Subgroups — C₃×C₁₃²×A₅ #44478356

Order 30420.

336 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×A₄×C₁₃²	—	5	1	no	maximal, Hall
3	C₃×D₅×C₁₃²	—	6	1	no	maximal
4	C₃×D₃×C₁₃²	—	10	1	no	maximal
5	C₃×C₅×C₁₃²	—	6	1	no	—
6	C₃×C₁₃×A₅	C₁₃	1	14	yes	maximal, direct product factor
7	A₄×C₁₃²	—	5	1	no	—
8	A₄×C₁₃²	—	5	2	no	—
9	C₂²×C₃×C₁₃²	—	5	1	no	—
10	D₅×C₁₃²	—	6	1	no	—
11	C₃²×C₁₃²	—	10	1	no	Hall
12	C₂×C₃×C₁₃²	—	15	1	no	—
13	D₃×C₁₃²	—	10	1	no	—
14	C₅×C₁₃²	—	6	1	no	Hall
15	C₁₃×A₅	C₃×C₁₃	1	14	yes	direct product factor
16	C₂²×C₁₃²	—	5	1	no	Hall
17	C₃×C₁₃²	—	10	1	no	—
18	C₃×C₁₃²	—	20	1	no	—
19	C₃×C₁₃²	A₅	1	1	yes	maximal normal, characteristic, direct product factor
20	C₃×A₄×C₁₃	—	5	14	no	—
21	C₃×D₅×C₁₃	—	6	14	no	—
22	C₂×C₁₃²	—	15	1	no	—
23	C₃×D₃×C₁₃	—	10	14	no	—
24	C₃×C₅×C₁₃	—	6	14	no	—
25	C₃×A₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
26	C₁₃²	C₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²×C₃×C₁₃	—	5	14	no	—
28	A₄×C₁₃	—	5	14	no	—
29	A₄×C₁₃	—	5	28	no	—
30	D₅×C₁₃	—	6	14	no	—
31	C₃²×C₁₃	—	10	14	no	—
32	C₂×C₃×C₁₃	—	15	14	no	—
33	D₃×C₁₃	—	10	14	no	—
34	C₅×C₁₃	—	6	14	no	—
35	A₅	C₃×C₁₃²	1	1	yes	characteristic, direct product factor
36	C₂²×C₁₃	—	5	14	no	—
37	C₃×C₁₃	—	10	14	no	—
38	C₃×C₁₃	—	20	14	no	—
39	C₃×C₁₃	C₁₃×A₅	1	14	yes	direct product factor
40	C₃×A₄	—	5	1	no	Hall
41	C₃×D₅	—	6	1	no	—
42	C₂×C₁₃	—	15	14	no	—
43	C₃×D₃	—	10	1	no	—
44	C₃×C₅	—	6	1	no	—
45	C₁₃	C₃×C₁₃×A₅	1	14	yes	direct product factor
46	C₂²×C₃	—	5	1	no	—
47	A₄	—	5	1	no	—
48	A₄	—	5	2	no	—
49	D₅	—	6	1	no	—
50	C₃²	—	10	1	no	Sylow
51	C₂×C₃	—	15	1	no	—
52	D₃	—	10	1	no	—
53	C₅	—	6	1	no	Sylow
54	C₂²	—	5	1	no	Sylow
55	C₃	—	10	1	no	—
56	C₃	—	20	1	no	—
57	C₃	C₁₃²×A₅	1	1	yes	characteristic, direct product factor
58	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃×C₁₃²	A₅
commutator, hypocenter	A₅	C₃×C₁₃²
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₃×C₁₃²

Complements

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

N	H ≅ G/N	type
1. C₁₃²×A₅	C₃	direct (N × H)
6. C₃×C₁₃×A₅	C₁₃	direct (N × H)
15. C₁₃×A₅	C₃×C₁₃	direct (N × H)
19. C₃×C₁₃²	A₅	direct (N × H)
25. C₃×A₅	C₁₃²	direct (N × H)
26. C₁₃²	C₃×A₅	direct (N × H)
35. A₅	C₃×C₁₃²	direct (N × H)
39. C₃×C₁₃	C₁₃×A₅	direct (N × H)
45. C₁₃	C₃×C₁₃×A₅	direct (N × H)
57. C₃	C₁₃²×A₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃²×A₅	3
C₃×A₄×C₁₃²	5
C₃×D₅×C₁₃²	6
C₃×D₃×C₁₃²	10
C₃×C₁₃×A₅	13

Subgroups — C3×C132×A5 #44478356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃²×A₅ #44478356