Subgroups — C₂⁵×C₃²×C₄×C₁₉ #72199374

Order 21888.

63312 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃²×C₄×C₁₉	C₂	1	62	yes	maximal, direct product factor
3	C₂⁵×C₃×C₄×C₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₂⁵×C₃²×C₁₉	C₄	1	32	yes	direct product factor
5	C₂⁵×C₃²×C₁₉	C₂²	1	31	yes	—
6	C₂³×C₃²×C₄×C₁₉	C₂²	1	620	yes	direct product factor
7	C₂⁴×C₃×C₄×C₁₉	C₂×C₃	1	248	yes	direct product factor
8	C₂⁶×C₃×C₁₉	C₂×C₃	1	4	yes	—
9	C₂⁴×C₃²×C₁₉	C₂×C₄	1	496	yes	direct product factor
10	C₂⁴×C₃²×C₁₉	C₂³	1	155	yes	—
11	C₂²×C₃²×C₄×C₁₉	C₂³	1	1240	yes	direct product factor
12	C₂⁵×C₄×C₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
13	C₂⁵×C₃×C₁₉	C₃×C₄	1	128	yes	direct product factor
14	C₂⁵×C₃×C₁₉	C₂²×C₃	1	124	yes	—
15	C₂³×C₃×C₄×C₁₉	C₂²×C₃	1	2480	yes	direct product factor
16	C₂³×C₃²×C₁₉	C₂²×C₄	1	1240	yes	direct product factor
17	C₂³×C₃²×C₁₉	C₂⁴	1	155	yes	—
18	C₂×C₃²×C₄×C₁₉	C₂⁴	1	496	yes	direct product factor
19	C₂⁶×C₁₉	C₂×C₃²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₉	C₂×C₃²	1	62	yes	direct product factor
21	C₂⁵×C₃²×C₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂⁴×C₃×C₁₉	C₂×C₃×C₄	1	1984	yes	direct product factor
23	C₂⁴×C₃×C₁₉	C₂³×C₃	1	620	yes	—
24	C₂²×C₃×C₄×C₁₉	C₂³×C₃	1	4960	yes	direct product factor
25	C₂²×C₃²×C₁₉	C₂³×C₄	1	620	yes	direct product factor
26	C₂²×C₃²×C₁₉	C₂⁵	1	31	yes	—
27	C₃²×C₄×C₁₉	C₂⁵	1	32	yes	direct product factor
28	C₂⁵×C₁₉	C₃²×C₄	1	32	yes	direct product factor
29	C₂⁵×C₁₉	C₂²×C₃²	1	31	yes	—
30	C₂³×C₄×C₁₉	C₂²×C₃²	1	620	yes	direct product factor
31	C₂⁶×C₃²	C₂×C₁₉	1	1	yes	characteristic
32	C₂⁴×C₃²×C₄	C₂×C₁₉	1	62	yes	direct product factor
33	C₂³×C₃×C₁₉	C₂²×C₃×C₄	1	4960	yes	direct product factor
34	C₂³×C₃×C₁₉	C₂⁴×C₃	1	620	yes	—
35	C₂×C₃×C₄×C₁₉	C₂⁴×C₃	1	1984	yes	direct product factor
36	C₂⁵×C₃×C₄	C₃×C₁₉	1	4	yes	direct product factor
37	C₂×C₃²×C₁₉	C₂⁴×C₄	1	62	yes	direct product factor
38	C₂×C₃²×C₁₉	C₂⁶	1	1	yes	characteristic
39	C₂⁴×C₁₉	C₂×C₃²×C₄	1	496	yes	direct product factor
40	C₂⁴×C₁₉	C₂³×C₃²	1	155	yes	—
