Subgroups — C₈×Q₈×C₂₅ #13098594

Order 1600.

153 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₄⋊C₈	C₂	1	3	yes	maximal
3	C₄×C₈×C₂₅	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₅	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₅	C₂²	1	3	yes	—
6	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₅	C₄	1	3	yes	—
8	C₄²×C₂₅	C₂²	1	3	yes	—
9	C₅×C₈×Q₈	C₅	1	1	yes	maximal, characteristic
10	Q₈×C₂₅	C₈	1	4	yes	direct product factor
11	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
14	C₈×C₂₅	—	2	3	no	—
15	C₈×C₂₅	Q₈	1	2	yes	direct product factor
16	C₄×C₅×Q₈	C₂×C₅	1	1	yes	characteristic
17	C₅×C₄⋊C₈	C₂×C₅	1	3	yes	—
18	C₄×C₅×C₈	C₂×C₅	1	3	yes	—
19	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₂₅	—	2	3	no	—
21	C₄×C₂₅	C₂×C₈	1	6	yes	—
22	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₂₅	#41	1	1	yes	characteristic
24	C₂×C₅×Q₈	C₄×C₅	1	1	yes	characteristic
25	C₂×C₅×C₈	C₂²×C₅	1	3	yes	—
26	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic
27	C₅×C₄⋊C₄	C₄×C₅	1	3	yes	—
28	C₄²×C₅	C₂²×C₅	1	3	yes	—
29	C₈×Q₈	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₂₅	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₂₅	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₂₅	#131	1	1	yes	characteristic
33	C₅×Q₈	C₅×C₈	1	4	yes	—
34	C₂×C₄×C₅	C₂×C₄×C₅	1	3	yes	—
35	C₂×C₄×C₅	C₂×C₄×C₅	1	3	yes	—
36	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
37	C₅×C₈	—	2	3	no	—
38	C₅×C₈	C₅×Q₈	1	2	yes	—
39	C₄×Q₈	C₂×C₂₅	1	1	yes	characteristic
40	C₄⋊C₈	C₂×C₂₅	1	3	yes	—
41	C₄×C₈	C₂×C₂₅	1	3	yes	—
42	C₂₅	C₈×Q₈	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
44	C₄×C₅	—	2	3	no	—
45	C₄×C₅	C₂×C₅×C₈	1	6	yes	—
46	C₄×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
47	C₄×C₅	C₅×#41	1	1	yes	characteristic
48	C₂×Q₈	C₄×C₂₅	1	1	yes	characteristic
49	C₂×C₈	C₂²×C₂₅	1	3	yes	—
50	C₂×C₈	C₂²×C₂₅	1	1	yes	characteristic
51	C₄⋊C₄	C₄×C₂₅	1	3	yes	—
52	C₄²	C₂²×C₂₅	1	3	yes	—
53	C₂×C₅	C₄×C₅×Q₈	1	1	yes	characteristic
54	C₂×C₅	C₂²×C₅×C₈	1	1	yes	characteristic
55	C₂×C₅	C₅×#131	1	1	yes	characteristic
56	Q₈	C₈×C₂₅	1	4	yes	direct product factor
57	C₂×C₄	C₂×C₄×C₂₅	1	3	yes	—
58	C₂×C₄	C₂×C₄×C₂₅	1	3	yes	—
59	C₂×C₄	C₂³×C₂₅	1	1	yes	characteristic
60	C₈	—	2	3	no	—
61	C₈	Q₈×C₂₅	1	2	yes	direct product factor
62	C₅	C₅×C₈×Q₈	1	1	yes	characteristic
63	C₂²	C₂²×C₄×C₂₅	1	1	yes	characteristic
64	C₄	—	2	3	no	—
65	C₄	C₂×C₈×C₂₅	1	6	yes	—
66	C₄	C₂×Q₈×C₂₅	1	1	yes	characteristic
67	C₄	#41×C₂₅	1	1	yes	characteristic
68	C₂	C₄×Q₈×C₂₅	1	1	yes	characteristic
69	C₂	C₂²×C₈×C₂₅	1	1	yes	characteristic
70	C₂	C₂₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₅	C₂²
commutator	C₂	C₂²×C₈×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂³×C₅
socle, prime radical	C₂²×C₅	C₂²×C₄×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
10. Q₈×C₂₅	C₈	direct (N × H)
15. C₈×C₂₅	Q₈	direct (N × H)
29. C₈×Q₈	C₂₅	direct (N × H)
42. C₂₅	C₈×Q₈	direct (N × H)
56. Q₈	C₈×C₂₅	direct (N × H)
61. C₈	Q₈×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
C₄×Q₈×C₂₅	2
C₂₅×C₄⋊C₈	2
C₄×C₈×C₂₅	2
C₅×C₈×Q₈	5

Subgroups — C8×Q8×C25 #13098594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×Q₈×C₂₅ #13098594