Subgroups — C₂³×C₃×C₁₉×C₄₉ #72199767

Order 22344.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂³×C₃×C₇×C₁₉	C₇	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₁₉×C₄₉	C₂	1	7	yes	maximal, direct product factor
4	C₂×C₃×C₁₉×C₄₉	C₂²	1	7	yes	direct product factor
5	C₂²×C₁₉×C₄₉	C₂×C₃	1	7	yes	direct product factor
6	C₃×C₁₉×C₄₉	C₂³	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₉×C₄₉	C₂²×C₃	1	7	yes	direct product factor
8	C₂²×C₃×C₇×C₁₉	C₂×C₇	1	7	yes	—
9	C₂³×C₃×C₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic
11	C₁₉×C₄₉	C₂³×C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₇×C₁₉	C₂²×C₇	1	7	yes	—
13	C₂²×C₃×C₄₉	C₂×C₁₉	1	7	yes	direct product factor
14	C₂²×C₇×C₁₉	C₂×C₃×C₇	1	7	yes	—
15	C₂³×C₃×C₁₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₇×C₁₉	C₂³×C₇	1	1	yes	characteristic
17	C₂³×C₄₉	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₄₉	C₂²×C₁₉	1	7	yes	direct product factor
19	C₂×C₇×C₁₉	C₂²×C₃×C₇	1	7	yes	—
20	C₂²×C₃×C₁₉	C₂×C₄₉	1	7	yes	direct product factor
21	C₂²×C₄₉	C₂×C₃×C₁₉	1	7	yes	direct product factor
22	C₂³×C₃×C₇	C₇×C₁₉	1	1	yes	characteristic
23	C₂³×C₁₉	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₄₉	C₂³×C₁₉	1	1	yes	characteristic, direct product factor, Hall
25	C₇×C₁₉	C₂³×C₃×C₇	1	1	yes	characteristic
26	C₂×C₃×C₁₉	C₂²×C₄₉	1	7	yes	direct product factor
27	C₂×C₄₉	C₂²×C₃×C₁₉	1	7	yes	direct product factor
28	C₂²×C₃×C₇	C₂×C₇×C₁₉	1	7	yes	—
29	C₂²×C₁₉	C₂×C₃×C₄₉	1	7	yes	direct product factor
30	C₃×C₁₉	C₂³×C₄₉	1	1	yes	characteristic, direct product factor, Hall
31	C₂³×C₇	C₃×C₇×C₁₉	1	1	yes	characteristic
32	C₄₉	C₂³×C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₇	C₂²×C₇×C₁₉	1	7	yes	—
34	C₂×C₁₉	C₂²×C₃×C₄₉	1	7	yes	direct product factor
35	C₂²×C₇	C₂×C₃×C₇×C₁₉	1	7	yes	—
36	C₂³×C₃	C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇	C₂³×C₇×C₁₉	1	1	yes	characteristic
38	C₁₉	C₂³×C₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₇	C₂²×C₃×C₇×C₁₉	1	7	yes	—
40	C₂²×C₃	C₂×C₁₉×C₄₉	1	7	yes	direct product factor
41	C₂³	C₃×C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂³×C₃×C₇×C₁₉	1	1	yes	characteristic
43	C₂×C₃	C₂²×C₁₉×C₄₉	1	7	yes	direct product factor
44	C₂²	C₂×C₃×C₁₉×C₄₉	1	7	yes	direct product factor
45	C₃	C₂³×C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂²×C₃×C₁₉×C₄₉	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂³×C₃×C₇×C₁₉
socle, prime radical	C₂³×C₃×C₇×C₁₉	C₇
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×C₄₉	C₃	direct (N × H)
3. C₂²×C₃×C₁₉×C₄₉	C₂	direct (N × H)
4. C₂×C₃×C₁₉×C₄₉	C₂²	direct (N × H)
5. C₂²×C₁₉×C₄₉	C₂×C₃	direct (N × H)
6. C₃×C₁₉×C₄₉	C₂³	direct (N × H)
7. C₂×C₁₉×C₄₉	C₂²×C₃	direct (N × H)
9. C₂³×C₃×C₄₉	C₁₉	direct (N × H)
11. C₁₉×C₄₉	C₂³×C₃	direct (N × H)
13. C₂²×C₃×C₄₉	C₂×C₁₉	direct (N × H)
15. C₂³×C₃×C₁₉	C₄₉	direct (N × H)
17. C₂³×C₄₉	C₃×C₁₉	direct (N × H)
18. C₂×C₃×C₄₉	C₂²×C₁₉	direct (N × H)
20. C₂²×C₃×C₁₉	C₂×C₄₉	direct (N × H)
21. C₂²×C₄₉	C₂×C₃×C₁₉	direct (N × H)
23. C₂³×C₁₉	C₃×C₄₉	direct (N × H)
24. C₃×C₄₉	C₂³×C₁₉	direct (N × H)
26. C₂×C₃×C₁₉	C₂²×C₄₉	direct (N × H)
27. C₂×C₄₉	C₂²×C₃×C₁₉	direct (N × H)
29. C₂²×C₁₉	C₂×C₃×C₄₉	direct (N × H)
30. C₃×C₁₉	C₂³×C₄₉	direct (N × H)
32. C₄₉	C₂³×C₃×C₁₉	direct (N × H)
34. C₂×C₁₉	C₂²×C₃×C₄₉	direct (N × H)
36. C₂³×C₃	C₁₉×C₄₉	direct (N × H)
38. C₁₉	C₂³×C₃×C₄₉	direct (N × H)
40. C₂²×C₃	C₂×C₁₉×C₄₉	direct (N × H)
41. C₂³	C₃×C₁₉×C₄₉	direct (N × H)
43. C₂×C₃	C₂²×C₁₉×C₄₉	direct (N × H)
44. C₂²	C₂×C₃×C₁₉×C₄₉	direct (N × H)
45. C₃	C₂³×C₁₉×C₄₉	direct (N × H)
46. C₂	C₂²×C₃×C₁₉×C₄₉	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×C₄₉	3
C₂³×C₃×C₇×C₁₉	7
C₂²×C₃×C₁₉×C₄₉	2
C₂³×C₃×C₄₉	19

Subgroups — C23×C3×C19×C49 #72199767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₁₉×C₄₉ #72199767