Subgroups — C₂×C₃×C₅⋊#11759815 #44478160

Order 30420.

960 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#92788	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅⋊#11759815	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊#11759815	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅×#92788	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×#11759815	—	5	1	no	maximal, Hall
7	C₃×C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×#92788	C₂×C₃	1	3	yes	complemented
9	C₅⋊#11759815	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅⋊(C₁₃⋊D₁₃)	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×#92788	D₅	1	1	yes	characteristic, complemented
13	C₃×#11759815	—	5	2	no	—
14	C₅×#92788	C₂²×C₃	1	3	yes	complemented
15	C₃×C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅⋊(D₁₃⋊C₃)	—	13	14	no	maximal
17	C₂×C₃×C₁₃⋊D₁₃	—	5	1	no	—
18	C₂×#11759815	—	5	3	no	—
19	C₂×C₅×C₁₃²	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₅⋊(C₁₃⋊D₁₃)	C₂×C₃²	1	2	yes	complemented
21	C₃×#92788	C₂×D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅×C₁₃⋊C₃	—	13	14	no	—
23	C₃×C₅⋊(D₁₃⋊C₃)	—	13	28	no	—
24	C₂×C₃×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
25	C₃×C₁₃⋊D₁₃	—	5	2	no	—
26	C₂×#92788	C₃×D₅	1	3	yes	complemented
27	#11759815	—	5	6	no	—
28	C₅×C₁₃²	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×D₆₅	—	13	14	no	—
30	C₂×C₅⋊(D₁₃⋊C₃)	—	13	42	no	—
31	C₂×C₁₃⋊D₁₃	—	5	1	no	Hall
32	C₃×C₅×C₁₃⋊C₃	—	13	14	no	—
33	C₃×C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
34	#92788	C₂×C₃×D₅	1	3	yes	complemented
35	C₂×C₃×D₁₃⋊C₃	—	65	14	no	—
36	C₂×C₃×C₅×C₁₃	D₁₃⋊C₃	1	14	yes	complemented
37	C₃×D₆₅	—	13	28	no	—
38	C₂×C₅×C₁₃⋊C₃	—	13	42	no	—
39	C₅⋊(D₁₃⋊C₃)	—	13	84	no	—
40	C₂×C₁₃²	C₃²×D₅	1	1	yes	characteristic, complemented
41	C₁₃⋊D₁₃	—	5	2	no	—
42	C₂×D₆₅	—	13	14	no	—
43	C₂×C₃×C₁₃⋊C₃	—	13	14	no	—
44	C₃×D₁₃⋊C₃	—	65	28	no	—
45	C₃×C₅×C₁₃	C₂×D₁₃⋊C₃	1	14	yes	complemented
46	C₅×C₁₃⋊C₃	—	13	42	no	—
47	C₂×C₃²×D₅	—	169	1	no	Hall
48	C₁₃²	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×D₁₃	—	65	14	no	—
50	C₂×D₁₃⋊C₃	—	65	42	no	—
51	C₂×C₅×C₁₃	C₃×D₁₃⋊C₃	1	14	yes	complemented
52	D₆₅	—	13	28	no	—
53	C₃×C₁₃⋊C₃	—	13	14	no	—
54	C₂×C₃²×C₅	—	169	1	no	—
55	C₃²×D₅	—	169	2	no	—
56	C₂×C₃×C₁₃	C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
57	C₃×D₁₃	—	65	28	no	—
58	C₂×C₁₃⋊C₃	—	13	42	no	—
59	D₁₃⋊C₃	—	65	84	no	—
60	C₅×C₁₃	C₂×C₃×D₁₃⋊C₃	1	14	yes	complemented
61	C₂×C₃×D₅	—	169	3	no	—
62	C₂×C₃×D₅	—	169	1	no	—
63	C₂×D₁₃	—	65	14	no	—
64	C₃²×C₅	—	169	1	no	Hall
65	C₃×C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
66	C₁₃⋊C₃	—	13	42	no	—
67	C₂²×C₃²	—	845	1	no	Hall
68	C₂×C₃×C₅	—	169	3	no	—
