Subgroups — C₂²×#15692552 #27189815

Order 13088.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692552	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#13109888	C₂	1	1	yes	maximal, characteristic
3	#15692552	C₂²	1	4	yes	direct product factor
4	C₂×#13109888	C₄	1	3	yes	—
5	C₂×#13109888	C₂²	1	3	yes	—
6	C₂²×D₄₀₉	C₄	1	1	yes	characteristic
7	C₂²×C₄₀₉	C₈	1	1	yes	characteristic, complemented
8	C₂×D₄₀₉	C₈	1	3	yes	complemented
9	C₂×D₄₀₉	C₂×C₄	1	3	yes	—
10	#13109888	C₂×C₄	1	3	yes	—
11	#13109888	C₂³	1	1	yes	characteristic
12	C₂×C₄₀₉	C₂×C₈	1	3	yes	complemented
13	D₄₀₉	C₂×C₈	1	3	yes	complemented
14	D₄₀₉	C₂²×C₄	1	1	yes	characteristic
15	C₄₀₉	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₈	—	409	1	no	maximal, Sylow
17	C₂²×C₄	—	409	1	no	—
18	C₂×C₈	—	409	6	no	—
19	C₂³	—	409	1	no	—
20	C₂×C₄	—	409	3	no	—
21	C₂×C₄	—	409	3	no	—
22	C₈	—	409	4	no	—
23	C₂²	—	409	3	no	—
24	C₂²	—	409	3	no	—
25	C₂²	#15692552	1	1	yes	characteristic, direct product factor
26	C₄	—	409	1	no	—
27	C₄	—	409	3	no	—
28	C₂	—	409	1	no	—
29	C₂	—	409	3	no	—
30	C₂	C₂×#15692552	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.