Finite Group Databasebeta

← #14471461

Subgroups — #14471461

Order 1920.

852 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756312C211yesmaximal, characteristic, complemented
2#11752552C211yesmaximal, characteristic, complemented
3C5×#5007C211yesmaximal, characteristic, complemented
4C3×C4×#686C211yesmaximal, characteristic, complemented
5#11748983C212yesmaximal, complemented
6#11748943C212yesmaximal, complemented
7#11747226C212yesmaximal, complemented
8#11747180C212yesmaximal, complemented
9#11747028C211yesmaximal, characteristic, complemented
10#11746912C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612723—31nomaximal, Hall
13C2×#6817—21no—
14C2×D5×Dic6—21no—
15C3×C4×C5×D4C2211yescharacteristic
16#91829C2212yes—
17#91819—21no—
18#91782C2212yes—
19#91773—22no—
20#91763C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C2×C3×#686C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91470C2212yes—
26#91434C2212yes—
27#91430—22no—
28#91359—21no—
29C2×#6653C2212yes—
30C5×#832C2212yes—
31C5×#807C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3964C2211yescharacteristic
34C3×#3941C2211yescharacteristic
35C3×#3939C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90969C2212yes—
39#90969C2212yes—
40#90968C2212yes—
41#90951C2212yes—
42#79567—51nomaximal, Hall
43#66061—31no—
44#65887—31no—
45C5×#474—31no—
46#65377—31no—
47C4×#686D311yescharacteristic, complemented
48#65179—32no—
49#65161—32no—
50#65132—31no—
51#65119—31no—
52#65075—32no—
53#65049—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×#1220—22no—
57C2×#1220—22no—
58#6817—44no—
59C2×D60—21no—
60C2×D60—21no—
61C2×D60C2312yes—
62C2×C4×D15—22no—
63C2×Dic30D411yescharacteristic
64C2×C5×Dic6—21no—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×#1204—22no—
68C2×D5×Dic3—22no—
69D5×Dic6—44no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6714—22no—
74C4⋊Dic15D411yescharacteristic
75#6712D412yes—
76C4×Dic15C2312yes—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C2×C5×C3⋊C8C2312yes—
80C3×#686—22no—
81C3×#685—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85#6669—22no—
86#6665—22no—
87#6653—24no—
88#5553—51no—
89D4×Dic6—51no—
90C3×C4×D8—51no—
91#5150—52no—
92#5015—51no—
93#5007D511yescharacteristic, complemented
94#4890—52no—
95#4760—52no—
96#4756—52no—
97#4694—51no—
98C8×Dic6—51no—
99C2×Q8×D5—61no—
100C2×#709—61no—
101C5×C4⋊Q8—31no—
102C4×C5×D4C2×D311yescharacteristic
103#4092—61no—
104#4086—32no—
105C2×#686C2×D311yescharacteristic
106#4076—61no—
107C2×D40—32no—
108#4042—62no—
109#4039—32no—
110#4039—32no—
111#4034—32no—
112#4030—62no—
113#4020—31no—
114C4×D20C2×D311yescharacteristic
115C4×Dic10—31no—
116C5×#107—32no—
117C5×C4⋊C8—31no—
118C5×#102—32no—
119#3964C2×D311yescharacteristic
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3941—32no—
125#3941C2×D311yescharacteristic
126#3939C2×D311yescharacteristic
127C4×#168C2×D311yescharacteristic
128#3358—151noSylow
129C23×C3×C5—21no—
130C22×D15—22no—
131C22×C3×D5—21no—
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139#1220—44no—
140#1220—82no—
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143D60—22no—
144D60—22no—
145D60—42no—
146D60—81no—
147C4×D15—44no—
148Dic30D814yescomplemented
149C2×C5×Dic3—22no—
150C5×Dic6—42no—
151C2×C3×Dic5—21no—
152C3×D20—21no—
153C3×D20#4112yescomplemented
154C3×C4×D5—42no—
155#1204—44no—
156D5×Dic3—44no—
157C3×#168—21no—
158C3×#168—21no—
159C5×C3⋊C8—22no—
160C2×#235—101no—
161C22×Dic6—101no—
162C2×C3×D8—51no—
163C3×C4×D4—51no—
164C3×C4×D4C2×D511yescharacteristic
165#940—52no—
166D4×Dic3—52no—
167C2×#213—52no—
168#930—101no—
169#924—101no—
170#893—52no—
171#888—52no—
