Subgroups — #39909024

Order 26176.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27189657	C₂	1	1	yes	maximal, characteristic
2	#27189627	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₄₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15692543	C₄	1	1	yes	characteristic
5	C₄×Dic₄₀₉	C₄	1	1	yes	characteristic
6	#20266963	C₄	1	2	yes	complemented
7	C₂×C₈×C₄₀₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₄₀₉	C₄	1	2	yes	complemented
9	C₂×Dic₄₀₉	—	2	1	no	—
10	#15692543	—	2	1	no	—
11	C₂×C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₀₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₄₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄₀₉	M₁₆	1	1	yes	characteristic
15	C₄×C₄₀₉	C₄²	1	1	yes	characteristic
16	C₄×C₄₀₉	M₁₆	1	1	yes	characteristic
17	Dic₄₀₉	—	4	1	no	—
18	C₂×C₄₀₉	—	2	1	no	—
19	C₂×C₄₀₉	#97	1	1	yes	characteristic
20	C₄₀₉	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	409	1	no	maximal, Sylow
22	M₃₂	—	409	1	no	—
23	M₃₂	D₄₀₉	1	1	yes	characteristic
24	#97	—	409	1	no	—
25	C₂×C₈	—	409	1	no	—
26	C₂×C₈	C₂×D₄₀₉	1	1	yes	characteristic
27	C₄²	—	409	1	no	—
28	C₁₆	—	409	2	no	—
29	C₁₆	Dic₄₀₉	1	2	yes	complemented
30	C₂×C₄	—	818	1	no	—
31	C₂×C₄	C₄×D₄₀₉	1	1	yes	characteristic
32	C₈	—	818	1	no	—
33	C₈	C₄×D₄₀₉	1	1	yes	characteristic
34	C₈	C₂×Dic₄₀₉	1	1	yes	characteristic
35	C₂²	#20266971	1	1	yes	characteristic
36	C₄	—	1636	1	no	—
37	C₄	C₄×Dic₄₀₉	1	1	yes	characteristic
38	C₄	#20266971	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#27189627	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.