Subgroups — C₄×C₈×C₁₃×C₅₃ #72199549

Order 22048.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₃×C₅₃	C₂	1	2	yes	maximal
2	C₄²×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₅₃	C₄	1	2	yes	—
4	C₂×C₄×C₁₃×C₅₃	C₂²	1	1	yes	characteristic
5	C₈×C₁₃×C₅₃	C₄	1	4	yes	direct product factor
6	C₂²×C₁₃×C₅₃	C₂×C₄	1	1	yes	characteristic
7	C₄×C₁₃×C₅₃	C₈	1	4	yes	direct product factor
8	C₄×C₁₃×C₅₃	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₅₃	C₄²	1	1	yes	characteristic
11	C₂×C₁₃×C₅₃	C₂×C₈	1	2	yes	—
12	C₂×C₈×C₅₃	C₂×C₁₃	1	2	yes	—
13	C₄²×C₅₃	C₂×C₁₃	1	1	yes	characteristic
14	C₁₃×C₅₃	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄×C₅₃	C₄×C₁₃	1	2	yes	—
16	C₂×C₄×C₅₃	C₂²×C₁₃	1	1	yes	characteristic
17	C₈×C₅₃	C₄×C₁₃	1	4	yes	direct product factor
18	C₄×C₈×C₁₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₅₃	C₂×C₄×C₁₃	1	1	yes	characteristic
20	C₄×C₅₃	C₈×C₁₃	1	4	yes	direct product factor
21	C₄×C₅₃	C₂×C₄×C₁₃	1	2	yes	—
22	C₂×C₈×C₁₃	C₂×C₅₃	1	2	yes	—
23	C₄²×C₁₃	C₂×C₅₃	1	1	yes	characteristic
24	C₂×C₅₃	C₄²×C₁₃	1	1	yes	characteristic
25	C₂×C₅₃	C₂×C₈×C₁₃	1	2	yes	—
26	C₂×C₄×C₁₃	C₄×C₅₃	1	2	yes	—
27	C₂×C₄×C₁₃	C₂²×C₅₃	1	1	yes	characteristic
28	C₈×C₁₃	C₄×C₅₃	1	4	yes	direct product factor
29	C₅₃	C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₁₃	C₂×C₄×C₅₃	1	1	yes	characteristic
31	C₄×C₁₃	C₈×C₅₃	1	4	yes	direct product factor
32	C₄×C₁₃	C₂×C₄×C₅₃	1	2	yes	—
33	C₄×C₈	C₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₃	C₄²×C₅₃	1	1	yes	characteristic
35	C₂×C₁₃	C₂×C₈×C₅₃	1	2	yes	—
36	C₂×C₈	C₂×C₁₃×C₅₃	1	2	yes	—
37	C₄²	C₂×C₁₃×C₅₃	1	1	yes	characteristic
38	C₁₃	C₄×C₈×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₄	C₄×C₁₃×C₅₃	1	2	yes	—
40	C₂×C₄	C₂²×C₁₃×C₅₃	1	1	yes	characteristic
41	C₈	C₄×C₁₃×C₅₃	1	4	yes	direct product factor
42	C₂²	C₂×C₄×C₁₃×C₅₃	1	1	yes	characteristic
43	C₄	C₈×C₁₃×C₅₃	1	4	yes	direct product factor
44	C₄	C₂×C₄×C₁₃×C₅₃	1	2	yes	—
45	C₂	C₄²×C₁₃×C₅₃	1	1	yes	characteristic
46	C₂	C₂×C₈×C₁₃×C₅₃	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₁₃×C₅₃
socle, prime radical	C₂²×C₁₃×C₅₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈×C₁₃×C₅₃	C₄	direct (N × H)
7. C₄×C₁₃×C₅₃	C₈	direct (N × H)
9. C₄×C₈×C₅₃	C₁₃	direct (N × H)
14. C₁₃×C₅₃	C₄×C₈	direct (N × H)
17. C₈×C₅₃	C₄×C₁₃	direct (N × H)
18. C₄×C₈×C₁₃	C₅₃	direct (N × H)
20. C₄×C₅₃	C₈×C₁₃	direct (N × H)
28. C₈×C₁₃	C₄×C₅₃	direct (N × H)
29. C₅₃	C₄×C₈×C₁₃	direct (N × H)
31. C₄×C₁₃	C₈×C₅₃	direct (N × H)
33. C₄×C₈	C₁₃×C₅₃	direct (N × H)
38. C₁₃	C₄×C₈×C₅₃	direct (N × H)
41. C₈	C₄×C₁₃×C₅₃	direct (N × H)
43. C₄	C₈×C₁₃×C₅₃	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×C₈×C₁₃×C₅₃	2
C₄²×C₁₃×C₅₃	2
C₄×C₈×C₅₃	13
C₄×C₈×C₁₃	53

Subgroups — C4×C8×C13×C53 #72199549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₈×C₁₃×C₅₃ #72199549