Subgroups — C₅×C₇×#10621729 #37556849

Order 23660.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#10621729	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×#10621729	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₃⋊D₁₃	C₂×C₅	1	1	yes	characteristic
6	C₅×C₇×#261	—	13	2	no	maximal
7	C₅×C₁₃⋊D₁₃	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₃²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₇×D₁₃	—	13	2	no	—
10	C₅×C₇×D₁₃	—	26	6	no	—
11	C₅×C₁₃²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	#10621729	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₇×C₁₃	—	2	6	no	—
14	C₅×C₇×C₁₃	#261	1	2	yes	complemented
15	C₇×#261	—	13	2	no	—
16	C₁₃⋊D₁₃	C₂×C₅×C₇	1	1	yes	characteristic
17	C₅×#261	—	13	2	no	—
18	C₇×D₁₃	—	13	2	no	—
19	C₇×D₁₃	—	26	6	no	—
20	C₁₃²	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₅×C₇	—	169	1	no	Hall
22	C₅×D₁₃	—	13	2	no	—
23	C₅×D₁₃	—	26	6	no	—
24	C₇×C₁₃	—	2	6	no	—
25	C₇×C₁₃	C₅×#261	1	2	yes	complemented
26	C₂×C₅×C₇	—	169	1	no	—
27	C₅×C₁₃	—	2	6	no	—
28	C₅×C₁₃	C₇×#261	1	2	yes	complemented
29	#261	—	13	2	no	—
30	C₅×C₇	#10621729	1	1	yes	characteristic, direct product factor, Hall
31	C₄×C₇	—	169	1	no	Hall
32	D₁₃	—	13	2	no	—
33	D₁₃	—	26	6	no	—
34	C₄×C₅	—	169	1	no	Hall
35	C₂×C₇	—	169	1	no	—
36	C₁₃	—	2	6	no	—
37	C₁₃	C₅×C₇×#261	1	2	yes	complemented
38	C₂×C₅	—	169	1	no	—
39	C₇	C₅×#10621729	1	1	yes	characteristic, direct product factor, Sylow
40	C₅	C₇×#10621729	1	1	yes	characteristic, direct product factor, Sylow
41	C₄	—	169	1	no	Sylow
42	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	#10621729
commutator, hypocenter	C₁₃²	C₄×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃²	C₄
prime radical	C₅×C₇×C₁₃⋊D₁₃	C₂
cosocle	C₁₃⋊D₁₃	C₂×C₅×C₇
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₃²	C₄	semidirect
3. C₇×#10621729	C₅	direct (N × H)
4. C₅×#10621729	C₇	direct (N × H)
8. C₇×C₁₃²	C₄×C₅	semidirect
11. C₅×C₁₃²	C₄×C₇	semidirect
12. #10621729	C₅×C₇	direct (N × H)
14. C₅×C₇×C₁₃	#261	semidirect
20. C₁₃²	C₄×C₅×C₇	semidirect
25. C₇×C₁₃	C₅×#261	semidirect
28. C₅×C₁₃	C₇×#261	semidirect
30. C₅×C₇	#10621729	direct (N × H)
37. C₁₃	C₅×C₇×#261	semidirect
39. C₇	C₅×#10621729	direct (N × H)
40. C₅	C₇×#10621729	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⋊D₁₃	2
C₇×#10621729	5
C₅×#10621729	7
C₅×C₇×#261	13

Subgroups — C5×C7×#10621729 #37556849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×#10621729 #37556849