Subgroups — C₂⁵×C₅×C₈×C₁₉ #72201621

Order 24320.

30908 conjugacy classes of subgroups.

The subgroup lattice has 116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₅×C₈×C₁₉	C₂	1	62	yes	maximal, direct product factor
3	C₂⁴×C₄×C₅×C₁₉	C₄	1	31	yes	—
4	C₂⁴×C₄×C₅×C₁₉	C₂²	1	31	yes	—
5	C₂⁶×C₅×C₁₉	C₄	1	1	yes	characteristic
6	C₂³×C₅×C₈×C₁₉	C₂²	1	620	yes	direct product factor
7	C₂⁵×C₅×C₁₉	C₈	1	32	yes	direct product factor
8	C₂⁵×C₅×C₁₉	C₂×C₄	1	31	yes	—
9	C₂³×C₄×C₅×C₁₉	C₂×C₄	1	465	yes	—
10	C₂³×C₄×C₅×C₁₉	C₂³	1	155	yes	—
11	C₂²×C₅×C₈×C₁₉	C₂³	1	1240	yes	direct product factor
12	C₂⁵×C₈×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁵×C₄×C₁₉	C₂×C₅	1	1	yes	characteristic
14	C₂⁴×C₈×C₁₉	C₂×C₅	1	62	yes	direct product factor
15	C₂⁴×C₅×C₁₉	C₂×C₈	1	496	yes	direct product factor
16	C₂⁴×C₅×C₁₉	C₂²×C₄	1	155	yes	—
17	C₂²×C₄×C₅×C₁₉	C₂²×C₄	1	1085	yes	—
18	C₂²×C₄×C₅×C₁₉	C₂⁴	1	155	yes	—
19	C₂×C₅×C₈×C₁₉	C₂⁴	1	496	yes	direct product factor
20	C₂⁵×C₅×C₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂⁶×C₁₉	C₄×C₅	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₉	C₄×C₅	1	31	yes	—
23	C₂⁴×C₄×C₁₉	C₂²×C₅	1	31	yes	—
24	C₂³×C₈×C₁₉	C₂²×C₅	1	620	yes	direct product factor
25	C₂³×C₅×C₁₉	C₂²×C₈	1	1240	yes	direct product factor
26	C₂³×C₅×C₁₉	C₂³×C₄	1	155	yes	—
27	C₂×C₄×C₅×C₁₉	C₂³×C₄	1	465	yes	—
28	C₂×C₄×C₅×C₁₉	C₂⁵	1	31	yes	—
29	C₅×C₈×C₁₉	C₂⁵	1	32	yes	direct product factor
30	C₂⁵×C₄×C₅	C₂×C₁₉	1	1	yes	characteristic
31	C₂⁴×C₅×C₈	C₂×C₁₉	1	62	yes	direct product factor
32	C₂⁵×C₁₉	C₅×C₈	1	32	yes	direct product factor
33	C₂⁵×C₁₉	C₂×C₄×C₅	1	31	yes	—
34	C₂³×C₄×C₁₉	C₂×C₄×C₅	1	465	yes	—
35	C₂³×C₄×C₁₉	C₂³×C₅	1	155	yes	—
36	C₂²×C₈×C₁₉	C₂³×C₅	1	1240	yes	direct product factor
37	C₂²×C₅×C₁₉	C₂³×C₈	1	620	yes	direct product factor
38	C₂²×C₅×C₁₉	C₂⁴×C₄	1	31	yes	—
39	C₄×C₅×C₁₉	C₂⁴×C₄	1	31	yes	—
40	C₄×C₅×C₁₉	C₂⁶	1	1	yes	characteristic
41	C₂⁶×C₅	C₄×C₁₉	1	1	yes	characteristic
42	C₂⁴×C₄×C₅	C₄×C₁₉	1	31	yes	—
43	C₂⁴×C₄×C₅	C₂²×C₁₉	1	31	yes	—
44	C₂³×C₅×C₈	C₂²×C₁₉	1	620	yes	direct product factor
45	C₂⁴×C₁₉	C₂×C₅×C₈	1	496	yes	direct product factor
46	C₂⁴×C₁₉	C₂²×C₄×C₅	1	155	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄×C₅	1	1085	yes	—
48	C₂²×C₄×C₁₉	C₂⁴×C₅	1	155	yes	—
49	C₂×C₈×C₁₉	C₂⁴×C₅	1	496	yes	direct product factor
50	C₂⁵×C₈	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₅×C₁₉	C₂⁴×C₈	1	62	yes	direct product factor
