Subgroups — C₂×#19097681 #23757221

Order 10048.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11929434	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097681	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₅₇	C₄	1	2	yes	—
6	C₂×#11929434	C₄	1	4	yes	complemented
7	C₂×#11929434	C₂²	1	2	yes	—
8	C₄×Dic₁₅₇	C₄	1	2	yes	—
9	C₄×Dic₁₅₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₅₇	C₄	1	4	yes	complemented
12	C₂×C₈×C₁₅₇	C₂²	1	2	yes	—
13	C₂×Dic₁₅₇	—	2	4	no	—
14	C₂×Dic₁₅₇	C₂×C₄	1	4	yes	—
15	#11929434	C₂×C₄	1	4	yes	complemented
16	C₂³×C₁₅₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₅₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₅₇	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
21	C₈×C₁₅₇	C₂×C₄	1	4	yes	complemented
22	C₂²×C₁₅₇	C₄²	1	2	yes	—
23	C₂²×C₁₅₇	M₁₆	1	4	yes	—
24	C₂²×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₁₅₇	C₄²	1	2	yes	—
26	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₅₇	—	2	4	no	—
29	C₂×C₁₅₇	#97	1	4	yes	complemented
30	C₂×C₁₅₇	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₁₅₇	C₂×M₁₆	1	2	yes	—
32	C₁₅₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
33	C₂×#97	—	157	1	no	maximal, Sylow
34	C₂²×C₈	—	157	1	no	—
35	C₂²×C₈	D₁₅₇	1	1	yes	characteristic
36	C₂×C₄²	—	157	1	no	—
37	#97	—	157	4	no	—
38	C₂²×C₄	—	157	2	no	—
39	C₂²×C₄	C₂×D₁₅₇	1	1	yes	characteristic
40	C₂×C₈	—	157	4	no	—
41	C₂×C₈	—	157	2	no	—
42	C₂×C₈	Dic₁₅₇	1	4	yes	complemented
43	C₂×C₈	C₂×D₁₅₇	1	2	yes	—
44	C₄²	—	157	2	no	—
45	C₄²	—	157	2	no	—
46	C₂³	C₄×D₁₅₇	1	1	yes	characteristic
47	C₂×C₄	—	314	4	no	—
48	C₂×C₄	—	157	4	no	—
49	C₂×C₄	C₄×D₁₅₇	1	2	yes	—
50	C₂×C₄	C₄×D₁₅₇	1	1	yes	characteristic
51	C₂×C₄	C₂×Dic₁₅₇	1	2	yes	—
52	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
53	C₈	—	157	4	no	—
54	C₈	C₂×Dic₁₅₇	1	4	yes	complemented
55	C₂²	C₄×Dic₁₅₇	1	2	yes	—
56	C₂²	#14578937	1	4	yes	—
57	C₂²	C₂×C₄×D₁₅₇	1	1	yes	characteristic
58	C₄	—	314	4	no	—
59	C₄	C₄×Dic₁₅₇	1	2	yes	—
60	C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
61	C₄	C₂²×Dic₁₅₇	1	1	yes	characteristic
62	C₂	#19097681	1	4	yes	direct product factor
63	C₂	C₂×C₄×Dic₁₅₇	1	1	yes	characteristic
64	C₂	C₂×#14578937	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₅₇
commutator	C₂×C₁₅₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	C₂²×C₈×C₁₅₇	C₂
socle, prime radical	C₂³×C₁₅₇	C₂×C₄
cosocle	C₂×C₄×C₁₅₇	C₂³
hypercenter	C₂²×C₈	D₁₅₇
hypocenter	C₁₅₇	C₂×#97
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #19097681	C₂	direct (N × H)
6. C₂×#11929434	C₄	semidirect
11. C₂×C₈×C₁₅₇	C₄	semidirect
15. #11929434	C₂×C₄	semidirect
21. C₈×C₁₅₇	C₂×C₄	semidirect
29. C₂×C₁₅₇	#97	semidirect
32. C₁₅₇	C₂×#97	semidirect
42. C₂×C₈	Dic₁₅₇	semidirect
54. C₈	C₂×Dic₁₅₇	semidirect
62. C₂	#19097681	direct (N × H)

Subgroups — C2×#19097681 #23757221

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19097681 #23757221