Finite Group Databasebeta

← #14472154

Subgroups — #14472154

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
1#11756491C211yesmaximal, characteristic
2#11752482C211yesmaximal, characteristic, complemented
3C5×#5090C211yesmaximal, characteristic, complemented
4C3×#65370C211yesmaximal, characteristic, complemented
5#11749335C212yesmaximal, complemented
6#11749265C212yesmaximal, complemented
7#11749261C212yesmaximal
8#11749190C212yesmaximal
9C4×#6660C211yesmaximal, characteristic
10#11746971C211yesmaximal, characteristic
11#11746851C211yesmaximal, characteristic, complemented
12#10612194—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91836C2212yes—
15Q8×Dic15C2212yes—
16#91787—22no—
17#91786—21no—
18#91781—21no—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#216C2212yes—
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91389—21no—
25#91384C2212yes—
26#91346—22no—
27#91344C2212yes—
28Dic3×Dic10—21no—
29C2×#6660C2211yescharacteristic
30C5×#835C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3967C2212yes—
33C3×#3967C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90990C2212yes—
36#90985C2211yescharacteristic
37#90983C2212yes—
38#90973C2211yescharacteristic
39#90969C2211yescharacteristic
40#90968C2212yes—
41#90951C2212yes—
42#81625—51nomaximal, Hall
43#66066—31no—
44#65904—31no—
45C5×#462—31no—
46#65474—32no—
47Q16×Dic5—32no—
48#65370D311yescharacteristic, complemented
49C4×#688—31no—
50#65135—31no—
51#65119—31no—
52#65089—32no—
53#65085—32no—
54C2×C3×C5×Q8C2312yes—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30D411yescharacteristic
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×Dic10—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63#6714—21no—
64#6714—22no—
65#6714—22no—
66C4⋊Dic15—22no—
67C4⋊Dic15D411yescharacteristic
68C4⋊Dic15C2311yescharacteristic
69#6712D412yes—
70C4×Dic15—22no—
71C4×Dic15C2312yes—
72C5×#216—24no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2312yes—
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81Dic3⋊Dic5—22no—
82Dic3⋊Dic5—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6660—22no—
86#5732—51no—
87#5721—51no—
88C3×#487—51no—
89#5090D511yescharacteristic, complemented
90#5087—51no—
91#4800—52no—
92#4799—52no—
93#4798—52no—
94#4790—52no—
95C4×#204—51no—
96C8×Dic6—51no—
97C2×C5×Q16—32no—
98C5×C4⋊Q8C2×D311yescharacteristic
99C4×C5×Q8—31no—
100#4093—32no—
101Q8×Dic5—32no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4044—62no—
105#4043—61no—
106#4038—61no—
107#4036—32no—
108#4036—62no—
109C4×D20—31no—
110#4015—61no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×C4⋊C8—31no—
115C5×#103—32no—
116#3967—31no—
117#3967C2×D312yes—
118#3967C2×D312yes—
119#3953—32no—
120#3950—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3940—31no—
125C4×#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×D15—21no—
128C3×C5×Q8—22no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137D60—21no—
138D60—21no—
139C4×D15—42no—
140Dic30—22no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—21no—
143C5×Dic6—21no—
144C5×Dic6#4112yes—
145C2×C3×Dic5—22no—
146C3×Dic10—42no—
147C3×#168—21no—
148C3×#168—21no—
149C5×C3⋊C8—22no—
150C3×C4⋊Q8—51no—
151C3×C4⋊Q8C2×D511yescharacteristic
152#947—52no—
153Q8×Dic3—52no—
154Q8×Dic3—101no—
155#944—101no—
156C2×#216C2×D512yes—
157C2×#204—51no—
158#898—102no—
159#897—101no—
160#892—101no—
161#890—52no—
162#889—102no—
163#887—52no—
164C4×D12—51no—
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#103—52no—
168C3×#103—52no—
169C3×C4×C8—51no—
170#835C2×D512yes—
171#821—51no—
172#817—51no—
173#816—51no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—52no—
177#807—52no—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C2×C5×Q8—31no—
180C2×C5×Q8C22×D312yes—
181C2×D20—31no—
182C2×C4×D5—61no—
183C2×Dic10—21no—
184C2×Dic10—31no—
185C5×Q16—64no—
186C2×C5×C8—32no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—31no—
190C5×C4⋊C4—61no—
191C42×C5—61no—
192C42×C5C22×D311yescharacteristic
193#688—62no—
194#685—62no—
195#685—62no—
196#685—61no—
197C4⋊Dic5—21no—
198C4⋊Dic5—31no—
199C4⋊Dic5—31no—
200C4⋊Dic5—62no—
201C4⋊Dic5—62no—
202C4⋊Dic5—62no—
203C4⋊Dic5C22×D312yes—
204#683—32no—
205#683—62no—
206C4×Dic5—32no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C2×#168C22×D311yescharacteristic
210C2×#168C22×D311yescharacteristic
211#557—151no—
212#556—151no—
213#488—152no—
