Subgroups — #13099672

Order 1600.

387 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, complemented
3	D₂₅⋊M₁₆	C₂	1	6	yes	maximal, complemented
4	C₂×Q₈×C₂₅	C₄	1	1	yes	characteristic
5	#87748	C₄	1	4	yes	—
6	#87748	C₂²	1	4	yes	—
7	C₂×D₁₀₀	C₄	1	3	yes	—
8	C₂×C₄×D₂₅	C₂²	1	3	yes	—
9	#87739	C₂²	1	4	yes	—
10	#87735	C₂²	1	12	yes	complemented
11	D₂₅⋊C₈	C₂²	1	12	yes	complemented
12	#66260	—	5	1	no	maximal
13	C₂²×D₂₅	C₂×C₄	1	3	yes	—
14	Q₈×C₂₅	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	3	yes	—
16	C₂×Dic₂₅	C₂³	1	1	yes	characteristic
17	D₁₀₀	C₂×C₄	1	12	yes	—
18	C₄×D₂₅	C₂×C₄	1	6	yes	—
19	C₄×D₂₅	C₂³	1	6	yes	—
20	#6016	C₂³	1	8	yes	—
21	C₂×#713	—	5	1	no	—
22	#4133	—	5	8	no	—
23	D₅⋊M₁₆	—	5	6	no	—
24	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
25	C₂×D₂₅	—	4	3	no	—
26	C₂×D₂₅	C₂²×C₄	1	6	yes	—
27	C₄×C₂₅	C₂²×C₄	1	6	yes	—
28	Dic₂₅	C₂²×C₄	1	1	yes	characteristic
29	Dic₂₅	C₂⁴	1	1	yes	characteristic
30	C₂×C₅×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
31	#713	—	5	4	no	—
32	#713	—	5	4	no	—
33	C₂×D₂₀	—	5	3	no	—
34	C₂×C₄×D₅	—	5	3	no	—
35	#704	—	5	4	no	—
36	#700	—	5	12	no	—
37	D₅⋊C₈	—	5	12	no	—
38	#568	—	25	1	no	Sylow
39	C₂×C₂₅	—	2	1	no	—
40	C₂×C₂₅	C₂³×C₄	1	1	yes	characteristic
41	D₂₅	—	2	6	no	—
42	C₂²×D₅	—	5	3	no	—
43	C₅×Q₈	C₂×AGL(1,𝔽₅)	1	4	yes	—
44	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	3	yes	—
45	C₂×Dic₅	—	5	1	no	—
46	D₂₀	—	5	12	no	—
47	C₄×D₅	—	5	6	no	—
48	C₄×D₅	—	5	6	no	—
49	#170	—	5	8	no	—
50	C₂×#41	—	25	1	no	—
51	#131	—	25	8	no	—
52	C₂×M₁₆	—	25	6	no	—
53	C₂₅	#568	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂×D₅	—	5	6	no	—
56	C₂×D₅	—	20	3	no	—
57	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	6	yes	—
58	Dic₅	—	5	1	no	—
59	Dic₅	—	5	1	no	—
60	#41	—	25	4	no	—
61	#41	—	25	4	no	—
62	C₂×Q₈	#1035	1	1	yes	characteristic
63	C₂×D₄	—	25	3	no	—
64	C₂²×C₄	—	25	3	no	—
65	M₁₆	—	25	4	no	—
66	M₁₆	—	25	12	no	—
67	C₂×C₈	—	25	12	no	—
68	C₂×C₅	—	2	1	no	—
69	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
70	D₅	—	10	6	no	—
71	C₂³	—	25	3	no	—
72	Q₈	C₂×#1035	1	4	yes	—
73	D₄	—	25	12	no	—
74	C₂×C₄	—	25	1	no	—
75	C₂×C₄	—	25	6	no	—
76	C₂×C₄	—	25	6	no	—
77	C₂×C₄	C₂×#1035	1	3	yes	—
78	C₈	—	25	8	no	—
79	C₅	#66260	1	1	yes	characteristic
80	C₂²	—	25	6	no	—
81	C₂²	—	100	3	no	—
82	C₂²	C₂²×#1035	1	1	yes	characteristic
83	C₄	—	25	1	no	—
84	C₄	—	25	1	no	—
85	C₄	C₂²×#1035	1	6	yes	—
86	C₂	—	2	1	no	—
87	C₂	—	50	6	no	—
88	C₂	C₂³×#1035	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×#1035
commutator	C₂×C₂₅	C₂³×C₄
Frattini, socle	C₂×C₅	C₂³×AGL(1,𝔽₅)
Fitting	C₂×Q₈×C₂₅	C₄
prime radical	C₂×#87748	C₂
cosocle	Dic₂₅	C₂⁴
hypercenter	C₂×Q₈	#1035
hypocenter	C₂₅	#568
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11716552	C₂	semidirect
3. D₂₅⋊M₁₆	C₂	semidirect
10. #87735	C₂²	semidirect
11. D₂₅⋊C₈	C₂²	semidirect
53. C₂₅	#568	semidirect

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
D₂₅⋊M₁₆	2
#66260	5