Subgroups — C₂×#19097740 #23757759

Order 10048.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊D₁₅₇	C₂	1	3	yes	maximal, complemented
2	#19097740	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₂²⋊Dic₁₅₇	C₂	1	3	yes	maximal, complemented
4	C₂⁵×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₅₇	C₂²	1	1	yes	characteristic, complemented
6	C₂×C₂²⋊D₁₅₇	—	2	12	no	—
7	C₂×C₂²⋊D₁₅₇	C₂²	1	12	yes	complemented
8	C₂²×Dic₁₅₇	C₂²	1	3	yes	complemented
9	C₂²⋊Dic₁₅₇	C₂²	1	12	yes	complemented
10	C₂⁴×C₁₅₇	—	2	12	no	—
11	C₂⁴×C₁₅₇	C₂²	1	3	yes	—
12	C₂⁴×C₁₅₇	C₂²	1	4	yes	complemented
13	C₂²×D₁₅₇	—	2	6	no	—
14	C₂²×D₁₅₇	C₂³	1	2	yes	complemented
15	C₂²⋊D₁₅₇	—	2	24	no	—
16	C₂×Dic₁₅₇	—	2	6	no	—
17	C₂×Dic₁₅₇	C₂³	1	6	yes	complemented
18	C₂³×C₁₅₇	—	2	32	no	—
19	C₂³×C₁₅₇	—	2	12	no	—
20	C₂³×C₁₅₇	—	2	24	no	—
21	C₂³×C₁₅₇	D₄	1	12	yes	complemented
22	C₂³×C₁₅₇	C₂³	1	6	yes	—
23	C₂³×C₁₅₇	C₂³	1	1	yes	characteristic
24	C₂²×C₁₅₇	—	2	32	no	—
25	C₂²×C₁₅₇	—	2	24	no	—
26	C₂²×C₁₅₇	—	2	12	no	—
27	C₂²×C₁₅₇	C₂×D₄	1	6	yes	—
28	C₂²×C₁₅₇	C₂×D₄	1	12	yes	complemented
29	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
30	C₂×D₁₅₇	—	2	6	no	—
31	C₂×D₁₅₇	—	4	4	no	—
32	Dic₁₅₇	—	2	6	no	—
33	C₂×C₁₅₇	—	2	12	no	—
34	C₂×C₁₅₇	#120	1	4	yes	complemented
35	C₂×C₁₅₇	C₂²×D₄	1	3	yes	—
36	D₁₅₇	—	4	2	no	—
37	C₁₅₇	C₂×#120	1	1	yes	characteristic, complemented, Sylow
38	C₂×#120	—	157	1	no	maximal, Sylow
39	C₂⁵	D₁₅₇	1	1	yes	characteristic, complemented
40	C₂²×D₄	—	157	3	no	—
41	#120	—	157	8	no	—
42	C₂×C₂²⋊C₄	—	157	3	no	—
43	C₂⁴	—	2	12	no	—
44	C₂⁴	—	157	1	no	—
45	C₂⁴	C₂×D₁₅₇	1	3	yes	—
46	C₂⁴	C₂×D₁₅₇	1	4	yes	complemented
47	C₂×D₄	—	314	12	no	—
48	C₂×D₄	—	157	12	no	—
49	C₂²×C₄	—	157	3	no	—
50	C₂²⋊C₄	—	157	12	no	—
51	C₂³	—	2	32	no	—
52	C₂³	—	2	12	no	—
53	C₂³	—	2	24	no	—
54	C₂³	—	314	6	no	—
55	C₂³	—	157	2	no	—
56	C₂³	C₂²⋊D₁₅₇	1	12	yes	complemented
57	C₂³	C₂²×D₁₅₇	1	6	yes	—
58	C₂³	C₂²×D₁₅₇	1	1	yes	characteristic
59	D₄	—	314	24	no	—
60	C₂×C₄	—	314	6	no	—
61	C₂×C₄	—	157	6	no	—
62	C₂²	—	2	32	no	—
63	C₂²	—	2	24	no	—
64	C₂²	—	2	12	no	—
65	C₂²	—	314	6	no	—
66	C₂²	—	628	4	no	—
67	C₂²	C₂×C₂²⋊D₁₅₇	1	6	yes	—
68	C₂²	C₂×C₂²⋊D₁₅₇	1	12	yes	complemented
69	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
70	C₄	—	314	6	no	—
71	C₂	—	2	12	no	—
72	C₂	—	628	2	no	—
73	C₂	#19097740	1	4	yes	direct product factor
74	C₂	C₂²×C₂²⋊D₁₅₇	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₅₇
commutator, cosocle	C₂²×C₁₅₇	C₂⁴
Frattini	C₂²	C₂³×D₁₅₇
Fitting	C₂⁵×C₁₅₇	C₂
socle	C₂³×C₁₅₇	C₂³
hypercenter	C₂⁵	D₁₅₇
hypocenter	C₁₅₇	C₂×#120
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂³ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊D₁₅₇	C₂	semidirect
2. #19097740	C₂	direct (N × H)
3. C₂×C₂²⋊Dic₁₅₇	C₂	semidirect
4. C₂⁵×C₁₅₇	C₂	semidirect
5. C₂³×D₁₅₇	C₂²	semidirect
7. C₂×C₂²⋊D₁₅₇	C₂²	semidirect
8. C₂²×Dic₁₅₇	C₂²	semidirect
9. C₂²⋊Dic₁₅₇	C₂²	semidirect
12. C₂⁴×C₁₅₇	C₂²	semidirect
14. C₂²×D₁₅₇	C₂³	semidirect
17. C₂×Dic₁₅₇	C₂³	semidirect
21. C₂³×C₁₅₇	D₄	semidirect
28. C₂²×C₁₅₇	C₂×D₄	semidirect
34. C₂×C₁₅₇	#120	semidirect
37. C₁₅₇	C₂×#120	semidirect
39. C₂⁵	D₁₅₇	semidirect
46. C₂⁴	C₂×D₁₅₇	semidirect
56. C₂³	C₂²⋊D₁₅₇	semidirect
68. C₂²	C₂×C₂²⋊D₁₅₇	semidirect
73. C₂	#19097740	direct (N × H)

Subgroups — C2×#19097740 #23757759

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19097740 #23757759