Subgroups — C₂³×C₃×C₄×C₁₃×C₁₉ #72201049

Order 23712.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃×C₁₉	C₂	1	14	yes	maximal, direct product factor
2	C₂⁴×C₃×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₁₃×C₁₉	C₄	1	8	yes	direct product factor
5	C₂³×C₃×C₁₃×C₁₉	C₂²	1	7	yes	—
6	C₂×C₃×C₄×C₁₃×C₁₉	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂²×C₄×C₁₃×C₁₉	C₂×C₃	1	14	yes	direct product factor
9	C₂²×C₃×C₁₃×C₁₉	C₂×C₄	1	28	yes	direct product factor
10	C₂²×C₃×C₁₃×C₁₉	C₂³	1	7	yes	—
11	C₃×C₄×C₁₃×C₁₉	C₂³	1	8	yes	direct product factor
12	C₂³×C₁₃×C₁₉	C₃×C₄	1	8	yes	direct product factor
13	C₂³×C₁₃×C₁₉	C₂²×C₃	1	7	yes	—
14	C₂×C₄×C₁₃×C₁₉	C₂²×C₃	1	28	yes	direct product factor
15	C₂³×C₃×C₄×C₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₁₃×C₁₉	C₂²×C₄	1	14	yes	direct product factor
17	C₂×C₃×C₁₃×C₁₉	C₂⁴	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₁₃×C₁₉	C₂×C₃×C₄	1	28	yes	direct product factor
20	C₂²×C₁₃×C₁₉	C₂³×C₃	1	7	yes	—
21	C₄×C₁₃×C₁₉	C₂³×C₃	1	8	yes	direct product factor
22	C₂⁴×C₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₁₉	C₂×C₁₃	1	14	yes	direct product factor
24	C₃×C₁₃×C₁₉	C₂³×C₄	1	1	yes	characteristic, direct product factor, Hall
25	C₂⁴×C₃×C₁₃	C₂×C₁₉	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₁₃	C₂×C₁₉	1	14	yes	direct product factor
27	C₂³×C₄×C₁₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₁₃×C₁₉	C₂²×C₃×C₄	1	14	yes	direct product factor
29	C₂×C₁₃×C₁₉	C₂⁴×C₃	1	1	yes	characteristic
30	C₂³×C₃×C₁₉	C₄×C₁₃	1	8	yes	direct product factor
31	C₂³×C₃×C₁₉	C₂²×C₁₃	1	7	yes	—
32	C₂×C₃×C₄×C₁₉	C₂²×C₁₃	1	28	yes	direct product factor
33	C₂³×C₄×C₁₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂³×C₃×C₁₃	C₄×C₁₉	1	8	yes	direct product factor
35	C₂³×C₃×C₁₃	C₂²×C₁₉	1	7	yes	—
36	C₂×C₃×C₄×C₁₃	C₂²×C₁₉	1	28	yes	direct product factor
37	C₂⁴×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂×C₃×C₁₃	1	14	yes	direct product factor
39	C₁₃×C₁₉	C₂³×C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₃×C₁₉	C₂×C₄×C₁₃	1	28	yes	direct product factor
41	C₂²×C₃×C₁₉	C₂³×C₁₃	1	7	yes	—
42	C₃×C₄×C₁₉	C₂³×C₁₃	1	8	yes	direct product factor
43	C₂⁴×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×C₃×C₁₉	1	14	yes	direct product factor
45	C₂²×C₃×C₁₃	C₂×C₄×C₁₉	1	28	yes	direct product factor
46	C₂²×C₃×C₁₃	C₂³×C₁₉	1	7	yes	—
47	C₃×C₄×C₁₃	C₂³×C₁₉	1	8	yes	direct product factor
48	C₂³×C₁₉	C₃×C₄×C₁₃	1	8	yes	direct product factor
49	C₂³×C₁₉	C₂²×C₃×C₁₃	1	7	yes	—
50	C₂×C₄×C₁₉	C₂²×C₃×C₁₃	1	28	yes	direct product factor
