Subgroups — #13098506

Order 1600.

303 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#87720	C₂	1	3	yes	maximal
3	#11716379	C₂	1	3	yes	maximal, complemented
4	C₂³×D₂₅	C₂²	1	1	yes	characteristic
5	C₂×Q₈×C₂₅	—	2	6	no	—
6	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
7	C₂²×Dic₂₅	C₂²	1	3	yes	—
8	#87720	—	2	6	no	—
9	#65520	—	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	complemented
14	Q₈×C₂₅	—	2	8	no	—
15	C₂×C₄×C₂₅	—	2	6	no	—
16	C₂×C₄×C₂₅	D₄	1	6	yes	—
17	C₂×Dic₂₅	—	2	3	no	—
18	C₂×Dic₂₅	—	2	6	no	—
19	C₂²×C₅×Q₈	D₅	1	1	yes	characteristic
20	C₂×#685	—	5	3	no	—
21	#3963	—	5	3	no	—
22	C₂²×C₂₅	C₂×D₄	1	3	yes	—
23	C₂²×C₂₅	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₂₅	#41	1	3	yes	—
25	C₂×D₂₅	—	2	6	no	—
26	C₂×D₂₅	—	4	1	no	—
27	C₂×D₂₅	—	4	3	no	—
28	C₄×C₂₅	—	2	6	no	—
29	Dic₂₅	—	4	3	no	—
30	C₂³×D₅	—	5	1	no	—
31	C₂×C₅×Q₈	—	2	6	no	—
32	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
33	C₂²×Dic₅	—	5	3	no	—
34	#685	—	10	6	no	—
35	#393	—	25	1	no	Sylow
36	C₂×C₂₅	#120	1	1	yes	characteristic
37	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
38	C₂×C₂₅	#124	1	3	yes	—
39	D₂₅	—	4	2	no	—
40	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
41	C₂²×D₅	—	5	2	no	—
42	C₂²×D₅	—	10	3	no	—
43	C₂²×D₅	—	10	3	no	—
44	C₅×Q₈	—	2	8	no	—
45	C₂×C₄×C₅	—	2	6	no	—
46	C₂×C₄×C₅	C₂²⋊D₅	1	6	yes	—
47	C₂×Dic₅	—	10	6	no	—
48	C₂×Dic₅	—	10	3	no	—
49	C₂²×Q₈	D₂₅	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊C₄	—	25	3	no	—
51	#95	—	25	3	no	—
52	C₂₅	#393	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₅	Q₈×D₅	1	1	yes	characteristic
54	C₂²×C₅	#713	1	3	yes	—
55	C₂²×C₅	C₂×C₂²⋊D₅	1	3	yes	—
56	C₂×D₅	—	10	6	no	—
57	C₂×D₅	—	20	1	no	—
58	C₂×D₅	—	20	3	no	—
59	C₄×C₅	—	2	6	no	—
60	Dic₅	—	20	3	no	—
61	C₂⁴	—	25	1	no	—
62	C₂×Q₈	—	2	6	no	—
63	C₂²×C₄	—	25	3	no	—
64	C₂²×C₄	C₂×D₂₅	1	3	yes	—
65	C₂²⋊C₄	—	50	6	no	—
66	C₂×C₅	#4092	1	3	yes	—
67	C₂×C₅	#4093	1	3	yes	—
68	C₂×C₅	#4099	1	1	yes	characteristic
69	D₅	—	20	2	no	—
70	C₂³	—	25	2	no	—
71	C₂³	—	50	3	no	—
72	C₂³	—	50	3	no	—
73	C₂³	C₂²×D₂₅	1	1	yes	characteristic
74	Q₈	—	2	8	no	—
75	C₂×C₄	—	2	6	no	—
76	C₂×C₄	—	50	6	no	—
77	C₂×C₄	—	50	3	no	—
78	C₂×C₄	C₂²⋊D₂₅	1	6	yes	—
79	C₅	#65520	1	1	yes	characteristic
80	C₂²	—	50	6	no	—
81	C₂²	—	100	3	no	—
82	C₂²	—	100	1	no	—
83	C₂²	Q₈×D₂₅	1	1	yes	characteristic
84	C₂²	#87748	1	3	yes	—
85	C₂²	C₂×C₂²⋊D₂₅	1	3	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	100	3	no	—
88	C₂	—	100	2	no	—
89	C₂	#11716508	1	3	yes	—
90	C₂	#11716509	1	3	yes	—
91	C₂	#11716515	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂³×C₂₅	C₂³
Frattini, socle	C₂³×C₅	C₂²×D₅
Fitting	C₂²×Q₈×C₂₅	C₂
prime radical	C₂³×D₂₅	C₂²
hypercenter	C₂²×Q₈	D₂₅
hypocenter	C₂₅	#393
LCS	G ▷ C₂³×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₂₅	C₂	semidirect
3. #11716379	C₂	semidirect
13. C₂²×D₂₅	Q₈	semidirect
49. C₂²×Q₈	D₂₅	semidirect
52. C₂₅	#393	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₂₅	2
C₂×#87720	2
#11716379	2
#65520	5