Subgroups — C₁₃×Dic₅₈₅ #44477609

Order 30420.

144 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	C₁₃×Dic₁₉₅	—	3	1	no	maximal
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×Dic₁₁₇	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₃²	D₃	1	1	yes	characteristic
6	C₁₃×Dic₆₅	—	9	1	no	Hall
7	C₂×C₉×C₁₃²	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	Dic₅₈₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor
10	C₁₃×Dic₄₅	—	13	1	no	maximal
11	C₁₃×Dic₃₉	—	15	1	no	—
12	C₂×C₅×C₁₃²	D₉	1	1	yes	characteristic
13	C₉×C₁₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₉×C₁₃	—	2	6	no	—
15	C₂×C₅×C₉×C₁₃	D₁₃	1	1	yes	characteristic
16	C₂×C₅×C₉×C₁₃	C₂×C₁₃	1	1	yes	characteristic
17	C₂×C₃×C₁₃²	D₁₅	1	1	yes	characteristic
18	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
19	Dic₁₉₅	—	3	1	no	—
20	C₁₃×Dic₁₅	—	39	1	no	—
21	C₁₃×Dic₁₃	—	45	1	no	Hall
22	C₅×C₉×C₁₃	—	2	6	no	—
23	C₅×C₉×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
24	C₅×C₉×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
25	C₃×C₁₃²	Dic₁₅	1	1	yes	characteristic
26	Dic₁₁₇	—	5	1	no	—
27	C₁₃×Dic₉	—	65	1	no	—
28	C₂×C₃×C₅×C₁₃	—	2	6	no	—
29	C₂×C₃×C₅×C₁₃	D₃×C₁₃	1	1	yes	characteristic
30	C₂×C₃×C₅×C₁₃	D₃₉	1	1	yes	characteristic
31	C₂×C₁₃²	D₄₅	1	1	yes	characteristic
32	Dic₆₅	—	9	1	no	—
33	C₁₃×Dic₅	—	117	1	no	—
34	C₂×C₉×C₁₃	—	2	6	no	—
35	C₂×C₉×C₁₃	D₅×C₁₃	1	1	yes	characteristic
36	C₂×C₉×C₁₃	D₆₅	1	1	yes	characteristic
37	C₃×C₅×C₁₃	—	2	6	no	—
38	C₃×C₅×C₁₃	Dic₃×C₁₃	1	1	yes	characteristic
39	C₃×C₅×C₁₃	Dic₃₉	1	1	yes	characteristic
40	Dic₄₅	—	13	1	no	Hall
41	C₁₃²	Dic₄₅	1	1	yes	characteristic, complemented, Sylow
42	Dic₃₉	—	15	1	no	—
43	Dic₃×C₁₃	—	195	1	no	—
44	C₂×C₅×C₁₃	—	2	6	no	—
45	C₂×C₅×C₁₃	C₁₃×D₉	1	1	yes	characteristic
46	C₂×C₅×C₁₃	D₁₁₇	1	1	yes	characteristic
47	C₉×C₁₃	—	2	6	no	—
48	C₉×C₁₃	C₁₃×Dic₅	1	1	yes	characteristic, complemented
49	C₉×C₁₃	Dic₆₅	1	1	yes	characteristic, complemented
50	C₂×C₅×C₉	C₁₃×D₁₃	1	1	yes	characteristic
51	C₂×C₃×C₁₃	—	2	6	no	—
52	C₂×C₃×C₁₃	C₁₃×D₁₅	1	1	yes	characteristic
53	C₂×C₃×C₁₃	D₁₉₅	1	1	yes	characteristic
54	C₅×C₁₃	—	2	6	no	—
55	C₅×C₁₃	C₁₃×Dic₉	1	1	yes	characteristic, complemented
56	C₅×C₁₃	Dic₁₁₇	1	1	yes	characteristic, complemented
57	Dic₁₅	—	39	1	no	—
58	C₄×C₁₃	—	585	1	no	—
59	Dic₁₃	—	45	1	no	—
60	C₅×C₉	C₁₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
61	C₃×C₁₃	—	2	6	no	—
62	C₃×C₁₃	C₁₃×Dic₁₅	1	1	yes	characteristic
63	C₃×C₁₃	Dic₁₉₅	1	1	yes	characteristic
64	Dic₉	—	65	1	no	Hall
65	C₂×C₃×C₅	C₁₃×D₃₉	1	1	yes	characteristic
66	C₂×C₁₃	—	2	6	no	—
67	C₂×C₁₃	C₁₃×D₄₅	1	1	yes	characteristic
68	C₂×C₁₃	D₅₈₅	1	1	yes	characteristic
69	Dic₅	—	117	1	no	Hall
70	C₂×C₉	C₁₃×D₆₅	1	1	yes	characteristic
71	C₃×C₅	C₁₃×Dic₃₉	1	1	yes	characteristic
72	C₁₃	—	2	6	no	—
73	C₁₃	C₁₃×Dic₄₅	1	1	yes	characteristic, complemented
74	C₁₃	Dic₅₈₅	1	1	yes	characteristic, direct product factor
75	Dic₃	—	195	1	no	—
76	C₂×C₅	C₁₃×D₁₁₇	1	1	yes	characteristic
77	C₉	C₁₃×Dic₆₅	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₃	C₁₃×D₁₉₅	1	1	yes	characteristic
79	C₅	C₁₃×Dic₁₁₇	1	1	yes	characteristic, complemented, Sylow
80	C₄	—	585	1	no	Sylow
81	C₃	C₁₃×Dic₁₉₅	1	1	yes	characteristic
82	C₂	C₁₃×D₅₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₅₈₅
commutator, hypocenter	C₅×C₉×C₁₃	C₄×C₁₃
Frattini	C₂×C₃	C₁₃×D₁₉₅
Fitting	C₂×C₅×C₉×C₁₃²	C₂
socle, prime radical	C₂×C₃×C₅×C₁₃²	D₃
cosocle	C₂×C₅×C₉×C₁₃	C₂×C₁₃
LCS	G ▷ C₅×C₉×C₁₃
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
9. Dic₅₈₅	C₁₃	direct (N × H)
13. C₉×C₁₃²	Dic₅	semidirect
18. C₅×C₁₃²	Dic₉	semidirect
23. C₅×C₉×C₁₃	Dic₁₃	semidirect
24. C₅×C₉×C₁₃	C₄×C₁₃	semidirect
41. C₁₃²	Dic₄₅	semidirect
48. C₉×C₁₃	C₁₃×Dic₅	semidirect
49. C₉×C₁₃	Dic₆₅	semidirect
55. C₅×C₁₃	C₁₃×Dic₉	semidirect
56. C₅×C₁₃	Dic₁₁₇	semidirect
60. C₅×C₉	C₁₃×Dic₁₃	semidirect
73. C₁₃	C₁₃×Dic₄₅	semidirect
74. C₁₃	Dic₅₈₅	direct (N × H)
77. C₉	C₁₃×Dic₆₅	semidirect
79. C₅	C₁₃×Dic₁₁₇	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
C₁₃×Dic₁₉₅	3
C₁₃×Dic₁₁₇	5
Dic₅₈₅	13
C₁₃×Dic₄₅	13

Subgroups — C13×Dic585 #44477609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×Dic₅₈₅ #44477609