52	C₂×C₅×C₁₉	C₂⁵×C₄	1	1	yes	characteristic
53	C₂⁵×C₅	C₈×C₁₉	1	32	yes	direct product factor
54	C₂⁵×C₅	C₂×C₄×C₁₉	1	31	yes	—
55	C₂³×C₄×C₅	C₂×C₄×C₁₉	1	465	yes	—
56	C₂³×C₄×C₅	C₂³×C₁₉	1	155	yes	—
57	C₂²×C₅×C₈	C₂³×C₁₉	1	1240	yes	direct product factor
58	C₂³×C₁₉	C₂²×C₅×C₈	1	1240	yes	direct product factor
59	C₂³×C₁₉	C₂³×C₄×C₅	1	155	yes	—
60	C₂×C₄×C₁₉	C₂³×C₄×C₅	1	465	yes	—
61	C₂×C₄×C₁₉	C₂⁵×C₅	1	31	yes	—
62	C₈×C₁₉	C₂⁵×C₅	1	32	yes	direct product factor
63	C₂⁵×C₄	C₂×C₅×C₁₉	1	1	yes	characteristic
64	C₂⁴×C₈	C₂×C₅×C₁₉	1	62	yes	direct product factor
65	C₅×C₁₉	C₂⁵×C₈	1	1	yes	characteristic, direct product factor, Hall
66	C₂⁴×C₅	C₂×C₈×C₁₉	1	496	yes	direct product factor
67	C₂⁴×C₅	C₂²×C₄×C₁₉	1	155	yes	—
68	C₂²×C₄×C₅	C₂²×C₄×C₁₉	1	1085	yes	—
69	C₂²×C₄×C₅	C₂⁴×C₁₉	1	155	yes	—
70	C₂×C₅×C₈	C₂⁴×C₁₉	1	496	yes	direct product factor
71	C₂²×C₁₉	C₂³×C₅×C₈	1	620	yes	direct product factor
72	C₂²×C₁₉	C₂⁴×C₄×C₅	1	31	yes	—
73	C₄×C₁₉	C₂⁴×C₄×C₅	1	31	yes	—
74	C₄×C₁₉	C₂⁶×C₅	1	1	yes	characteristic
75	C₂⁶	C₄×C₅×C₁₉	1	1	yes	characteristic
76	C₂⁴×C₄	C₄×C₅×C₁₉	1	31	yes	—
77	C₂⁴×C₄	C₂²×C₅×C₁₉	1	31	yes	—
78	C₂³×C₈	C₂²×C₅×C₁₉	1	620	yes	direct product factor
79	C₂³×C₅	C₂²×C₈×C₁₉	1	1240	yes	direct product factor
80	C₂³×C₅	C₂³×C₄×C₁₉	1	155	yes	—
81	C₂×C₄×C₅	C₂³×C₄×C₁₉	1	465	yes	—
82	C₂×C₄×C₅	C₂⁵×C₁₉	1	31	yes	—
83	C₅×C₈	C₂⁵×C₁₉	1	32	yes	direct product factor
84	C₂×C₁₉	C₂⁴×C₅×C₈	1	62	yes	direct product factor
85	C₂×C₁₉	C₂⁵×C₄×C₅	1	1	yes	characteristic
86	C₂⁵	C₅×C₈×C₁₉	1	32	yes	direct product factor
87	C₂⁵	C₂×C₄×C₅×C₁₉	1	31	yes	—
88	C₂³×C₄	C₂×C₄×C₅×C₁₉	1	465	yes	—
89	C₂³×C₄	C₂³×C₅×C₁₉	1	155	yes	—
90	C₂²×C₈	C₂³×C₅×C₁₉	1	1240	yes	direct product factor
91	C₂²×C₅	C₂³×C₈×C₁₉	1	620	yes	direct product factor
92	C₂²×C₅	C₂⁴×C₄×C₁₉	1	31	yes	—
93	C₄×C₅	C₂⁴×C₄×C₁₉	1	31	yes	—
94	C₄×C₅	C₂⁶×C₁₉	1	1	yes	characteristic
95	C₁₉	C₂⁵×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
96	C₂⁴	C₂×C₅×C₈×C₁₉	1	496	yes	direct product factor
97	C₂⁴	C₂²×C₄×C₅×C₁₉	1	155	yes	—
98	C₂²×C₄	C₂²×C₄×C₅×C₁₉	1	1085	yes	—
99	C₂²×C₄	C₂⁴×C₅×C₁₉	1	155	yes	—
100	C₂×C₈	C₂⁴×C₅×C₁₉	1	496	yes	direct product factor
101	C₂×C₅	C₂⁴×C₈×C₁₉	1	62	yes	direct product factor
102	C₂×C₅	C₂⁵×C₄×C₁₉	1	1	yes	characteristic
103	C₂³	C₂²×C₅×C₈×C₁₉	1	1240	yes	direct product factor
104	C₂³	C₂³×C₄×C₅×C₁₉	1	155	yes	—
105	C₂×C₄	C₂³×C₄×C₅×C₁₉	1	465	yes	—
106	C₂×C₄	C₂⁵×C₅×C₁₉	1	31	yes	—
