Subgroups — C₁₂₇⋊#401 #22549819

Order 8128.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇⋊#95	C₂	1	3	yes	maximal
2	C₁₂₇⋊#95	C₂	1	3	yes	maximal
3	#95×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₂₇	C₂²	1	3	yes	—
5	C₂²×Dic₁₂₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₁₂₇	C₂²	1	3	yes	—
7	C₂×Dic₁₂₇	—	2	3	no	—
8	C₂×Dic₁₂₇	—	2	3	no	—
9	C₂×Dic₁₂₇	—	2	3	no	—
10	C₂×Dic₁₂₇	—	2	3	no	—
11	C₂³×C₁₂₇	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₂₇	—	2	6	no	—
13	C₂×C₄×C₁₂₇	—	2	3	no	—
14	C₂²×C₁₂₇	#41	1	3	yes	—
15	C₂²×C₁₂₇	#41	1	3	yes	—
16	C₂²×C₁₂₇	#41	1	1	yes	characteristic
17	C₄×C₁₂₇	—	4	3	no	—
18	Dic₁₂₇	—	4	1	no	—
19	Dic₁₂₇	—	4	3	no	—
20	C₂×C₁₂₇	#126	1	3	yes	—
21	C₂×C₁₂₇	#126	1	1	yes	characteristic
22	C₂×C₁₂₇	#126	1	3	yes	—
23	C₁₂₇	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	127	1	no	maximal, Sylow
25	#95	—	127	3	no	—
26	#95	—	127	3	no	—
27	#95	D₁₂₇	1	1	yes	characteristic
28	C₂²×C₄	—	127	3	no	—
29	C₂²×C₄	—	127	1	no	—
30	C₂²×C₄	C₂×D₁₂₇	1	3	yes	—
31	C₂³	C₂²×D₁₂₇	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	254	3	no	—
35	C₂×C₄	—	254	3	no	—
36	C₂×C₄	—	254	3	no	—
37	C₂×C₄	—	254	3	no	—
38	C₂²	#14523247	1	3	yes	—
39	C₂²	#14523248	1	3	yes	—
40	C₂²	#14523249	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	508	1	no	—
43	C₄	—	508	3	no	—
44	C₂	#16861202	1	3	yes	—
45	C₂	#16861203	1	1	yes	characteristic
46	C₂	#16861204	1	3	yes	—

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

N	H ≅ G/N	type
23. C₁₂₇	#401	semidirect