Subgroups — C₃×(C₇⋊D₇)⋊D₁₃ #21439751

Order 7644.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₉₁	C₂	1	2	yes	maximal, complemented
3	(C₇⋊D₇)⋊D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₉₁	C₂×C₃	1	2	yes	complemented
7	C₃×D₇×D₁₃	—	7	2	no	maximal
8	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₇²	—	13	1	no	maximal, Hall
10	C₃×D₉₁	D₇	1	2	yes	complemented
11	C₃×C₁₃×D₇	—	7	2	no	—
12	C₃×C₁₃×D₇	—	14	3	no	—
13	C₃×C₇×D₁₃	—	7	2	no	—
14	D₇×D₁₃	—	7	2	no	—
15	C₃×C₇⋊D₇	D₁₃	1	1	yes	characteristic, complemented
16	C₃×C₇×D₇	—	13	2	no	—
17	C₃×C₇×C₁₃	—	2	3	no	—
18	C₃×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
19	D₇²	—	13	1	no	Hall
20	D₉₁	C₃×D₇	1	2	yes	complemented
21	C₇×D₁₃	—	7	2	no	—
22	C₁₃×D₇	—	7	2	no	—
23	C₁₃×D₇	—	14	3	no	—
24	C₂×C₃×D₁₃	—	49	1	no	Hall
25	C₃×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₇⋊D₇	C₃×D₁₃	1	1	yes	characteristic, complemented
27	C₇×D₇	—	13	2	no	—
28	C₇×C₁₃	—	2	3	no	—
29	C₇×C₁₃	C₂×C₃×D₇	1	2	yes	complemented
30	C₂×C₃×D₇	—	91	2	no	—
31	C₂×C₃×C₁₃	—	49	1	no	—
32	C₃×D₁₃	—	7	2	no	—
33	C₂×D₁₃	—	49	1	no	Hall
34	C₇²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	91	2	no	—
36	C₃×D₇	—	7	2	no	—
37	C₃×D₇	—	13	2	no	—
38	C₃×D₇	—	14	3	no	—
39	C₃×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
40	C₂×D₇	—	91	2	no	—
41	C₂×C₁₃	—	49	1	no	—
42	D₁₃	—	7	2	no	—
43	C₃×C₇	—	2	3	no	—
44	C₃×C₇	D₇×D₁₃	1	2	yes	complemented
45	C₂×C₇	—	91	2	no	—
46	D₇	—	7	2	no	—
47	D₇	—	13	2	no	—
48	D₇	—	14	3	no	—
49	C₁₃	C₃×D₇²	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₃	—	637	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₃×D₇×D₁₃	1	2	yes	complemented
53	C₂×C₃	—	49	1	no	—
54	C₂×C₃	—	91	2	no	—
55	C₂²	—	637	1	no	Sylow
56	C₃	(C₇⋊D₇)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	49	1	no	—
58	C₂	—	91	2	no	—

	subgroup	G/H
center, hypercenter	C₃	(C₇⋊D₇)⋊D₁₃
commutator, hypocenter	C₇²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₃×C₇×D₉₁	C₂	semidirect
3. (C₇⋊D₇)⋊D₁₃	C₃	direct (N × H)
4. C₃×C₇²×C₁₃	C₂²	semidirect
5. C₁₃×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₉₁	C₂×C₃	semidirect
8. C₇²×C₁₃	C₂²×C₃	semidirect
10. C₃×D₉₁	D₇	semidirect
15. C₃×C₇⋊D₇	D₁₃	semidirect
18. C₃×C₇×C₁₃	C₂×D₇	semidirect
20. D₉₁	C₃×D₇	semidirect
25. C₃×C₇²	C₂×D₁₃	semidirect
26. C₇⋊D₇	C₃×D₁₃	semidirect
29. C₇×C₁₃	C₂×C₃×D₇	semidirect
34. C₇²	C₂×C₃×D₁₃	semidirect
39. C₃×C₁₃	D₇²	semidirect
44. C₃×C₇	D₇×D₁₃	semidirect
49. C₁₃	C₃×D₇²	semidirect
52. C₇	C₃×D₇×D₁₃	semidirect
56. C₃	(C₇⋊D₇)⋊D₁₃	direct (N × H)

Subgroups — C3×(C7⋊D7)⋊D13 #21439751

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₇⋊D₇)⋊D₁₃ #21439751