Subgroups — C₂×C₄×Dic₂₅ #11716484

Order 800.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₂₅	C₂	1	2	yes	maximal
3	C₄×Dic₂₅	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₂₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₂₅	C₄	1	4	yes	complemented
6	C₂×C₄×C₂₅	C₂²	1	2	yes	—
7	C₂×Dic₂₅	C₄	1	8	yes	direct product factor
8	C₂×Dic₂₅	C₂²	1	4	yes	—
9	C₂×C₄×Dic₅	—	5	1	no	maximal
10	C₂²×C₂₅	C₂×C₄	1	4	yes	—
11	C₂²×C₂₅	C₂×C₄	1	2	yes	—
12	C₂²×C₂₅	C₂³	1	1	yes	characteristic
13	C₄×C₂₅	C₂×C₄	1	4	yes	complemented
14	Dic₂₅	C₂×C₄	1	8	yes	direct product factor
15	C₂²×C₄×C₅	D₅	1	1	yes	characteristic
16	C₂²×Dic₅	—	5	2	no	—
17	C₄×Dic₅	—	5	4	no	—
18	C₂×C₂₅	C₄²	1	4	yes	complemented
19	C₂×C₂₅	C₂²×C₄	1	2	yes	—
20	C₂×C₂₅	C₂²×C₄	1	1	yes	characteristic
21	C₂³×C₅	C₂×D₅	1	1	yes	characteristic
22	C₂×C₄×C₅	Dic₅	1	4	yes	—
23	C₂×C₄×C₅	C₂×D₅	1	2	yes	—
24	C₂×Dic₅	—	5	8	no	—
25	C₂×Dic₅	—	5	4	no	—
26	C₂×C₄²	—	25	1	no	Sylow
27	C₂₅	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₅	C₄×D₅	1	4	yes	—
29	C₂²×C₅	C₂×Dic₅	1	2	yes	—
30	C₂²×C₅	C₂²×D₅	1	1	yes	characteristic
31	C₄×C₅	C₂×Dic₅	1	4	yes	—
32	Dic₅	—	5	8	no	—
33	C₂²×C₄	—	25	2	no	—
34	C₂²×C₄	D₂₅	1	1	yes	characteristic
35	C₄²	—	25	4	no	—
36	C₂×C₅	C₄×Dic₅	1	4	yes	—
37	C₂×C₅	C₂×C₄×D₅	1	2	yes	—
38	C₂×C₅	C₂²×Dic₅	1	1	yes	characteristic
39	C₂³	C₂×D₂₅	1	1	yes	characteristic
40	C₂×C₄	—	25	8	no	—
41	C₂×C₄	—	25	4	no	—
42	C₂×C₄	Dic₂₅	1	4	yes	direct product factor
43	C₂×C₄	C₂×D₂₅	1	2	yes	—
44	C₅	C₂×C₄×Dic₅	1	1	yes	characteristic
45	C₂²	C₄×D₂₅	1	4	yes	—
46	C₂²	C₂×Dic₂₅	1	2	yes	—
47	C₂²	C₂²×D₂₅	1	1	yes	characteristic
48	C₄	—	25	8	no	—
49	C₄	C₂×Dic₂₅	1	4	yes	direct product factor
50	C₂	C₄×Dic₂₅	1	4	yes	direct product factor
51	C₂	C₂×C₄×D₂₅	1	2	yes	—
52	C₂	C₂²×Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₂₅
commutator, hypocenter	C₂₅	C₂×C₄²
Frattini	C₂²×C₅	C₂²×D₅
Fitting	C₂²×C₄×C₂₅	C₂
socle, prime radical	C₂³×C₅	C₂×D₅
cosocle	C₂²×C₂₅	C₂³
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×Dic₂₅	C₂	direct (N × H)
5. C₂×C₄×C₂₅	C₄	semidirect
7. C₂×Dic₂₅	C₄	direct (N × H)
13. C₄×C₂₅	C₂×C₄	semidirect
14. Dic₂₅	C₂×C₄	direct (N × H)
18. C₂×C₂₅	C₄²	semidirect
27. C₂₅	C₂×C₄²	semidirect
42. C₂×C₄	Dic₂₅	direct (N × H)
49. C₄	C₂×Dic₂₅	direct (N × H)
50. C₂	C₄×Dic₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₂₅	2
C₂²×Dic₂₅	2
C₄×Dic₂₅	2
C₂×C₄×Dic₅	5

Subgroups — C2×C4×Dic25 #11716484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₂₅ #11716484