Finite Group Databasebeta

← #14471938

Subgroups — #14471938

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65887C211yesmaximal, characteristic
2#11752473C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic, complemented
4C5×#5008C211yesmaximal, characteristic, complemented
5#11749102C212yesmaximal, complemented
6#11749000C212yesmaximal, complemented
7#11747415C212yesmaximal, complemented
8#11747268C212yesmaximal, complemented
9#11747083C211yesmaximal, characteristic, complemented
10#11746895C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612821—31nomaximal, Hall
13C2×C3×#709—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C2×#6716C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4086C2212yes—
19C3×#4076—21no—
20C3×#4039C2212yes—
21C3×#4030—22no—
22C3×#4020C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91470—21no—
25#91468C2212yes—
26#91333C2212yes—
27#91331—21no—
28#91329—22no—
29C2×#6657C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#832C2212yes—
35C5×#808C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90982C2212yes—
38#90965C2212yes—
39#90964C2212yes—
40#90964C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83586—51nomaximal, Hall
43#66056—31no—
44#65887D311yescharacteristic
45C5×#476—31no—
46#65377—31no—
47C4×#687—31no—
48#65159—32no—
49#65141—32no—
50#65137—31no—
51#65119—31no—
52#65051—32no—
53#65049—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6—21no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5—22no—
60C3×#709—44no—
61C2×C3×D20—21no—
62C2×C3×D20—21no—
63C2×C3×D20C2312yes—
64C2×C3×C4×D5—22no—
65C2×C3×Dic10D411yescharacteristic
66C2×#1204—22no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6716—22no—
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73C4×Dic15—21no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2312yes—
79C3×#685—22no—
80C3×C4⋊Dic5D411yescharacteristic
81C3×#683D412yes—
82C3×C4×Dic5C2312yes—
83#6669—22no—
84#6668—22no—
85Dic3×Dic5—22no—
86#6657—24no—
87C3×#550—51no—
88Q8×Dic6—51no—
89#5075—52no—
90#5075—51no—
91#5070—51no—
92#5070—52no—
93Q8×C3⋊C8—51no—
94C4×#214—51no—
95C4×#214—52no—
96#5008—52no—
97#5008D511yescharacteristic, complemented
98C2×#709—21no—
99C5×C4⋊Q8—31no—
100C4×C5×D4C2×D311yescharacteristic
101#4090—62no—
102#4086C2×D312yes—
103C2×#687—31no—
104#4076—21no—
105C2×#677—32no—
106#4039C2×D312yes—
107#4034—32no—
108#4034—61no—
109#4033—32no—
110#4033—61no—
111#4030—22no—
112#4020C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#102—32no—
118#3964—31no—
119#3953—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—31no—
123#3941—32no—
124#3941—32no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C23×C3×C5—21no—
129C22×C3×D5—22no—
130C3×C5×D4—21no—
131C3×C5×D4—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—42no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139Dic30—21no—
140Dic30#4112yescomplemented
141C2×C5×Dic3—22no—
142C5×Dic6—81no—
143C3×C22⋊D5—44no—
144C3×C22⋊D5—82no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×D20—22no—
148C3×D20—22no—
149C3×D20—42no—
150C3×D20—81no—
151C3×C4×D5—44no—
152C3×Dic10SD1614yescomplemented
153#1204—82no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×C3×#41—101no—
158C3×#127—52no—
159C3×#127—51no—
160C3×#121—102no—
161C3×#121—101no—
162C3×C4×Q8—51no—
163C3×C4×D4—52no—
164C3×C4×D4C2×D511yescharacteristic
165Q8×Dic3—101no—
166C2×#214—51no—
167C2×#214—52no—
168#888—101no—
169#888—102no—
170#869—52no—
171#869C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—52no—
174#832—51no—
175#832—52no—
176#832—52no—
177#832—52no—
178#832C2×D512yes—
179#810—51no—
180#808—51no—
181#808C2×D512yes—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)C2×D511yescharacteristic
184C4×C3⋊C8—51no—
185C4×C3⋊C8—52no—
186C2×C5×Q8—61no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C2×C22⋊D5—22no—
190C2×C22⋊D5—22no—
191#709—44no—
192C2×D20—21no—
193C2×D20—21no—
194C2×D20C22×D312yes—
195C2×C4×D5—22no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10#6711yescharacteristic
199C2×C5×C8—32no—
200C5×C4⋊C4—32no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4C22×D311yescharacteristic
203C5×C22⋊C4—21no—
204C42×C5C22×D311yescharacteristic
205#687—62no—
206#685—22no—
207C4⋊Dic5—31no—
208C4⋊Dic5#6711yescharacteristic
209#683—61no—
210#683—62no—
211#683—62no—
212#683#6712yes—
213C4×Dic5—61no—
214C4×Dic5—62no—
215C4×Dic5C22×D312yes—
216C2×#168—31no—
217C2×#168—31no—
218#677—64no—
219Q82—151no—
220#550—51no—
221#486—152no—
222#486—151no—
223#476—31no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5C22×D411yescharacteristic
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—21no—
238C3×C4×C5—41no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15—41no—
244C3×Dic5—22no—
245C3×Dic5C2×SD1614yes—
246C5×Dic3—42no—
247C3×#41—204no—
248C2×C3×Q8—51no—
249C2×C3×D4—52no—
250C2×C3×D4—102no—
251C2×C3×D4—102no—
