Subgroups — C₁₃×#13183531 #37524352

Order 22932.

80 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×C₇×C₁₃×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	C₄×C₁₃×C₇⋊C₉	—	7	1	no	maximal
6	C₁₃×Dic₇⋊C₉	—	7	1	no	maximal
7	C₇×C₁₃×Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
9	#13183531	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₇⋊C₉	—	7	1	no	—
11	C₂×C₁₃×C₇⋊C₉	—	7	1	no	—
12	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
13	C₃×C₄×C₇×C₁₃	—	7	1	no	—
14	C₃×C₁₃×Dic₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂×#89205	C₂×C₁₃	1	1	yes	characteristic
16	C₁₃×C₇⋊C₉	—	7	1	no	—
17	C₁₃×C₇⋊C₉	—	7	1	no	—
18	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×Dic₇	C₃×C₁₃	1	1	yes	characteristic
20	C₂×C₃×C₇×C₁₃	—	6	1	no	—
21	C₂×C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
23	C₄×C₉×C₁₃	—	49	1	no	Hall
24	#89205	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₄×C₇×C₁₃	—	7	1	no	—
26	C₁₃×Dic₇	C₇⋊C₉	1	1	yes	characteristic, complemented
27	C₂×C₃×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic
28	C₃×C₇×C₁₃	—	6	1	no	—
29	C₃×C₇×C₁₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
30	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₄×C₇⋊C₉	—	7	1	no	—
32	Dic₇⋊C₉	—	7	1	no	—
33	C₂×C₉×C₁₃	—	49	1	no	—
34	C₇×Dic₇	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₇×C₁₃	—	6	1	no	—
36	C₂×C₇×C₁₃	D₇⋊C₉	1	1	yes	characteristic
37	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic
38	C₃×C₄×C₁₃	—	7	1	no	—
39	C₃×C₇²	C₃×C₄×C₁₃	1	1	yes	characteristic
40	C₂×C₇⋊C₉	—	7	1	no	—
41	C₂×C₇⋊C₉	—	7	1	no	—
42	C₉×C₁₃	—	49	1	no	Hall
43	C₂×C₇²	C₂×C₉×C₁₃	1	1	yes	characteristic
44	C₇×C₁₃	—	6	1	no	—
45	C₇×C₁₃	Dic₇⋊C₉	1	1	yes	characteristic, complemented
46	C₇×C₁₃	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
47	C₃×C₄×C₇	—	7	1	no	—
48	C₃×Dic₇	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₂×C₃×C₁₃	#64422	1	1	yes	characteristic
50	C₇⋊C₉	—	7	1	no	—
51	C₇⋊C₉	—	7	1	no	—
52	C₄×C₁₃	—	7	1	no	Hall
53	C₇²	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃×C₇	—	6	1	no	—
55	C₂×C₃×C₇	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic
56	C₂×C₃×C₇	C₂×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
57	C₃×C₁₃	#10596872	1	1	yes	characteristic
58	C₄×C₉	—	49	1	no	Hall
59	C₄×C₇	—	7	1	no	—
60	Dic₇	C₁₃×C₇⋊C₉	1	1	yes	characteristic, complemented
61	C₂×C₁₃	#11725075	1	1	yes	characteristic
62	C₃×C₇	—	6	1	no	—
63	C₃×C₇	C₁₃×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
64	C₃×C₇	C₄×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
65	C₂×C₉	—	49	1	no	—
66	C₂×C₇	—	6	1	no	—
67	C₂×C₇	C₁₃×D₇⋊C₉	1	1	yes	characteristic
68	C₂×C₇	C₂×C₁₃×C₇⋊C₉	1	1	yes	characteristic
69	C₁₃	#13183531	1	1	yes	characteristic, direct product factor, Sylow
70	C₃×C₄	—	7	1	no	—
71	C₉	—	49	1	no	Sylow
72	C₇	—	6	1	no	—
73	C₇	C₁₃×Dic₇⋊C₉	1	1	yes	characteristic, complemented
74	C₇	C₄×C₁₃×C₇⋊C₉	1	1	yes	characteristic, complemented
75	C₂×C₃	C₁₃×#64422	1	1	yes	characteristic
76	C₄	—	7	1	no	Sylow
77	C₃	C₁₃×#10596872	1	1	yes	characteristic
78	C₂	C₁₃×#11725075	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	#64422
commutator, hypocenter	C₇²	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₁₃×#64422
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
7. C₇×C₁₃×Dic₇	C₉	semidirect
9. #13183531	C₁₃	direct (N × H)
18. C₇²×C₁₃	C₄×C₉	semidirect
24. #89205	C₄×C₁₃	semidirect
26. C₁₃×Dic₇	C₇⋊C₉	semidirect
34. C₇×Dic₇	C₉×C₁₃	semidirect
45. C₇×C₁₃	Dic₇⋊C₉	semidirect
46. C₇×C₁₃	C₄×C₇⋊C₉	semidirect
53. C₇²	C₄×C₉×C₁₃	semidirect
60. Dic₇	C₁₃×C₇⋊C₉	semidirect
69. C₁₃	#13183531	direct (N × H)
73. C₇	C₁₃×Dic₇⋊C₉	semidirect
74. C₇	C₄×C₁₃×C₇⋊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×C₇×C₁₃×Dic₇	3
C₄×C₁₃×C₇⋊C₉	7
C₁₃×Dic₇⋊C₉	7
#13183531	13

Subgroups — C13×#13183531 #37524352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13183531 #37524352