Subgroups — #1315×C₂₅₁ #44545902

Order 32128.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#408×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₁₆×C₂₅₁	C₂	1	2	yes	maximal, complemented
3	C₂×#41×C₂₅₁	C₄	1	1	yes	characteristic
4	C₂×M₁₆×C₂₅₁	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₂₅₁	—	2	2	no	—
7	C₂²⋊C₈×C₂₅₁	—	2	2	no	—
8	#41×C₂₅₁	—	4	1	no	—
9	#41×C₂₅₁	—	4	1	no	—
10	C₂×Q₈×C₂₅₁	C₈	1	1	yes	characteristic
11	C₂×D₄×C₂₅₁	—	2	1	no	—
12	C₂×D₄×C₂₅₁	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₂₅₁	—	2	1	no	—
14	C₂²×C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
15	M₁₆×C₂₅₁	—	4	1	no	—
16	C₂×C₈×C₂₅₁	—	2	1	no	—
17	C₂×C₈×C₂₅₁	—	4	1	no	—
18	C₂×C₈×C₂₅₁	D₄	1	2	yes	—
19	C₁₆×C₂₅₁	—	4	2	no	—
20	C₂³×C₂₅₁	—	2	1	no	—
21	C₂³×C₂₅₁	M₁₆	1	1	yes	characteristic
22	Q₈×C₂₅₁	—	4	1	no	—
23	D₄×C₂₅₁	—	4	1	no	—
24	D₄×C₂₅₁	—	4	2	no	—
25	C₂×C₄×C₂₅₁	—	2	1	no	—
26	C₂×C₄×C₂₅₁	—	2	1	no	—
27	C₂×C₄×C₂₅₁	—	2	1	no	—
28	C₂×C₄×C₂₅₁	—	4	1	no	—
29	C₂×C₄×C₂₅₁	—	4	1	no	—
30	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₅₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₂₅₁	—	2	2	no	—
33	C₈×C₂₅₁	—	4	1	no	—
34	C₂²×C₂₅₁	—	2	1	no	—
35	C₂²×C₂₅₁	—	2	2	no	—
36	C₂²×C₂₅₁	—	4	1	no	—
37	C₂²×C₂₅₁	—	4	2	no	—
38	C₂²×C₂₅₁	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₂₅₁	—	2	1	no	—
40	C₄×C₂₅₁	—	4	1	no	—
41	C₄×C₂₅₁	#99	1	1	yes	characteristic
42	C₄×C₂₅₁	#100	1	1	yes	characteristic
43	C₂×C₂₅₁	—	4	1	no	—
44	C₂×C₂₅₁	—	8	1	no	—
45	C₂×C₂₅₁	#323	1	1	yes	characteristic
46	C₂×C₂₅₁	#350	1	2	yes	—
47	C₂₅₁	#1315	1	1	yes	characteristic, direct product factor, Sylow
48	#1315	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	#408	C₂×C₂₅₁	1	1	yes	characteristic
50	C₂²⋊C₁₆	C₂×C₂₅₁	1	2	yes	complemented
51	C₂×#41	C₄×C₂₅₁	1	1	yes	characteristic
52	C₂×M₁₆	C₄×C₂₅₁	1	1	yes	characteristic
53	C₂²×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
54	C₂×C₁₆	—	2	2	no	—
55	C₂²⋊C₈	—	2	2	no	—
56	#41	—	4	1	no	—
57	#41	—	4	1	no	—
58	C₂×Q₈	C₈×C₂₅₁	1	1	yes	characteristic
59	C₂×D₄	—	2	1	no	—
60	C₂×D₄	C₈×C₂₅₁	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	C₂²×C₄	C₂×C₄×C₂₅₁	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	4	1	no	—
66	C₂×C₈	D₄×C₂₅₁	1	2	yes	—
67	C₁₆	—	4	2	no	—
68	C₂³	—	2	1	no	—
69	C₂³	M₁₆×C₂₅₁	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	D₄	—	4	1	no	—
72	D₄	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	1	yes	characteristic
79	C₂×C₄	C₂×C₈×C₂₅₁	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	4	1	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	1	no	—
84	C₂²	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂²⋊C₈×C₂₅₁	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	#99×C₂₅₁	1	1	yes	characteristic
90	C₄	#100×C₂₅₁	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	8	1	no	—
93	C₂	#323×C₂₅₁	1	1	yes	characteristic
94	C₂	#350×C₂₅₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₅₁	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₈×C₂₅₁
Frattini, cosocle	C₂²×C₈	C₂²×C₂₅₁
socle	C₂²×C₂₅₁	C₂²⋊C₈
prime radical	C₂×#41×C₂₅₁	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₅₁ ◁ C₂²×C₈×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²⋊C₁₆×C₂₅₁	C₂	semidirect
47. C₂₅₁	#1315	direct (N × H)
48. #1315	C₂₅₁	direct (N × H)
50. C₂²⋊C₁₆	C₂×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#408×C₂₅₁	2
C₂²⋊C₁₆×C₂₅₁	2
#1315	251

Subgroups — #1315×C251 #44545902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1315×C₂₅₁ #44545902