Subgroups — C₁₃×(C₃⋊D₃)⋊(C₇⋊D₇) #37525623

Order 22932.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₃⋊(C₇⋊D₇)	C₂	1	2	yes	maximal, complemented
2	C₇²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₁₃×C₇⋊D₇	—	3	2	no	maximal
4	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₃⋊(C₇⋊D₇)	D₃	1	2	yes	complemented
6	D₃×C₇²×C₁₃	—	3	2	no	—
7	D₃×C₇²×C₁₃	—	6	1	no	—
8	C₃×C₁₃×C₇⋊D₇	—	3	2	no	—
9	C₁₃×(C₃⋊D₃)⋊D₇	—	7	8	no	maximal
10	C₂×C₁₃×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₃	—	2	1	no	—
12	C₃×C₇²×C₁₃	C₂×D₃	1	2	yes	complemented
13	(C₃⋊D₃)⋊(C₇⋊D₇)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₇×C₁₃×C₃⋊D₃	D₇	1	8	yes	complemented
15	C₃×C₁₃×D₂₁	—	7	16	no	—
16	C₂×C₇²×C₁₃	—	9	1	no	—
17	C₁₃×C₇⋊D₇	—	3	2	no	—
18	D₃×C₁₃×D₇	—	21	16	no	—
19	C₇²×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃×C₃⋊(C₇⋊D₇)	C₂×C₁₃	1	2	yes	complemented
21	C₃²×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
22	C₇²×C₁₃	D₃²	1	1	yes	characteristic, complemented, Hall
23	D₃×C₇⋊D₇	—	3	2	no	—
24	C₁₃×D₂₁	—	7	16	no	—
25	D₃×C₇×C₁₃	—	3	16	no	—
26	D₃×C₇×C₁₃	—	6	8	no	—
27	C₃×C₁₃×D₇	—	21	16	no	—
28	D₃²×C₁₃	—	49	1	no	Hall
29	C₃²×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×D₇	—	63	8	no	—
31	C₃⋊(C₇⋊D₇)	D₃×C₁₃	1	2	yes	complemented
32	D₃×C₇²	—	3	2	no	—
33	D₃×C₇²	—	6	1	no	—
34	C₃×C₇⋊D₇	—	3	2	no	—
35	C₃×C₇×C₁₃	—	2	8	no	—
36	C₃×C₇×C₁₃	D₃×D₇	1	16	yes	complemented
37	(C₃⋊D₃)⋊D₇	—	7	8	no	—
38	C₁₃×C₃⋊D₃	C₇⋊D₇	1	1	yes	characteristic, complemented
39	C₃×D₃×C₁₃	—	49	2	no	—
40	C₂×C₇⋊D₇	—	9	1	no	Hall
41	C₂×C₇×C₁₃	—	9	8	no	—
42	C₁₃×D₇	—	21	16	no	—
43	C₂×D₃×C₁₃	—	147	2	no	—
44	C₃×C₇²	—	2	1	no	—
45	C₃×C₇²	C₂×D₃×C₁₃	1	2	yes	complemented
46	C₇×C₃⋊D₃	C₁₃×D₇	1	8	yes	complemented
47	C₃×D₂₁	—	7	16	no	—
48	C₃²×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇²	—	9	1	no	—
50	C₇⋊D₇	—	3	2	no	—
51	C₇×C₁₃	(C₃⋊D₃)⋊D₇	1	8	yes	complemented
52	D₃×D₇	—	21	16	no	—
53	C₂×C₃×C₁₃	—	147	2	no	—
54	D₃×C₁₃	—	3	2	no	—
55	D₃×C₁₃	—	6	1	no	—
56	D₃×C₁₃	—	49	2	no	—
57	C₃²×C₇	C₂×C₁₃×D₇	1	8	yes	complemented
58	C₂²×C₁₃	—	441	1	no	Hall
59	C₇²	D₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
60	D₂₁	—	7	16	no	—
61	C₃×D₇	—	21	16	no	—
62	D₃×C₇	—	3	16	no	—
63	D₃×C₇	—	6	8	no	—
64	C₃×C₁₃	—	2	1	no	—
65	C₃×C₁₃	D₃×C₇⋊D₇	1	2	yes	complemented
66	D₃²	—	49	1	no	Hall
67	C₂×D₇	—	63	8	no	—
68	C₂×C₁₃	—	9	1	no	—
69	C₂×C₁₃	—	147	2	no	—
70	C₃×C₇	—	2	8	no	—
71	C₃×C₇	D₃×C₁₃×D₇	1	16	yes	complemented
72	C₃⋊D₃	C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented
73	C₃×D₃	—	49	2	no	—
74	C₂×C₇	—	9	8	no	—
75	D₇	—	21	16	no	—
76	C₁₃	(C₃⋊D₃)⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
77	C₂×D₃	—	147	2	no	—
78	C₃²	C₂×C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
79	C₇	C₁₃×(C₃⋊D₃)⋊D₇	1	8	yes	complemented
80	C₂×C₃	—	147	2	no	—
81	D₃	—	3	2	no	—
82	D₃	—	6	1	no	—
83	D₃	—	49	2	no	—
84	C₂²	—	441	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×C₁₃×C₇⋊D₇	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	147	2	no	—

