Finite Group Databasebeta

← #14411760

Subgroups — #14411760

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic
2C2×D5⋊#208C212yesmaximal, complemented
3#11752446C218yesmaximal, complemented
4#11752414C214yesmaximal, complemented
5#10617516—31nomaximal, Hall
6C22×C3×C5×Q8C411yescharacteristic
7C2×C3×#713—28no—
8C2×C3×#713C414yes—
9C2×C3×#713C2214yes—
10C22×C3×D20C412yes—
11C22×C3×D20C411yescharacteristic
12C22×C3×C4×D5C2212yes—
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6762C2214yes—
15D5⋊#208—28no—
16C2×#6758C2214yescomplemented
17C2×D5⋊(C3⋊C8)C2214yescomplemented
18#91232C22116yescomplemented
19#84074—51nomaximal, Hall
20C22×#713D311yescharacteristic
21C2×D5⋊M16—32no—
22#65787—38no—
23#65755—34no—
24C23×C3×D5C2×C412yes—
25C23×C3×D5C2×C411yescharacteristic
26C2×C3×C5×Q8—24no—
27C2×C3×C5×Q8C2×C414yes—
28C22×C3×C4×C5C2×C412yes—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×Dic5C2311yescharacteristic
31C3×#713—216no—
32C3×#713—28no—
33C3×#713—28no—
34C2×C3×D20—28no—
35C2×C3×D20—24no—
36C2×C3×D20C2×C418yes—
37C2×C3×D20C2×C414yes—
38C2×C3×C4×D5—28no—
39C2×C3×C4×D5C2×C414yes—
40C2×C3×C4×D5C2×C412yes—
41C2×C3×C4×D5D418yes—
42C2×C3×C4×D5C2314yes—
43C2×C3×C4×D5C2312yes—
44#6762—28no—
45C2×C3⋊#170C2318yes—
46#6758—28no—
47D5⋊(C3⋊C8)—28no—
48C22×C3×#41—51no—
49C22×#208—52no—
50#5234—58no—
51#5207—54no—
52C22×C5×Q8Dic311yescharacteristic
53C2×#713—28no—
54C2×#713Dic314yes—
55C2×#713C2×D314yes—
56C22×D20Dic312yes—
57C22×D20Dic311yescharacteristic
58C22×C4×D5C2×D312yes—
59C22×C4×D5C2×D311yescharacteristic
60C2×#704—34no—
61D5⋊M16—68no—
62C2×#700—34no—
63C2×D5⋊C8—34no—
64#4003—316no—
65#2879—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C22×C3×D5—24no—
68C22×C3×D5—42no—
69C22×C3×D5—44no—
70C22×C3×D5C22⋊C414yes—
71C22×C3×D5C22×C414yes—
72C22×C3×D5C22×C412yes—
73C3×C5×Q8—28no—
74C2×C3×C4×C5—24no—
75C2×C3×C4×C5C22⋊C414yes—
76C2×C3×C4×C5C22×C414yes—
77C2×C3×C4×C5C22×C412yes—
78C2×C3×Dic5C22×C411yescharacteristic
79C2×C3×Dic5C2×D414yes—
80C2×C3×Dic5C2411yescharacteristic
81C3×D20—216no—
82C3×D20—28no—
83C3×C4×D5—28no—
84C3×C4×D5—28no—
85C3×C4×D5C22⋊C418yes—
86C3×C4×D5C2×D414yes—
87C3×C4×D5C2×D414yes—
88C3⋊#170—28no—
89C2×C3×#41—54no—
90C2×C3×#41—54no—
91C2×C3×#41—108no—
92C22×C3×Q8AGL(1,𝔽5)11yescharacteristic
93C22×C3×D4—52no—
94C22×C3×D4—51no—
95C23×C3×C4—51no—
96C23×C3×C4—52no—
97C2×#208—54no—
98C2×#208—54no—
99C2×#208—108no—
100C22×C3⋊C8—54no—
101#830—516no—
102C23×D5C2×Dic312yes—
103C23×D5C2×Dic311yescharacteristic
104C2×C5×Q8—24no—
105C2×C5×Q8C2×Dic314yes—
106C22×C4×C5C2×Dic312yes—
