Subgroups — D₅₁⋊(C₁₃⋊D₁₃) #46828366

Order 34476.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊D₂₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃²×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₃⋊(C₁₃⋊D₁₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×C₁₃⋊D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₁₃²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃⋊D₂₂₁	D₃	1	1	yes	characteristic, complemented
7	C₁₇×C₁₃⋊D₁₃	—	3	1	no	—
8	C₁₃²×D₁₇	—	3	1	no	—
9	C₁₃²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃₉⋊D₁₇	—	13	14	no	maximal
11	D₃×C₁₃⋊D₁₃	—	17	1	no	maximal, Hall
12	C₁₇×D₃₉	—	13	14	no	—
13	C₁₃×D₅₁	D₁₃	1	14	yes	complemented
14	C₃×D₂₂₁	—	13	14	no	—
15	C₃⋊(C₁₃⋊D₁₃)	D₁₇	1	1	yes	characteristic, complemented
16	D₃×C₁₃²	—	17	1	no	—
17	C₃×C₁₃⋊D₁₃	—	17	1	no	—
18	D₁₃×D₁₇	—	39	14	no	—
19	C₂×C₁₃⋊D₁₃	—	51	1	no	Hall
20	C₃×C₁₃×C₁₇	C₂×D₁₃	1	14	yes	complemented
21	C₃×C₁₃²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	D₂₂₁	—	13	14	no	—
23	C₁₃×D₁₇	—	3	14	no	—
24	C₁₇×D₁₃	—	39	14	no	—
25	C₂×C₁₃²	—	51	1	no	—
26	C₁₃⋊D₁₃	—	3	1	no	—
27	C₁₃⋊D₁₃	—	17	1	no	—
28	C₁₃×C₁₇	D₃×D₁₃	1	14	yes	complemented
29	D₃×D₁₇	—	169	1	no	Hall
30	C₁₃²	D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
31	D₃×D₁₃	—	221	14	no	—
32	D₅₁	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
33	C₃×D₁₇	—	169	1	no	—
34	D₃×C₁₇	—	169	1	no	—
35	D₃₉	—	13	14	no	—
36	C₃×D₁₃	—	221	14	no	—
37	D₃×C₁₃	—	17	14	no	—
38	C₂×D₁₇	—	507	1	no	Hall
39	C₂×D₁₃	—	663	14	no	—
40	C₃×C₁₇	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₃	D₁₃×D₁₇	1	14	yes	complemented
42	C₂×C₁₇	—	507	1	no	—
43	D₁₇	—	3	1	no	—
44	D₁₇	—	169	1	no	—
45	C₂×C₁₃	—	51	14	no	—
46	D₁₃	—	39	14	no	—
47	D₁₃	—	221	14	no	—
48	C₁₇	D₃×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
49	C₁₃	D₃₉⋊D₁₇	1	14	yes	complemented
50	C₂×D₃	—	2873	1	no	Hall
51	C₂×C₃	—	2873	1	no	—
52	D₃	—	17	1	no	—
53	D₃	—	169	1	no	—
54	C₂²	—	8619	1	no	Sylow
55	C₃	D₁₇×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	51	1	no	—
57	C₂	—	2873	1	no	—
58	C₂	—	507	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃²×C₁₇	C₂²
LCS	G ▷ C₃×C₁₃²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊D₂₂₁	C₂	semidirect
2. C₁₃²×D₅₁	C₂	semidirect
3. C₁₇×C₃⋊(C₁₃⋊D₁₃)	C₂	semidirect
5. C₃×C₁₃²×C₁₇	C₂²	semidirect
6. C₁₃⋊D₂₂₁	D₃	semidirect
9. C₁₃²×C₁₇	C₂×D₃	semidirect
13. C₁₃×D₅₁	D₁₃	semidirect
15. C₃⋊(C₁₃⋊D₁₃)	D₁₇	semidirect
20. C₃×C₁₃×C₁₇	C₂×D₁₃	semidirect
21. C₃×C₁₃²	C₂×D₁₇	semidirect
28. C₁₃×C₁₇	D₃×D₁₃	semidirect
30. C₁₃²	D₃×D₁₇	semidirect
32. D₅₁	C₁₃⋊D₁₃	semidirect
40. C₃×C₁₇	C₂×C₁₃⋊D₁₃	semidirect
41. C₃×C₁₃	D₁₃×D₁₇	semidirect
48. C₁₇	D₃×C₁₃⋊D₁₃	semidirect
49. C₁₃	D₃₉⋊D₁₇	semidirect
55. C₃	D₁₇×C₁₃⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃⋊D₂₂₁	2
C₁₃²×D₅₁	2
C₁₇×C₃⋊(C₁₃⋊D₁₃)	2
D₁₇×C₁₃⋊D₁₃	3
D₃₉⋊D₁₇	13
D₃×C₁₃⋊D₁₃	17

Subgroups — D51⋊(C13⋊D13) #46828366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₁⋊(C₁₃⋊D₁₃) #46828366