41	C₂²×C₄×C₁₉	C₂³×C₃²	1	1240	yes	direct product factor
42	C₂⁵×C₃²	C₄×C₁₉	1	32	yes	direct product factor
43	C₂⁵×C₃²	C₂²×C₁₉	1	31	yes	—
44	C₂³×C₃²×C₄	C₂²×C₁₉	1	620	yes	direct product factor
45	C₂²×C₃×C₁₉	C₂³×C₃×C₄	1	2480	yes	direct product factor
46	C₂²×C₃×C₁₉	C₂⁵×C₃	1	124	yes	—
47	C₃×C₄×C₁₉	C₂⁵×C₃	1	128	yes	direct product factor
48	C₂⁶×C₃	C₂×C₃×C₁₉	1	4	yes	—
49	C₂⁴×C₃×C₄	C₂×C₃×C₁₉	1	248	yes	direct product factor
50	C₃²×C₁₉	C₂⁵×C₄	1	1	yes	characteristic, direct product factor, Hall
51	C₂³×C₁₉	C₂²×C₃²×C₄	1	1240	yes	direct product factor
52	C₂³×C₁₉	C₂⁴×C₃²	1	155	yes	—
53	C₂×C₄×C₁₉	C₂⁴×C₃²	1	496	yes	direct product factor
54	C₂⁴×C₃²	C₂×C₄×C₁₉	1	496	yes	direct product factor
55	C₂⁴×C₃²	C₂³×C₁₉	1	155	yes	—
56	C₂²×C₃²×C₄	C₂³×C₁₉	1	1240	yes	direct product factor
57	C₂⁵×C₄	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃×C₁₉	C₂⁴×C₃×C₄	1	248	yes	direct product factor
59	C₂×C₃×C₁₉	C₂⁶×C₃	1	4	yes	—
60	C₂⁵×C₃	C₃×C₄×C₁₉	1	128	yes	direct product factor
61	C₂⁵×C₃	C₂²×C₃×C₁₉	1	124	yes	—
62	C₂³×C₃×C₄	C₂²×C₃×C₁₉	1	2480	yes	direct product factor
63	C₂²×C₁₉	C₂³×C₃²×C₄	1	620	yes	direct product factor
64	C₂²×C₁₉	C₂⁵×C₃²	1	31	yes	—
65	C₄×C₁₉	C₂⁵×C₃²	1	32	yes	direct product factor
66	C₂³×C₃²	C₂²×C₄×C₁₉	1	1240	yes	direct product factor
67	C₂³×C₃²	C₂⁴×C₁₉	1	155	yes	—
68	C₂×C₃²×C₄	C₂⁴×C₁₉	1	496	yes	direct product factor
69	C₂⁶	C₂×C₃²×C₁₉	1	1	yes	characteristic
70	C₂⁴×C₄	C₂×C₃²×C₁₉	1	62	yes	direct product factor
71	C₃×C₁₉	C₂⁵×C₃×C₄	1	4	yes	direct product factor
72	C₂⁴×C₃	C₂×C₃×C₄×C₁₉	1	1984	yes	direct product factor
73	C₂⁴×C₃	C₂³×C₃×C₁₉	1	620	yes	—
74	C₂²×C₃×C₄	C₂³×C₃×C₁₉	1	4960	yes	direct product factor
75	C₂×C₁₉	C₂⁴×C₃²×C₄	1	62	yes	direct product factor
76	C₂×C₁₉	C₂⁶×C₃²	1	1	yes	characteristic
77	C₂²×C₃²	C₂³×C₄×C₁₉	1	620	yes	direct product factor
78	C₂²×C₃²	C₂⁵×C₁₉	1	31	yes	—
79	C₃²×C₄	C₂⁵×C₁₉	1	32	yes	direct product factor
80	C₂⁵	C₃²×C₄×C₁₉	1	32	yes	direct product factor
81	C₂⁵	C₂²×C₃²×C₁₉	1	31	yes	—
82	C₂³×C₄	C₂²×C₃²×C₁₉	1	620	yes	direct product factor
83	C₂³×C₃	C₂²×C₃×C₄×C₁₉	1	4960	yes	direct product factor
