Subgroups — C₃×C₂₅×D₂₁₃ #44544021

Order 31950.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×D₂₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₅×D₇₁	—	3	1	no	maximal
4	C₃×C₅×D₂₁₃	C₅	1	1	yes	maximal, characteristic
5	C₃×C₂₅×C₇₁	—	2	1	no	—
6	C₃×C₂₅×C₇₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₅×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₅×D₇₁	—	3	1	no	Hall
9	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic
10	C₅×D₂₁₃	C₃×C₅	1	1	yes	characteristic
11	C₃×C₅×D₇₁	—	3	1	no	—
12	C₂₅×C₇₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₁₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₇₁	—	2	1	no	—
15	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic
16	C₃×C₅×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
17	C₅×D₇₁	—	3	1	no	—
18	C₃²×C₇₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
19	C₃×D₃×C₂₅	—	71	1	no	maximal, Hall
20	D₂₁₃	C₃×C₂₅	1	1	yes	characteristic, direct product factor
21	C₃×D₇₁	—	3	1	no	—
22	C₅×C₇₁	C₃×C₅×D₃	1	1	yes	characteristic
23	C₃²×C₂₅	D₇₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇₁	—	2	1	no	—
25	C₃×C₇₁	D₃×C₂₅	1	1	yes	characteristic, complemented
26	C₃×C₇₁	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂₅	—	213	1	no	—
28	D₃×C₂₅	—	71	1	no	—
29	D₇₁	—	3	1	no	Hall
30	C₃×C₅×D₃	—	71	1	no	—
31	C₃×C₂₅	—	2	1	no	—
32	C₃×C₂₅	C₃×D₇₁	1	1	yes	characteristic, complemented
33	C₃×C₂₅	D₂₁₃	1	1	yes	characteristic, direct product factor
34	C₇₁	C₃×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₂₅	—	213	1	no	Hall
36	C₃²×C₅	C₅×D₇₁	1	1	yes	characteristic
37	C₂×C₃×C₅	—	213	1	no	—
38	C₅×D₃	—	71	1	no	—
39	C₂₅	C₃×D₂₁₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×D₃	—	71	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×C₅×D₇₁	1	1	yes	characteristic
43	C₃×C₅	C₅×D₂₁₃	1	1	yes	characteristic
44	C₂×C₅	—	213	1	no	—
45	C₃²	C₂₅×D₇₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	213	1	no	—
47	D₃	—	71	1	no	—
48	C₅	C₃×C₅×D₂₁₃	1	1	yes	characteristic
49	C₃	—	2	1	no	—
50	C₃	C₃×C₂₅×D₇₁	1	1	yes	characteristic, complemented
51	C₃	C₂₅×D₂₁₃	1	1	yes	characteristic, direct product factor
52	C₂	—	213	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₅	D₂₁₃
commutator, hypocenter	C₃×C₇₁	C₂×C₃×C₂₅
Frattini	C₅	C₃×C₅×D₂₁₃
Fitting	C₃²×C₂₅×C₇₁	C₂
socle	C₃²×C₅×C₇₁	C₂×C₅
prime radical	C₃×C₅×D₂₁₃	C₅
cosocle	C₃×C₅×C₇₁	C₂×C₃×C₅
LCS	G ▷ C₃×C₇₁
UCS	C₁ ◁ C₃×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅×C₇₁	C₂	semidirect
2. C₂₅×D₂₁₃	C₃	direct (N × H)
6. C₃×C₂₅×C₇₁	D₃	semidirect
7. C₃×C₂₅×C₇₁	C₂×C₃	semidirect
12. C₂₅×C₇₁	C₃×D₃	semidirect
13. C₃×D₂₁₃	C₂₅	direct (N × H)
18. C₃²×C₇₁	C₂×C₂₅	semidirect
20. D₂₁₃	C₃×C₂₅	direct (N × H)
23. C₃²×C₂₅	D₇₁	semidirect
25. C₃×C₇₁	D₃×C₂₅	semidirect
26. C₃×C₇₁	C₂×C₃×C₂₅	semidirect
32. C₃×C₂₅	C₃×D₇₁	semidirect
33. C₃×C₂₅	D₂₁₃	direct (N × H)
34. C₇₁	C₃×D₃×C₂₅	semidirect
39. C₂₅	C₃×D₂₁₃	direct (N × H)
45. C₃²	C₂₅×D₇₁	semidirect
50. C₃	C₃×C₂₅×D₇₁	semidirect
51. C₃	C₂₅×D₂₁₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₂₅×C₇₁	2
C₂₅×D₂₁₃	3
C₃×C₂₅×D₇₁	3
C₃×C₅×D₂₁₃	5
C₃×D₃×C₂₅	71

Subgroups — C3×C25×D213 #44544021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₅×D₂₁₃ #44544021