69	C₂×C₃×C₅	#11759815	1	1	yes	characteristic, complemented
70	C₃×D₅	—	169	6	no	—
71	C₃×D₅	—	169	2	no	—
72	C₂×C₁₃	C₃×C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
73	D₁₃	—	65	28	no	—
74	C₂×D₅	—	169	1	no	Hall
75	C₂×C₃²	—	845	2	no	—
76	C₂×C₃²	—	169	1	no	—
77	C₃×C₅	—	169	3	no	—
78	C₃×C₅	C₂×#11759815	1	1	yes	characteristic, complemented
79	C₁₃	C₂×C₃×C₅⋊(D₁₃⋊C₃)	1	14	yes	complemented
80	C₂²×C₃	—	845	3	no	—
81	C₂²×C₃	—	845	1	no	—
82	C₂×C₅	C₃×#11759815	1	1	yes	characteristic, complemented
83	D₅	—	169	2	no	—
84	C₃²	—	169	1	no	Sylow
85	C₂×C₃	—	845	6	no	—
86	C₂×C₃	—	845	2	no	—
87	C₂×C₃	—	169	3	no	—
88	C₂×C₃	C₅⋊#11759815	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₃×#11759815	1	1	yes	characteristic, complemented, Sylow
90	C₂²	—	845	1	no	Sylow
91	C₃	—	169	3	no	—
92	C₃	C₂×C₅⋊#11759815	1	1	yes	characteristic, direct product factor
93	C₂	—	845	2	no	—
94	C₂	C₃×C₅⋊#11759815	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊#11759815
commutator, cosocle, hypocenter	C₅×C₁₃²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#92788	C₂	semidirect
2. C₃×C₅⋊#11759815	C₂	direct (N × H)
3. C₂×C₃×C₅⋊(C₁₃⋊D₁₃)	C₃	semidirect
4. C₂×C₅⋊#11759815	C₃	direct (N × H)
5. C₃×C₅×#92788	C₂²	semidirect
7. C₃×C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	semidirect
8. C₂×C₅×#92788	C₂×C₃	semidirect
9. C₅⋊#11759815	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₁₃²	C₂×C₃	semidirect
11. C₂×C₅⋊(C₁₃⋊D₁₃)	C₃²	semidirect
12. C₂×C₃×#92788	D₅	semidirect
14. C₅×#92788	C₂²×C₃	semidirect
15. C₃×C₅×C₁₃²	C₂²×C₃	semidirect
19. C₂×C₅×C₁₃²	C₂×C₃²	semidirect
20. C₅⋊(C₁₃⋊D₁₃)	C₂×C₃²	semidirect
21. C₃×#92788	C₂×D₅	semidirect
24. C₂×C₃×C₁₃²	C₃×D₅	semidirect
26. C₂×#92788	C₃×D₅	semidirect
28. C₅×C₁₃²	C₂²×C₃²	semidirect
33. C₃×C₁₃²	C₂×C₃×D₅	semidirect
34. #92788	C₂×C₃×D₅	semidirect
36. C₂×C₃×C₅×C₁₃	D₁₃⋊C₃	semidirect
40. C₂×C₁₃²	C₃²×D₅	semidirect
45. C₃×C₅×C₁₃	C₂×D₁₃⋊C₃	semidirect
48. C₁₃²	C₂×C₃²×D₅	semidirect
51. C₂×C₅×C₁₃	C₃×D₁₃⋊C₃	semidirect
56. C₂×C₃×C₁₃	C₅⋊(D₁₃⋊C₃)	semidirect
60. C₅×C₁₃	C₂×C₃×D₁₃⋊C₃	semidirect
65. C₃×C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
69. C₂×C₃×C₅	#11759815	semidirect
72. C₂×C₁₃	C₃×C₅⋊(D₁₃⋊C₃)	semidirect
78. C₃×C₅	C₂×#11759815	semidirect
79. C₁₃	C₂×C₃×C₅⋊(D₁₃⋊C₃)	semidirect
82. C₂×C₅	C₃×#11759815	semidirect
88. C₂×C₃	C₅⋊#11759815	direct (N × H)
89. C₅	C₂×C₃×#11759815	semidirect
92. C₃	C₂×C₅⋊#11759815	direct (N × H)
94. C₂	C₃×C₅⋊#11759815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#92788	2
C₃×C₅⋊#11759815	2
C₂×C₃×C₅⋊(C₁₃⋊D₁₃)	3
C₂×C₅⋊#11759815	3
C₂×C₃×#11759815	5
C₂×C₃×C₅⋊(D₁₃⋊C₃)	13

Subgroups — C2×C3×C5⋊#11759815 #44478160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅⋊#11759815 #44478160