Subgroups — C₁₃×C₇⋊Dic₆₃ #37524397

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₃⋊(C₇⋊Dic₇)	—	3	1	no	maximal
3	C₇²×C₉×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₃	D₃	1	1	yes	characteristic
5	C₁₃×Dic₆₃	—	7	8	no	maximal
6	C₁₃×C₇⋊Dic₇	—	9	1	no	Hall
7	C₃×C₇²×C₁₃	Dic₃	1	1	yes	characteristic
8	C₇⋊Dic₆₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₉×C₁₃	D₇	1	8	yes	—
10	C₂×C₇²×C₁₃	D₉	1	1	yes	characteristic
11	C₁₃×Dic₂₁	—	21	8	no	—
12	C₂×C₇²×C₉	C₂×C₁₃	1	1	yes	characteristic
13	C₇×C₉×C₁₃	Dic₇	1	8	yes	complemented
14	C₇²×C₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₇⋊Dic₇)	—	3	1	no	—
16	C₂×C₃×C₇×C₁₃	D₂₁	1	8	yes	—
17	C₁₃×Dic₉	—	49	1	no	Hall
18	C₇²×C₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₁₃×Dic₇	—	63	8	no	—
20	C₂×C₃×C₇²	D₃×C₁₃	1	1	yes	characteristic
21	C₃×C₇×C₁₃	Dic₂₁	1	8	yes	—
22	Dic₆₃	—	7	8	no	—
23	C₂×C₉×C₁₃	C₇⋊D₇	1	1	yes	characteristic
24	C₇⋊Dic₇	—	9	1	no	Hall
25	C₂×C₇×C₁₃	D₆₃	1	8	yes	—
26	Dic₃×C₁₃	—	147	1	no	—
27	C₃×C₇²	Dic₃×C₁₃	1	1	yes	characteristic
28	C₂×C₇×C₉	C₁₃×D₇	1	8	yes	—
29	C₉×C₁₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇²	C₁₃×D₉	1	1	yes	characteristic
31	C₇×C₁₃	Dic₆₃	1	8	yes	complemented
32	Dic₂₁	—	21	8	no	—
33	C₂×C₃×C₁₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
34	C₇×C₉	C₁₃×Dic₇	1	8	yes	complemented
35	C₄×C₁₃	—	441	1	no	Hall
36	C₇²	C₁₃×Dic₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	C₁₃×D₂₁	1	8	yes	—
38	C₃×C₁₃	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic
39	Dic₉	—	49	1	no	Hall
40	Dic₇	—	63	8	no	—
41	C₂×C₁₃	C₇⋊D₆₃	1	1	yes	characteristic
42	C₃×C₇	C₁₃×Dic₂₁	1	8	yes	—
43	C₂×C₉	C₁₃×C₇⋊D₇	1	1	yes	characteristic
44	C₂×C₇	C₁₃×D₆₃	1	8	yes	—
45	C₁₃	C₇⋊Dic₆₃	1	1	yes	characteristic, direct product factor, Sylow
46	Dic₃	—	147	1	no	—
47	C₉	C₁₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₁₃×Dic₆₃	1	8	yes	complemented
49	C₂×C₃	C₁₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
50	C₄	—	441	1	no	Sylow
51	C₃	C₁₃×C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic
52	C₂	C₁₃×C₇⋊D₆₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₇⋊D₆₃
commutator, hypocenter	C₇²×C₉	C₄×C₁₃
Frattini	C₂×C₃	C₁₃×C₃⋊(C₇⋊D₇)
Fitting	C₂×C₇²×C₉×C₁₃	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₃	D₃
cosocle	C₂×C₇²×C₉	C₂×C₁₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₃	C₄	semidirect
8. C₇⋊Dic₆₃	C₁₃	direct (N × H)
13. C₇×C₉×C₁₃	Dic₇	semidirect
14. C₇²×C₁₃	Dic₉	semidirect
18. C₇²×C₉	C₄×C₁₃	semidirect
29. C₉×C₁₃	C₇⋊Dic₇	semidirect
31. C₇×C₁₃	Dic₆₃	semidirect
34. C₇×C₉	C₁₃×Dic₇	semidirect
36. C₇²	C₁₃×Dic₉	semidirect
45. C₁₃	C₇⋊Dic₆₃	direct (N × H)
47. C₉	C₁₃×C₇⋊Dic₇	semidirect
48. C₇	C₁₃×Dic₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇²×C₉×C₁₃	2
C₁₃×C₃⋊(C₇⋊Dic₇)	3
C₁₃×Dic₆₃	7
C₇⋊Dic₆₃	13

Subgroups — C13×C7⋊Dic63 #37524397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₇⋊Dic₆₃ #37524397