Subgroups — #13098459

Order 1600.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₂₅	C₂	1	2	yes	maximal
3	#11716384	C₂	1	2	yes	maximal
4	#11716366	C₂	1	1	yes	maximal, characteristic
5	#11716364	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₅	C₂²	1	2	yes	—
7	Q₁₆×C₂₅	C₄	1	4	yes	complemented
8	C₂×C₈×C₂₅	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₅	—	2	2	no	—
10	C₄⋊Dic₂₅	C₂²	1	2	yes	—
11	C₄×Dic₂₅	—	2	2	no	—
12	C₄×Dic₂₅	C₂²	1	1	yes	characteristic
13	C₂×#6014	C₂²	1	1	yes	characteristic
14	#65473	—	5	1	no	maximal
15	Q₈×C₂₅	—	2	2	no	—
16	Q₈×C₂₅	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₂₅	—	2	2	no	—
18	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₅	—	2	2	no	—
20	C₂×Dic₂₅	D₄	1	2	yes	—
21	C₈×C₂₅	C₂×C₄	1	2	yes	—
22	#6014	—	2	1	no	—
23	C₂×C₅×Q₁₆	D₅	1	1	yes	characteristic
24	Q₈×Dic₅	—	5	2	no	—
25	#3967	—	5	2	no	—
26	#3949	—	5	1	no	—
27	#3947	—	5	1	no	—
28	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₅	—	2	4	no	—
30	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₅	#41	1	1	yes	characteristic
32	Dic₂₅	—	2	2	no	—
33	Dic₂₅	—	4	2	no	—
34	C₂×C₅×Q₈	C₂×D₅	1	2	yes	—
35	C₅×Q₁₆	Dic₅	1	4	yes	—
36	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic
37	C₄⋊Dic₅	—	5	2	no	—
38	C₄⋊Dic₅	—	10	2	no	—
39	C₄×Dic₅	—	5	1	no	—
40	C₄×Dic₅	—	10	2	no	—
41	C₂×#168	—	5	1	no	—
42	#441	—	25	1	no	Sylow
43	C₂×C₂₅	C₄×D₄	1	1	yes	characteristic
44	C₂×C₂₅	#137	1	2	yes	—
45	C₅×Q₈	—	2	2	no	—
46	C₅×Q₈	C₂×Dic₅	1	4	yes	—
47	C₂×C₄×C₅	—	2	2	no	—
48	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
49	C₂×Dic₅	—	5	2	no	—
50	C₂×Dic₅	—	10	2	no	—
51	C₅×C₈	C₂×Dic₅	1	2	yes	—
52	#168	—	10	1	no	—
53	C₂×Q₁₆	D₂₅	1	1	yes	characteristic
54	C₄×Q₈	—	25	2	no	—
55	#106	—	25	1	no	—
56	#103	—	25	2	no	—
57	#97	—	25	1	no	—
58	C₂₅	#441	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
60	C₄×C₅	—	2	4	no	—
61	C₄×C₅	#711	1	1	yes	characteristic
62	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
63	Dic₅	—	10	2	no	—
64	Dic₅	—	20	2	no	—
65	C₂×Q₈	C₂×D₂₅	1	2	yes	—
66	Q₁₆	Dic₂₅	1	4	yes	complemented
67	C₂×C₈	—	25	1	no	—
68	C₂×C₈	C₂×D₂₅	1	1	yes	characteristic
69	C₄⋊C₄	—	25	2	no	—
70	C₄⋊C₄	—	50	2	no	—
71	C₄²	—	25	1	no	—
72	C₄²	—	50	2	no	—
73	C₂×C₅	#4064	1	2	yes	—
74	C₂×C₅	D₄×Dic₅	1	1	yes	characteristic
75	Q₈	—	2	2	no	—
76	Q₈	C₂×Dic₂₅	1	4	yes	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	25	2	no	—
79	C₂×C₄	—	50	2	no	—
80	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
81	C₈	—	50	1	no	—
82	C₈	C₂×Dic₂₅	1	2	yes	—
83	C₅	#65473	1	1	yes	characteristic
84	C₂²	D₄×D₂₅	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	50	2	no	—
87	C₄	—	100	2	no	—
88	C₄	#87746	1	1	yes	characteristic
89	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
90	C₂	#11716480	1	2	yes	—
91	C₂	D₄×Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₅
commutator	C₄×C₂₅	C₂²×C₄
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂×Q₁₆×C₂₅	C₂
socle, prime radical	C₂²×C₅	D₄×D₅
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₂×Q₁₆	D₂₅
hypocenter	C₂₅	#441
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
7. Q₁₆×C₂₅	C₄	semidirect
58. C₂₅	#441	semidirect
66. Q₁₆	Dic₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₅	2
Q₈×Dic₂₅	2
#11716384	2
#11716366	2
#11716364	2
#65473	5