Subgroups — C₁₃×#13183534 #37524342

Order 22932.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#89205	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×Dic₇⋊C₉	—	7	2	no	maximal
6	C₁₃×C₇⋊Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
8	#13183534	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₃×C₇⋊C₉	—	7	2	no	—
10	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
11	C₃×C₁₃×Dic₇	—	7	2	no	—
12	C₃×C₁₃×Dic₇	—	21	2	no	—
13	C₂×#89205	C₂×C₁₃	1	1	yes	characteristic
14	C₁₃×C₇⋊C₉	—	7	2	no	—
15	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇⋊Dic₇	C₃×C₁₃	1	1	yes	characteristic
17	C₂×C₃×C₇×C₁₃	—	3	2	no	—
18	C₂×C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	2	yes	—
19	C₄×C₉×C₁₃	—	49	1	no	Hall
20	#89205	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×Dic₇	—	7	2	no	—
22	C₁₃×Dic₇	—	21	2	no	—
23	C₂×C₃×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic
24	C₃×C₇×C₁₃	—	3	2	no	—
25	C₃×C₇×C₁₃	ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
26	Dic₇⋊C₉	—	7	2	no	—
27	C₂×C₉×C₁₃	—	49	1	no	—
28	C₇⋊Dic₇	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×C₁₃	—	3	2	no	—
30	C₂×C₇×C₁₃	D₇⋊C₉	1	2	yes	—
31	C₃×C₄×C₁₃	—	49	1	no	—
32	C₃×C₇²	C₃×C₄×C₁₃	1	1	yes	characteristic
33	C₂×C₇⋊C₉	—	7	2	no	—
34	C₉×C₁₃	—	49	1	no	Hall
35	C₂×C₇²	C₂×C₉×C₁₃	1	1	yes	characteristic
36	C₇×C₁₃	—	3	2	no	—
37	C₇×C₁₃	Dic₇⋊C₉	1	2	yes	complemented
38	C₃×Dic₇	—	7	2	no	—
39	C₃×Dic₇	—	21	2	no	—
40	C₂×C₃×C₁₃	#64425	1	1	yes	characteristic
41	C₇⋊C₉	—	7	2	no	—
42	C₄×C₁₃	—	49	1	no	Hall
43	C₇²	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₇	—	3	2	no	—
45	C₂×C₃×C₇	C₁₃×AGL(1,𝔽₇)	1	2	yes	—
46	C₃×C₁₃	#10596875	1	1	yes	characteristic
47	C₄×C₉	—	49	1	no	Hall
48	Dic₇	—	7	2	no	—
49	Dic₇	—	21	2	no	—
50	C₂×C₁₃	#11725078	1	1	yes	characteristic
51	C₃×C₇	—	3	2	no	—
52	C₃×C₇	C₁₃×ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
53	C₂×C₉	—	49	1	no	—
54	C₂×C₇	—	3	2	no	—
55	C₂×C₇	C₁₃×D₇⋊C₉	1	2	yes	—
56	C₁₃	#13183534	1	1	yes	characteristic, direct product factor, Sylow
57	C₃×C₄	—	49	1	no	—
58	C₉	—	49	1	no	Sylow
59	C₇	—	3	2	no	—
60	C₇	C₁₃×Dic₇⋊C₉	1	2	yes	complemented
61	C₂×C₃	C₁₃×#64425	1	1	yes	characteristic
62	C₄	—	49	1	no	Sylow
63	C₃	C₁₃×#10596875	1	1	yes	characteristic
64	C₂	C₁₃×#11725078	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	#64425
commutator, hypocenter	C₇²	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₁₃×#64425
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₃	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₁₃×#89205	C₄	semidirect
6. C₁₃×C₇⋊Dic₇	C₉	semidirect
8. #13183534	C₁₃	direct (N × H)
15. C₇²×C₁₃	C₄×C₉	semidirect
20. #89205	C₄×C₁₃	semidirect
28. C₇⋊Dic₇	C₉×C₁₃	semidirect
37. C₇×C₁₃	Dic₇⋊C₉	semidirect
43. C₇²	C₄×C₉×C₁₃	semidirect
56. C₁₃	#13183534	direct (N × H)
60. C₇	C₁₃×Dic₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#89205	2
C₃×C₁₃×C₇⋊Dic₇	3
C₁₃×Dic₇⋊C₉	7
#13183534	13

Subgroups — C13×#13183534 #37524342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13183534 #37524342