51	C₂×C₃×C₁₉	C₂²×C₄×C₁₃	1	14	yes	direct product factor
52	C₂×C₃×C₁₉	C₂⁴×C₁₃	1	1	yes	characteristic
53	C₂³×C₁₃	C₃×C₄×C₁₉	1	8	yes	direct product factor
54	C₂³×C₁₃	C₂²×C₃×C₁₉	1	7	yes	—
55	C₂×C₄×C₁₃	C₂²×C₃×C₁₉	1	28	yes	direct product factor
56	C₂³×C₃×C₄	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
57	C₂×C₃×C₁₃	C₂²×C₄×C₁₉	1	14	yes	direct product factor
58	C₂×C₃×C₁₃	C₂⁴×C₁₉	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×C₃×C₄×C₁₃	1	28	yes	direct product factor
60	C₂²×C₁₉	C₂³×C₃×C₁₃	1	7	yes	—
61	C₄×C₁₉	C₂³×C₃×C₁₃	1	8	yes	direct product factor
62	C₃×C₁₉	C₂³×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
63	C₂²×C₁₃	C₂×C₃×C₄×C₁₉	1	28	yes	direct product factor
64	C₂²×C₁₃	C₂³×C₃×C₁₉	1	7	yes	—
65	C₄×C₁₃	C₂³×C₃×C₁₉	1	8	yes	direct product factor
66	C₂⁴×C₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic
67	C₂²×C₃×C₄	C₂×C₁₃×C₁₉	1	14	yes	direct product factor
68	C₃×C₁₃	C₂³×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
69	C₂×C₁₉	C₂²×C₃×C₄×C₁₃	1	14	yes	direct product factor
70	C₂×C₁₉	C₂⁴×C₃×C₁₃	1	1	yes	characteristic
71	C₂³×C₄	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×C₁₃	C₂²×C₃×C₄×C₁₉	1	14	yes	direct product factor
73	C₂×C₁₃	C₂⁴×C₃×C₁₉	1	1	yes	characteristic
74	C₂³×C₃	C₄×C₁₃×C₁₉	1	8	yes	direct product factor
75	C₂³×C₃	C₂²×C₁₃×C₁₉	1	7	yes	—
76	C₂×C₃×C₄	C₂²×C₁₃×C₁₉	1	28	yes	direct product factor
77	C₁₉	C₂³×C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
78	C₂⁴	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic
79	C₂²×C₄	C₂×C₃×C₁₃×C₁₉	1	14	yes	direct product factor
80	C₁₃	C₂³×C₃×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₃	C₂×C₄×C₁₃×C₁₉	1	28	yes	direct product factor
82	C₂²×C₃	C₂³×C₁₃×C₁₉	1	7	yes	—
83	C₃×C₄	C₂³×C₁₃×C₁₉	1	8	yes	direct product factor
84	C₂³	C₃×C₄×C₁₃×C₁₉	1	8	yes	direct product factor
85	C₂³	C₂²×C₃×C₁₃×C₁₉	1	7	yes	—
86	C₂×C₄	C₂²×C₃×C₁₃×C₁₉	1	28	yes	direct product factor
87	C₂×C₃	C₂²×C₄×C₁₃×C₁₉	1	14	yes	direct product factor
88	C₂×C₃	C₂⁴×C₁₃×C₁₉	1	1	yes	characteristic
89	C₂²	C₂×C₃×C₄×C₁₃×C₁₉	1	28	yes	direct product factor
90	C₂²	C₂³×C₃×C₁₃×C₁₉	1	7	yes	—
91	C₄	C₂³×C₃×C₁₃×C₁₉	1	8	yes	direct product factor
92	C₃	C₂³×C₄×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	C₂⁴×C₃×C₁₃×C₁₉	1	1	yes	characteristic
94	C₂	C₂²×C₃×C₄×C₁₃×C₁₉	1	14	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₃×C₁₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₃×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₄×C₁₃×C₁₉	C₂	direct (N × H)
3. C₂³×C₄×C₁₃×C₁₉	C₃	direct (N × H)
4. C₂³×C₃×C₁₃×C₁₉	C₄	direct (N × H)
