Subgroups — #23758129

Order 10048.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097826	C₂	1	2	yes	maximal, complemented
2	#19097760	C₂	1	1	yes	maximal, characteristic
3	C₂×#11929441	—	2	2	no	—
4	C₂×D₆₂₈	C₄	1	1	yes	characteristic
5	#14578931	—	2	2	no	—
6	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₅₇	C₄	1	1	yes	characteristic
8	#11929441	—	2	4	no	—
9	C₂²×D₁₅₇	—	2	1	no	—
10	D₆₂₈	—	4	1	no	—
11	C₂×Dic₁₅₇	D₄	1	2	yes	—
12	Q₈×C₁₅₇	—	4	1	no	—
13	C₂×C₄×C₁₅₇	—	2	1	no	—
14	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₁₅₇	—	4	1	no	—
17	C₂×D₁₅₇	—	4	2	no	—
18	C₄×C₁₅₇	—	2	1	no	—
19	C₄×C₁₅₇	—	4	1	no	—
20	Dic₁₅₇	—	2	2	no	—
21	C₂×C₁₅₇	#100	1	1	yes	characteristic
22	C₂×C₁₅₇	#104	1	2	yes	—
23	D₁₅₇	—	8	1	no	—
24	C₁₅₇	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	157	1	no	maximal, Sylow
26	#124	—	157	1	no	—
27	#97	—	157	2	no	—
28	C₂×Q₈	#10597845	1	1	yes	characteristic
29	C₂×D₄	—	157	1	no	—
30	C₂×C₈	—	314	2	no	—
31	C₂²⋊C₄	—	314	2	no	—
32	C₄²	—	157	1	no	—
33	C₂³	—	314	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	628	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	157	2	no	—
38	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
39	C₈	—	314	4	no	—
40	C₂²	—	628	1	no	—
41	C₂²	—	628	2	no	—
42	C₂²	C₂²⋊#10597845	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	314	2	no	—
46	C₂	—	1256	1	no	—
47	C₂	#19097831	1	1	yes	characteristic
48	C₂	#19097836	1	2	yes	—

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

N	H ≅ G/N	type
1. #19097826	C₂	semidirect
24. C₁₅₇	#329	semidirect