Subgroups — C₃×#10587906 #13132303

Order 1680.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₇⋊#168	C₂	1	1	yes	maximal, characteristic
4	#10587906	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×C₅×C₇	—	2	1	no	—
6	C₃×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	C₃×Dic₃₅	—	2	1	no	—
8	C₃×#1144	—	5	1	no	maximal, Hall
9	C₅×C₇×Q₈	C₂×C₃	1	1	yes	characteristic
10	Dic₇₀	C₂×C₃	1	1	yes	characteristic
11	C₇⋊#168	C₂×C₃	1	1	yes	characteristic
12	C₃×#689	—	7	1	no	maximal, Hall
13	C₂×C₃×C₅×C₇	D₄	1	1	yes	characteristic
14	C₃×C₇×Q₈	D₅	1	1	yes	characteristic
15	C₃×Dic₁₄	—	5	1	no	—
16	C₃×C₇⋊C₈	—	5	1	no	—
17	C₄×C₅×C₇	—	2	1	no	—
18	C₄×C₅×C₇	C₂²×C₃	1	1	yes	characteristic
19	Dic₃₅	—	2	1	no	—
20	C₃×C₅×Q₈	D₇	1	1	yes	characteristic
21	C₃×Dic₁₀	—	7	1	no	—
22	C₃×#168	—	7	1	no	—
23	#1144	—	5	1	no	Hall
24	C₃×C₅×C₇	Q₁₆	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄×C₇	—	2	1	no	—
26	C₃×C₄×C₇	C₂×D₅	1	1	yes	characteristic
27	C₃×Dic₇	—	10	1	no	—
28	#689	—	7	1	no	Hall
29	C₂×C₅×C₇	C₃×D₄	1	1	yes	characteristic
30	C₃×C₄×C₅	—	2	1	no	—
31	C₃×C₄×C₅	C₂×D₇	1	1	yes	characteristic
32	C₃×Dic₅	—	14	1	no	—
33	C₇×Q₈	C₃×D₅	1	1	yes	characteristic
34	Dic₁₄	—	5	1	no	—
35	C₇⋊C₈	—	5	1	no	—
36	C₃×Q₁₆	—	35	1	no	Hall
37	C₂×C₃×C₇	C₂²⋊D₅	1	1	yes	characteristic
38	C₅×Q₈	C₃×D₇	1	1	yes	characteristic
39	Dic₁₀	—	7	1	no	—
40	#168	—	7	1	no	—
41	C₅×C₇	C₃×Q₁₆	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅	C₂²⋊D₇	1	1	yes	characteristic
43	C₄×C₇	—	2	1	no	—
44	C₄×C₇	C₂×C₃×D₅	1	1	yes	characteristic
45	Dic₇	—	10	1	no	—
46	C₃×Q₈	—	35	1	no	—
47	C₃×Q₈	D₃₅	1	1	yes	characteristic
48	C₃×C₈	—	35	1	no	—
49	C₃×C₇	#689	1	1	yes	characteristic, complemented, Hall
50	C₄×C₅	—	2	1	no	—
51	C₄×C₅	C₂×C₃×D₇	1	1	yes	characteristic
52	Dic₅	—	14	1	no	—
53	Q₁₆	—	35	1	no	Sylow
54	C₃×C₅	#1144	1	1	yes	characteristic, complemented, Hall
55	C₂×C₇	C₃×C₂²⋊D₅	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	70	1	no	—
58	C₃×C₄	C₂×D₃₅	1	1	yes	characteristic
59	C₂×C₅	C₃×C₂²⋊D₇	1	1	yes	characteristic
60	Q₈	—	35	1	no	—
61	Q₈	C₃×D₃₅	1	1	yes	characteristic
62	C₈	—	35	1	no	—
63	C₇	C₃×#689	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₂²⋊D₃₅	1	1	yes	characteristic
65	C₅	C₃×#1144	1	1	yes	characteristic, complemented, Sylow
66	C₄	—	2	1	no	—
67	C₄	—	70	1	no	—
68	C₄	C₂×C₃×D₃₅	1	1	yes	characteristic
69	C₃	#10587906	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	C₃×C₂²⋊D₃₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²⋊D₃₅
commutator, cosocle	C₄×C₅×C₇	C₂²×C₃
Frattini	C₄	C₂×C₃×D₃₅
Fitting	C₃×C₅×C₇×Q₈	C₂
socle, prime radical	C₂×C₃×C₅×C₇	D₄
hypercenter	C₃×Q₈	D₃₅
hypocenter	C₅×C₇	C₃×Q₁₆
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
4. #10587906	C₃	direct (N × H)
24. C₃×C₅×C₇	Q₁₆	semidirect
41. C₅×C₇	C₃×Q₁₆	semidirect
49. C₃×C₇	#689	semidirect
54. C₃×C₅	#1144	semidirect
63. C₇	C₃×#689	semidirect
65. C₅	C₃×#1144	semidirect
69. C₃	#10587906	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×Q₈	2
C₃×Dic₇₀	2
C₃×C₇⋊#168	2
#10587906	3
C₃×#1144	5
C₃×#689	7

Subgroups — C3×#10587906 #13132303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10587906 #13132303