Finite Group Databasebeta

← #14281348

Subgroups — #14281348

Order 1920.

644 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2C2×#91114C211yesmaximal, characteristic, complemented
3C5×#5207C211yesmaximal, characteristic, complemented
4#11745948C214yesmaximal, complemented
5#10600763—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×C22⋊D5C412yes—
8C22×C3×D20C411yescharacteristic
9C22×C3⋊#168—21no—
10C2×C5×#208—21no—
11C3×#4076—21no—
12C3×#4076—21no—
13C3×#4076—21no—
14C3×#4076—21no—
15C2×C3×#685C2212yes—
16C2×C3×C4⋊Dic5C411yescharacteristic
17#91114—21no—
18#91114C2212yes—
19C5×#830—21no—
20C5×#830C2212yes—
21#71676—51nomaximal, Hall
22C2×#4076D311yescharacteristic
23C5×#407—31no—
24C2×C22⋊#168—31no—
25#64688—34no—
26C24×C3×C5C2×C411yescharacteristic
27C23×C3×D5C2×C412yes—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—44no—
38C22×C3×Dic5C2×C412yes—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—42no—
42C2×C3⋊#168—22no—
43C2×C3⋊#168—42no—
44C5×#208—42no—
45C2×C5×C3⋊C8—22no—
46C3×#685—22no—
47C3×#685—22no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C2×C3×#121—51no—
51#5207D511yescharacteristic, complemented
52C2×#830—51no—
53#4525—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×C22⋊D5Dic312yes—
56C22×D20Dic311yescharacteristic
57C2×C5×M16—61no—
58#4076—21no—
59#4076—21no—
60#4076—21no—
61#4076—21no—
62C2×#685C2×D312yes—
63C2×C4⋊Dic5Dic311yescharacteristic
64C22×#168—61no—
65C5×C22⋊C8—32no—
66C5×C22⋊C8—61no—
67C22⋊#168—32no—
68C22⋊#168—61no—
69#1471—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22×C411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—24no—
78C22×C3×D5—42no—
79C22×C3×D5—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C3×C22⋊D5—44no—
91C3×C22⋊D5—44no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—42no—
94C3×D20—42no—
95C3×D20—42no—
96C3⋊#168—42no—
97C5×C3⋊C8—42no—
98C22×C3×D4—52no—
99C22×C3×D4—51no—
100C23×C3×C4C2×D511yescharacteristic
101C3×#121—101no—
102C3×#121—101no—
103C3×#121—101no—
104C3×#121—101no—
105C2×C3×C4⋊C4—51no—
106C2×C3×C22⋊C4—52no—
107C2×#208—21no—
108C22×C3⋊C8—101no—
109#830—21no—
110#830—52no—
111#830—101no—
112#830C2×D512yes—
113C24×C5C2×Dic311yescharacteristic
114C23×D5C2×Dic312yes—
115C22×C4×C5—42no—
116C22×C4×C5C2×Dic311yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C22×C4×C5#6711yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5C22×D311yescharacteristic
122C2×C22⋊D5—22no—
123C2×C22⋊D5—22no—
124C2×C22⋊D5—44no—
125C22×Dic5C2×Dic312yes—
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—42no—
129C5×M16—122no—
130C2×C5×C8—62no—
131#685—22no—
132#685—22no—
133C4⋊Dic5—21no—
134C4⋊Dic5—21no—
135C2×#168—62no—
136C2×#168—122no—
137C2×#121—51no—
138#407—31no—
139C2×C22⋊C8—151no—
140#323—154no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—44no—
149C22×C3×C5#10012yes—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C22×C3×C5#13112yes—
152C2×C3×D5—42no—
153C2×C3×D5—42no—
154C2×C3×D5—42no—
155C2×C3×D5—84no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5#9912yes—
160C3×Dic5—42no—
161C24×C3—52no—
162C24×C3C4×D511yescharacteristic
163C2×C3×D4—102no—
164C2×C3×D4—102no—
165C2×C3×D4—101no—
166C2×C3×D4—101no—
167C2×C3×D4—202no—
168C2×C3×D4—204no—
169C22×C3×C4—42no—
170C22×C3×C4—52no—
171C22×C3×C4C4×D511yescharacteristic
172C22×C3×C4D2011yescharacteristic
173C22×C3×C4D2011yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C22×C3×C4C22⋊D511yescharacteristic
176C22×C3×C4C22×D511yescharacteristic
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C22⋊C4—102no—
180C3×C22⋊C4—102no—
181#208—42no—
182C2×C3⋊C8—22no—
183C2×C3⋊C8—102no—
184C2×C3⋊C8—202no—
185C23×C5—22no—
186C23×C5—22no—
187C23×C5—41no—
188C23×C5#21711yescharacteristic
189C23×C5#21711yescharacteristic
190C23×C5C22×Dic311yescharacteristic
191C22×D5—22no—
192C22×D5—24no—
193C22×D5—42no—
194C22×D5—42no—
195C2×C4×C5—22no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5#21711yescharacteristic
202C2×C4×C5#21711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×C4×C5C2×#6711yescharacteristic
