Subgroups — C₂×C₃×C₈×C₁₃×C₂₃ #72192511

Order 14352.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₁₃×C₂₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₄×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₈×C₁₃×C₂₃	C₂×C₃	1	2	yes	direct product factor
6	C₂²×C₃×C₁₃×C₂₃	C₄	1	1	yes	characteristic
7	C₃×C₄×C₁₃×C₂₃	C₄	1	1	yes	characteristic
8	C₃×C₄×C₁₃×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₁₃×C₂₃	C₈	1	2	yes	direct product factor
10	C₂×C₃×C₁₃×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
12	C₄×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
13	C₄×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic
14	C₂×C₃×C₈×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₁₃×C₂₃	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₈×C₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₃×C₂₃	C₃×C₈	1	2	yes	direct product factor
18	C₂×C₁₃×C₂₃	C₂×C₃×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄×C₂₃	C₂×C₁₃	1	1	yes	characteristic
20	C₃×C₈×C₂₃	C₂×C₁₃	1	2	yes	direct product factor
21	C₂×C₈×C₂₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₄×C₁₃	C₂×C₂₃	1	1	yes	characteristic
23	C₃×C₈×C₁₃	C₂×C₂₃	1	2	yes	direct product factor
24	C₁₃×C₂₃	C₂×C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃×C₂₃	C₄×C₁₃	1	1	yes	characteristic
26	C₃×C₄×C₂₃	C₄×C₁₃	1	1	yes	characteristic
27	C₃×C₄×C₂₃	C₂²×C₁₃	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₄×C₂₃	C₂×C₃×C₁₃	1	1	yes	characteristic
30	C₈×C₂₃	C₂×C₃×C₁₃	1	2	yes	direct product factor
31	C₂²×C₃×C₁₃	C₄×C₂₃	1	1	yes	characteristic
32	C₃×C₄×C₁₃	C₄×C₂₃	1	1	yes	characteristic
33	C₃×C₄×C₁₃	C₂²×C₂₃	1	1	yes	characteristic
34	C₂×C₃×C₂₃	C₈×C₁₃	1	2	yes	direct product factor
35	C₂×C₃×C₂₃	C₂×C₄×C₁₃	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
37	C₈×C₁₃	C₂×C₃×C₂₃	1	2	yes	direct product factor
38	C₂²×C₂₃	C₃×C₄×C₁₃	1	1	yes	characteristic
39	C₄×C₂₃	C₃×C₄×C₁₃	1	1	yes	characteristic
40	C₄×C₂₃	C₂²×C₃×C₁₃	1	1	yes	characteristic
41	C₂×C₃×C₁₃	C₈×C₂₃	1	2	yes	direct product factor
42	C₂×C₃×C₁₃	C₂×C₄×C₂₃	1	1	yes	characteristic
43	C₃×C₂₃	C₂×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₁₃	C₃×C₄×C₂₃	1	1	yes	characteristic
45	C₄×C₁₃	C₃×C₄×C₂₃	1	1	yes	characteristic
46	C₄×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic
47	C₂×C₃×C₈	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₂₃	C₃×C₈×C₁₃	1	2	yes	direct product factor
49	C₂×C₂₃	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
