Subgroups — C₂×C₃×C₈×C₁₉×C₂₃ #72198549

Order 20976.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₁₉×C₂₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₁₉×C₂₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₄×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₈×C₁₉×C₂₃	C₂×C₃	1	2	yes	direct product factor
6	C₂²×C₃×C₁₉×C₂₃	C₄	1	1	yes	characteristic
7	C₃×C₄×C₁₉×C₂₃	C₄	1	1	yes	characteristic
8	C₃×C₄×C₁₉×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₁₉×C₂₃	C₈	1	2	yes	direct product factor
10	C₂×C₃×C₁₉×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₉×C₂₃	C₃×C₄	1	1	yes	characteristic
12	C₄×C₁₉×C₂₃	C₃×C₄	1	1	yes	characteristic
13	C₄×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic
14	C₃×C₁₉×C₂₃	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₈×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₈×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₉×C₂₃	C₃×C₈	1	2	yes	direct product factor
18	C₂×C₁₉×C₂₃	C₂×C₃×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄×C₂₃	C₂×C₁₉	1	1	yes	characteristic
20	C₃×C₈×C₂₃	C₂×C₁₉	1	2	yes	direct product factor
21	C₂×C₃×C₄×C₁₉	C₂×C₂₃	1	1	yes	characteristic
22	C₃×C₈×C₁₉	C₂×C₂₃	1	2	yes	direct product factor
23	C₁₉×C₂₃	C₂×C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₈×C₂₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₈×C₁₉	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₂₃	C₄×C₁₉	1	1	yes	characteristic
27	C₃×C₄×C₂₃	C₄×C₁₉	1	1	yes	characteristic
28	C₃×C₄×C₂₃	C₂²×C₁₉	1	1	yes	characteristic
29	C₂²×C₃×C₁₉	C₄×C₂₃	1	1	yes	characteristic
30	C₃×C₄×C₁₉	C₄×C₂₃	1	1	yes	characteristic
31	C₃×C₄×C₁₉	C₂²×C₂₃	1	1	yes	characteristic
32	C₂×C₄×C₂₃	C₂×C₃×C₁₉	1	1	yes	characteristic
33	C₈×C₂₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
34	C₂×C₄×C₁₉	C₂×C₃×C₂₃	1	1	yes	characteristic
35	C₈×C₁₉	C₂×C₃×C₂₃	1	2	yes	direct product factor
36	C₂×C₃×C₂₃	C₈×C₁₉	1	2	yes	direct product factor
37	C₂×C₃×C₂₃	C₂×C₄×C₁₉	1	1	yes	characteristic
38	C₂×C₃×C₁₉	C₈×C₂₃	1	2	yes	direct product factor
39	C₂×C₃×C₁₉	C₂×C₄×C₂₃	1	1	yes	characteristic
40	C₂²×C₂₃	C₃×C₄×C₁₉	1	1	yes	characteristic
41	C₄×C₂₃	C₃×C₄×C₁₉	1	1	yes	characteristic
42	C₄×C₂₃	C₂²×C₃×C₁₉	1	1	yes	characteristic
43	C₂²×C₁₉	C₃×C₄×C₂₃	1	1	yes	characteristic
44	C₄×C₁₉	C₃×C₄×C₂₃	1	1	yes	characteristic
45	C₄×C₁₉	C₂²×C₃×C₂₃	1	1	yes	characteristic
46	C₃×C₂₃	C₂×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Hall
47	C₃×C₁₉	C₂×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₃×C₈	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₂₃	C₃×C₈×C₁₉	1	2	yes	direct product factor
