Subgroups — C₄×#95×C₂₅₁ #44546019

Order 32128.

752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₂₅₁	C₂	1	3	yes	maximal
2	C₂×#95×C₂₅₁	C₂	1	4	yes	maximal
3	C₂³×C₄×C₂₅₁	C₂²	1	6	yes	—
4	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₅₁	—	2	12	no	—
6	C₂×C₄²×C₂₅₁	C₄	1	12	yes	complemented
7	#95×C₂₅₁	C₄	1	16	yes	direct product factor
8	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₂₅₁	—	2	12	no	—
10	C₂²×C₄×C₂₅₁	—	2	12	no	—
11	C₂²×C₄×C₂₅₁	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₂₅₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₂₅₁	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₂₅₁	D₄	1	6	yes	—
15	C₂²×C₄×C₂₅₁	Q₈	1	2	yes	—
16	C₄²×C₂₅₁	—	2	24	no	—
17	C₂³×C₂₅₁	C₂²×C₄	1	3	yes	—
18	C₂³×C₂₅₁	C₂²×C₄	1	4	yes	—
19	C₂³×C₂₅₁	C₂×D₄	1	3	yes	—
20	C₂³×C₂₅₁	C₂×Q₈	1	1	yes	characteristic
21	C₂³×C₂₅₁	#41	1	4	yes	—
22	C₂×C₄×C₂₅₁	—	2	12	no	—
23	C₂×C₄×C₂₅₁	—	2	12	no	—
24	C₂×C₄×C₂₅₁	—	2	48	no	—
25	C₂×C₄×C₂₅₁	C₄²	1	4	yes	—
26	C₂×C₄×C₂₅₁	C₄²	1	24	yes	complemented
27	C₂×C₄×C₂₅₁	C₂²⋊C₄	1	12	yes	—
28	C₂×C₄×C₂₅₁	C₄⋊C₄	1	12	yes	—
29	C₂²×C₂₅₁	C₂×C₄²	1	1	yes	characteristic
30	C₂²×C₂₅₁	C₂×C₄²	1	6	yes	—
31	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	3	yes	—
32	C₂²×C₂₅₁	C₂×C₄⋊C₄	1	3	yes	—
33	C₂²×C₂₅₁	#117	1	6	yes	—
34	C₂²×C₂₅₁	C₄×D₄	1	12	yes	—
35	C₂²×C₂₅₁	C₄×Q₈	1	4	yes	—
36	C₄×C₂₅₁	—	2	24	no	—
37	C₄×C₂₅₁	#95	1	8	yes	direct product factor
38	C₂×C₂₅₁	C₄³	1	1	yes	characteristic
39	C₂×C₂₅₁	C₂×#95	1	1	yes	characteristic
40	C₂×C₂₅₁	#376	1	1	yes	characteristic
41	C₂×C₂₅₁	C₄×C₂²⋊C₄	1	6	yes	—
42	C₂×C₂₅₁	C₄×C₄⋊C₄	1	6	yes	—
43	C₂₅₁	C₄×#95	1	1	yes	characteristic, direct product factor, Sylow
44	C₄×#95	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₄²	C₂×C₂₅₁	1	3	yes	—
46	C₂×#95	C₂×C₂₅₁	1	4	yes	—
47	C₂³×C₄	C₂²×C₂₅₁	1	6	yes	—
48	C₂³×C₄	C₂²×C₂₅₁	1	1	yes	characteristic
49	C₂×C₄²	—	2	12	no	—
50	C₂×C₄²	C₄×C₂₅₁	1	12	yes	complemented
51	#95	C₄×C₂₅₁	1	16	yes	direct product factor
52	C₂⁴	C₂³×C₂₅₁	1	1	yes	characteristic
53	C₂²×C₄	—	2	12	no	—
54	C₂²×C₄	—	2	12	no	—
55	C₂²×C₄	C₂×C₄×C₂₅₁	1	24	yes	—
56	C₂²×C₄	C₂×C₄×C₂₅₁	1	12	yes	—
57	C₂²×C₄	C₂×C₄×C₂₅₁	1	6	yes	—
58	C₂²×C₄	D₄×C₂₅₁	1	6	yes	—
59	C₂²×C₄	Q₈×C₂₅₁	1	2	yes	—
60	C₄²	—	2	24	no	—
61	C₂³	C₂²×C₄×C₂₅₁	1	3	yes	—
62	C₂³	C₂²×C₄×C₂₅₁	1	4	yes	—
63	C₂³	C₂×D₄×C₂₅₁	1	3	yes	—
64	C₂³	C₂×Q₈×C₂₅₁	1	1	yes	characteristic
65	C₂³	#41×C₂₅₁	1	4	yes	—
66	C₂×C₄	—	2	12	no	—
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	—	2	48	no	—
69	C₂×C₄	C₄²×C₂₅₁	1	4	yes	—
70	C₂×C₄	C₄²×C₂₅₁	1	24	yes	complemented
71	C₂×C₄	C₂²⋊C₄×C₂₅₁	1	12	yes	—
72	C₂×C₄	C₄⋊C₄×C₂₅₁	1	12	yes	—
73	C₂²	C₂×C₄²×C₂₅₁	1	1	yes	characteristic
74	C₂²	C₂×C₄²×C₂₅₁	1	6	yes	—
75	C₂²	C₂×C₂²⋊C₄×C₂₅₁	1	3	yes	—
76	C₂²	C₂×C₄⋊C₄×C₂₅₁	1	3	yes	—
77	C₂²	#117×C₂₅₁	1	6	yes	—
78	C₂²	C₄×D₄×C₂₅₁	1	12	yes	—
79	C₂²	C₄×Q₈×C₂₅₁	1	4	yes	—
80	C₄	—	2	24	no	—
81	C₄	#95×C₂₅₁	1	8	yes	direct product factor
82	C₂	C₄³×C₂₅₁	1	1	yes	characteristic
83	C₂	C₂×#95×C₂₅₁	1	1	yes	characteristic
84	C₂	#376×C₂₅₁	1	1	yes	characteristic
85	C₂	C₄×C₂²⋊C₄×C₂₅₁	1	6	yes	—
86	C₂	C₄×C₄⋊C₄×C₂₅₁	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄×C₂₅₁	C₂²
commutator	C₂	C₄³×C₂₅₁
Frattini, cosocle	C₂⁴	C₂³×C₂₅₁
socle, prime radical	C₂⁴×C₂₅₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₄²×C₂₅₁	C₄	semidirect
7. #95×C₂₅₁	C₄	direct (N × H)
26. C₂×C₄×C₂₅₁	C₄²	semidirect
37. C₄×C₂₅₁	#95	direct (N × H)
43. C₂₅₁	C₄×#95	direct (N × H)
44. C₄×#95	C₂₅₁	direct (N × H)
50. C₂×C₄²	C₄×C₂₅₁	semidirect
51. #95	C₄×C₂₅₁	direct (N × H)
70. C₂×C₄	C₄²×C₂₅₁	semidirect
81. C₄	#95×C₂₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₂₅₁	2
C₂×#95×C₂₅₁	2
C₄×#95	251

Subgroups — C4×#95×C251 #44546019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#95×C₂₅₁ #44546019