Subgroups — C₇²×C₃⋊D₃×D₁₃ #37525630

Order 22932.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇²×D₁₃	—	3	4	no	maximal
5	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇²×D₃₉	—	3	4	no	—
7	D₃×C₇²×C₁₃	—	3	4	no	—
8	C₃×C₇²×D₁₃	D₃	1	4	yes	complemented
9	C₇×C₃⋊D₃×D₁₃	C₇	1	8	yes	maximal, direct product factor
10	C₂×C₇²×D₁₃	—	9	1	no	Hall
11	C₃×C₇²×C₁₃	C₂×D₃	1	4	yes	complemented
12	C₂×C₇²×C₃⋊D₃	—	13	1	no	maximal, Hall
13	C₇×C₃⋊D₃₉	C₂×C₇	1	8	yes	complemented
14	C₇×C₁₃×C₃⋊D₃	C₂×C₇	1	8	yes	complemented
15	C₃²×C₇×D₁₃	C₂×C₇	1	8	yes	complemented
16	C₂×C₇²×C₁₃	—	9	1	no	—
17	C₇²×D₁₃	—	9	1	no	—
18	C₇²×D₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	D₃×C₇×D₁₃	—	3	32	no	—
20	C₂×C₃²×C₇²	—	13	1	no	—
21	C₇²×C₃⋊D₃	—	13	1	no	—
22	C₇²×C₃⋊D₃	D₁₃	1	1	yes	characteristic, direct product factor
23	C₃²×C₇×C₁₃	C₂²×C₇	1	8	yes	complemented
24	C₇²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃×C₇²	—	39	4	no	—
26	C₇×D₃₉	—	3	32	no	—
27	D₃×C₇×C₁₃	—	3	32	no	—
28	C₃×C₇×D₁₃	D₃×C₇	1	32	yes	complemented
29	C₃⋊D₃×D₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
30	C₃²×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×D₁₃	—	9	8	no	—
32	C₂×C₃×C₇²	—	13	4	no	—
33	D₃×C₇²	—	3	4	no	—
34	D₃×C₇²	—	39	4	no	—
35	C₃×C₇×C₁₃	C₂×D₃×C₇	1	32	yes	complemented
36	C₂×C₇×C₃⋊D₃	—	13	8	no	—
37	C₃⋊D₃₉	C₂×C₇²	1	1	yes	characteristic, complemented
38	C₁₃×C₃⋊D₃	C₂×C₇²	1	1	yes	characteristic, complemented
39	C₃²×D₁₃	C₂×C₇²	1	1	yes	characteristic, complemented
40	C₂²×C₇²	—	117	1	no	Hall
41	C₂×C₇×C₁₃	—	9	8	no	—
42	C₇×D₁₃	—	9	8	no	—
43	C₇×D₁₃	C₇×C₃⋊D₃	1	8	yes	direct product factor
44	D₃×D₁₃	—	3	4	no	—
45	C₃×C₇²	D₃×D₁₃	1	4	yes	complemented
46	C₂×C₃²×C₇	—	13	8	no	—
47	C₇×C₃⋊D₃	—	13	8	no	—
48	C₇×C₃⋊D₃	C₇×D₁₃	1	8	yes	direct product factor
49	C₃²×C₁₃	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇²	—	9	1	no	—
51	C₂×C₇²	—	13	1	no	—
52	C₂×C₇²	—	117	1	no	—
53	C₇×C₁₃	C₂×C₇×C₃⋊D₃	1	8	yes	complemented
54	C₂×D₃×C₇	—	39	32	no	—
55	D₃₉	—	3	4	no	—
56	C₃×D₁₃	D₃×C₇²	1	4	yes	complemented
57	D₃×C₁₃	—	3	4	no	—
58	C₃²×C₇	C₂×C₇×D₁₃	1	8	yes	complemented
59	C₂×D₁₃	—	9	1	no	Hall
60	C₇²	C₃⋊D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₃×C₇	—	13	32	no	—
62	D₃×C₇	—	3	32	no	—
63	D₃×C₇	—	39	32	no	—
64	C₃×C₁₃	C₂×D₃×C₇²	1	4	yes	complemented