	subgroup	G/H
center, hypercenter	C₁₃	(C₃⋊D₃)⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₃²×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. C₇²×C₁₃×C₃⋊D₃	C₂	semidirect
4. C₃²×C₇²×C₁₃	C₂²	semidirect
5. C₁₃×C₃⋊(C₇⋊D₇)	D₃	semidirect
12. C₃×C₇²×C₁₃	C₂×D₃	semidirect
13. (C₃⋊D₃)⋊(C₇⋊D₇)	C₁₃	direct (N × H)
14. C₇×C₁₃×C₃⋊D₃	D₇	semidirect
19. C₇²×C₃⋊D₃	C₂×C₁₃	semidirect
20. C₃×C₃⋊(C₇⋊D₇)	C₂×C₁₃	semidirect
21. C₃²×C₇×C₁₃	C₂×D₇	semidirect
22. C₇²×C₁₃	D₃²	semidirect
29. C₃²×C₇²	C₂²×C₁₃	semidirect
31. C₃⋊(C₇⋊D₇)	D₃×C₁₃	semidirect
36. C₃×C₇×C₁₃	D₃×D₇	semidirect
38. C₁₃×C₃⋊D₃	C₇⋊D₇	semidirect
45. C₃×C₇²	C₂×D₃×C₁₃	semidirect
46. C₇×C₃⋊D₃	C₁₃×D₇	semidirect
48. C₃²×C₁₃	C₂×C₇⋊D₇	semidirect
51. C₇×C₁₃	(C₃⋊D₃)⋊D₇	semidirect
57. C₃²×C₇	C₂×C₁₃×D₇	semidirect
59. C₇²	D₃²×C₁₃	semidirect
65. C₃×C₁₃	D₃×C₇⋊D₇	semidirect
71. C₃×C₇	D₃×C₁₃×D₇	semidirect
72. C₃⋊D₃	C₁₃×C₇⋊D₇	semidirect
76. C₁₃	(C₃⋊D₃)⋊(C₇⋊D₇)	direct (N × H)
78. C₃²	C₂×C₁₃×C₇⋊D₇	semidirect
79. C₇	C₁₃×(C₃⋊D₃)⋊D₇	semidirect
86. C₃	D₃×C₁₃×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₃⋊(C₇⋊D₇)	2
C₇²×C₁₃×C₃⋊D₃	2
D₃×C₁₃×C₇⋊D₇	3
C₁₃×(C₃⋊D₃)⋊D₇	7
(C₃⋊D₃)⋊(C₇⋊D₇)	13

Subgroups — C13×(C3⋊D3)⋊(C7⋊D7) #37525623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₃⋊D₃)⋊(C₇⋊D₇) #37525623