172#884—102no—
173#878—102no—
174#874—51no—
175#869C2×D511yescharacteristic
176C4×Dic6—51no—
177C3×#107—51no—
178C3×#102—51no—
179C3×#102—51no—
180C3×C4×C8—51no—
181#832C2×D512yes—
182#821—52no—
183#821—52no—
184Dic3⋊C8—52no—
185C8×Dic3—52no—
186#809—52no—
187#807C2×D512yes—
188C4⋊(C3⋊C8)C2×D511yescharacteristic
189C2×C5×Q8—61no—
190C2×C5×D4C22×D311yescharacteristic
191C22×C4×C5—21no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194Q8×D5—124no—
195#709—124no—
196C2×D20—32no—
197C2×D20—61no—
198C2×D20—61no—
199C2×D20C22×D311yescharacteristic
200C2×C4×D5—21no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×Dic10—31no—
204C2×Dic10—62no—
205C2×C5×C8—32no—
206C5×C4⋊C4—32no—
207C5×C4⋊C4—61no—
208C5×C4⋊C4C22×D311yescharacteristic
209C5×C22⋊C4—21no—
210C42×C5C22×D311yescharacteristic
211#686—22no—
212#685—21no—
213#685—62no—
214#685—62no—
215C4⋊Dic5—31no—
216C4⋊Dic5C22×D311yescharacteristic
217#683—32no—
218#683—62no—
219C4×Dic5—32no—
220C2×#168C22×D311yescharacteristic
221C2×#168C22×D311yescharacteristic
222D40—64no—
223#550—151no—
224D4×Q8—151no—
225#486—151no—
226#486—152no—
227#474—31no—
228#474—152no—
229#459—152no—
230#459—151no—
231C8×Q8—151no—
232C4×D8—51no—
233C4×D8—152no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C2×C3×D5—22no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D812yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C52−1+411yescharacteristic
249Dic15—22no—
250Dic15C2×D814yes—
251C3×Dic5—41no—
252C5×Dic3—42no—
253C2×C3×D4—51no—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4—101no—
257C2×#67—102no—
258C2×#67—102no—
259C22×Dic3—102no—
260#235—204no—
261C2×D12—52no—
262C2×D12—101no—
263C2×D12—101no—
264C2×C4×D3—102no—
265C2×Dic6—21no—
266C2×Dic6—51no—
267C2×Dic6—102no—
268C2×Dic6—204no—
269C3×D8—102no—
270C2×C3×C8—51no—
271C2×C3×C8—51no—
272C3×C4⋊C4—51no—
273C3×C4⋊C4C22×D511yescharacteristic
274C3×C22⋊C4—21no—
275C3×C22⋊C4—101no—
276C3×C42C22×D511yescharacteristic
277#217—102no—
278#213—104no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—21no—
281C4⋊Dic3—51no—
282C4⋊Dic3C22×D512yes—
283Dic3⋊C4—52no—
284Dic3⋊C4—102no—
285C4×Dic3—52no—
286C2×C3⋊C8C22×D512yes—
287C23×C5—21no—
288C22×D5—21no—
289C22×D5—62no—
290C5×Q8—122no—
291C5×D4—21no—
292C5×D4—21no—
293C2×C4×C5—21no—
294C2×C4×C5—42no—
295C2×C4×C5—62no—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—124no—
300C22⋊D5—242no—
301C2×Dic5—21no—
302C2×Dic5—32no—
303C2×Dic5—32no—
304D20—21no—
305D20—62no—
306D20—62no—
307D20—122no—
308D20—241no—
309D20#23512yescomplemented
310C4×D5—42no—
311C4×D5—124no—
312C4×D5—124no—
313Dic10—34no—
314Dic10—124no—
315C5×C8—62no—
316#168—21no—
317#168—21no—
318C2×#41—301no—
319C22×Q8—301no—
320C2×D8—51no—
321C2×D8—152no—
322C4⋊Q8—31no—
323C4⋊Q8—152no—
324#127—152no—
325#127—151no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—302no—
329#121—301no—
330C4×Q8—151no—
331C4×D4—51no—
332C4×D4—152no—
333C4×D4—152no—
334C4×D4D3×D511yescharacteristic
335#107—32no—
336#107—51no—
337C4⋊C8—31no—
338C4⋊C8—152no—
339#102—32no—
340#102—51no—
341#102—51no—
342#102—152no—
343#102—152no—
344#102—152no—
345C4×C8—51no—
346C4×C8—152no—
347C2×C3×C5—81no—
348C2×C3×C5#54811yescharacteristic
349C2×C3×C5C22×D811yescharacteristic
350C2×C3×C5#57711yescharacteristic
351D15—82no—
352C3×D5—42no—
353C23×C3—21no—
354C23×C3—101no—
355C22×D3—102no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—52no—
359C3×D4—101no—
360C2×C3×C4—21no—
361C2×C3×C4—42no—
362C2×C3×C4—101no—
363C2×C3×C4—202no—
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4C23×D511yescharacteristic
367#67—204no—
368#67—402no—
369C2×Dic3—22no—
370C2×Dic3—52no—
371C2×Dic3—52no—