107C22×C4×C5C2×Dic311yescharacteristic
108C22×Dic5C22×D311yescharacteristic
109#713—216no—
110#713—28no—
111#713—28no—
112C2×D20—28no—
113C2×D20—24no—
114C2×D20C2×Dic318yes—
115C2×D20C2×Dic314yes—
116C2×C4×D5—28no—
117C2×C4×D5C2×Dic314yes—
118C2×C4×D5C2×Dic312yes—
119C2×C4×D5#6718yes—
120C2×C4×D5C22×D314yes—
121C2×C4×D5C22×D312yes—
122#704—68no—
123C2×#170—38no—
124#700—68no—
125D5⋊C8—68no—
126C22×#41—51no—
127C22×M16—152no—
128#408—158no—
129#407—154no—
130C22×C3×C5—22no—
131C22×C3×C5C2×C22⋊C412yes—
132C22×C3×C5C23×C411yescharacteristic
133C2×C3×D5—24no—
134C2×C3×D5—24no—
135C2×C3×D5—28no—
136C2×C3×D5—44no—
137C2×C3×D5—48no—
138C2×C3×D5C2×C22⋊C414yes—
139C3×C4×C5—24no—
140C3×C4×C5C2×C22⋊C414yes—
141C3×Dic5C2×C22⋊C412yes—
142C3×Dic5C22×D412yes—
143C24×C3—51no—
144C24×C3—52no—
145C3×#41—1016no—
146C3×#41—108no—
147C3×#41—108no—
148C2×C3×Q8—24no—
149C2×C3×Q8C2×AGL(1,𝔽5)14yes—
150C2×C3×D4—58no—
151C2×C3×D4—54no—
152C2×C3×D4—108no—
153C2×C3×D4—104no—
154C22×C3×C4—51no—
155C22×C3×C4—58no—
156C22×C3×C4—52no—
157C22×C3×C4—52no—
158C22×C3×C4—54no—
159C22×C3×C4—54no—
160C22×C3×C4—108no—
161C22×C3×C4C2×AGL(1,𝔽5)12yes—
162C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
163#208—108no—
164#208—108no—
165C2×C3⋊C8—58no—
166C2×C3⋊C8—108no—
167C23×C5C22×Dic311yescharacteristic
168C22×D5—24no—
169C22×D5—42no—
170C22×D5—44no—
171C22×D5#21714yes—
172C22×D5C22×Dic314yes—
173C22×D5C22×Dic312yes—
174C5×Q8—28no—
175C2×C4×C5—24no—
176C2×C4×C5#21714yes—
177C2×C4×C5C22×Dic314yes—
178C2×C4×C5C22×Dic312yes—
179C2×Dic5C22×Dic311yescharacteristic
180C2×Dic5C2×#6714yes—
181C2×Dic5C23×D311yescharacteristic
182D20—216no—
183D20—28no—
184C4×D5—28no—
185C4×D5—28no—
186C4×D5#21718yes—
187C4×D5C2×#6714yes—
188C4×D5C2×#6714yes—
189#170—68no—
190C2×#41—54no—
191C2×#41—54no—
192C2×#41—108no—
193C22×Q8ΓL(1,𝔽16)11yescharacteristic
194C22×D4—52no—
195C22×D4—51no—
196C23×C4—51no—
197C23×C4—52no—
198C2×M16—154no—
199C2×M16—154no—
200C2×M16—308no—
201C22×C8—154no—
202C22⋊C8—1516no—
203C2×C3×C5—22no—
204C2×C3×C5C22×C22⋊C411yescharacteristic
205C2×C3×C5#56812yes—
206C3×D5—24no—
207C3×D5—44no—
208C23×C3—52no—
209C23×C3—54no—
210C23×C3—54no—
211C23×C3—104no—
212C23×C3—202no—
213C23×C3—204no—
214C23×C3C22×AGL(1,𝔽5)11yescharacteristic
215C3×Q8—28no—
216C3×D4—1016no—
217C3×D4—108no—
218C2×C3×C4—24no—
219C2×C3×C4—54no—
220C2×C3×C4—51no—
221C2×C3×C4—51no—
222C2×C3×C4—58no—
223C2×C3×C4—54no—
224C2×C3×C4—54no—
225C2×C3×C4—108no—
226C2×C3×C4—108no—
227C2×C3×C4C22⋊AGL(1,𝔽5)14yes—
228C2×C3×C4C22×AGL(1,𝔽5)14yes—
229C2×C3×C4C22×AGL(1,𝔽5)12yes—
230C3⋊C8—108no—
231C22×C5—22no—
232C22×C5C2×#21712yes—
