Finite Group Databasebeta

← #14297742

Subgroups — #14297742

Order 1920.

712 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
1C2×C3×C4×D20C211yesmaximal, characteristic
2#11751037C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×#90965C212yesmaximal
5#11745980C212yesmaximal, complemented
6#10601273—31nomaximal, Hall
7C22×C3×D20C2211yescharacteristic
8C22×C3×C4×D5—21no—
9C2×C3×C42×C5C2211yescharacteristic
10C2×C4⋊Dic15C2212yes—
11C22×C5×C3⋊C8C2212yes—
12C2×C3×#685—21no—
13C2×C3×C4⋊Dic5C2211yescharacteristic
14C3×C4×D20—22no—
15C3×C4×D20C414yescomplemented
16#91115—21no—
17#91115—21no—
18C5×C4⋊(C3⋊C8)—22no—
19#90965—24no—
20#71605—51nomaximal, Hall
21C2×C4×D20D311yescharacteristic
22C2×C5×C4⋊C8—31no—
23C2×#3953—32no—
24#65225—31no—
25#64771—32no—
26C23×C3×D5—21no—
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C22×Dic15—22no—
31C22×C3×Dic5—21no—
32C2×C3×D20—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×D20C2×C412yes—
36C2×C3×D20D412yes—
37C2×C3×D20Q812yes—
38C2×C3×C4×D5—24no—
39C2×C3×C4×D5—44no—
40C3×C42×C5C2×C412yes—
41C3×C42×C5D412yes—
42C4⋊Dic15—22no—
43C4⋊Dic15—22no—
44C2×C5×C3⋊C8—22no—
45C2×C5×C3⋊C8—22no—
46C2×C5×C3⋊C8—22no—
47C3×#685—24no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C412yes—
50C2×C3×C4×D4—51no—
51C2×#832—52no—
52#4936—51no—
53C2×C4⋊(C3⋊C8)D511yescharacteristic, complemented
54#4529—52no—
55C22×D20C2×D311yescharacteristic
56C22×C4×D5—21no—
57C22×C5×C8—32no—
58C2×C42×C5C2×D311yescharacteristic
59C2×#685—21no—
60C2×C4⋊Dic5—32no—
61C2×C4⋊Dic5C2×D311yescharacteristic
62C4×D20—22no—
63C4×D20Dic314yescomplemented
64C5×C4⋊C8—62no—
65#3963—61no—
66#3963—61no—
67#3953—64no—
68#1804—151noSylow
69C23×C3×C5C2×D411yescharacteristic
70C22×C3×D5—22no—
71C22×C3×D5—22no—
72C22×C3×D5—22no—
73C22×C3×D5—42no—
74C22×C3×D5—42no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5C22⋊C412yes—
78C2×C3×C4×C5C22⋊C412yes—
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×Q811yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×Dic15—42no—
86C2×Dic15—42no—
87C2×Dic15—42no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5—42no—
90C3×D20—22no—
91C3×D20—22no—
92C3×D20—22no—
93C3×D20C4⋊C414yes—
94C3×C4×D5—48no—
95C5×C3⋊C8—42no—
96C22×C3×D4—51no—
97C23×C3×C4—101no—
98C3×C4×D4—54no—
99C3×C4×D4—102no—
100C2×C3×C4⋊C4—51no—
101C2×C3×C22⋊C4—101no—
102C2×C3×C42C2×D511yescharacteristic
103C2×C4⋊Dic3—52no—
104C22×C3⋊C8C2×D512yes—
105#832—104no—
106C3⋊#95—101no—
107C3⋊#95—101no—
108C4⋊(C3⋊C8)—22no—
109C23×D5—21no—
110C22×C4×C5#6711yescharacteristic
111C22×C4×C5#6711yescharacteristic
112C22×C4×C5C22×D311yescharacteristic
113C22×Dic5—21no—
114C22×Dic5—62no—
115C2×D20—21no—
116C2×D20—21no—
117C2×D20—21no—
118C2×D20Dic612yes—
119C2×D20D1212yes—
120C2×D20C2×Dic312yes—
121C2×C4×D5—24no—
122C2×C4×D5—44no—
123C2×C5×C8—62no—
124C2×C5×C8—62no—
125C2×C5×C8—62no—
126C42×C5C2×Dic312yes—
127C42×C5#6712yes—
128#685—24no—
129C4⋊Dic5—21no—
130C4⋊Dic5—62no—
131C4⋊Dic5—62no—
132C4⋊Dic5C2×Dic312yes—
133C2×C4×D4—51no—
134C2×C4⋊C8—31no—
