Subgroups — C₂×C₅²×#4294⋊C₂ #30685559

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	C₅²×#4294⋊C₂	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅²×D₁₉	C₃	1	1	yes	maximal, characteristic
4	C₅²×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×#4294⋊C₂	C₅	1	6	yes	maximal, direct product factor
6	C₃×C₅²×D₁₉	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅²×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×#4294	C₂×C₅	1	6	yes	complemented
10	C₅×#4294⋊C₂	C₂×C₅	1	12	yes	direct product factor
11	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×C₅×D₁₉	C₃×C₅	1	6	yes	—
13	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅²×D₁₉	C₂×C₉	1	2	yes	complemented
15	C₂²×C₅²×C₉	—	19	1	no	maximal, Hall
16	C₅×#4294	C₂²×C₅	1	6	yes	complemented
17	C₂×#4294⋊C₂	C₅²	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	6	yes	—
19	C₃×C₅×D₁₉	C₂×C₃×C₅	1	12	yes	—
20	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²×C₉	—	19	2	no	—
22	C₂×C₅²×C₉	—	19	1	no	—
23	C₂×C₅×D₁₉	C₅×C₉	1	6	yes	complemented
24	C₂×#4294	C₂×C₅²	1	1	yes	characteristic, complemented
25	#4294⋊C₂	C₂×C₅²	1	2	yes	direct product factor
26	C₂²×C₃×C₅²	—	19	1	no	—
27	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	—
28	C₂×C₃×D₁₉	C₃×C₅²	1	1	yes	characteristic
29	C₅²×C₉	—	19	1	no	Hall
30	C₂×C₅×C₁₉	C₂×C₅×C₉	1	6	yes	complemented
31	C₅×D₁₉	C₂×C₅×C₉	1	12	yes	complemented
32	C₂²×C₅×C₉	—	19	6	no	—
33	#4294	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅²	—	19	2	no	—
35	C₂×C₃×C₅²	D₁₉⋊C₃	1	1	yes	characteristic
36	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic
37	C₃×D₁₉	C₂×C₃×C₅²	1	2	yes	—
38	C₂²×C₅²	—	19	1	no	Hall
39	C₅×C₁₉	C₂²×C₅×C₉	1	6	yes	complemented
40	C₂×C₅×C₉	—	19	12	no	—
41	C₂×C₅×C₉	—	19	6	no	—
42	C₂×D₁₉	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
43	C₃×C₅²	C₂×D₁₉⋊C₃	1	1	yes	characteristic
44	C₂²×C₃×C₅	—	19	6	no	—
45	C₃×C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic
46	C₂×C₅²	—	19	2	no	—
47	C₂×C₅²	#4294⋊C₂	1	1	yes	characteristic, direct product factor
48	C₅×C₉	—	19	6	no	—
49	C₂×C₁₉	C₂×C₅²×C₉	1	1	yes	characteristic, complemented
50	D₁₉	C₂×C₅²×C₉	1	2	yes	complemented
51	C₂²×C₉	—	19	1	no	Hall
52	C₂×C₃×C₅	—	19	12	no	—
53	C₂×C₃×C₅	C₅×D₁₉⋊C₃	1	6	yes	—
54	C₅²	C₂×#4294⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	—	19	6	no	—
56	C₁₉	C₂²×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₉	—	19	2	no	—
58	C₂×C₉	—	19	1	no	—
59	C₃×C₅	C₂×C₅×D₁₉⋊C₃	1	6	yes	—
60	C₂²×C₃	—	19	1	no	—
61	C₂×C₅	—	19	12	no	—
62	C₂×C₅	C₅×#4294⋊C₂	1	6	yes	direct product factor
63	C₉	—	19	1	no	Sylow
64	C₂×C₃	—	19	2	no	—
65	C₂×C₃	C₅²×D₁₉⋊C₃	1	1	yes	characteristic
66	C₅	C₂×C₅×#4294⋊C₂	1	6	yes	direct product factor
67	C₂²	—	19	1	no	Sylow
68	C₃	C₂×C₅²×D₁₉⋊C₃	1	1	yes	characteristic
69	C₂	—	19	2	no	—
70	C₂	C₅²×#4294⋊C₂	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₅²×C₉
Frattini	C₃	C₂×C₅²×D₁₉⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅²×D₁₉	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₅²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#4294	C₂	semidirect
2. C₅²×#4294⋊C₂	C₂	direct (N × H)
4. C₅²×#4294	C₂²	semidirect
5. C₂×C₅×#4294⋊C₂	C₅	direct (N × H)
8. C₂×C₅²×D₁₉	C₉	semidirect
9. C₂×C₅×#4294	C₂×C₅	semidirect
10. C₅×#4294⋊C₂	C₂×C₅	direct (N × H)
13. C₂×C₅²×C₁₉	C₂×C₉	semidirect
14. C₅²×D₁₉	C₂×C₉	semidirect
16. C₅×#4294	C₂²×C₅	semidirect
17. C₂×#4294⋊C₂	C₅²	direct (N × H)
20. C₅²×C₁₉	C₂²×C₉	semidirect
23. C₂×C₅×D₁₉	C₅×C₉	semidirect
24. C₂×#4294	C₂×C₅²	semidirect
25. #4294⋊C₂	C₂×C₅²	direct (N × H)
30. C₂×C₅×C₁₉	C₂×C₅×C₉	semidirect
31. C₅×D₁₉	C₂×C₅×C₉	semidirect
33. #4294	C₂²×C₅²	semidirect
39. C₅×C₁₉	C₂²×C₅×C₉	semidirect
42. C₂×D₁₉	C₅²×C₉	semidirect
47. C₂×C₅²	#4294⋊C₂	direct (N × H)
49. C₂×C₁₉	C₂×C₅²×C₉	semidirect
50. D₁₉	C₂×C₅²×C₉	semidirect
54. C₅²	C₂×#4294⋊C₂	direct (N × H)
56. C₁₉	C₂²×C₅²×C₉	semidirect
62. C₂×C₅	C₅×#4294⋊C₂	direct (N × H)
66. C₅	C₂×C₅×#4294⋊C₂	direct (N × H)
70. C₂	C₅²×#4294⋊C₂	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
C₅²×#4294⋊C₂	2
C₂×C₃×C₅²×D₁₉	3
C₂×C₅×#4294⋊C₂	5
C₂²×C₅²×C₉	19

Subgroups — C2×C52×#4294⋊C2 #30685559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×#4294⋊C₂ #30685559