233C22×C5C23×Dic311yescharacteristic
234C2×D5—24no—
235C2×D5—28no—
236C2×D5—24no—
237C2×D5—44no—
238C2×D5—48no—
239C2×D5C2×#21714yes—
240C4×C5—24no—
241C4×C5C2×#21714yes—
242Dic5C2×#21712yes—
243Dic5C22×#6712yes—
244C24—51no—
245C24—52no—
246#41—108no—
247#41—108no—
248#41—1016no—
249C2×Q8—24no—
250C2×Q8C2×ΓL(1,𝔽16)14yes—
251C2×D4—58no—
252C2×D4—54no—
253C2×D4—108no—
254C2×D4—104no—
255C22×C4—51no—
256C22×C4—58no—
257C22×C4—52no—
258C22×C4—52no—
259C22×C4—54no—
260C22×C4—54no—
261C22×C4—108no—
262C22×C4C2×ΓL(1,𝔽16)12yes—
263C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
264M16—308no—
265M16—308no—
266C2×C8—158no—
267C2×C8—308no—
268C3×C5#287911yescharacteristic, complemented, Hall
269C22×C3—22no—
270C22×C3—54no—
271C22×C3—104no—
272C22×C3—108no—
273C22×C3—104no—
274C22×C3—204no—
275C22×C3—208no—
276C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
277C22×C3C23×AGL(1,𝔽5)11yescharacteristic
278C3×C4—24no—
279C3×C4—52no—
280C3×C4—52no—
281C3×C4C2×C22⋊AGL(1,𝔽5)14yes—
282C2×C5—22no—
283C2×C5#581912yes—
284C2×C5C22×#21711yescharacteristic
285D5—24no—
286D5—44no—
287C23—52no—
288C23—54no—
289C23—54no—
290C23—104no—
291C23—202no—
292C23—204no—
293C23C22×ΓL(1,𝔽16)11yescharacteristic
294Q8—28no—
295D4—1016no—
296D4—108no—
297C2×C4—24no—
298C2×C4—54no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—54no—
302C2×C4—54no—
303C2×C4—58no—
304C2×C4—108no—
305C2×C4—108no—
306C2×C4#676314yes—
307C2×C4C22×ΓL(1,𝔽16)14yes—
308C2×C4C22×ΓL(1,𝔽16)12yes—
309C8—308no—
310C2×C3—22no—
311C2×C3—104no—
312C2×C3—204no—
313C2×C3#6626012yes—
314C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
315C5#8407411yescharacteristic, complemented, Sylow
316C22—22no—
317C22—54no—
318C22—104no—
319C22—108no—
320C22—104no—
321C22—204no—
322C22—208no—
323C22C2×#676312yes—
324C22C23×ΓL(1,𝔽16)11yescharacteristic
325C4—24no—
326C4—52no—
327C4—52no—
328C4C2×#676314yes—
329C3#1061751611yescharacteristic, complemented, Sylow
330C2—22no—
331C2—104no—
332C2—204no—
333C2#1175698912yes—
334C2C22×#676311yescharacteristic
subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C4
prime radicalC22×C3×#713C2
cosocleC2×C3×Dic5C24
hypercenterC22×Q8ΓL(1,𝔽16)
hypocenterC3×C5#2879
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×D5⋊#208C2semidirect
3. #11752446C2semidirect
4. #11752414C2semidirect
16. C2×#6758C22semidirect
17. C2×D5⋊(C3⋊C8)C22semidirect
18. #91232C22semidirect
268. C3×C5#2879semidirect
315. C5#84074semidirect
329. C3#10617516semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×D5⋊#2082
#117524462
#117524142
#106175163
#840745