Finite Group Databasebeta

← #14413528

Subgroups — #14413528

Order 1920.

952 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#11756282C211yesmaximal, characteristic
2#11754496C211yesmaximal, characteristic
3C2×#91291C211yesmaximal, characteristic
4C5×#4998C211yesmaximal, characteristic, complemented
5C3×#65284C211yesmaximal, characteristic, complemented
6C2×#90990C211yesmaximal, characteristic, complemented
7#11748460C211yesmaximal, characteristic, complemented
8#11747459C212yesmaximal, complemented
9#11747457C212yesmaximal, complemented
10#11747440C212yesmaximal, complemented
11#11747438C212yesmaximal, complemented
12#10610910—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16#91781C2212yes—
17C4⋊C4×D15C2212yes—
18#91770—22no—
19C4×D60—21no—
20C4×Dic30—21no—
21C5×#926C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91552—22no—
26#91437C2212yes—
27#91428—21no—
28#91347C2212yes—
29#91340—21no—
30C2×#6651C2212yes—
31#91291C418yescomplemented
32C2×#6648C2212yes—
33C5×#808C2211yescharacteristic
34C5×#808C2211yescharacteristic
35C5×#807C2211yescharacteristic
36C5×#807C2211yescharacteristic
37C3×#3940C2212yes—
38C3×#3939C2212yes—
39#90990C2212yes—
40#90990C2212yes—
41#90988C2212yes—
42#90985C2212yes—
43#79210—51nomaximal, Hall
44C2×#4047—31no—
45#65857—31no—
46#65857—31no—
47C5×#427—31no—
48C2×#3950—31no—
49#65284—31no—
50#65284D311yescharacteristic, complemented
51#65169—32no—
52D5×#107—32no—
53#65150—32no—
54#65150—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220D412yes—
57C22×Dic15—21no—
58#6817C2×C414yes—
59#6817Q814yes—
60C2×D60D411yescharacteristic
61C2×C4×D15—22no—
62C2×C4×D15C2312yes—
63C2×Dic30D411yescharacteristic
64C22×C3×Dic5—21no—
65C2×#1200—22no—
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5—21no—
70#6714—22no—
71C4⋊Dic15—21no—
72C4⋊Dic15C2312yes—
73#6712—22no—
74C4×Dic15—22no—
75C5×#217—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
79C2×C5×C3⋊C8C2×C414yescomplemented
80C2×C5×C3⋊C8C2311yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×#681C2×C414yescomplemented
85C2×C3×#168C2312yes—
86#6669—22no—
87#6667—22no—
88Dic3×Dic5—22no—
89#6651C2×C418yescomplemented
90#6648C2×C418yescomplemented
91C2×#907—51no—
92#5523—51no—
93#5504—51no—
94C3×#428—51no—
95#5121—51no—
96#4998D511yescharacteristic, complemented
97C2×#807—51no—
98#4881—52no—
99D3×#107—52no—
100#4861—52no—
101#4860—52no—
102C2×#709—31no—
103C22×C5×C8—31no—
104C5×#117—31no—
105C5×#117C2×D311yescharacteristic
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5C2×D311yescharacteristic
108C2×#681C2×D311yescharacteristic
109#4047—38no—
110C2×#676—32no—
111C2×C8×D5—32no—
112#4038—32no—
113#4038—32no—
114D5×C4⋊C4—32no—
115D5×C4⋊C4—32no—
116#4027—62no—
117#4027—62no—
118C4×D20—61no—
119C4×D20—61no—
120C4×Dic10—61no—
121C4×Dic10—61no—
122C5×#107—31no—
123C5×#107—31no—
124C5×#106—31no—
125C5×#106—31no—
126#3950—32no—
127#3950—32no—
128#3940—32no—
129#3940C2×D312yes—
130#3939—32no—
131#3939C2×D312yes—
132#2913—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×D15C2×D412yes—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×Q812yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220C4⋊C418yes—
142C2×Dic15—22no—
143C2×Dic15—81no—
144C2×Dic15C2×D412yes—
145D60C4⋊C414yes—
146C4×D15—82no—
147C4×D15C22×C414yes—
148C4×D15C2×Q814yes—
149Dic30C4⋊C414yes—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—81no—
154#1200—82no—
155C3×#168C22×C414yes—
