Subgroups — C₁₃×#14556844 #44478195

Order 30420.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×#90865	—	5	1	no	maximal, Hall
4	C₁₃²×D₁₅	—	6	2	no	—
5	C₁₃×#63120	—	9	1	no	maximal, Hall
6	C₁₃²×C₃⋊D₃	—	5	1	no	—
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	#14556844	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₁₃×#4380	—	13	1	no	maximal
10	D₅×C₁₃²	—	9	1	no	—
11	C₃²×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₃⋊D₁₅	—	2	6	no	—
13	C₁₃×C₃⋊D₁₅	D₁₃	1	1	yes	characteristic
14	C₁₃×C₃⋊D₁₅	C₂×C₁₃	1	1	yes	characteristic
15	D₃×C₁₃²	—	30	2	no	—
16	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
17	C₁₃×Dic₁₃	—	45	1	no	Hall
18	C₃²×C₅×C₁₃	—	2	6	no	—
19	C₃²×C₅×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
20	C₃²×C₅×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
21	C₃×C₁₃²	—	2	2	no	—
22	#90865	—	5	1	no	—
23	C₁₃×#157	—	65	1	no	—
24	C₁₃×D₁₅	—	6	2	no	—
25	C₁₃×D₁₅	—	6	2	no	—
26	C₁₃×D₁₅	—	6	24	no	—
27	C₂×C₁₃²	—	45	1	no	—
28	#63120	—	9	1	no	—
29	C₁₃×AGL(1,𝔽₅)	—	117	1	no	—
30	C₁₃×C₃⋊D₃	—	5	1	no	—
31	C₁₃×C₃⋊D₃	—	5	1	no	—
32	C₁₃×C₃⋊D₃	—	10	6	no	—
33	C₃×C₅×C₁₃	—	2	24	no	—
34	C₃×C₅×C₁₃	—	2	2	no	—
35	C₃×C₅×C₁₃	—	2	2	no	—
36	#4380	—	13	1	no	Hall
37	C₁₃²	#4380	1	1	yes	characteristic, complemented, Sylow
38	D₅×C₁₃	—	9	1	no	—
39	D₅×C₁₃	—	9	1	no	—
40	D₅×C₁₃	—	18	6	no	—
41	C₃²×C₁₃	—	2	6	no	—
42	C₃²×C₁₃	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
43	C₃²×C₁₃	#63120	1	1	yes	characteristic, complemented
44	C₃⋊D₁₅	C₁₃×D₁₃	1	1	yes	characteristic
45	D₃×C₁₃	—	30	2	no	—
46	D₃×C₁₃	—	30	2	no	—
47	D₃×C₁₃	—	30	24	no	—
48	C₅×C₁₃	—	2	6	no	—
49	C₅×C₁₃	C₁₃×#157	1	1	yes	characteristic, complemented
50	C₅×C₁₃	#90865	1	1	yes	characteristic, complemented
51	C₄×C₁₃	—	585	1	no	—
52	Dic₁₃	—	45	1	no	—
53	C₃²×C₅	C₁₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
54	C₃×C₁₃	—	2	24	no	—
55	C₃×C₁₃	—	2	2	no	—
56	C₃×C₁₃	—	2	2	no	—
57	#157	—	65	1	no	Hall
58	D₁₅	—	6	2	no	—
59	C₂×C₁₃	—	45	1	no	—
60	C₂×C₁₃	—	45	1	no	—
61	C₂×C₁₃	—	90	6	no	—
62	AGL(1,𝔽₅)	—	117	1	no	Hall
63	C₃⋊D₃	—	5	1	no	—
64	C₃×C₅	—	2	2	no	—
65	C₁₃	—	2	6	no	—
66	C₁₃	C₁₃×#4380	1	1	yes	characteristic, complemented
67	C₁₃	#14556844	1	1	yes	characteristic, direct product factor
68	D₅	—	9	1	no	—
69	C₃²	C₁₃×#63120	1	1	yes	characteristic, complemented, Sylow
70	D₃	—	30	2	no	—
71	C₅	C₁₃×#90865	1	1	yes	characteristic, complemented, Sylow
72	C₄	—	585	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#14556844
commutator, hypocenter	C₃²×C₅×C₁₃	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₄
prime radical	C₁₃²×C₃⋊D₁₅	C₂
cosocle	C₁₃×C₃⋊D₁₅	C₂×C₁₃
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
8. #14556844	C₁₃	direct (N × H)
11. C₃²×C₁₃²	AGL(1,𝔽₅)	semidirect
16. C₅×C₁₃²	#157	semidirect
19. C₃²×C₅×C₁₃	Dic₁₃	semidirect
20. C₃²×C₅×C₁₃	C₄×C₁₃	semidirect
37. C₁₃²	#4380	semidirect
42. C₃²×C₁₃	C₁₃×AGL(1,𝔽₅)	semidirect
43. C₃²×C₁₃	#63120	semidirect
49. C₅×C₁₃	C₁₃×#157	semidirect
50. C₅×C₁₃	#90865	semidirect
53. C₃²×C₅	C₁₃×Dic₁₃	semidirect
66. C₁₃	C₁₃×#4380	semidirect
67. C₁₃	#14556844	direct (N × H)
69. C₃²	C₁₃×#63120	semidirect
71. C₅	C₁₃×#90865	semidirect

Maximal subgroups

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

subgroup	index
C₁₃²×C₃⋊D₁₅	2
C₁₃×#90865	5
C₁₃×#63120	9
#14556844	13
C₁₃×#4380	13

Subgroups — C13×#14556844 #44478195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14556844 #44478195