214#487—51no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—31no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—22no—
232Dic15—22no—
233Dic15—41no—
234C3×Dic5—42no—
235C5×Dic3—22no—
236C5×Dic3—41no—
237C2×C3×Q8—101no—
238C2×C3×Q8C22×D512yes—
239C2×D12—51no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6C22×D511yescharacteristic
243C2×C3×C8—51no—
244C2×C3×C8—51no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—52no—
248C3×C4⋊C4—101no—
249C3×C42C22×D511yescharacteristic
250#216—24no—
251(C2×D3)⋊C4—102no—
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—101no—
254C4⋊Dic3—51no—
255C4⋊Dic3—51no—
256C4⋊Dic3—102no—
257C4⋊Dic3—102no—
258C4⋊Dic3C22×D511yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—52no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263C4×Dic3—21no—
264C4×Dic3—52no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8C22×D512yes—
268#204—102no—
269C22×D5—61no—
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—32no—
273C5×Q8—61no—
274C2×C4×C5—22no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—32no—
282C2×Dic5—32no—
283C2×Dic5—61no—
284D20—61no—
285D20—61no—
286C4×D5—122no—
287Dic10—42no—
288Dic10—62no—
289C5×C8—62no—
290#168—21no—
291#168—21no—
292C2×Q16—32no—
293C2×SD16—151no—
294C4⋊Q8—51no—
295C4⋊Q8—301no—
296C4⋊Q8D3×D511yescharacteristic
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—31no—
312C4⋊C8—152no—
313#103—32no—
314#103—52no—
315#103—52no—
316#103—151no—
317#102—151no—
318#102—152no—
319C4×C8—51no—
320C4×C8—152no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—202no—
329C2×C3×C4—22no—
330C2×C3×C4—102no—
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4C23×D511yescharacteristic
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—52no—
337C2×Dic3—52no—
338C2×Dic3—101no—
339D12—101no—
340D12—101no—
341C4×D3—202no—
342Dic6—21no—
343Dic6—102no—
344Dic6#71112yes—
345C3×C8—101no—
346C3×C8—101no—
347C3⋊C8—22no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—62no—
355C4×C5—121no—
356C4×C5#91612yes—
357C4×C5D3×#4111yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—42no—
360Dic5—62no—
361Dic5—62no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—101no—
365C2×Q8—151no—
366C2×Q8C2×D3×D512yes—
367C2×D4—151no—
368C22×C4—301no—
369Q16—64no—
370SD16—302no—
371C2×C8—32no—
372C2×C8—51no—
373C2×C8—51no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—31no—
377C4⋊C4—52no—
378C4⋊C4—61no—
379C4⋊C4—101no—
380C4⋊C4—151no—
381C4⋊C4—152no—
382C4⋊C4—151no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—61no—
391C42—152no—
392C42—302no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—202no—
403C3×C4#406512yes—
404C3×C4C2×#71111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—22no—
407Dic3—41no—
408Dic3—102no—
409Dic3—102no—
410Dic3—201no—
411C2×C5#567711yescharacteristic
412C2×C5C2×#91611yescharacteristic
413C2×C5#576611yescharacteristic
414D5—241no—
415C23—301no—
416Q8—22no—
417Q8—22no—
418Q8—32no—
419Q8—61no—
420Q8—202no—
421Q8—302no—
422D4—301no—
423D4—301no—
424C2×C4—22no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—102no—
428C2×C4—152no—
429C2×C4—152no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4#679011yescharacteristic
433C2×C4#679011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—62no—
436C8—101no—
437C8—101no—
438C2×C3#6593211yescharacteristic
439C2×C3C2×#406511yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—401no—
442C5#8162511yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×#679011yescharacteristic
447C4—21no—
448C4—42no—
449C4—62no—
450C4—121no—
451C4—202no—
452C4—302no—
453C4—302no—
454C4—601no—
455C4#9152112yes—
456C4#9202011yescharacteristic
457C4D3×#71111yescharacteristic
458C3#1061219411yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175482711yescharacteristic
461C2C2×#9152111yescharacteristic
462C2#1175512211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
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
2. #11752482C2semidirect
3. C5×#5090C2semidirect
4. C3×#65370C2semidirect
5. #11749335C2semidirect
6. #11749265C2semidirect
11. #11746851C2semidirect
48. #65370D3semidirect
89. #5090D5semidirect
395. C3×C5#3364semidirect
442. C5#81625semidirect
458. C3#10612194semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117524822
C5×#50902
C3×#653702
#117493352
#117492652
#117492612
#117491902
C4×#66602
#117469712
#117468512
#106121943
#816255