Subgroups — #23758198

Order 10048.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097841	C₂	1	1	yes	maximal, characteristic
2	#19097839	C₂	1	1	yes	maximal, characteristic
3	#19097710	C₂	1	1	yes	maximal, characteristic
4	#14578964	—	2	1	no	—
5	C₄⋊#10597845	—	2	1	no	—
6	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
7	#14578929	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#10597845	—	4	1	no	—
10	#11929441	—	4	1	no	—
11	C₄×D₁₅₇	D₄	1	1	yes	characteristic
12	#11929434	Q₈	1	1	yes	characteristic
13	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₁₅₇	SD₁₆	1	1	yes	characteristic
15	#10597845	—	8	1	no	—
16	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₁₅₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₅₇	#106	1	1	yes	characteristic
19	D₁₅₇	—	2	1	no	—
20	C₁₅₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	157	1	no	maximal, Sylow
22	M₃₂	—	157	1	no	—
23	#108	—	157	1	no	—
24	#106	—	157	1	no	—
25	M₁₆	—	314	1	no	—
26	C₂×C₈	—	157	1	no	—
27	C₄⋊C₄	—	314	1	no	—
28	C₁₆	—	157	1	no	—
29	C₁₆	#10597845	1	1	yes	characteristic, complemented
30	C₂×C₄	—	628	1	no	—
31	C₂×C₄	—	157	1	no	—
32	C₈	—	628	1	no	—
33	C₈	—	157	1	no	—
34	C₈	C₂×#10597845	1	1	yes	characteristic
35	C₂²	—	157	1	no	—
36	C₄	—	157	1	no	—
37	C₄	—	1256	1	no	—
38	C₄	C₄⋊#10597845	1	1	yes	characteristic
39	C₂	—	314	1	no	—
40	C₂	#19097839	1	1	yes	characteristic

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