Subgroups — C₅×C₇×#90865 #30655752

Order 16380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#90865	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₇×C₁₃	—	6	2	no	—
5	C₅×#90865	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×Dic₁₃	—	9	1	no	maximal, Hall
7	C₇×C₁₃×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₇×C₁₃	—	2	2	no	—
9	C₅×C₇×#157	—	13	1	no	maximal, Hall
10	C₅×C₁₃×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
11	C₂×C₅×C₇×C₁₃	—	9	1	no	—
12	C₃²×C₇×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇×C₃⋊D₃	D₁₃	1	1	yes	characteristic
14	C₃²×C₅×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
15	D₃×C₇×C₁₃	—	6	2	no	—
16	#90865	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
18	C₅×D₃×C₁₃	—	6	2	no	—
19	C₇×Dic₁₃	—	9	1	no	Hall
20	C₃²×C₅×C₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×C₁₃	—	2	2	no	—
22	C₅×Dic₁₃	—	9	1	no	Hall
23	C₇×#157	—	13	1	no	Hall
24	C₁₃×C₃⋊D₃	C₂×C₅×C₇	1	1	yes	characteristic
25	C₅×D₃×C₇	—	6	2	no	—
26	C₃×C₅×C₁₃	—	2	2	no	—
27	C₂×C₇×C₁₃	—	9	1	no	—
28	C₅×#157	—	13	1	no	Hall
29	C₄×C₅×C₇	—	117	1	no	Hall
30	C₂×C₅×C₁₃	—	9	1	no	—
31	C₇×C₃⋊D₃	C₅×D₁₃	1	1	yes	characteristic
32	C₃²×C₁₃	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₇	—	2	2	no	—
34	C₇×C₁₃	C₅×#157	1	1	yes	characteristic, complemented, Hall
35	C₅×C₃⋊D₃	C₇×D₁₃	1	1	yes	characteristic
36	D₃×C₁₃	—	6	2	no	—
37	C₂×C₅×C₇	—	9	1	no	—
38	C₅×C₁₃	C₇×#157	1	1	yes	characteristic, complemented, Hall
39	C₃²×C₇	C₅×Dic₁₃	1	1	yes	characteristic, complemented, Hall
40	Dic₁₃	—	9	1	no	Hall
41	C₃²×C₅	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
42	D₃×C₇	—	6	2	no	—
43	C₃×C₁₃	—	2	2	no	—
44	#157	—	13	1	no	Hall
45	C₅×C₇	#90865	1	1	yes	characteristic, direct product factor, Hall
46	C₅×D₃	—	6	2	no	—
47	C₄×C₇	—	117	1	no	Hall
48	C₂×C₁₃	—	9	1	no	—
49	C₃×C₇	—	2	2	no	—
50	C₄×C₅	—	117	1	no	Hall
51	C₃⋊D₃	C₅×C₇×D₁₃	1	1	yes	characteristic
52	C₃×C₅	—	2	2	no	—
53	C₂×C₇	—	9	1	no	—
54	C₁₃	C₅×C₇×#157	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₅	—	9	1	no	—
56	C₃²	C₅×C₇×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
57	C₇	C₅×#90865	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₇×#90865	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	117	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	#90865
commutator, hypocenter	C₃²×C₁₃	C₄×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₄
prime radical	C₅×C₇×C₁₃×C₃⋊D₃	C₂
cosocle	C₁₃×C₃⋊D₃	C₂×C₅×C₇
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₃	C₄	semidirect
3. C₇×#90865	C₅	direct (N × H)
5. C₅×#90865	C₇	direct (N × H)
12. C₃²×C₇×C₁₃	C₄×C₅	semidirect
14. C₃²×C₅×C₁₃	C₄×C₇	semidirect
16. #90865	C₅×C₇	direct (N × H)
17. C₅×C₇×C₁₃	#157	semidirect
20. C₃²×C₅×C₇	Dic₁₃	semidirect
32. C₃²×C₁₃	C₄×C₅×C₇	semidirect
34. C₇×C₁₃	C₅×#157	semidirect
38. C₅×C₁₃	C₇×#157	semidirect
39. C₃²×C₇	C₅×Dic₁₃	semidirect
41. C₃²×C₅	C₇×Dic₁₃	semidirect
45. C₅×C₇	#90865	direct (N × H)
54. C₁₃	C₅×C₇×#157	semidirect
56. C₃²	C₅×C₇×Dic₁₃	semidirect
57. C₇	C₅×#90865	direct (N × H)
59. C₅	C₇×#90865	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃×C₃⋊D₃	2
C₇×#90865	5
C₅×#90865	7
C₅×C₇×Dic₁₃	9
C₅×C₇×#157	13

Subgroups — C5×C7×#90865 #30655752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×#90865 #30655752