Finite Group Databasebeta

← #14300708

Subgroups — #14300708

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic, complemented
4C2×#90964C212yesmaximal, complemented
5#11745979C212yesmaximal, complemented
6#10602353—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C23×C5×Dic3—21no—
9C22×C3×C22⋊D5—21no—
10C22×C3×D20C2211yescharacteristic
11C22×C3⋊#168C2212yes—
12C2×C5×C4⋊Dic3—21no—
13C2×C5×C4⋊Dic3—24no—
14C2×C5×C4⋊Dic3C2212yes—
15C3×#4076—22no—
16C3×#4076C414yescomplemented
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19#91114—22no—
20#90964—24no—
21#71677—51nomaximal, Hall
22C22×C5×C4⋊C4—31no—
23C2×#4076D311yescharacteristic
24C2×C22⋊#168—31no—
25C2×#3941—32no—
26#64749—32no—
27C24×C3×C5D411yescharacteristic
28C23×C3×D5—21no—
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5C2×C412yes—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3—24no—
36C22×C5×Dic3—22no—
37C22×C5×Dic3—42no—
38C22×C5×Dic3—42no—
39C2×C3×C22⋊D5—24no—
40C2×C3×C22⋊D5—42no—
41C2×C3×C22⋊D5—42no—
42C22×C3×Dic5—21no—
43C2×C3×D20—22no—
44C2×C3×D20—22no—
45C2×C3×D20—21no—
46C2×C3×D20C2×C412yescomplemented
47C2×C3⋊#168—22no—
48C2×C3⋊#168—22no—
49C2×C3⋊#168—22no—
50C5×C4⋊Dic3—24no—
51C5×C4⋊Dic3—22no—
52C5×C4⋊Dic3D414yescomplemented
53C3×#685—24no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C412yescomplemented
56C2×C3×#121—51no—
57C22×C4⋊Dic3D511yescharacteristic, complemented
58C2×#832—52no—
59C2×#830—51no—
60#4529—52no—
61C23×C4×C5—61no—
62C23×C4×C5C2×D311yescharacteristic
63C22×C22⋊D5—21no—
64C22×D20C2×D311yescharacteristic
65C2×C5×C4⋊C4—32no—
66C2×C5×C4⋊C4—64no—
67C2×C5×C4⋊C4—61no—
68#4076—22no—
69#4076Dic314yescomplemented
70C2×#685—21no—
71C2×C4⋊Dic5C2×D311yescharacteristic
72C22×#168—32no—
73C22⋊#168—62no—
74#3941—64no—
75#1874—151noSylow
76C23×C3×C5—21no—
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—21no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5D812yes—
82C23×C3×C5SD1612yes—
83C23×C3×C5C2×D411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5—41no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—24no—
94C2×C3×C4×C5—24no—
95C2×C3×C4×C5C22⋊C412yes—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D412yes—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4112yes—
100C2×C5×Dic3—24no—
101C2×C5×Dic3—48no—
102C2×C5×Dic3—42no—
103C2×C5×Dic3—42no—
104C3×C22⋊D5—48no—
105C2×C3×Dic5—22no—
106C2×C3×Dic5—41no—
107C2×C3×Dic5—41no—
108C3×D20—24no—
109C3×D20—42no—
110C3⋊#168—42no—
111C22×C3×D4—51no—
112C22×C3×D4—101no—
113C23×C3×C4C2×D511yescharacteristic
114C23×Dic3—21no—
115C3×#121—54no—
116C3×#121—102no—
117C2×C3×C4⋊C4—51no—
118C2×C3×C22⋊C4—101no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—24no—
121C2×C4⋊Dic3C2×D512yes—
122C22×C3⋊C8—52no—
123#832—104no—
124#830—102no—
125C24×C5#6711yescharacteristic
126C23×D5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—64no—
130C22×C4×C5—62no—
131C22×C4×C5—122no—
132C22×C4×C5—122no—
133C22×C4×C5C2×Dic312yes—
134C22×C4×C5#6711yescharacteristic
135C22×C4×C5#6712yes—
136C22×C4×C5C22×D311yescharacteristic
137C2×C22⋊D5—24no—
138C2×C22⋊D5—42no—
139C2×C22⋊D5—42no—
140C22×Dic5—21no—
141C2×D20—22no—
142C2×D20—22no—
143C2×D20—21no—
144C2×D20C2×Dic312yescomplemented
145C5×C4⋊C4—34no—
146C5×C4⋊C4—64no—
147C5×C4⋊C4—62no—
148#685—24no—
149C4⋊Dic5—21no—
150C4⋊Dic5C2×Dic312yescomplemented
151C2×#168—62no—
152C2×#168—62no—
153C2×#168—62no—
154C2×#121—51no—
155C22×C4⋊C4—31no—
156C2×#102—152no—
157C2×C22⋊C8—151no—
158#340—152no—
159C22×C3×C5—22no—
160C22×C3×C5—22no—
161C22×C3×C5—22no—
162C22×C3×C5—22no—
163C22×C3×C5—22no—
164C22×C3×C5—22no—
165C22×C3×C5#10214yescomplemented
166C22×C3×C5C2×C22⋊C411yescharacteristic
