Subgroups — C₃×C₉×C₁₉×C₄₉ #72202391

Order 25137.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₉×C₁₉	C₇	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉×C₄₉	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₉×C₄₉	C₉	1	3	yes	direct product factor
5	C₃×C₁₉×C₄₉	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic
8	C₇×C₉×C₁₉	C₃×C₇	1	3	yes	—
9	C₁₉×C₄₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₉×C₁₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×C₄₉	C₃×C₁₉	1	1	yes	characteristic
12	C₉×C₄₉	C₃×C₁₉	1	3	yes	direct product factor
13	C₃×C₇×C₁₉	C₇×C₉	1	3	yes	—
14	C₃×C₇×C₁₉	C₃²×C₇	1	1	yes	characteristic
15	C₃×C₇×C₉	C₇×C₁₉	1	1	yes	characteristic
16	C₃²×C₁₉	C₃×C₄₉	1	1	yes	characteristic
17	C₉×C₁₉	C₃×C₄₉	1	3	yes	direct product factor
18	C₃×C₄₉	C₉×C₁₉	1	3	yes	direct product factor
19	C₃×C₄₉	C₃²×C₁₉	1	1	yes	characteristic
20	C₇×C₁₉	C₃×C₇×C₉	1	1	yes	characteristic
21	C₃²×C₇	C₃×C₇×C₁₉	1	1	yes	characteristic
22	C₇×C₉	C₃×C₇×C₁₉	1	3	yes	—
23	C₃×C₁₉	C₉×C₄₉	1	3	yes	direct product factor
24	C₃×C₁₉	C₃²×C₄₉	1	1	yes	characteristic
25	C₄₉	C₃×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₉	C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×C₇	C₇×C₉×C₁₉	1	3	yes	—
28	C₃×C₇	C₃²×C₇×C₁₉	1	1	yes	characteristic
29	C₁₉	C₃×C₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₃²	C₃×C₁₉×C₄₉	1	1	yes	characteristic
31	C₉	C₃×C₁₉×C₄₉	1	3	yes	direct product factor
32	C₇	C₃×C₇×C₉×C₁₉	1	1	yes	characteristic
33	C₃	C₉×C₁₉×C₄₉	1	3	yes	direct product factor
34	C₃	C₃²×C₁₉×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₇	C₃²×C₇×C₁₉
socle, prime radical	C₃²×C₇×C₁₉	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₉×C₄₉	C₃	direct (N × H)
4. C₃×C₁₉×C₄₉	C₉	direct (N × H)
6. C₃×C₉×C₄₉	C₁₉	direct (N × H)
9. C₁₉×C₄₉	C₃×C₉	direct (N × H)
10. C₃×C₉×C₁₉	C₄₉	direct (N × H)
12. C₉×C₄₉	C₃×C₁₉	direct (N × H)
17. C₉×C₁₉	C₃×C₄₉	direct (N × H)
18. C₃×C₄₉	C₉×C₁₉	direct (N × H)
23. C₃×C₁₉	C₉×C₄₉	direct (N × H)
25. C₄₉	C₃×C₉×C₁₉	direct (N × H)
26. C₃×C₉	C₁₉×C₄₉	direct (N × H)
29. C₁₉	C₃×C₉×C₄₉	direct (N × H)
31. C₉	C₃×C₁₉×C₄₉	direct (N × H)
33. C₃	C₉×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
C₃×C₇×C₉×C₁₉	7
C₃²×C₁₉×C₄₉	3
C₉×C₁₉×C₄₉	3
C₃×C₉×C₄₉	19

Subgroups — C3×C9×C19×C49 #72202391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₁₉×C₄₉ #72202391