Subgroups — C₂×C₄⋊#3926 #12019780

Order 1280.

230 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3926	C₂	1	2	yes	maximal
3	C₄⋊#3926	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
7	C₄×C₅×C₁₆	C₄	1	2	yes	—
8	C₄×C₅×C₁₆	C₂²	1	2	yes	—
9	C₂×#3926	—	2	4	no	—
10	C₂×#3926	C₂²	1	4	yes	—
11	C₂×C₄⋊C₃₂	—	5	1	no	maximal, Sylow
12	C₂²×C₅×C₈	C₈	1	1	yes	characteristic
13	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²×C₅	C₈	1	1	yes	characteristic
15	C₂×C₅×C₁₆	—	2	2	no	—
16	C₂×C₅×C₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₅×C₁₆	D₄	1	2	yes	—
19	C₂×C₅×C₁₆	Q₈	1	2	yes	—
20	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
21	C₄×C₅×C₈	C₈	1	2	yes	—
22	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
23	#3926	—	2	4	no	—
24	C₂²×C₃₂	—	5	2	no	—
25	C₂×C₄×C₁₆	D₅	1	1	yes	characteristic
26	C₄⋊C₃₂	—	5	4	no	—
27	C₂²×C₄×C₅	C₁₆	1	1	yes	characteristic
28	C₂²×C₄×C₅	C₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
30	C₂×C₅×C₈	—	2	2	no	—
31	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
32	C₂×C₅×C₈	C₂×C₈	1	2	yes	—
33	C₂×C₅×C₈	C₂×C₈	1	1	yes	characteristic
34	C₂×C₅×C₈	M₁₆	1	2	yes	—
35	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₅	C₁₆	1	2	yes	—
37	C₄²×C₅	C₂×C₈	1	2	yes	—
38	C₅×C₁₆	—	2	2	no	—
39	C₅×C₁₆	C₄⋊C₄	1	2	yes	—
40	C₅×C₁₆	C₂×D₄	1	1	yes	characteristic
41	C₅×C₁₆	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₁₆	Dic₅	1	1	yes	characteristic
43	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
44	C₂×C₄×C₈	Dic₅	1	1	yes	characteristic
45	C₂×C₃₂	—	5	4	no	—
46	C₂×C₃₂	—	10	4	no	—
47	C₄×C₁₆	Dic₅	1	2	yes	—
48	C₄×C₁₆	C₂×D₅	1	2	yes	—
49	C₂³×C₅	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₅	—	2	2	no	—
51	C₂×C₄×C₅	C₃₂	1	4	yes	complemented
52	C₂×C₄×C₅	C₄⋊C₈	1	2	yes	—
53	C₂×C₄×C₅	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
55	C₂×C₄×C₅	C₂×C₁₆	1	2	yes	—
56	C₂×C₄×C₅	M₃₂	1	2	yes	—
57	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
58	C₅×C₈	—	2	2	no	—
59	C₅×C₈	C₄⋊C₈	1	2	yes	—
60	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₅×C₈	C₂×M₁₆	1	1	yes	characteristic
62	C₂²×C₈	#168	1	1	yes	characteristic
63	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
64	C₂×C₄²	#168	1	1	yes	characteristic
65	C₂×C₁₆	—	2	2	no	—
66	C₂×C₁₆	Dic₁₀	1	2	yes	—
67	C₂×C₁₆	D₂₀	1	2	yes	—
68	C₂×C₁₆	C₂×Dic₅	1	2	yes	—
69	C₂×C₁₆	C₂×Dic₅	1	1	yes	characteristic
70	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
71	C₄×C₈	#168	1	2	yes	—
72	C₄×C₈	C₂×Dic₅	1	2	yes	—
73	C₃₂	—	10	4	no	—
74	C₂²×C₅	C₄⋊C₁₆	1	2	yes	—
75	C₂²×C₅	C₂×C₃₂	1	2	yes	—
