Subgroups — C₂×SD₁₆×C₂₅ #11716535

Order 800.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₂₅	C₂	1	1	yes	maximal, characteristic
3	SD₁₆×C₂₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₂₅	—	2	1	no	—
6	Q₈×C₂₅	—	2	1	no	—
7	Q₈×C₂₅	C₂²	1	2	yes	complemented
8	D₄×C₂₅	—	2	1	no	—
9	D₄×C₂₅	C₂²	1	2	yes	—
10	C₂×C₄×C₂₅	—	2	1	no	—
11	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
12	C₈×C₂₅	C₂²	1	2	yes	complemented
13	C₂×C₅×SD₁₆	C₅	1	1	yes	maximal, characteristic
14	C₂²×C₂₅	—	2	2	no	—
15	C₂²×C₂₅	—	4	2	no	—
16	C₂²×C₂₅	D₄	1	1	yes	characteristic
17	C₄×C₂₅	—	2	2	no	—
18	C₄×C₂₅	D₄	1	1	yes	characteristic
19	C₄×C₂₅	C₂³	1	1	yes	characteristic
20	C₂×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
21	C₂×C₅×D₄	C₂×C₅	1	1	yes	characteristic
22	C₅×SD₁₆	C₂×C₅	1	4	yes	—
23	C₂×C₅×C₈	C₂×C₅	1	1	yes	characteristic
24	C₂×C₂₅	—	4	2	no	—
25	C₂×C₂₅	SD₁₆	1	2	yes	direct product factor
26	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
27	C₂³×C₅	—	2	1	no	—
28	C₅×Q₈	—	2	1	no	—
29	C₅×Q₈	C₂²×C₅	1	2	yes	—
30	C₅×D₄	—	2	1	no	—
31	C₅×D₄	C₂²×C₅	1	2	yes	—
32	C₂×C₄×C₅	—	2	1	no	—
33	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
34	C₅×C₈	C₂²×C₅	1	2	yes	—
35	C₂×SD₁₆	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂₅	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₅	—	2	2	no	—
38	C₂²×C₅	—	4	2	no	—
39	C₂²×C₅	C₅×D₄	1	1	yes	characteristic
40	C₄×C₅	—	2	2	no	—
41	C₄×C₅	C₅×D₄	1	1	yes	characteristic
42	C₄×C₅	C₂³×C₅	1	1	yes	characteristic
43	C₂×Q₈	C₂×C₂₅	1	1	yes	characteristic, complemented
44	C₂×D₄	C₂×C₂₅	1	1	yes	characteristic
45	SD₁₆	C₂×C₂₅	1	4	yes	direct product factor
46	C₂×C₈	C₂×C₂₅	1	1	yes	characteristic, complemented
47	C₂×C₅	—	4	2	no	—
48	C₂×C₅	C₅×SD₁₆	1	2	yes	—
49	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
50	C₂³	—	2	1	no	—
51	Q₈	—	2	1	no	—
52	Q₈	C₂²×C₂₅	1	2	yes	complemented
53	D₄	—	2	1	no	—
54	D₄	C₂²×C₂₅	1	2	yes	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	C₂²×C₂₅	1	1	yes	characteristic
57	C₈	C₂²×C₂₅	1	2	yes	complemented
58	C₅	C₂×C₅×SD₁₆	1	1	yes	characteristic
59	C₂²	—	2	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	D₄×C₂₅	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	D₄×C₂₅	1	1	yes	characteristic
64	C₄	C₂³×C₂₅	1	1	yes	characteristic
65	C₂	—	4	2	no	—
66	C₂	SD₁₆×C₂₅	1	2	yes	direct product factor
67	C₂	C₂×D₄×C₂₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₂₅	C₂	semidirect
3. SD₁₆×C₂₅	C₂	direct (N × H)
4. C₂×C₈×C₂₅	C₂	semidirect
7. Q₈×C₂₅	C₂²	semidirect
12. C₈×C₂₅	C₂²	semidirect
25. C₂×C₂₅	SD₁₆	direct (N × H)
35. C₂×SD₁₆	C₂₅	direct (N × H)
36. C₂₅	C₂×SD₁₆	direct (N × H)
43. C₂×Q₈	C₂×C₂₅	semidirect
45. SD₁₆	C₂×C₂₅	direct (N × H)
46. C₂×C₈	C₂×C₂₅	semidirect
52. Q₈	C₂²×C₂₅	semidirect
57. C₈	C₂²×C₂₅	semidirect
66. C₂	SD₁₆×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₂₅	2
C₂×D₄×C₂₅	2
SD₁₆×C₂₅	2
C₂×C₈×C₂₅	2
C₂×C₅×SD₁₆	5

Subgroups — C2×SD16×C25 #11716535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×SD₁₆×C₂₅ #11716535