Subgroups — C₂×#19097728 #23757727

Order 10048.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₅₇	C₂	1	1	yes	maximal, characteristic
2	#19097728	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14578933	C₂	1	2	yes	maximal, complemented
4	C₂×#14578931	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₁₅₇	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₅₇	C₂²	1	2	yes	—
9	C₂²×Dic₁₅₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₁₅₇	C₄	1	8	yes	complemented
11	C₂×C₄×D₁₅₇	C₂²	1	4	yes	—
12	#14578933	C₂²	1	8	yes	complemented
13	#14578931	C₂²	1	8	yes	—
14	C₄×Dic₁₅₇	C₂²	1	4	yes	complemented
15	C₂²×C₄×C₁₅₇	C₂²	1	2	yes	—
16	C₂²×C₄×C₁₅₇	C₂²	1	1	yes	characteristic
17	C₄²×C₁₅₇	C₂²	1	4	yes	complemented
18	C₂²×D₁₅₇	—	2	4	no	—
19	C₂²×D₁₅₇	C₂×C₄	1	4	yes	—
20	C₂²×D₁₅₇	C₂³	1	2	yes	—
21	C₂×Dic₁₅₇	—	2	4	no	—
22	C₂×Dic₁₅₇	C₂×C₄	1	4	yes	—
23	C₂×Dic₁₅₇	C₂³	1	4	yes	—
24	C₂×Dic₁₅₇	C₂³	1	2	yes	—
25	C₄×D₁₅₇	C₂×C₄	1	16	yes	complemented
26	C₂³×C₁₅₇	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₁₅₇	—	2	4	no	—
28	C₂×C₄×C₁₅₇	C₂×C₄	1	4	yes	—
29	C₂×C₄×C₁₅₇	C₂³	1	4	yes	—
30	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
31	C₂²×C₁₅₇	C₂²×C₄	1	2	yes	—
32	C₂²×C₁₅₇	#41	1	4	yes	—
33	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
34	C₂×D₁₅₇	—	2	8	no	—
35	C₂×D₁₅₇	—	2	4	no	—
36	C₂×D₁₅₇	C₂²×C₄	1	4	yes	—
37	C₄×C₁₅₇	—	2	4	no	—
38	C₄×C₁₅₇	C₂²×C₄	1	4	yes	—
39	Dic₁₅₇	—	2	4	no	—
40	Dic₁₅₇	C₂²×C₄	1	4	yes	—
41	C₂×C₁₅₇	#117	1	4	yes	complemented
42	C₂×C₁₅₇	C₂³×C₄	1	1	yes	characteristic
43	C₂×C₁₅₇	C₂×#41	1	2	yes	—
44	D₁₅₇	—	2	4	no	—
45	C₁₅₇	C₂×#117	1	1	yes	characteristic, complemented, Sylow
46	C₂×#117	—	157	1	no	maximal, Sylow
47	C₂³×C₄	—	157	1	no	—
48	#117	—	157	8	no	—
49	C₂×C₄⋊C₄	—	157	2	no	—
50	C₂×C₂²⋊C₄	—	157	2	no	—
51	C₂×C₄²	—	157	1	no	—
52	C₂×C₄²	D₁₅₇	1	1	yes	characteristic, complemented
53	C₂⁴	—	157	1	no	—
54	C₂²×C₄	—	157	2	no	—
55	C₂²×C₄	—	157	1	no	—
56	C₂²×C₄	—	157	8	no	—
57	C₂²×C₄	—	157	4	no	—
58	C₂²×C₄	C₂×D₁₅₇	1	2	yes	—
59	C₂²×C₄	C₂×D₁₅₇	1	1	yes	characteristic
60	C₄⋊C₄	—	157	8	no	—
61	C₂²⋊C₄	—	157	8	no	—
62	C₄²	—	157	4	no	—
63	C₄²	C₂×D₁₅₇	1	4	yes	complemented
64	C₂³	—	314	4	no	—
65	C₂³	—	157	4	no	—
66	C₂³	—	157	2	no	—
67	C₂³	C₂²×D₁₅₇	1	1	yes	characteristic
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	314	4	no	—
70	C₂×C₄	—	157	4	no	—
71	C₂×C₄	—	157	4	no	—
72	C₂×C₄	—	157	2	no	—
73	C₂×C₄	—	157	16	no	—
74	C₂×C₄	C₄×D₁₅₇	1	4	yes	—
75	C₂×C₄	C₂²×D₁₅₇	1	4	yes	—
76	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
77	C₂²	—	314	8	no	—
78	C₂²	—	314	4	no	—
79	C₂²	—	157	4	no	—
80	C₂²	C₂×C₄×D₁₅₇	1	2	yes	—
81	C₂²	#14578954	1	4	yes	—
82	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
83	C₄	—	2	4	no	—
84	C₄	—	314	4	no	—
85	C₄	—	157	4	no	—
86	C₄	C₂×C₄×D₁₅₇	1	4	yes	—
87	C₂	—	314	4	no	—
88	C₂	#19097728	1	4	yes	direct product factor
89	C₂	C₂²×C₄×D₁₅₇	1	1	yes	characteristic
90	C₂	C₂×#14578954	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₅₇
commutator	C₂×C₁₅₇	C₂³×C₄
Frattini	C₂²	C₂³×D₁₅₇
Fitting	C₂×C₄²×C₁₅₇	C₂
socle	C₂³×C₁₅₇	C₂³
prime radical	C₂³×D₁₅₇	C₂²
cosocle	C₂²×C₁₅₇	C₂⁴
hypercenter	C₂×C₄²	D₁₅₇
hypocenter	C₁₅₇	C₂×#117
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #19097728	C₂	direct (N × H)
3. C₂×#14578933	C₂	semidirect
5. C₂×C₄×Dic₁₅₇	C₂	semidirect
6. C₂×C₄²×C₁₅₇	C₂	semidirect
10. C₂×C₄×D₁₅₇	C₄	semidirect
12. #14578933	C₂²	semidirect
14. C₄×Dic₁₅₇	C₂²	semidirect
17. C₄²×C₁₅₇	C₂²	semidirect
25. C₄×D₁₅₇	C₂×C₄	semidirect
41. C₂×C₁₅₇	#117	semidirect
45. C₁₅₇	C₂×#117	semidirect
52. C₂×C₄²	D₁₅₇	semidirect
63. C₄²	C₂×D₁₅₇	semidirect
88. C₂	#19097728	direct (N × H)

Subgroups — C2×#19097728 #23757727

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19097728 #23757727