Subgroups — C₂×C₅×C₁₃×C₁₆ #72182103

Order 2080.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₃×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₅×C₁₃	C₄	1	1	yes	characteristic
4	C₅×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₅×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₃×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₁₃	C₈	1	1	yes	characteristic
8	C₄×C₅×C₁₃	C₈	1	1	yes	characteristic
9	C₄×C₅×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₁₃	C₂×C₅	1	1	yes	characteristic
11	C₁₃×C₁₆	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₅×C₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₃	C₁₆	1	2	yes	direct product factor
14	C₂×C₅×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₄×C₅	1	1	yes	characteristic
16	C₈×C₁₃	C₄×C₅	1	1	yes	characteristic
17	C₈×C₁₃	C₂²×C₅	1	1	yes	characteristic
18	C₂×C₅×C₈	C₂×C₁₃	1	1	yes	characteristic
19	C₅×C₁₆	C₂×C₁₃	1	2	yes	direct product factor
20	C₅×C₁₃	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₁₃	C₅×C₈	1	1	yes	characteristic
22	C₄×C₁₃	C₅×C₈	1	1	yes	characteristic
23	C₄×C₁₃	C₂×C₄×C₅	1	1	yes	characteristic
24	C₂×C₄×C₅	C₄×C₁₃	1	1	yes	characteristic
25	C₅×C₈	C₄×C₁₃	1	1	yes	characteristic
26	C₅×C₈	C₂²×C₁₃	1	1	yes	characteristic
27	C₂×C₁₆	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₃	C₅×C₁₆	1	2	yes	direct product factor
29	C₂×C₁₃	C₂×C₅×C₈	1	1	yes	characteristic
30	C₂²×C₅	C₈×C₁₃	1	1	yes	characteristic
31	C₄×C₅	C₈×C₁₃	1	1	yes	characteristic
32	C₄×C₅	C₂×C₄×C₁₃	1	1	yes	characteristic
33	C₂×C₈	C₂×C₅×C₁₃	1	1	yes	characteristic
34	C₁₆	C₂×C₅×C₁₃	1	2	yes	direct product factor
35	C₁₃	C₂×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₅	C₁₃×C₁₆	1	2	yes	direct product factor
37	C₂×C₅	C₂×C₈×C₁₃	1	1	yes	characteristic
38	C₂×C₄	C₄×C₅×C₁₃	1	1	yes	characteristic
39	C₈	C₄×C₅×C₁₃	1	1	yes	characteristic
40	C₈	C₂²×C₅×C₁₃	1	1	yes	characteristic
41	C₅	C₂×C₁₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₅×C₈×C₁₃	1	1	yes	characteristic
43	C₄	C₅×C₈×C₁₃	1	1	yes	characteristic
44	C₄	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic
45	C₂	C₅×C₁₃×C₁₆	1	2	yes	direct product factor
46	C₂	C₂×C₅×C₈×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₅×C₁₃
socle, prime radical	C₂²×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. C₅×C₁₃×C₁₆	C₂	direct (N × H)
6. C₂×C₁₃×C₁₆	C₅	direct (N × H)
11. C₁₃×C₁₆	C₂×C₅	direct (N × H)
12. C₂×C₅×C₁₆	C₁₃	direct (N × H)
13. C₂×C₅×C₁₃	C₁₆	direct (N × H)
19. C₅×C₁₆	C₂×C₁₃	direct (N × H)
20. C₅×C₁₃	C₂×C₁₆	direct (N × H)
27. C₂×C₁₆	C₅×C₁₃	direct (N × H)
28. C₂×C₁₃	C₅×C₁₆	direct (N × H)
34. C₁₆	C₂×C₅×C₁₃	direct (N × H)
35. C₁₃	C₂×C₅×C₁₆	direct (N × H)
36. C₂×C₅	C₁₃×C₁₆	direct (N × H)
41. C₅	C₂×C₁₃×C₁₆	direct (N × H)
45. C₂	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×C₅×C₈×C₁₃	2
C₅×C₁₃×C₁₆	2
C₂×C₁₃×C₁₆	5
C₂×C₅×C₁₆	13

Subgroups — C2×C5×C13×C16 #72182103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃×C₁₆ #72182103