Subgroups — C₂×#11716366 #13098379

Order 1600.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₅	C₂	1	2	yes	maximal
3	#11716366	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
5	C₂²×Dic₂₅	—	2	2	no	—
6	C₂×C₈×C₂₅	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₄⋊Dic₂₅	—	2	2	no	—
9	C₄⋊Dic₂₅	C₂²	1	4	yes	—
10	C₂×#3949	—	5	1	no	maximal
11	C₂³×C₂₅	D₄	1	1	yes	characteristic
12	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₂₅	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₅	Q₈	1	2	yes	—
15	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₅	—	2	4	no	—
17	C₂×Dic₂₅	—	4	4	no	—
18	C₈×C₂₅	C₂×C₄	1	4	yes	complemented
19	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
20	C₂×C₄⋊Dic₅	—	5	2	no	—
21	#3949	—	5	4	no	—
22	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₅	SD₁₆	1	4	yes	—
24	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
25	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
26	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
28	Dic₂₅	—	4	4	no	—
29	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
30	C₂²×Dic₅	—	10	2	no	—
31	C₂×C₅×C₈	Dic₅	1	4	yes	—
32	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
33	C₄⋊Dic₅	—	5	4	no	—
34	C₄⋊Dic₅	—	10	2	no	—
35	C₂×#106	—	25	1	no	Sylow
36	C₂×C₂₅	#106	1	4	yes	complemented
37	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₂₅	C₂×SD₁₆	1	2	yes	—
39	C₂³×C₅	D₂₀	1	1	yes	characteristic
40	C₂×C₄×C₅	Dic₁₀	1	2	yes	—
41	C₂×C₄×C₅	D₂₀	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂×Dic₅	1	2	yes	—
43	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
44	C₂×Dic₅	—	10	4	no	—
45	C₂×Dic₅	—	20	4	no	—
46	C₅×C₈	C₂×Dic₅	1	4	yes	—
47	C₂²×C₈	D₂₅	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	25	2	no	—
49	#106	—	25	4	no	—
50	C₂₅	C₂×#106	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	#677	1	4	yes	—
52	C₂²×C₅	C₄⋊Dic₅	1	2	yes	—
53	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
54	C₄×C₅	C₄⋊Dic₅	1	2	yes	—
55	C₄×C₅	C₂×Dic₁₀	1	1	yes	characteristic
56	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
57	Dic₅	—	20	4	no	—
58	C₂²×C₄	—	50	2	no	—
59	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
60	C₂×C₈	Dic₂₅	1	4	yes	complemented
61	C₂×C₈	C₂×D₂₅	1	2	yes	—
62	C₄⋊C₄	—	25	4	no	—
63	C₄⋊C₄	—	50	2	no	—
64	C₂×C₅	#3949	1	4	yes	—
65	C₂×C₅	C₂×#677	1	2	yes	—
66	C₂×C₅	C₂×C₄⋊Dic₅	1	1	yes	characteristic
67	C₂³	D₁₀₀	1	1	yes	characteristic
68	C₂×C₄	—	50	4	no	—
69	C₂×C₄	—	100	4	no	—
70	C₂×C₄	Dic₅₀	1	2	yes	—
71	C₂×C₄	D₁₀₀	1	1	yes	characteristic
72	C₂×C₄	C₂×Dic₂₅	1	2	yes	—
73	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
74	C₈	C₂×Dic₂₅	1	4	yes	complemented
75	C₅	C₂×#3949	1	1	yes	characteristic
76	C₂²	#87713	1	4	yes	—
77	C₂²	C₄⋊Dic₂₅	1	2	yes	—
78	C₂²	C₂×D₁₀₀	1	1	yes	characteristic
79	C₄	—	100	4	no	—
80	C₄	C₄⋊Dic₂₅	1	2	yes	—
81	C₄	C₂×Dic₅₀	1	1	yes	characteristic
82	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
83	C₂	#11716366	1	4	yes	direct product factor
84	C₂	C₂×#87713	1	2	yes	—
85	C₂	C₂×C₄⋊Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₀₀
commutator	C₄×C₂₅	C₂²×C₄
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂²×C₈×C₂₅	C₂
socle, prime radical	C₂³×C₅	D₂₀
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₂²×C₈	D₂₅
hypocenter	C₂₅	C₂×#106
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #11716366	C₂	direct (N × H)
6. C₂×C₈×C₂₅	C₄	semidirect
18. C₈×C₂₅	C₂×C₄	semidirect
36. C₂×C₂₅	#106	semidirect
50. C₂₅	C₂×#106	semidirect
60. C₂×C₈	Dic₂₅	semidirect
74. C₈	C₂×Dic₂₅	semidirect
83. C₂	#11716366	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₅	2
C₂×C₄⋊Dic₂₅	2
#11716366	2
C₂×#3949	5

Subgroups — C2×#11716366 #13098379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716366 #13098379