Finite Group Databasebeta

← #14472163

Subgroups — #14472163

Order 1920.

672 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
1C3×#66055C211yesmaximal, characteristic, complemented
2#11752491C211yesmaximal, characteristic
3#11751194C211yesmaximal, characteristic, complemented
4C5×#5087C211yesmaximal, characteristic
5#11747370C212yesmaximal
6#11747288C212yesmaximal, complemented
7#11747270C212yesmaximal, complemented
8#11747142C212yesmaximal
9#11747095C211yesmaximal, characteristic, complemented
10C4×#6656C211yesmaximal, characteristic
11#11746846C211yesmaximal, characteristic, complemented
12#10612725—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91758C2211yescharacteristic
15C4×C5×D12C2211yescharacteristic
16C3×Q8×Dic5—21no—
17C3×#4090—21no—
18C3×#4036C2212yes—
19C3×#4035—22no—
20C3×#4033C2212yes—
21C3×C4×Dic10C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91373C2212yes—
24#91369—21no—
25#91342—22no—
26#91338—21no—
27#91333C2212yes—
28C2×#6662C2212yes—
29C2×#6656C2211yescharacteristic
30#91094C2212yes—
31#91094C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C5×#809C2212yes—
34C5×#807C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90986C2211yescharacteristic
37#90982C2212yes—
38#90974C2212yes—
39#90970C2211yescharacteristic
40#90966C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83689—51nomaximal, Hall
43#66055D311yescharacteristic, complemented
44#65876—31no—
45C5×#474—31no—
46#65382—31no—
47C4×#687—31no—
48#65166—32no—
49#65162—32no—
50#65138—31no—
51#65119—31no—
52#65057—32no—
53#65056—32no—
54C2×C3×C5×Q8—21no—
55C2×Dic30C2312yes—
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C3×Dic10D411yescharacteristic
59C2×C3×Dic10C2311yescharacteristic
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4C2312yes—
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15—21no—
64C4⋊Dic15—21no—
65C2×C3⋊#168C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×(C2×D3)⋊C4—21no—
68C5×C4⋊Dic3C2311yescharacteristic
69C2×C5×C3⋊C8C2312yes—
70C3×C4⋊Dic5—22no—
71C3×C4⋊Dic5D411yescharacteristic
72C3×C4⋊Dic5C2311yescharacteristic
73C3×#683—21no—
74C3×#683—22no—
75C3×#683—22no—
76C3×#683D412yes—
77C3×C4×Dic5—21no—
78C3×C4×Dic5—22no—
79C3×C4×Dic5C2312yes—
80#6669—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83Dic3×Dic5—22no—
84#6662—24no—
85#6656—22no—
86C3×#557—51no—
87#5584—51no—
88#5093—51no—
89#5087D511yescharacteristic
90#5068—52no—
91#5063—52no—
92#5031—51no—
93C4×#216—52no—
94#5028—52no—
95C4×#215—51no—
96Q8×C3⋊C8—51no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C4×C5×D4—31no—
99Q8×Dic5—21no—
100#4090—21no—
101#4082—32no—
102C2×#687—31no—
103#4072—61no—
104#4070—61no—
105C2×Dic20—32no—
106#4036C2×D312yes—
107#4035—22no—
108#4033—32no—
109#4033C2×D312yes—
110#4025—62no—
111#4015—31no—
112C4×Dic10C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×#107—32no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3964—31no—
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—31no—
122#3942—32no—
123#3942—32no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C22×C5×D3—21no—
128C3×C5×Q8—42no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—22no—
134Dic30—22no—
135Dic30—22no—
136C2×C5×Dic3—21no—
137C5×D12—21no—
138C5×D12—21no—
139C4×C5×D3—42no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5C2×D412yes—
143C2×C3×Dic5C2×D412yes—
144C3×Dic10—22no—
145C3×Dic10—21no—
146C3×Dic10#4112yes—
147C3⋊#168—21no—
148C3⋊#168—21no—
149C5×C3⋊C8—22no—
150C3×C4⋊Q8—101no—
151C3×C4⋊Q8C2×D511yescharacteristic
152C3×#125—52no—
153C3×#125—102no—
154C3×C4×Q8—51no—
155C3×C4×Q8—52no—
156C3×C4×Q8—51no—
157C3×C4×Q8—101no—
158#946—101no—
159C2×#216—52no—
160C2×#215—51no—
161#898—102no—
162#892—101no—
163#875—52no—
164C4×D12C2×D511yescharacteristic
165#869—51no—
166C4×Dic6—52no—
167#835—51no—
168#810—52no—
169#810—52no—
170#810—52no—
171#809—51no—
172#809C2×D512yes—
173#808—51no—
174#807C2×D512yes—
175C4⋊(C3⋊C8)—52no—
176C4⋊(C3⋊C8)C2×D511yescharacteristic
177C4×C3⋊C8—51no—
178C4×C3⋊C8—52no—
179C2×C5×Q8—21no—
180C2×C5×D4—31no—
181C22×C4×C5—61no—
182C2×Dic10—32no—
183C2×Dic10#6711yescharacteristic
184C2×Dic10C22×D311yescharacteristic
185C2×C5×C8—32no—
186C5×C4⋊C4—21no—
187C5×C4⋊C4—31no—
188C5×C4⋊C4C22×D312yes—
189C5×C22⋊C4—61no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—62no—
192C22⋊Dic5—62no—
193#687—62no—
194C4⋊Dic5—22no—
195C4⋊Dic5—61no—
196C4⋊Dic5—61no—
197C4⋊Dic5#6711yescharacteristic
198C4⋊Dic5C22×D311yescharacteristic
199#683—21no—
200#683—22no—
201#683—22no—
202#683—62no—
203#683#6712yes—
204C4×Dic5—21no—
205C4×Dic5—22no—
206C4×Dic5—62no—
207C4×Dic5C22×D312yes—
208C2×#168—31no—
209C2×#168—31no—
210Dic20—64no—
