Subgroups — D₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃)) #44478327

Order 30420.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₁₃²	2
C₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃))	2
C₃⋊(C₃⋊(C₅⋊(C₁₃⋊D₁₃)))	2
D₅×C₃⋊(C₁₃⋊D₁₃)	3
C₂×C₃⋊(C₃⋊(C₁₃⋊D₁₃))	5
D₅×C₃⋊D₃₉	13

Subgroups — D5×C3⋊(C3⋊(C13⋊D13)) #44478327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃)) #44478327