84	C₂³×C₃	C₂⁴×C₃×C₁₉	1	620	yes	—
85	C₂×C₃×C₄	C₂⁴×C₃×C₁₉	1	1984	yes	direct product factor
86	C₁₉	C₂⁵×C₃²×C₄	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₃²	C₂⁴×C₄×C₁₉	1	62	yes	direct product factor
88	C₂×C₃²	C₂⁶×C₁₉	1	1	yes	characteristic
89	C₂⁴	C₂×C₃²×C₄×C₁₉	1	496	yes	direct product factor
90	C₂⁴	C₂³×C₃²×C₁₉	1	155	yes	—
91	C₂²×C₄	C₂³×C₃²×C₁₉	1	1240	yes	direct product factor
92	C₂²×C₃	C₂³×C₃×C₄×C₁₉	1	2480	yes	direct product factor
93	C₂²×C₃	C₂⁵×C₃×C₁₉	1	124	yes	—
94	C₃×C₄	C₂⁵×C₃×C₁₉	1	128	yes	direct product factor
95	C₃²	C₂⁵×C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	C₂²×C₃²×C₄×C₁₉	1	1240	yes	direct product factor
97	C₂³	C₂⁴×C₃²×C₁₉	1	155	yes	—
98	C₂×C₄	C₂⁴×C₃²×C₁₉	1	496	yes	direct product factor
99	C₂×C₃	C₂⁶×C₃×C₁₉	1	4	yes	—
100	C₂×C₃	C₂⁴×C₃×C₄×C₁₉	1	248	yes	direct product factor
101	C₂²	C₂³×C₃²×C₄×C₁₉	1	620	yes	direct product factor
102	C₂²	C₂⁵×C₃²×C₁₉	1	31	yes	—
103	C₄	C₂⁵×C₃²×C₁₉	1	32	yes	direct product factor
104	C₃	C₂⁵×C₃×C₄×C₁₉	1	4	yes	direct product factor
105	C₂	C₂⁴×C₃²×C₄×C₁₉	1	62	yes	direct product factor
106	C₂	C₂⁶×C₃²×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁶×C₃²×C₁₉
socle, prime radical	C₂⁶×C₃²×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃²×C₄×C₁₉	C₂	direct (N × H)
3. C₂⁵×C₃×C₄×C₁₉	C₃	direct (N × H)
4. C₂⁵×C₃²×C₁₉	C₄	direct (N × H)
6. C₂³×C₃²×C₄×C₁₉	C₂²	direct (N × H)
7. C₂⁴×C₃×C₄×C₁₉	C₂×C₃	direct (N × H)
9. C₂⁴×C₃²×C₁₉	C₂×C₄	direct (N × H)
11. C₂²×C₃²×C₄×C₁₉	C₂³	direct (N × H)
12. C₂⁵×C₄×C₁₉	C₃²	direct (N × H)
13. C₂⁵×C₃×C₁₉	C₃×C₄	direct (N × H)
15. C₂³×C₃×C₄×C₁₉	C₂²×C₃	direct (N × H)
16. C₂³×C₃²×C₁₉	C₂²×C₄	direct (N × H)
18. C₂×C₃²×C₄×C₁₉	C₂⁴	direct (N × H)
20. C₂⁴×C₄×C₁₉	C₂×C₃²	direct (N × H)
21. C₂⁵×C₃²×C₄	C₁₉	direct (N × H)
22. C₂⁴×C₃×C₁₉	C₂×C₃×C₄	direct (N × H)
24. C₂²×C₃×C₄×C₁₉	C₂³×C₃	direct (N × H)
25. C₂²×C₃²×C₁₉	C₂³×C₄	direct (N × H)
27. C₃²×C₄×C₁₉	C₂⁵	direct (N × H)
28. C₂⁵×C₁₉	C₃²×C₄	direct (N × H)
30. C₂³×C₄×C₁₉	C₂²×C₃²	direct (N × H)
32. C₂⁴×C₃²×C₄	C₂×C₁₉	direct (N × H)
33. C₂³×C₃×C₁₉	C₂²×C₃×C₄	direct (N × H)
