Subgroups — #13098505

Order 1600.

273 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
2	C₂×#87718	C₂	1	3	yes	maximal
3	#11716379	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₅	—	2	6	no	—
5	C₂²×C₄×C₂₅	C₂²	1	3	yes	—
6	C₂²×Dic₂₅	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₅	C₂²	1	3	yes	—
8	#87718	—	2	6	no	—
9	#65518	—	5	1	no	maximal
10	C₂³×C₂₅	C₂³	1	1	yes	characteristic
11	Q₈×C₂₅	—	2	8	no	—
12	C₂×C₄×C₂₅	—	2	6	no	—
13	C₂×C₄×C₂₅	D₄	1	6	yes	—
14	C₂×Dic₂₅	—	2	3	no	—
15	C₂×Dic₂₅	—	2	3	no	—
16	C₂×Dic₂₅	—	2	3	no	—
17	C₂×Dic₂₅	Q₈	1	6	yes	complemented
18	C₂²×C₅×Q₈	D₅	1	1	yes	characteristic
19	C₂×#683	—	5	3	no	—
20	#3963	—	5	3	no	—
21	C₂²×C₂₅	C₂×D₄	1	3	yes	—
22	C₂²×C₂₅	C₂×Q₈	1	3	yes	—
23	C₂²×C₂₅	#41	1	1	yes	characteristic
24	C₄×C₂₅	—	2	6	no	—
25	Dic₂₅	—	2	6	no	—
26	Dic₂₅	—	4	1	no	—
27	C₂×C₅×Q₈	—	2	6	no	—
28	C₂²×C₄×C₅	C₂×D₅	1	3	yes	—
29	C₂²×Dic₅	—	5	3	no	—
30	C₂²×Dic₅	—	5	1	no	—
31	#683	—	10	6	no	—
32	#395	—	25	1	no	Sylow
33	C₂×C₂₅	#120	1	1	yes	characteristic
34	C₂×C₂₅	C₂²⋊Q₈	1	3	yes	—
35	C₂×C₂₅	C₄⋊Q₈	1	3	yes	—
36	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
37	C₅×Q₈	—	2	8	no	—
38	C₂×C₄×C₅	—	2	6	no	—
39	C₂×C₄×C₅	C₂²⋊D₅	1	6	yes	—
40	C₂×Dic₅	—	5	6	no	—
41	C₂×Dic₅	—	10	3	no	—
42	C₂×Dic₅	—	10	3	no	—
43	C₂×Dic₅	—	10	3	no	—
44	C₂²×Q₈	D₂₅	1	1	yes	characteristic
45	C₂×C₄⋊C₄	—	25	3	no	—
46	#95	—	25	3	no	—
47	C₂₅	#395	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₅	Q₈×D₅	1	3	yes	—
49	C₂²×C₅	#713	1	1	yes	characteristic
50	C₂²×C₅	C₂×C₂²⋊D₅	1	3	yes	—
51	C₄×C₅	—	2	6	no	—
52	Dic₅	—	10	6	no	—
53	Dic₅	—	20	1	no	—
54	C₂×Q₈	—	2	6	no	—
55	C₂²×C₄	—	25	3	no	—
56	C₂²×C₄	—	25	1	no	—
57	C₂²×C₄	C₂×D₂₅	1	3	yes	—
58	C₄⋊C₄	—	50	6	no	—
59	C₂×C₅	#4090	1	3	yes	—
60	C₂×C₅	#4092	1	3	yes	—
61	C₂×C₅	#4099	1	1	yes	characteristic
62	C₂³	C₂²×D₂₅	1	1	yes	characteristic
63	Q₈	—	2	8	no	—
64	C₂×C₄	—	2	6	no	—
65	C₂×C₄	—	25	6	no	—
66	C₂×C₄	—	50	3	no	—
67	C₂×C₄	—	50	3	no	—
68	C₂×C₄	—	50	3	no	—
69	C₂×C₄	C₂²⋊D₂₅	1	6	yes	—
70	C₅	#65518	1	1	yes	characteristic
71	C₂²	Q₈×D₂₅	1	3	yes	—
72	C₂²	#87748	1	1	yes	characteristic
73	C₂²	C₂×C₂²⋊D₂₅	1	3	yes	—
74	C₄	—	2	6	no	—
75	C₄	—	50	6	no	—
76	C₄	—	100	1	no	—
77	C₂	#11716506	1	3	yes	—
78	C₂	#11716508	1	3	yes	—
79	C₂	#11716515	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₅
commutator, cosocle	C₂³×C₂₅	C₂³
Frattini, socle, prime radical	C₂³×C₅	C₂²×D₅
Fitting	C₂²×Q₈×C₂₅	C₂
hypercenter	C₂²×Q₈	D₂₅
hypocenter	C₂₅	#395
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
17. C₂×Dic₂₅	Q₈	semidirect
47. C₂₅	#395	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×#87718	2
#11716379	2
#65518	5