Subgroups — C₁₃×(C₃⋊D₃)⋊D₇₃ #46802986

Order 34164.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₂₁₉	C₂	1	2	yes	maximal, complemented
2	C₁₃×C₃⋊D₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₁₃×D₇₃	—	3	2	no	maximal
4	C₃²×C₁₃×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₂₁₉	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₇₃	—	3	2	no	—
7	D₃×C₁₃×C₇₃	—	6	1	no	—
8	C₃×C₁₃×D₇₃	—	3	2	no	—
9	C₂×C₁₃×D₇₃	—	9	1	no	Hall
10	C₃×C₁₃×C₇₃	—	2	1	no	—
11	C₃×C₁₃×C₇₃	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×C₇₃	—	9	1	no	—
14	C₁₃×D₇₃	—	3	2	no	—
15	C₃⋊D₃×C₇₃	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₃×D₂₁₉	C₂×C₁₃	1	2	yes	complemented
17	C₁₃×C₇₃	D₃²	1	1	yes	characteristic, complemented, Hall
18	D₃×D₇₃	—	3	2	no	—
19	C₃²×C₇₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	D₃²×C₁₃	—	73	1	no	maximal, Hall
21	D₂₁₉	D₃×C₁₃	1	2	yes	complemented
22	C₃×D₇₃	—	3	2	no	—
23	D₃×C₇₃	—	3	2	no	—
24	D₃×C₇₃	—	6	1	no	—
25	C₂×D₇₃	—	9	1	no	Hall
26	C₁₃×C₃⋊D₃	D₇₃	1	1	yes	characteristic, complemented
27	C₃×D₃×C₁₃	—	73	2	no	—
28	C₃×C₇₃	—	2	1	no	—
29	C₃×C₇₃	C₂×D₃×C₁₃	1	2	yes	complemented
30	C₂×D₃×C₁₃	—	219	2	no	—
31	C₂×C₇₃	—	9	1	no	—
32	D₇₃	—	3	2	no	—
33	C₃²×C₁₃	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₁₃	—	219	2	no	—
35	D₃×C₁₃	—	3	2	no	—
36	D₃×C₁₃	—	6	1	no	—
37	D₃×C₁₃	—	73	2	no	—
38	C₇₃	D₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₁₃	—	657	1	no	Hall
40	C₃×C₁₃	—	2	1	no	—
41	C₃×C₁₃	D₃×D₇₃	1	2	yes	complemented
42	D₃²	—	73	1	no	Hall
43	C₂×C₁₃	—	9	1	no	—
44	C₂×C₁₃	—	219	2	no	—
45	C₃⋊D₃	C₁₃×D₇₃	1	1	yes	characteristic, complemented
46	C₃×D₃	—	73	2	no	—
47	C₁₃	(C₃⋊D₃)⋊D₇₃	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₃	—	219	2	no	—
49	C₃²	C₂×C₁₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	219	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	73	2	no	—
54	C₂²	—	657	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₁₃×D₇₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	219	2	no	—

	subgroup	G/H
center, hypercenter	C₁₃	(C₃⋊D₃)⋊D₇₃
commutator, cosocle, hypocenter	C₃²×C₇₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₇₃	C₂²
LCS	G ▷ C₃²×C₇₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₂₁₉	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₇₃	C₂	semidirect
4. C₃²×C₁₃×C₇₃	C₂²	semidirect
5. C₁₃×D₂₁₉	D₃	semidirect
11. C₃×C₁₃×C₇₃	C₂×D₃	semidirect
12. (C₃⋊D₃)⋊D₇₃	C₁₃	direct (N × H)
15. C₃⋊D₃×C₇₃	C₂×C₁₃	semidirect
16. C₃×D₂₁₉	C₂×C₁₃	semidirect
17. C₁₃×C₇₃	D₃²	semidirect
19. C₃²×C₇₃	C₂²×C₁₃	semidirect
21. D₂₁₉	D₃×C₁₃	semidirect
26. C₁₃×C₃⋊D₃	D₇₃	semidirect
29. C₃×C₇₃	C₂×D₃×C₁₃	semidirect
33. C₃²×C₁₃	C₂×D₇₃	semidirect
38. C₇₃	D₃²×C₁₃	semidirect
41. C₃×C₁₃	D₃×D₇₃	semidirect
45. C₃⋊D₃	C₁₃×D₇₃	semidirect
47. C₁₃	(C₃⋊D₃)⋊D₇₃	direct (N × H)
49. C₃²	C₂×C₁₃×D₇₃	semidirect
56. C₃	D₃×C₁₃×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×D₂₁₉	2
C₁₃×C₃⋊D₃×C₇₃	2
D₃×C₁₃×D₇₃	3
(C₃⋊D₃)⋊D₇₃	13
D₃²×C₁₃	73

Subgroups — C13×(C3⋊D3)⋊D73 #46802986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₃⋊D₃)⋊D₇₃ #46802986