Subgroups — C₂×C₇×D₉₀₉ #38764142

Order 25452.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₉₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₀₃	—	3	1	no	maximal
4	C₇×C₉×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₀₃	—	3	2	no	—
6	C₂×C₃×C₇×C₁₀₁	D₃	1	1	yes	characteristic
7	C₂×D₉₀₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₁₀₁	—	9	1	no	Hall
9	C₃×C₇×C₁₀₁	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₁₀₁	C₂×C₇	1	1	yes	characteristic, complemented
11	D₉₀₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₁₀₁	D₉	1	1	yes	characteristic, complemented
13	C₇×D₁₀₁	—	9	2	no	—
14	C₂×D₃₀₃	—	3	1	no	—
15	C₉×C₁₀₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₀₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₀₁	D₃×C₇	1	1	yes	characteristic
18	D₃₀₃	—	3	2	no	—
19	C₂×D₁₀₁	—	9	1	no	Hall
20	C₃×C₁₀₁	C₂×D₃×C₇	1	1	yes	characteristic
21	C₂×C₇×D₉	—	101	1	no	maximal, Hall
22	C₂×C₁₀₁	C₇×D₉	1	1	yes	characteristic, complemented
23	D₁₀₁	—	9	2	no	—
24	C₂×C₇×C₉	D₁₀₁	1	1	yes	characteristic, complemented
25	C₇×D₉	—	101	2	no	—
26	C₁₀₁	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₃×C₇	—	303	1	no	—
28	C₇×C₉	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₃₀₃	1	1	yes	characteristic
30	D₃×C₇	—	303	2	no	—
31	C₂×D₉	—	101	1	no	Hall
32	C₂²×C₇	—	909	1	no	Hall
33	C₃×C₇	C₂×D₃₀₃	1	1	yes	characteristic
34	C₂×C₉	C₇×D₁₀₁	1	1	yes	characteristic, complemented
35	D₉	—	101	2	no	—
36	C₂×C₇	—	909	2	no	—
37	C₂×C₇	D₉₀₉	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	303	1	no	—
39	C₉	C₂×C₇×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₉₀₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₃₀₃	1	1	yes	characteristic
42	D₃	—	303	2	no	—
43	C₂²	—	909	1	no	Sylow
44	C₃	C₂×C₇×D₃₀₃	1	1	yes	characteristic
45	C₂	—	909	2	no	—
46	C₂	C₇×D₉₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₉₀₉
commutator, cosocle, hypocenter	C₉×C₁₀₁	C₂²×C₇
Frattini	C₃	C₂×C₇×D₃₀₃
Fitting	C₂×C₇×C₉×C₁₀₁	C₂
socle	C₂×C₃×C₇×C₁₀₁	D₃
LCS	G ▷ C₉×C₁₀₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₉₀₉	C₂	direct (N × H)
2. C₂×C₇×C₉×C₁₀₁	C₂	semidirect
4. C₇×C₉×C₁₀₁	C₂²	semidirect
7. C₂×D₉₀₉	C₇	direct (N × H)
10. C₂×C₉×C₁₀₁	C₂×C₇	semidirect
11. D₉₀₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₁₀₁	D₉	semidirect
15. C₉×C₁₀₁	C₂²×C₇	semidirect
16. C₇×C₁₀₁	C₂×D₉	semidirect
22. C₂×C₁₀₁	C₇×D₉	semidirect
24. C₂×C₇×C₉	D₁₀₁	semidirect
26. C₁₀₁	C₂×C₇×D₉	semidirect
28. C₇×C₉	C₂×D₁₀₁	semidirect
34. C₂×C₉	C₇×D₁₀₁	semidirect
37. C₂×C₇	D₉₀₉	direct (N × H)
39. C₉	C₂×C₇×D₁₀₁	semidirect
40. C₇	C₂×D₉₀₉	direct (N × H)
46. C₂	C₇×D₉₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₉₀₉	2
C₂×C₇×C₉×C₁₀₁	2
C₂×C₇×D₃₀₃	3
C₂×D₉₀₉	7
C₂×C₇×D₉	101

Subgroups — C2×C7×D909 #38764142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₉₀₉ #38764142