Subgroups — C₂²×#6057 #11717543

Order 800.

237 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#1044	C₂	1	3	yes	maximal
2	C₂×#6057	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₅⋊D₅	C₂²	1	1	yes	characteristic
4	C₂×#1044	C₂²	1	18	yes	—
5	#6057	C₂²	1	16	yes	direct product factor
6	C₂²×C₅²	Q₈	1	1	yes	characteristic, complemented
7	C₂×C₅⋊D₅	Q₈	1	3	yes	complemented
8	C₂×C₅⋊D₅	C₂³	1	3	yes	—
9	#1044	C₂³	1	12	yes	—
10	C₂²×AGL(1,𝔽₅)	—	10	3	no	—
11	C₂×C₅²	C₂×Q₈	1	3	yes	complemented
12	C₅⋊D₅	C₂×Q₈	1	3	yes	complemented
13	C₅⋊D₅	C₂⁴	1	1	yes	characteristic
14	C₂²×D₅	—	10	3	no	—
15	C₂×AGL(1,𝔽₅)	—	10	18	no	—
16	C₂²×Q₈	—	25	1	no	maximal, Sylow
17	C₅²	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅	—	2	3	no	—
19	C₂×D₅	—	10	9	no	—
20	C₂×D₅	—	10	9	no	—
21	AGL(1,𝔽₅)	—	10	12	no	—
22	C₂×Q₈	—	25	12	no	—
23	C₂²×C₄	—	25	3	no	—
24	C₂×C₅	—	2	9	no	—
25	D₅	—	10	9	no	—
26	D₅	—	10	3	no	—
27	C₂³	—	25	1	no	—
28	Q₈	—	25	16	no	—
29	C₂×C₄	—	25	18	no	—
30	C₅	—	2	3	no	—
31	C₂²	—	25	3	no	—
32	C₂²	—	25	3	no	—
33	C₂²	#6057	1	1	yes	characteristic, direct product factor
34	C₄	—	25	12	no	—
35	C₂	—	25	1	no	—
36	C₂	—	25	3	no	—
37	C₂	C₂×#6057	1	3	yes	direct product factor

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

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