Subgroups — C₄⋊C₄×D₂₅ #11716453

Order 800.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₂₅	C₂	1	2	yes	maximal
2	C₂×C₄×D₂₅	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#87718	C₂	1	2	yes	maximal, complemented
6	C₂²×D₂₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₅	C₂²	1	2	yes	—
8	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₅	C₂²	1	2	yes	—
10	C₂×Dic₂₅	C₂²	1	1	yes	characteristic
11	C₄×D₂₅	—	2	4	no	—
12	C₄×D₂₅	C₄	1	4	yes	complemented
13	D₅×C₄⋊C₄	—	5	1	no	maximal
14	C₂²×C₂₅	C₂³	1	1	yes	characteristic
15	C₂×D₂₅	C₂×C₄	1	2	yes	—
16	C₂×D₂₅	D₄	1	2	yes	—
17	C₂×D₂₅	Q₈	1	2	yes	—
18	C₄×C₂₅	—	2	2	no	—
19	C₄×C₂₅	C₂×C₄	1	2	yes	complemented
20	Dic₂₅	—	2	2	no	—
21	Dic₂₅	C₂×C₄	1	2	yes	complemented
22	C₂×C₄×D₅	—	5	1	no	—
23	C₂×C₄×D₅	—	5	2	no	—
24	C₅×C₄⋊C₄	D₅	1	1	yes	characteristic
25	C₄⋊Dic₅	—	5	1	no	—
26	#683	—	5	2	no	—
27	C₂×C₂₅	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
29	C₂×C₂₅	C₂×Q₈	1	1	yes	characteristic
30	D₂₅	C₄⋊C₄	1	4	yes	direct product factor
31	C₂²×D₅	—	5	1	no	—
32	C₂×C₄×C₅	C₂×D₅	1	2	yes	—
33	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
34	C₂×Dic₅	—	5	1	no	—
35	C₂×Dic₅	—	5	2	no	—
36	C₄×D₅	—	5	4	no	—
37	C₄×D₅	—	10	4	no	—
38	C₂×C₄⋊C₄	—	25	1	no	Sylow
39	C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₅	C₂²×D₅	1	1	yes	characteristic
41	C₂×D₅	—	5	2	no	—
42	C₂×D₅	—	5	2	no	—
43	C₂×D₅	—	5	2	no	—
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	C₄×D₅	1	2	yes	—
46	Dic₅	—	5	2	no	—
47	Dic₅	—	10	2	no	—
48	C₂²×C₄	—	25	1	no	—
49	C₂²×C₄	—	25	2	no	—
50	C₄⋊C₄	—	25	2	no	—
51	C₄⋊C₄	—	25	1	no	—
52	C₄⋊C₄	D₂₅	1	1	yes	characteristic, direct product factor
53	C₂×C₅	C₂×C₄×D₅	1	1	yes	characteristic
54	C₂×C₅	D₄×D₅	1	1	yes	characteristic
55	C₂×C₅	Q₈×D₅	1	1	yes	characteristic
56	D₅	—	5	4	no	—
57	C₂³	—	25	1	no	—
58	C₂×C₄	—	25	1	no	—
59	C₂×C₄	—	25	4	no	—
60	C₂×C₄	—	25	2	no	—
61	C₂×C₄	—	50	4	no	—
62	C₂×C₄	C₂×D₂₅	1	2	yes	—
63	C₂×C₄	C₂×D₂₅	1	1	yes	characteristic
64	C₅	D₅×C₄⋊C₄	1	1	yes	characteristic
65	C₂²	—	25	2	no	—
66	C₂²	—	25	2	no	—
67	C₂²	—	25	2	no	—
68	C₂²	C₂²×D₂₅	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	25	2	no	—
71	C₄	—	50	2	no	—
72	C₄	C₄×D₂₅	1	2	yes	complemented
73	C₂	—	25	4	no	—
74	C₂	C₂×C₄×D₂₅	1	1	yes	characteristic
75	C₂	D₄×D₂₅	1	1	yes	characteristic
76	C₂	Q₈×D₂₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₄×C₂₅	C₂	semidirect
4. C₄⋊Dic₂₅	C₂	semidirect
5. #87718	C₂	semidirect
12. C₄×D₂₅	C₄	semidirect
19. C₄×C₂₅	C₂×C₄	semidirect
21. Dic₂₅	C₂×C₄	semidirect
30. D₂₅	C₄⋊C₄	direct (N × H)
39. C₂₅	C₂×C₄⋊C₄	semidirect
52. C₄⋊C₄	D₂₅	direct (N × H)
72. C₄	C₄×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₂₅	2
C₄⋊C₄×C₂₅	2
C₄⋊Dic₂₅	2
#87718	2
D₅×C₄⋊C₄	5

Subgroups — C4⋊C4×D25 #11716453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×D₂₅ #11716453