205C22⋊D5—44no—
206C22⋊D5—44no—
207C2×Dic5—22no—
208C2×Dic5—42no—
209D20—42no—
210D20—42no—
211C5×C8—122no—
212#168—122no—
213C22×D4—52no—
214C22×D4—51no—
215C23×C4D3×D511yescharacteristic
216C2×M16—61no—
217C22×C8—301no—
218#121—101no—
219#121—101no—
220#121—101no—
221#121—101no—
222C2×C4⋊C4—51no—
223C2×C22⋊C4—52no—
224C22⋊C8—32no—
225C22⋊C8—61no—
226C22⋊C8—152no—
227C22⋊C8—301no—
228C2×C3×C5—22no—
229C2×C3×C5—22no—
230C2×C3×C5—41no—
231C2×C3×C5#40811yescharacteristic
232C2×C3×C5C2×#9911yescharacteristic
233C2×C3×C5C2×#10011yescharacteristic
234C3×D5—82no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—41no—
238C23×C3—102no—
239C23×C3—104no—
240C23×C3—202no—
241C23×C3—202no—
242C23×C3#68511yescharacteristic
243C23×C3#68511yescharacteristic
244C23×C3C2×C4×D511yescharacteristic
245C3×D4—202no—
246C3×D4—204no—
247C3×D4—204no—
248C3×D4—202no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—102no—
256C2×C3×C4—202no—
257C2×C3×C4#68511yescharacteristic
258C2×C3×C4#68511yescharacteristic
259C2×C3×C4C2×D2011yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C3⋊C8—42no—
262C3⋊C8—202no—
263C22×C5—21no—
264C22×C5—21no—
265C22×C5—21no—
266C22×C5—21no—
267C22×C5—21no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—44no—
271C22×C5#83312yes—
272C22×C5#94812yes—
273C22×C5C2×#21711yescharacteristic
274C2×D5—42no—
275C2×D5—42no—
276C2×D5—42no—
277C2×D5—84no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5#83412yes—
282Dic5—42no—
283C24—52no—
284C24D5×Dic311yescharacteristic
285C2×D4—102no—
286C2×D4—102no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—202no—
290C2×D4—204no—
291C22×C4—42no—
292C22×C4—52no—
293C22×C4D5×Dic311yescharacteristic
294C22×C4#120111yescharacteristic
295C22×C4#120111yescharacteristic
296C22×C4#120211yescharacteristic
297C22×C4#120211yescharacteristic
298C22×C4C2×D3×D511yescharacteristic
299M16—122no—
300C2×C8—62no—
301C2×C8—302no—
302C2×C8—602no—
303C4⋊C4—101no—
304C4⋊C4—101no—
305C22⋊C4—102no—
306C22⋊C4—102no—
307C3×C5#147111yescharacteristic, complemented, Hall
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—44no—
316C22×C3—202no—
317C22×C3—202no—
318C22×C3—202no—
319C22×C3—404no—
320C22×C3#395512yes—
321C22×C3#405312yes—
322C22×C3C2×#68511yescharacteristic
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—202no—
327C3×C4#393812yes—
328C2×C5—22no—
329C2×C5—22no—
330C2×C5—41no—
331C2×C5C2×#83311yescharacteristic
332C2×C5C2×#83411yescharacteristic
333C2×C5#523411yescharacteristic
334D5—82no—
335C23—22no—
336C23—22no—
337C23—41no—
338C23—102no—
339C23—104no—
340C23—202no—
341C23—202no—
342C23#666511yescharacteristic
343C23#666511yescharacteristic
344C23C2×D5×Dic311yescharacteristic
345D4—202no—
346D4—204no—
347D4—204no—
348D4—202no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—102no—
356C2×C4—202no—
357C2×C4#666511yescharacteristic
358C2×C4#666511yescharacteristic
359C2×C4C2×#120111yescharacteristic
360C2×C4C2×#120211yescharacteristic
361C8—122no—
362C8—602no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—41no—
366C2×C3—402no—
367C2×C3C2×#393811yescharacteristic
368C2×C3#6541811yescharacteristic
369C2×C3C2×#395511yescharacteristic
370C5#7167611yescharacteristic, complemented, Sylow
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—202no—
380C22—202no—
381C22—202no—
382C22—404no—
383C22#9095812yes—
384C22#9128412yes—
385C22C2×#666511yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—202no—
390C4#9099512yes—
391C3#1060076311yescharacteristic, complemented, Sylow
392C2—22no—
393C2—22no—
394C2—41no—
395C2—402no—
396C2#1174834311yescharacteristic
397C2C2×#9095811yescharacteristic
398C2C2×#9099511yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1471
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91114C2semidirect
3. C5×#5207C2semidirect
4. #11745948C2semidirect
51. #5207D5semidirect
307. C3×C5#1471semidirect
370. C5#71676semidirect
391. C3#10600763semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40762
C2×#911142
C5×#52072
#117459482
#106007633
#716765