Finite Group Databasebeta

← #14471937

Subgroups — #14471937

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
1#11756312C211yesmaximal, characteristic
2#11752473C211yesmaximal, characteristic, complemented
3C5×#5008C211yesmaximal, characteristic, complemented
4C3×C4×#687C211yesmaximal, characteristic, complemented
5#11749008C212yesmaximal, complemented
6#11748943C212yesmaximal, complemented
7#11747272C212yesmaximal, complemented
8#11747183C212yesmaximal, complemented
9#11747064C211yesmaximal, characteristic, complemented
10#11746912C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612821—31nomaximal, Hall
13C2×#6817—21no—
14C3×C4×C5×D4C2211yescharacteristic
15#91829C2212yes—
16#91819—21no—
17#91782C2212yes—
18#91773—22no—
19#91763C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#687C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91470C2212yes—
25#91468—21no—
26#91333—21no—
27#91331C2212yes—
28#91329—22no—
29C2×#6658C2212yes—
30C5×#832C2212yes—
31C5×#808C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3964C2211yescharacteristic
34C3×#3942C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90969C2212yes—
39#90969C2212yes—
40#90968C2212yes—
41#90951C2212yes—
42#79622—51nomaximal, Hall
43#66056—31no—
44#65887—31no—
45C5×#476—31no—
46#65377—31no—
47C4×#687D311yescharacteristic, complemented
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×#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×Dic10C2311yescharacteristic
66C2×#1204—22no—
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6714—22no—
71C4⋊Dic15D411yescharacteristic
72#6712D412yes—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2312yes—
77C3×#687—22no—
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C2×C3×#168C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83#6669—22no—
84#6668—22no—
85Dic3×Dic5—22no—
86#6658—24no—
87Q8×Dic6—51no—
88#5553—51no—
89C3×C4×SD16—51no—
90#5163—52no—
91#5027—51no—
92#5008D511yescharacteristic, complemented
93#4870—52no—
94#4788—52no—
95#4760—52no—
96#4694—51no—
97C8×Dic6—51no—
98C2×#709—61no—
99C5×C4⋊Q8—31no—
100C4×C5×D4C2×D311yescharacteristic
101#4090—62no—
102#4086—32no—
103C2×#687C2×D311yescharacteristic
104#4076—61no—
105C2×#677—32no—
106#4039—32no—
107#4034—32no—
108#4034—61no—
109#4033—32no—
110#4033—61no—
111#4030—62no—
112#4020—31no—
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#102—32no—
118#3964C2×D311yescharacteristic
119#3953—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942C2×D311yescharacteristic
123#3941—32no—
124#3941—32no—
125#3940C2×D311yescharacteristic
126C4×#168C2×D311yescharacteristic
127#3362—151noSylow
128C23×C3×C5—21no—
129C22×D15—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
137#1220—44no—
138#1220—82no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141D60—22no—
142D60—22no—
143D60—42no—
144D60—81no—
145C4×D15—44no—
146Dic30SD1614yescomplemented
147C2×C5×Dic3—22no—
148C5×Dic6—81no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C3×Dic10—21no—
152C3×Dic10#4112yescomplemented
153#1204—82no—
154C3×#168—21no—
155C3×#168—21no—
156C5×C3⋊C8—22no—
157C2×#235—101no—
158C2×C3×SD16—51no—
159C3×C4×Q8—51no—
160C3×C4×D4C2×D511yescharacteristic
161Q8×Dic3—52no—
162C2×#215—52no—
163#940—52no—
164#930—101no—
165#893—52no—
166#888—52no—
167#888—102no—
168#884—102no—
169#874—51no—
170#869—101no—
171#869C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×#106—51no—
175C3×#103—51no—
176C3×#102—51no—
177C3×C4×C8—51no—
178#832C2×D512yes—
179#821—52no—
180#821—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808C2×D512yes—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8—61no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
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—22no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—32no—
211#683—62no—
212#683—62no—
213C4×Dic5—21no—
214C4×Dic5—32no—
215C4×Dic5—62no—
216C2×#168C22×D311yescharacteristic
217C2×#168C22×D311yescharacteristic
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—31no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—51no—
229C4×SD16—152no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—42no—
237C3×C4×C5—21no—
238C3×C4×C5—41no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15C2×SD1614yes—
244C3×Dic5—22no—
245C3×Dic5—41no—
246C5×Dic3—42no—