50	C₃×C₁₃	C₂×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₁₃	C₃×C₈×C₂₃	1	2	yes	direct product factor
52	C₂×C₁₃	C₂×C₃×C₄×C₂₃	1	1	yes	characteristic
53	C₂×C₃×C₄	C₂×C₁₃×C₂₃	1	1	yes	characteristic
54	C₃×C₈	C₂×C₁₃×C₂₃	1	2	yes	direct product factor
55	C₂₃	C₂×C₃×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₈	C₃×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₁₃	C₂×C₃×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃	C₄×C₁₃×C₂₃	1	1	yes	characteristic
59	C₃×C₄	C₄×C₁₃×C₂₃	1	1	yes	characteristic
60	C₃×C₄	C₂²×C₁₃×C₂₃	1	1	yes	characteristic
61	C₂×C₄	C₂×C₃×C₁₃×C₂₃	1	1	yes	characteristic
62	C₈	C₂×C₃×C₁₃×C₂₃	1	2	yes	direct product factor
63	C₂×C₃	C₈×C₁₃×C₂₃	1	2	yes	direct product factor
64	C₂×C₃	C₂×C₄×C₁₃×C₂₃	1	1	yes	characteristic
65	C₂²	C₃×C₄×C₁₃×C₂₃	1	1	yes	characteristic
66	C₄	C₃×C₄×C₁₃×C₂₃	1	1	yes	characteristic
67	C₄	C₂²×C₃×C₁₃×C₂₃	1	1	yes	characteristic
68	C₃	C₂×C₈×C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×C₈×C₁₃×C₂₃	1	2	yes	direct product factor
70	C₂	C₂×C₃×C₄×C₁₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₃×C₂₃
socle, prime radical	C₂²×C₃×C₁₃×C₂₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₁₃×C₂₃	C₂	direct (N × H)
3. C₂×C₈×C₁₃×C₂₃	C₃	direct (N × H)
5. C₈×C₁₃×C₂₃	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₃×C₂₃	C₈	direct (N × H)
14. C₂×C₃×C₈×C₂₃	C₁₃	direct (N × H)
15. C₃×C₁₃×C₂₃	C₂×C₈	direct (N × H)
16. C₂×C₃×C₈×C₁₃	C₂₃	direct (N × H)
17. C₂×C₁₃×C₂₃	C₃×C₈	direct (N × H)
20. C₃×C₈×C₂₃	C₂×C₁₃	direct (N × H)
21. C₂×C₈×C₂₃	C₃×C₁₃	direct (N × H)
23. C₃×C₈×C₁₃	C₂×C₂₃	direct (N × H)
24. C₁₃×C₂₃	C₂×C₃×C₈	direct (N × H)
28. C₂×C₈×C₁₃	C₃×C₂₃	direct (N × H)
30. C₈×C₂₃	C₂×C₃×C₁₃	direct (N × H)
34. C₂×C₃×C₂₃	C₈×C₁₃	direct (N × H)
37. C₈×C₁₃	C₂×C₃×C₂₃	direct (N × H)
41. C₂×C₃×C₁₃	C₈×C₂₃	direct (N × H)
43. C₃×C₂₃	C₂×C₈×C₁₃	direct (N × H)
47. C₂×C₃×C₈	C₁₃×C₂₃	direct (N × H)
48. C₂×C₂₃	C₃×C₈×C₁₃	direct (N × H)
50. C₃×C₁₃	C₂×C₈×C₂₃	direct (N × H)
51. C₂×C₁₃	C₃×C₈×C₂₃	direct (N × H)
54. C₃×C₈	C₂×C₁₃×C₂₃	direct (N × H)
55. C₂₃	C₂×C₃×C₈×C₁₃	direct (N × H)
56. C₂×C₈	C₃×C₁₃×C₂₃	direct (N × H)
57. C₁₃	C₂×C₃×C₈×C₂₃	direct (N × H)
62. C₈	C₂×C₃×C₁₃×C₂₃	direct (N × H)
63. C₂×C₃	C₈×C₁₃×C₂₃	direct (N × H)
68. C₃	C₂×C₈×C₁₃×C₂₃	direct (N × H)
69. C₂	C₃×C₈×C₁₃×C₂₃	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×C₄×C₁₃×C₂₃	2
C₃×C₈×C₁₃×C₂₃	2
C₂×C₈×C₁₃×C₂₃	3
C₂×C₃×C₈×C₂₃	13
C₂×C₃×C₈×C₁₃	23

Subgroups — C2×C3×C8×C13×C23 #72192511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₈×C₁₃×C₂₃ #72192511