Subgroups — #23757101

Order 10048.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097705	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₅₇	—	2	2	no	—
4	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₅₇	C₄	1	2	yes	complemented
6	C₂×Dic₁₅₇	—	4	2	no	—
7	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
8	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₅₇	Q₈	1	1	yes	characteristic
10	C₂²×C₁₅₇	D₈	1	1	yes	characteristic
11	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₅₇	Q₁₆	1	1	yes	characteristic
13	Dic₁₅₇	—	8	2	no	—
14	C₂×C₁₅₇	#107	1	1	yes	characteristic
15	C₂×C₁₅₇	SD₃₂	1	2	yes	—
16	C₁₅₇	#367	1	1	yes	characteristic, complemented, Sylow
17	#367	—	157	1	no	maximal, Sylow
18	C₂×C₁₆	D₁₅₇	1	1	yes	characteristic
19	#107	—	157	2	no	—
20	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
21	C₄⋊C₄	—	314	2	no	—
22	C₁₆	Dic₁₅₇	1	2	yes	complemented
23	C₂×C₄	—	628	2	no	—
24	C₂×C₄	D₆₂₈	1	1	yes	characteristic
25	C₈	C₂×Dic₁₅₇	1	1	yes	characteristic
26	C₈	Dic₃₁₄	1	1	yes	characteristic
27	C₂²	D₁₂₅₆	1	1	yes	characteristic
28	C₄	—	1256	2	no	—
29	C₄	C₄⋊Dic₁₅₇	1	1	yes	characteristic
30	C₄	Dic₆₂₈	1	1	yes	characteristic
31	C₂	#19097705	1	1	yes	characteristic
32	C₂	#19097716	1	2	yes	—

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