247C2×C3×Q8—51no—
248C2×C3×D4C22×D511yescharacteristic
249C22×C3×C4—21no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—52no—
254C2×D12—101no—
255C2×D12—101no—
256C2×C4×D3—102no—
257C2×Dic6—21no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C3×SD16—102no—
261C2×C3×C8—51no—
262C2×C3×C8—51no—
263C3×C4⋊C4—51no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—21no—
267C3×C42—101no—
268C3×C42C22×D511yescharacteristic
269#215—104no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—21no—
272C4⋊Dic3—51no—
273C4⋊Dic3—102no—
274C4⋊Dic3C22×D512yes—
275Dic3⋊C4—52no—
276Dic3⋊C4—102no—
277C4×Dic3—52no—
278C4×Dic3—102no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—21no—
281C22×D5—62no—
282C5×Q8—241no—
283C5×D4—21no—
284C5×D4—21no—
285C2×C4×C5—21no—
286C2×C4×C5—42no—
287C2×C4×C5—62no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297D20—62no—
298D20—62no—
299D20—122no—
300D20—241no—
301C4×D5—124no—
302Dic10—21no—
303Dic10—34no—
304Dic10—242no—
305Dic10#23512yescomplemented
306C5×C8—62no—
307#168—21no—
308#168—21no—
309C2×#41—301no—
310C2×SD16—51no—
311C2×SD16—152no—
312C4⋊Q8—31no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—51no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4D3×D511yescharacteristic
326#106—32no—
327#106—51no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—51no—
331#102—32no—
332#102—51no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—51no—
337C4×C8—152no—
338C2×C3×C5—81no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—82no—
343C23×C3—21no—
344C22×D3—102no—
345C3×Q8—52no—
346C3×Q8—101no—
347C3×D4—21no—
348C3×D4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—42no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—22no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361D12—102no—
362D12—102no—
363D12—202no—
364D12—401no—
365C4×D3—204no—
366Dic6—54no—
367Dic6—81no—
368Dic6—402no—
369C3×C8—101no—
370C3×C8—101no—
371C3⋊C8—22no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—122no—
382C4×C5D3×SD1612yes—
383C4×C5C2×#23511yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—22no—
386Dic5—34no—
387Dic5—41no—
388Dic5—62no—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—61no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—152no—
395C2×D4—302no—
396C2×D4—302no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—302no—
402SD16—102no—
403SD16—304no—
404C2×C8—32no—
405C2×C8—51no—
406C2×C8—51no—
407C4⋊C4—32no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—302no—
418C42—101no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—41no—
432C3×C4—102no—
433C3×C4—201no—
434C3×C4D5×SD1612yes—
435C3×C4#414711yescharacteristic
436C3×C4D5×#4111yescharacteristic
437Dic3—42no—
438Dic3—54no—
439Dic3—102no—
440C2×C5—81no—
441C2×C5#555211yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#576911yescharacteristic
444D5—242no—
445C23—21no—
446C23—302no—
447Q8—52no—
448Q8—101no—
449Q8—154no—
450Q8—241no—
451Q8—1202no—
452D4—21no—
453D4—21no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—62no—
463C2×C4—101no—
464C2×C4—101no—
465C2×C4—152no—
466C2×C4—152no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—101no—
473C8—101no—
474C2×C3—81no—
475C2×C3#6596711yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—402no—
479C5#7962211yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—41no—
489C4—102no—
490C4—122no—
491C4—154no—
492C4—201no—
493C4—302no—
494C4#9148712yes—
495C4#9200011yescharacteristic
496C4D5×#23511yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—81no—
499C2—1202no—
500C2#1175436711yescharacteristic
501C2C2×#9148711yescharacteristic
502C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756312C2
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. C5×#5008C2semidirect
4. C3×C4×#687C2semidirect
5. #11749008C2semidirect
6. #11748943C2semidirect
7. #11747272C2semidirect
8. #11747183C2semidirect
9. #11747064C2semidirect
10. #11746912C2semidirect
11. #11746851C2semidirect
47. C4×#687D3semidirect
92. #5008D5semidirect
146. Dic30SD16semidirect
152. C3×Dic10#41semidirect
305. Dic10#235semidirect
422. C3×C5#3362semidirect
479. C5#79622semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
#117563122
#117524732
C5×#50082
C3×C4×#6872
#117490082
#117489432
#117472722
#117471832
#117470642
#117469122
#117468512
#106128213
#796225