Subgroups — C₄×AΣL(1,𝔽₂₇) #66339

Order 324.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AΣL(1,𝔽₂₇)	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₄	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
4	C₄×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
5	AΣL(1,𝔽₂₇)	C₄	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₃³	C₂×C₃	1	1	yes	characteristic
7	C₂×3₋¹⁺²	C₂×C₃	1	2	yes	—
8	C₂×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₄	—	3	1	no	—
10	C₃²×C₄	—	3	3	no	—
11	C₃²×C₄	—	3	1	no	—
12	C₃²×C₄	C₃²	1	1	yes	characteristic
13	C₄×C₉	—	3	2	no	—
14	C₃³	C₃×C₄	1	1	yes	characteristic, complemented
15	3₋¹⁺²	C₃×C₄	1	2	yes	complemented
16	H(3,𝔽₃)	C₃×C₄	1	1	yes	characteristic, complemented
17	C₂×C₃²	—	3	1	no	—
18	C₂×C₃²	—	3	3	no	—
19	C₂×C₃²	—	3	1	no	—
20	C₂×C₃²	C₂×C₃²	1	1	yes	characteristic
21	C₂×C₉	—	3	2	no	—
22	C₃×C₄	—	3	3	no	—
23	C₃×C₄	—	3	1	no	—
24	C₃×C₄	—	9	1	no	—
25	C₃×C₄	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃²	—	3	3	no	—
27	C₃²	—	3	1	no	—
28	C₃²	—	3	1	no	—
29	C₃²	C₃²×C₄	1	1	yes	characteristic
30	C₉	—	3	2	no	—
31	C₂×C₃	—	3	3	no	—
32	C₂×C₃	—	3	1	no	—
33	C₂×C₃	—	9	1	no	—
34	C₂×C₃	C₂×H(3,𝔽₃)	1	1	yes	characteristic
35	C₄	AΣL(1,𝔽₂₇)	1	1	yes	characteristic, direct product factor, Sylow
36	C₃	—	3	3	no	—
37	C₃	—	3	1	no	—
38	C₃	—	9	1	no	—
39	C₃	C₄×H(3,𝔽₃)	1	1	yes	characteristic
40	C₂	C₂×AΣL(1,𝔽₂₇)	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.