Subgroups — C₂×C₂₅⋊(D₃₁⋊C₃) #22604759

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅⋊(D₃₁⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₇₇₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₅×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅⋊(D₃₁⋊C₃)	—	5	1	no	maximal
6	C₂×C₂₅×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	D₇₇₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×C₃₁⋊C₃	D₅	1	1	yes	characteristic
9	C₅⋊(D₃₁⋊C₃)	—	5	2	no	—
10	C₂₅×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₁₅₅	—	5	1	no	—
12	C₅×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic
13	C₂×D₃₁⋊C₃	—	25	1	no	Hall
14	C₂×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic
15	D₁₅₅	—	5	2	no	—
16	C₂×C₃×D₂₅	—	31	1	no	maximal, Hall
17	C₂×C₃₁⋊C₃	D₂₅	1	1	yes	characteristic, complemented
18	D₃₁⋊C₃	—	25	2	no	—
19	C₅×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic
20	C₂×C₃×C₂₅	—	31	1	no	—
21	C₃×D₂₅	—	31	2	no	—
22	C₂×D₃₁	—	25	1	no	Hall
23	C₂×D₂₅	—	31	1	no	Hall
24	C₃₁⋊C₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
25	C₃×C₂₅	—	31	1	no	Hall
26	C₂×C₃₁	C₃×D₂₅	1	1	yes	characteristic, complemented
27	D₃₁	—	25	2	no	—
28	C₂×C₃×D₅	—	155	1	no	—
29	C₂×C₂₅	D₃₁⋊C₃	1	1	yes	characteristic, complemented
30	D₂₅	—	31	2	no	—
31	C₃₁	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₅	—	31	1	no	—
33	C₃×D₅	—	155	2	no	—
34	C₂₅	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	155	1	no	—
36	C₃×C₅	—	31	1	no	—
37	C₂²×C₃	—	775	1	no	Hall
38	C₂×C₅	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic
39	D₅	—	155	2	no	—
40	C₂×C₃	—	775	2	no	—
41	C₂×C₃	—	31	1	no	—
42	C₅	C₂×C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic
43	C₂²	—	775	1	no	Sylow
44	C₃	—	31	1	no	Sylow
45	C₂	—	775	2	no	—
46	C₂	C₂₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂₅⋊(D₃₁⋊C₃)
commutator, hypocenter	C₂₅×C₃₁	C₂²×C₃
Frattini	C₅	C₂×C₅⋊(D₃₁⋊C₃)
Fitting	C₂×C₂₅×C₃₁	C₂×C₃
socle	C₂×C₅×C₃₁	C₃×D₅
LCS	G ▷ C₂₅×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₅×C₃₁⋊C₃	C₂	semidirect
2. C₂₅⋊(D₃₁⋊C₃)	C₂	direct (N × H)
3. C₂×D₇₇₅	C₃	semidirect
4. C₂₅×C₃₁⋊C₃	C₂²	semidirect
6. C₂×C₂₅×C₃₁	C₂×C₃	semidirect
7. D₇₇₅	C₂×C₃	semidirect
10. C₂₅×C₃₁	C₂²×C₃	semidirect
17. C₂×C₃₁⋊C₃	D₂₅	semidirect
24. C₃₁⋊C₃	C₂×D₂₅	semidirect
26. C₂×C₃₁	C₃×D₂₅	semidirect
29. C₂×C₂₅	D₃₁⋊C₃	semidirect
31. C₃₁	C₂×C₃×D₂₅	semidirect
34. C₂₅	C₂×D₃₁⋊C₃	semidirect
46. C₂	C₂₅⋊(D₃₁⋊C₃)	direct (N × H)

Subgroups — C2×C25⋊(D31⋊C3) #22604759

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₅⋊(D₃₁⋊C₃) #22604759