Finite Group Databasebeta

← #14471934

Subgroups — #14471934

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#11752472C211yesmaximal, characteristic, complemented
3C4×C5×#214C211yesmaximal, characteristic, complemented
4C3×#65297C211yesmaximal, characteristic, complemented
5#11749016C212yesmaximal, complemented
6#11748943C212yesmaximal, complemented
7#11747279C212yesmaximal, complemented
8#11747183C212yesmaximal, complemented
9#11747078C211yesmaximal, characteristic, complemented
10#11746910C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10611353—31nomaximal, Hall
13C2×#6817—21no—
14C3×C4×C5×D4C2211yescharacteristic
15#91829C2212yes—
16#91819—21no—
17#91782C2212yes—
18#91773—22no—
19#91763C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#214C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91470C2212yes—
25#91469—21no—
26#91344C2212yes—
27#91340—21no—
28#91327—22no—
29C2×#6660C2212yes—
30C5×#832C2211yescharacteristic
31C5×#810C2211yescharacteristic
32C5×#808C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3964C2212yes—
35C3×#3940C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37#90983C2212yes—
38#90969C2212yes—
39#90968C2212yes—
40#90968C2212yes—
41#90951C2212yes—
42#81090—51nomaximal, Hall
43Q8×Dic10—31no—
44#65887—31no—
45C4×C5×SD16—31no—
46#65452—32no—
47#65316—31no—
48#65297D311yescharacteristic, complemented
49#65159—32no—
50#65077—32no—
51#65049—32no—
52#64983—31no—
53C8×Dic10—31no—
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×Dic6C2311yescharacteristic
65C2×C3×Dic10—21no—
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×#214—22no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×Dic3⋊C4—21no—
77C4×C5×Dic3—21no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C2×C3×#168C2312yes—
83Dic3⋊Dic5—22no—
84#6669—22no—
85Dic3×Dic5—22no—
86#6660—24no—
87#5722—51no—
88#5553—51no—
89C3×#476—51no—
90#5088—51no—
91C4×#214D511yescharacteristic, complemented
92#4870—52no—
93#4852—52no—
94#4848—51no—
95#4830—51no—
96#4762—52no—
97#4760—52no—
98C2×#709—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8—31no—
101C4×C5×D4C2×D311yescharacteristic
102Q8×Dic5—32no—
103C2×#688—32no—
104#4086—32no—
105#4076—61no—
106#4039—32no—
107#4034—32no—
108#4034—62no—
109#4030—62no—
110#4020—31no—
111#4015—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3964C2×D312yes—
120#3953—32no—
121#3953—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940C2×D312yes—
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—21no—
148C2×C5×Dic3—21no—
149C5×Dic6—21no—
150C5×Dic6#4112yescomplemented
151C2×C3×Dic5—22no—
152C3×Dic10—81no—
153#1204—82no—
154C3×#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#235—101no—
158C3×C4⋊Q8—51no—
159C3×C4×D4C2×D511yescharacteristic
160#944—102no—
161#940—52no—
162C2×#214C2×D511yescharacteristic
163#930—101no—
164C2×#204—52no—
165#893—52no—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—102no—
171#874—51no—
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#106—52no—
175C3×C4⋊C8—51no—
176C3×#102—52no—
177#832C2×D511yescharacteristic
178#821—52no—
179Dic3⋊C8—52no—
180C8×Dic3—52no—
181#810C2×D511yescharacteristic
182#809—52no—
183#809—52no—
184#808C2×D511yescharacteristic
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—31no—
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—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C5×SD16—62no—
200C2×C5×C8—31no—
201C2×C5×C8—31no—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—61no—
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—21no—
206C42×C5—61no—
207C42×C5C22×D311yescharacteristic
208#688—64no—
209#685—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5—31no—
212C4⋊Dic5—62no—
213C4⋊Dic5C22×D312yes—
214#683—32no—
215#683—62no—
216C4×Dic5—32no—
217C4×Dic5—62no—
218C2×#168C22×D312yes—
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—51no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—31no—
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—42no—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C2×C3×Q8—101no—
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—51no—
258C2×Dic6—102no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8—52no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4C22×D511yescharacteristic
264C3×C22⋊C4—21no—
265C3×C42C22×D511yescharacteristic
266#214—22no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—51no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C2×C3⋊C8C22×D511yescharacteristic
278C2×C3⋊C8C22×D511yescharacteristic
279#204—104no—
280C23×C5—21no—
281C22×D5—62no—
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—21no—
285C5×D4—21no—
286C2×C4×C5—21no—
287C2×C4×C5—42no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298D20—62no—
299D20—62no—
300D20—122no—
301D20—241no—
302C4×D5—124no—
303Dic10—34no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—61no—
307C5×C8—61no—
308#168—22no—
309C2×#41—301no—
310C2×SD16—31no—
311C2×SD16—152no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—31no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4D3×D511yescharacteristic
326#106—31no—
327#106—52no—
328C4⋊C8—51no—
329C4⋊C8—152no—
330#103—31no—
331#102—31no—
332#102—52no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—31no—
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—401no—
346C3×D4—21no—
347C3×D4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—42no—
350C2×C3×C4—102no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360D12—102no—
361D12—102no—
362D12—202no—
363D12—401no—
364C4×D3—204no—
365Dic6—21no—
366Dic6—54no—
367Dic6—402no—
368Dic6#70912yescomplemented
369C3×C8—102no—
370C3⋊C8—21no—
371C3⋊C8—21no—
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—62no—
382C4×C5—121no—
383C4×C5D3×SD1612yes—
384C4×C5#100711yescharacteristic
385C4×C5D3×#4111yescharacteristic
386Dic5—34no—
387Dic5—42no—
388Dic5—62no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
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—62no—
403SD16—304no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—52no—
407C4⋊C4—31no—
408C4⋊C4—52no—
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—61no—
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—202no—
433C3×C4D5×SD1612yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—22no—
437Dic3—41no—
438Dic3—54no—
439Dic3—102no—
440C2×C5—81no—
441C2×C5#563311yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—242no—
445C23—21no—
446C23—302no—
447Q8—32no—
448Q8—61no—
449Q8—154no—
450Q8—401no—
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—61no—
463C2×C4—61no—
464C2×C4—102no—
465C2×C4—152no—
466C2×C4—152no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—102no—
474C2×C3—81no—
475C2×C3#6588611yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610311yescharacteristic
478D3—402no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—41no—
489C4—62no—
490C4—121no—
491C4—154no—
492C4—202no—
493C4—302no—
494C4#9148712yes—
495C4#9200411yescharacteristic
496C4D3×#70911yescharacteristic
497C3#1061135311yescharacteristic, complemented, Sylow
498C2—81no—
499C2—1202no—
500C2#1175437811yescharacteristic
501C2C2×#9148711yescharacteristic
502C2#1175533011yescharacteristic
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. #11752472C2semidirect
3. C4×C5×#214C2semidirect
4. C3×#65297C2semidirect
5. #11749016C2semidirect
6. #11748943C2semidirect
7. #11747279C2semidirect
8. #11747183C2semidirect
9. #11747078C2semidirect
10. #11746910C2semidirect
11. #11746855C2semidirect
48. #65297D3semidirect
91. C4×#214D5semidirect
146. Dic30SD16semidirect
150. C5×Dic6#41semidirect
368. Dic6#709semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10611353semidirect

Maximal subgroups

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

subgroupindex
#117563122
#117524722
C4×C5×#2142
C3×#652972
#117490162
#117489432
#117472792
#117471832
#117470782
#117469102
#117468552
#106113533
#810905