Finite Group Databasebeta

← #14302460

Subgroups — #14302460

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4054C211yesmaximal, characteristic
2#11754488C211yesmaximal, characteristic, complemented
3#11748624C211yesmaximal, characteristic, complemented
4#11748420C211yesmaximal, characteristic, complemented
5#11748367C211yesmaximal, characteristic, complemented
6#11746378C211yesmaximal, characteristic, complemented
7C5×#4556C211yesmaximal, characteristic, complemented
8#10599820—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13#91815C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C3×#4054—22no—
17C3×#4054—22no—
18C2×C3×D40C412yescomplemented
19C2×C3×#677C412yescomplemented
20D5×#217—22no—
21#91434—22no—
22Dic3×D20—22no—
23#90995—22no—
24#90976—22no—
25#90965—22no—
26#72089—51nomaximal, Hall
27C2×#4054D311yescharacteristic
28#65855—31no—
29#65428—31no—
30#65420—31no—
31#65295—31no—
32C5×#344—31no—
33#64777—31no—
34C23×C3×D5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C3×#709—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20C2×C412yes—
45C2×C3×D20C2×C411yescharacteristic, complemented
46C2×C3×D20D412yes—
47C2×C3×D20D412yes—
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic, complemented
50C2×D5×Dic3—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8C2×C412yescomplemented
54#6719—21no—
55#6719—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4×Dic15—21no—
59C4×Dic15D412yes—
60C5×#217D412yes—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3—21no—
63C5×#208—21no—
64C5×#208—21no—
65C2×C5×C3⋊C8—21no—
66C3×D40—24no—
67C3×#677—24no—
68#6665—24no—
69C2×C3×AGL(1,ℤ/8)—51no—
70#5798—51no—
71#5240—51no—
72#5236—51no—
73#5215—51no—
74#4557—51no—
75#4556D511yescharacteristic, complemented
76C2×#709C2×D311yescharacteristic
77C22×D20C2×D311yescharacteristic
78C2×C5×M16—31no—
79C2×C5×M16C2×D311yescharacteristic
80C5×#117—31no—
81#4072—31no—
82#4072—31no—
83#4054—22no—
84#4054—22no—
85C2×D40Dic312yescomplemented
86C2×#677Dic312yescomplemented
87#4039—62no—
88D5×C22⋊C4—62no—
89C4×D20—62no—
90#3957—62no—
91#3953—62no—
92#3938—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—22no—
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5—21no—
99C22×C3×D5—82no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—22no—
107C2×Dic15—41no—
108C2×C5×Dic3—22no—
109C3×C22⋊D5—41no—
110C3×C22⋊D5—41no—
111C2×C3×Dic5—21no—
112C3×D20—21no—
113C3×D20—22no—
114C3×D20—21no—
115C3×D20—22no—
116C3×D20—22no—
117C3×D20C22⋊C414yes—
118C3×C4×D5—41no—
119C3×C4×D5—41no—
120C3×Dic10—21no—
121C3×Dic10—21no—
122D5×Dic3—84no—
123C3×C5×C8—22no—
124C5×C3⋊C8—41no—
125C2×C3×#41—51no—
126C22×C3×D4—51no—
127C3×AGL(1,ℤ/8)—102no—
128C3×AGL(1,ℤ/8)—102no—
129C2×C3×SD16—52no—
130C2×C3×D8—52no—
131C2×C3×M16C2×D511yescharacteristic
132C2×#217—102no—
133D4×Dic3—102no—
134D4×Dic3—102no—
135#926—51no—
136#926—51no—
137#926C2×D511yescharacteristic
138C2×#208C2×D511yescharacteristic
139#837—102no—
140#834—102no—
141#832—102no—
142C23×D5—21no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—21no—
145#709—21no—
146#709—21no—
147#709—21no—
148#709—21no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20—21no—
152C2×D20C2×Dic312yes—
153C2×D20C2×Dic311yescharacteristic, complemented
154C2×D20#6712yes—
