Finite Group Databasebeta

← #14294785

Subgroups — #14294785

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5⋊#208C212yesmaximal
2C2×C3×#4018C211yesmaximal, characteristic
3#11746790C214yesmaximal, complemented
4#10604192—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6762C2214yes—
7D5⋊#208—24no—
8D5⋊#208C418yescomplemented
9C2×#6758—22no—
10C2×D5⋊(C3⋊C8)—22no—
11C2×C3×C42×C5C411yescharacteristic
12C2×C3×#685C412yes—
13C2×C3×#683C2212yes—
14C2×C3×C4×Dic5C411yescharacteristic
15C3×#4018—22no—
16C3×#4018—22no—
17#71587—51nomaximal, Hall
18C2×D5⋊M16—32no—
19C2×#4018D311yescharacteristic
20#64919—34no—
21C23×C3×D5C2×C411yescharacteristic
22C22×C3×C4×C5C2×C412yes—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×Dic5C2×C412yes—
25C22×C3×Dic5C2311yescharacteristic
26C2×C3×C4×D5C2×C414yes—
27C2×C3×C4×D5D412yes—
28C2×C3×C4×D5D412yes—
29C2×C3×C4×D5D412yes—
30C2×C3×C4×D5Q812yes—
31#6762—24no—
32#6762C2×C418yes—
33C2×C3⋊#170—24no—
34#6758—28no—
35D5⋊(C3⋊C8)—28no—
36C3×C42×C5—21no—
37C3×C42×C5—21no—
38C3×#685—24no—
39C3×#683—24no—
40C3×C4×Dic5—21no—
41C3×C4×Dic5—21no—
42C2×C3×#117—51no—
43C22×#208—52no—
44#4530—54no—
45C22×C4×D5C2×D311yescharacteristic
46C2×#704—34no—
47D5⋊M16—38no—
48D5⋊M16—64no—
49C2×#700—62no—
50C2×D5⋊C8—62no—
51C2×C42×C5Dic311yescharacteristic
52C2×#685Dic312yes—
53C2×#683C2×D312yes—
54C2×C4×Dic5Dic311yescharacteristic
55#4018—22no—
56#4018—22no—
57#1742—151noSylow
58C23×C3×C5C22×C411yescharacteristic
59C22×C3×D5—42no—
60C22×C3×D5C4212yes—
61C22×C3×D5C22⋊C412yes—
62C22×C3×D5C4⋊C412yes—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5C4212yes—
66C2×C3×C4×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C4⋊C412yes—
69C2×C3×Dic5—22no—
70C2×C3×Dic5—42no—
71C2×C3×Dic5C22×C412yes—
72C2×C3×Dic5C2×D411yescharacteristic
73C2×C3×Dic5C2×D412yes—
74C2×C3×Dic5C2×Q811yescharacteristic
75C3×C4×D5C22⋊C414yes—
76C3×C4×D5C22⋊C414yes—
77C3×C4×D5C4⋊C414yes—
78C3×C4×D5C4⋊C414yes—
79C3⋊#170—28no—
80C23×C3×C4—51no—
81C3×#117—102no—
82C3×#117—102no—
83C2×C3×C4⋊C4—52no—
84C2×C3×C22⋊C4—52no—
85C2×C3×C42—51no—
86C2×C3×C42AGL(1,𝔽5)11yescharacteristic
87C2×#208—58no—
88C2×#208—54no—
89C2×#208—102no—
90C2×#208—104no—
91C22×C3⋊C8—102no—
92C23×D5C2×Dic311yescharacteristic
93C22×C4×C5C2×Dic312yes—
94C22×C4×C5C2×Dic311yescharacteristic
95C22×Dic5C2×Dic312yes—
96C22×Dic5C22×D311yescharacteristic
97C2×C4×D5Dic612yes—
98C2×C4×D5C4×D314yes—
99C2×C4×D5D1212yes—
100C2×C4×D5#6712yes—
101C2×C4×D5#6712yes—
102#704—38no—
103#704—64no—
104C2×#170—64no—
105#700—68no—
106D5⋊C8—68no—
107C42×C5—21no—
108C42×C5—21no—
109#685—24no—
110#683—24no—
111C4×Dic5—21no—
112C4×Dic5—21no—
113C22×M16—152no—
114C2×#117—51no—
115#343—154no—
116C22×C3×C5—22no—
117C22×C3×C5C2×C4211yescharacteristic
118C22×C3×C5C2×C22⋊C411yescharacteristic
119C22×C3×C5C2×C4⋊C411yescharacteristic
120C2×C3×D5—24no—
121C2×C3×D5—42no—
122C2×C3×D5—42no—
123C2×C3×D5#9514yes—
124C3×C4×C5—42no—
125C3×C4×C5#9512yes—
126C3×C4×C5#9512yes—
127C3×Dic5—42no—
128C3×Dic5C2×C22⋊C412yes—
129C3×Dic5C2×C4⋊C412yes—
130C24×C3—51no—
131C22×C3×C4—51no—
132C22×C3×C4—54no—
133C22×C3×C4—52no—
134C22×C3×C4—52no—
135C22×C3×C4—52no—
136C22×C3×C4—52no—
137C22×C3×C4—52no—
138C22×C3×C4C2×AGL(1,𝔽5)12yes—
139C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
140C3×C4⋊C4—104no—
141C3×C22⋊C4—104no—
142C3×C42—21no—
143C3×C42—21no—
144C3×C42—101no—
145C3×C42—101no—
146#208—58no—
147#208—108no—
148#208—104no—
149C2×C3⋊C8—108no—
150C2×C3⋊C8—104no—
151C23×C5C22×Dic311yescharacteristic
152C22×D5—42no—
153C22×D5C4×Dic312yes—
154C22×D5C4⋊Dic312yes—
155C22×D5#21712yes—
156C2×C4×C5—22no—
157C2×C4×C5—42no—
158C2×C4×C5C4×Dic312yes—
159C2×C4×C5C4⋊Dic312yes—
160C2×C4×C5#21711yescharacteristic
161C2×C4×C5#21711yescharacteristic
162C2×Dic5—22no—
163C2×Dic5—42no—
164C2×Dic5C2×Dic611yescharacteristic
165C2×Dic5C2×C4×D312yes—
