Subgroups — C₃×C₅×Q₈×C₉ #11761903

Order 1080.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×C₉	C₂	1	3	yes	maximal
2	C₃²×C₅×Q₈	C₃	1	1	yes	maximal, characteristic
3	C₅×Q₈×C₉	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₃×Q₈×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₄×C₅	C₂×C₃	1	3	yes	—
7	C₄×C₅×C₉	C₂×C₃	1	9	yes	—
8	C₃×C₅×C₉	Q₈	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×Q₈	C₉	1	3	yes	direct product factor
10	C₃×C₅×Q₈	C₃²	1	1	yes	characteristic
11	C₃×C₄×C₉	C₂×C₅	1	3	yes	—
12	C₂×C₃²×C₅	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₅×C₉	C₂²×C₃	1	3	yes	—
14	C₃²×Q₈	C₃×C₅	1	1	yes	characteristic
15	Q₈×C₉	C₃×C₅	1	3	yes	direct product factor
16	C₃×C₄×C₅	C₂×C₉	1	9	yes	—
17	C₃×C₄×C₅	C₂×C₃²	1	3	yes	—
18	C₂×C₃×C₉	C₂²×C₅	1	1	yes	characteristic
19	C₃²×C₅	C₃×Q₈	1	1	yes	characteristic
20	C₅×C₉	C₃×Q₈	1	3	yes	direct product factor
21	C₅×Q₈	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃²×C₄	C₂×C₃×C₅	1	3	yes	—
23	C₄×C₉	C₂×C₃×C₅	1	9	yes	—
24	C₂×C₃×C₅	C₂²×C₉	1	3	yes	—
25	C₂×C₃×C₅	C₂²×C₃²	1	1	yes	characteristic
26	C₃×C₉	C₅×Q₈	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×Q₈	C₅×C₉	1	3	yes	direct product factor
28	C₃×Q₈	C₃²×C₅	1	1	yes	characteristic
29	C₄×C₅	C₂×C₃×C₉	1	3	yes	—
30	C₂×C₃²	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₉	C₂²×C₃×C₅	1	3	yes	—
32	C₃×C₅	Q₈×C₉	1	3	yes	direct product factor
33	C₃×C₅	C₃²×Q₈	1	1	yes	characteristic
34	C₃×C₄	C₂×C₅×C₉	1	9	yes	—
35	C₃×C₄	C₂×C₃²×C₅	1	3	yes	—
36	C₂×C₅	C₂²×C₃×C₉	1	1	yes	characteristic
37	C₃²	C₃×C₅×Q₈	1	1	yes	characteristic
38	C₉	C₃×C₅×Q₈	1	3	yes	direct product factor
39	Q₈	C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	C₂²×C₅×C₉	1	3	yes	—
41	C₂×C₃	C₂²×C₃²×C₅	1	1	yes	characteristic
42	C₅	C₃×Q₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₄	C₂×C₃×C₅×C₉	1	3	yes	—
44	C₃	C₅×Q₈×C₉	1	3	yes	direct product factor
45	C₃	C₃²×C₅×Q₈	1	1	yes	characteristic
46	C₂	C₂²×C₃×C₅×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₅×C₉	C₂²
commutator	C₂	C₂²×C₃×C₅×C₉
Frattini, cosocle	C₂×C₃	C₂²×C₃²×C₅
socle, prime radical	C₂×C₃²×C₅	C₂²×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×Q₈×C₉	C₃	direct (N × H)
5. C₃×Q₈×C₉	C₅	direct (N × H)
8. C₃×C₅×C₉	Q₈	direct (N × H)
9. C₃×C₅×Q₈	C₉	direct (N × H)
15. Q₈×C₉	C₃×C₅	direct (N × H)
20. C₅×C₉	C₃×Q₈	direct (N × H)
21. C₅×Q₈	C₃×C₉	direct (N × H)
26. C₃×C₉	C₅×Q₈	direct (N × H)
27. C₃×Q₈	C₅×C₉	direct (N × H)
32. C₃×C₅	Q₈×C₉	direct (N × H)
38. C₉	C₃×C₅×Q₈	direct (N × H)
39. Q₈	C₃×C₅×C₉	direct (N × H)
42. C₅	C₃×Q₈×C₉	direct (N × H)
44. C₃	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
C₃×C₄×C₅×C₉	2
C₃²×C₅×Q₈	3
C₅×Q₈×C₉	3
C₃×Q₈×C₉	5

Subgroups — C3×C5×Q8×C9 #11761903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×Q₈×C₉ #11761903