65	C₂×C₃⋊D₃	—	13	1	no	Hall
66	C₂²×C₇	—	117	8	no	—
67	C₂×C₁₃	—	9	1	no	—
68	D₁₃	—	9	1	no	—
69	D₁₃	C₇²×C₃⋊D₃	1	1	yes	characteristic, direct product factor
70	C₃×C₇	D₃×C₇×D₁₃	1	32	yes	complemented
71	C₂×C₃²	—	13	1	no	—
72	C₃⋊D₃	—	13	1	no	—
73	C₃⋊D₃	C₇²×D₁₃	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	8	no	—
75	C₂×C₇	—	13	8	no	—
76	C₂×C₇	—	117	8	no	—
77	C₁₃	C₂×C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₃	—	39	4	no	—
79	C₃²	C₂×C₇²×D₁₃	1	1	yes	characteristic, complemented, Sylow
80	C₇	C₇×C₃⋊D₃×D₁₃	1	8	yes	direct product factor
81	C₂×C₃	—	13	4	no	—
82	D₃	—	3	4	no	—
83	D₃	—	39	4	no	—
84	C₂²	—	117	1	no	Sylow
85	C₃	D₃×C₇²×D₁₃	1	4	yes	complemented
86	C₂	—	9	1	no	—
87	C₂	—	13	1	no	—
88	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	C₃⋊D₃×D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×D₁₃	C₂	semidirect
2. C₇²×C₁₃×C₃⋊D₃	C₂	semidirect
3. C₇²×C₃⋊D₃₉	C₂	semidirect
5. C₃²×C₇²×C₁₃	C₂²	semidirect
8. C₃×C₇²×D₁₃	D₃	semidirect
9. C₇×C₃⋊D₃×D₁₃	C₇	direct (N × H)
11. C₃×C₇²×C₁₃	C₂×D₃	semidirect
13. C₇×C₃⋊D₃₉	C₂×C₇	semidirect
14. C₇×C₁₃×C₃⋊D₃	C₂×C₇	semidirect
15. C₃²×C₇×D₁₃	C₂×C₇	semidirect
18. C₇²×D₁₃	C₃⋊D₃	direct (N × H)
22. C₇²×C₃⋊D₃	D₁₃	direct (N × H)
23. C₃²×C₇×C₁₃	C₂²×C₇	semidirect
24. C₇²×C₁₃	C₂×C₃⋊D₃	semidirect
28. C₃×C₇×D₁₃	D₃×C₇	semidirect
29. C₃⋊D₃×D₁₃	C₇²	direct (N × H)
30. C₃²×C₇²	C₂×D₁₃	semidirect
35. C₃×C₇×C₁₃	C₂×D₃×C₇	semidirect
37. C₃⋊D₃₉	C₂×C₇²	semidirect
38. C₁₃×C₃⋊D₃	C₂×C₇²	semidirect
39. C₃²×D₁₃	C₂×C₇²	semidirect
43. C₇×D₁₃	C₇×C₃⋊D₃	direct (N × H)
45. C₃×C₇²	D₃×D₁₃	semidirect
48. C₇×C₃⋊D₃	C₇×D₁₃	direct (N × H)
49. C₃²×C₁₃	C₂²×C₇²	semidirect
53. C₇×C₁₃	C₂×C₇×C₃⋊D₃	semidirect
56. C₃×D₁₃	D₃×C₇²	semidirect
58. C₃²×C₇	C₂×C₇×D₁₃	semidirect
60. C₇²	C₃⋊D₃×D₁₃	direct (N × H)
64. C₃×C₁₃	C₂×D₃×C₇²	semidirect
69. D₁₃	C₇²×C₃⋊D₃	direct (N × H)
70. C₃×C₇	D₃×C₇×D₁₃	semidirect
73. C₃⋊D₃	C₇²×D₁₃	direct (N × H)
77. C₁₃	C₂×C₇²×C₃⋊D₃	semidirect
79. C₃²	C₂×C₇²×D₁₃	semidirect
80. C₇	C₇×C₃⋊D₃×D₁₃	direct (N × H)
85. C₃	D₃×C₇²×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×D₁₃	2
C₇²×C₁₃×C₃⋊D₃	2
C₇²×C₃⋊D₃₉	2
D₃×C₇²×D₁₃	3
C₇×C₃⋊D₃×D₁₃	7
C₂×C₇²×C₃⋊D₃	13

Subgroups — C72×C3⋊D3×D13 #37525630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₃⋊D₃×D₁₃ #37525630