Subgroups — C₄⁴×C₅×C₁₉ #72201622

Order 24320.

7932 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₅×C₁₉	C₂	1	15	yes	maximal
2	C₂²×C₄²×C₅×C₁₉	C₂²	1	35	yes	—
3	C₄³×C₅×C₁₉	C₄	1	120	yes	direct product factor
4	C₂³×C₄×C₅×C₁₉	C₂³	1	15	yes	—
5	C₂×C₄²×C₅×C₁₉	C₂×C₄	1	420	yes	—
6	C₄⁴×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₄³×C₁₉	C₂×C₅	1	15	yes	—
8	C₂⁴×C₅×C₁₉	C₂⁴	1	1	yes	characteristic
9	C₂²×C₄×C₅×C₁₉	C₂²×C₄	1	210	yes	—
10	C₄²×C₅×C₁₉	C₄²	1	560	yes	direct product factor
11	C₄⁴×C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₄²×C₁₉	C₂²×C₅	1	35	yes	—
13	C₄³×C₁₉	C₄×C₅	1	120	yes	direct product factor
14	C₂³×C₅×C₁₉	C₂³×C₄	1	15	yes	—
15	C₂×C₄×C₅×C₁₉	C₂×C₄²	1	420	yes	—
16	C₂×C₄³×C₅	C₂×C₁₉	1	15	yes	—
17	C₂³×C₄×C₁₉	C₂³×C₅	1	15	yes	—
18	C₂×C₄²×C₁₉	C₂×C₄×C₅	1	420	yes	—
19	C₂²×C₅×C₁₉	C₂²×C₄²	1	35	yes	—
20	C₄×C₅×C₁₉	C₄³	1	120	yes	direct product factor
21	C₂²×C₄²×C₅	C₂²×C₁₉	1	35	yes	—
22	C₄³×C₅	C₄×C₁₉	1	120	yes	direct product factor
23	C₂⁴×C₁₉	C₂⁴×C₅	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂²×C₄×C₅	1	210	yes	—
25	C₄²×C₁₉	C₄²×C₅	1	560	yes	direct product factor
26	C₄⁴	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₅×C₁₉	C₂×C₄³	1	15	yes	—
28	C₂³×C₄×C₅	C₂³×C₁₉	1	15	yes	—
29	C₂×C₄²×C₅	C₂×C₄×C₁₉	1	420	yes	—
30	C₂³×C₁₉	C₂³×C₄×C₅	1	15	yes	—
31	C₂×C₄×C₁₉	C₂×C₄²×C₅	1	420	yes	—
32	C₂×C₄³	C₂×C₅×C₁₉	1	15	yes	—
33	C₅×C₁₉	C₄⁴	1	1	yes	characteristic, direct product factor, Hall
34	C₂⁴×C₅	C₂⁴×C₁₉	1	1	yes	characteristic
35	C₂²×C₄×C₅	C₂²×C₄×C₁₉	1	210	yes	—
36	C₄²×C₅	C₄²×C₁₉	1	560	yes	direct product factor
37	C₂²×C₁₉	C₂²×C₄²×C₅	1	35	yes	—
38	C₄×C₁₉	C₄³×C₅	1	120	yes	direct product factor
39	C₂²×C₄²	C₂²×C₅×C₁₉	1	35	yes	—
40	C₄³	C₄×C₅×C₁₉	1	120	yes	direct product factor
41	C₂³×C₅	C₂³×C₄×C₁₉	1	15	yes	—
42	C₂×C₄×C₅	C₂×C₄²×C₁₉	1	420	yes	—
43	C₂×C₁₉	C₂×C₄³×C₅	1	15	yes	—
44	C₂³×C₄	C₂³×C₅×C₁₉	1	15	yes	—
45	C₂×C₄²	C₂×C₄×C₅×C₁₉	1	420	yes	—
46	C₂²×C₅	C₂²×C₄²×C₁₉	1	35	yes	—
47	C₄×C₅	C₄³×C₁₉	1	120	yes	direct product factor
48	C₁₉	C₄⁴×C₅	1	1	yes	characteristic, direct product factor, Sylow
49	C₂⁴	C₂⁴×C₅×C₁₉	1	1	yes	characteristic
50	C₂²×C₄	C₂²×C₄×C₅×C₁₉	1	210	yes	—
51	C₄²	C₄²×C₅×C₁₉	1	560	yes	direct product factor
52	C₂×C₅	C₂×C₄³×C₁₉	1	15	yes	—
53	C₂³	C₂³×C₄×C₅×C₁₉	1	15	yes	—
54	C₂×C₄	C₂×C₄²×C₅×C₁₉	1	420	yes	—
55	C₅	C₄⁴×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	C₂²×C₄²×C₅×C₁₉	1	35	yes	—
57	C₄	C₄³×C₅×C₁₉	1	120	yes	direct product factor
58	C₂	C₂×C₄³×C₅×C₁₉	1	15	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂⁴	C₂⁴×C₅×C₁₉
socle, prime radical	C₂⁴×C₅×C₁₉	C₂⁴
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄³×C₅×C₁₉	C₄	direct (N × H)
6. C₄⁴×C₁₉	C₅	direct (N × H)
10. C₄²×C₅×C₁₉	C₄²	direct (N × H)
11. C₄⁴×C₅	C₁₉	direct (N × H)
13. C₄³×C₁₉	C₄×C₅	direct (N × H)
20. C₄×C₅×C₁₉	C₄³	direct (N × H)
22. C₄³×C₅	C₄×C₁₉	direct (N × H)
25. C₄²×C₁₉	C₄²×C₅	direct (N × H)
26. C₄⁴	C₅×C₁₉	direct (N × H)
33. C₅×C₁₉	C₄⁴	direct (N × H)
36. C₄²×C₅	C₄²×C₁₉	direct (N × H)
38. C₄×C₁₉	C₄³×C₅	direct (N × H)
40. C₄³	C₄×C₅×C₁₉	direct (N × H)
47. C₄×C₅	C₄³×C₁₉	direct (N × H)
48. C₁₉	C₄⁴×C₅	direct (N × H)
51. C₄²	C₄²×C₅×C₁₉	direct (N × H)
55. C₅	C₄⁴×C₁₉	direct (N × H)
57. C₄	C₄³×C₅×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
C₂×C₄³×C₅×C₁₉	2
C₄⁴×C₁₉	5
C₄⁴×C₅	19

Subgroups — C44×C5×C19 #72201622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⁴×C₅×C₁₉ #72201622