Subgroups — C₂×#19097821 #23758203

Order 10048.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097821	C₂	1	2	yes	maximal, direct product factor
2	C₂×#14578929	C₂	1	1	yes	maximal, characteristic
3	#14578929	C₄	1	1	yes	characteristic
4	#14578929	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
6	C₂×C₄×C₁₅₇	C₈	1	1	yes	characteristic
7	C₈×C₁₅₇	C₈	1	1	yes	characteristic
8	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₅₇	C₁₆	1	1	yes	characteristic
10	C₄×C₁₅₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₅₇	C₃₂	1	2	yes	complemented
13	C₂×C₁₅₇	C₂×C₁₆	1	1	yes	characteristic
14	C₁₅₇	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	157	1	no	maximal, Sylow
16	C₂×C₁₆	—	157	1	no	—
17	C₃₂	—	157	2	no	—
18	C₂×C₈	#10597845	1	1	yes	characteristic
19	C₁₆	—	157	1	no	—
20	C₁₆	—	157	1	no	—
21	C₂×C₄	#11929441	1	1	yes	characteristic
22	C₈	#11929441	1	1	yes	characteristic
23	C₈	C₂×#10597845	1	1	yes	characteristic
24	C₂²	#14578957	1	1	yes	characteristic
25	C₄	#14578957	1	1	yes	characteristic
26	C₄	C₂×#11929441	1	1	yes	characteristic
27	C₂	#19097821	1	2	yes	direct product factor
28	C₂	C₂×#14578957	1	1	yes	characteristic

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