252C2×C3×D4—101no—
253C2×C3×D4—101no—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4—102no—
257C2×Dic6—21no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C3×C4⋊C4—52no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4C22×D511yescharacteristic
263C3×C22⋊C4—21no—
264C3×C22⋊C4—102no—
265C3×C42—52no—
266C3×C42C22×D511yescharacteristic
267#214—104no—
268#214—102no—
269C4⋊Dic3—21no—
270C4⋊Dic3—51no—
271C4⋊Dic3—102no—
272C4⋊Dic3C22×D512yes—
273Dic3⋊C4—102no—
274Dic3⋊C4—101no—
275C4×Dic3—102no—
276C4×Dic3—101no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—21no—
281C22×D5—22no—
282C5×Q8—241no—
283C5×D4—21no—
284C5×D4—21no—
285C2×C4×C5—21no—
286C2×C4×C5—42no—
287C2×C4×C5—62no—
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—44no—
292C22⋊D5—82no—
293C2×Dic5—61no—
294C2×Dic5—61no—
295C2×Dic5C2×#6712yes—
296C2×Dic5C2×#6712yes—
297D20—22no—
298D20—22no—
299D20—42no—
300D20—81no—
301C4×D5—44no—
302Dic10—32no—
303Dic10—61no—
304Dic10—242no—
305Dic10#21414yescomplemented
306C5×C8—62no—
307#168—61no—
308#168—61no—
309C2×#41—101no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—31no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—52no—
317#127—51no—
318#121—102no—
319#121—101no—
320C4×Q8—51no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—52no—
325C4×D4D3×D511yescharacteristic
326#106—32no—
327#106—151no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—151no—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5—81no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342C3×D5—82no—
343C23×C3—21no—
344C23×C3—102no—
345C3×Q8—54no—
346C3×D4—21no—
347C3×D4—21no—
348C3×D4—102no—
349C3×D4—102no—
350C3×D4—204no—
351C3×D4—202no—
352C3×D4—401no—
353C3×D4—402no—
354C2×C3×C4—21no—
355C2×C3×C4—42no—
356C2×C3×C4—52no—
357C2×C3×C4—52no—
358C2×C3×C4—204no—
359C2×C3×C4D4×D511yescharacteristic
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—101no—
364C2×Dic3—101no—
365Dic6—52no—
366Dic6—81no—
367Dic6—101no—
368Dic6—402no—
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—42no—
377C2×D5—42no—
378C2×D5—42no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—122no—
382C4×C5C2×#21412yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—22no—
386Dic5—62no—
387Dic5—121no—
388Dic5C2×#21414yes—
389#41—204no—
390C2×Q8—51no—
391C2×Q8—61no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—52no—
395C2×D4—102no—
396C2×D4—102no—
397C2×D4—101no—
398C2×D4—101no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—102no—
402SD16—304no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—151no—
406C2×C8—151no—
407C4⋊C4—32no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—61no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—102no—
418C42—52no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—202no—
427C22×C3—202no—
428C22×C3—202no—
429C22×C3C2×D4×D511yescharacteristic
430C3×C4—21no—
431C3×C4—41no—
432C3×C4—54no—
433C3×C4—102no—
434C3×C4D5×SD1612yes—
435C3×C4#414711yescharacteristic
436C3×C4D5×#4111yescharacteristic
437Dic3—42no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—81no—
441C2×C5C22×#21411yescharacteristic
442C2×C5#583111yescharacteristic
443C2×C5#583511yescharacteristic
444D5—82no—
445C23—21no—
446C23—102no—
447Q8—54no—
448Q8—152no—
449Q8—241no—
450Q8—301no—
451Q8—1202no—
452D4—21no—
453D4—21no—
454D4—102no—
455D4—102no—
456D4—204no—
457D4—202no—
458D4—401no—
459D4—402no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—52no—
463C2×C4—52no—
464C2×C4—62no—
465C2×C4—204no—
466C2×C4—301no—
467C2×C4—301no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3—81no—
475C2×C3—402no—
476C2×C3#6596711yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478C2×C3#6610811yescharacteristic
479C5#8358611yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—202no—
484C22—202no—
485C22—202no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—41no—
489C4—54no—
490C4—102no—
491C4—122no—
492C4—302no—
493C4—601no—
494C4D5×#21412yes—
495C4#9200011yescharacteristic
496C4#9201611yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—81no—
499C2—402no—
500C2#1175421511yescharacteristic
501C2C2×D5×#21411yescharacteristic
502C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65887C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3362
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
2. #11752473C2semidirect
3. C4×#6716C2semidirect
4. C5×#5008C2semidirect
5. #11749102C2semidirect
6. #11749000C2semidirect
7. #11747415C2semidirect
8. #11747268C2semidirect
9. #11747083C2semidirect
10. #11746895C2semidirect
11. #11746846C2semidirect
97. #5008D5semidirect
140. Dic30#41semidirect
152. C3×Dic10SD16semidirect
305. Dic10#214semidirect
422. C3×C5#3362semidirect
479. C5#83586semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
C3×#658872
#117524732
C4×#67162
C5×#50082
#117491022
#117490002
#117474152
#117472682
#117470832
#117468952
#117468462
#106128213
#835865