Subgroups — #13097936

Order 1600.

279 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87720	C₂	1	3	yes	maximal
2	C₂×#87718	C₂	1	3	yes	maximal, complemented
3	C₂₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₂₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
6	C₂²×Dic₂₅	C₂²	1	3	yes	—
7	#87720	—	2	6	no	—
8	#87718	—	2	6	no	—
9	#64965	—	5	1	no	maximal
10	C₂³×C₂₅	C₂³	1	1	yes	characteristic
11	C₂²×D₂₅	—	2	3	no	—
12	C₂²×D₂₅	—	2	3	no	—
13	C₂²×D₂₅	Q₈	1	2	yes	—
14	C₂×C₄×C₂₅	—	2	3	no	—
15	C₂×C₄×C₂₅	—	2	3	no	—
16	C₂×C₄×C₂₅	—	2	3	no	—
17	C₂×Dic₂₅	—	2	3	no	—
18	C₂×Dic₂₅	—	2	3	no	—
19	C₂×Dic₂₅	D₄	1	6	yes	—
20	C₂×#685	—	5	3	no	—
21	C₂×#683	—	5	3	no	—
22	C₅×#95	D₅	1	1	yes	characteristic
23	C₂²×C₂₅	C₂×D₄	1	3	yes	—
24	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
25	C₂²×C₂₅	#41	1	3	yes	—
26	C₂×D₂₅	—	2	6	no	—
27	C₂×D₂₅	—	4	3	no	—
28	C₂×D₂₅	—	4	1	no	—
29	C₄×C₂₅	—	4	3	no	—
30	Dic₂₅	—	2	6	no	—
31	C₂³×D₅	—	5	1	no	—
32	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
33	C₂²×Dic₅	—	5	3	no	—
34	#685	—	10	6	no	—
35	#683	—	10	6	no	—
36	#396	—	25	1	no	Sylow
37	C₂×C₂₅	#121	1	3	yes	—
38	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
39	C₂×C₂₅	#126	1	1	yes	characteristic
40	D₂₅	—	4	2	no	—
41	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
42	C₂²×D₅	—	5	2	no	—
43	C₂²×D₅	—	10	3	no	—
44	C₂²×D₅	—	10	3	no	—
45	C₂×C₄×C₅	—	2	3	no	—
46	C₂×C₄×C₅	—	2	3	no	—
47	C₂×C₄×C₅	—	2	3	no	—
48	C₂×Dic₅	—	5	6	no	—
49	C₂×Dic₅	—	10	3	no	—
50	C₂×Dic₅	—	10	3	no	—
51	C₂×C₄⋊C₄	—	25	3	no	—
52	C₂×C₂²⋊C₄	—	25	3	no	—
53	#95	D₂₅	1	1	yes	characteristic, complemented
54	C₂₅	#396	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	#709	1	3	yes	—
56	C₂²×C₅	D₄×D₅	1	3	yes	—
57	C₂²×C₅	Q₈×D₅	1	1	yes	characteristic
58	C₂×D₅	—	10	6	no	—
59	C₂×D₅	—	20	1	no	—
60	C₂×D₅	—	20	3	no	—
61	C₄×C₅	—	4	3	no	—
62	Dic₅	—	10	6	no	—
63	C₂⁴	—	25	1	no	—
64	C₂²×C₄	—	25	3	no	—
65	C₂²×C₄	C₂×D₂₅	1	3	yes	—
66	C₄⋊C₄	—	50	6	no	—
67	C₂²⋊C₄	—	50	6	no	—
68	C₂×C₅	#4022	1	1	yes	characteristic
69	C₂×C₅	#4030	1	3	yes	—
70	C₂×C₅	#4042	1	3	yes	—
71	D₅	—	20	2	no	—
72	C₂³	—	25	2	no	—
73	C₂³	—	50	3	no	—
74	C₂³	—	50	3	no	—
75	C₂³	C₂²×D₂₅	1	1	yes	characteristic
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	25	6	no	—
80	C₂×C₄	—	50	3	no	—
81	C₂×C₄	—	50	3	no	—
82	C₅	#64965	1	1	yes	characteristic
83	C₂²	—	50	6	no	—
84	C₂²	—	100	1	no	—
85	C₂²	—	100	3	no	—
86	C₂²	#87744	1	3	yes	—
87	C₂²	D₄×D₂₅	1	3	yes	—
88	C₂²	Q₈×D₂₅	1	1	yes	characteristic
89	C₄	—	4	3	no	—
90	C₄	—	50	6	no	—
91	C₂	—	100	2	no	—
92	C₂	#11716438	1	1	yes	characteristic
93	C₂	#11716446	1	3	yes	—
94	C₂	#11716458	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂³×C₂₅	C₂³
Frattini, socle	C₂³×C₅	C₂²×D₅
Fitting	C₂₅×#95	C₂
prime radical	C₂³×D₂₅	C₂²
hypercenter	#95	D₂₅
hypocenter	C₂₅	#396
LCS	G ▷ C₂³×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×#87718	C₂	semidirect
3. C₂₅×#95	C₂	semidirect
53. #95	D₂₅	semidirect
54. C₂₅	#396	semidirect

Maximal subgroups

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

subgroup	index
C₂×#87720	2
C₂×#87718	2
C₂₅×#95	2
#64965	5