Subgroups — #125×D₁₅₇ #23757792

Order 10048.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19097763	C₂	1	1	yes	maximal, characteristic, complemented
2	#19097762	C₂	1	2	yes	maximal, complemented
3	#19097761	C₂	1	4	yes	maximal, complemented
4	C₄⋊C₄×D₁₅₇	C₂	1	4	yes	maximal
5	C₄⋊C₄×D₁₅₇	C₂	1	2	yes	maximal
6	C₄²×D₁₅₇	C₂	1	1	yes	maximal, characteristic
7	#125×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₅₇	C₂²	1	2	yes	—
9	C₂×C₄×D₁₅₇	C₂²	1	4	yes	—
10	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₅₇	C₂²	1	4	yes	—
12	C₄⋊Dic₁₅₇	C₂²	1	2	yes	—
13	#14578933	C₂²	1	4	yes	—
14	#14578933	C₂²	1	4	yes	—
15	#14578933	C₂²	1	4	yes	—
16	C₄×Dic₁₅₇	C₂²	1	2	yes	—
17	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₅₇	C₂²	1	4	yes	—
19	C₄⋊C₄×C₁₅₇	C₂²	1	2	yes	—
20	C₄²×C₁₅₇	C₂²	1	1	yes	characteristic
21	C₂²×D₁₅₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₅₇	C₂³	1	2	yes	—
23	C₂×Dic₁₅₇	C₂³	1	4	yes	—
24	C₂×Dic₁₅₇	C₂³	1	1	yes	characteristic
25	C₄×D₁₅₇	—	2	4	no	—
26	C₄×D₁₅₇	—	2	8	no	—
27	C₄×D₁₅₇	Q₈	1	4	yes	—
28	C₂×C₄×C₁₅₇	C₂³	1	2	yes	—
29	C₂×C₄×C₁₅₇	C₂³	1	4	yes	—
30	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
31	C₂²×C₁₅₇	C₂⁴	1	1	yes	characteristic
32	C₂×D₁₅₇	C₂×Q₈	1	2	yes	—
33	C₂×D₁₅₇	#41	1	4	yes	—
34	C₄×C₁₅₇	—	2	2	no	—
35	C₄×C₁₅₇	—	2	4	no	—
36	C₄×C₁₅₇	C₂×Q₈	1	2	yes	—
37	Dic₁₅₇	—	2	2	no	—
38	Dic₁₅₇	—	2	4	no	—
39	Dic₁₅₇	C₂×Q₈	1	2	yes	—
40	C₂×C₁₅₇	C₂²×Q₈	1	1	yes	characteristic
41	C₂×C₁₅₇	C₂×#41	1	2	yes	—
42	D₁₅₇	#125	1	4	yes	direct product factor
43	C₁₅₇	C₂×#125	1	1	yes	characteristic, complemented, Sylow
44	C₂×#125	—	157	1	no	maximal, Sylow
45	#125	—	157	4	no	—
46	#125	—	157	2	no	—
47	#125	—	157	1	no	—
48	#125	D₁₅₇	1	1	yes	characteristic, direct product factor
49	C₂×C₄⋊C₄	—	157	4	no	—
50	C₂×C₄⋊C₄	—	157	2	no	—
51	C₂×C₄²	—	157	1	no	—
52	C₂²×C₄	—	157	2	no	—
53	C₂²×C₄	—	157	4	no	—
54	C₂²×C₄	—	157	1	no	—
55	C₄⋊C₄	—	157	4	no	—
56	C₄⋊C₄	—	157	4	no	—
57	C₄⋊C₄	—	157	4	no	—
58	C₄⋊C₄	—	157	4	no	—
59	C₄⋊C₄	—	157	2	no	—
60	C₄⋊C₄	C₂×D₁₅₇	1	4	yes	—
61	C₄⋊C₄	C₂×D₁₅₇	1	2	yes	—
62	C₄²	—	157	1	no	—
63	C₄²	—	157	2	no	—
64	C₄²	C₂×D₁₅₇	1	1	yes	characteristic
65	C₂³	—	157	1	no	—
66	C₂×C₄	—	314	4	no	—
67	C₂×C₄	—	314	8	no	—
68	C₂×C₄	—	157	2	no	—
69	C₂×C₄	—	157	4	no	—
70	C₂×C₄	—	157	1	no	—
71	C₂×C₄	—	157	4	no	—
72	C₂×C₄	C₂²×D₁₅₇	1	2	yes	—
73	C₂×C₄	C₂²×D₁₅₇	1	4	yes	—
74	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
75	C₂²	—	157	2	no	—
76	C₂²	—	157	4	no	—
77	C₂²	C₂³×D₁₅₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	314	2	no	—
81	C₄	—	314	4	no	—
82	C₄	—	157	2	no	—
83	C₄	Q₈×D₁₅₇	1	2	yes	—
84	C₂	—	157	4	no	—
85	C₂	C₂×Q₈×D₁₅₇	1	1	yes	characteristic
86	C₂	#41×D₁₅₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₅₇
commutator, socle, cosocle	C₂²×C₁₅₇	C₂⁴
Fitting	#125×C₁₅₇	C₂
prime radical	C₂²×D₁₅₇	C₂³
hypercenter	#125	D₁₅₇
hypocenter	C₁₅₇	C₂×#125
LCS	G ▷ C₂²×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #19097763	C₂	semidirect
2. #19097762	C₂	semidirect
3. #19097761	C₂	semidirect
7. #125×C₁₅₇	C₂	semidirect
42. D₁₅₇	#125	direct (N × H)
43. C₁₅₇	C₂×#125	semidirect
48. #125	D₁₅₇	direct (N × H)

Subgroups — #125×D157 #23757792

Conjugacy classes of subgroups

Complements

Subgroups — #125×D₁₅₇ #23757792