Subgroups — C₁₃×#13183676 #37525555

Order 22932.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×C₃⋊(C₇⋊D₇)	—	6	2	no	—
4	C₁₃×#5997	—	9	1	no	maximal, Hall
5	C₃×C₇²×C₁₃	—	2	2	no	—
6	#13183676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×C₃⋊D₂₁	—	14	4	no	—
8	C₁₃×C₇⋊D₇	—	9	1	no	—
9	C₃⋊(C₃⋊(C₇⋊D₇))	C₂×C₁₃	1	1	yes	characteristic
10	C₃²×C₇×C₁₃	—	2	4	no	—
11	C₇²×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
12	C₁₃×D₂₁	—	42	16	no	—
13	C₁₃×#157	—	49	1	no	maximal, Hall
14	C₃²×C₇²	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₇⋊D₇)	—	6	2	no	—
16	C₃×C₇×C₁₃	—	2	16	no	—
17	C₁₃×C₃⋊D₃	—	49	1	no	—
18	#5997	—	9	1	no	Hall
19	C₁₃×D₇	—	126	4	no	—
20	C₃×C₇²	—	2	2	no	—
21	C₃⋊D₂₁	—	14	4	no	—
22	C₃²×C₁₃	#5997	1	1	yes	characteristic, complemented, Hall
23	C₇⋊D₇	—	9	1	no	—
24	C₇×C₁₃	—	2	4	no	—
25	D₃×C₁₃	—	294	2	no	—
26	C₃²×C₇	—	2	4	no	—
27	C₄×C₁₃	—	441	1	no	Hall
28	C₇²	C₁₃×#157	1	1	yes	characteristic, complemented, Sylow
29	D₂₁	—	42	16	no	—
30	C₃×C₁₃	—	2	2	no	—
31	#157	—	49	1	no	Hall
32	C₂×C₁₃	—	441	1	no	—
33	C₃×C₇	—	2	16	no	—
34	C₃⋊D₃	—	49	1	no	—
35	D₇	—	126	4	no	—
36	C₁₃	#13183676	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²	C₁₃×#5997	1	1	yes	characteristic, complemented, Sylow
38	C₇	—	2	4	no	—
39	D₃	—	294	2	no	—
40	C₄	—	441	1	no	Sylow
41	C₃	—	2	2	no	—
42	C₂	—	441	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	#13183676
commutator, hypocenter	C₃²×C₇²	C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂
cosocle	C₃⋊(C₃⋊(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
2. C₃²×C₇²×C₁₃	C₄	semidirect
6. #13183676	C₁₃	direct (N × H)
11. C₇²×C₁₃	#157	semidirect
14. C₃²×C₇²	C₄×C₁₃	semidirect
22. C₃²×C₁₃	#5997	semidirect
28. C₇²	C₁₃×#157	semidirect
36. C₁₃	#13183676	direct (N × H)
37. C₃²	C₁₃×#5997	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	2
C₁₃×#5997	9
#13183676	13
C₁₃×#157	49

Subgroups — C13×#13183676 #37525555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13183676 #37525555