Subgroups — C₃×C₇²×Dic₁₃⋊C₃ #37524695

Order 22932.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇²×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×Dic₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇²×Dic₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₇²×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₃⋊C₃	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₃×C₇×Dic₁₃⋊C₃	C₇	1	8	yes	maximal, direct product factor
8	C₇²×Dic₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
10	C₇²×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
11	C₃²×C₄×C₇²	—	13	1	no	maximal, Hall
12	C₂×C₃×C₇×C₁₃⋊C₃	C₂×C₇	1	8	yes	—
13	C₂×C₇²×C₁₃	C₂×C₃²	1	1	yes	characteristic
14	C₃×C₇×Dic₁₃	C₃×C₇	1	8	yes	complemented
15	C₇×Dic₁₃⋊C₃	C₃×C₇	1	24	yes	direct product factor
16	C₂×C₃²×C₇²	—	13	1	no	—
17	C₃×C₇×C₁₃⋊C₃	C₄×C₇	1	8	yes	complemented
18	C₇²×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄×C₇²	—	13	3	no	—
20	C₃×C₄×C₇²	—	13	1	no	—
21	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	8	yes	—
22	C₂×C₇×C₁₃⋊C₃	C₂×C₃×C₇	1	24	yes	—
23	C₃×Dic₁₃⋊C₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₇²	—	13	1	no	Hall
25	C₇×Dic₁₃	C₃²×C₇	1	8	yes	complemented
26	C₂×C₃×C₇²	—	13	3	no	—
27	C₂×C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic
28	C₃×C₇×C₁₃	C₃×C₄×C₇	1	8	yes	complemented
29	C₇×C₁₃⋊C₃	C₃×C₄×C₇	1	24	yes	complemented
30	C₃²×C₄×C₇	—	13	8	no	—
31	C₂×C₃×C₁₃⋊C₃	C₂×C₇²	1	1	yes	characteristic
32	C₄×C₇²	—	13	1	no	Hall
33	C₂×C₇×C₁₃	C₂×C₃²×C₇	1	8	yes	—
34	C₃×Dic₁₃	C₃×C₇²	1	1	yes	characteristic, complemented
35	Dic₁₃⋊C₃	C₃×C₇²	1	3	yes	direct product factor
36	C₃×C₇²	—	13	3	no	—
37	C₃×C₇²	Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₃²×C₇	—	13	8	no	—
39	C₃×C₁₃⋊C₃	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇²	C₃×D₁₃⋊C₃	1	1	yes	characteristic
41	C₇×C₁₃	C₃²×C₄×C₇	1	8	yes	complemented
42	C₃×C₄×C₇	—	13	24	no	—
43	C₃×C₄×C₇	—	13	8	no	—
44	C₂×C₃×C₁₃	C₂×C₃×C₇²	1	1	yes	characteristic
45	C₂×C₁₃⋊C₃	C₂×C₃×C₇²	1	3	yes	—
46	C₃²×C₇	—	13	8	no	—
47	Dic₁₃	C₃²×C₇²	1	1	yes	characteristic, complemented, Hall
48	C₇²	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×C₇	—	13	24	no	—
50	C₂×C₃×C₇	C₇×D₁₃⋊C₃	1	8	yes	—
51	C₃×C₁₃	C₃×C₄×C₇²	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	C₃×C₄×C₇²	1	3	yes	complemented
53	C₃²×C₄	—	13	1	no	Hall
54	C₄×C₇	—	13	8	no	—
55	C₂×C₁₃	C₂×C₃²×C₇²	1	1	yes	characteristic
56	C₃×C₇	—	13	24	no	—
57	C₃×C₇	C₇×Dic₁₃⋊C₃	1	8	yes	direct product factor
58	C₂×C₃²	—	13	1	no	—
59	C₂×C₇	C₃×C₇×D₁₃⋊C₃	1	8	yes	—
60	C₁₃	C₃²×C₄×C₇²	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₄	—	13	3	no	—
62	C₃×C₄	—	13	1	no	—
63	C₃²	—	13	1	no	Sylow
64	C₇	C₃×C₇×Dic₁₃⋊C₃	1	8	yes	direct product factor
65	C₂×C₃	—	13	3	no	—
66	C₂×C₃	C₇²×D₁₃⋊C₃	1	1	yes	characteristic
67	C₄	—	13	1	no	Sylow
68	C₃	—	13	3	no	—
69	C₃	C₇²×Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor
70	C₂	C₃×C₇²×D₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇²	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃²×C₄×C₇²
Frattini	C₂	C₃×C₇²×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₇²×C₁₃⋊C₃	C₂
cosocle	C₂×C₁₃	C₂×C₃²×C₇²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇²

Complements

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

N	H ≅ G/N	type
2. C₃×C₇²×Dic₁₃	C₃	semidirect
3. C₇²×Dic₁₃⋊C₃	C₃	direct (N × H)
4. C₃×C₇²×C₁₃⋊C₃	C₄	semidirect
7. C₃×C₇×Dic₁₃⋊C₃	C₇	direct (N × H)
8. C₇²×Dic₁₃	C₃²	semidirect
9. C₃×C₇²×C₁₃	C₃×C₄	semidirect
10. C₇²×C₁₃⋊C₃	C₃×C₄	semidirect
14. C₃×C₇×Dic₁₃	C₃×C₇	semidirect
15. C₇×Dic₁₃⋊C₃	C₃×C₇	direct (N × H)
17. C₃×C₇×C₁₃⋊C₃	C₄×C₇	semidirect
18. C₇²×C₁₃	C₃²×C₄	semidirect
23. C₃×Dic₁₃⋊C₃	C₇²	direct (N × H)
25. C₇×Dic₁₃	C₃²×C₇	semidirect
28. C₃×C₇×C₁₃	C₃×C₄×C₇	semidirect
29. C₇×C₁₃⋊C₃	C₃×C₄×C₇	semidirect
34. C₃×Dic₁₃	C₃×C₇²	semidirect
35. Dic₁₃⋊C₃	C₃×C₇²	direct (N × H)
37. C₃×C₇²	Dic₁₃⋊C₃	direct (N × H)
39. C₃×C₁₃⋊C₃	C₄×C₇²	semidirect
41. C₇×C₁₃	C₃²×C₄×C₇	semidirect
47. Dic₁₃	C₃²×C₇²	semidirect
48. C₇²	C₃×Dic₁₃⋊C₃	direct (N × H)
51. C₃×C₁₃	C₃×C₄×C₇²	semidirect
52. C₁₃⋊C₃	C₃×C₄×C₇²	semidirect
57. C₃×C₇	C₇×Dic₁₃⋊C₃	direct (N × H)
60. C₁₃	C₃²×C₄×C₇²	semidirect
64. C₇	C₃×C₇×Dic₁₃⋊C₃	direct (N × H)
69. C₃	C₇²×Dic₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇²×C₁₃⋊C₃	2
C₃×C₇²×Dic₁₃	3
C₇²×Dic₁₃⋊C₃	3
C₃×C₇×Dic₁₃⋊C₃	7
C₃²×C₄×C₇²	13

Subgroups — C3×C72×Dic13⋊C3 #37524695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×Dic₁₃⋊C₃ #37524695