Subgroups — C₁₃×C₃⋊(C₃⋊#5997) #37525626

Order 22932.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₃⋊#5997	—	3	4	no	maximal
3	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×C₇⋊D₇	D₃	1	4	yes	—
5	C₁₃×#5997	—	9	1	no	Hall
6	C₃×C₇²×C₁₃	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#5997)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₁₃×D₇	—	14	4	no	—
9	C₁₃×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic
10	C₃²×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic
11	C₃²×C₇×C₁₃	—	2	4	no	—
12	C₇²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊#5997	—	3	4	no	—
14	C₃×C₁₃×D₇	—	14	16	no	—
15	C₁₃×C₃⋊Dic₃	—	49	1	no	maximal, Hall
16	C₃²×C₇²	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇⋊D₇	D₃×C₁₃	1	4	yes	—
18	C₃×C₇×C₁₃	—	2	16	no	—
19	C₂×C₃²×C₁₃	—	49	1	no	—
20	#5997	—	9	1	no	Hall
21	C₁₃×D₇	—	14	4	no	—
22	Dic₃×C₁₃	—	147	4	no	—
23	C₃×C₇²	Dic₃×C₁₃	1	4	yes	complemented
24	C₃²×D₇	—	14	4	no	—
25	C₃²×C₁₃	#5997	1	1	yes	characteristic, complemented, Hall
26	C₇⋊D₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic
27	C₇×C₁₃	—	2	4	no	—
28	C₂×C₃×C₁₃	—	49	4	no	—
29	C₃²×C₇	—	2	4	no	—
30	C₄×C₁₃	—	441	1	no	Hall
31	C₇²	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	14	16	no	—
33	C₃×C₁₃	C₃⋊#5997	1	4	yes	complemented
34	C₃⋊Dic₃	—	49	1	no	Hall
35	C₂×C₁₃	—	49	1	no	—
36	C₃×C₇	—	2	16	no	—
37	C₂×C₃²	—	49	1	no	—
38	D₇	—	14	4	no	—
39	C₁₃	C₃⋊(C₃⋊#5997)	1	1	yes	characteristic, direct product factor, Sylow
40	Dic₃	—	147	4	no	—
41	C₃²	C₁₃×#5997	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	4	no	—
44	C₄	—	441	1	no	Sylow
45	C₃	C₁₃×C₃⋊#5997	1	4	yes	complemented
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊(C₃⋊#5997)
commutator, hypocenter	C₃²×C₇²	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₃²×C₁₃×C₇⋊D₇	C₂
cosocle	C₃²×C₇⋊D₇	C₂×C₁₃
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇²×C₁₃	C₄	semidirect
6. C₃×C₇²×C₁₃	Dic₃	semidirect
7. C₃⋊(C₃⋊#5997)	C₁₃	direct (N × H)
12. C₇²×C₁₃	C₃⋊Dic₃	semidirect
16. C₃²×C₇²	C₄×C₁₃	semidirect
23. C₃×C₇²	Dic₃×C₁₃	semidirect
25. C₃²×C₁₃	#5997	semidirect
31. C₇²	C₁₃×C₃⋊Dic₃	semidirect
33. C₃×C₁₃	C₃⋊#5997	semidirect
39. C₁₃	C₃⋊(C₃⋊#5997)	direct (N × H)
41. C₃²	C₁₃×#5997	semidirect
45. C₃	C₁₃×C₃⋊#5997	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇⋊D₇	2
C₁₃×C₃⋊#5997	3
C₃⋊(C₃⋊#5997)	13
C₁₃×C₃⋊Dic₃	49

Subgroups — C13×C3⋊(C3⋊#5997) #37525626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊(C₃⋊#5997) #37525626