Subgroups — D₄×Dic₂₅ #11716496

Order 800.

141 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₂₅	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₂₅	C₂	1	2	yes	maximal, complemented
4	C₄⋊Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×C₂₅	C₂²	1	2	yes	—
7	D₄×C₂₅	C₄	1	4	yes	complemented
8	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₅	—	2	4	no	—
10	C₂×Dic₂₅	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₅	C₂²	1	2	yes	—
12	C₂×Dic₂₅	C₂²	1	1	yes	characteristic
13	D₄×Dic₅	—	5	1	no	maximal
14	C₂²×C₂₅	—	2	2	no	—
15	C₂²×C₂₅	—	2	2	no	—
16	C₂²×C₂₅	C₂×C₄	1	4	yes	complemented
17	C₂²×C₂₅	C₂³	1	1	yes	characteristic
18	C₄×C₂₅	C₂×C₄	1	2	yes	complemented
19	Dic₂₅	—	2	2	no	—
20	Dic₂₅	—	2	1	no	—
21	Dic₂₅	D₄	1	2	yes	direct product factor
22	C₂×C₅×D₄	D₅	1	1	yes	characteristic
23	C₂²×Dic₅	—	5	2	no	—
24	C₂²⋊Dic₅	—	5	2	no	—
25	C₄⋊Dic₅	—	5	1	no	—
26	C₄×Dic₅	—	5	1	no	—
27	C₂×C₂₅	—	2	4	no	—
28	C₂×C₂₅	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
30	C₂×C₂₅	#41	1	1	yes	characteristic
31	C₂³×C₅	C₂×D₅	1	2	yes	—
32	C₅×D₄	Dic₅	1	4	yes	—
33	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
34	C₂×Dic₅	—	5	1	no	—
35	C₂×Dic₅	—	5	1	no	—
36	C₂×Dic₅	—	5	2	no	—
37	C₂×Dic₅	—	10	4	no	—
38	C₄×D₄	—	25	1	no	Sylow
39	C₂₅	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₅	—	2	2	no	—
41	C₂²×C₅	—	2	2	no	—
42	C₂²×C₅	C₂×Dic₅	1	4	yes	—
43	C₂²×C₅	C₂²×D₅	1	1	yes	characteristic
44	C₄×C₅	C₂×Dic₅	1	2	yes	—
45	Dic₅	—	5	2	no	—
46	Dic₅	—	10	2	no	—
47	Dic₅	—	10	1	no	—
48	C₂×D₄	D₂₅	1	1	yes	characteristic
49	C₂²×C₄	—	25	2	no	—
50	C₄⋊C₄	—	25	1	no	—
51	C₂²⋊C₄	—	25	2	no	—
52	C₄²	—	25	1	no	—
53	C₂×C₅	—	2	4	no	—
54	C₂×C₅	D₄×D₅	1	1	yes	characteristic
55	C₂×C₅	#711	1	1	yes	characteristic
56	C₂×C₅	C₂²×Dic₅	1	1	yes	characteristic
57	C₂³	C₂×D₂₅	1	2	yes	—
58	D₄	Dic₂₅	1	4	yes	direct product factor
59	C₂×C₄	—	25	1	no	—
60	C₂×C₄	—	25	1	no	—
61	C₂×C₄	—	25	2	no	—
62	C₂×C₄	—	50	4	no	—
63	C₂×C₄	C₂×D₂₅	1	1	yes	characteristic
64	C₅	D₄×Dic₅	1	1	yes	characteristic
65	C₂²	—	2	2	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂×Dic₂₅	1	4	yes	complemented
68	C₂²	C₂²×D₂₅	1	1	yes	characteristic
69	C₄	—	25	2	no	—
70	C₄	—	50	2	no	—
71	C₄	—	50	1	no	—
72	C₄	C₂×Dic₂₅	1	2	yes	complemented
73	C₂	—	2	4	no	—
74	C₂	D₄×D₂₅	1	1	yes	characteristic
75	C₂	#87746	1	1	yes	characteristic
76	C₂	C₂²×Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₅
commutator	C₂×C₂₅	C₂²×C₄
Frattini, socle	C₂²×C₅	C₂²×D₅
Fitting	C₂×D₄×C₂₅	C₂
prime radical	C₂×C₅×D₄	D₅
cosocle	C₂²×C₂₅	C₂³
hypercenter	C₂×D₄	D₂₅
hypocenter	C₂₅	C₄×D₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₂₅	C₂	semidirect
3. C₂²⋊Dic₂₅	C₂	semidirect
4. C₄⋊Dic₂₅	C₂	semidirect
5. C₄×Dic₂₅	C₂	semidirect
7. D₄×C₂₅	C₄	semidirect
16. C₂²×C₂₅	C₂×C₄	semidirect
18. C₄×C₂₅	C₂×C₄	semidirect
21. Dic₂₅	D₄	direct (N × H)
39. C₂₅	C₄×D₄	semidirect
58. D₄	Dic₂₅	direct (N × H)
67. C₂²	C₂×Dic₂₅	semidirect
72. C₄	C₂×Dic₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₂₅	2
C₂²×Dic₂₅	2
C₂²⋊Dic₂₅	2
C₄⋊Dic₂₅	2
C₄×Dic₂₅	2
D₄×Dic₅	5

Subgroups — D4×Dic25 #11716496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×Dic₂₅ #11716496