Subgroups — C₂²×#13095201 #20258809

Order 6084.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095201	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃²	C₃	1	1	yes	maximal, characteristic
3	#13095201	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃²	C₂×C₃	1	3	yes	—
5	C₂²×C₁₃²	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃²	C₂²×C₃	1	1	yes	characteristic
7	C₂²×C₁₃⋊C₉	—	13	2	no	maximal
8	C₂×C₁₃²	C₂×C₉	1	3	yes	complemented
9	C₂×C₁₃⋊C₉	—	13	6	no	—
10	C₁₃²	C₂²×C₉	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₃×C₁₃	—	3	4	no	—
12	C₂²×C₃×C₁₃	C₁₃⋊C₃	1	2	yes	—
13	C₁₃⋊C₉	—	13	2	no	—
14	C₂×C₃×C₁₃	—	3	12	no	—
15	C₂×C₃×C₁₃	C₂×C₁₃⋊C₃	1	6	yes	—
16	C₂²×C₁₃	—	3	4	no	—
17	C₂²×C₁₃	C₁₃⋊C₉	1	2	yes	complemented
18	C₃×C₁₃	—	3	4	no	—
19	C₃×C₁₃	C₂²×C₁₃⋊C₃	1	2	yes	—
20	C₂²×C₉	—	169	1	no	Hall
21	C₂×C₁₃	—	3	12	no	—
22	C₂×C₁₃	C₂×C₁₃⋊C₉	1	6	yes	complemented
23	C₂×C₉	—	169	3	no	—
24	C₁₃	—	3	4	no	—
25	C₁₃	C₂²×C₁₃⋊C₉	1	2	yes	complemented
26	C₂²×C₃	#92789	1	1	yes	characteristic
27	C₉	—	169	1	no	Sylow
28	C₂×C₃	C₂×#92789	1	3	yes	—
29	C₂²	#13095201	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	C₂²×#92789	1	1	yes	characteristic
31	C₂	C₂×#13095201	1	3	yes	direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.