Subgroups — C₂²×C₃×C₁₃×C₁₂₁ #34038331

Order 18876.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₂₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃×C₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₂₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₁₂₁	C₂×C₃	1	3	yes	direct product factor
5	C₂²×C₃×C₁₁×C₁₃	C₁₁	1	1	yes	maximal, characteristic
6	C₁₃×C₁₂₁	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₃×C₁₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₁₃	C₂×C₁₁	1	3	yes	—
9	C₂×C₃×C₁₂₁	C₂×C₁₃	1	3	yes	direct product factor
10	C₂²×C₁₁×C₁₃	C₃×C₁₁	1	1	yes	characteristic
11	C₂²×C₁₂₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₁×C₁₃	C₂²×C₁₁	1	1	yes	characteristic
13	C₃×C₁₂₁	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₁×C₁₃	C₂×C₃×C₁₁	1	3	yes	—
15	C₂×C₁₂₁	C₂×C₃×C₁₃	1	3	yes	direct product factor
16	C₂²×C₃×C₁₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic
18	C₂²×C₃×C₁₁	C₁₁×C₁₃	1	1	yes	characteristic
19	C₁₂₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₁₃	C₂×C₁₂₁	1	3	yes	direct product factor
21	C₂×C₃×C₁₁	C₂×C₁₁×C₁₃	1	3	yes	—
22	C₂²×C₁₃	C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₁₁	C₃×C₁₁×C₁₃	1	1	yes	characteristic
24	C₃×C₁₃	C₂²×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₁₁	C₂²×C₁₁×C₁₃	1	1	yes	characteristic
26	C₂×C₁₃	C₂×C₃×C₁₂₁	1	3	yes	direct product factor
27	C₂×C₁₁	C₂×C₃×C₁₁×C₁₃	1	3	yes	—
28	C₁₃	C₂²×C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	C₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
30	C₁₁	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic
31	C₂×C₃	C₂×C₁₃×C₁₂₁	1	3	yes	direct product factor
32	C₂²	C₃×C₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₁₃×C₁₂₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₁	C₂²×C₃×C₁₁×C₁₃
socle, prime radical	C₂²×C₃×C₁₁×C₁₃	C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃×C₁₂₁	C₂	direct (N × H)
2. C₂²×C₁₃×C₁₂₁	C₃	direct (N × H)
3. C₃×C₁₃×C₁₂₁	C₂²	direct (N × H)
4. C₂×C₁₃×C₁₂₁	C₂×C₃	direct (N × H)
6. C₁₃×C₁₂₁	C₂²×C₃	direct (N × H)
7. C₂²×C₃×C₁₂₁	C₁₃	direct (N × H)
9. C₂×C₃×C₁₂₁	C₂×C₁₃	direct (N × H)
11. C₂²×C₁₂₁	C₃×C₁₃	direct (N × H)
13. C₃×C₁₂₁	C₂²×C₁₃	direct (N × H)
15. C₂×C₁₂₁	C₂×C₃×C₁₃	direct (N × H)
16. C₂²×C₃×C₁₃	C₁₂₁	direct (N × H)
19. C₁₂₁	C₂²×C₃×C₁₃	direct (N × H)
20. C₂×C₃×C₁₃	C₂×C₁₂₁	direct (N × H)
22. C₂²×C₁₃	C₃×C₁₂₁	direct (N × H)
24. C₃×C₁₃	C₂²×C₁₂₁	direct (N × H)
26. C₂×C₁₃	C₂×C₃×C₁₂₁	direct (N × H)
28. C₁₃	C₂²×C₃×C₁₂₁	direct (N × H)
29. C₂²×C₃	C₁₃×C₁₂₁	direct (N × H)
31. C₂×C₃	C₂×C₁₃×C₁₂₁	direct (N × H)
32. C₂²	C₃×C₁₃×C₁₂₁	direct (N × H)
33. C₃	C₂²×C₁₃×C₁₂₁	direct (N × H)
34. C₂	C₂×C₃×C₁₃×C₁₂₁	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×C₃×C₁₃×C₁₂₁	2
C₂²×C₁₃×C₁₂₁	3
C₂²×C₃×C₁₁×C₁₃	11
C₂²×C₃×C₁₂₁	13

Subgroups — C22×C3×C13×C121 #34038331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₁₃×C₁₂₁ #34038331