Subgroups — C₂×C₃×C₅×C₁₃×C₁₆ #72185404

Order 6240.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₃×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₃×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅×C₁₃	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic
9	C₅×C₁₃×C₁₆	C₂×C₃	1	2	yes	direct product factor
10	C₂²×C₃×C₅×C₁₃	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅×C₁₃	C₈	1	1	yes	characteristic
12	C₃×C₄×C₅×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₈×C₁₃	C₂×C₅	1	1	yes	characteristic
14	C₃×C₁₃×C₁₆	C₂×C₅	1	2	yes	direct product factor
15	C₂×C₄×C₅×C₁₃	C₃×C₄	1	1	yes	characteristic
16	C₅×C₈×C₁₃	C₃×C₄	1	1	yes	characteristic
17	C₅×C₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₃×C₅×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₃×C₁₆	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₅×C₁₃	C₁₆	1	2	yes	direct product factor
21	C₂×C₃×C₅×C₁₃	C₂×C₈	1	1	yes	characteristic
22	C₂×C₃×C₄×C₁₃	C₄×C₅	1	1	yes	characteristic
23	C₃×C₈×C₁₃	C₄×C₅	1	1	yes	characteristic
24	C₃×C₈×C₁₃	C₂²×C₅	1	1	yes	characteristic
25	C₂²×C₅×C₁₃	C₃×C₈	1	1	yes	characteristic
26	C₄×C₅×C₁₃	C₃×C₈	1	1	yes	characteristic
27	C₄×C₅×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
28	C₂×C₃×C₅×C₈	C₂×C₁₃	1	1	yes	characteristic
29	C₃×C₅×C₁₆	C₂×C₁₃	1	2	yes	direct product factor
30	C₂×C₈×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
31	C₁₃×C₁₆	C₂×C₃×C₅	1	2	yes	direct product factor
32	C₃×C₅×C₁₃	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₅×C₁₆	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
34	C₂²×C₃×C₁₃	C₅×C₈	1	1	yes	characteristic
35	C₃×C₄×C₁₃	C₅×C₈	1	1	yes	characteristic
36	C₃×C₄×C₁₃	C₂×C₄×C₅	1	1	yes	characteristic
37	C₂×C₅×C₁₃	C₃×C₁₆	1	2	yes	direct product factor
38	C₂×C₅×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
39	C₂×C₃×C₄×C₅	C₄×C₁₃	1	1	yes	characteristic
40	C₃×C₅×C₈	C₄×C₁₃	1	1	yes	characteristic
41	C₃×C₅×C₈	C₂²×C₁₃	1	1	yes	characteristic
42	C₂×C₄×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic
43	C₈×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic
44	C₈×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
45	C₂×C₃×C₁₆	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
46	C₂×C₅×C₈	C₂×C₃×C₁₃	1	1	yes	characteristic
47	C₅×C₁₆	C₂×C₃×C₁₃	1	2	yes	direct product factor
48	C₂×C₃×C₁₃	C₅×C₁₆	1	2	yes	direct product factor
49	C₂×C₃×C₁₃	C₂×C₅×C₈	1	1	yes	characteristic
50	C₅×C₁₃	C₂×C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
51	C₂²×C₃×C₅	C₈×C₁₃	1	1	yes	characteristic
52	C₃×C₄×C₅	C₈×C₁₃	1	1	yes	characteristic
53	C₃×C₄×C₅	C₂×C₄×C₁₃	1	1	yes	characteristic
54	C₂²×C₁₃	C₃×C₅×C₈	1	1	yes	characteristic
55	C₄×C₁₃	C₃×C₅×C₈	1	1	yes	characteristic
56	C₄×C₁₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic
57	C₂×C₃×C₈	C₂×C₅×C₁₃	1	1	yes	characteristic
58	C₃×C₁₆	C₂×C₅×C₁₃	1	2	yes	direct product factor
59	C₂×C₄×C₅	C₃×C₄×C₁₃	1	1	yes	characteristic
60	C₅×C₈	C₃×C₄×C₁₃	1	1	yes	characteristic
61	C₅×C₈	C₂²×C₃×C₁₃	1	1	yes	characteristic
62	C₃×C₁₃	C₂×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Hall