135C2×#102—152no—
136#382—151no—
137#340—152no—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C22×C3×C5#12111yescharacteristic
140C22×C3×C5C22⋊Q811yescharacteristic
141C22×C3×C5#13512yes—
142C22×C3×C5AGL(1,ℤ/8)12yes—
143C2×C3×D5—24no—
144C2×C3×D5—42no—
145C2×C3×D5—42no—
146C2×C3×D5—44no—
147C2×C3×D5—44no—
148C3×C4×C5—22no—
149C3×C4×C5—22no—
150C3×C4×C5C2×C4⋊C411yescharacteristic
151C3×C4×C5#11711yescharacteristic
152C3×C4×C5#12111yescharacteristic
153C3×C4×C5C22⋊Q811yescharacteristic
154Dic15—82no—
155C3×Dic5—42no—
156C24×C3—101no—
157C2×C3×D4—52no—
158C2×C3×D4—52no—
159C2×C3×D4—52no—
160C2×C3×D4—101no—
161C2×C3×D4—101no—
162C2×C3×D4—101no—
163C22×C3×C4—101no—
164C22×C3×C4—104no—
165C22×C3×C4—204no—
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4D2011yescharacteristic
168C22×C3×C4C22×D511yescharacteristic
169C22×Dic3—102no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—101no—
172C3×C22⋊C4—104no—
173C3×C42C4×D512yes—
174C3×C42C22⋊D512yes—
175C4⋊Dic3—102no—
176C4⋊Dic3—102no—
177C2×C3⋊C8—22no—
178C2×C3⋊C8—22no—
179C2×C3⋊C8—22no—
180C23×C5C2×#6711yescharacteristic
181C22×D5—22no—
182C22×D5—22no—
183C22×D5—22no—
184C22×D5—42no—
185C22×D5—42no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5#21712yes—
189C2×C4×C5#21712yes—
190C2×C4×C5C2×Dic611yescharacteristic
191C2×C4×C5C2×D1211yescharacteristic
192C2×C4×C5#23511yescharacteristic
193C2×C4×C5#23511yescharacteristic
194C2×C4×C5C22×Dic311yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—22no—
197C2×Dic5—42no—
198C2×Dic5—122no—
199C2×Dic5—122no—
200C2×Dic5—122no—
201D20—22no—
202D20—22no—
203D20—22no—
204D20C4⋊Dic314yes—
205C4×D5—48no—
206C5×C8—122no—
207C22×D4—51no—
208C23×C4—101no—
209C22×C8—32no—
210C4×D4—54no—
211C4×D4—102no—
212C2×C4⋊C4—51no—
213C2×C4⋊C4—152no—
214C2×C22⋊C4—101no—
215C2×C42D3×D511yescharacteristic
216C4⋊C8—62no—
217#102—304no—
218#95—301no—
219#95—301no—
220C2×C3×C5#38011yescharacteristic
221C2×C3×C5#41611yescharacteristic
222C2×C3×C5#41811yescharacteristic
223C2×C3×C5#46312yes—
224C2×C3×C5#47812yes—
225C3×D5—44no—
226C23×C3—102no—
227C23×C3—102no—
228C23×C3—102no—
229C23×C3—202no—
230C23×C3—202no—
231C23×C3C2×D2011yescharacteristic
232C3×D4—54no—
233C3×D4—102no—
234C3×D4—102no—
235C3×D4—102no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—102no—
239C2×C3×C4—208no—
240C2×C3×C4—202no—
241C2×C3×C4#68512yes—
242C2×C3×C4#68512yes—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4#71111yescharacteristic
246C2×C3×C4Q8×D511yescharacteristic
247C2×C3×C4#71311yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×Dic3—202no—
250C2×Dic3—202no—
251C2×Dic3—202no—
252C3⋊C8—42no—
253C22×C5#92411yescharacteristic
254C22×C5#93011yescharacteristic
255C22×C5#93212yes—
256C22×C5#95012yes—
257C22×C5C2×#21711yescharacteristic
258C2×D5—24no—
259C2×D5—42no—
260C2×D5—42no—
261C2×D5—44no—
262C2×D5—44no—
263C4×C5—22no—
264C4×C5—22no—
265C4×C5#92411yescharacteristic
266C4×C5C2×C4⋊Dic311yescharacteristic
267C4×C5#92611yescharacteristic
