Subgroups — C₇×Dic₃₈₅ #24924739

Order 10780.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₇₇	—	5	1	no	maximal, Hall
4	Dic₃₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×Dic₅₅	—	7	1	no	maximal
6	C₂×C₇²×C₁₁	D₅	1	1	yes	characteristic
7	C₇×Dic₃₅	—	11	1	no	maximal, Hall
8	C₂×C₅×C₇×C₁₁	—	2	3	no	—
9	C₂×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
10	C₂×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
11	C₇²×C₁₁	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	D₁₁	1	1	yes	characteristic
13	C₅×C₇×C₁₁	—	2	3	no	—
14	C₅×C₇×C₁₁	Dic₇	1	1	yes	characteristic, complemented
15	C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic, complemented
16	Dic₇₇	—	5	1	no	—
17	C₇×Dic₁₁	—	35	1	no	—
18	C₅×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
19	Dic₅₅	—	7	1	no	Hall
20	C₇×Dic₇	—	55	1	no	Hall
21	C₂×C₇×C₁₁	—	2	3	no	—
22	C₂×C₇×C₁₁	C₇×D₅	1	1	yes	characteristic
23	C₂×C₇×C₁₁	D₃₅	1	1	yes	characteristic
24	Dic₃₅	—	11	1	no	—
25	C₇×Dic₅	—	77	1	no	—
26	C₂×C₅×C₁₁	C₇×D₇	1	1	yes	characteristic
27	C₂×C₇²	D₅₅	1	1	yes	characteristic
28	C₇×C₁₁	—	2	3	no	—
29	C₇×C₁₁	C₇×Dic₅	1	1	yes	characteristic, complemented
30	C₇×C₁₁	Dic₃₅	1	1	yes	characteristic, complemented
31	C₂×C₅×C₇	—	2	3	no	—
32	C₂×C₅×C₇	C₇×D₁₁	1	1	yes	characteristic
33	C₂×C₅×C₇	D₇₇	1	1	yes	characteristic
34	C₅×C₁₁	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
35	C₇²	Dic₅₅	1	1	yes	characteristic, complemented, Sylow
36	Dic₁₁	—	35	1	no	Hall
37	C₅×C₇	—	2	3	no	—
38	C₅×C₇	C₇×Dic₁₁	1	1	yes	characteristic, complemented
39	C₅×C₇	Dic₇₇	1	1	yes	characteristic, complemented
40	C₄×C₇	—	385	1	no	—
41	Dic₇	—	55	1	no	—
42	C₂×C₁₁	C₇×D₃₅	1	1	yes	characteristic
43	Dic₅	—	77	1	no	Hall
44	C₂×C₇	—	2	3	no	—
45	C₂×C₇	C₇×D₅₅	1	1	yes	characteristic
46	C₂×C₇	D₃₈₅	1	1	yes	characteristic
47	C₁₁	C₇×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	C₇×D₇₇	1	1	yes	characteristic
49	C₇	—	2	3	no	—
50	C₇	C₇×Dic₅₅	1	1	yes	characteristic, complemented
51	C₇	Dic₃₈₅	1	1	yes	characteristic, direct product factor
52	C₅	C₇×Dic₇₇	1	1	yes	characteristic, complemented, Sylow
53	C₄	—	385	1	no	Sylow
54	C₂	C₇×D₃₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	D₃₈₅
commutator, hypocenter	C₅×C₇×C₁₁	C₄×C₇
Frattini	C₂	C₇×D₃₈₅
Fitting, socle, prime radical	C₂×C₅×C₇²×C₁₁	C₂
cosocle	C₂×C₅×C₇×C₁₁	C₂×C₇
LCS	G ▷ C₅×C₇×C₁₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₁₁	C₄	semidirect
4. Dic₃₈₅	C₇	direct (N × H)
11. C₇²×C₁₁	Dic₅	semidirect
14. C₅×C₇×C₁₁	Dic₇	semidirect
15. C₅×C₇×C₁₁	C₄×C₇	semidirect
18. C₅×C₇²	Dic₁₁	semidirect
29. C₇×C₁₁	C₇×Dic₅	semidirect
30. C₇×C₁₁	Dic₃₅	semidirect
34. C₅×C₁₁	C₇×Dic₇	semidirect
35. C₇²	Dic₅₅	semidirect
38. C₅×C₇	C₇×Dic₁₁	semidirect
39. C₅×C₇	Dic₇₇	semidirect
47. C₁₁	C₇×Dic₃₅	semidirect
50. C₇	C₇×Dic₅₅	semidirect
51. C₇	Dic₃₈₅	direct (N × H)
52. C₅	C₇×Dic₇₇	semidirect

Subgroups — C7×Dic385 #24924739

Conjugacy classes of subgroups

Complements

Subgroups — C₇×Dic₃₈₅ #24924739