Subgroups — ((C₁₃⋊C₃)⋊D₁₃)⋊D₁₇ #46828239

Order 34476.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₂₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×(C₁₃⋊C₃)⋊D₁₃	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	C₁₇×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₂₂₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₂₂₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₃×D₁₇	—	13	1	no	maximal
11	D₁₇×D₁₃⋊C₃	—	13	1	no	maximal
12	D₁₃×D₁₃⋊C₃	—	17	1	no	maximal, Hall
13	C₃×D₂₂₁	—	13	1	no	—
14	C₃×C₁₇×D₁₃	—	13	1	no	—
15	C₃×C₁₃×D₁₇	—	13	1	no	—
16	C₁₇⋊(D₁₃⋊C₃)	D₁₃	1	1	yes	characteristic, complemented
17	C₁₇×D₁₃⋊C₃	—	13	1	no	—
18	D₁₇×C₁₃⋊C₃	—	13	1	no	—
19	D₁₃×C₁₃⋊C₃	—	17	1	no	—
20	(C₁₃⋊C₃)⋊D₁₃	D₁₇	1	1	yes	characteristic, complemented
21	C₁₃×D₁₃⋊C₃	—	17	1	no	—
22	D₁₃×D₁₇	—	13	1	no	—
23	D₁₃×D₁₇	—	13	1	no	—
24	D₁₃²	—	17	1	no	Hall
25	C₃×C₁₃×C₁₇	—	13	1	no	—
26	C₁₇×C₁₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented
27	C₁₃×C₁₃⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
28	D₂₂₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
29	D₂₂₁	C₃×D₁₃	1	1	yes	characteristic, complemented
30	C₁₃×D₁₇	—	13	1	no	—
31	C₁₃×D₁₇	—	13	1	no	—
32	C₁₇×D₁₃	—	13	1	no	—
33	C₁₇×D₁₃	—	13	1	no	—
34	C₁₇×D₁₃	—	78	2	no	—
35	C₁₃⋊D₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
36	C₁₃×D₁₃	—	17	1	no	—
37	C₁₃×D₁₃	—	17	1	no	—
38	C₁₃×C₁₇	—	6	2	no	—
39	C₁₃×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
40	C₁₃×C₁₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
41	C₂×C₃×D₁₇	—	169	1	no	Hall
42	C₁₃²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×D₁₃	—	221	1	no	—
44	C₂×D₁₃⋊C₃	—	221	1	no	—
45	C₂×C₃×C₁₇	—	169	1	no	—
46	C₃×D₁₇	—	13	1	no	—
47	C₃×D₁₇	—	169	1	no	—
48	C₂×C₃×C₁₃	—	221	1	no	—
49	C₃×D₁₃	—	13	1	no	—
50	C₃×D₁₃	—	221	1	no	—
51	C₂×C₁₃⋊C₃	—	221	1	no	—
52	D₁₃⋊C₃	—	13	1	no	—
53	D₁₃⋊C₃	—	17	1	no	—
54	C₂×D₁₇	—	169	1	no	Hall
55	C₂×D₁₃	—	221	1	no	—
56	C₂×D₁₃	—	221	1	no	—
57	C₃×C₁₇	—	13	1	no	Hall
58	C₃×C₁₃	—	13	1	no	—
59	C₁₃⋊C₃	D₁₃×D₁₇	1	1	yes	characteristic, complemented
60	C₂×C₁₇	—	169	1	no	—
61	D₁₇	—	13	1	no	—
62	D₁₇	—	13	1	no	—
63	C₂×C₁₃	—	221	1	no	—
64	C₂×C₁₃	—	221	1	no	—
65	D₁₃	—	13	1	no	—
66	D₁₃	—	13	1	no	—
67	D₁₃	—	17	1	no	—
68	D₁₃	—	17	1	no	—
69	D₁₃	—	78	2	no	—
70	C₁₇	D₁₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₁₃	—	6	2	no	—
72	C₁₃	D₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
73	C₁₃	C₃×D₁₃×D₁₇	1	1	yes	characteristic, complemented
74	C₂²×C₃	—	2873	1	no	Hall
75	C₂×C₃	—	2873	1	no	—
76	C₂×C₃	—	169	1	no	—
77	C₂×C₃	—	221	1	no	—
78	C₂²	—	2873	1	no	Sylow
79	C₃	—	13	1	no	Sylow
80	C₂	—	169	1	no	—
81	C₂	—	221	1	no	—
82	C₂	—	221	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊C₃×D₂₂₁	C₂	semidirect
2. C₁₇×(C₁₃⋊C₃)⋊D₁₃	C₂	semidirect
3. C₁₃×C₁₇⋊(D₁₃⋊C₃)	C₂	semidirect
4. (C₁₃⋊D₁₃)⋊D₁₇	C₃	semidirect
5. C₁₃×C₁₇×C₁₃⋊C₃	C₂²	semidirect
6. C₁₇×C₁₃⋊D₁₃	C₂×C₃	semidirect
7. C₁₃×D₂₂₁	C₂×C₃	semidirect
8. C₁₃×D₂₂₁	C₂×C₃	semidirect
9. C₁₃²×C₁₇	C₂²×C₃	semidirect
16. C₁₇⋊(D₁₃⋊C₃)	D₁₃	semidirect
20. (C₁₃⋊C₃)⋊D₁₃	D₁₇	semidirect
26. C₁₇×C₁₃⋊C₃	C₂×D₁₃	semidirect
27. C₁₃×C₁₃⋊C₃	C₂×D₁₇	semidirect
28. D₂₂₁	D₁₃⋊C₃	semidirect
29. D₂₂₁	C₃×D₁₃	semidirect
35. C₁₃⋊D₁₃	C₃×D₁₇	semidirect
39. C₁₃×C₁₇	C₂×D₁₃⋊C₃	semidirect
40. C₁₃×C₁₇	C₂×C₃×D₁₃	semidirect
42. C₁₃²	C₂×C₃×D₁₇	semidirect
59. C₁₃⋊C₃	D₁₃×D₁₇	semidirect
70. C₁₇	D₁₃×D₁₃⋊C₃	semidirect
72. C₁₃	D₁₇×D₁₃⋊C₃	semidirect
73. C₁₃	C₃×D₁₃×D₁₇	semidirect

Maximal subgroups

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

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

Subgroups — ((C13⋊C3)⋊D13)⋊D17 #46828239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₁₃⋊C₃)⋊D₁₃)⋊D₁₇ #46828239