Finite Group Databasebeta

← #14285229

Subgroups — #14285229

Order 1920.

664 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×C3×#4086C211yesmaximal, characteristic
2#11752416C212yesmaximal, complemented
3#11746796C214yesmaximal, complemented
4#10604927—31nomaximal, Hall
5C22×C3×C5×D4C411yescharacteristic
6C22×C3×C22⋊D5—22no—
7C22×C3×D20C411yescharacteristic
8C3×#4086—22no—
9C3×#4086C412yes—
10C3×#4086C2212yes—
11C2×C3×C4×Dic5C2211yescharacteristic
12#91241—22no—
13#91233C2214yescomplemented
14#91231—22no—
15#71760—51nomaximal, Hall
16C2×#4086D311yescharacteristic
17#65757—32no—
18#64925—34no—
19C24×C3×C5—21no—
20C23×C3×D5—21no—
21C2×C3×C5×D4—21no—
22C2×C3×C5×D4—42no—
23C2×C3×C5×D4C2×C412yes—
24C22×C3×C4×C5C2×C411yescharacteristic
25C2×C3×C22⋊D5—24no—
26C2×C3×C22⋊D5—24no—
27C2×C3×C22⋊D5—48no—
28C22×C3×Dic5D412yes—
29C2×C3×D20—21no—
30C2×C3×D20—42no—
31C2×C3×D20C2×C412yes—
32C2×C3⋊#170—24no—
33C3×C4×Dic5C2×C411yescharacteristic
34C3×C4×Dic5D412yes—
35C3×C4×Dic5C2311yescharacteristic
36C2×C3×#127—51no—
37#4926—52no—
38#4544—54no—
39C22×C5×D4Dic311yescharacteristic
40C22×C22⋊D5—22no—
41C22×D20Dic311yescharacteristic
42#4086—22no—
43#4086Dic312yes—
44#4086C2×D312yes—
45C2×C4×Dic5C2×D311yescharacteristic
46C22⋊#170—62no—
47#4004—34no—
48#4002—62no—
49#1555—151noSylow
50C23×C3×C5—22no—
51C23×C3×C5—44no—
52C23×C3×C5—42no—
53C23×C3×C5C22⋊C411yescharacteristic
54C22×C3×D5—22no—
55C22×C3×D5—44no—
56C22×C3×D5—42no—
57C3×C5×D4—42no—
58C3×C5×D4—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22⋊C411yescharacteristic
61C2×C3×C4×C5C22×C411yescharacteristic
62C3×C22⋊D5—48no—
63C3×C22⋊D5—48no—
64C2×C3×Dic5—24no—
65C2×C3×Dic5C22⋊C412yes—
66C2×C3×Dic5C2×D412yes—
67C3×D20—42no—
68C3×D20—42no—
69C3⋊#170—44no—
70C22×C3×D4—51no—
71C22×C3×D4—102no—
72C22×C3×D4AGL(1,𝔽5)11yescharacteristic
73C3×#127—52no—
74C3×#127—52no—
75C3×#127—102no—
76C2×C3×C42—51no—
77#830—102no—
78C4⋊(C3⋊C8)—54no—
79#803—102no—
80C24×C5—21no—
81C23×D5—21no—
82C2×C5×D4—21no—
83C2×C5×D4—42no—
84C2×C5×D4C2×Dic312yes—
85C22×C4×C5C2×Dic311yescharacteristic
86C2×C22⋊D5—24no—
87C2×C22⋊D5—24no—
88C2×C22⋊D5—48no—
89C22×Dic5#6712yes—
90C2×D20—21no—
91C2×D20—42no—
92C2×D20C2×Dic312yes—
93C2×#170—64no—
94C4×Dic5C2×Dic311yescharacteristic
95C4×Dic5#6712yes—
96C4×Dic5C22×D311yescharacteristic
97C2×#127—51no—
98#432—152no—
99#331—154no—
100C22×C3×C5—22no—
101C22×C3×C5—42no—
102C22×C3×C5—44no—
103C22×C3×C5—84no—
104C22×C3×C5#10012yes—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×C3×D5—42no—
107C2×C3×D5—44no—
108C2×C3×D5—84no—
109C3×C4×C5—21no—
110C3×C4×C5—21no—
111C3×Dic5—22no—
112C3×Dic5AGL(1,ℤ/8)14yes—
113C24×C3—21no—
114C24×C3—101no—
115C2×C3×D4—21no—
116C2×C3×D4—42no—
117C2×C3×D4—52no—
118C2×C3×D4—104no—
119C2×C3×D4—104no—
120C2×C3×D4—101no—
121C2×C3×D4—202no—
122C2×C3×D4—208no—
123C2×C3×D4C2×AGL(1,𝔽5)12yes—
124C22×C3×C4—52no—
125C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
126C3×C42—52no—
127C3×C42—51no—
128C3×C42—51no—
129C2×C3⋊C8—104no—
130C23×C5—22no—
131C23×C5—44no—
132C23×C5—42no—
133C23×C5#21711yescharacteristic
134C22×D5—22no—
135C22×D5—44no—
136C22×D5—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5—22no—
