Subgroups — C₅²×Q₈×C₉ #14268020

Order 1800.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²×C₉	C₂	1	3	yes	maximal
2	C₃×C₅²×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅²×C₉	C₂²	1	1	yes	characteristic
4	C₅×Q₈×C₉	C₅	1	6	yes	maximal, direct product factor
5	C₃×C₄×C₅²	C₂×C₃	1	3	yes	—
6	C₅²×C₉	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×Q₈	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₄×C₅×C₉	C₂×C₅	1	18	yes	—
9	C₂×C₃×C₅²	C₂²×C₃	1	1	yes	characteristic
10	C₃×C₅×Q₈	C₃×C₅	1	6	yes	—
11	C₄×C₅²	C₂×C₉	1	3	yes	—
12	C₂×C₅×C₉	C₂²×C₅	1	6	yes	—
13	C₃×C₅²	C₃×Q₈	1	1	yes	characteristic
14	Q₈×C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₄×C₅	C₂×C₃×C₅	1	18	yes	—
16	C₂×C₅²	C₂²×C₉	1	1	yes	characteristic
17	C₅×C₉	C₅×Q₈	1	6	yes	direct product factor
18	C₅×Q₈	C₅×C₉	1	6	yes	direct product factor
19	C₄×C₉	C₂×C₅²	1	3	yes	—
20	C₂×C₃×C₅	C₂²×C₃×C₅	1	6	yes	—
21	C₅²	Q₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×Q₈	C₃×C₅²	1	1	yes	characteristic
23	C₄×C₅	C₂×C₅×C₉	1	18	yes	—
24	C₂×C₉	C₂²×C₅²	1	1	yes	characteristic
25	C₃×C₅	C₃×C₅×Q₈	1	6	yes	—
26	C₃×C₄	C₂×C₃×C₅²	1	3	yes	—
27	C₂×C₅	C₂²×C₅×C₉	1	6	yes	—
28	C₉	C₅²×Q₈	1	1	yes	characteristic, direct product factor, Sylow
29	Q₈	C₅²×C₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂²×C₃×C₅²	1	1	yes	characteristic
31	C₅	C₅×Q₈×C₉	1	6	yes	direct product factor
32	C₄	C₂×C₅²×C₉	1	3	yes	—
33	C₃	C₃×C₅²×Q₈	1	1	yes	characteristic
34	C₂	C₂²×C₅²×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅²×C₉	C₂²
commutator	C₂	C₂²×C₅²×C₉
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₅²
socle, prime radical	C₂×C₃×C₅²	C₂²×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×Q₈×C₉	C₅	direct (N × H)
6. C₅²×C₉	Q₈	direct (N × H)
7. C₅²×Q₈	C₉	direct (N × H)
14. Q₈×C₉	C₅²	direct (N × H)
17. C₅×C₉	C₅×Q₈	direct (N × H)
18. C₅×Q₈	C₅×C₉	direct (N × H)
21. C₅²	Q₈×C₉	direct (N × H)
28. C₉	C₅²×Q₈	direct (N × H)
29. Q₈	C₅²×C₉	direct (N × H)
31. C₅	C₅×Q₈×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅²×C₉	2
C₃×C₅²×Q₈	3
C₅×Q₈×C₉	5

Subgroups — C52×Q8×C9 #14268020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×Q₈×C₉ #14268020