Subgroups — C₂×C₅×#13109896 #30655083

Order 16380.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13109896	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#11717941	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₇×D₁₃	C₃	1	1	yes	maximal, characteristic
4	C₅×#11717941	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#13109896	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×D₁₃	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×D₁₃⋊C₉	—	7	1	no	maximal, Hall
9	C₂×C₅×C₇×D₁₃	C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×#11717941	C₂×C₅	1	1	yes	characteristic, complemented
11	#13109896	C₂×C₅	1	2	yes	direct product factor
12	C₃×C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₅×C₇⋊C₉	—	13	1	no	maximal, Hall
14	C₂×C₅×C₁₃⋊C₉	—	7	1	no	—
15	C₅×D₁₃⋊C₉	—	7	2	no	—
16	C₂×C₃×C₇×D₁₃	C₃×C₅	1	1	yes	characteristic
17	C₂×C₅×C₇×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
18	C₅×C₇×D₁₃	C₂×C₉	1	2	yes	complemented
19	#11717941	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₂×C₅×C₇⋊C₉	—	13	2	no	—
22	C₂×C₅×C₇⋊C₉	—	13	1	no	—
23	C₅×C₁₃⋊C₉	—	7	1	no	Hall
24	C₂×C₃×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
25	C₃×C₇×D₁₃	C₂×C₃×C₅	1	2	yes	—
26	C₂×D₁₃⋊C₉	—	7	1	no	Hall
27	C₅×C₇×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₃×C₅×C₇	—	39	1	no	—
29	C₂×C₃×C₅×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₃×C₅×D₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	—
31	C₂×C₇×D₁₃	C₅×C₉	1	1	yes	characteristic, complemented, Hall
32	C₅×C₇⋊C₉	—	13	1	no	Hall
33	C₃×C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
34	C₂×C₅×D₁₃	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₇⋊C₉	—	13	1	no	Hall
36	C₂×C₁₃⋊C₉	—	7	1	no	—
37	D₁₃⋊C₉	—	7	2	no	—
38	C₂×C₃×C₅×C₇	—	39	2	no	—
39	C₂×C₃×C₅×C₇	D₁₃⋊C₃	1	1	yes	characteristic
40	C₃×C₅×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
41	C₂×C₇×C₁₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented
42	C₇×D₁₃	C₂×C₅×C₉	1	2	yes	complemented
43	C₂²×C₅×C₉	—	91	1	no	Hall
44	C₂×C₃×D₁₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
45	C₂²×C₅×C₇	—	39	1	no	Hall
46	C₂×C₅×C₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
47	C₅×D₁₃	C₂×C₇⋊C₉	1	2	yes	complemented
48	C₂×C₇⋊C₉	—	13	2	no	—
49	C₂×C₇⋊C₉	—	13	1	no	—
50	C₁₃⋊C₉	—	7	1	no	Hall
51	C₃×C₅×C₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic
52	C₇×C₁₃	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₅×C₉	—	91	2	no	—
54	C₂×C₅×C₉	—	91	1	no	—
55	C₂²×C₃×C₇	—	39	1	no	—
56	C₂×C₃×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
57	C₃×D₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	2	yes	—
58	C₂×C₅×C₇	—	39	2	no	—
59	C₂×C₅×C₇	D₁₃⋊C₉	1	1	yes	characteristic, complemented
60	C₅×C₁₃	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
61	C₇⋊C₉	—	13	1	no	Hall
62	C₂²×C₃×C₅	—	39	1	no	—
