Subgroups — C₃²×C₇²×Dic₁₃ #37524839

Order 22932.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₇²×Dic₁₃	C₃	direct (N × H)
3. C₃²×C₇²×C₁₃	C₄	semidirect
5. C₃²×C₇×Dic₁₃	C₇	direct (N × H)
6. C₇²×Dic₁₃	C₃²	direct (N × H)
7. C₃×C₇²×C₁₃	C₃×C₄	semidirect
11. C₃×C₇×Dic₁₃	C₃×C₇	direct (N × H)
13. C₃²×C₇×C₁₃	C₄×C₇	semidirect
14. C₇²×C₁₃	C₃²×C₄	semidirect
17. C₃²×Dic₁₃	C₇²	direct (N × H)
18. C₃²×C₇²	Dic₁₃	direct (N × H)
19. C₇×Dic₁₃	C₃²×C₇	direct (N × H)
21. C₃×C₇×C₁₃	C₃×C₄×C₇	semidirect
26. C₃×Dic₁₃	C₃×C₇²	direct (N × H)
27. C₃×C₇²	C₃×Dic₁₃	direct (N × H)
29. C₃²×C₁₃	C₄×C₇²	semidirect
31. C₇×C₁₃	C₃²×C₄×C₇	semidirect
34. C₃²×C₇	C₇×Dic₁₃	direct (N × H)
35. Dic₁₃	C₃²×C₇²	direct (N × H)
36. C₇²	C₃²×Dic₁₃	direct (N × H)
38. C₃×C₁₃	C₃×C₄×C₇²	semidirect
42. C₃×C₇	C₃×C₇×Dic₁₃	direct (N × H)
45. C₁₃	C₃²×C₄×C₇²	semidirect
47. C₃²	C₇²×Dic₁₃	direct (N × H)
48. C₇	C₃²×C₇×Dic₁₃	direct (N × H)
51. C₃	C₃×C₇²×Dic₁₃	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×C₃²×C₇²×C₁₃	2
C₃×C₇²×Dic₁₃	3
C₃²×C₇×Dic₁₃	7
C₃²×C₄×C₇²	13

Subgroups — C32×C72×Dic13 #37524839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇²×Dic₁₃ #37524839