Subgroups — C₄×#20267000 #39910339

Order 26176.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20267000	C₂	1	2	yes	maximal
2	C₄×#15692550	C₂	1	1	yes	maximal, characteristic
3	#20267000	C₄	1	4	yes	direct product factor
4	C₂×#15692550	C₄	1	1	yes	characteristic
5	C₂×#15692550	C₂²	1	1	yes	characteristic
6	C₄×Dic₄₀₉	C₄	1	1	yes	characteristic
7	#15692550	C₈	1	2	yes	—
8	#15692550	C₂×C₄	1	2	yes	—
9	C₂×Dic₄₀₉	C₈	1	1	yes	characteristic
10	C₂×Dic₄₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₄₀₉	C₈	1	1	yes	characteristic
12	C₂²×C₄₀₉	C₂×C₈	1	1	yes	characteristic
13	C₄×C₄₀₉	C₁₆	1	2	yes	complemented
14	Dic₄₀₉	C₁₆	1	2	yes	complemented
15	Dic₄₀₉	C₄²	1	1	yes	characteristic
16	Dic₄₀₉	C₂×C₈	1	1	yes	characteristic
17	C₂×C₄₀₉	C₄×C₈	1	1	yes	characteristic
18	C₂×C₄₀₉	C₂×C₁₆	1	1	yes	characteristic
19	C₂×C₄₀₉	C₂×C₁₆	1	1	yes	characteristic
20	C₄₀₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	409	1	no	maximal, Sylow
22	C₂×C₁₆	—	409	2	no	—
23	C₄×C₈	—	409	1	no	—
24	C₂×C₈	—	409	1	no	—
25	C₂×C₈	—	409	1	no	—
26	C₄²	—	409	1	no	—
27	C₁₆	—	409	4	no	—
28	C₂×C₄	—	409	1	no	—
29	C₂×C₄	—	409	1	no	—
30	C₂×C₄	#15692552	1	1	yes	characteristic
31	C₈	—	409	2	no	—
32	C₈	—	409	2	no	—
33	C₂²	C₂×#15692552	1	1	yes	characteristic
34	C₄	—	409	1	no	—
35	C₄	—	409	1	no	—
36	C₄	—	409	2	no	—
37	C₄	#20267000	1	2	yes	direct product factor
38	C₂	C₄×#15692552	1	1	yes	characteristic
39	C₂	C₂×#20267000	1	1	yes	characteristic
40	C₂	#27189812	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.