63	C₂×D₁₃	C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
64	C₅×C₉	—	91	1	no	Hall
65	C₂×C₃×C₇	—	39	2	no	—
66	C₂×C₃×C₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic
67	C₃×C₁₃	C₂²×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
68	C₂²×C₉	—	91	1	no	Hall
69	C₅×C₇	C₂×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
70	C₂×C₃×C₅	—	39	2	no	—
71	C₂×C₃×C₅	#10587716	1	1	yes	characteristic
72	C₂²×C₇	—	39	1	no	Hall
73	C₂×C₁₃	C₂×C₅×C₇⋊C₉	1	1	yes	characteristic, complemented
74	D₁₃	C₂×C₅×C₇⋊C₉	1	2	yes	complemented
75	C₃×C₇	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic
76	C₂²×C₅	—	39	1	no	Hall
77	C₂×C₉	—	91	2	no	—
78	C₂×C₉	—	91	1	no	—
79	C₃×C₅	C₂×#10587716	1	1	yes	characteristic
80	C₂×C₇	—	39	2	no	—
81	C₂×C₇	C₅×D₁₃⋊C₉	1	1	yes	characteristic, complemented
82	C₁₃	C₂²×C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₃	—	39	1	no	—
84	C₂×C₅	—	39	2	no	—
85	C₂×C₅	#13109896	1	1	yes	characteristic, direct product factor
86	C₉	—	91	1	no	Sylow
87	C₇	C₂×C₅×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	39	2	no	—
89	C₂×C₃	C₅×#10587716	1	1	yes	characteristic
90	C₅	C₂×#13109896	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	39	1	no	Sylow
92	C₃	C₂×C₅×#10587716	1	1	yes	characteristic
93	C₂	—	39	2	no	—
94	C₂	C₅×#13109896	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#10587716
commutator, hypocenter	C₇×C₁₃	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×#10587716
Fitting, socle	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₅×C₇×D₁₃	C₃
cosocle	C₃×C₇×C₁₃	C₂²×C₃×C₅
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#13109896	C₂	direct (N × H)
2. C₂×C₅×#11717941	C₂	semidirect
4. C₅×#11717941	C₂²	semidirect
5. C₂×#13109896	C₅	direct (N × H)
9. C₂×C₅×C₇×D₁₃	C₉	semidirect
10. C₂×#11717941	C₂×C₅	semidirect
11. #13109896	C₂×C₅	direct (N × H)
17. C₂×C₅×C₇×C₁₃	C₂×C₉	semidirect
18. C₅×C₇×D₁₃	C₂×C₉	semidirect
19. #11717941	C₂²×C₅	semidirect
27. C₅×C₇×C₁₃	C₂²×C₉	semidirect
31. C₂×C₇×D₁₃	C₅×C₉	semidirect
34. C₂×C₅×D₁₃	C₇⋊C₉	semidirect
41. C₂×C₇×C₁₃	C₂×C₅×C₉	semidirect
42. C₇×D₁₃	C₂×C₅×C₉	semidirect
46. C₂×C₅×C₁₃	C₂×C₇⋊C₉	semidirect
47. C₅×D₁₃	C₂×C₇⋊C₉	semidirect
52. C₇×C₁₃	C₂²×C₅×C₉	semidirect
59. C₂×C₅×C₇	D₁₃⋊C₉	semidirect
60. C₅×C₁₃	C₂²×C₇⋊C₉	semidirect
63. C₂×D₁₃	C₅×C₇⋊C₉	semidirect
69. C₅×C₇	C₂×D₁₃⋊C₉	semidirect
73. C₂×C₁₃	C₂×C₅×C₇⋊C₉	semidirect
74. D₁₃	C₂×C₅×C₇⋊C₉	semidirect
81. C₂×C₇	C₅×D₁₃⋊C₉	semidirect
82. C₁₃	C₂²×C₅×C₇⋊C₉	semidirect
85. C₂×C₅	#13109896	direct (N × H)
87. C₇	C₂×C₅×D₁₃⋊C₉	semidirect
90. C₅	C₂×#13109896	direct (N × H)
94. C₂	C₅×#13109896	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×#13109896	2
C₂×C₅×#11717941	2
C₂×C₃×C₅×C₇×D₁₃	3
C₂×#13109896	5
C₂×C₅×D₁₃⋊C₉	7
C₂²×C₅×C₇⋊C₉	13

Subgroups — C2×C5×#13109896 #30655083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#13109896 #30655083