Subgroups — C₅×C₉×C₁₁×C₁₆ #72186826

Order 7920.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₁×C₁₆	C₃	1	1	yes	maximal, characteristic
3	C₄×C₅×C₉×C₁₁	C₄	1	1	yes	characteristic
4	C₉×C₁₁×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₈×C₁₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₅×C₉×C₁₁	C₈	1	1	yes	characteristic
7	C₅×C₁₁×C₁₆	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₈×C₉×C₁₁	C₂×C₅	1	1	yes	characteristic
9	C₅×C₉×C₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₄×C₅×C₁₁	C₃×C₄	1	1	yes	characteristic
11	C₃×C₁₁×C₁₆	C₃×C₅	1	1	yes	characteristic
12	C₅×C₉×C₁₁	C₁₆	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₈×C₁₁	C₂×C₉	1	1	yes	characteristic
14	C₄×C₉×C₁₁	C₄×C₅	1	1	yes	characteristic
15	C₅×C₈×C₉	C₂×C₁₁	1	1	yes	characteristic
16	C₂×C₃×C₅×C₁₁	C₃×C₈	1	1	yes	characteristic
17	C₃×C₈×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
18	C₃×C₅×C₁₆	C₃×C₁₁	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₄×C₉	1	1	yes	characteristic
20	C₂×C₉×C₁₁	C₅×C₈	1	1	yes	characteristic
21	C₄×C₅×C₉	C₄×C₁₁	1	1	yes	characteristic
22	C₁₁×C₁₆	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₁	C₃×C₁₆	1	1	yes	characteristic
24	C₉×C₁₆	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic
26	C₃×C₅×C₈	C₂×C₃×C₁₁	1	1	yes	characteristic
27	C₂×C₅×C₁₁	C₈×C₉	1	1	yes	characteristic
28	C₉×C₁₁	C₅×C₁₆	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅×C₉	C₈×C₁₁	1	1	yes	characteristic
30	C₈×C₁₁	C₂×C₅×C₉	1	1	yes	characteristic
31	C₅×C₁₆	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
32	C₈×C₉	C₂×C₅×C₁₁	1	1	yes	characteristic
33	C₂×C₃×C₁₁	C₃×C₅×C₈	1	1	yes	characteristic
34	C₃×C₄×C₅	C₃×C₄×C₁₁	1	1	yes	characteristic
35	C₅×C₁₁	C₉×C₁₆	1	1	yes	characteristic, direct product factor, Hall
36	C₃×C₁₆	C₃×C₅×C₁₁	1	1	yes	characteristic
37	C₅×C₉	C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Hall
38	C₄×C₁₁	C₄×C₅×C₉	1	1	yes	characteristic
39	C₅×C₈	C₂×C₉×C₁₁	1	1	yes	characteristic
40	C₄×C₉	C₄×C₅×C₁₁	1	1	yes	characteristic
41	C₃×C₁₁	C₃×C₅×C₁₆	1	1	yes	characteristic
42	C₂×C₃×C₅	C₃×C₈×C₁₁	1	1	yes	characteristic
43	C₃×C₈	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
44	C₂×C₁₁	C₅×C₈×C₉	1	1	yes	characteristic
45	C₄×C₅	C₄×C₉×C₁₁	1	1	yes	characteristic
46	C₂×C₉	C₅×C₈×C₁₁	1	1	yes	characteristic
47	C₁₆	C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
48	C₃×C₅	C₃×C₁₁×C₁₆	1	1	yes	characteristic
49	C₃×C₄	C₃×C₄×C₅×C₁₁	1	1	yes	characteristic
50	C₁₁	C₅×C₉×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₅	C₈×C₉×C₁₁	1	1	yes	characteristic
52	C₉	C₅×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
53	C₈	C₂×C₅×C₉×C₁₁	1	1	yes	characteristic
54	C₂×C₃	C₃×C₅×C₈×C₁₁	1	1	yes	characteristic
55	C₅	C₉×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
56	C₄	C₄×C₅×C₉×C₁₁	1	1	yes	characteristic
57	C₃	C₃×C₅×C₁₁×C₁₆	1	1	yes	characteristic
58	C₂	C₅×C₈×C₉×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃×C₅×C₁₁
socle, prime radical	C₂×C₃×C₅×C₁₁	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₉×C₁₁×C₁₆	C₅	direct (N × H)
7. C₅×C₁₁×C₁₆	C₉	direct (N × H)
9. C₅×C₉×C₁₆	C₁₁	direct (N × H)
12. C₅×C₉×C₁₁	C₁₆	direct (N × H)
22. C₁₁×C₁₆	C₅×C₉	direct (N × H)
24. C₉×C₁₆	C₅×C₁₁	direct (N × H)
28. C₉×C₁₁	C₅×C₁₆	direct (N × H)
31. C₅×C₁₆	C₉×C₁₁	direct (N × H)
35. C₅×C₁₁	C₉×C₁₆	direct (N × H)
37. C₅×C₉	C₁₁×C₁₆	direct (N × H)
47. C₁₆	C₅×C₉×C₁₁	direct (N × H)
50. C₁₁	C₅×C₉×C₁₆	direct (N × H)
52. C₉	C₅×C₁₁×C₁₆	direct (N × H)
55. C₅	C₉×C₁₁×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
C₅×C₈×C₉×C₁₁	2
C₃×C₅×C₁₁×C₁₆	3
C₉×C₁₁×C₁₆	5
C₅×C₉×C₁₆	11

Subgroups — C5×C9×C11×C16 #72186826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₁×C₁₆ #72186826