Subgroups — C₁₃×C₁₃⋊C₃×A₅ #44478357

Order 30420.

120 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, complemented
2	A₄×C₁₃×C₁₃⋊C₃	—	5	1	no	maximal, Hall
3	D₅×C₁₃×C₁₃⋊C₃	—	6	1	no	maximal
4	D₃×C₁₃×C₁₃⋊C₃	—	10	1	no	maximal
5	C₅×C₁₃×C₁₃⋊C₃	—	6	1	no	—
6	C₁₃⋊C₃×A₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃×C₁₃×A₅	—	13	1	no	maximal
8	C₁₃×C₂²⋊(C₁₃⋊C₃)	—	5	2	no	—
9	A₄×C₁₃²	—	5	1	no	—
10	C₂²×C₁₃×C₁₃⋊C₃	—	5	1	no	—
11	D₅×C₁₃²	—	6	1	no	—
12	C₃×C₁₃×C₁₃⋊C₃	—	10	1	no	Hall
13	D₃×C₁₃²	—	10	1	no	—
14	C₂×C₁₃×C₁₃⋊C₃	—	15	1	no	—
15	C₅×C₁₃²	—	6	1	no	Hall
16	C₁₃×A₅	—	3	4	no	—
17	C₁₃×A₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₁₃×A₅	C₃×C₁₃	1	1	yes	characteristic, complemented
19	C₂²×C₁₃²	—	5	1	no	Hall
20	C₃×C₁₃²	—	10	1	no	—
21	C₁₃×C₁₃⋊C₃	—	20	1	no	—
22	C₁₃×C₁₃⋊C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
23	C₃×A₄×C₁₃	—	65	1	no	—
24	A₄×C₁₃⋊C₃	—	5	1	no	—
25	C₃×D₅×C₁₃	—	78	1	no	—
26	D₅×C₁₃⋊C₃	—	6	1	no	—
27	C₂×C₁₃²	—	15	1	no	—
28	C₃×D₃×C₁₃	—	130	1	no	—
29	D₃×C₁₃⋊C₃	—	10	1	no	—
30	C₃×C₅×C₁₃	—	78	1	no	—
31	C₅×C₁₃⋊C₃	—	6	1	no	—
32	C₃×A₅	—	13	1	no	Hall
33	C₁₃²	C₃×A₅	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₃×C₁₃	—	65	1	no	—
35	C₂²⋊(C₁₃⋊C₃)	—	5	2	no	—
36	A₄×C₁₃	—	5	1	no	—
37	A₄×C₁₃	—	5	1	no	—
38	A₄×C₁₃	—	15	4	no	—
39	A₄×C₁₃	—	65	2	no	—
40	C₂²×C₁₃⋊C₃	—	5	1	no	—
41	D₅×C₁₃	—	6	1	no	—
42	D₅×C₁₃	—	6	1	no	—
43	D₅×C₁₃	—	18	4	no	—
44	C₃²×C₁₃	—	130	1	no	—
45	C₃×C₁₃⋊C₃	—	10	1	no	—
46	C₂×C₃×C₁₃	—	195	1	no	—
47	D₃×C₁₃	—	10	1	no	—
48	D₃×C₁₃	—	10	1	no	—
49	D₃×C₁₃	—	30	4	no	—
50	C₂×C₁₃⋊C₃	—	15	1	no	—
51	C₅×C₁₃	—	6	1	no	—
52	C₅×C₁₃	—	6	1	no	—
53	C₅×C₁₃	—	18	4	no	—
54	A₅	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
55	C₂²×C₁₃	—	5	1	no	—
56	C₂²×C₁₃	—	5	1	no	—
57	C₂²×C₁₃	—	15	4	no	—
58	C₃×C₁₃	—	260	1	no	—
59	C₃×C₁₃	—	10	1	no	—
60	C₃×C₁₃	—	10	1	no	—
61	C₃×C₁₃	—	13	1	no	—
62	C₃×C₁₃	—	30	4	no	—
63	C₁₃⋊C₃	—	20	1	no	—
64	C₁₃⋊C₃	C₁₃×A₅	1	1	yes	characteristic, direct product factor
65	C₃×A₄	—	65	1	no	Hall
66	C₃×D₅	—	78	1	no	—
67	C₂×C₁₃	—	15	1	no	—
68	C₂×C₁₃	—	15	1	no	—
69	C₂×C₁₃	—	45	4	no	—
70	C₃×D₃	—	130	1	no	—
71	C₃×C₅	—	78	1	no	—
72	C₁₃	—	3	4	no	—
73	C₁₃	C₃×C₁₃×A₅	1	1	yes	characteristic, complemented
74	C₁₃	C₁₃⋊C₃×A₅	1	1	yes	characteristic, direct product factor
75	C₂²×C₃	—	65	1	no	—
76	A₄	—	5	1	no	—
77	A₄	—	65	2	no	—
78	D₅	—	6	1	no	—
79	C₃²	—	130	1	no	Sylow
80	C₂×C₃	—	195	1	no	—
81	D₃	—	10	1	no	—
82	C₅	—	6	1	no	Sylow
83	C₂²	—	5	1	no	Sylow
84	C₃	—	260	1	no	—
85	C₃	—	10	1	no	—
86	C₃	—	13	1	no	—
87	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₁₃⋊C₃×A₅
commutator, hypocenter	C₁₃×A₅	C₃×C₁₃
Frattini	C₁	G
Fitting	C₁₃²	C₃×A₅
socle	C₁₃²×A₅	C₃
cosocle	C₁₃	C₃×C₁₃×A₅
LCS	G ▷ C₁₃×A₅
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃²×A₅	C₃	semidirect
6. C₁₃⋊C₃×A₅	C₁₃	direct (N × H)
17. C₁₃×A₅	C₁₃⋊C₃	direct (N × H)
18. C₁₃×A₅	C₃×C₁₃	semidirect
22. C₁₃×C₁₃⋊C₃	A₅	direct (N × H)
33. C₁₃²	C₃×A₅	semidirect
54. A₅	C₁₃×C₁₃⋊C₃	direct (N × H)
64. C₁₃⋊C₃	C₁₃×A₅	direct (N × H)
73. C₁₃	C₃×C₁₃×A₅	semidirect
74. C₁₃	C₁₃⋊C₃×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
A₄×C₁₃×C₁₃⋊C₃	5
D₅×C₁₃×C₁₃⋊C₃	6
D₃×C₁₃×C₁₃⋊C₃	10
C₁₃⋊C₃×A₅	13
C₃×C₁₃×A₅	13

Subgroups — C13×C13⋊C3×A5 #44478357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₃⋊C₃×A₅ #44478357