76	C₂²×C₅	M₆₄	1	2	yes	—
77	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
78	C₄×C₅	—	2	2	no	—
79	C₄×C₅	C₄⋊C₁₆	1	2	yes	—
80	C₄×C₅	C₂×C₃₂	1	4	yes	complemented
81	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₄×C₅	C₂×M₃₂	1	1	yes	characteristic
83	C₂²×C₄	#672	1	1	yes	characteristic
84	C₂²×C₄	#672	1	1	yes	characteristic
85	C₂²×C₄	C₂×#168	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	C₂×#168	1	2	yes	—
88	C₂×C₈	C₂×#168	1	1	yes	characteristic
89	C₂×C₈	#681	1	2	yes	—
90	C₂×C₈	C₄⋊Dic₅	1	2	yes	—
91	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
92	C₄²	#672	1	2	yes	—
93	C₄²	C₂×#168	1	2	yes	—
94	C₁₆	—	2	2	no	—
95	C₁₆	C₄⋊Dic₅	1	2	yes	—
96	C₁₆	C₂×Dic₁₀	1	1	yes	characteristic
97	C₁₆	C₂×D₂₀	1	1	yes	characteristic
98	C₂×C₅	C₄⋊C₃₂	1	4	yes	complemented
99	C₂×C₅	C₂×C₄⋊C₁₆	1	1	yes	characteristic
100	C₂×C₅	C₂²×C₃₂	1	1	yes	characteristic
101	C₂×C₅	C₂×M₆₄	1	1	yes	characteristic
102	C₂³	C₂×#672	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	#3926	1	4	yes	complemented
105	C₂×C₄	C₄⋊#168	1	2	yes	—
106	C₂×C₄	C₂×#672	1	2	yes	—
107	C₂×C₄	C₂×#672	1	1	yes	characteristic
108	C₂×C₄	C₂×#672	1	2	yes	—
109	C₂×C₄	#3944	1	2	yes	—
110	C₂×C₄	C₂²×#168	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	C₄⋊#168	1	2	yes	—
113	C₈	C₂×#681	1	1	yes	characteristic
114	C₈	C₂×C₄⋊Dic₅	1	1	yes	characteristic
115	C₅	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
116	C₂²	C₄⋊#672	1	2	yes	—
117	C₂²	C₂×#3926	1	2	yes	—
118	C₂²	#64719	1	2	yes	—
119	C₂²	C₂²×#672	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	C₄⋊#672	1	2	yes	—
122	C₄	C₂×#3926	1	4	yes	complemented
123	C₄	C₂×C₄⋊#168	1	1	yes	characteristic
124	C₄	C₂×#3944	1	1	yes	characteristic
125	C₂	C₄⋊#3926	1	4	yes	direct product factor
126	C₂	C₂×C₄⋊#672	1	1	yes	characteristic
127	C₂	C₂²×#3926	1	1	yes	characteristic
128	C₂	C₂×#64719	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂×D₅
commutator	C₂×C₅	C₂²×C₃₂
Frattini	C₂×C₁₆	C₂²×D₅
Fitting	C₂×C₄×C₅×C₁₆	C₂
socle, prime radical	C₂³×C₅	C₂×C₁₆
cosocle	C₂×C₅×C₁₆	C₂³
hypercenter	C₂×C₄×C₁₆	D₅
hypocenter	C₅	C₂×C₄⋊C₃₂
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₄⋊#3926	C₂	direct (N × H)
51. C₂×C₄×C₅	C₃₂	semidirect
80. C₄×C₅	C₂×C₃₂	semidirect
98. C₂×C₅	C₄⋊C₃₂	semidirect
104. C₂×C₄	#3926	semidirect
115. C₅	C₂×C₄⋊C₃₂	semidirect
122. C₄	C₂×#3926	semidirect
125. C₂	C₄⋊#3926	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₆	2
C₂²×#3926	2
C₄⋊#3926	2
C₂×C₄⋊C₃₂	5

Subgroups — C2×C4⋊#3926 #12019780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊#3926 #12019780