Subgroups — C₁₃²×Dic₄₅ #44477608

Order 30420.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×Dic₁₅	—	3	1	no	maximal
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃²×Dic₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₃²	D₃	1	1	yes	characteristic
6	C₁₃²×Dic₅	—	9	1	no	Hall
7	C₂×C₉×C₁₃²	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	C₁₃×Dic₄₅	C₁₃	1	14	yes	maximal, direct product factor
10	Dic₃×C₁₃²	—	15	1	no	—
11	C₂×C₅×C₁₃²	D₉	1	1	yes	characteristic
12	C₉×C₁₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₉×C₁₃	C₂×C₁₃	1	14	yes	—
14	C₂×C₃×C₁₃²	D₁₅	1	1	yes	characteristic
15	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₁₃×Dic₁₅	—	3	14	no	—
17	C₄×C₁₃²	—	45	1	no	Hall
18	C₅×C₉×C₁₃	C₄×C₁₃	1	14	yes	complemented
19	C₃×C₁₃²	Dic₁₅	1	1	yes	characteristic
20	C₁₃×Dic₉	—	5	14	no	—
21	C₂×C₃×C₅×C₁₃	D₃×C₁₃	1	14	yes	—
22	C₂×C₁₃²	D₄₅	1	1	yes	characteristic
23	C₁₃×Dic₅	—	9	14	no	—
24	C₂×C₉×C₁₃	D₅×C₁₃	1	14	yes	—
25	C₃×C₅×C₁₃	Dic₃×C₁₃	1	14	yes	—
26	Dic₄₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
27	C₁₃²	Dic₄₅	1	1	yes	characteristic, direct product factor, Sylow
28	Dic₃×C₁₃	—	15	14	no	—
29	C₂×C₅×C₁₃	C₁₃×D₉	1	14	yes	—
30	C₉×C₁₃	C₁₃×Dic₅	1	14	yes	complemented
31	C₂×C₅×C₉	C₂×C₁₃²	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₁₃×D₁₅	1	14	yes	—
33	C₅×C₁₃	C₁₃×Dic₉	1	14	yes	complemented
34	Dic₁₅	—	3	1	no	—
35	C₄×C₁₃	—	45	14	no	—
36	C₅×C₉	C₄×C₁₃²	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₁₃×Dic₁₅	1	14	yes	—
38	Dic₉	—	5	1	no	Hall
39	C₂×C₃×C₅	D₃×C₁₃²	1	1	yes	characteristic
40	C₂×C₁₃	C₁₃×D₄₅	1	14	yes	—
41	Dic₅	—	9	1	no	Hall
42	C₂×C₉	D₅×C₁₃²	1	1	yes	characteristic
43	C₃×C₅	Dic₃×C₁₃²	1	1	yes	characteristic
44	C₁₃	C₁₃×Dic₄₅	1	14	yes	direct product factor
45	Dic₃	—	15	1	no	—
46	C₂×C₅	C₁₃²×D₉	1	1	yes	characteristic
47	C₉	C₁₃²×Dic₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₁₃²×D₁₅	1	1	yes	characteristic
49	C₅	C₁₃²×Dic₉	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	45	1	no	Sylow
51	C₃	C₁₃²×Dic₁₅	1	1	yes	characteristic
52	C₂	C₁₃²×D₄₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃²	D₄₅
commutator, hypocenter	C₅×C₉	C₄×C₁₃²
Frattini	C₂×C₃	C₁₃²×D₁₅
Fitting	C₂×C₅×C₉×C₁₃²	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃²	D₃
cosocle	C₂×C₅×C₉	C₂×C₁₃²
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₁₃²

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
9. C₁₃×Dic₄₅	C₁₃	direct (N × H)
12. C₉×C₁₃²	Dic₅	semidirect
15. C₅×C₁₃²	Dic₉	semidirect
18. C₅×C₉×C₁₃	C₄×C₁₃	semidirect
26. Dic₄₅	C₁₃²	direct (N × H)
27. C₁₃²	Dic₄₅	direct (N × H)
30. C₉×C₁₃	C₁₃×Dic₅	semidirect
33. C₅×C₁₃	C₁₃×Dic₉	semidirect
36. C₅×C₉	C₄×C₁₃²	semidirect
44. C₁₃	C₁₃×Dic₄₅	direct (N × H)
47. C₉	C₁₃²×Dic₅	semidirect
49. C₅	C₁₃²×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₃²	2
C₁₃²×Dic₁₅	3
C₁₃²×Dic₉	5
C₁₃×Dic₄₅	13

Subgroups — C132×Dic45 #44477608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃²×Dic₄₅ #44477608