Subgroups — C₂×#11716552 #13099671

Order 1600.

399 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87748	C₂	1	1	yes	maximal, characteristic
2	#11716552	C₂	1	8	yes	maximal, direct product factor
3	C₂×#87735	C₂	1	3	yes	maximal, complemented
4	C₂×D₂₅⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×C₂₅	C₄	1	1	yes	characteristic
6	#87748	C₄	1	4	yes	—
7	#87748	C₂²	1	4	yes	—
8	C₂×D₁₀₀	C₄	1	3	yes	—
9	C₂×C₄×D₂₅	C₂²	1	3	yes	—
10	C₂×#6016	C₂²	1	1	yes	characteristic
11	C₂×#6016	C₂²	1	3	yes	—
12	#87735	C₂²	1	12	yes	complemented
13	D₂₅⋊C₈	C₂²	1	12	yes	complemented
14	C₂×#4133	—	5	1	no	maximal
15	C₂²×D₂₅	C₂×C₄	1	3	yes	—
16	Q₈×C₂₅	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
18	C₂×Dic₂₅	C₂³	1	1	yes	characteristic
19	D₁₀₀	C₂×C₄	1	12	yes	—
20	C₄×D₂₅	C₂×C₄	1	6	yes	—
21	C₄×D₂₅	C₂³	1	6	yes	—
22	#6016	C₂³	1	2	yes	—
23	#6016	C₂³	1	6	yes	—
24	C₂×#713	—	5	1	no	—
25	#4133	—	5	8	no	—
26	C₂×#700	—	5	3	no	—
27	C₂×D₅⋊C₈	—	5	3	no	—
28	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₂₅	—	2	6	no	—
30	C₂×D₂₅	C₂²×C₄	1	6	yes	—
31	C₄×C₂₅	C₂²×C₄	1	6	yes	—
32	Dic₂₅	C₂²×C₄	1	1	yes	characteristic
33	Dic₂₅	C₂⁴	1	1	yes	characteristic
34	C₂×C₅×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
35	#713	—	5	4	no	—
36	#713	—	5	4	no	—
37	C₂×D₂₀	—	5	3	no	—
38	C₂×C₄×D₅	—	5	3	no	—
39	C₂×#170	—	5	1	no	—
40	C₂×#170	—	5	3	no	—
41	#700	—	5	12	no	—
42	D₅⋊C₈	—	5	12	no	—
43	C₂×#131	—	25	1	no	Sylow
44	C₂×C₂₅	#131	1	2	yes	complemented
45	C₂×C₂₅	C₂³×C₄	1	1	yes	characteristic
46	D₂₅	—	2	6	no	—
47	C₂²×D₅	—	5	3	no	—
48	C₅×Q₈	C₂×AGL(1,𝔽₅)	1	4	yes	—
49	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	3	yes	—
50	C₂×Dic₅	—	5	1	no	—
51	D₂₀	—	5	12	no	—
52	C₄×D₅	—	5	6	no	—
53	C₄×D₅	—	5	6	no	—
54	#170	—	5	2	no	—
55	#170	—	5	6	no	—
56	C₂×#41	—	25	1	no	—
57	#131	—	25	8	no	—
58	C₂×M₁₆	—	25	3	no	—
59	C₂²×C₈	—	25	3	no	—
60	C₂₅	C₂×#131	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
62	C₂×D₅	—	5	6	no	—
63	C₂×D₅	—	10	6	no	—
64	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	6	yes	—
65	Dic₅	—	5	1	no	—
66	Dic₅	—	5	1	no	—
67	#41	—	25	4	no	—
68	#41	—	25	4	no	—
69	C₂×Q₈	#1035	1	1	yes	characteristic
70	C₂×D₄	—	25	3	no	—
71	C₂²×C₄	—	25	3	no	—
72	M₁₆	—	25	12	no	—
73	C₂×C₈	—	25	1	no	—
74	C₂×C₈	—	25	3	no	—
75	C₂×C₈	—	25	12	no	—
76	C₂×C₅	#4133	1	2	yes	—
77	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
78	D₅	—	10	6	no	—
79	C₂³	—	25	3	no	—
80	Q₈	C₂×#1035	1	4	yes	—
81	D₄	—	25	12	no	—
82	C₂×C₄	—	25	1	no	—
83	C₂×C₄	—	25	6	no	—
84	C₂×C₄	—	25	6	no	—
85	C₂×C₄	C₂×#1035	1	3	yes	—
86	C₈	—	25	2	no	—
87	C₈	—	25	6	no	—
88	C₅	C₂×#4133	1	1	yes	characteristic
89	C₂²	—	25	6	no	—
90	C₂²	—	50	6	no	—
91	C₂²	C₂²×#1035	1	1	yes	characteristic
92	C₄	—	25	1	no	—
93	C₄	—	25	1	no	—
94	C₄	C₂²×#1035	1	6	yes	—
95	C₂	—	50	6	no	—
96	C₂	#11716552	1	2	yes	direct product factor
97	C₂	C₂³×#1035	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#1035
commutator	C₂×C₂₅	C₂³×C₄
Frattini	C₂×C₅	C₂³×AGL(1,𝔽₅)
Fitting	C₂×Q₈×C₂₅	C₄
socle	C₂²×C₅	C₂²×AGL(1,𝔽₅)
prime radical	C₂×#87748	C₂
cosocle	Dic₂₅	C₂⁴
hypercenter	C₂×Q₈	#1035
hypocenter	C₂₅	C₂×#131
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11716552	C₂	direct (N × H)
3. C₂×#87735	C₂	semidirect
4. C₂×D₂₅⋊C₈	C₂	semidirect
12. #87735	C₂²	semidirect
13. D₂₅⋊C₈	C₂²	semidirect
44. C₂×C₂₅	#131	semidirect
60. C₂₅	C₂×#131	semidirect
96. C₂	#11716552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#87748	2
#11716552	2
C₂×#87735	2
C₂×D₂₅⋊C₈	2
C₂×#4133	5

Subgroups — C2×#11716552 #13099671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716552 #13099671