Subgroups — C₂×C₅×#10624391 #20300074

Order 7260.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#10624391	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₁₁×D₁₁	—	3	1	no	maximal, Hall
4	C₅×C₁₁²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#10624391	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁²	D₃	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₁	—	3	2	no	—
8	C₂×C₁₁²⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
9	#10624391	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×D₁₁	—	3	1	no	Hall
12	C₁₁²⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
14	C₁₁×D₁₁	—	3	2	no	—
15	C₂²×C₅×C₁₁	—	33	1	no	—
16	C₂×C₅×D₁₁	—	3	1	no	—
17	C₁₁²	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×C₁₁	—	3	1	no	—
19	C₂×C₅×C₁₁	—	3	1	no	—
20	C₂×C₅×C₁₁	—	6	1	no	—
21	C₂×C₅×C₁₁	—	33	2	no	—
22	C₅×D₁₁	—	3	2	no	—
23	C₂×C₅×D₃	—	121	1	no	maximal, Hall
24	C₅×C₁₁	—	3	1	no	—
25	C₅×C₁₁	—	3	1	no	—
26	C₅×C₁₁	—	6	1	no	—
27	C₂²×C₁₁	—	33	1	no	—
28	C₂×D₁₁	—	3	1	no	—
29	C₂×C₃×C₅	—	121	1	no	—
30	C₅×D₃	—	121	2	no	—
31	C₂×C₁₁	—	3	1	no	—
32	C₂×C₁₁	—	3	1	no	—
33	C₂×C₁₁	—	6	1	no	—
34	C₂×C₁₁	—	33	2	no	—
35	D₁₁	—	3	2	no	—
36	C₂²×C₅	—	33	1	no	Hall
37	C₃×C₅	—	121	1	no	Hall
38	C₂×D₃	—	121	1	no	Hall
39	C₁₁	—	3	1	no	—
40	C₁₁	—	3	1	no	—
41	C₁₁	—	6	1	no	—
42	C₂×C₅	—	33	2	no	—
43	C₂×C₅	#10624391	1	1	yes	characteristic, direct product factor
44	C₂×C₃	—	121	1	no	—
45	D₃	—	121	2	no	—
46	C₅	C₂×#10624391	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²	—	33	1	no	Sylow
48	C₃	—	121	1	no	Sylow
49	C₂	—	33	2	no	—
50	C₂	C₅×#10624391	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	#10624391
commutator, hypocenter	C₁₁²⋊C₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁²	D₃
LCS	G ▷ C₁₁²⋊C₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₁²⋊C₃	C₂	semidirect
2. C₅×#10624391	C₂	direct (N × H)
4. C₅×C₁₁²⋊C₃	C₂²	semidirect
5. C₂×#10624391	C₅	direct (N × H)
6. C₂×C₅×C₁₁²	D₃	semidirect
8. C₂×C₁₁²⋊C₃	C₂×C₅	semidirect
9. #10624391	C₂×C₅	direct (N × H)
10. C₅×C₁₁²	C₂×D₃	semidirect
12. C₁₁²⋊C₃	C₂²×C₅	semidirect
13. C₂×C₁₁²	C₅×D₃	semidirect
17. C₁₁²	C₂×C₅×D₃	semidirect
43. C₂×C₅	#10624391	direct (N × H)
46. C₅	C₂×#10624391	direct (N × H)
50. C₂	C₅×#10624391	direct (N × H)

Subgroups — C2×C5×#10624391 #20300074

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×#10624391 #20300074