166C2×Dic5C2×D1211yescharacteristic
167C2×Dic5C2×#6712yes—
168C4×D5Dic3⋊C414yes—
169C4×D5Dic3⋊C414yes—
170C4×D5(C2×D3)⋊C414yes—
171C4×D5(C2×D3)⋊C414yes—
172#170—68no—
173C23×C4—51no—
174C2×M16—158no—
175C2×M16—154no—
176C2×M16—302no—
177C2×M16—304no—
178C22×C8—302no—
179#117—102no—
180#117—102no—
181C2×C4⋊C4—52no—
182C2×C22⋊C4—52no—
183C2×C42—51no—
184C2×C42ΓL(1,𝔽16)11yescharacteristic
185C2×C3×C5—21no—
186C2×C3×C5—21no—
187C2×C3×C5C2×#9511yescharacteristic
188C2×C3×C5#41312yes—
189C3×D5—24no—
190C23×C3—52no—
191C23×C3—52no—
192C23×C3—52no—
193C23×C3—202no—
194C23×C3C22×AGL(1,𝔽5)11yescharacteristic
195C2×C3×C4—22no—
196C2×C3×C4—42no—
197C2×C3×C4—52no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—52no—
201C2×C3×C4—54no—
202C2×C3×C4—54no—
203C2×C3×C4—54no—
204C2×C3×C4—54no—
205C2×C3×C4—102no—
206C2×C3×C4—202no—
207C2×C3×C4C4×AGL(1,𝔽5)12yes—
208C2×C3×C4C4⋊AGL(1,𝔽5)12yes—
209C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
210C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
211C3⋊C8—108no—
212C22×C5—22no—
213C22×C5C2×C4×Dic311yescharacteristic
214C22×C5C2×C4⋊Dic311yescharacteristic
215C22×C5C2×#21711yescharacteristic
216C2×D5—24no—
217C2×D5—42no—
218C2×D5—42no—
219C2×D5C3⋊#9514yes—
220C4×C5—42no—
221C4×C5C3⋊#9512yes—
222C4×C5C3⋊#9512yes—
223Dic5—42no—
224Dic5C2×Dic3⋊C412yes—
225Dic5C2×(C2×D3)⋊C412yes—
226C24—51no—
227C22×C4—51no—
228C22×C4—54no—
229C22×C4—52no—
230C22×C4—52no—
231C22×C4—52no—
232C22×C4—52no—
233C22×C4—52no—
234C22×C4C2×ΓL(1,𝔽16)12yes—
235C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
236M16—158no—
237M16—308no—
238M16—304no—
239C2×C8—308no—
240C2×C8—304no—
241C4⋊C4—104no—
242C22⋊C4—104no—
243C42—21no—
244C42—21no—
245C42—101no—
246C42—101no—
247C3×C5#174211yescharacteristic, complemented, Hall
248C22×C3—22no—
249C22×C3—54no—
250C22×C3—104no—
251C22×C3—202no—
252C22×C3—202no—
253C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
254C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
255C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
256C3×C4—42no—
257C3×C4—52no—
258C3×C4—52no—
259C3×C4—202no—
260C3×C4(C2×AGL(1,𝔽5))⋊C412yes—
261C3×C4(C2×AGL(1,𝔽5))⋊C412yes—
262C2×C5—21no—
263C2×C5—21no—
264C2×C5C2×C3⋊#9511yescharacteristic
265C2×C5#523712yes—
266D5—24no—
267C23—52no—
268C23—52no—
269C23—52no—
270C23—202no—
271C23C22×ΓL(1,𝔽16)11yescharacteristic
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—52no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—52no—
278C2×C4—54no—
279C2×C4—54no—
280C2×C4—54no—
281C2×C4—54no—
282C2×C4—102no—
283C2×C4—202no—
284C2×C4C4×ΓL(1,𝔽16)12yes—
285C2×C4C4⋊ΓL(1,𝔽16)12yes—
286C2×C4#676311yescharacteristic
287C2×C4#676311yescharacteristic
288C8—308no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—104no—
292C2×C3#6576112yes—
293C2×C3C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
294C5#7158711yescharacteristic, complemented, Sylow
295C22—22no—
296C22—54no—
297C22—104no—
298C22—202no—
299C22—202no—
300C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
301C22C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
302C22C2×#676311yescharacteristic
303C4—42no—
304C4—52no—
305C4—52no—
306C4—202no—
307C4#9123512yes—
308C4#9123512yes—
309C3#1060419211yescharacteristic, complemented, Sylow
310C2—21no—
311C2—21no—
312C2—104no—
313C2#1175242012yes—
314C2C2×#9123511yescharacteristic
subgroupG/H
centerC2×C4#6763
commutatorC22×C3×C5C2×C42
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C42×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C42ΓL(1,𝔽16)
hypocenterC3×C5#1742
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
8. D5⋊#208C4semidirect
247. C3×C5#1742semidirect
294. C5#71587semidirect
309. C3#10604192semidirect

Maximal subgroups

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

subgroupindex
C2×D5⋊#2082
C2×C3×#40182
#117467902
#106041923
#715875