268C4×C5#93011yescharacteristic
269Dic5—42no—
270Dic5—242no—
271C24—101no—
272C2×D4—52no—
273C2×D4—52no—
274C2×D4—52no—
275C2×D4—101no—
276C2×D4—101no—
277C2×D4—101no—
278C22×C4—101no—
279C22×C4—104no—
280C22×C4—204no—
281C22×C4—302no—
282C22×C4#120211yescharacteristic
283C22×C4#120211yescharacteristic
284C22×C4C2×D3×D511yescharacteristic
285C2×C8—62no—
286C2×C8—62no—
287C2×C8—62no—
288C4⋊C4—52no—
289C4⋊C4—101no—
290C4⋊C4—302no—
291C4⋊C4—302no—
292C22⋊C4—104no—
293C42D5×Dic312yes—
294C42#120112yes—
295C3×C5#180411yescharacteristic, complemented, Hall
296C22×C3—104no—
297C22×C3—204no—
298C22×C3—204no—
299C22×C3—202no—
300C22×C3—202no—
301C22×C3#404111yescharacteristic
302C22×C3#404311yescharacteristic
303C22×C3#405012yes—
304C22×C3#405412yes—
305C22×C3C2×#68511yescharacteristic
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—202no—
309C3×C4D5×C4⋊C411yescharacteristic
310C3×C4#403811yescharacteristic
311C3×C4#408411yescharacteristic
312C3×C4#409211yescharacteristic
313Dic3—402no—
314C2×C5#500912yes—
315C2×C5#501612yes—
316C2×C5#521211yescharacteristic
317C2×C5#521511yescharacteristic
318C2×C5#523311yescharacteristic
319D5—44no—
320C23—102no—
321C23—102no—
322C23—102no—
323C23—202no—
324C23—202no—
325C23C2×#120211yescharacteristic
326D4—54no—
327D4—102no—
328D4—102no—
329D4—102no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—102no—
333C2×C4—208no—
334C2×C4—202no—
335C2×C4—602no—
336C2×C4—602no—
337C2×C4—602no—
338C2×C4#666512yes—
339C2×C4#666512yes—
340C2×C4D5×Dic611yescharacteristic
341C2×C4#677211yescharacteristic
342C2×C4#677311yescharacteristic
343C2×C4D5×D1211yescharacteristic
344C2×C4C2×D5×Dic311yescharacteristic
345C2×C4C2×#120111yescharacteristic
346C8—122no—
347C2×C3—204no—
348C2×C3#6513312yes—
349C2×C3#6513612yes—
350C2×C3#6527611yescharacteristic
351C2×C3#6540211yescharacteristic
352C2×C3#6542011yescharacteristic
353C5#7160511yescharacteristic, complemented, Sylow
354C22—104no—
355C22—202no—
356C22—202no—
357C22—204no—
358C22—204no—
359C22#9131112yes—
360C22#9131212yes—
361C22#9136011yescharacteristic
362C22#9145011yescharacteristic
363C22C2×#666511yescharacteristic
364C4—22no—
365C4—22no—
366C4—202no—
367C4—1202no—
368C4#9135811yescharacteristic
369C4#9135911yescharacteristic
370C4D5×C4⋊Dic311yescharacteristic
371C4#9144911yescharacteristic
372C3#1060127311yescharacteristic, complemented, Sylow
373C2—204no—
374C2#1174688812yes—
375C2#1174706312yes—
376C2#1174836511yescharacteristic
377C2#1174836711yescharacteristic
378C2#1174875911yescharacteristic
subgroupG/H
centerC23C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1804
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751037C2semidirect
3. C2×C5×C4⋊(C3⋊C8)C2semidirect
5. #11745980C2semidirect
15. C3×C4×D20C4semidirect
53. C2×C4⋊(C3⋊C8)D5semidirect
63. C4×D20Dic3semidirect
295. C3×C5#1804semidirect
353. C5#71605semidirect
372. C3#10601273semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
#117510372
C2×C5×C4⋊(C3⋊C8)2
C2×#909652
#117459802
#106012733
#716055