Subgroups — C₁₃⋊C₃×Dic₉₃ #28408221

Order 14508.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃⋊C₃×Dic₃₁	—	3	1	no	maximal
3	C₁₃×Dic₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₁₃⋊C₃	—	2	1	no	—
6	C₂×C₃₁×C₁₃⋊C₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₁₃×Dic₃₁	—	3	1	no	Hall
9	C₃×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃₁×C₁₃⋊C₃	—	2	1	no	—
11	C₃₁×C₁₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃×Dic₉₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₃₁	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₃₁	—	13	1	no	—
15	Dic₃×C₁₃⋊C₃	—	31	1	no	maximal, Hall
16	C₁₃×C₃₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	Dic₉₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₃×Dic₃₁	—	39	1	no	—
19	C₃²×C₃₁	—	13	1	no	Hall
20	C₂×C₃×C₁₃⋊C₃	D₃₁	1	1	yes	characteristic
21	C₂×C₃×C₃₁	—	13	1	no	—
22	C₂×C₃×C₃₁	—	26	1	no	—
23	C₂×C₃×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
24	Dic₃×C₁₃	—	31	1	no	—
25	C₄×C₁₃⋊C₃	—	93	1	no	—
26	Dic₃₁	—	3	1	no	Hall
27	C₃×C₁₃⋊C₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	—	13	1	no	—
29	C₃×C₃₁	—	26	1	no	—
30	C₃×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×C₁₃	C₃×D₃₁	1	1	yes	characteristic
32	C₂×C₁₃⋊C₃	—	2	1	no	—
33	C₂×C₁₃⋊C₃	D₉₃	1	1	yes	characteristic
34	C₂×C₃₁	D₃×C₁₃⋊C₃	1	1	yes	characteristic
35	C₄×C₁₃	—	93	1	no	Hall
36	C₃×C₁₃	C₃×Dic₃₁	1	1	yes	characteristic, complemented
37	C₁₃⋊C₃	—	2	1	no	—
38	C₁₃⋊C₃	Dic₉₃	1	1	yes	characteristic, direct product factor
39	C₃×Dic₃	—	403	1	no	Hall
40	C₃₁	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₁₃	C₃×D₉₃	1	1	yes	characteristic
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₉₃	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	1209	1	no	—
45	Dic₃	—	31	1	no	—
46	C₃²	—	13	1	no	Sylow
47	C₂×C₃	—	13	1	no	—
48	C₂×C₃	—	26	1	no	—
49	C₂×C₃	C₁₃⋊C₃×D₃₁	1	1	yes	characteristic
50	C₄	—	93	1	no	Sylow
51	C₃	—	13	1	no	—
52	C₃	—	26	1	no	—
53	C₃	C₁₃⋊C₃×Dic₃₁	1	1	yes	characteristic, complemented
54	C₂	C₁₃⋊C₃×D₉₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₃⋊C₃×D₉₃
commutator, hypocenter	C₃×C₁₃×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₃₁×C₁₃⋊C₃	C₂
LCS	G ▷ C₃×C₁₃×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₁₃×Dic₉₃	C₃	semidirect
4. C₃×C₃₁×C₁₃⋊C₃	C₄	semidirect
9. C₃×C₁₃×C₃₁	C₃×C₄	semidirect
11. C₃₁×C₁₃⋊C₃	Dic₃	semidirect
16. C₁₃×C₃₁	C₃×Dic₃	semidirect
17. Dic₉₃	C₁₃⋊C₃	direct (N × H)
27. C₃×C₁₃⋊C₃	Dic₃₁	semidirect
30. C₃×C₃₁	C₄×C₁₃⋊C₃	semidirect
36. C₃×C₁₃	C₃×Dic₃₁	semidirect
38. C₁₃⋊C₃	Dic₉₃	direct (N × H)
40. C₃₁	Dic₃×C₁₃⋊C₃	semidirect
43. C₁₃	C₃×Dic₉₃	semidirect
53. C₃	C₁₃⋊C₃×Dic₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₃₁×C₁₃⋊C₃	2
C₁₃⋊C₃×Dic₃₁	3
C₁₃×Dic₉₃	3
C₃×Dic₉₃	13
Dic₃×C₁₃⋊C₃	31

Subgroups — C13⋊C3×Dic93 #28408221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×Dic₉₃ #28408221