Subgroups — C₂³×C₄×D₂₅ #13099683

Order 1600.

2043 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₂₅	C₂	1	28	yes	maximal, direct product factor
5	C₂⁴×C₂₅	C₂²	1	1	yes	characteristic
6	C₂³×D₂₅	C₄	1	16	yes	direct product factor
7	C₂³×D₂₅	C₂²	1	14	yes	—
8	C₂²×C₄×C₂₅	C₂²	1	14	yes	complemented
9	C₂²×Dic₂₅	C₂²	1	14	yes	complemented
10	C₂×C₄×D₂₅	C₂²	1	112	yes	direct product factor
11	C₂³×C₄×D₅	—	5	1	no	maximal
12	C₂³×C₂₅	C₂×C₄	1	8	yes	complemented
13	C₂³×C₂₅	C₂³	1	7	yes	—
14	C₂²×D₂₅	C₂×C₄	1	112	yes	direct product factor
15	C₂²×D₂₅	C₂³	1	28	yes	—
16	C₂×C₄×C₂₅	C₂³	1	28	yes	complemented
17	C₂×Dic₂₅	C₂³	1	28	yes	complemented
18	C₄×D₂₅	C₂³	1	64	yes	direct product factor
19	C₂⁴×D₅	—	5	1	no	—
20	C₂³×C₄×C₅	D₅	1	1	yes	characteristic
21	C₂³×Dic₅	—	5	1	no	—
22	C₂²×C₄×D₅	—	5	28	no	—
23	C₂²×C₂₅	C₂²×C₄	1	28	yes	complemented
24	C₂²×C₂₅	C₂⁴	1	7	yes	—
25	C₂×D₂₅	C₂²×C₄	1	112	yes	direct product factor
26	C₂×D₂₅	C₂⁴	1	8	yes	—
27	C₄×C₂₅	C₂⁴	1	8	yes	complemented
28	Dic₂₅	C₂⁴	1	8	yes	complemented
29	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
30	C₂³×D₅	—	5	16	no	—
31	C₂³×D₅	—	5	14	no	—
32	C₂²×C₄×C₅	C₂×D₅	1	14	yes	—
33	C₂²×Dic₅	—	5	14	no	—
34	C₂×C₄×D₅	—	5	112	no	—
35	C₂⁴×C₄	—	25	1	no	Sylow
36	C₂×C₂₅	C₂³×C₄	1	14	yes	complemented
37	C₂×C₂₅	C₂⁵	1	1	yes	characteristic
38	D₂₅	C₂³×C₄	1	16	yes	direct product factor
39	C₂³×C₅	C₄×D₅	1	8	yes	—
40	C₂³×C₅	C₂²×D₅	1	7	yes	—
41	C₂²×D₅	—	5	112	no	—
42	C₂²×D₅	—	5	28	no	—
43	C₂×C₄×C₅	C₂²×D₅	1	28	yes	—
44	C₂×Dic₅	—	5	28	no	—
45	C₄×D₅	—	5	64	no	—
46	C₂⁵	—	25	1	no	—
47	C₂³×C₄	—	25	1	no	—
48	C₂³×C₄	—	25	28	no	—
49	C₂³×C₄	D₂₅	1	1	yes	characteristic, direct product factor
50	C₂₅	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	C₂×C₄×D₅	1	28	yes	—
52	C₂²×C₅	C₂³×D₅	1	7	yes	—
53	C₂×D₅	—	5	112	no	—
54	C₂×D₅	—	5	8	no	—
55	C₄×C₅	C₂³×D₅	1	8	yes	—
56	Dic₅	—	5	8	no	—
57	C₂⁴	—	25	16	no	—
58	C₂⁴	—	25	14	no	—
59	C₂⁴	C₂×D₂₅	1	1	yes	characteristic
60	C₂²×C₄	—	25	14	no	—
61	C₂²×C₄	—	25	112	no	—
62	C₂²×C₄	C₂×D₂₅	1	14	yes	direct product factor
63	C₂×C₅	C₂²×C₄×D₅	1	14	yes	—
64	C₂×C₅	C₂⁴×D₅	1	1	yes	characteristic
65	D₅	—	5	16	no	—
66	C₂³	—	25	112	no	—
67	C₂³	—	25	28	no	—
68	C₂³	C₄×D₂₅	1	8	yes	direct product factor
69	C₂³	C₂²×D₂₅	1	7	yes	—
70	C₂×C₄	—	25	28	no	—
71	C₂×C₄	—	25	64	no	—
72	C₂×C₄	C₂²×D₂₅	1	28	yes	direct product factor
73	C₅	C₂³×C₄×D₅	1	1	yes	characteristic
74	C₂²	—	25	8	no	—
75	C₂²	—	25	112	no	—
76	C₂²	C₂×C₄×D₂₅	1	28	yes	direct product factor
77	C₂²	C₂³×D₂₅	1	7	yes	—
78	C₄	—	25	8	no	—
79	C₄	C₂³×D₂₅	1	8	yes	direct product factor
80	C₂	—	25	16	no	—
81	C₂	C₂²×C₄×D₂₅	1	14	yes	direct product factor
82	C₂	C₂⁴×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₂₅
commutator, hypocenter	C₂₅	C₂⁴×C₄
Frattini	C₂×C₅	C₂⁴×D₅
Fitting	C₂³×C₄×C₂₅	C₂
socle	C₂⁴×C₅	C₂×D₅
prime radical	C₂⁴×D₂₅	C₂
cosocle	C₂×C₂₅	C₂⁵
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×C₂₅	C₂	semidirect
3. C₂³×Dic₂₅	C₂	semidirect
4. C₂²×C₄×D₂₅	C₂	direct (N × H)
6. C₂³×D₂₅	C₄	direct (N × H)
8. C₂²×C₄×C₂₅	C₂²	semidirect
9. C₂²×Dic₂₅	C₂²	semidirect
10. C₂×C₄×D₂₅	C₂²	direct (N × H)
12. C₂³×C₂₅	C₂×C₄	semidirect
14. C₂²×D₂₅	C₂×C₄	direct (N × H)
16. C₂×C₄×C₂₅	C₂³	semidirect
17. C₂×Dic₂₅	C₂³	semidirect
18. C₄×D₂₅	C₂³	direct (N × H)
23. C₂²×C₂₅	C₂²×C₄	semidirect
25. C₂×D₂₅	C₂²×C₄	direct (N × H)
27. C₄×C₂₅	C₂⁴	semidirect
28. Dic₂₅	C₂⁴	semidirect
36. C₂×C₂₅	C₂³×C₄	semidirect
38. D₂₅	C₂³×C₄	direct (N × H)
49. C₂³×C₄	D₂₅	direct (N × H)
50. C₂₅	C₂⁴×C₄	semidirect
62. C₂²×C₄	C₂×D₂₅	direct (N × H)
68. C₂³	C₄×D₂₅	direct (N × H)
72. C₂×C₄	C₂²×D₂₅	direct (N × H)
76. C₂²	C₂×C₄×D₂₅	direct (N × H)
79. C₄	C₂³×D₂₅	direct (N × H)
81. C₂	C₂²×C₄×D₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₂₅	2
C₂³×C₄×C₂₅	2
C₂³×Dic₂₅	2
C₂²×C₄×D₂₅	2
C₂³×C₄×D₅	5

Subgroups — C23×C4×D25 #13099683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×D₂₅ #13099683