Subgroups — C₂×#17987871 #22604885

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#17987871	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊D₁₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅⋊D₁₅₅	C₂×C₃	1	2	yes	complemented
7	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₅₅	—	15	2	no	—
9	C₂×C₃×D₃₁	—	25	1	no	maximal, Hall
10	C₂×C₅×C₃₁	—	3	2	no	—
11	D₁₅₅	—	15	4	no	—
12	C₂×(C₅⋊D₅)⋊C₃	—	31	1	no	maximal, Hall
13	C₂×C₃×C₃₁	—	25	1	no	—
14	C₃×D₃₁	—	25	2	no	—
15	C₅×C₃₁	—	3	2	no	—
16	C₂×C₅²⋊C₃	D₃₁	1	1	yes	characteristic, complemented
17	(C₅⋊D₅)⋊C₃	—	31	2	no	—
18	C₂×D₃₁	—	25	1	no	Hall
19	C₂×C₅⋊D₅	—	31	1	no	Hall
20	C₃×C₃₁	—	25	1	no	Hall
21	C₅²⋊C₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
23	D₃₁	—	25	2	no	—
24	C₂×C₅²	C₃×D₃₁	1	1	yes	characteristic, complemented
25	C₅⋊D₅	—	31	2	no	—
26	C₃₁	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₅²	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×D₅	—	465	2	no	—
29	C₂²×C₃	—	775	1	no	Hall
30	C₂×C₅	—	3	2	no	—
31	D₅	—	465	4	no	—
32	C₂×C₃	—	775	2	no	—
33	C₂×C₃	—	25	1	no	—
34	C₅	—	3	2	no	—
35	C₂²	—	775	1	no	Sylow
36	C₃	—	25	1	no	Sylow
37	C₂	—	775	2	no	—
38	C₂	#17987871	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#17987871
commutator, hypocenter	C₅²×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₅²⋊C₃	C₂	semidirect
2. #17987871	C₂	direct (N × H)
3. C₂×C₅⋊D₁₅₅	C₃	semidirect
4. C₃₁×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₃₁	C₂×C₃	semidirect
6. C₅⋊D₁₅₅	C₂×C₃	semidirect
7. C₅²×C₃₁	C₂²×C₃	semidirect
16. C₂×C₅²⋊C₃	D₃₁	semidirect
21. C₅²⋊C₃	C₂×D₃₁	semidirect
22. C₂×C₃₁	(C₅⋊D₅)⋊C₃	semidirect
24. C₂×C₅²	C₃×D₃₁	semidirect
26. C₃₁	C₂×(C₅⋊D₅)⋊C₃	semidirect
27. C₅²	C₂×C₃×D₃₁	semidirect
38. C₂	#17987871	direct (N × H)

Subgroups — C2×#17987871 #22604885

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17987871 #22604885