Finite Group Databasebeta

← #14301713

Subgroups — #14301713

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#525C211yesmaximal, characteristic
2#11756578C211yesmaximal, characteristic, complemented
3#11751338C211yesmaximal, characteristic, complemented
4#11751308C212yesmaximal, complemented
5#11746354C212yesmaximal, complemented
6#10602507—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic
9C3×C5×#123C412yes—
10C3×C5×C22⋊Q8—21no—
11C3×C5×#121—21no—
12C3×C5×#120C412yes—
13C3×C4×C5×D4—22no—
14C3×C5×#117C2211yescharacteristic
15#91837—24no—
16C2×#6710—22no—
17C2×#6710C2212yes—
18C2×#6710C2212yes—
19#91120—21no—
20#91117—21no—
21#91114—24no—
22#71714—51nomaximal, Hall
23C5×#525D311yescharacteristic
24#66153—31no—
25#65526—31no—
26#65496—32no—
27#64753—32no—
28C24×C3×C5C2×C411yescharacteristic
29C3×C5×#41—22no—
30C3×C5×#41—22no—
31C2×C3×C5×Q8D411yescharacteristic
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5D412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4C2×C412yes—
47C3×C42×C5—21no—
48#6710—24no—
49#6710—22no—
50#6710—22no—
51#6710—22no—
52#6710—22no—
53C2×C3⋊#168—24no—
54C2×C3⋊#168—22no—
55C2×C3⋊#168D414yescomplemented
56C3×#525D511yescharacteristic
57#5819—51no—
58#5237—51no—
59#5207—52no—
60#4533—52no—
61C2×C5×#41C2×D311yescharacteristic
62C23×C4×C5C2×D311yescharacteristic
63C5×#123Dic312yes—
64C5×C22⋊Q8—21no—
65C5×#121—21no—
66C5×#120Dic312yes—
67C4×C5×D4—22no—
68C5×#117C2×D311yescharacteristic
69#4094—64no—
70C2×#681—32no—
71C2×#681—32no—
72C2×#681—62no—
73#3968—61no—
74#3965—61no—
75C22⋊#168—64no—
76#1891—151noSylow
77C23×C3×C5—21no—
78C23×C3×C5—22no—
79C23×C3×C5—42no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5C22×C411yescharacteristic
82C3×C5×Q8—22no—
83C3×C5×D4—24no—
84C3×C5×D4—22no—
85C3×C5×D4—44no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—22no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22⋊C412yes—
95C2×C3×C4×C5C2×D412yes—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5#4112yes—
99C3⋊#168—24no—
100C3⋊#168—42no—
101C2×C3×#41C2×D511yescharacteristic
102C23×C3×C4C2×D511yescharacteristic
103C3×#123Dic512yes—
104C3×C22⋊Q8—21no—
105C3×#121—21no—
106C3×#120Dic512yes—
107C3×C4×D4—22no—
108C3×#117C2×D511yescharacteristic
109#948—104no—
110C2×#208—52no—
111C2×#208—52no—
112C2×#208—102no—
113#836—101no—
114#833—101no—
115#830—104no—
116C24×C5C2×Dic311yescharacteristic
117C5×#41—22no—
118C5×#41—22no—
119C2×C5×Q8#6711yescharacteristic
120C2×C5×D4—22no—
121C2×C5×D4C2×Dic312yes—
122C2×C5×D4#6711yescharacteristic
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5C2×Dic311yescharacteristic
128C22×C4×C5#6712yes—
129C22×C4×C5C22×D311yescharacteristic
130C5×C4⋊C4—22no—
131C5×C4⋊C4—21no—
132C5×C22⋊C4—22no—
133C5×C22⋊C4—22no—
134C5×C22⋊C4C2×Dic312yes—
135C42×C5—21no—
136#681—64no—
137#681—62no—
138#681—62no—
139#681—62no—
140#681—62no—
141C2×#168—34no—
142C2×#168—64no—
143C2×#168—62no—
144#568—151no—
145#525D1511yescharacteristic
146#413—151no—
147#407—152no—
148#344—152no—
149C22×C3×C5—22no—
150C22×C3×C5—24no—
151C22×C3×C5—22no—
152C22×C3×C5—41no—
153C22×C3×C5—42no—
154C22×C3×C5—41no—
155C22×C3×C5—42no—
156C22×C3×C5—41no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C22×C3×C5C4×D412yes—
159C3×C4×C5—22no—
160C3×C4×C5—42no—
161C3×C4×C5—41no—
162C3×C4×C5#12011yescharacteristic
163C3×C4×C5#12112yes—
164C3×C4×C5#12311yescharacteristic
165C24×C3C2×Dic511yescharacteristic
166C3×#41—22no—
167C3×#41—22no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×D4—22no—
170C2×C3×D4C2×Dic512yes—
171C2×C3×D4C22⋊D511yescharacteristic
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4C2×Dic511yescharacteristic
177C22×C3×C4C22⋊D512yes—
178C22×C3×C4C22×D511yescharacteristic
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4C2×Dic512yes—
184C3×C42—21no—
185#208—104no—
186#208—102no—
187#208—102no—
188#208—102no—
189#208—102no—
190C2×C3⋊C8—54no—
191C2×C3⋊C8—104no—
192C2×C3⋊C8—102no—
193C23×C5—22no—
194C23×C5—21no—
195C23×C5—42no—
196C23×C5#21712yes—