35. C₂×C₃×C₄×C₁₉	C₂⁴×C₃	direct (N × H)
36. C₂⁵×C₃×C₄	C₃×C₁₉	direct (N × H)
37. C₂×C₃²×C₁₉	C₂⁴×C₄	direct (N × H)
39. C₂⁴×C₁₉	C₂×C₃²×C₄	direct (N × H)
41. C₂²×C₄×C₁₉	C₂³×C₃²	direct (N × H)
42. C₂⁵×C₃²	C₄×C₁₉	direct (N × H)
44. C₂³×C₃²×C₄	C₂²×C₁₉	direct (N × H)
45. C₂²×C₃×C₁₉	C₂³×C₃×C₄	direct (N × H)
47. C₃×C₄×C₁₉	C₂⁵×C₃	direct (N × H)
49. C₂⁴×C₃×C₄	C₂×C₃×C₁₉	direct (N × H)
50. C₃²×C₁₉	C₂⁵×C₄	direct (N × H)
51. C₂³×C₁₉	C₂²×C₃²×C₄	direct (N × H)
53. C₂×C₄×C₁₉	C₂⁴×C₃²	direct (N × H)
54. C₂⁴×C₃²	C₂×C₄×C₁₉	direct (N × H)
56. C₂²×C₃²×C₄	C₂³×C₁₉	direct (N × H)
57. C₂⁵×C₄	C₃²×C₁₉	direct (N × H)
58. C₂×C₃×C₁₉	C₂⁴×C₃×C₄	direct (N × H)
60. C₂⁵×C₃	C₃×C₄×C₁₉	direct (N × H)
62. C₂³×C₃×C₄	C₂²×C₃×C₁₉	direct (N × H)
63. C₂²×C₁₉	C₂³×C₃²×C₄	direct (N × H)
65. C₄×C₁₉	C₂⁵×C₃²	direct (N × H)
66. C₂³×C₃²	C₂²×C₄×C₁₉	direct (N × H)
68. C₂×C₃²×C₄	C₂⁴×C₁₉	direct (N × H)
70. C₂⁴×C₄	C₂×C₃²×C₁₉	direct (N × H)
71. C₃×C₁₉	C₂⁵×C₃×C₄	direct (N × H)
72. C₂⁴×C₃	C₂×C₃×C₄×C₁₉	direct (N × H)
74. C₂²×C₃×C₄	C₂³×C₃×C₁₉	direct (N × H)
75. C₂×C₁₉	C₂⁴×C₃²×C₄	direct (N × H)
77. C₂²×C₃²	C₂³×C₄×C₁₉	direct (N × H)
79. C₃²×C₄	C₂⁵×C₁₉	direct (N × H)
80. C₂⁵	C₃²×C₄×C₁₉	direct (N × H)
82. C₂³×C₄	C₂²×C₃²×C₁₉	direct (N × H)
83. C₂³×C₃	C₂²×C₃×C₄×C₁₉	direct (N × H)
85. C₂×C₃×C₄	C₂⁴×C₃×C₁₉	direct (N × H)
86. C₁₉	C₂⁵×C₃²×C₄	direct (N × H)
87. C₂×C₃²	C₂⁴×C₄×C₁₉	direct (N × H)
89. C₂⁴	C₂×C₃²×C₄×C₁₉	direct (N × H)
91. C₂²×C₄	C₂³×C₃²×C₁₉	direct (N × H)
92. C₂²×C₃	C₂³×C₃×C₄×C₁₉	direct (N × H)
94. C₃×C₄	C₂⁵×C₃×C₁₉	direct (N × H)
95. C₃²	C₂⁵×C₄×C₁₉	direct (N × H)
96. C₂³	C₂²×C₃²×C₄×C₁₉	direct (N × H)
98. C₂×C₄	C₂⁴×C₃²×C₁₉	direct (N × H)
100. C₂×C₃	C₂⁴×C₃×C₄×C₁₉	direct (N × H)
101. C₂²	C₂³×C₃²×C₄×C₁₉	direct (N × H)
103. C₄	C₂⁵×C₃²×C₁₉	direct (N × H)
104. C₃	C₂⁵×C₃×C₄×C₁₉	direct (N × H)
105. C₂	C₂⁴×C₃²×C₄×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
C₂⁶×C₃²×C₁₉	2
C₂⁴×C₃²×C₄×C₁₉	2
C₂⁵×C₃×C₄×C₁₉	3
C₂⁵×C₃²×C₄	19

Subgroups — C25×C32×C4×C19 #72199374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₃²×C₄×C₁₉ #72199374