167C22×C3×C5#12011yescharacteristic
168C22×C3×C5#12311yescharacteristic
169C22×C3×C5C2×D811yescharacteristic
170C22×C3×C5C2×SD1611yescharacteristic
171C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×C3×D5—42no—
174C2×C3×D5—42no—
175C2×C3×D5—42no—
176C2×C3×D5—81no—
177C2×C3×D5—81no—
178C2×C3×D5—81no—
179C2×C3×D5—81no—
180C3×C4×C5—22no—
181C3×C4×C5C4×D412yes—
182C3×C4×C5#12112yes—
183C3×Dic5—42no—
184C5×Dic3—44no—
185C24×C3—101no—
186C24×C3C22⋊D511yescharacteristic
187C2×C3×D4—52no—
188C2×C3×D4—104no—
189C2×C3×D4—101no—
190C2×C3×D4—102no—
191C2×C3×D4—102no—
192C2×C3×D4—202no—
193C2×C3×D4—202no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—101no—
197C22×C3×C4C4×D512yes—
198C22×C3×C4D2012yes—
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—24no—
202C22×Dic3—22no—
203C22×Dic3—42no—
204C22×Dic3—42no—
205C3×C4⋊C4—52no—
206C3×C4⋊C4—101no—
207C3×C22⋊C4—104no—
208C4⋊Dic3—24no—
209C4⋊Dic3—22no—
210C4⋊Dic3C22⋊D514yescomplemented
211C2×C3⋊C8—102no—
212C2×C3⋊C8—102no—
213C2×C3⋊C8—102no—
214C23×C5—21no—
215C23×C5—21no—
216C23×C5—21no—
217C23×C5—21no—
218C23×C5#21312yes—
219C23×C5#21412yes—
220C23×C5#21712yes—
221C23×C5C2×#6711yescharacteristic
222C22×D5—22no—
223C22×D5—41no—
224C22×D5—41no—
225C22×D5—41no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5—41no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—24no—
232C2×C4×C5—24no—
233C2×C4×C5—64no—
234C2×C4×C5—128no—
235C2×C4×C5—122no—
236C2×C4×C5—122no—
237C2×C4×C5#21712yes—
238C2×C4×C5D3×D412yes—
239C2×C4×C5#23712yes—
240C2×C4×C5C22×Dic311yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—48no—
243C2×Dic5—22no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246D20—24no—
247D20—42no—
248#168—122no—
249C22×D4—51no—
250C22×D4—101no—
251C23×C4—61no—
252C23×C4D3×D511yescharacteristic
253C22×C8—152no—
254#121—54no—
255#121—102no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—51no—
258C2×C4⋊C4—64no—
259C2×C4⋊C4—61no—
260C2×C22⋊C4—101no—
261#102—304no—
262C22⋊C8—302no—
263C2×C3×C5—24no—
264C2×C3×C5#38611yescharacteristic
265C2×C3×C5C2×#10211yescharacteristic
266C2×C3×C5#41711yescharacteristic
267C2×C3×C5#44711yescharacteristic
268C2×C3×C5#44811yescharacteristic
269C2×C3×C5#48011yescharacteristic
270C2×C3×C5#48111yescharacteristic
271C3×D5—82no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—102no—
277C23×C3—201no—
278C23×C3—201no—
279C23×C3—201no—
280C23×C3—201no—
281C23×C3—201no—
282C23×C3—201no—
283C23×C3#68512yes—
284C23×C3#68612yes—
285C23×C3#68812yes—
286C23×C3C2×C22⋊D511yescharacteristic
287C3×D4—104no—
288C3×D4—208no—
289C3×D4—202no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—102no—
295C2×C3×C4—201no—
296C2×C3×C4—201no—
297C2×C3×C4#68512yes—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4#70912yes—
301C2×C3×C4C2×C22⋊D512yes—
302C2×Dic3—24no—
303C2×Dic3—48no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C3⋊C8—202no—
307C22×C5—22no—
308C22×C5—22no—
309C22×C5—22no—
310C22×C5—22no—
311C22×C5—22no—
312C22×C5—22no—
313C22×C5#83214yescomplemented
314C22×C5C2×#21311yescharacteristic
315C22×C5C2×#21411yescharacteristic
316C22×C5#93511yescharacteristic
317C22×C5#93711yescharacteristic
318C22×C5#94911yescharacteristic
319C22×C5#95111yescharacteristic
320C22×C5C2×#21711yescharacteristic
321C2×D5—42no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5—81no—
325C2×D5—81no—
326C2×D5—81no—
327C2×D5—81no—
328C4×C5—22no—
329C4×C5—124no—
330C4×C5D4×Dic312yes—
331C4×C5#93912yes—
332Dic5—42no—
333C24—101no—
334C24#120111yescharacteristic
335C2×D4—52no—
336C2×D4—104no—
337C2×D4—102no—
338C2×D4—101no—
339C2×D4—102no—
340C2×D4—202no—
341C2×D4—202no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—64no—
