Subgroups — C₁₃⋊C₃×Dic₂₃₇ #49149484

Order 36972.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃⋊C₃×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃⋊C₃×Dic₇₉	—	3	1	no	maximal
3	C₁₃×Dic₂₃₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃⋊C₃×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃⋊C₃×C₇₉	—	2	1	no	—
6	C₂×C₁₃⋊C₃×C₇₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic
8	C₁₃×Dic₇₉	—	3	1	no	Hall
9	C₃×C₁₃×C₇₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₃⋊C₃×C₇₉	—	2	1	no	—
11	C₁₃⋊C₃×C₇₉	Dic₃	1	1	yes	characteristic, complemented
12	C₃×Dic₂₃₇	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₇₉	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₇₉	—	13	1	no	—
15	C₁₃×C₇₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	Dic₂₃₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃×Dic₇₉	—	39	1	no	—
18	C₃²×C₇₉	—	13	1	no	Hall
19	C₂×C₃×C₇₉	—	13	1	no	—
20	C₂×C₃×C₇₉	—	26	1	no	—
21	C₂×C₃×C₇₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	Dic₃×C₁₃⋊C₃	—	79	1	no	maximal, Hall
23	Dic₇₉	—	3	1	no	Hall
24	C₃×C₇₉	—	13	1	no	—
25	C₃×C₇₉	—	26	1	no	—
26	C₃×C₇₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×C₁₃⋊C₃	D₇₉	1	1	yes	characteristic
28	C₂×C₇₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic
29	Dic₃×C₁₃	—	79	1	no	—
30	C₄×C₁₃⋊C₃	—	237	1	no	—
31	C₃×C₁₃⋊C₃	Dic₇₉	1	1	yes	characteristic, complemented, Hall
32	C₇₉	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₁₃	C₃×D₇₉	1	1	yes	characteristic
34	C₂×C₁₃⋊C₃	—	2	1	no	—
35	C₂×C₁₃⋊C₃	D₂₃₇	1	1	yes	characteristic
36	C₄×C₁₃	—	237	1	no	Hall
37	C₃×C₁₃	C₃×Dic₇₉	1	1	yes	characteristic, complemented
38	C₁₃⋊C₃	—	2	1	no	—
39	C₁₃⋊C₃	Dic₂₃₇	1	1	yes	characteristic, direct product factor
40	C₃×Dic₃	—	1027	1	no	Hall
41	C₂×C₁₃	C₃×D₂₃₇	1	1	yes	characteristic
42	C₂×C₃²	—	13	1	no	—
43	C₁₃	C₃×Dic₂₃₇	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	3081	1	no	—
45	Dic₃	—	79	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×D₇₉	1	1	yes	characteristic
50	C₄	—	237	1	no	Sylow
51	C₃	—	13	1	no	—
52	C₃	—	26	1	no	—
53	C₃	C₁₃⋊C₃×Dic₇₉	1	1	yes	characteristic, complemented
54	C₂	C₁₃⋊C₃×D₂₃₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₃⋊C₃×D₂₃₇
commutator, hypocenter	C₃×C₁₃×C₇₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₂×C₃×C₁₃⋊C₃×C₇₉	C₂
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₁₃×Dic₂₃₇	C₃	semidirect
4. C₃×C₁₃⋊C₃×C₇₉	C₄	semidirect
9. C₃×C₁₃×C₇₉	C₃×C₄	semidirect
11. C₁₃⋊C₃×C₇₉	Dic₃	semidirect
15. C₁₃×C₇₉	C₃×Dic₃	semidirect
16. Dic₂₃₇	C₁₃⋊C₃	direct (N × H)
26. C₃×C₇₉	C₄×C₁₃⋊C₃	semidirect
31. C₃×C₁₃⋊C₃	Dic₇₉	semidirect
32. C₇₉	Dic₃×C₁₃⋊C₃	semidirect
37. C₃×C₁₃	C₃×Dic₇₉	semidirect
39. C₁₃⋊C₃	Dic₂₃₇	direct (N × H)
43. C₁₃	C₃×Dic₂₃₇	semidirect
53. C₃	C₁₃⋊C₃×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃⋊C₃×C₇₉	2
C₁₃⋊C₃×Dic₇₉	3
C₁₃×Dic₂₃₇	3
C₃×Dic₂₃₇	13
Dic₃×C₁₃⋊C₃	79

Subgroups — C13⋊C3×Dic237 #49149484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×Dic₂₃₇ #49149484