155C2×D20#6712yes—
156C2×C4×D5—21no—
157C2×C4×D5—64no—
158C2×Dic10C2×Dic311yescharacteristic, complemented
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C2×C5×C8C2×Dic312yescomplemented
165C5×C4⋊C4—61no—
166C5×C22⋊C4—32no—
167C42×C5—61no—
168C22⋊Dic5—61no—
169C22⋊Dic5—61no—
170#685—64no—
171C4⋊Dic5—61no—
172C4⋊Dic5—61no—
173C4×Dic5—32no—
174C4×Dic5—61no—
175D40—24no—
176#677—24no—
177C2×AGL(1,ℤ/8)—51no—
178#518—151no—
179#421—151no—
180#418—151no—
181#410—151no—
182#344—31no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×C3×D5—24no—
189C2×C3×D5—44no—
190C2×C3×D5—41no—
191C2×C3×D5—82no—
192C2×C3×D5—82no—
193C2×C3×D5—81no—
194C3×C4×C5C2×C22⋊C411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12111yescharacteristic
197C3×C4×C5#12311yescharacteristic
198Dic15—42no—
199Dic15—81no—
200C3×Dic5—41no—
201C5×Dic3—42no—
202C24×C3—101no—
203C3×#41—101no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C2×C3×Q8—51no—
208C2×C3×D4—52no—
209C2×C3×D4—51no—
210C2×C3×D4—52no—
211C2×C3×D4—52no—
212C2×C3×D4—101no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C22×C3×C4—101no—
217C22×C3×C4C22×D511yescharacteristic
218C22×Dic3—104no—
219C3×SD16—104no—
220C3×D8—104no—
221C3×M16—21no—
222C3×M16—21no—
223C2×C3×C8C4×D512yescomplemented
224#217—104no—
225#217—101no—
226#217—101no—
227#217D2012yes—
228C4⋊Dic3—21no—
229C4⋊Dic3—101no—
230C4⋊Dic3—101no—
231C4×Dic3—21no—
232C4×Dic3—52no—
233C4×Dic3—101no—
234#208—21no—
235#208—21no—
236C2×C3⋊C8—21no—
237C23×C5D3×D411yescharacteristic
238C22×D5—22no—
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—21no—
242C22×D5—82no—
243C2×C4×C5—62no—
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C22×Dic311yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C22⋊D5—41no—
251C22⋊D5—41no—
252C2×Dic5—21no—
253C2×Dic5—62no—
254C2×Dic5—121no—
255D20—22no—
256D20—21no—
257D20—22no—
258D20—22no—
259D20—21no—
260D20#21714yes—
261C4×D5—41no—
262C4×D5—41no—
263C4×D5—244no—
264Dic10—21no—
265Dic10—21no—
266C5×C8—22no—
267C5×C8—121no—
268C2×#41—51no—
269C22×D4—51no—
270AGL(1,ℤ/8)—102no—
271AGL(1,ℤ/8)—102no—
272C2×SD16—52no—
273C2×D8—52no—
274C2×M16—31no—
275C2×M16D3×D511yescharacteristic
276C4×D4—302no—
277C4×D4—302no—
278#117—31no—
279#117—151no—
280#117—151no—
281C2×C22⋊C4—302no—
282#104—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289C3×D5—44no—
290C3×D5—81no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—101no—
295C23×C3—402no—
296C23×C3C2×D2011yescharacteristic
297C3×Q8—101no—
298C3×Q8—101no—
299C3×D4—54no—
300C3×D4—101no—
301C3×D4—102no—
302C3×D4—102no—
303C3×D4—101no—
304C3×D4—102no—
305C3×D4—201no—
306C3×D4—201no—
307C2×C3×C4—101no—
308C2×C3×C4—201no—
309C2×C3×C4—201no—
310C2×C3×C4C2×C4×D511yescharacteristic
311C2×C3×C4#70911yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×C3×C4#71311yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—102no—
318C2×Dic3—201no—
319C2×Dic3—404no—
320C3×C8—22no—
321C3⋊C8—41no—
322C22×C5—41no—
323C22×C5D4×Dic311yescharacteristic
324C22×C5#93711yescharacteristic
325C22×C5#93911yescharacteristic
326C2×D5—24no—
327C2×D5—44no—
328C2×D5—41no—
329C2×D5—82no—
330C2×D5—82no—
331C2×D5—81no—
332C4×C5—122no—
333C4×C5D4×Dic311yescharacteristic
334C4×C5#93511yescharacteristic
335C4×C5#93911yescharacteristic