345C22×C4—62no—
346C22×C4—101no—
347C22×C4—122no—
348C22×C4—122no—
349C22×C4D5×Dic312yes—
350C22×C4#120111yescharacteristic
351C22×C4#120212yes—
352C22×C4C2×D3×D511yescharacteristic
353C2×C8—302no—
354C2×C8—302no—
355C2×C8—302no—
356C4⋊C4—34no—
357C4⋊C4—52no—
358C4⋊C4—64no—
359C4⋊C4—62no—
360C4⋊C4—101no—
361C22⋊C4—104no—
362C3×C5#187411yescharacteristic, complemented, Hall
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—202no—
370C22×C3—202no—
371C22×C3—202no—
372C22×C3—401no—
373C22×C3—401no—
374C22×C3—401no—
375C22×C3—401no—
376C22×C3#394114yescomplemented
377C22×C3C2×#68511yescharacteristic
378C22×C3#407511yescharacteristic
379C22×C3C2×#68611yescharacteristic
380C22×C3#407811yescharacteristic
381C22×C3C2×#68811yescharacteristic
382C22×C3#408811yescharacteristic
383C22×C3#409911yescharacteristic
384C3×C4—22no—
385C3×C4—202no—
386C3×C4C4×C22⋊D512yes—
387C3×C4#407612yes—
388Dic3—44no—
389C2×C5—24no—
390C2×C5#503311yescharacteristic
391C2×C5#503411yescharacteristic
392C2×C5#503611yescharacteristic
393C2×C5#504011yescharacteristic
394C2×C5C2×#83211yescharacteristic
395C2×C5#522011yescharacteristic
396C2×C5#523211yescharacteristic
397D5—82no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—102no—
403C23—201no—
404C23—201no—
405C23—201no—
406C23—201no—
407C23—201no—
408C23—201no—
409C23#665212yes—
410C23#665512yes—
411C23#666512yes—
412C23C2×#120111yescharacteristic
413D4—104no—
414D4—208no—
415D4—202no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—64no—
421C2×C4—102no—
422C2×C4—128no—
423C2×C4—122no—
424C2×C4—122no—
425C2×C4—201no—
426C2×C4—201no—
427C2×C4#666512yes—
428C2×C4C2×D5×Dic311yescharacteristic
429C2×C4#677912yes—
430C2×C4C2×#120211yescharacteristic
431C2×C4D3×C22⋊D512yes—
432C8—602no—
433C2×C3—24no—
434C2×C3—402no—
435C2×C3C2×#394111yescharacteristic
436C2×C3#6525511yescharacteristic
437C2×C3#6525611yescharacteristic
438C2×C3#6525711yescharacteristic
439C2×C3#6550211yescharacteristic
440C2×C3#6550611yescharacteristic
441C2×C3#6551611yescharacteristic
442C5#7167711yescharacteristic, complemented, Sylow
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—202no—
450C22—202no—
451C22—202no—
452C22—401no—
453C22—401no—
454C22—401no—
455C22—401no—
456C22#9096414yescomplemented
457C22C2×#665211yescharacteristic
458C22#9129911yescharacteristic
459C22C2×#665511yescharacteristic
460C22#9130711yescharacteristic
461C22C2×#666511yescharacteristic
462C22#9153611yescharacteristic
463C22#9156811yescharacteristic
464C4—22no—
465C4—124no—
466C4—202no—
467C4Dic3×C22⋊D512yes—
468C4#9156912yes—
469C3#1060235311yescharacteristic, complemented, Sylow
470C2—24no—
471C2—402no—
472C2C2×#9096411yescharacteristic
473C2#1174836811yescharacteristic
474C2#1174837011yescharacteristic
475C2#1174837211yescharacteristic
476C2#1174851611yescharacteristic
477C2#1174853611yescharacteristic
478C2#1174949511yescharacteristic
subgroupG/H
centerC23C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1874
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×C4⋊Dic3C2semidirect
3. C2×#91114C2semidirect
4. C2×#90964C2semidirect
5. #11745979C2semidirect
16. C3×#4076C4semidirect
46. C2×C3×D20C2×C4semidirect
52. C5×C4⋊Dic3D4semidirect
55. C3×C4⋊Dic5C2×C4semidirect
57. C22×C4⋊Dic3D5semidirect
69. #4076Dic3semidirect
144. C2×D20C2×Dic3semidirect
150. C4⋊Dic5C2×Dic3semidirect
165. C22×C3×C5#102semidirect
210. C4⋊Dic3C22⋊D5semidirect
313. C22×C5#832semidirect
362. C3×C5#1874semidirect
376. C22×C3#3941semidirect
442. C5#71677semidirect
456. C22#90964semidirect
469. C3#10602353semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C4⋊Dic32
C2×C3×#40762
C2×#911142
C2×#909642
#117459792
#106023533
#716775