Subgroups — #1340×C₁₅₇ #34095698

Order 20096.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#470×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	#349×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	H(3,ℤ/4)×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
5	C₂×M₁₆×C₁₅₇	C₂²	1	1	yes	characteristic
6	C₂²⋊Q₈×C₁₅₇	—	2	1	no	—
7	#117×C₁₅₇	—	2	1	no	—
8	M₃₂×C₁₅₇	—	2	1	no	—
9	#106×C₁₅₇	C₄	1	1	yes	characteristic, complemented
10	#103×C₁₅₇	—	2	1	no	—
11	C₂×Q₈×C₁₅₇	—	2	1	no	—
12	C₂²×C₄×C₁₅₇	D₄	1	1	yes	characteristic
13	Q₁₆×C₁₅₇	—	4	1	no	—
14	M₁₆×C₁₅₇	—	4	1	no	—
15	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₁₅₇	—	2	1	no	—
18	C₄⋊C₄×C₁₅₇	—	4	1	no	—
19	C₄⋊C₄×C₁₅₇	—	4	1	no	—
20	C₂²⋊C₄×C₁₅₇	—	4	1	no	—
21	C₂²⋊C₄×C₁₅₇	—	4	1	no	—
22	C₄²×C₁₅₇	—	2	2	no	—
23	C₁₆×C₁₅₇	—	4	1	no	—
24	C₂³×C₁₅₇	D₈	1	1	yes	characteristic
25	Q₈×C₁₅₇	—	4	1	no	—
26	Q₈×C₁₅₇	—	4	1	no	—
27	C₂×C₄×C₁₅₇	—	2	1	no	—
28	C₂×C₄×C₁₅₇	—	2	1	no	—
29	C₂×C₄×C₁₅₇	—	4	2	no	—
30	C₂×C₄×C₁₅₇	—	4	1	no	—
31	C₂×C₄×C₁₅₇	—	4	1	no	—
32	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₅₇	SD₁₆	1	1	yes	characteristic
34	C₈×C₁₅₇	—	2	1	no	—
35	C₈×C₁₅₇	—	2	1	no	—
36	C₂²×C₁₅₇	—	2	1	no	—
37	C₂²×C₁₅₇	—	4	1	no	—
38	C₂²×C₁₅₇	#102	1	1	yes	characteristic
39	C₄×C₁₅₇	—	2	1	no	—
40	C₄×C₁₅₇	—	8	1	no	—
41	C₄×C₁₅₇	—	8	2	no	—
42	C₄×C₁₅₇	—	8	1	no	—
43	C₄×C₁₅₇	#99	1	1	yes	characteristic
44	C₄×C₁₅₇	#104	1	1	yes	characteristic
45	C₂×C₁₅₇	—	2	1	no	—
46	C₂×C₁₅₇	—	4	1	no	—
47	C₂×C₁₅₇	#327	1	1	yes	characteristic
48	C₁₅₇	#1340	1	1	yes	characteristic, direct product factor, Sylow
49	#1340	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	#470	C₂×C₁₅₇	1	1	yes	characteristic
51	#349	C₂×C₁₅₇	1	1	yes	characteristic
52	H(3,ℤ/4)	C₂×C₁₅₇	1	1	yes	characteristic
53	C₂×Q₁₆	C₄×C₁₅₇	1	1	yes	characteristic, complemented
54	C₂×M₁₆	C₂²×C₁₅₇	1	1	yes	characteristic
55	C₂²⋊Q₈	—	2	1	no	—
56	#117	—	2	1	no	—
57	M₃₂	—	2	1	no	—
58	#106	C₄×C₁₅₇	1	1	yes	characteristic, complemented
59	#103	—	2	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	D₄×C₁₅₇	1	1	yes	characteristic
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₂×C₄×C₁₅₇	1	1	yes	characteristic
65	C₂×C₈	D₄×C₁₅₇	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₄²	—	2	2	no	—
72	C₁₆	—	4	1	no	—
73	C₂³	D₈×C₁₅₇	1	1	yes	characteristic
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	C₂²⋊C₄×C₁₅₇	1	1	yes	characteristic
82	C₂×C₄	SD₁₆×C₁₅₇	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#102×C₁₅₇	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	1	no	—
90	C₄	—	8	2	no	—
91	C₄	—	8	1	no	—
92	C₄	#99×C₁₅₇	1	1	yes	characteristic
93	C₄	#104×C₁₅₇	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#327×C₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₅₇	#327
commutator	C₂×C₈	C₂×C₄×C₁₅₇
Frattini, cosocle	C₂×M₁₆	C₂²×C₁₅₇
prime radical	C₂³×C₁₅₇	D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₇ ◁ C₂×C₄×C₁₅₇ ◁ C₂×M₁₆×C₁₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×Q₁₆×C₁₅₇	C₄	semidirect
9. #106×C₁₅₇	C₄	semidirect
48. C₁₅₇	#1340	direct (N × H)
49. #1340	C₁₅₇	direct (N × H)
53. C₂×Q₁₆	C₄×C₁₅₇	semidirect
58. #106	C₄×C₁₅₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#470×C₁₅₇	2
#349×C₁₅₇	2
H(3,ℤ/4)×C₁₅₇	2
#1340	157

Subgroups — #1340×C157 #34095698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1340×C₁₅₇ #34095698