Subgroups — (C₃⋊D₃)⋊(C₅⋊(C₁₃⋊D₁₃)) #44478293

Order 30420.

704 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₅⋊(C₁₃⋊D₁₃))	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₅⋊(C₁₃⋊D₁₃)	—	3	2	no	maximal
4	C₃²×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊(C₁₃⋊D₁₃)	—	5	1	no	maximal, Hall
6	C₃⋊(C₅⋊(C₁₃⋊D₁₃))	D₃	1	2	yes	complemented
7	C₅×D₃×C₁₃²	—	3	2	no	—
8	C₅×D₃×C₁₃²	—	6	1	no	—
9	C₃×C₅⋊(C₁₃⋊D₁₃)	—	3	2	no	—
10	C₂×C₅⋊(C₁₃⋊D₁₃)	—	9	1	no	Hall
11	C₁₃²×C₃⋊D₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₃⋊(C₁₃⋊D₁₃)	—	5	2	no	—
13	C₃×C₅×C₁₃²	—	2	1	no	—
14	C₃×C₅×C₁₃²	C₂×D₃	1	2	yes	complemented
15	(C₃⋊D₃)⋊D₆₅	—	13	14	no	maximal
16	D₃×C₁₃⋊D₁₃	—	15	2	no	—
17	C₂×C₅×C₁₃²	—	9	1	no	—
18	C₅⋊(C₁₃⋊D₁₃)	—	3	2	no	—
19	C₃²×C₁₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₃×C₃⋊D₃	D₁₃	1	14	yes	complemented
21	C₃×D₁₉₅	—	13	28	no	—
22	C₃⋊(C₁₃⋊D₁₃)	—	5	2	no	—
23	D₃×C₁₃²	—	3	2	no	—
24	D₃×C₁₃²	—	6	1	no	—
25	C₃×C₁₃⋊D₁₃	—	15	2	no	—
26	C₅×C₁₃²	D₃²	1	1	yes	characteristic, complemented, Hall
27	D₃×D₆₅	—	39	28	no	—
28	C₂×C₁₃⋊D₁₃	—	45	1	no	Hall
29	C₃²×C₅×C₁₃	C₂×D₁₃	1	14	yes	complemented
30	C₃×C₁₃²	—	2	1	no	—
31	C₃×C₁₃²	D₃×D₅	1	2	yes	complemented
32	(C₃⋊D₃)⋊D₁₃	—	65	14	no	—
33	D₁₉₅	—	13	28	no	—
34	C₅×D₃×C₁₃	—	3	28	no	—
35	C₅×D₃×C₁₃	—	6	14	no	—
36	C₃×D₆₅	—	39	28	no	—
37	C₂×C₁₃²	—	9	1	no	—
38	C₁₃⋊D₁₃	—	15	2	no	—
39	C₂×D₆₅	—	117	14	no	—
40	C₁₃×C₃⋊D₃	D₆₅	1	14	yes	complemented
41	C₃×D₃₉	—	65	28	no	—
42	C₃×C₅×C₁₃	—	2	14	no	—
43	C₃×C₅×C₁₃	D₃×D₁₃	1	28	yes	complemented
44	(C₃⋊D₃)⋊D₅	—	169	1	no	Hall
45	C₁₃²	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic, complemented, Sylow
46	D₃×D₁₃	—	195	28	no	—
47	C₂×C₅×C₁₃	—	9	14	no	—
48	D₆₅	—	39	28	no	—
49	C₃²×C₁₃	C₂×D₆₅	1	14	yes	complemented
50	C₅×C₃⋊D₃	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
51	C₃×D₁₅	—	169	2	no	—
52	D₃₉	—	65	28	no	—
53	C₃×D₁₃	—	195	28	no	—
54	D₃×C₁₃	—	3	28	no	—
55	D₃×C₁₃	—	6	14	no	—
56	C₅×C₁₃	(C₃⋊D₃)⋊D₁₃	1	14	yes	complemented
57	D₃×D₅	—	507	2	no	—
58	C₂×D₁₃	—	585	14	no	—
59	C₃²×C₅	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
