Subgroups — C₇²×C₉×Dic₁₃ #37524388

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₇×C₉×Dic₁₃	C₇	1	8	yes	maximal, direct product factor
6	C₇²×Dic₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
8	C₄×C₇²×C₉	—	13	1	no	maximal, Hall
9	C₂×C₇×C₉×C₁₃	C₂×C₇	1	8	yes	—
10	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
11	C₃×C₇×Dic₁₃	C₃×C₇	1	8	yes	—
12	C₂×C₇²×C₉	D₁₃	1	1	yes	characteristic
13	C₇×C₉×C₁₃	C₄×C₇	1	8	yes	complemented
14	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₇²	—	13	1	no	—
16	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	8	yes	—
17	C₉×Dic₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₇²×C₉	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₇×Dic₁₃	C₇×C₉	1	8	yes	direct product factor
20	C₂×C₃×C₇²	C₃×D₁₃	1	1	yes	characteristic
21	C₃×C₇×C₁₃	C₃×C₄×C₇	1	8	yes	—
22	C₄×C₇×C₉	—	13	8	no	—
23	C₂×C₉×C₁₃	C₂×C₇²	1	1	yes	characteristic
24	C₄×C₇²	—	13	1	no	Hall
25	C₂×C₇×C₁₃	C₂×C₇×C₉	1	8	yes	—
26	C₃×Dic₁₃	C₃×C₇²	1	1	yes	characteristic
27	C₃×C₇²	C₃×Dic₁₃	1	1	yes	characteristic
28	C₂×C₇×C₉	C₇×D₁₃	1	8	yes	—
29	C₉×C₁₃	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇²	C₉×D₁₃	1	1	yes	characteristic
31	C₇×C₁₃	C₄×C₇×C₉	1	8	yes	complemented
32	C₃×C₄×C₇	—	13	8	no	—
33	C₂×C₃×C₁₃	C₂×C₃×C₇²	1	1	yes	characteristic
34	C₇×C₉	C₇×Dic₁₃	1	8	yes	direct product factor
35	Dic₁₃	C₇²×C₉	1	1	yes	characteristic, direct product factor, Hall
36	C₇²	C₉×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₇	C₃×C₇×D₁₃	1	8	yes	—
38	C₃×C₁₃	C₃×C₄×C₇²	1	1	yes	characteristic
39	C₄×C₉	—	13	1	no	Hall
40	C₄×C₇	—	13	8	no	—
41	C₂×C₁₃	C₂×C₇²×C₉	1	1	yes	characteristic
42	C₃×C₇	C₃×C₇×Dic₁₃	1	8	yes	—
43	C₂×C₉	C₇²×D₁₃	1	1	yes	characteristic
44	C₂×C₇	C₇×C₉×D₁₃	1	8	yes	—
45	C₁₃	C₄×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₄	—	13	1	no	—
47	C₉	C₇²×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₇×C₉×Dic₁₃	1	8	yes	direct product factor
49	C₂×C₃	C₃×C₇²×D₁₃	1	1	yes	characteristic
50	C₄	—	13	1	no	Sylow
51	C₃	C₃×C₇²×Dic₁₃	1	1	yes	characteristic
52	C₂	C₇²×C₉×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₉	D₁₃
commutator, hypocenter	C₁₃	C₄×C₇²×C₉
Frattini	C₂×C₃	C₃×C₇²×D₁₃
Fitting	C₂×C₇²×C₉×C₁₃	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₇²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₇²×C₉

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₃	C₄	semidirect
5. C₇×C₉×Dic₁₃	C₇	direct (N × H)
6. C₇²×Dic₁₃	C₉	direct (N × H)
13. C₇×C₉×C₁₃	C₄×C₇	semidirect
14. C₇²×C₁₃	C₄×C₉	semidirect
17. C₉×Dic₁₃	C₇²	direct (N × H)
18. C₇²×C₉	Dic₁₃	direct (N × H)
19. C₇×Dic₁₃	C₇×C₉	direct (N × H)
29. C₉×C₁₃	C₄×C₇²	semidirect
31. C₇×C₁₃	C₄×C₇×C₉	semidirect
34. C₇×C₉	C₇×Dic₁₃	direct (N × H)
35. Dic₁₃	C₇²×C₉	direct (N × H)
36. C₇²	C₉×Dic₁₃	direct (N × H)
45. C₁₃	C₄×C₇²×C₉	semidirect
47. C₉	C₇²×Dic₁₃	direct (N × H)
48. C₇	C₇×C₉×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×C₇²×C₉×C₁₃	2
C₃×C₇²×Dic₁₃	3
C₇×C₉×Dic₁₃	7
C₄×C₇²×C₉	13

Subgroups — C72×C9×Dic13 #37524388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₉×Dic₁₃ #37524388