Subgroups — C₂²×C₇×C₁₉×C₂₇ #72192521

Order 14364.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉×C₂₇	C₂	1	3	yes	maximal, direct product factor
2	C₇×C₁₉×C₂₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₉×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₇×C₉×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₂×C₇×C₉×C₁₉	C₂×C₃	1	3	yes	—
6	C₂²×C₃×C₇×C₁₉	C₉	1	1	yes	characteristic
7	C₇×C₉×C₁₉	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₁₉×C₂₇	C₂×C₇	1	3	yes	direct product factor
9	C₂×C₃×C₇×C₁₉	C₂×C₉	1	3	yes	—
10	C₂²×C₇×C₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₉×C₁₉	C₃×C₇	1	1	yes	characteristic
12	C₂²×C₇×C₁₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
13	C₁₉×C₂₇	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₉	C₂²×C₉	1	1	yes	characteristic
15	C₂×C₇×C₂₇	C₂×C₁₉	1	3	yes	direct product factor
16	C₂×C₉×C₁₉	C₂×C₃×C₇	1	3	yes	—
17	C₂×C₇×C₁₉	C₂×C₂₇	1	3	yes	direct product factor
18	C₂²×C₇×C₉	C₃×C₁₉	1	1	yes	characteristic
19	C₂²×C₃×C₁₉	C₇×C₉	1	1	yes	characteristic
20	C₇×C₂₇	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₉×C₁₉	C₂²×C₃×C₇	1	1	yes	characteristic
22	C₇×C₁₉	C₂²×C₂₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₉	C₂×C₃×C₁₉	1	3	yes	—
24	C₂×C₃×C₁₉	C₂×C₇×C₉	1	3	yes	—
25	C₂²×C₂₇	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₇	C₉×C₁₉	1	1	yes	characteristic
27	C₂²×C₁₉	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₉	C₂²×C₃×C₁₉	1	1	yes	characteristic
29	C₃×C₁₉	C₂²×C₇×C₉	1	1	yes	characteristic
30	C₂×C₂₇	C₂×C₇×C₁₉	1	3	yes	direct product factor
31	C₂×C₃×C₇	C₂×C₉×C₁₉	1	3	yes	—
32	C₂×C₁₉	C₂×C₇×C₂₇	1	3	yes	direct product factor
33	C₂²×C₉	C₃×C₇×C₁₉	1	1	yes	characteristic
34	C₂²×C₇	C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂₇	C₂²×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₇	C₂²×C₉×C₁₉	1	1	yes	characteristic
37	C₁₉	C₂²×C₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₉	C₂×C₃×C₇×C₁₉	1	3	yes	—
39	C₂×C₇	C₂×C₁₉×C₂₇	1	3	yes	direct product factor
40	C₂²×C₃	C₇×C₉×C₁₉	1	1	yes	characteristic
41	C₉	C₂²×C₃×C₇×C₁₉	1	1	yes	characteristic
42	C₇	C₂²×C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₂×C₇×C₉×C₁₉	1	3	yes	—
44	C₂²	C₇×C₁₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂²×C₇×C₉×C₁₉	1	1	yes	characteristic
46	C₂	C₂×C₇×C₁₉×C₂₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂²×C₃×C₇×C₁₉
socle, prime radical	C₂²×C₃×C₇×C₁₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₉×C₂₇	C₂	direct (N × H)
2. C₇×C₁₉×C₂₇	C₂²	direct (N × H)
3. C₂²×C₁₉×C₂₇	C₇	direct (N × H)
8. C₂×C₁₉×C₂₇	C₂×C₇	direct (N × H)
10. C₂²×C₇×C₂₇	C₁₉	direct (N × H)
12. C₂²×C₇×C₁₉	C₂₇	direct (N × H)
13. C₁₉×C₂₇	C₂²×C₇	direct (N × H)
15. C₂×C₇×C₂₇	C₂×C₁₉	direct (N × H)
17. C₂×C₇×C₁₉	C₂×C₂₇	direct (N × H)
20. C₇×C₂₇	C₂²×C₁₉	direct (N × H)
22. C₇×C₁₉	C₂²×C₂₇	direct (N × H)
25. C₂²×C₂₇	C₇×C₁₉	direct (N × H)
27. C₂²×C₁₉	C₇×C₂₇	direct (N × H)
30. C₂×C₂₇	C₂×C₇×C₁₉	direct (N × H)
32. C₂×C₁₉	C₂×C₇×C₂₇	direct (N × H)
34. C₂²×C₇	C₁₉×C₂₇	direct (N × H)
35. C₂₇	C₂²×C₇×C₁₉	direct (N × H)
37. C₁₉	C₂²×C₇×C₂₇	direct (N × H)
39. C₂×C₇	C₂×C₁₉×C₂₇	direct (N × H)
42. C₇	C₂²×C₁₉×C₂₇	direct (N × H)
44. C₂²	C₇×C₁₉×C₂₇	direct (N × H)
46. C₂	C₂×C₇×C₁₉×C₂₇	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×C₇×C₁₉×C₂₇	2
C₂²×C₁₉×C₂₇	7
C₂²×C₇×C₉×C₁₉	3
C₂²×C₇×C₂₇	19

Subgroups — C22×C7×C19×C27 #72192521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₉×C₂₇ #72192521