Subgroups — C₂₅×#488 #13098637

Order 1600.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₂₅×#103	C₂	1	2	yes	maximal, complemented
4	C₂₅×#102	C₂	1	2	yes	maximal
5	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₂₅	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₂₅	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₅	C₂²	1	2	yes	—
9	C₄⋊C₄×C₂₅	—	2	2	no	—
10	C₄⋊C₄×C₂₅	C₂²	1	2	yes	—
11	C₂²⋊C₄×C₂₅	—	2	2	no	—
12	C₄²×C₂₅	C₂²	1	1	yes	characteristic
13	C₅×#488	C₅	1	1	yes	maximal, characteristic
14	C₂³×C₂₅	—	2	1	no	—
15	Q₈×C₂₅	—	2	2	no	—
16	D₄×C₂₅	—	2	2	no	—
17	C₂×C₄×C₂₅	—	2	1	no	—
18	C₂×C₄×C₂₅	—	2	2	no	—
19	C₂×C₄×C₂₅	D₄	1	2	yes	—
20	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
21	C₈×C₂₅	—	2	2	no	—
22	C₅×#125	C₂×C₅	1	1	yes	characteristic
23	C₅×#124	C₂×C₅	1	1	yes	characteristic
24	C₅×#103	C₂×C₅	1	2	yes	—
25	C₅×#102	C₂×C₅	1	2	yes	—
26	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
27	C₂²×C₂₅	—	4	1	no	—
28	C₂²×C₂₅	—	4	2	no	—
29	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₅	—	2	2	no	—
31	C₄×C₂₅	—	4	1	no	—
32	C₄×C₂₅	—	4	2	no	—
33	C₄×C₂₅	#41	1	2	yes	—
34	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic
35	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
36	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
37	C₅×C₄⋊C₄	—	2	2	no	—
38	C₅×C₄⋊C₄	C₂²×C₅	1	2	yes	—
39	C₅×C₂²⋊C₄	—	2	2	no	—
40	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
41	#488	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₂₅	—	8	1	no	—
43	C₂×C₂₅	#124	1	1	yes	characteristic
44	C₂×C₂₅	#135	1	2	yes	—
45	C₂³×C₅	—	2	1	no	—
46	C₅×Q₈	—	2	2	no	—
47	C₅×D₄	—	2	2	no	—
48	C₂×C₄×C₅	—	2	1	no	—
49	C₂×C₄×C₅	—	2	2	no	—
50	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
51	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
52	C₅×C₈	—	2	2	no	—
53	#125	C₂×C₂₅	1	1	yes	characteristic, complemented
54	#124	C₂×C₂₅	1	1	yes	characteristic
55	#103	C₂×C₂₅	1	2	yes	complemented
56	#102	C₂×C₂₅	1	2	yes	—
57	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic, complemented
58	C₂₅	#488	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²×C₅	—	4	1	no	—
60	C₂²×C₅	—	4	2	no	—
61	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	—	4	1	no	—
64	C₄×C₅	—	4	2	no	—
65	C₄×C₅	C₅×#41	1	2	yes	—
66	C₂×Q₈	C₂²×C₂₅	1	1	yes	characteristic
67	C₂×D₄	C₂²×C₂₅	1	1	yes	characteristic
68	C₂×C₈	C₂²×C₂₅	1	2	yes	—
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	C₂²×C₂₅	1	2	yes	—
71	C₂²⋊C₄	—	2	2	no	—
72	C₄²	C₂²×C₂₅	1	1	yes	characteristic
73	C₂×C₅	—	8	1	no	—
74	C₂×C₅	C₅×#124	1	1	yes	characteristic
75	C₂×C₅	C₅×#135	1	2	yes	—
76	C₂³	—	2	1	no	—
77	Q₈	—	2	2	no	—
78	D₄	—	2	2	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	D₄×C₂₅	1	2	yes	—
82	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₅	C₅×#488	1	1	yes	characteristic
85	C₂²	—	4	1	no	—
86	C₂²	—	4	2	no	—
87	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	4	1	no	—
90	C₄	—	4	2	no	—
91	C₄	#41×C₂₅	1	2	yes	—
92	C₂	—	8	1	no	—
93	C₂	C₂₅×#124	1	1	yes	characteristic
94	C₂	C₂₅×#135	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	C₂×C₅×D₄	C₂²×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
1. C₂₅×#125	C₂	semidirect
3. C₂₅×#103	C₂	semidirect
5. C₄×C₈×C₂₅	C₂	semidirect
41. #488	C₂₅	direct (N × H)
53. #125	C₂×C₂₅	semidirect
55. #103	C₂×C₂₅	semidirect
57. C₄×C₈	C₂×C₂₅	semidirect
58. C₂₅	#488	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×#125	2
C₂₅×#124	2
C₂₅×#103	2
C₂₅×#102	2
C₄×C₈×C₂₅	2
C₅×#488	5

Subgroups — C25×#488 #13098637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#488 #13098637