372C2×Dic3—204no—
373D12—102no—
374D12—102no—
375D12—202no—
376D12—401no—
377C4×D3—204no—
378Dic6—42no—
379Dic6—54no—
380Dic6—204no—
381C3×C8—101no—
382C3×C8—101no—
383C3⋊C8—22no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5C2×D3×D411yescharacteristic
388C2×D5—22no—
389C2×D5—41no—
390C2×D5—41no—
391C2×D5—122no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—21no—
395C4×C5—41no—
396C4×C5—122no—
397C4×C5D3×D812yes—
398C4×C5C2×#23511yescharacteristic
399C4×C5#101011yescharacteristic
400Dic5—34no—
401Dic5—41no—
402Dic5—62no—
403#41—604no—
404C2×Q8—61no—
405C2×Q8—151no—
406C2×Q8—302no—
407C2×Q8—604no—
408C2×D4—51no—
409C2×D4—152no—
410C2×D4—302no—
411C2×D4—302no—
412C2×D4—301no—
413C2×D4—301no—
414C2×D4C2×D3×D511yescharacteristic
415C22×C4—21no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4—302no—
419D8—102no—
420D8—304no—
421C2×C8—32no—
422C2×C8—51no—
423C2×C8—51no—
424C4⋊C4—32no—
425C4⋊C4—51no—
426C4⋊C4—61no—
427C4⋊C4—152no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4C2×D3×D511yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—101no—
433C22⋊C4—302no—
434C22⋊C4—302no—
435C42—152no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—102no—
442C22×C3—201no—
443C22×C3—201no—
444C22×C3C2×D4×D511yescharacteristic
445C2×D3—202no—
446C2×D3—202no—
447C2×D3—202no—
448C3×C4—21no—
449C3×C4—41no—
450C3×C4—201no—
451C3×C4D5×D812yes—
452C3×C4#414711yescharacteristic
453C3×C4D5×#4111yescharacteristic
454Dic3—42no—
455Dic3—54no—
456Dic3—102no—
457C2×C5—81no—
458C2×C5#555211yescharacteristic
459C2×C5C2×D3×D811yescharacteristic
460C2×C5#577011yescharacteristic
461D5—42no—
462D5—242no—
463C23—21no—
464C23—101no—
465C23—302no—
466Q8—122no—
467Q8—154no—
468Q8—604no—
469D4—21no—
470D4—21no—
471D4—52no—
472D4—101no—
473D4—302no—
474D4—302no—
475D4—604no—
476D4—602no—
477D4—1201no—
478D4—1202no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—62no—
482C2×C4—101no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—202no—
486C2×C4—604no—
487C2×C4—604no—
488C2×C4#679011yescharacteristic
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—62no—
492C8—101no—
493C8—101no—
494C2×C3—81no—
495C2×C3—202no—
496C2×C3#6596711yescharacteristic
497C2×C3C2×D5×D811yescharacteristic
498C2×C3#6611211yescharacteristic
499D3—402no—
500C5#7956711yescharacteristic, complemented, Sylow
501C22—41no—
502C22—41no—
503C22—41no—
504C22—102no—
505C22—201no—
506C22—201no—
507C22—602no—
508C22—602no—
509C22—602no—
510C22C2×#679011yescharacteristic
511C4—21no—
512C4—41no—
513C4—122no—
514C4—154no—
515C4—201no—
516C4—302no—
517C4#9148112yes—
518C4#9200011yescharacteristic
519C4D5×#23511yescharacteristic
520C3#1061272311yescharacteristic, complemented, Sylow
521C2—81no—
522C2—202no—
523C2—1202no—
524C2#1175436711yescharacteristic
525C2C2×#9148111yescharacteristic
526C2#1175535111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3358
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756312C2semidirect
2. #11752552C2semidirect
3. C5×#5007C2semidirect
4. C3×C4×#686C2semidirect
5. #11748983C2semidirect
6. #11748943C2semidirect
7. #11747226C2semidirect
8. #11747180C2semidirect
9. #11747028C2semidirect
10. #11746912C2semidirect
11. #11746851C2semidirect
47. C4×#686D3semidirect
93. #5007D5semidirect
148. Dic30D8semidirect
153. C3×D20#41semidirect
309. D20#235semidirect
437. C3×C5#3358semidirect
500. C5#79567semidirect
520. C3#10612723semidirect

Maximal subgroups

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

subgroupindex
#117563122
#117525522
C5×#50072
C3×C4×#6862
#117489832
#117489432
#117472262
#117471802
#117470282
#117469122
#117468512
#106127233
#795675