140C2×C4×C5#21711yescharacteristic
141C2×C4×C5C22×Dic311yescharacteristic
142C22⋊D5—48no—
143C22⋊D5—48no—
144C2×Dic5—24no—
145C2×Dic5#21712yes—
146C2×Dic5C2×#6712yes—
147D20—42no—
148D20—42no—
149#170—124no—
150C22×D4—51no—
151C22×D4—102no—
152C22×D4ΓL(1,𝔽16)11yescharacteristic
153#127—52no—
154#127—52no—
155#127—102no—
156C2×C42—51no—
157C4⋊C8—154no—
158C22⋊C8—302no—
159#97—302no—
160C2×C3×C5—22no—
161C2×C3×C5—82no—
162C2×C3×C5C2×#10011yescharacteristic
163C2×C3×C5#41812yes—
164C3×D5—82no—
165C23×C3—22no—
166C23×C3—44no—
167C23×C3—42no—
168C23×C3—102no—
169C23×C3—204no—
170C23×C3—202no—
171C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
172C3×D4—42no—
173C3×D4—42no—
174C3×D4—202no—
175C3×D4—202no—
176C3×D4—208no—
177C3×D4—208no—
178C2×C3×C4—22no—
179C2×C3×C4—52no—
180C2×C3×C4—52no—
181C2×C3×C4—104no—
182C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
183C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
184C3⋊C8—204no—
185C22×C5—22no—
186C22×C5—44no—
187C22×C5—42no—
188C22×C5—84no—
189C22×C5#83312yes—
190C22×C5C2×#21711yescharacteristic
191C2×D5—44no—
192C2×D5—42no—
193C2×D5—84no—
194C4×C5—21no—
195C4×C5—21no—
196Dic5—22no—
197Dic5#93214yes—
198C24—21no—
199C24—101no—
200C2×D4—21no—
201C2×D4—42no—
202C2×D4—52no—
203C2×D4—104no—
204C2×D4—104no—
205C2×D4—101no—
206C2×D4—202no—
207C2×D4—208no—
208C2×D4C2×ΓL(1,𝔽16)12yes—
209C22×C4—52no—
210C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
211C2×C8—304no—
212C42—52no—
213C42—51no—
214C42—51no—
215C3×C5#155511yescharacteristic, complemented, Hall
216C22×C3—22no—
217C22×C3—42no—
218C22×C3—44no—
219C22×C3—84no—
220C22×C3—202no—
221C22×C3—204no—
222C22×C3—404no—
223C22×C3#401312yes—
224C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—54no—
228C3×C4—102no—
229C2×C5—22no—
230C2×C5—82no—
231C2×C5#521512yes—
232C2×C5C2×#83311yescharacteristic
233D5—82no—
234C23—22no—
235C23—44no—
236C23—42no—
237C23—102no—
238C23—204no—
239C23—202no—
240C23#676311yescharacteristic
241D4—42no—
242D4—42no—
243D4—202no—
244D4—202no—
245D4—208no—
246D4—208no—
247C2×C4—22no—
248C2×C4—52no—
249C2×C4—52no—
250C2×C4—104no—
251C2×C4#676311yescharacteristic
252C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
253C8—604no—
254C2×C3—22no—
255C2×C3—82no—
256C2×C3—402no—
257C2×C3#6576712yes—
258C2×C3C2×#401311yescharacteristic
259C5#7176011yescharacteristic, complemented, Sylow
260C22—22no—
261C22—42no—
262C22—44no—
263C22—84no—
264C22—202no—
265C22—204no—
266C22—404no—
267C22#9124212yes—
268C22C2×#676311yescharacteristic
269C4—21no—
270C4—21no—
271C4—54no—
272C4—102no—
273C3#1060492711yescharacteristic, complemented, Sylow
274C2—22no—
275C2—82no—
276C2—402no—
277C2#1175242612yes—
278C2C2×#9124211yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4086C2
cosocleC3×C4×Dic5C23
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#1555
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11752416C2semidirect
3. #11746796C2semidirect
13. #91233C22semidirect
215. C3×C5#1555semidirect
259. C5#71760semidirect
273. C3#10604927semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40862
#117524162
#117467962
#106049273
#717605