Subgroups — C₂×D₉×C₂₉² #44475607

Order 30276.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉×C₂₉²	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₂₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₂₉²	—	3	1	no	maximal
4	C₉×C₂₉²	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₂₉²	—	3	2	no	—
6	C₂×C₃×C₂₉²	D₃	1	1	yes	characteristic
7	C₂²×C₂₉²	—	9	1	no	Hall
8	C₃×C₂₉²	C₂×D₃	1	1	yes	characteristic
9	C₂×C₂₉²	—	9	2	no	—
10	C₂×C₂₉²	D₉	1	1	yes	characteristic, direct product factor
11	C₂×D₉×C₂₉	C₂₉	1	30	yes	maximal, direct product factor
12	C₂₉²	C₂×D₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₉×C₂₉	C₂×C₂₉	1	30	yes	complemented
14	D₉×C₂₉	C₂×C₂₉	1	60	yes	direct product factor
15	C₂×D₃×C₂₉	—	3	30	no	—
16	C₉×C₂₉	C₂²×C₂₉	1	30	yes	complemented
17	C₂×C₃×C₂₉	D₃×C₂₉	1	30	yes	—
18	D₃×C₂₉	—	3	60	no	—
19	C₂²×C₂₉	—	9	30	no	—
20	C₃×C₂₉	C₂×D₃×C₂₉	1	30	yes	—
21	C₂×C₂₉	—	9	60	no	—
22	C₂×C₂₉	D₉×C₂₉	1	30	yes	direct product factor
23	C₂×D₉	C₂₉²	1	1	yes	characteristic, direct product factor, Hall
24	C₂₉	C₂×D₉×C₂₉	1	30	yes	direct product factor
25	C₂×C₉	C₂×C₂₉²	1	1	yes	characteristic, complemented
26	D₉	C₂×C₂₉²	1	2	yes	direct product factor
27	C₂×D₃	—	3	1	no	—
28	C₉	C₂²×C₂₉²	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	D₃×C₂₉²	1	1	yes	characteristic
30	D₃	—	3	2	no	—
31	C₂²	—	9	1	no	Sylow
32	C₃	C₂×D₃×C₂₉²	1	1	yes	characteristic
33	C₂	—	9	2	no	—
34	C₂	D₉×C₂₉²	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉²	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₂₉²
Frattini	C₃	C₂×D₃×C₂₉²
Fitting	C₂×C₉×C₂₉²	C₂
socle	C₂×C₃×C₂₉²	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₂₉²

Complements

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

N	H ≅ G/N	type
1. D₉×C₂₉²	C₂	direct (N × H)
2. C₂×C₉×C₂₉²	C₂	semidirect
4. C₉×C₂₉²	C₂²	semidirect
10. C₂×C₂₉²	D₉	direct (N × H)
11. C₂×D₉×C₂₉	C₂₉	direct (N × H)
12. C₂₉²	C₂×D₉	direct (N × H)
13. C₂×C₉×C₂₉	C₂×C₂₉	semidirect
14. D₉×C₂₉	C₂×C₂₉	direct (N × H)
16. C₉×C₂₉	C₂²×C₂₉	semidirect
22. C₂×C₂₉	D₉×C₂₉	direct (N × H)
23. C₂×D₉	C₂₉²	direct (N × H)
24. C₂₉	C₂×D₉×C₂₉	direct (N × H)
25. C₂×C₉	C₂×C₂₉²	semidirect
26. D₉	C₂×C₂₉²	direct (N × H)
28. C₉	C₂²×C₂₉²	semidirect
34. C₂	D₉×C₂₉²	direct (N × H)

Maximal subgroups

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

subgroup	index
D₉×C₂₉²	2
C₂×C₉×C₂₉²	2
C₂×D₃×C₂₉²	3
C₂×D₉×C₂₉	29

Subgroups — C2×D9×C292 #44475607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×C₂₉² #44475607