Subgroups — C₂×C₃₁⋊#3874 #22604881

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	C₃₁⋊#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₁₅₅	—	3	1	no	maximal, Hall
4	C₃₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
6	C₅×D₁₅₅	—	3	2	no	—
7	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₅₅	—	3	1	no	—
9	C₂×C₅×D₃₁	—	15	1	no	—
10	C₂×D₉₃	—	25	1	no	maximal, Hall
11	C₂×C₅×C₃₁	—	3	1	no	—
12	C₂×C₅×C₃₁	—	3	1	no	—
13	D₁₅₅	—	3	2	no	—
14	C₅×D₃₁	—	15	2	no	—
15	C₂×#3874	—	31	1	no	maximal, Hall
16	C₂×C₃×C₃₁	—	25	1	no	—
17	D₉₃	—	25	2	no	—
18	C₅×C₃₁	—	3	1	no	—
19	C₅×C₃₁	—	3	1	no	—
20	C₂×C₅²⋊C₃	D₃₁	1	1	yes	characteristic, complemented
21	#3874	—	31	2	no	—
22	C₂×D₃₁	—	15	1	no	Hall
23	C₂×C₅×D₅	—	93	1	no	Hall
24	C₃×C₃₁	—	25	1	no	Hall
25	C₅²⋊C₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃₁	#3874	1	1	yes	characteristic, complemented
27	D₃₁	—	15	2	no	—
28	C₂×C₅²	D₉₃	1	1	yes	characteristic, complemented
29	C₅×D₅	—	93	2	no	—
30	C₃₁	C₂×#3874	1	1	yes	characteristic, complemented, Sylow
31	C₅²	C₂×D₉₃	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₅	—	465	1	no	—
33	C₂×D₅	—	93	1	no	—
34	C₂×D₃	—	775	1	no	Hall
35	C₂×C₅	—	3	1	no	—
36	C₂×C₅	—	3	1	no	—
37	C₂×C₅	—	465	2	no	—
38	D₅	—	93	2	no	—
39	C₂×C₃	—	25	1	no	—
40	D₃	—	775	2	no	—
41	C₅	—	3	1	no	—
42	C₅	—	3	1	no	—
43	C₂²	—	465	1	no	Sylow
44	C₃	—	25	1	no	Sylow
45	C₂	—	465	2	no	—
46	C₂	C₃₁⋊#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃₁⋊#3874
commutator, hypocenter	C₃₁×C₅²⋊C₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁	D₃
LCS	G ▷ C₃₁×C₅²⋊C₃
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. C₃₁⋊#3874	C₂	direct (N × H)
4. C₃₁×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₃₁	D₃	semidirect
7. C₅²×C₃₁	C₂×D₃	semidirect
20. C₂×C₅²⋊C₃	D₃₁	semidirect
25. C₅²⋊C₃	C₂×D₃₁	semidirect
26. C₂×C₃₁	#3874	semidirect
28. C₂×C₅²	D₉₃	semidirect
30. C₃₁	C₂×#3874	semidirect
31. C₅²	C₂×D₉₃	semidirect
46. C₂	C₃₁⋊#3874	direct (N × H)

Subgroups — C2×C31⋊#3874 #22604881

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃₁⋊#3874 #22604881