336C4×C5C2×#21711yescharacteristic
337Dic5—41no—
338Dic5—122no—
339Dic5—241no—
340C24—101no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—52no—
347C2×D4—51no—
348C2×D4—52no—
349C2×D4—52no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—101no—
354C22×C4—101no—
355C22×C4—304no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—104no—
358D8—104no—
359M16—21no—
360M16—21no—
361M16—61no—
362M16—61no—
363C2×C8—61no—
364C2×C8D5×Dic312yescomplemented
365C4⋊C4—61no—
366C4⋊C4—301no—
367C4⋊C4—301no—
368C22⋊C4—32no—
369C22⋊C4—304no—
370C22⋊C4—301no—
371C22⋊C4—301no—
372C42—61no—
373C42—152no—
374C42—301no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—104no—
378C22×C3—204no—
379C22×C3—201no—
380C22×C3—402no—
381C22×C3—402no—
382C22×C3—401no—
383C22×C3C4×D2011yescharacteristic
384C22×C3#402811yescharacteristic
385C22×C3#404111yescharacteristic
386C3×C4—201no—
387C3×C4D5×C22⋊C411yescharacteristic
388C3×C4#403011yescharacteristic
389C3×C4#403911yescharacteristic
390C3×C4#404011yescharacteristic
391Dic3—42no—
392Dic3—202no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5#522011yescharacteristic
398D5—44no—
399D5—81no—
400C23—102no—
401C23—102no—
402C23—102no—
403C23—101no—
404C23—402no—
405C23D3×D2011yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—54no—
409D4—102no—
410D4—102no—
411D4—102no—
412D4—101no—
413D4—101no—
414D4—201no—
415D4—201no—
416C2×C4—62no—
417C2×C4—101no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—302no—
421C2×C4—601no—
422C2×C4—1204no—
423C2×C4#676511yescharacteristic
424C2×C4#676611yescharacteristic
425C2×C4#677711yescharacteristic
426C2×C4C2×D5×Dic311yescharacteristic
427C2×C4D5×#6711yescharacteristic
428C2×C4D5×#6711yescharacteristic
429C8—22no—
430C8—121no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—204no—
435C2×C3—401no—
436C2×C3#6495411yescharacteristic
437C5#7208911yescharacteristic, complemented, Sylow
438C22—41no—
439C22—104no—
440C22—204no—
441C22—201no—
442C22—402no—
443C22—402no—
444C22—401no—
445C22#9140911yescharacteristic
446C22Dic3×D2011yescharacteristic
447C22#9147411yescharacteristic
448C4—122no—
449C4—201no—
450C4—602no—
451C4—1201no—
452C4#9140711yescharacteristic
453C4#9140811yescharacteristic
454C4#9143411yescharacteristic
455C4D5×#21711yescharacteristic
456C3#1059982011yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—204no—
461C2—401no—
462C2#1174889611yescharacteristic
subgroupG/H
centerC2#11748896
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C3×#4054C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754488C2semidirect
3. #11748624C2semidirect
4. #11748420C2semidirect
5. #11748367C2semidirect
6. #11746378C2semidirect
7. C5×#4556C2semidirect
18. C2×C3×D40C4semidirect
19. C2×C3×#677C4semidirect
45. C2×C3×D20C2×C4semidirect
49. C2×C3×Dic10C2×C4semidirect
53. C2×C3×C5×C8C2×C4semidirect
75. #4556D5semidirect
85. C2×D40Dic3semidirect
86. C2×#677Dic3semidirect
153. C2×D20C2×Dic3semidirect
158. C2×Dic10C2×Dic3semidirect
164. C2×C5×C8C2×Dic3semidirect
223. C2×C3×C8C4×D5semidirect
364. C2×C8D5×Dic3semidirect
375. C3×C5#1904semidirect
437. C5#72089semidirect
456. C3#10599820semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40542
#117544882
#117486242
#117484202
#117483672
#117463782
C5×#45562
#105998203
#720895