Subgroups — C₂₅×Dic₂₆₁ #39907772

Order 26100.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₅×Dic₈₇	—	3	1	no	maximal
3	C₉×C₂₅×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₂₆₁	C₅	1	1	yes	maximal, characteristic
5	C₂×C₃×C₂₅×C₂₉	D₃	1	1	yes	characteristic
6	C₂₅×Dic₂₉	—	9	1	no	Hall
7	C₂×C₅×C₉×C₂₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₂₅×C₂₉	Dic₃	1	1	yes	characteristic
9	C₅×Dic₈₇	—	3	1	no	—
10	C₂×C₂₅×C₂₉	D₉	1	1	yes	characteristic
11	C₅×C₉×C₂₉	C₄×C₅	1	1	yes	characteristic
12	Dic₂₆₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂₅×Dic₉	—	29	1	no	maximal, Hall
14	C₂×C₃×C₅×C₂₉	C₅×D₃	1	1	yes	characteristic
15	C₂₅×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₂₉	—	9	1	no	—
17	C₂×C₉×C₂₉	C₂×C₂₅	1	1	yes	characteristic
18	C₂×C₉×C₂₅	D₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	C₅×Dic₃	1	1	yes	characteristic
20	Dic₈₇	—	3	1	no	—
21	Dic₃×C₂₅	—	87	1	no	—
22	C₂×C₅×C₂₉	C₅×D₉	1	1	yes	characteristic
23	C₉×C₂₉	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
24	C₉×C₂₅	Dic₂₉	1	1	yes	characteristic, complemented, Hall
25	C₅×Dic₉	—	29	1	no	—
26	C₂×C₃×C₂₉	D₃×C₂₅	1	1	yes	characteristic
27	C₂×C₃×C₂₅	D₈₇	1	1	yes	characteristic
28	C₅×C₂₉	C₅×Dic₉	1	1	yes	characteristic
29	Dic₂₉	—	9	1	no	Hall
30	C₄×C₂₅	—	261	1	no	Hall
31	C₂×C₅×C₉	C₅×D₂₉	1	1	yes	characteristic
32	C₃×C₂₉	Dic₃×C₂₅	1	1	yes	characteristic
33	C₃×C₂₅	Dic₈₇	1	1	yes	characteristic
34	C₅×Dic₃	—	87	1	no	—
35	C₂×C₂₉	D₉×C₂₅	1	1	yes	characteristic
36	C₂×C₂₅	D₂₆₁	1	1	yes	characteristic
37	C₅×C₉	C₅×Dic₂₉	1	1	yes	characteristic
38	Dic₉	—	29	1	no	Hall
39	C₂×C₃×C₅	C₅×D₈₇	1	1	yes	characteristic
40	C₂₉	C₂₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
41	C₂₅	Dic₂₆₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₄×C₅	—	261	1	no	—
43	C₂×C₉	C₂₅×D₂₉	1	1	yes	characteristic
44	C₃×C₅	C₅×Dic₈₇	1	1	yes	characteristic
45	Dic₃	—	87	1	no	—
46	C₂×C₅	C₅×D₂₆₁	1	1	yes	characteristic
47	C₉	C₂₅×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₂₅×D₈₇	1	1	yes	characteristic
49	C₅	C₅×Dic₂₆₁	1	1	yes	characteristic
50	C₄	—	261	1	no	Sylow
51	C₃	C₂₅×Dic₈₇	1	1	yes	characteristic
52	C₂	C₂₅×D₂₆₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₂₆₁
commutator, hypocenter	C₉×C₂₉	C₄×C₂₅
Frattini	C₂×C₃×C₅	C₅×D₈₇
Fitting	C₂×C₉×C₂₅×C₂₉	C₂
socle, prime radical	C₂×C₃×C₅×C₂₉	C₅×D₃
cosocle	C₂×C₅×C₉×C₂₉	C₂×C₅
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₂×C₂₅

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₅×C₂₉	C₄	semidirect
12. Dic₂₆₁	C₂₅	direct (N × H)
15. C₂₅×C₂₉	Dic₉	semidirect
23. C₉×C₂₉	C₄×C₂₅	semidirect
24. C₉×C₂₅	Dic₂₉	semidirect
40. C₂₉	C₂₅×Dic₉	semidirect
41. C₂₅	Dic₂₆₁	direct (N × H)
47. C₉	C₂₅×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₂₅×C₂₉	2
C₂₅×Dic₈₇	3
C₅×Dic₂₆₁	5
C₂₅×Dic₉	29

Subgroups — C25×Dic261 #39907772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×Dic₂₆₁ #39907772