6. C₂×C₃×C₄×C₁₃×C₁₉	C₂²	direct (N × H)
8. C₂²×C₄×C₁₃×C₁₉	C₂×C₃	direct (N × H)
9. C₂²×C₃×C₁₃×C₁₉	C₂×C₄	direct (N × H)
11. C₃×C₄×C₁₃×C₁₉	C₂³	direct (N × H)
12. C₂³×C₁₃×C₁₉	C₃×C₄	direct (N × H)
14. C₂×C₄×C₁₃×C₁₉	C₂²×C₃	direct (N × H)
15. C₂³×C₃×C₄×C₁₉	C₁₃	direct (N × H)
16. C₂×C₃×C₁₃×C₁₉	C₂²×C₄	direct (N × H)
18. C₂³×C₃×C₄×C₁₃	C₁₉	direct (N × H)
19. C₂²×C₁₃×C₁₉	C₂×C₃×C₄	direct (N × H)
21. C₄×C₁₃×C₁₉	C₂³×C₃	direct (N × H)
23. C₂²×C₃×C₄×C₁₉	C₂×C₁₃	direct (N × H)
24. C₃×C₁₃×C₁₉	C₂³×C₄	direct (N × H)
26. C₂²×C₃×C₄×C₁₃	C₂×C₁₉	direct (N × H)
27. C₂³×C₄×C₁₉	C₃×C₁₃	direct (N × H)
28. C₂×C₁₃×C₁₉	C₂²×C₃×C₄	direct (N × H)
30. C₂³×C₃×C₁₉	C₄×C₁₃	direct (N × H)
32. C₂×C₃×C₄×C₁₉	C₂²×C₁₃	direct (N × H)
33. C₂³×C₄×C₁₃	C₃×C₁₉	direct (N × H)
34. C₂³×C₃×C₁₃	C₄×C₁₉	direct (N × H)
36. C₂×C₃×C₄×C₁₃	C₂²×C₁₉	direct (N × H)
38. C₂²×C₄×C₁₉	C₂×C₃×C₁₃	direct (N × H)
39. C₁₃×C₁₉	C₂³×C₃×C₄	direct (N × H)
40. C₂²×C₃×C₁₉	C₂×C₄×C₁₃	direct (N × H)
42. C₃×C₄×C₁₉	C₂³×C₁₃	direct (N × H)
44. C₂²×C₄×C₁₃	C₂×C₃×C₁₉	direct (N × H)
45. C₂²×C₃×C₁₃	C₂×C₄×C₁₉	direct (N × H)
47. C₃×C₄×C₁₃	C₂³×C₁₉	direct (N × H)
48. C₂³×C₁₉	C₃×C₄×C₁₃	direct (N × H)
50. C₂×C₄×C₁₉	C₂²×C₃×C₁₃	direct (N × H)
51. C₂×C₃×C₁₉	C₂²×C₄×C₁₃	direct (N × H)
53. C₂³×C₁₃	C₃×C₄×C₁₉	direct (N × H)
55. C₂×C₄×C₁₃	C₂²×C₃×C₁₉	direct (N × H)
56. C₂³×C₃×C₄	C₁₃×C₁₉	direct (N × H)
57. C₂×C₃×C₁₃	C₂²×C₄×C₁₉	direct (N × H)
59. C₂²×C₁₉	C₂×C₃×C₄×C₁₃	direct (N × H)
61. C₄×C₁₉	C₂³×C₃×C₁₃	direct (N × H)
62. C₃×C₁₉	C₂³×C₄×C₁₃	direct (N × H)
63. C₂²×C₁₃	C₂×C₃×C₄×C₁₉	direct (N × H)
65. C₄×C₁₃	C₂³×C₃×C₁₉	direct (N × H)
67. C₂²×C₃×C₄	C₂×C₁₃×C₁₉	direct (N × H)
68. C₃×C₁₃	C₂³×C₄×C₁₉	direct (N × H)
69. C₂×C₁₉	C₂²×C₃×C₄×C₁₃	direct (N × H)
71. C₂³×C₄	C₃×C₁₃×C₁₉	direct (N × H)
72. C₂×C₁₃	C₂²×C₃×C₄×C₁₉	direct (N × H)
74. C₂³×C₃	C₄×C₁₃×C₁₉	direct (N × H)
76. C₂×C₃×C₄	C₂²×C₁₃×C₁₉	direct (N × H)
77. C₁₉	C₂³×C₃×C₄×C₁₃	direct (N × H)
79. C₂²×C₄	C₂×C₃×C₁₃×C₁₉	direct (N × H)
80. C₁₃	C₂³×C₃×C₄×C₁₉	direct (N × H)
81. C₂²×C₃	C₂×C₄×C₁₃×C₁₉	direct (N × H)
83. C₃×C₄	C₂³×C₁₃×C₁₉	direct (N × H)
84. C₂³	C₃×C₄×C₁₃×C₁₉	direct (N × H)
86. C₂×C₄	C₂²×C₃×C₁₃×C₁₉	direct (N × H)
87. C₂×C₃	C₂²×C₄×C₁₃×C₁₉	direct (N × H)
89. C₂²	C₂×C₃×C₄×C₁₃×C₁₉	direct (N × H)
91. C₄	C₂³×C₃×C₁₃×C₁₉	direct (N × H)
92. C₃	C₂³×C₄×C₁₃×C₁₉	direct (N × H)
94. C₂	C₂²×C₃×C₄×C₁₃×C₁₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₄×C₁₃×C₁₉	2
C₂⁴×C₃×C₁₃×C₁₉	2
C₂³×C₄×C₁₃×C₁₉	3
C₂³×C₃×C₄×C₁₉	13
C₂³×C₃×C₄×C₁₃	19

Subgroups — C23×C3×C4×C13×C19 #72201049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₄×C₁₃×C₁₉ #72201049