Subgroups — C₂⁴×C₁₉×C₈₁ #72201949

Order 24624.

670 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉×C₈₁	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×C₈₁	C₂²	1	35	yes	direct product factor
4	C₂³×C₁₉×C₂₇	C₂×C₃	1	15	yes	—
5	C₂×C₁₉×C₈₁	C₂³	1	15	yes	direct product factor
6	C₂⁴×C₉×C₁₉	C₉	1	1	yes	characteristic
7	C₂²×C₁₉×C₂₇	C₂²×C₃	1	35	yes	—
8	C₁₉×C₈₁	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
9	C₂³×C₉×C₁₉	C₂×C₉	1	15	yes	—
10	C₂⁴×C₈₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₉×C₂₇	C₂³×C₃	1	15	yes	—
12	C₂⁴×C₃×C₁₉	C₂₇	1	1	yes	characteristic
13	C₂²×C₉×C₁₉	C₂²×C₉	1	35	yes	—
14	C₂³×C₈₁	C₂×C₁₉	1	15	yes	direct product factor
15	C₁₉×C₂₇	C₂⁴×C₃	1	1	yes	characteristic
16	C₂³×C₃×C₁₉	C₂×C₂₇	1	15	yes	—
17	C₂⁴×C₂₇	C₃×C₁₉	1	1	yes	characteristic
18	C₂×C₉×C₁₉	C₂³×C₉	1	15	yes	—
19	C₂²×C₈₁	C₂²×C₁₉	1	35	yes	direct product factor
20	C₂⁴×C₁₉	C₈₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₃×C₁₉	C₂²×C₂₇	1	35	yes	—
22	C₂³×C₂₇	C₂×C₃×C₁₉	1	15	yes	—
23	C₉×C₁₉	C₂⁴×C₉	1	1	yes	characteristic
24	C₂×C₈₁	C₂³×C₁₉	1	15	yes	direct product factor
25	C₂³×C₁₉	C₂×C₈₁	1	15	yes	direct product factor
26	C₂⁴×C₉	C₉×C₁₉	1	1	yes	characteristic
27	C₂×C₃×C₁₉	C₂³×C₂₇	1	15	yes	—
28	C₂²×C₂₇	C₂²×C₃×C₁₉	1	35	yes	—
29	C₈₁	C₂⁴×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₁₉	C₂²×C₈₁	1	35	yes	direct product factor
31	C₂³×C₉	C₂×C₉×C₁₉	1	15	yes	—
32	C₃×C₁₉	C₂⁴×C₂₇	1	1	yes	characteristic
33	C₂×C₂₇	C₂³×C₃×C₁₉	1	15	yes	—
34	C₂⁴×C₃	C₁₉×C₂₇	1	1	yes	characteristic
35	C₂×C₁₉	C₂³×C₈₁	1	15	yes	direct product factor
36	C₂²×C₉	C₂²×C₉×C₁₉	1	35	yes	—
37	C₂₇	C₂⁴×C₃×C₁₉	1	1	yes	characteristic
38	C₂³×C₃	C₂×C₁₉×C₂₇	1	15	yes	—
39	C₁₉	C₂⁴×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₉	C₂³×C₉×C₁₉	1	15	yes	—
41	C₂⁴	C₁₉×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₃	C₂²×C₁₉×C₂₇	1	35	yes	—
43	C₉	C₂⁴×C₉×C₁₉	1	1	yes	characteristic
44	C₂³	C₂×C₁₉×C₈₁	1	15	yes	direct product factor
45	C₂×C₃	C₂³×C₁₉×C₂₇	1	15	yes	—
46	C₂²	C₂²×C₁₉×C₈₁	1	35	yes	direct product factor
47	C₃	C₂⁴×C₁₉×C₂₇	1	1	yes	characteristic
48	C₂	C₂³×C₁₉×C₈₁	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂⁴×C₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₉×C₈₁	C₂	direct (N × H)
3. C₂²×C₁₉×C₈₁	C₂²	direct (N × H)
5. C₂×C₁₉×C₈₁	C₂³	direct (N × H)
8. C₁₉×C₈₁	C₂⁴	direct (N × H)
10. C₂⁴×C₈₁	C₁₉	direct (N × H)
14. C₂³×C₈₁	C₂×C₁₉	direct (N × H)
19. C₂²×C₈₁	C₂²×C₁₉	direct (N × H)
20. C₂⁴×C₁₉	C₈₁	direct (N × H)
24. C₂×C₈₁	C₂³×C₁₉	direct (N × H)
25. C₂³×C₁₉	C₂×C₈₁	direct (N × H)
29. C₈₁	C₂⁴×C₁₉	direct (N × H)
30. C₂²×C₁₉	C₂²×C₈₁	direct (N × H)
35. C₂×C₁₉	C₂³×C₈₁	direct (N × H)
39. C₁₉	C₂⁴×C₈₁	direct (N × H)
41. C₂⁴	C₁₉×C₈₁	direct (N × H)
44. C₂³	C₂×C₁₉×C₈₁	direct (N × H)
46. C₂²	C₂²×C₁₉×C₈₁	direct (N × H)
48. C₂	C₂³×C₁₉×C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₉×C₈₁	2
C₂⁴×C₁₉×C₂₇	3
C₂⁴×C₈₁	19

Subgroups — C24×C19×C81 #72201949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₁₉×C₈₁ #72201949