107	C₈	C₂⁵×C₅×C₁₉	1	32	yes	direct product factor
108	C₅	C₂⁵×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
109	C₂²	C₂³×C₅×C₈×C₁₉	1	620	yes	direct product factor
110	C₂²	C₂⁴×C₄×C₅×C₁₉	1	31	yes	—
111	C₄	C₂⁶×C₅×C₁₉	1	1	yes	characteristic
112	C₄	C₂⁴×C₄×C₅×C₁₉	1	31	yes	—
113	C₂	C₂⁴×C₅×C₈×C₁₉	1	62	yes	direct product factor
114	C₂	C₂⁵×C₄×C₅×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁶×C₅×C₁₉
socle, prime radical	C₂⁶×C₅×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₅×C₈×C₁₉	C₂	direct (N × H)
6. C₂³×C₅×C₈×C₁₉	C₂²	direct (N × H)
7. C₂⁵×C₅×C₁₉	C₈	direct (N × H)
11. C₂²×C₅×C₈×C₁₉	C₂³	direct (N × H)
12. C₂⁵×C₈×C₁₉	C₅	direct (N × H)
14. C₂⁴×C₈×C₁₉	C₂×C₅	direct (N × H)
15. C₂⁴×C₅×C₁₉	C₂×C₈	direct (N × H)
19. C₂×C₅×C₈×C₁₉	C₂⁴	direct (N × H)
20. C₂⁵×C₅×C₈	C₁₉	direct (N × H)
24. C₂³×C₈×C₁₉	C₂²×C₅	direct (N × H)
25. C₂³×C₅×C₁₉	C₂²×C₈	direct (N × H)
29. C₅×C₈×C₁₉	C₂⁵	direct (N × H)
31. C₂⁴×C₅×C₈	C₂×C₁₉	direct (N × H)
32. C₂⁵×C₁₉	C₅×C₈	direct (N × H)
36. C₂²×C₈×C₁₉	C₂³×C₅	direct (N × H)
37. C₂²×C₅×C₁₉	C₂³×C₈	direct (N × H)
44. C₂³×C₅×C₈	C₂²×C₁₉	direct (N × H)
45. C₂⁴×C₁₉	C₂×C₅×C₈	direct (N × H)
49. C₂×C₈×C₁₉	C₂⁴×C₅	direct (N × H)
50. C₂⁵×C₈	C₅×C₁₉	direct (N × H)
51. C₂×C₅×C₁₉	C₂⁴×C₈	direct (N × H)
53. C₂⁵×C₅	C₈×C₁₉	direct (N × H)
57. C₂²×C₅×C₈	C₂³×C₁₉	direct (N × H)
58. C₂³×C₁₉	C₂²×C₅×C₈	direct (N × H)
62. C₈×C₁₉	C₂⁵×C₅	direct (N × H)
64. C₂⁴×C₈	C₂×C₅×C₁₉	direct (N × H)
65. C₅×C₁₉	C₂⁵×C₈	direct (N × H)
66. C₂⁴×C₅	C₂×C₈×C₁₉	direct (N × H)
70. C₂×C₅×C₈	C₂⁴×C₁₉	direct (N × H)
71. C₂²×C₁₉	C₂³×C₅×C₈	direct (N × H)
78. C₂³×C₈	C₂²×C₅×C₁₉	direct (N × H)
79. C₂³×C₅	C₂²×C₈×C₁₉	direct (N × H)
83. C₅×C₈	C₂⁵×C₁₉	direct (N × H)
84. C₂×C₁₉	C₂⁴×C₅×C₈	direct (N × H)
86. C₂⁵	C₅×C₈×C₁₉	direct (N × H)
90. C₂²×C₈	C₂³×C₅×C₁₉	direct (N × H)
91. C₂²×C₅	C₂³×C₈×C₁₉	direct (N × H)
95. C₁₉	C₂⁵×C₅×C₈	direct (N × H)
96. C₂⁴	C₂×C₅×C₈×C₁₉	direct (N × H)
100. C₂×C₈	C₂⁴×C₅×C₁₉	direct (N × H)
101. C₂×C₅	C₂⁴×C₈×C₁₉	direct (N × H)
103. C₂³	C₂²×C₅×C₈×C₁₉	direct (N × H)
107. C₈	C₂⁵×C₅×C₁₉	direct (N × H)
108. C₅	C₂⁵×C₈×C₁₉	direct (N × H)
109. C₂²	C₂³×C₅×C₈×C₁₉	direct (N × H)
113. C₂	C₂⁴×C₅×C₈×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
C₂⁵×C₄×C₅×C₁₉	2
C₂⁴×C₅×C₈×C₁₉	2
C₂⁵×C₈×C₁₉	5
C₂⁵×C₅×C₈	19

Subgroups — C25×C5×C8×C19 #72201621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₅×C₈×C₁₉ #72201621