Subgroups — C₅×C₁₃×#90866 #44478189

Order 30420.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×#90866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×D₃₉	—	6	2	no	—
5	C₅×C₁₃×#261	—	9	1	no	maximal, Hall
6	C₁₃×C₃⋊D₃₉	C₂×C₅	1	1	yes	characteristic
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	C₅×#90866	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₅×C₁₃×#157	—	13	1	no	maximal
10	C₅×C₁₃×D₁₃	—	9	1	no	—
11	C₃²×C₁₃²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₃⋊D₃₉	C₂×C₁₃	1	1	yes	characteristic
13	C₅×C₁₃×C₃⋊D₃	—	13	1	no	—
14	C₁₃×D₃₉	—	6	2	no	—
15	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
16	C₁₃×#261	—	9	1	no	Hall
17	C₃²×C₅×C₁₃	—	4	3	no	—
18	C₃²×C₅×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
19	C₃²×C₅×C₁₃	#261	1	1	yes	characteristic, complemented
20	C₃×C₁₃²	—	2	2	no	—
21	#90866	C₅×C₁₃	1	1	yes	characteristic, direct product factor
22	C₁₃×#157	—	13	1	no	—
23	C₅×D₃₉	—	6	2	no	—
24	C₅×D₃×C₁₃	—	78	2	no	—
25	C₁₃×D₁₃	—	9	1	no	—
26	C₅×#261	—	9	1	no	—
27	C₄×C₅×C₁₃	—	117	1	no	—
28	C₃⋊D₃₉	C₂×C₅×C₁₃	1	1	yes	characteristic
29	C₁₃×C₃⋊D₃	—	13	1	no	—
30	C₃×C₅×C₁₃	—	2	2	no	—
31	C₃×C₅×C₁₃	—	2	2	no	—
32	C₃×C₅×C₁₃	—	4	12	no	—
33	C₅×#157	—	13	1	no	Hall
34	C₁₃²	C₅×#157	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₅×C₁₃	—	117	1	no	—
36	C₅×D₁₃	—	9	1	no	—
37	C₃²×C₁₃	—	4	3	no	—
38	C₃²×C₁₃	C₄×C₅×C₁₃	1	1	yes	characteristic, complemented
39	C₃²×C₁₃	C₅×#261	1	1	yes	characteristic, complemented
40	C₅×C₃⋊D₃	—	13	1	no	—
41	D₃₉	—	6	2	no	—
42	D₃×C₁₃	—	78	2	no	—
43	C₅×C₁₃	—	4	3	no	—
44	C₅×C₁₃	C₁₃×#157	1	1	yes	characteristic, complemented
45	C₅×C₁₃	#90866	1	1	yes	characteristic, direct product factor
46	#261	—	9	1	no	—
47	C₄×C₁₃	—	117	1	no	—
48	C₃²×C₅	C₁₃×#261	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	—	2	2	no	—
50	C₃×C₁₃	—	2	2	no	—
51	C₃×C₁₃	—	4	12	no	—
52	#157	—	13	1	no	Hall
53	C₅×D₃	—	78	2	no	—
54	C₂×C₁₃	—	117	1	no	—
55	D₁₃	—	9	1	no	—
56	C₄×C₅	—	117	1	no	Hall
57	C₃⋊D₃	—	13	1	no	—
58	C₃×C₅	—	2	2	no	—
59	C₁₃	—	4	3	no	—
60	C₁₃	C₅×C₁₃×#157	1	1	yes	characteristic, complemented
61	C₁₃	C₅×#90866	1	1	yes	characteristic, direct product factor
62	C₂×C₅	—	117	1	no	—
63	C₃²	C₅×C₁₃×#261	1	1	yes	characteristic, complemented, Sylow
64	D₃	—	78	2	no	—
65	C₅	C₁₃×#90866	1	1	yes	characteristic, direct product factor, Sylow
66	C₄	—	117	1	no	Sylow
67	C₃	—	2	2	no	—
68	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₃	#90866
commutator, hypocenter	C₃²×C₁₃	C₄×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₄
prime radical	C₅×C₁₃×C₃⋊D₃₉	C₂
cosocle	C₃⋊D₃₉	C₂×C₅×C₁₃
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
3. C₁₃×#90866	C₅	direct (N × H)
8. C₅×#90866	C₁₃	direct (N × H)
11. C₃²×C₁₃²	C₄×C₅	semidirect
15. C₅×C₁₃²	#157	semidirect
18. C₃²×C₅×C₁₃	C₄×C₁₃	semidirect
19. C₃²×C₅×C₁₃	#261	semidirect
21. #90866	C₅×C₁₃	direct (N × H)
34. C₁₃²	C₅×#157	semidirect
38. C₃²×C₁₃	C₄×C₅×C₁₃	semidirect
39. C₃²×C₁₃	C₅×#261	semidirect
44. C₅×C₁₃	C₁₃×#157	semidirect
45. C₅×C₁₃	#90866	direct (N × H)
48. C₃²×C₅	C₁₃×#261	semidirect
60. C₁₃	C₅×C₁₃×#157	semidirect
61. C₁₃	C₅×#90866	direct (N × H)
63. C₃²	C₅×C₁₃×#261	semidirect
65. C₅	C₁₃×#90866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₃⋊D₃₉	2
C₁₃×#90866	5
C₅×C₁₃×#261	9
C₅×#90866	13
C₅×C₁₃×#157	13

Subgroups — C5×C13×#90866 #44478189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×#90866 #44478189