Subgroups — C₂×#11716367 #13098380

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	#11716367	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×#3950	—	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	#3950	—	5	4	no	—
22	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
23	C₂²×C₂₅	D₈	1	2	yes	—
24	C₂²×C₂₅	Q₁₆	1	2	yes	—
25	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
27	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
29	Dic₂₅	—	4	4	no	—
30	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
31	C₂²×Dic₅	—	10	2	no	—
32	C₂×C₅×C₈	Dic₅	1	4	yes	—
33	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
34	C₄⋊Dic₅	—	5	4	no	—
35	C₄⋊Dic₅	—	10	2	no	—
36	C₂×#107	—	25	1	no	Sylow
37	C₂×C₂₅	#107	1	4	yes	complemented
38	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₂₅	C₂×D₈	1	1	yes	characteristic
40	C₂×C₂₅	C₂×Q₁₆	1	1	yes	characteristic
41	C₂³×C₅	D₂₀	1	1	yes	characteristic
42	C₂×C₄×C₅	Dic₁₀	1	2	yes	—
43	C₂×C₄×C₅	D₂₀	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×Dic₅	1	2	yes	—
45	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
46	C₂×Dic₅	—	10	4	no	—
47	C₂×Dic₅	—	20	4	no	—
48	C₅×C₈	C₂×Dic₅	1	4	yes	—
49	C₂²×C₈	D₂₅	1	1	yes	characteristic
50	C₂×C₄⋊C₄	—	25	2	no	—
51	#107	—	25	4	no	—
52	C₂₅	C₂×#107	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₅	D₄₀	1	2	yes	—
54	C₂²×C₅	Dic₂₀	1	2	yes	—
55	C₂²×C₅	C₄⋊Dic₅	1	2	yes	—
56	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
57	C₄×C₅	C₄⋊Dic₅	1	2	yes	—
58	C₄×C₅	C₂×Dic₁₀	1	1	yes	characteristic
59	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
60	Dic₅	—	20	4	no	—
61	C₂²×C₄	—	50	2	no	—
62	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
63	C₂×C₈	Dic₂₅	1	4	yes	complemented
64	C₂×C₈	C₂×D₂₅	1	2	yes	—
65	C₄⋊C₄	—	25	4	no	—
66	C₄⋊C₄	—	50	2	no	—
67	C₂×C₅	#3950	1	4	yes	—
68	C₂×C₅	C₂×D₄₀	1	1	yes	characteristic
69	C₂×C₅	C₂×Dic₂₀	1	1	yes	characteristic
70	C₂×C₅	C₂×C₄⋊Dic₅	1	1	yes	characteristic
71	C₂³	D₁₀₀	1	1	yes	characteristic
72	C₂×C₄	—	50	4	no	—
73	C₂×C₄	—	100	4	no	—
74	C₂×C₄	Dic₅₀	1	2	yes	—
75	C₂×C₄	D₁₀₀	1	1	yes	characteristic
76	C₂×C₄	C₂×Dic₂₅	1	2	yes	—
77	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
78	C₈	C₂×Dic₂₅	1	4	yes	complemented
79	C₅	C₂×#3950	1	1	yes	characteristic
80	C₂²	Dic₁₀₀	1	2	yes	—
81	C₂²	D₂₀₀	1	2	yes	—
82	C₂²	C₄⋊Dic₂₅	1	2	yes	—
83	C₂²	C₂×D₁₀₀	1	1	yes	characteristic
84	C₄	—	100	4	no	—
85	C₄	C₄⋊Dic₂₅	1	2	yes	—
86	C₄	C₂×Dic₅₀	1	1	yes	characteristic
87	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
88	C₂	#11716367	1	4	yes	direct product factor
89	C₂	C₂×Dic₁₀₀	1	1	yes	characteristic
90	C₂	C₂×D₂₀₀	1	1	yes	characteristic
91	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×#107
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. #11716367	C₂	direct (N × H)
6. C₂×C₈×C₂₅	C₄	semidirect
18. C₈×C₂₅	C₂×C₄	semidirect
37. C₂×C₂₅	#107	semidirect
52. C₂₅	C₂×#107	semidirect
63. C₂×C₈	Dic₂₅	semidirect
78. C₈	C₂×Dic₂₅	semidirect
88. C₂	#11716367	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
#11716367	2
C₂×#3950	5

Subgroups — C2×#11716367 #13098380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716367 #13098380