197C23×C5C22×Dic311yescharacteristic
198C5×Q8—22no—
199C5×D4—24no—
200C5×D4—22no—
201C5×D4—44no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—22no—
205C2×C4×C5—22no—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—42no—
210C2×C4×C5#21712yes—
211C2×C4×C5D3×D412yes—
212C2×C4×C5#23712yes—
213C2×C4×C5C2×#6711yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215#168—64no—
216#168—122no—
217C2×#41C2×D1511yescharacteristic
218C23×C4C2×D1511yescharacteristic
219#131—304no—
220C2×M16—152no—
221C2×M16—152no—
222C2×M16—302no—
223#123Dic1512yes—
224C22⋊Q8—21no—
225#121—21no—
226#120Dic1512yes—
227C4×D4—22no—
228#117C2×D1511yescharacteristic
229#101—301no—
230#100—301no—
231C22⋊C8—304no—
232C2×C3×C5—21no—
233C2×C3×C5—22no—
234C2×C3×C5—42no—
235C2×C3×C5—42no—
236C2×C3×C5#38611yescharacteristic
237C23×C3—21no—
238C23×C3—22no—
239C23×C3—42no—
240C23×C3C22⋊Dic512yes—
241C23×C3C22×Dic511yescharacteristic
242C3×Q8—22no—
243C3×D4—24no—
244C3×D4—22no—
245C3×D4—44no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—22no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—42no—
254C2×C3×C4C22⋊Dic512yes—
255C2×C3×C4D4×D512yes—
256C2×C3×C4#71112yes—
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C3⋊C8—104no—
260C3⋊C8—202no—
261C22×C5—22no—
262C22×C5—24no—
263C22×C5—22no—
264C22×C5—41no—
265C22×C5—42no—
266C22×C5—41no—
267C22×C5—42no—
268C22×C5—41no—
269C22×C5D4×Dic312yes—
270C22×C5C2×#21711yescharacteristic
271C4×C5—22no—
272C4×C5—42no—
273C4×C5—41no—
274C4×C5#93511yescharacteristic
275C4×C5#93711yescharacteristic
276C4×C5#93912yes—
277C24C2×Dic1511yescharacteristic
278#41—22no—
279#41—22no—
280C2×Q8#122011yescharacteristic
281C2×D4—22no—
282C2×D4C2×Dic1512yes—
283C2×D4#122011yescharacteristic
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C2×Dic1511yescharacteristic
289C22×C4#122012yes—
290C22×C4C22×D1511yescharacteristic
291M16—304no—
292M16—302no—
293M16—302no—
294M16—302no—
295M16—302no—
296C2×C8—154no—
297C2×C8—304no—
298C2×C8—302no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4C2×Dic1512yes—
304C42—21no—
305C3×C5#189111yescharacteristic, complemented, Hall
306C22×C3—22no—
307C22×C3—24no—
308C22×C3—22no—
309C22×C3—41no—
310C22×C3—42no—
311C22×C3—41no—
312C22×C3—42no—
313C22×C3—41no—
314C22×C3D4×Dic512yes—
315C22×C3C2×C22⋊Dic511yescharacteristic
316C3×C4—22no—
317C3×C4—42no—
318C3×C4—41no—
319C3×C4#408111yescharacteristic
320C3×C4#408311yescharacteristic
321C3×C4#408512yes—
322C2×C5—21no—
323C2×C5—22no—
324C2×C5—42no—
325C2×C5—42no—
326C2×C5#522011yescharacteristic
327C23—22no—
328C23—21no—
329C23—42no—
330C23#671912yes—
331C23C22×Dic1511yescharacteristic
332Q8—22no—
333D4—24no—
334D4—22no—
335D4—44no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4#671912yes—
345C2×C4D4×D1512yes—
346C2×C4#681912yes—
347C2×C4C2×#122011yescharacteristic
348C2×C4C2×#122011yescharacteristic
349C8—304no—
350C8—602no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—42no—
354C2×C3—42no—
355C2×C3#6550911yescharacteristic
356C5#7171411yescharacteristic, complemented, Sylow
357C22—22no—
358C22—24no—
359C22—22no—
360C22—41no—
361C22—42no—
362C22—41no—
363C22—42no—
364C22—41no—
365C22D4×Dic1512yes—
366C22C2×#671911yescharacteristic
367C4—22no—
368C4—42no—
369C4—41no—
370C4#9182411yescharacteristic
371C4#9182611yescharacteristic
372C4#9182812yes—
373C3#1060250711yescharacteristic, complemented, Sylow
374C2—21no—
375C2—22no—
376C2—42no—
377C2—42no—
378C2#1175132111yescharacteristic
subgroupG/H
centerC4#91826
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
Fitting, prime radicalC3×C5×#525C2
socleC2×C3×C5#386
cosocleC22×C3×C4×C5C23
hypercenter#525D15
hypocenterC3×C5#1891
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. #11756578C2semidirect
3. #11751338C2semidirect
4. #11751308C2semidirect
5. #11746354C2semidirect
55. C2×C3⋊#168D4semidirect
305. C3×C5#1891semidirect
356. C5#71714semidirect
373. C3#10602507semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5252
#117565782
#117513382
#117513082
#117463542
#106025073
#717145