Subgroups — C₂×C₉×D₁₀₀₇ #49136239

Order 36252.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₁₀₀₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₀₀₇	C₃	1	1	yes	maximal, characteristic
4	C₉×C₁₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₀₀₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₁₉×C₅₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₀₀₇	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₉×C₅₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₁₉×C₅₃	C₂×C₉	1	1	yes	characteristic, complemented
10	D₁₀₀₇	C₂×C₉	1	2	yes	direct product factor
11	C₂×C₉×D₅₃	—	19	1	no	maximal, Hall
12	C₁₉×C₅₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₅₃	D₁₉	1	1	yes	characteristic, complemented
14	C₉×D₅₃	—	19	2	no	—
15	C₂×C₉×D₁₉	—	53	1	no	maximal, Hall
16	C₂×C₃×D₅₃	—	19	1	no	—
17	C₉×C₅₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₉×C₁₉	D₅₃	1	1	yes	characteristic, complemented
19	C₉×D₁₉	—	53	2	no	—
20	C₂×C₃×C₅₃	C₃×D₁₉	1	1	yes	characteristic
21	C₃×D₅₃	—	19	2	no	—
22	C₂×C₃×D₁₉	—	53	1	no	—
23	C₂×D₅₃	—	19	1	no	Hall
24	C₉×C₁₉	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅₃	C₂×C₃×D₁₉	1	1	yes	characteristic
26	C₂×C₃×C₁₉	C₃×D₅₃	1	1	yes	characteristic
27	C₃×D₁₉	—	53	2	no	—
28	C₂×C₅₃	C₉×D₁₉	1	1	yes	characteristic, complemented
29	D₅₃	—	19	2	no	—
30	C₂×D₁₉	—	53	1	no	Hall
31	C₃×C₁₉	C₂×C₃×D₅₃	1	1	yes	characteristic
32	C₅₃	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₉	C₉×D₅₃	1	1	yes	characteristic, complemented
34	D₁₉	—	53	2	no	—
35	C₂²×C₉	—	1007	1	no	Hall
36	C₁₉	C₂×C₉×D₅₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	1007	2	no	—
38	C₂×C₉	D₁₀₀₇	1	1	yes	characteristic, direct product factor
39	C₂²×C₃	—	1007	1	no	—
40	C₉	C₂×D₁₀₀₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	1007	2	no	—
42	C₂×C₃	C₃×D₁₀₀₇	1	1	yes	characteristic
43	C₂²	—	1007	1	no	Sylow
44	C₃	C₂×C₃×D₁₀₀₇	1	1	yes	characteristic
45	C₂	—	1007	2	no	—
46	C₂	C₉×D₁₀₀₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₀₀₇
commutator, hypocenter	C₁₉×C₅₃	C₂²×C₉
Frattini	C₃	C₂×C₃×D₁₀₀₇
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle	C₂×C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₂×C₃×D₁₀₀₇	C₃
cosocle	C₃×C₁₉×C₅₃	C₂²×C₃
LCS	G ▷ C₁₉×C₅₃
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₁₀₀₇	C₂	direct (N × H)
2. C₂×C₉×C₁₉×C₅₃	C₂	semidirect
4. C₉×C₁₉×C₅₃	C₂²	semidirect
7. C₂×D₁₀₀₇	C₉	direct (N × H)
9. C₂×C₁₉×C₅₃	C₂×C₉	semidirect
10. D₁₀₀₇	C₂×C₉	direct (N × H)
12. C₁₉×C₅₃	C₂²×C₉	semidirect
13. C₂×C₉×C₅₃	D₁₉	semidirect
17. C₉×C₅₃	C₂×D₁₉	semidirect
18. C₂×C₉×C₁₉	D₅₃	semidirect
24. C₉×C₁₉	C₂×D₅₃	semidirect
28. C₂×C₅₃	C₉×D₁₉	semidirect
32. C₅₃	C₂×C₉×D₁₉	semidirect
33. C₂×C₁₉	C₉×D₅₃	semidirect
36. C₁₉	C₂×C₉×D₅₃	semidirect
38. C₂×C₉	D₁₀₀₇	direct (N × H)
40. C₉	C₂×D₁₀₀₇	direct (N × H)
46. C₂	C₉×D₁₀₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₁₀₀₇	2
C₂×C₉×C₁₉×C₅₃	2
C₂×C₃×D₁₀₀₇	3
C₂×C₉×D₅₃	19
C₂×C₉×D₁₉	53

Subgroups — C2×C9×D1007 #49136239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₁₀₀₇ #49136239