Finite Group Databasebeta

← #14513963

Subgroups — #14513963

Order 1920.

458 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×C22⋊A4C211yesmaximal, characteristic
2#10602919—31nomaximal, Hall
3C2×C5×C22⋊A4C411yescharacteristic
4A4⋊#168—43nomaximal
5#85561—51nomaximal, Hall
6C24×C4×C5D311yescharacteristic
7C2×C22⋊#168—33no—
8C2×C22⋊#168—33no—
9C5×C22⋊A4C811yescharacteristic, complemented
10C4×C5×A4—43no—
11C4×C5×A4—81no—
12C4×C22⋊A4D511yescharacteristic
13C25×C5Dic311yescharacteristic
14C23×C4×C5—33no—
15C23×C4×C5—33no—
16C23×C4×C5—61no—
17C23×C4×C5—61no—
18C22×#168—33no—
19C22×#168—31no—
20C22⋊#168—63no—
21C22⋊#168—63no—
22C22⋊#168—63no—
23C22⋊#168—63no—
24#1779—151noSylow
25C2×C5×A4—43no—
26C2×C5×A4—81no—
27C3⋊#168—161no—
28C2×C22⋊A4Dic511yescharacteristic
29A4⋊C8—203no—
30C24×C5—33no—
31C24×C5—33no—
32C24×C5—61no—
33C24×C5—61no—
34C24×C5C3⋊C811yescharacteristic, complemented
35C22×C4×C5—21no—
36C22×C4×C5—31no—
37C22×C4×C5—33no—
38C22×C4×C5—33no—
39C22×C4×C5—33no—
40C22×C4×C5—33no—
41C22×C4×C5—66no—
42C22×C4×C5—63no—
43C22×C4×C5—63no—
44C22×C4×C5—61no—
45C22×C4×C5—63no—
46C22×C4×C5S413yes—
47C2×#168—66no—
48C2×#168—63no—
49C2×#168—63no—
50C24×C4D1511yescharacteristic
51C2×C22⋊C8—153no—
52C2×C22⋊C8—153no—
53C5×A4—43no—
54C5×A4—81no—
55C3×C4×C5—161no—
56C22⋊A4#16811yescharacteristic, complemented
57C4×A4—43no—
58C4×A4—81no—
59C23×C5—21no—
60C23×C5—31no—
61C23×C5—33no—
62C23×C5—33no—
63C23×C5—33no—
64C23×C5—33no—
65C23×C5—33no—
66C23×C5—61no—
67C23×C5—61no—
68C23×C5—63no—
69C23×C5—66no—
70C23×C5—63no—
71C23×C5—63no—
72C23×C5SL(2,ℤ/4)13yes—
73C2×C4×C5—33no—
74C2×C4×C5—33no—
75C2×C4×C5—33no—
76C2×C4×C5—33no—
77C2×C4×C5—63no—
78C2×C4×C5—66no—
79C2×C4×C5—63no—
80C2×C4×C5—61no—
81C2×C4×C5—61no—
82#168—123no—
83#168—121no—
84C25Dic1511yescharacteristic
85C23×C4—33no—
86C23×C4—33no—
87C23×C4—61no—
88C23×C4—61no—
89C22×C8—153no—
90C22×C8—151no—
91C22⋊C8—303no—
92C22⋊C8—303no—
93C22⋊C8—303no—
94C22⋊C8—303no—
95C2×C3×C5—161no—
96C2×A4—43no—
97C2×A4—81no—
98C3⋊C8—801no—
99C22×C5—21no—
100C22×C5—33no—
101C22×C5—31no—
102C22×C5—33no—
103C22×C5—33no—
104C22×C5—33no—
105C22×C5—33no—
106C22×C5—63no—
107C22×C5—66no—
108C22×C5—63no—
109C22×C5—63no—
110C22×C5—61no—
111C22×C5—61no—
112C22×C5A4⋊C813yescomplemented
113C4×C5—33no—
114C4×C5—61no—
115C4×C5#102011yescharacteristic
116C24—33no—
117C24—33no—
118C24—61no—
119C24—61no—
120C24C3⋊#16811yescharacteristic, complemented
121C22×C4—21no—
122C22×C4—31no—
123C22×C4—33no—
124C22×C4—33no—
125C22×C4—33no—
126C22×C4—33no—
127C22×C4—66no—
128C22×C4—63no—
129C22×C4—63no—
130C22×C4—61no—
131C22×C4—63no—
132C22×C4C5⋊S413yes—
133C2×C8—306no—
134C2×C8—303no—
135C2×C8—303no—
136C3×C5—161noHall
137A4—43no—
138A4—81no—
139C3×C4—161no—
140C2×C5—33no—
141C2×C5—33no—
142C2×C5—61no—
143C2×C5—61no—
144C2×C5#593611yescharacteristic
145C23—21no—
146C23—31no—
147C23—33no—
148C23—33no—
149C23—33no—
150C23—33no—
151C23—33no—
152C23—61no—
153C23—61no—
154C23—63no—
155C23—66no—
156C23—63no—
157C23—63no—
158C23A4⋊Dic513yes—
159C2×C4—33no—
160C2×C4—33no—
161C2×C4—33no—
162C2×C4—33no—
163C2×C4—63no—
164C2×C4—66no—
165C2×C4—63no—
166C2×C4—61no—
167C2×C4—61no—
168C8—603no—
169C8—601no—
170C2×C3—161no—
171C5#8556111yescharacteristic, complemented, Sylow
172C22—21no—
173C22—33no—
174C22—31no—
175C22—33no—
176C22—33no—
177C22—33no—
178C22—33no—
179C22—63no—
180C22—66no—
181C22—63no—
182C22—63no—
183C22—61no—
184C22—61no—
185C22A4⋊#16813yescomplemented
186C4—33no—
187C4—61no—
188C4C5⋊#102011yescharacteristic
189C3—161noSylow
190C2—33no—
191C2—33no—
192C2—61no—
193C2—61no—
194C2#1175692711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC4C5⋊#1020
commutator, hypocenterC5×C22⋊A4C8
FittingC24×C4×C5D3
socleC25×C5Dic3
prime radicalC2×C5×C22⋊A4C4
cosocleC4×C5×C22⋊A4C2
LCSG ▷ C5×C22⋊A4
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
9. C5×C22⋊A4C8semidirect
34. C24×C5C3⋊C8semidirect
56. C22⋊A4#168semidirect
112. C22×C5A4⋊C8semidirect
120. C24C3⋊#168semidirect
171. C5#85561semidirect
185. C22A4⋊#168semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊A42
#106029193
A4⋊#1684
#855615