211#557—51no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—31no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C5×D3—41no—
224C2×C5×D3—41no—
225C2×C5×D3—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—42no—
232C3×Dic5—22no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C3×Dic5—41no—
236C5×Dic3—41no—
237C2×C3×Q8—21no—
238C2×C3×Q8—51no—
239C2×C3×Q8—51no—
240C2×D12C22×D511yescharacteristic
241C2×C4×D3—21no—
242C2×Dic6—52no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—51no—
246C3×C4⋊C4—51no—
247C3×C4⋊C4—102no—
248C3×C4⋊C4—102no—
249C3×C4⋊C4—102no—
250C3×C4⋊C4—101no—
251C3×C4⋊C4C22×D512yes—
252C3×C42—52no—
253C3×C42—102no—
254C3×C42—101no—
255C3×C42C22×D511yescharacteristic
256#216—104no—
257#215—102no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261C4⋊Dic3—101no—
262C4⋊Dic3—101no—
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—102no—
265C4×Dic3—102no—
266C2×C3⋊C8—51no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8C22×D512yes—
269C23×C5—61no—
270C5×Q8—42no—
271C5×D4—61no—
272C5×D4—61no—
273C2×C4×C5—22no—
274C2×C4×C5—61no—
275C2×C4×C5—122no—
276C2×C4×C5C2×#6711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—62no—
282C2×Dic5C2×#6712yes—
283C2×Dic5C2×#6712yes—
284Dic10—22no—
285Dic10—21no—
286Dic10—62no—
287Dic10—62no—
288Dic10#23912yes—
289C5×C8—62no—
290#168—61no—
291#168—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—101no—
295C4⋊Q8—151no—
296C4⋊Q8D3×D511yescharacteristic
297#126—302no—
298#125—52no—
299#125—102no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—52no—
304C4×Q8—51no—
305C4×Q8—101no—
306C4×Q8—152no—
307C4×D4—31no—
308#117—301no—
309#107—32no—
310#106—151no—
311C4⋊C8—31no—
312C4⋊C8—152no—
313#103—151no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—32no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C5×D3—81no—
325C22×D3—21no—
326C3×Q8—42no—
327C3×Q8—52no—
328C3×Q8—101no—
329C3×Q8—102no—
330C2×C3×C4—22no—
331C2×C3×C4—52no—
332C2×C3×C4—52no—
333C2×C3×C4—101no—
334C2×C3×C4—101no—
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4C23×D511yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—102no—
340D12—21no—
341D12—21no—
342C4×D3—42no—
343Dic6—102no—
344Dic6—102no—
345C3⋊C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5C22×#6711yescharacteristic
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—121no—
355C4×C5#95012yes—
356C4×C5C2×#23911yescharacteristic
357C4×C5#100711yescharacteristic
358Dic5—22no—
359Dic5—22no—
360Dic5—22no—
361Dic5—41no—
362Dic5—122no—
363C2×Q8—21no—
364C2×Q8—51no—
365C2×Q8—51no—
366C2×Q8—152no—
367C2×D4—31no—
368C22×C4—61no—
369Q16—304no—
370SD16—302no—
371C2×C8—32no—
372C2×C8—151no—
373C2×C8—151no—
374C4⋊C4—21no—
375C4⋊C4—31no—
376C4⋊C4—51no—
377C4⋊C4—52no—
378C4⋊C4—51no—
379C4⋊C4—102no—
380C4⋊C4—102no—
381C4⋊C4—102no—
382C4⋊C4—101no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D512yes—
387C22⋊C4—61no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—52no—
391C42—102no—
392C42—101no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—102no—
403C3×C4—102no—
404C3×C4—102no—
405C3×C4—201no—
406C3×C4#405812yes—
407C3×C4#414711yescharacteristic
408C3×C4D5×#4111yescharacteristic
409Dic3—41no—
410Dic3—202no—
411C2×C5—241no—
412C2×C5#581711yescharacteristic
413C2×C5C2×#95011yescharacteristic
414C2×C5#583811yescharacteristic
415C23—61no—
416Q8—42no—
417Q8—52no—
418Q8—102no—
419Q8—101no—
420Q8—302no—
421Q8—302no—
422D4—61no—
423D4—61no—
424C2×C4—22no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—61no—
428C2×C4—101no—
429C2×C4—101no—
430C2×C4—122no—
431C2×C4—302no—
432C2×C4D5×#6711yescharacteristic
433C2×C4D5×#6711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—62no—
436C8—301no—
437C8—301no—
438C2×C3#6596711yescharacteristic
439C2×C3C2×#405811yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—81no—
442C5#8368911yescharacteristic, complemented, Sylow
443C22—121no—
444C22—121no—
445C22—121no—
446C22C2×D5×#6711yescharacteristic
447C4—21no—
448C4—42no—
449C4—102no—
450C4—102no—
451C4—102no—
452C4—121no—
453C4—201no—
454C4—602no—
455C4#9149012yes—
456C4#9202911yescharacteristic
457C4D5×#23911yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—241no—
460C2C2×#9149011yescharacteristic
461C2#1175510211yescharacteristic
462C2#1175522711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66055C2semidirect
3. #11751194C2semidirect
6. #11747288C2semidirect
7. #11747270C2semidirect
9. #11747095C2semidirect
11. #11746846C2semidirect
43. #66055D3semidirect
395. C3×C5#3364semidirect
442. C5#83689semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
C3×#660552
#117524912
#117511942
C5×#50872
#117473702
#117472882
#117472702
#117471422
#117470952
C4×#66562
#117468462
#106127253
#836895