Subgroups — C₂×D₁₃×C₁₁²⋊C₃ #34038432

Order 18876.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×C₁₁²⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁²×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₁₁²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁²×D₁₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₁₁²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₁₁²⋊C₃	—	13	1	no	maximal, Hall
9	C₂×C₁₁²⋊C₃	—	13	2	no	—
10	C₂×C₁₁²⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor
11	C₂×C₁₁×D₁₃	—	3	4	no	—
12	C₂²×C₁₁²	—	13	1	no	Hall
13	C₁₁²⋊C₃	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₁×C₁₃	—	3	4	no	—
15	C₁₁×D₁₃	—	3	8	no	—
16	C₂×C₁₁²	—	13	2	no	—
17	C₂×C₁₁²	C₃×D₁₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₁₃	—	121	1	no	maximal, Hall
19	C₁₁×C₁₃	—	3	4	no	—
20	C₁₁²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₃	—	121	1	no	—
22	C₃×D₁₃	—	121	2	no	—
23	C₂×D₁₃	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₁₁	—	39	4	no	—
25	C₃×C₁₃	—	121	1	no	Hall
26	C₂×C₁₃	C₂×C₁₁²⋊C₃	1	1	yes	characteristic, complemented
27	D₁₃	C₂×C₁₁²⋊C₃	1	2	yes	direct product factor
28	C₂×C₁₁	—	3	4	no	—
29	C₂×C₁₁	—	39	8	no	—
30	C₁₃	C₂²×C₁₁²⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₃	—	1573	1	no	Hall
32	C₁₁	—	3	4	no	—
33	C₂×C₃	—	1573	2	no	—
34	C₂×C₃	—	121	1	no	—
35	C₂²	—	13	1	no	Sylow
36	C₃	—	121	1	no	Sylow
37	C₂	—	13	2	no	—
38	C₂	D₁₃×C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₃×C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₁₁²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₁₃	C₂×C₃
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₁₁²⋊C₃	C₂	semidirect
2. D₁₃×C₁₁²⋊C₃	C₂	direct (N × H)
3. C₂×C₁₁²×D₁₃	C₃	semidirect
4. C₁₃×C₁₁²⋊C₃	C₂²	semidirect
5. C₁₁²×D₁₃	C₂×C₃	semidirect
6. C₂×C₁₁²×C₁₃	C₂×C₃	semidirect
7. C₁₁²×C₁₃	C₂²×C₃	semidirect
10. C₂×C₁₁²⋊C₃	D₁₃	direct (N × H)
13. C₁₁²⋊C₃	C₂×D₁₃	direct (N × H)
17. C₂×C₁₁²	C₃×D₁₃	semidirect
20. C₁₁²	C₂×C₃×D₁₃	semidirect
23. C₂×D₁₃	C₁₁²⋊C₃	direct (N × H)
26. C₂×C₁₃	C₂×C₁₁²⋊C₃	semidirect
27. D₁₃	C₂×C₁₁²⋊C₃	direct (N × H)
30. C₁₃	C₂²×C₁₁²⋊C₃	semidirect
38. C₂	D₁₃×C₁₁²⋊C₃	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×C₁₃×C₁₁²⋊C₃	2
D₁₃×C₁₁²⋊C₃	2
C₂×C₁₁²×D₁₃	3
C₂²×C₁₁²⋊C₃	13
C₂×C₃×D₁₃	121

Subgroups — C2×D13×C112⋊C3 #34038432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×C₁₁²⋊C₃ #34038432