50	C₂×C₂₃	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
51	C₂×C₁₉	C₃×C₈×C₂₃	1	2	yes	direct product factor
52	C₂×C₁₉	C₂×C₃×C₄×C₂₃	1	1	yes	characteristic
53	C₂×C₃×C₄	C₂×C₁₉×C₂₃	1	1	yes	characteristic
54	C₃×C₈	C₂×C₁₉×C₂₃	1	2	yes	direct product factor
55	C₂₃	C₂×C₃×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₁₉	C₂×C₃×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₈	C₃×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃	C₄×C₁₉×C₂₃	1	1	yes	characteristic
59	C₃×C₄	C₄×C₁₉×C₂₃	1	1	yes	characteristic
60	C₃×C₄	C₂²×C₁₉×C₂₃	1	1	yes	characteristic
61	C₂×C₄	C₂×C₃×C₁₉×C₂₃	1	1	yes	characteristic
62	C₈	C₂×C₃×C₁₉×C₂₃	1	2	yes	direct product factor
63	C₂×C₃	C₈×C₁₉×C₂₃	1	2	yes	direct product factor
64	C₂×C₃	C₂×C₄×C₁₉×C₂₃	1	1	yes	characteristic
65	C₂²	C₃×C₄×C₁₉×C₂₃	1	1	yes	characteristic
66	C₄	C₃×C₄×C₁₉×C₂₃	1	1	yes	characteristic
67	C₄	C₂²×C₃×C₁₉×C₂₃	1	1	yes	characteristic
68	C₃	C₂×C₈×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×C₈×C₁₉×C₂₃	1	2	yes	direct product factor
70	C₂	C₂×C₃×C₄×C₁₉×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₉×C₂₃
socle, prime radical	C₂²×C₃×C₁₉×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×C₁₉×C₂₃	C₂	direct (N × H)
3. C₂×C₈×C₁₉×C₂₃	C₃	direct (N × H)
5. C₈×C₁₉×C₂₃	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₉×C₂₃	C₈	direct (N × H)
14. C₃×C₁₉×C₂₃	C₂×C₈	direct (N × H)
15. C₂×C₃×C₈×C₂₃	C₁₉	direct (N × H)
16. C₂×C₃×C₈×C₁₉	C₂₃	direct (N × H)
17. C₂×C₁₉×C₂₃	C₃×C₈	direct (N × H)
20. C₃×C₈×C₂₃	C₂×C₁₉	direct (N × H)
22. C₃×C₈×C₁₉	C₂×C₂₃	direct (N × H)
23. C₁₉×C₂₃	C₂×C₃×C₈	direct (N × H)
24. C₂×C₈×C₂₃	C₃×C₁₉	direct (N × H)
25. C₂×C₈×C₁₉	C₃×C₂₃	direct (N × H)
33. C₈×C₂₃	C₂×C₃×C₁₉	direct (N × H)
35. C₈×C₁₉	C₂×C₃×C₂₃	direct (N × H)
36. C₂×C₃×C₂₃	C₈×C₁₉	direct (N × H)
38. C₂×C₃×C₁₉	C₈×C₂₃	direct (N × H)
46. C₃×C₂₃	C₂×C₈×C₁₉	direct (N × H)
47. C₃×C₁₉	C₂×C₈×C₂₃	direct (N × H)
48. C₂×C₃×C₈	C₁₉×C₂₃	direct (N × H)
49. C₂×C₂₃	C₃×C₈×C₁₉	direct (N × H)
51. C₂×C₁₉	C₃×C₈×C₂₃	direct (N × H)
54. C₃×C₈	C₂×C₁₉×C₂₃	direct (N × H)
55. C₂₃	C₂×C₃×C₈×C₁₉	direct (N × H)
56. C₁₉	C₂×C₃×C₈×C₂₃	direct (N × H)
57. C₂×C₈	C₃×C₁₉×C₂₃	direct (N × H)
62. C₈	C₂×C₃×C₁₉×C₂₃	direct (N × H)
63. C₂×C₃	C₈×C₁₉×C₂₃	direct (N × H)
68. C₃	C₂×C₈×C₁₉×C₂₃	direct (N × H)
69. C₂	C₃×C₈×C₁₉×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×C₁₉×C₂₃	2
C₃×C₈×C₁₉×C₂₃	2
C₂×C₈×C₁₉×C₂₃	3
C₂×C₃×C₈×C₂₃	19
C₂×C₃×C₈×C₁₉	23

Subgroups — C2×C3×C8×C19×C23 #72198549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₈×C₁₉×C₂₃ #72198549