Subgroups — C₂₅×#427 #13098576

Order 1600.

171 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#117	C₂	1	2	yes	maximal
3	C₂₅×#107	C₂	1	2	yes	maximal, complemented
4	C₂₅×#106	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₅	C₂²	1	4	yes	—
10	C₂²⋊C₄×C₂₅	—	2	2	no	—
11	C₄²×C₂₅	—	2	2	no	—
12	C₅×#427	C₅	1	1	yes	maximal, characteristic
13	C₂³×C₂₅	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅	—	2	4	no	—
15	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₅	Q₈	1	2	yes	—
18	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
19	C₈×C₂₅	C₂×C₄	1	2	yes	—
20	C₈×C₂₅	C₂×C₄	1	2	yes	—
21	C₂²×C₅×C₈	C₂×C₅	1	1	yes	characteristic
22	C₅×#117	C₂×C₅	1	2	yes	—
23	C₅×#107	C₂×C₅	1	2	yes	—
24	C₅×#106	C₂×C₅	1	2	yes	—
25	C₂²×C₂₅	—	2	2	no	—
26	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
27	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₅	—	4	4	no	—
29	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
30	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
32	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
33	C₂×C₅×C₈	C₄×C₅	1	4	yes	—
34	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
35	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
36	C₅×C₄⋊C₄	C₂²×C₅	1	4	yes	—
37	C₅×C₂²⋊C₄	—	2	2	no	—
38	C₄²×C₅	—	2	2	no	—
39	#427	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₂₅	—	2	2	no	—
41	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₂₅	#135	1	2	yes	—
43	C₂³×C₅	C₅×D₄	1	1	yes	characteristic
44	C₂×C₄×C₅	—	2	4	no	—
45	C₂×C₄×C₅	C₂×C₄×C₅	1	2	yes	—
46	C₂×C₄×C₅	C₅×D₄	1	1	yes	characteristic
47	C₂×C₄×C₅	C₅×Q₈	1	2	yes	—
48	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
49	C₅×C₈	C₂×C₄×C₅	1	2	yes	—
50	C₅×C₈	C₂×C₄×C₅	1	2	yes	—
51	C₂²×C₈	C₂×C₂₅	1	1	yes	characteristic
52	#117	C₂×C₂₅	1	2	yes	—
53	#107	C₂×C₂₅	1	2	yes	complemented
54	#106	C₂×C₂₅	1	2	yes	complemented
55	C₂₅	#427	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₅	—	2	2	no	—
57	C₂²×C₅	C₅×C₄⋊C₄	1	2	yes	—
58	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
59	C₄×C₅	—	4	4	no	—
60	C₄×C₅	C₅×C₄⋊C₄	1	2	yes	—
61	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
62	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
63	C₂²×C₄	C₂²×C₂₅	1	1	yes	characteristic
64	C₂×C₈	C₄×C₂₅	1	4	yes	complemented
65	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
66	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
67	C₄⋊C₄	C₂²×C₂₅	1	4	yes	—
68	C₂²⋊C₄	—	2	2	no	—
69	C₄²	—	2	2	no	—
70	C₂×C₅	—	2	2	no	—
71	C₂×C₅	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₅	C₅×#135	1	2	yes	—
73	C₂³	D₄×C₂₅	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₂×C₄×C₂₅	1	2	yes	—
76	C₂×C₄	D₄×C₂₅	1	1	yes	characteristic
77	C₂×C₄	Q₈×C₂₅	1	2	yes	—
78	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
79	C₈	C₂×C₄×C₂₅	1	2	yes	—
80	C₈	C₂×C₄×C₂₅	1	2	yes	—
81	C₅	C₅×#427	1	1	yes	characteristic
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊C₄×C₂₅	1	2	yes	—
84	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
85	C₄	—	4	4	no	—
86	C₄	C₄⋊C₄×C₂₅	1	2	yes	—
87	C₄	C₂²×C₄×C₂₅	1	1	yes	characteristic
88	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
89	C₂	—	2	2	no	—
90	C₂	C₂×C₄⋊C₄×C₂₅	1	1	yes	characteristic
91	C₂	C₂₅×#135	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂₅×#107	C₂	semidirect
4. C₂₅×#106	C₂	semidirect
6. C₂×C₈×C₂₅	C₄	semidirect
39. #427	C₂₅	direct (N × H)
53. #107	C₂×C₂₅	semidirect
54. #106	C₂×C₂₅	semidirect
55. C₂₅	#427	direct (N × H)
64. C₂×C₈	C₄×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₅	2
C₂₅×#117	2
C₂₅×#107	2
C₂₅×#106	2
C₅×#427	5

Subgroups — C25×#427 #13098576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#427 #13098576