Subgroups — C₂×C₅⋊D₅×#4294 #30685563

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#4294	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊D₅×#4294	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
4	C₅²×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅×#4294	—	5	6	no	maximal
6	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₁₉×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4294	D₅	1	6	yes	complemented
10	D₅×#4294	—	5	12	no	—
11	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₅×C₁₉	—	5	6	no	—
13	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₉×C₅⋊D₅	C₂×C₉	1	2	yes	complemented
15	C₂×C₉×C₅⋊D₅	—	19	1	no	maximal, Hall
16	C₅×#4294	C₂×D₅	1	6	yes	complemented
17	C₂²×#4294	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₉	C₃×D₅	1	6	yes	—
19	C₃×D₅×C₁₉	—	5	12	no	—
20	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²×C₉	—	19	1	no	—
22	C₉×C₅⋊D₅	—	19	2	no	—
23	C₂×D₅×C₁₉	—	5	6	no	—
24	C₂×#4294	—	25	2	no	—
25	C₂×#4294	C₅⋊D₅	1	1	yes	characteristic, direct product factor
26	C₂×C₃×C₅⋊D₅	C₁₉⋊C₃	1	1	yes	characteristic
27	C₃×C₅×C₁₉	C₂×C₃×D₅	1	6	yes	—
28	C₂²×C₃×C₁₉	—	25	1	no	—
29	C₅²×C₉	—	19	1	no	Hall
30	C₂×C₅×C₁₉	C₉×D₅	1	6	yes	complemented
31	D₅×C₁₉	—	5	12	no	—
32	C₂×C₉×D₅	—	95	6	no	—
33	#4294	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
35	C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	1	2	yes	—
36	C₂×C₃×C₁₉	—	25	2	no	—
37	C₂×C₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic
38	C₂×C₅⋊D₅	#4294	1	1	yes	characteristic, direct product factor, Hall
39	C₅×C₁₉	C₂×C₉×D₅	1	6	yes	complemented
40	C₂×C₅×C₉	—	19	6	no	—
41	C₉×D₅	—	95	12	no	—
42	C₂²×C₁₉	—	25	1	no	Hall
43	C₃×C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
44	C₂×C₃×D₅	—	5	6	no	—
45	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
46	C₂×C₅²	C₂×#4294	1	1	yes	characteristic, complemented
47	C₅⋊D₅	C₂×#4294	1	2	yes	direct product factor
48	C₅×C₉	—	19	6	no	—
49	C₂×C₁₉	—	25	2	no	—
50	C₂×C₁₉	C₉×C₅⋊D₅	1	1	yes	characteristic, complemented
51	C₂²×C₉	—	475	1	no	Hall
52	C₂×C₃×C₅	D₅×C₁₉⋊C₃	1	6	yes	—
53	C₃×D₅	—	5	12	no	—
54	C₅²	C₂²×#4294	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	5	6	no	—
56	C₁₉	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₉	—	19	1	no	—
58	C₂×C₉	—	475	2	no	—
59	C₃×C₅	C₂×D₅×C₁₉⋊C₃	1	6	yes	—
60	C₂²×C₃	—	25	1	no	—
61	C₂×C₅	D₅×#4294	1	6	yes	complemented
62	D₅	—	5	12	no	—
63	C₉	—	19	1	no	Sylow
64	C₂×C₃	—	25	2	no	—
65	C₂×C₃	C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic
66	C₅	C₂×D₅×#4294	1	6	yes	complemented
67	C₂²	—	25	1	no	Sylow
68	C₃	C₂×C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic
69	C₂	—	25	2	no	—
70	C₂	C₅⋊D₅×#4294	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₅×C₁₉⋊C₃
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₅⋊D₅×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₅⋊D₅	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#4294	C₂	semidirect
2. C₅⋊D₅×#4294	C₂	direct (N × H)
4. C₅²×#4294	C₂²	semidirect
8. C₂×C₁₉×C₅⋊D₅	C₉	semidirect
9. C₂×C₅×#4294	D₅	semidirect
13. C₂×C₅²×C₁₉	C₂×C₉	semidirect
14. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
16. C₅×#4294	C₂×D₅	semidirect
20. C₅²×C₁₉	C₂²×C₉	semidirect
25. C₂×#4294	C₅⋊D₅	direct (N × H)
30. C₂×C₅×C₁₉	C₉×D₅	semidirect
33. #4294	C₂×C₅⋊D₅	direct (N × H)
38. C₂×C₅⋊D₅	#4294	direct (N × H)
39. C₅×C₁₉	C₂×C₉×D₅	semidirect
46. C₂×C₅²	C₂×#4294	semidirect
47. C₅⋊D₅	C₂×#4294	direct (N × H)
50. C₂×C₁₉	C₉×C₅⋊D₅	semidirect
54. C₅²	C₂²×#4294	semidirect
56. C₁₉	C₂×C₉×C₅⋊D₅	semidirect
61. C₂×C₅	D₅×#4294	semidirect
66. C₅	C₂×D₅×#4294	semidirect
70. C₂	C₅⋊D₅×#4294	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×#4294	2
C₅⋊D₅×#4294	2
C₂×C₃×C₁₉×C₅⋊D₅	3
C₂×D₅×#4294	5
C₂×C₉×C₅⋊D₅	19

Subgroups — C2×C5⋊D5×#4294 #30685563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊D₅×#4294 #30685563