Subgroups — #13098378

Order 1600.

171 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	#11716488	C₂	1	1	yes	maximal, characteristic
3	C₂×#87716	C₂	1	1	yes	maximal, characteristic
4	#11716363	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅	—	2	2	no	—
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₂²⋊Dic₂₅	C₄	1	2	yes	—
9	C₄⋊Dic₂₅	C₄	1	2	yes	—
10	C₄×Dic₂₅	C₂²	1	2	yes	—
11	#87716	—	2	2	no	—
12	C₂×#6014	C₂²	1	2	yes	—
13	#65391	—	5	1	no	maximal
14	C₂³×C₂₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₅	D₄	1	2	yes	—
17	C₂×C₄×C₂₅	Q₈	1	2	yes	—
18	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₅	C₂×C₄	1	4	yes	—
20	C₈×C₂₅	—	2	2	no	—
21	#6014	—	2	2	no	—
22	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
23	#4072	—	5	1	no	—
24	C₂×#681	—	5	1	no	—
25	#3946	—	5	4	no	—
26	C₂²×C₂₅	—	2	2	no	—
27	C₂²×C₂₅	C₄⋊C₄	1	2	yes	—
28	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₅	C₄⋊C₄	1	2	yes	—
30	C₄×C₂₅	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₅	C₂×Q₈	1	1	yes	characteristic
32	Dic₂₅	—	2	4	no	—
33	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
34	C₂×C₅×C₈	—	2	2	no	—
35	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
36	C₂²⋊Dic₅	—	5	2	no	—
37	C₄⋊Dic₅	—	5	2	no	—
38	C₄×Dic₅	—	5	2	no	—
39	#681	—	10	2	no	—
40	C₂×#168	—	5	2	no	—
41	#424	—	25	1	no	Sylow
42	C₂×C₂₅	—	2	2	no	—
43	C₂×C₂₅	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₂₅	#131	1	2	yes	—
45	C₂³×C₅	C₄×D₅	1	1	yes	characteristic
46	C₂×C₄×C₅	Dic₁₀	1	2	yes	—
47	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic
48	C₂×C₄×C₅	C₂²⋊D₅	1	2	yes	—
49	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
50	C₂×Dic₅	—	5	4	no	—
51	C₅×C₈	—	2	2	no	—
52	#168	—	10	2	no	—
53	C₂×M₁₆	—	25	1	no	—
54	C₂²×C₈	D₂₅	1	1	yes	characteristic
55	#117	—	25	1	no	—
56	C₄⋊C₈	—	25	4	no	—
57	C₂₅	#424	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₅	—	2	2	no	—
59	C₂²×C₅	#683	1	2	yes	—
60	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
61	C₄×C₅	#683	1	2	yes	—
62	C₄×C₅	C₂×Dic₁₀	1	1	yes	characteristic
63	C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
64	Dic₅	—	10	4	no	—
65	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
66	M₁₆	—	50	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	25	2	no	—
69	C₂×C₈	C₂×D₂₅	1	2	yes	—
70	C₄⋊C₄	—	25	2	no	—
71	C₂²⋊C₄	—	25	2	no	—
72	C₄²	—	25	2	no	—
73	C₂×C₅	—	2	2	no	—
74	C₂×C₅	#4047	1	2	yes	—
75	C₂×C₅	C₂×#683	1	1	yes	characteristic
76	C₂³	C₄×D₂₅	1	1	yes	characteristic
77	C₂×C₄	—	25	4	no	—
78	C₂×C₄	Dic₅₀	1	2	yes	—
79	C₂×C₄	C₄×D₂₅	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊D₂₅	1	2	yes	—
81	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	50	2	no	—
84	C₅	#65391	1	1	yes	characteristic
85	C₂²	—	2	2	no	—
86	C₂²	#87718	1	2	yes	—
87	C₂²	C₂×C₄×D₂₅	1	1	yes	characteristic
88	C₄	—	50	4	no	—
89	C₄	#87718	1	2	yes	—
90	C₄	C₂×Dic₅₀	1	1	yes	characteristic
91	C₄	C₂×C₂²⋊D₂₅	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#11716464	1	2	yes	—
94	C₂	C₂×#87718	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₅
commutator	C₂²×C₂₅	C₂²×C₄
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂²×C₈×C₂₅	C₂
socle	C₂²×C₅	C₂×C₄×D₅
prime radical	C₂³×C₅	C₄×D₅
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₂²×C₈	D₂₅
hypocenter	C₂₅	#424
LCS	G ▷ C₂²×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11716363	C₂	semidirect
57. C₂₅	#424	semidirect

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
#11716488	2
C₂×#87716	2
#11716363	2
#65391	5