Subgroups — C₂×ΓL(1,𝔽₂₅) #900

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₂₅)	C₂	1	4	yes	maximal, direct product factor
5	C₂×M₁₆	—	3	1	no	maximal, Sylow
6	C₂²×D₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂×Dic₃	C₄	1	1	yes	characteristic
9	C₄×D₃	C₄	1	2	yes	—
10	C₄×D₃	C₂²	1	2	yes	—
11	C₃×C₈	C₂²	1	2	yes	complemented
12	C₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄	—	3	1	no	—
14	M₁₆	—	3	4	no	—
15	C₂×C₈	—	3	1	no	—
16	C₂×C₈	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
18	C₂×D₃	—	2	2	no	—
19	C₂×D₃	C₂×C₄	1	2	yes	—
20	C₃×C₄	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄	C₂³	1	1	yes	characteristic
22	Dic₃	C₂×C₄	1	2	yes	—
23	C₂³	—	3	1	no	—
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	2	no	—
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	C₂×D₃	1	1	yes	characteristic
28	C₈	—	3	2	no	—
29	C₈	C₂×D₃	1	2	yes	complemented
30	C₂×C₃	M₁₆	1	2	yes	complemented
31	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
32	D₃	—	2	2	no	—
33	C₂²	—	3	2	no	—
34	C₂²	—	6	2	no	—
35	C₂²	C₄×D₃	1	1	yes	characteristic
36	C₄	—	3	2	no	—
37	C₄	C₄×D₃	1	1	yes	characteristic
38	C₄	C₂²×D₃	1	1	yes	characteristic
39	C₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	6	2	no	—
41	C₂	ΓL(1,𝔽₂₅)	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₃	1	1	yes	characteristic

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.