Subgroups — C₂₅×#490 #13098639

Order 1600.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×#102	C₂	1	4	yes	maximal, complemented
4	C₂₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₂₅	—	2	2	no	—
6	C₂×D₄×C₂₅	C₂²	1	2	yes	—
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₅	—	2	2	no	—
9	C₄⋊C₄×C₂₅	C₂²	1	2	yes	—
10	C₄²×C₂₅	C₂²	1	1	yes	characteristic
11	C₅×#490	C₅	1	1	yes	maximal, characteristic
12	C₂³×C₂₅	—	2	2	no	—
13	D₄×C₂₅	—	2	4	no	—
14	D₄×C₂₅	—	4	4	no	—
15	C₂×C₄×C₂₅	—	2	2	no	—
16	C₂×C₄×C₂₅	D₄	1	2	yes	—
17	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
18	C₈×C₂₅	—	2	2	no	—
19	C₅×#127	C₂×C₅	1	1	yes	characteristic
20	C₅×#125	C₂×C₅	1	1	yes	characteristic
21	C₅×#102	C₂×C₅	1	4	yes	—
22	C₅×#97	C₂×C₅	1	1	yes	characteristic
23	C₂²×C₂₅	—	4	2	no	—
24	C₂²×C₂₅	—	4	4	no	—
25	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₅	—	2	2	no	—
27	C₄×C₂₅	—	4	2	no	—
28	C₄×C₂₅	#41	1	2	yes	—
29	C₂×C₅×D₄	—	2	2	no	—
30	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
31	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
32	C₅×C₄⋊C₄	—	2	2	no	—
33	C₅×C₄⋊C₄	C₂²×C₅	1	2	yes	—
34	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
35	#490	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₂₅	—	8	2	no	—
37	C₂×C₂₅	#124	1	1	yes	characteristic
38	C₂×C₂₅	AGL(1,ℤ/8)	1	2	yes	—
39	C₂³×C₅	—	2	2	no	—
40	C₅×D₄	—	2	4	no	—
41	C₅×D₄	—	4	4	no	—
42	C₂×C₄×C₅	—	2	2	no	—
43	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
44	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
45	C₅×C₈	—	2	2	no	—
46	#127	C₂×C₂₅	1	1	yes	characteristic
47	#125	C₂×C₂₅	1	1	yes	characteristic, complemented
48	#102	C₂×C₂₅	1	4	yes	complemented
49	#97	C₂×C₂₅	1	1	yes	characteristic, complemented
50	C₂₅	#490	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₅	—	4	2	no	—
52	C₂²×C₅	—	4	4	no	—
53	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
54	C₄×C₅	—	2	2	no	—
55	C₄×C₅	—	4	2	no	—
56	C₄×C₅	C₅×#41	1	2	yes	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	C₂²×C₂₅	1	2	yes	—
59	C₂×C₈	C₂²×C₂₅	1	2	yes	—
60	C₄⋊C₄	—	2	2	no	—
61	C₄⋊C₄	C₂²×C₂₅	1	2	yes	—
62	C₄²	C₂²×C₂₅	1	1	yes	characteristic
63	C₂×C₅	—	8	2	no	—
64	C₂×C₅	C₅×#124	1	1	yes	characteristic
65	C₂×C₅	C₅×AGL(1,ℤ/8)	1	2	yes	—
66	C₂³	—	2	2	no	—
67	D₄	—	2	4	no	—
68	D₄	—	4	4	no	—
69	C₂×C₄	—	2	2	no	—
70	C₂×C₄	D₄×C₂₅	1	2	yes	—
71	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₅	C₅×#490	1	1	yes	characteristic
74	C₂²	—	4	2	no	—
75	C₂²	—	4	4	no	—
76	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	4	2	no	—
79	C₄	#41×C₂₅	1	2	yes	—
80	C₂	—	8	2	no	—
81	C₂	C₂₅×#124	1	1	yes	characteristic
82	C₂	C₂₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle	C₂²×C₅	C₂×C₅×D₄
prime radical	C₅×#127	C₂×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₄²×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₅×#125	C₂	semidirect
3. C₂₅×#102	C₂	semidirect
4. C₂₅×#97	C₂	semidirect
35. #490	C₂₅	direct (N × H)
47. #125	C₂×C₂₅	semidirect
48. #102	C₂×C₂₅	semidirect
49. #97	C₂×C₂₅	semidirect
50. C₂₅	#490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×#127	2
C₂₅×#125	2
C₂₅×#102	2
C₂₅×#97	2
C₅×#490	5

Subgroups — C25×#490 #13098639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#490 #13098639