60	C₃×C₁₃	—	2	14	no	—
61	C₃×C₁₃	D₃×D₆₅	1	28	yes	complemented
62	D₃²	—	845	1	no	Hall
63	D₁₅	—	169	2	no	—
64	C₃×D₅	—	507	2	no	—
65	C₅×D₃	—	3	2	no	—
66	C₅×D₃	—	6	1	no	—
67	C₂×C₁₃	—	9	14	no	—
68	D₁₃	—	195	28	no	—
69	C₂×D₅	—	1521	1	no	Hall
70	C₃⋊D₃	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, complemented
71	C₃×D₃	—	845	2	no	—
72	C₃×C₅	—	2	1	no	—
73	C₃×C₅	D₃×C₁₃⋊D₁₃	1	2	yes	complemented
74	C₁₃	(C₃⋊D₃)⋊D₆₅	1	14	yes	complemented
75	C₂×D₃	—	2535	2	no	—
76	C₂×C₅	—	9	1	no	—
77	D₅	—	507	2	no	—
78	C₃²	C₂×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₃	—	2535	2	no	—
80	D₃	—	3	2	no	—
81	D₃	—	6	1	no	—
82	D₃	—	845	2	no	—
83	C₅	(C₃⋊D₃)⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	7605	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×C₅⋊(C₁₃⋊D₁₃)	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	2535	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₃²	C₂²
LCS	G ▷ C₃²×C₅×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃⋊(C₅⋊(C₁₃⋊D₁₃))	C₂	semidirect
2. C₅×C₁₃²×C₃⋊D₃	C₂	semidirect
4. C₃²×C₅×C₁₃²	C₂²	semidirect
6. C₃⋊(C₅⋊(C₁₃⋊D₁₃))	D₃	semidirect
11. C₁₃²×C₃⋊D₃	D₅	semidirect
14. C₃×C₅×C₁₃²	C₂×D₃	semidirect
19. C₃²×C₁₃²	C₂×D₅	semidirect
20. C₅×C₁₃×C₃⋊D₃	D₁₃	semidirect
26. C₅×C₁₃²	D₃²	semidirect
29. C₃²×C₅×C₁₃	C₂×D₁₃	semidirect
31. C₃×C₁₃²	D₃×D₅	semidirect
40. C₁₃×C₃⋊D₃	D₆₅	semidirect
43. C₃×C₅×C₁₃	D₃×D₁₃	semidirect
45. C₁₃²	(C₃⋊D₃)⋊D₅	semidirect
49. C₃²×C₁₃	C₂×D₆₅	semidirect
50. C₅×C₃⋊D₃	C₁₃⋊D₁₃	semidirect
56. C₅×C₁₃	(C₃⋊D₃)⋊D₁₃	semidirect
59. C₃²×C₅	C₂×C₁₃⋊D₁₃	semidirect
61. C₃×C₁₃	D₃×D₆₅	semidirect
70. C₃⋊D₃	C₅⋊(C₁₃⋊D₁₃)	semidirect
73. C₃×C₅	D₃×C₁₃⋊D₁₃	semidirect
74. C₁₃	(C₃⋊D₃)⋊D₆₅	semidirect
78. C₃²	C₂×C₅⋊(C₁₃⋊D₁₃)	semidirect
83. C₅	(C₃⋊D₃)⋊(C₁₃⋊D₁₃)	semidirect
86. C₃	D₃×C₅⋊(C₁₃⋊D₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃⋊(C₅⋊(C₁₃⋊D₁₃))	2
C₅×C₁₃²×C₃⋊D₃	2
D₃×C₅⋊(C₁₃⋊D₁₃)	3
(C₃⋊D₃)⋊(C₁₃⋊D₁₃)	5
(C₃⋊D₃)⋊D₆₅	13

Subgroups — (C3⋊D3)⋊(C5⋊(C13⋊D13)) #44478293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊(C₅⋊(C₁₃⋊D₁₃)) #44478293