Subgroups — C₁₃×D₁₇×D₁₃⋊C₃ #46828217

Order 34476.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₁₇⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₁₇×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₁₃×D₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃×C₁₇×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₂₂₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃²×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₃×D₁₇	—	13	1	no	maximal
11	D₁₇×D₁₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₁₃×D₁₃⋊C₃	—	17	1	no	maximal, Hall
13	C₂×C₃×C₁₃×C₁₇	—	13	1	no	—
14	C₃×C₁₃×D₁₇	—	13	1	no	—
15	C₃×C₁₃×D₁₇	—	13	1	no	—
16	C₁₇⋊(D₁₃⋊C₃)	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₁₇×D₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	D₁₇×C₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₂×C₁₃×C₁₃⋊C₃	—	17	1	no	—
20	C₁₃×D₁₃⋊C₃	—	17	1	no	—
21	C₁₃×D₁₃⋊C₃	D₁₇	1	1	yes	characteristic, direct product factor
22	C₂×C₁₃×D₁₇	—	13	1	no	—
23	D₁₃×D₁₇	C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₂×C₁₃×D₁₃	—	17	1	no	Hall
25	C₃×C₁₃×C₁₇	—	13	1	no	—
26	C₁₇×C₁₃⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
27	C₁₃×C₁₃⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₃×C₁₇	—	13	1	no	—
29	D₂₂₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
30	C₁₃×D₁₇	—	6	2	no	—
31	C₁₃×D₁₇	—	13	1	no	—
32	C₁₃×D₁₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
33	C₁₃×D₁₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
34	C₁₇×D₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
35	C₂×C₁₃²	—	17	1	no	—
36	C₁₃×D₁₃	—	17	1	no	—
37	C₁₃×D₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
38	C₁₃×C₁₇	—	6	2	no	—
39	C₁₃×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
40	C₁₃×C₁₇	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
41	C₂×C₃×D₁₇	—	13	1	no	Hall
42	C₁₃²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₃×C₁₃	—	221	1	no	—
44	C₂×D₁₃⋊C₃	—	17	1	no	—
45	C₂×C₃×C₁₇	—	13	1	no	—
46	C₃×D₁₇	—	13	1	no	—
47	C₃×D₁₇	—	13	1	no	—
48	C₂×C₃×C₁₃	—	13	1	no	—
49	C₂×C₃×C₁₃	—	221	1	no	—
50	C₂×C₃×C₁₃	—	221	1	no	—
51	C₂×C₁₃⋊C₃	—	17	1	no	—
52	D₁₃⋊C₃	—	17	1	no	—
53	D₁₃⋊C₃	C₁₃×D₁₇	1	1	yes	characteristic, direct product factor
54	C₂×D₁₇	—	13	1	no	Hall
55	C₂²×C₁₃	—	221	1	no	—
56	C₂×D₁₃	—	17	1	no	—
57	C₃×C₁₇	—	13	1	no	Hall
58	C₃×C₁₃	—	13	1	no	—
59	C₁₃⋊C₃	C₂×C₁₃×D₁₇	1	1	yes	characteristic, complemented
60	C₂×C₁₇	—	13	1	no	—
61	D₁₇	—	13	1	no	—
62	D₁₇	C₁₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
63	C₂×C₁₃	—	13	1	no	—
64	C₂×C₁₃	—	17	1	no	—
65	C₂×C₁₃	—	17	1	no	—
66	C₂×C₁₃	—	102	2	no	—
67	C₂×C₁₃	—	221	1	no	—
68	D₁₃	—	17	1	no	—
69	D₁₃	C₃×C₁₃×D₁₇	1	1	yes	characteristic, complemented
70	C₁₇	C₂×C₁₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₁₃	—	6	2	no	—
72	C₁₃	D₁₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
73	C₁₃	C₂×C₃×C₁₃×D₁₇	1	1	yes	characteristic, complemented
74	C₂²×C₃	—	221	1	no	Hall
75	C₂×C₃	—	13	1	no	—
76	C₂×C₃	—	221	1	no	—
77	C₂×C₃	—	221	1	no	—
78	C₂²	—	221	1	no	Sylow
79	C₃	—	13	1	no	Sylow
80	C₂	—	13	1	no	—
81	C₂	—	17	1	no	—
82	C₂	—	221	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₁₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₁₇	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃²×C₁₇	C₂²×C₃
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₇×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×C₁₇⋊(D₁₃⋊C₃)	C₂	semidirect
3. C₁₃×C₁₇×D₁₃⋊C₃	C₂	semidirect
4. C₁₃×D₁₃×D₁₇	C₃	semidirect
5. C₁₃×C₁₇×C₁₃⋊C₃	C₂²	semidirect
6. C₁₃×D₂₂₁	C₂×C₃	semidirect
7. C₁₃×C₁₇×D₁₃	C₂×C₃	semidirect
8. C₁₃²×D₁₇	C₂×C₃	semidirect
9. C₁₃²×C₁₇	C₂²×C₃	semidirect
11. D₁₇×D₁₃⋊C₃	C₁₃	direct (N × H)
16. C₁₇⋊(D₁₃⋊C₃)	C₂×C₁₃	semidirect
17. C₁₇×D₁₃⋊C₃	C₂×C₁₃	semidirect
18. D₁₇×C₁₃⋊C₃	C₂×C₁₃	semidirect
21. C₁₃×D₁₃⋊C₃	D₁₇	direct (N × H)
23. D₁₃×D₁₇	C₃×C₁₃	semidirect
26. C₁₇×C₁₃⋊C₃	C₂²×C₁₃	semidirect
27. C₁₃×C₁₃⋊C₃	C₂×D₁₇	semidirect
29. D₂₂₁	C₂×C₃×C₁₃	semidirect
32. C₁₃×D₁₇	D₁₃⋊C₃	direct (N × H)
33. C₁₃×D₁₇	C₂×C₃×C₁₃	semidirect
34. C₁₇×D₁₃	C₂×C₃×C₁₃	semidirect
37. C₁₃×D₁₃	C₃×D₁₇	semidirect
39. C₁₃×C₁₇	C₂×D₁₃⋊C₃	semidirect
40. C₁₃×C₁₇	C₂²×C₃×C₁₃	semidirect
42. C₁₃²	C₂×C₃×D₁₇	semidirect
53. D₁₃⋊C₃	C₁₃×D₁₇	direct (N × H)
59. C₁₃⋊C₃	C₂×C₁₃×D₁₇	semidirect
62. D₁₇	C₁₃×D₁₃⋊C₃	direct (N × H)
69. D₁₃	C₃×C₁₃×D₁₇	semidirect
70. C₁₇	C₂×C₁₃×D₁₃⋊C₃	semidirect
72. C₁₃	D₁₇×D₁₃⋊C₃	direct (N × H)
73. C₁₃	C₂×C₃×C₁₃×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₁₇×C₁₃⋊C₃	2
C₁₃×C₁₇⋊(D₁₃⋊C₃)	2
C₁₃×C₁₇×D₁₃⋊C₃	2
C₁₃×D₁₃×D₁₇	3
C₂×C₃×C₁₃×D₁₇	13
D₁₇×D₁₃⋊C₃	13
C₂×C₁₃×D₁₃⋊C₃	17

Subgroups — C13×D17×D13⋊C3 #46828217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₇×D₁₃⋊C₃ #46828217