Subgroups — C₁₀₉⋊#401 #20294969

Order 6976.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812606	C₂	1	3	yes	maximal
2	#16812606	C₂	1	3	yes	maximal
3	#95×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₉	C₂²	1	3	yes	—
5	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₁₀₉	C₂²	1	3	yes	—
7	C₂³×C₁₀₉	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₁₀₉	—	2	6	no	—
9	C₂×C₄×C₁₀₉	—	2	3	no	—
10	C₂×Dic₁₀₉	—	2	3	no	—
11	C₂×Dic₁₀₉	—	2	3	no	—
12	C₂×Dic₁₀₉	—	2	3	no	—
13	C₂×Dic₁₀₉	—	2	3	no	—
14	C₂²×C₁₀₉	#41	1	3	yes	—
15	C₂²×C₁₀₉	#41	1	3	yes	—
16	C₂²×C₁₀₉	#41	1	1	yes	characteristic
17	C₄×C₁₀₉	—	4	3	no	—
18	Dic₁₀₉	—	4	1	no	—
19	Dic₁₀₉	—	4	3	no	—
20	C₂×C₁₀₉	#126	1	3	yes	—
21	C₂×C₁₀₉	#126	1	1	yes	characteristic
22	C₂×C₁₀₉	#126	1	3	yes	—
23	C₁₀₉	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	109	1	no	maximal, Sylow
25	#95	—	109	3	no	—
26	#95	—	109	3	no	—
27	#95	D₁₀₉	1	1	yes	characteristic
28	C₂²×C₄	—	109	3	no	—
29	C₂²×C₄	—	109	1	no	—
30	C₂²×C₄	C₂×D₁₀₉	1	3	yes	—
31	C₂³	C₂²×D₁₀₉	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	218	3	no	—
35	C₂×C₄	—	218	3	no	—
36	C₂×C₄	—	218	3	no	—
37	C₂×C₄	—	218	3	no	—
38	C₂²	#13182028	1	3	yes	—
39	C₂²	#13182029	1	3	yes	—
40	C₂²	#13182030	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	436	1	no	—
43	C₄	—	436	3	no	—
44	C₂	#16812692	1	3	yes	—
45	C₂	#16812693	1	1	yes	characteristic
46	C₂	#16812694	1	3	yes	—

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

N	H ≅ G/N	type
23. C₁₀₉	#401	semidirect