Subgroups — C₂₅×#492 #13098641

Order 1600.

213 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×C₂₅	C₂	1	4	yes	maximal, complemented
2	C₂₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×#127	C₂	1	1	yes	maximal, characteristic
4	C₄×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₂₅	C₂²	1	2	yes	—
6	C₂×D₄×C₂₅	—	2	2	no	—
7	C₂×D₄×C₂₅	C₂²	1	2	yes	—
8	SD₁₆×C₂₅	—	2	8	no	—
9	C₂×C₈×C₂₅	C₂²	1	2	yes	—
10	C₄⋊C₄×C₂₅	—	2	2	no	—
11	C₄²×C₂₅	C₂²	1	1	yes	characteristic
12	C₅×#492	C₅	1	1	yes	maximal, characteristic
13	C₂³×C₂₅	—	2	2	no	—
14	Q₈×C₂₅	—	2	4	no	—
15	D₄×C₂₅	—	2	4	no	—
16	D₄×C₂₅	—	4	4	no	—
17	C₂×C₄×C₂₅	—	2	2	no	—
18	C₂×C₄×C₂₅	D₄	1	2	yes	—
19	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
20	C₈×C₂₅	D₄	1	4	yes	complemented
21	C₂×C₅×SD₁₆	C₂×C₅	1	4	yes	—
22	C₅×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
23	C₅×#127	C₂×C₅	1	1	yes	characteristic
24	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
25	C₂²×C₂₅	—	4	2	no	—
26	C₂²×C₂₅	—	4	4	no	—
27	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₅	—	4	2	no	—
29	C₄×C₂₅	SD₁₆	1	4	yes	complemented
30	C₄×C₂₅	C₂×D₄	1	2	yes	—
31	C₂×C₅×Q₈	C₂²×C₅	1	2	yes	—
32	C₂×C₅×D₄	—	2	2	no	—
33	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
34	C₅×SD₁₆	—	2	8	no	—
35	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
36	C₅×C₄⋊C₄	—	2	2	no	—
37	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
38	#492	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₂₅	—	8	2	no	—
40	C₂×C₂₅	#127	1	1	yes	characteristic
41	C₂×C₂₅	C₂×SD₁₆	1	2	yes	—
42	C₂³×C₅	—	2	2	no	—
43	C₅×Q₈	—	2	4	no	—
44	C₅×D₄	—	2	4	no	—
45	C₅×D₄	—	4	4	no	—
46	C₂×C₄×C₅	—	2	2	no	—
47	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
48	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
49	C₅×C₈	C₅×D₄	1	4	yes	—
50	C₂×SD₁₆	C₂×C₂₅	1	4	yes	complemented
51	C₄⋊Q₈	C₂×C₂₅	1	1	yes	characteristic, complemented
52	#127	C₂×C₂₅	1	1	yes	characteristic
53	C₄×C₈	C₂×C₂₅	1	1	yes	characteristic, complemented
54	C₂₅	#492	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	—	4	2	no	—
56	C₂²×C₅	—	4	4	no	—
57	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
58	C₄×C₅	—	4	2	no	—
59	C₄×C₅	C₅×SD₁₆	1	4	yes	—
60	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
61	C₂×Q₈	C₂²×C₂₅	1	2	yes	—
62	C₂×D₄	—	2	2	no	—
63	C₂×D₄	C₂²×C₂₅	1	2	yes	—
64	SD₁₆	—	2	8	no	—
65	C₂×C₈	C₂²×C₂₅	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄²	C₂²×C₂₅	1	1	yes	characteristic
68	C₂×C₅	—	8	2	no	—
69	C₂×C₅	C₅×#127	1	1	yes	characteristic
70	C₂×C₅	C₂×C₅×SD₁₆	1	2	yes	—
71	C₂³	—	2	2	no	—
72	Q₈	—	2	4	no	—
73	D₄	—	2	4	no	—
74	D₄	—	4	4	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	D₄×C₂₅	1	2	yes	—
77	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
78	C₈	D₄×C₂₅	1	4	yes	complemented
79	C₅	C₅×#492	1	1	yes	characteristic
80	C₂²	—	4	2	no	—
81	C₂²	—	4	4	no	—
82	C₂²	C₂×D₄×C₂₅	1	1	yes	characteristic
83	C₄	—	4	2	no	—
84	C₄	SD₁₆×C₂₅	1	4	yes	complemented
85	C₄	C₂×D₄×C₂₅	1	2	yes	—
86	C₂	—	8	2	no	—
87	C₂	C₂₅×#127	1	1	yes	characteristic
88	C₂	C₂×SD₁₆×C₂₅	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
1. C₂×SD₁₆×C₂₅	C₂	semidirect
2. C₂₅×C₄⋊Q₈	C₂	semidirect
4. C₄×C₈×C₂₅	C₂	semidirect
20. C₈×C₂₅	D₄	semidirect
29. C₄×C₂₅	SD₁₆	semidirect
38. #492	C₂₅	direct (N × H)
50. C₂×SD₁₆	C₂×C₂₅	semidirect
51. C₄⋊Q₈	C₂×C₂₅	semidirect
53. C₄×C₈	C₂×C₂₅	semidirect
54. C₂₅	#492	direct (N × H)
78. C₈	D₄×C₂₅	semidirect
84. C₄	SD₁₆×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×C₂₅	2
C₂₅×C₄⋊Q₈	2
C₂₅×#127	2
C₄×C₈×C₂₅	2
C₅×#492	5

Subgroups — C25×#492 #13098641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×#492 #13098641