Subgroups — #13097753

Order 1600.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6014	C₂	1	2	yes	maximal
3	C₂×Q₈×C₂₅	C₄	1	2	yes	—
4	C₄⋊C₄×C₂₅	—	2	2	no	—
5	C₄²×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×#6014	—	2	2	no	—
7	#64766	—	5	1	no	maximal
8	Q₈×C₂₅	—	4	2	no	—
9	C₂×C₄×C₂₅	—	2	2	no	—
10	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₅	D₄	1	2	yes	—
12	#6014	—	4	2	no	—
13	C₅×C₄⋊Q₈	D₅	1	1	yes	characteristic
14	C₄⋊#168	—	5	2	no	—
15	C₂²×C₂₅	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₂₅	—	2	1	no	—
17	C₄×C₂₅	—	4	2	no	—
18	C₄×C₂₅	SD₁₆	1	2	yes	—
19	C₄×C₂₅	Q₁₆	1	2	yes	—
20	C₂×C₅×Q₈	Dic₅	1	2	yes	—
21	C₅×C₄⋊C₄	—	2	2	no	—
22	C₄²×C₅	C₂×D₅	1	1	yes	characteristic
23	C₂×#168	—	10	2	no	—
24	#333	—	25	1	no	Sylow
25	C₂×C₂₅	#100	1	1	yes	characteristic
26	C₂×C₂₅	#103	1	2	yes	—
27	C₅×Q₈	—	4	2	no	—
28	C₂×C₄×C₅	—	2	2	no	—
29	C₂×C₄×C₅	C₂×Dic₅	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
31	#168	—	20	2	no	—
32	C₄⋊Q₈	D₂₅	1	1	yes	characteristic
33	C₄⋊C₈	—	25	2	no	—
34	C₂₅	#333	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₅	C₂²⋊Dic₅	1	1	yes	characteristic
36	C₄×C₅	—	2	1	no	—
37	C₄×C₅	—	4	2	no	—
38	C₄×C₅	#688	1	2	yes	—
39	C₄×C₅	#689	1	2	yes	—
40	C₂×Q₈	Dic₂₅	1	2	yes	—
41	C₂×C₈	—	50	2	no	—
42	C₄⋊C₄	—	2	2	no	—
43	C₄²	C₂×D₂₅	1	1	yes	characteristic
44	C₂×C₅	#3965	1	1	yes	characteristic
45	C₂×C₅	#3967	1	2	yes	—
46	Q₈	—	4	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	C₂×Dic₂₅	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₂₅	1	2	yes	—
50	C₈	—	100	2	no	—
51	C₅	#64766	1	1	yes	characteristic
52	C₂²	C₂²⋊Dic₂₅	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	2	no	—
55	C₄	#87723	1	2	yes	—
56	C₄	#87724	1	2	yes	—
57	C₂	#11716380	1	1	yes	characteristic
58	C₂	#11716384	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²⋊Dic₂₅
commutator	C₂×C₄×C₂₅	C₂×C₄
Frattini	C₄²×C₅	C₂×D₅
Fitting	C₂₅×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₅	C₂²⋊Dic₅
cosocle	C₄²×C₂₅	C₂²
hypercenter	C₄⋊Q₈	D₂₅
hypocenter	C₂₅	#333
LCS	G ▷ C₂×C₄×C₂₅ ▷ C₂²×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
34. C₂₅	#333	semidirect

Maximal subgroups

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

subgroup	index
C₂₅×C₄⋊Q₈	2
C₄⋊#6014	2
#64766	5