Hall
42	C₇²	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×C₇	—	25	1	no	—
44	C₂×C₃×C₇	—	75	7	no	—
45	C₅×C₇	—	3	2	no	—
46	C₅×C₇	—	3	14	no	—
47	C₃×D₅	—	15	2	no	—
48	C₅²	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
49	C₃×C₇	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	1	1	yes	characteristic
50	C₃×C₇	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	1	7	yes	—
51	C₂×C₉	—	1225	1	no	Hall
52	C₃×C₅	—	3	2	no	—
53	C₂×C₇	—	25	1	no	—
54	C₂×C₇	—	75	7	no	—
55	D₅	—	15	2	no	—
56	C₉	—	1225	1	no	Sylow
57	C₇	(C₅⋊D₅)⋊(C₇⋊C₉)	1	1	yes	characteristic, complemented
58	C₇	(C₅⋊D₅)⋊(C₇⋊C₉)	1	7	yes	complemented
59	C₂×C₃	—	75	1	no	—
60	C₅	—	3	2	no	—
61	C₃	(C₅⋊D₅)⋊#3861	1	1	yes	characteristic
62	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₅⋊D₅)⋊#3861
commutator, hypocenter	C₅²×C₇²	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²×C₇²	C₂×C₃
prime radical	C₃×C₇²×C₅⋊D₅	C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅²⋊#89204	C₂	semidirect
6. C₇²×C₅⋊D₅	C₉	semidirect
10. C₅²×C₇²	C₂×C₉	semidirect
20. C₇×C₅⋊D₅	C₇⋊C₉	semidirect
21. C₇×C₅⋊D₅	C₇⋊C₉	semidirect
27. C₅²×C₇	C₂×C₇⋊C₉	semidirect
28. C₅²×C₇	C₂×C₇⋊C₉	semidirect
41. C₅⋊D₅	#89204	semidirect
42. C₇²	(C₅⋊D₅)⋊C₉	semidirect
48. C₅²	C₂×#89204	semidirect
57. C₇	(C₅⋊D₅)⋊(C₇⋊C₉)	semidirect
58. C₇	(C₅⋊D₅)⋊(C₇⋊C₉)	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊#89204	2
C₃×C₇²×C₅⋊D₅	3
(C₅⋊D₅)⋊(C₇⋊C₉)	7
C₂×#89204	25

Subgroups — (C5⋊D5)⋊#89204 #36347828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊D₅)⋊#89204 #36347828