Subgroups — #13097877

Order 1600.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#6016	C₂	1	2	yes	maximal
2	C₈×Dic₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#6016	—	2	2	no	—
4	C₂×C₈×C₂₅	C₄	1	1	yes	characteristic
5	C₄×Dic₂₅	C₂²	1	1	yes	characteristic
6	C₂×#6014	C₄	1	1	yes	characteristic
7	#64884	—	5	1	no	maximal
8	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₂₅	D₄	1	1	yes	characteristic
10	C₂×Dic₂₅	Q₈	1	1	yes	characteristic
11	#6016	—	4	2	no	—
12	C₈×C₂₅	—	2	1	no	—
13	#6014	C₈	1	2	yes	complemented
14	C₄⋊#170	—	5	2	no	—
15	C₈×Dic₅	—	5	1	no	—
16	C₂²×C₂₅	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₅	C₂×C₈	1	1	yes	characteristic
18	C₄×C₂₅	M₁₆	1	1	yes	characteristic
19	Dic₂₅	—	2	1	no	—
20	Dic₂₅	D₈	1	1	yes	characteristic
21	Dic₂₅	Q₁₆	1	1	yes	characteristic
22	C₂×#170	—	10	2	no	—
23	C₂×C₅×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₄×Dic₅	—	5	1	no	—
25	C₂×#168	—	5	1	no	—
26	#335	—	25	1	no	Sylow
27	C₂×C₂₅	C₄⋊C₈	1	1	yes	characteristic
28	C₂×C₂₅	#107	1	1	yes	characteristic
29	C₂×C₂₅	#108	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₂×Dic₅	—	5	1	no	—
32	C₂×Dic₅	—	5	1	no	—
33	#170	—	20	2	no	—
34	C₅×C₈	—	2	1	no	—
35	#168	—	5	2	no	—
36	C₄⋊C₈	—	25	2	no	—
37	C₄×C₈	—	25	1	no	—
38	C₂₅	#335	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₅	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₄×C₅	D₅⋊C₈	1	1	yes	characteristic
41	C₄×C₅	#704	1	1	yes	characteristic
42	Dic₅	—	5	1	no	—
43	Dic₅	—	5	1	no	—
44	Dic₅	—	10	1	no	—
45	C₂×C₈	—	25	1	no	—
46	C₂×C₈	—	50	2	no	—
47	C₂×C₈	#1035	1	1	yes	characteristic
48	C₄²	—	25	1	no	—
49	C₂×C₅	#3994	1	1	yes	characteristic
50	C₂×C₅	#3995	1	1	yes	characteristic
51	C₂×C₅	#4004	1	1	yes	characteristic
52	C₂×C₄	—	25	1	no	—
53	C₂×C₄	—	25	1	no	—
54	C₂×C₄	C₂×#1035	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	—	25	2	no	—
57	C₈	—	100	2	no	—
58	C₅	#64884	1	1	yes	characteristic
59	C₂²	C₄⋊#1035	1	1	yes	characteristic
60	C₄	—	25	1	no	—
61	C₄	—	25	1	no	—
62	C₄	—	50	1	no	—
63	C₄	D₂₅⋊C₈	1	1	yes	characteristic
64	C₄	#87739	1	1	yes	characteristic
65	C₂	#11716407	1	1	yes	characteristic
66	C₂	#11716412	1	1	yes	characteristic
67	C₂	#11716419	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#1035
commutator	C₄×C₂₅	C₂×C₈
Frattini	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₈×C₂₅	C₄
socle, prime radical	C₂²×C₅	C₄⋊AGL(1,𝔽₅)
cosocle	C₄×Dic₂₅	C₂²
hypercenter	C₂×C₈	#1035
hypocenter	C₂₅	#335
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
13. #6014	C₈	semidirect
38. C₂₅	#335	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#6016	2
C₈×Dic₂₅	2
#64884	5