63	C₂×C₁₆	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃×C₅	C₁₃×C₁₆	1	2	yes	direct product factor
65	C₂×C₃×C₅	C₂×C₈×C₁₃	1	1	yes	characteristic
66	C₂×C₁₃	C₃×C₅×C₁₆	1	2	yes	direct product factor
67	C₂×C₁₃	C₂×C₃×C₅×C₈	1	1	yes	characteristic
68	C₂×C₃×C₄	C₄×C₅×C₁₃	1	1	yes	characteristic
69	C₃×C₈	C₄×C₅×C₁₃	1	1	yes	characteristic
70	C₃×C₈	C₂²×C₅×C₁₃	1	1	yes	characteristic
71	C₂²×C₅	C₃×C₈×C₁₃	1	1	yes	characteristic
72	C₄×C₅	C₃×C₈×C₁₃	1	1	yes	characteristic
73	C₄×C₅	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
74	C₂×C₈	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
75	C₁₆	C₂×C₃×C₅×C₁₃	1	2	yes	direct product factor
76	C₃×C₅	C₂×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
77	C₁₃	C₂×C₃×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²×C₃	C₅×C₈×C₁₃	1	1	yes	characteristic
79	C₃×C₄	C₅×C₈×C₁₃	1	1	yes	characteristic
80	C₃×C₄	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic
81	C₂×C₅	C₃×C₁₃×C₁₆	1	2	yes	direct product factor
82	C₂×C₅	C₂×C₃×C₈×C₁₃	1	1	yes	characteristic
83	C₂×C₄	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
84	C₈	C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
85	C₈	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic
86	C₂×C₃	C₅×C₁₃×C₁₆	1	2	yes	direct product factor
87	C₂×C₃	C₂×C₅×C₈×C₁₃	1	1	yes	characteristic
88	C₅	C₂×C₃×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₃×C₅×C₈×C₁₃	1	1	yes	characteristic
90	C₄	C₃×C₅×C₈×C₁₃	1	1	yes	characteristic
91	C₄	C₂×C₃×C₄×C₅×C₁₃	1	1	yes	characteristic
92	C₃	C₂×C₅×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	C₃×C₅×C₁₃×C₁₆	1	2	yes	direct product factor
94	C₂	C₂×C₃×C₅×C₈×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃×C₅×C₁₃
socle, prime radical	C₂²×C₃×C₅×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₁₃×C₁₆	C₂	direct (N × H)
3. C₂×C₅×C₁₃×C₁₆	C₃	direct (N × H)
7. C₂×C₃×C₁₃×C₁₆	C₅	direct (N × H)
9. C₅×C₁₃×C₁₆	C₂×C₃	direct (N × H)
14. C₃×C₁₃×C₁₆	C₂×C₅	direct (N × H)
18. C₂×C₃×C₅×C₁₆	C₁₃	direct (N × H)
19. C₂×C₁₃×C₁₆	C₃×C₅	direct (N × H)
20. C₂×C₃×C₅×C₁₃	C₁₆	direct (N × H)
29. C₃×C₅×C₁₆	C₂×C₁₃	direct (N × H)
31. C₁₃×C₁₆	C₂×C₃×C₅	direct (N × H)
32. C₃×C₅×C₁₃	C₂×C₁₆	direct (N × H)
33. C₂×C₅×C₁₆	C₃×C₁₃	direct (N × H)
37. C₂×C₅×C₁₃	C₃×C₁₆	direct (N × H)
45. C₂×C₃×C₁₆	C₅×C₁₃	direct (N × H)
47. C₅×C₁₆	C₂×C₃×C₁₃	direct (N × H)
48. C₂×C₃×C₁₃	C₅×C₁₆	direct (N × H)
50. C₅×C₁₃	C₂×C₃×C₁₆	direct (N × H)
58. C₃×C₁₆	C₂×C₅×C₁₃	direct (N × H)
62. C₃×C₁₃	C₂×C₅×C₁₆	direct (N × H)
63. C₂×C₁₆	C₃×C₅×C₁₃	direct (N × H)
64. C₂×C₃×C₅	C₁₃×C₁₆	direct (N × H)
66. C₂×C₁₃	C₃×C₅×C₁₆	direct (N × H)
75. C₁₆	C₂×C₃×C₅×C₁₃	direct (N × H)
76. C₃×C₅	C₂×C₁₃×C₁₆	direct (N × H)
77. C₁₃	C₂×C₃×C₅×C₁₆	direct (N × H)
81. C₂×C₅	C₃×C₁₃×C₁₆	direct (N × H)
86. C₂×C₃	C₅×C₁₃×C₁₆	direct (N × H)
88. C₅	C₂×C₃×C₁₃×C₁₆	direct (N × H)
92. C₃	C₂×C₅×C₁₃×C₁₆	direct (N × H)
93. C₂	C₃×C₅×C₁₃×C₁₆	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×C₈×C₁₃	2
C₃×C₅×C₁₃×C₁₆	2
C₂×C₅×C₁₃×C₁₆	3
C₂×C₃×C₁₃×C₁₆	5
C₂×C₃×C₅×C₁₆	13

Subgroups — C2×C3×C5×C13×C16 #72185404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₃×C₁₆ #72185404