Subgroups — D₁₃×C₃⋊(C₇⋊D₇) #21439764

Order 7644.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊D₉₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₉₁	—	3	1	no	—
7	C₁₃×C₇⋊D₇	—	3	1	no	—
8	C₇²×D₁₃	D₃	1	1	yes	characteristic, complemented
9	D₁₃×D₂₁	—	7	8	no	maximal
10	C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃⋊(C₇⋊D₇)	—	13	1	no	maximal, Hall
12	D₂₇₃	—	7	8	no	—
13	C₁₃×D₂₁	—	7	8	no	—
14	C₃×C₇×D₁₃	D₇	1	8	yes	complemented
15	D₇×D₁₃	—	21	8	no	—
16	C₂×C₃×C₇²	—	13	1	no	—
17	C₃⋊(C₇⋊D₇)	—	13	1	no	—
18	C₃⋊(C₇⋊D₇)	D₁₃	1	1	yes	characteristic, direct product factor
19	C₃×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
20	C₂×C₇⋊D₇	—	39	1	no	Hall
21	D₉₁	—	21	8	no	—
22	C₇×D₁₃	D₂₁	1	8	yes	complemented
23	C₁₃×D₇	—	21	8	no	—
24	D₃×D₁₃	—	49	1	no	Hall
25	C₃×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇²	—	13	1	no	—
27	C₇⋊D₇	—	3	1	no	—
28	C₇⋊D₇	—	39	1	no	—
29	C₇×C₁₃	C₂×D₂₁	1	8	yes	complemented
30	C₂×D₂₁	—	91	8	no	—
31	D₃₉	—	49	1	no	—
32	C₃×D₁₃	C₇⋊D₇	1	1	yes	characteristic, complemented
33	D₃×C₁₃	—	49	1	no	—
34	C₂×D₁₃	—	147	1	no	Hall
35	C₇²	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	13	8	no	—
37	D₂₁	—	7	8	no	—
38	D₂₁	—	91	8	no	—
39	C₃×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
40	C₂×D₇	—	273	8	no	—
41	C₂×C₁₃	—	147	1	no	—
42	D₁₃	—	147	1	no	—
43	D₁₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
44	C₃×C₇	D₇×D₁₃	1	8	yes	complemented
45	C₂×C₇	—	13	8	no	—
46	D₇	—	273	8	no	—
47	D₇	—	21	8	no	—
48	C₁₃	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	637	1	no	Hall
50	C₇	D₁₃×D₂₁	1	8	yes	complemented
51	C₂×C₃	—	13	1	no	—
52	D₃	—	49	1	no	—
53	D₃	—	637	1	no	—
54	C₂²	—	1911	1	no	Sylow
55	C₃	D₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	13	1	no	—
57	C₂	—	1911	1	no	—
58	C₂	—	147	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₇⋊D₉₁)	C₂	semidirect
2. C₁₃×C₃⋊(C₇⋊D₇)	C₂	semidirect
3. C₃×C₇²×D₁₃	C₂	semidirect
5. C₃×C₇²×C₁₃	C₂²	semidirect
8. C₇²×D₁₃	D₃	semidirect
10. C₇²×C₁₃	C₂×D₃	semidirect
14. C₃×C₇×D₁₃	D₇	semidirect
18. C₃⋊(C₇⋊D₇)	D₁₃	direct (N × H)
19. C₃×C₇×C₁₃	C₂×D₇	semidirect
22. C₇×D₁₃	D₂₁	semidirect
25. C₃×C₇²	C₂×D₁₃	semidirect
29. C₇×C₁₃	C₂×D₂₁	semidirect
32. C₃×D₁₃	C₇⋊D₇	semidirect
35. C₇²	D₃×D₁₃	semidirect
39. C₃×C₁₃	C₂×C₇⋊D₇	semidirect
43. D₁₃	C₃⋊(C₇⋊D₇)	direct (N × H)
44. C₃×C₇	D₇×D₁₃	semidirect
48. C₁₃	C₂×C₃⋊(C₇⋊D₇)	semidirect
50. C₇	D₁₃×D₂₁	semidirect
55. C₃	D₁₃×C₇⋊D₇	semidirect

Subgroups — D13×C3⋊(C7⋊D7) #21439764

Conjugacy classes of subgroups

Complements

Subgroups — D₁₃×C₃⋊(C₇⋊D₇) #21439764