156C5×C3⋊C8C22×C412yes—
157C5×C3⋊C8C22×C412yes—
158C2×#235—51no—
159C2×C3×M16—51no—
160C3×#117C2×D511yescharacteristic
161C2×C3×C4⋊C4—51no—
162C4×#67—102no—
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3—51no—
165C22×C3⋊C8C2×D511yescharacteristic
166#907—58no—
167C2×ΓL(1,𝔽25)—52no—
168C2×D3×C8—52no—
169#893—101no—
170#892—52no—
171#892—52no—
172D3×C4⋊C4—52no—
173D3×C4⋊C4—52no—
174#887—101no—
175#67⋊C4—102no—
176C4×D12—101no—
177C4×Dic6—101no—
178C3×#107—52no—
179C3×#106—52no—
180#818—52no—
181#817—52no—
182#808C2×D511yescharacteristic
183#808C2×D511yescharacteristic
184#807—52no—
185#807—52no—
186#807C2×D511yescharacteristic
187#807C2×D511yescharacteristic
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—32no—
190C22×Dic5—21no—
191C22×Dic5—61no—
192#709—34no—
193#709—34no—
194C2×D20—31no—
195C2×C4×D5—32no—
196C2×C4×D5—62no—
197C2×C4×D5—62no—
198C2×Dic10—31no—
199C2×C5×C8—34no—
200C2×C5×C8—31no—
201C2×C5×C8—31no—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C4⋊C4C22×D311yescharacteristic
206C5×C22⋊C4—21no—
207C5×C22⋊C4—61no—
208C42×C5—21no—
209C42×C5—61no—
210#685—62no—
211#685—62no—
212C4⋊Dic5—21no—
213C4⋊Dic5—32no—
214C4⋊Dic5—61no—
215C4⋊Dic5C22×D312yes—
216#683—62no—
217#683—62no—
218C4×Dic5—62no—
219C4×Dic5—62no—
220#681C4×D314yescomplemented
221C2×#168C22×D312yes—
222#676—38no—
223C8×D5—38no—
224C2×#131—151no—
225#520—151no—
226#520—151no—
227#428—51no—
228#428—152no—
229#428—152no—
230#428—151no—
231#427—31no—
232#427—152no—
233C2×#107—152no—
234C2×#107—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×D15—22no—
240C2×D15—22no—
241C2×D15C2×C4⋊C414yes—
242C3×C4×C5—41no—
243C3×C4×C5—41no—
244C3×C4×C5C2×C4⋊C412yes—
245C3×C4×C5C23×C411yescharacteristic
246C3×C4×C5C22×Q811yescharacteristic
247Dic15—42no—
248Dic15C2×C4⋊C414yes—
249C3×Dic5—42no—
250C5×Dic3—41no—
251C5×Dic3—41no—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67—52no—
255C22×Dic3—101no—
256#235—54no—
257#235—54no—
258C2×D12—51no—
259C2×C4×D3—52no—
260C2×C4×D3—102no—
261C2×C4×D3—102no—
262C2×Dic6—51no—
263C3×M16—54no—
264C2×C3×C8—52no—
265C3×C4⋊C4—52no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D511yescharacteristic
268C3×C4⋊C4C22×D511yescharacteristic
269C3×C22⋊C4—21no—
270C3×C42—21no—
271#217—21no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—52no—
275C4⋊Dic3—101no—
276C4⋊Dic3C22×D511yescharacteristic
277C4⋊Dic3C22×D511yescharacteristic
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—21no—
281C4×Dic3—102no—
282C4×Dic3—102no—
283C2×C3⋊C8C4×D514yescomplemented
284C2×C3⋊C8C22×D511yescharacteristic
285C2×C3⋊C8C22×D511yescharacteristic
286ΓL(1,𝔽25)—58no—
287D3×C8—58no—
288C23×C5D3×D411yescharacteristic
289C22×D5—32no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×Q812yes—
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—38no—
299C2×Dic5—22no—
300C2×Dic5—32no—
301C2×Dic5—62no—
302C2×Dic5—81no—
303C2×Dic5—241no—
304D20—34no—
305C4×D5—34no—
306C4×D5—34no—
307C4×D5—242no—
308C4×D5—242no—
309Dic10—34no—
310C5×C8—32no—
311C5×C8—32no—
312#168C2×C4×D314yes—
313C2×#41—151no—
314#131—158no—
315C2×M16—51no—
316C2×M16—152no—
317C22×C8—31no—
318C22×C8—152no—
319C4×Q8—301no—
320C4×Q8—301no—
321C4×D4—301no—
322C4×D4—301no—
323C4×D4—302no—
324C4×D4—302no—
325#117—31no—
326#117—152no—
327#117—152no—
328#117D3×D511yescharacteristic
329C2×C4⋊C4—51no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—151no—
332C2×C4⋊C4—152no—
333#107—31no—
334#107—31no—
335#107—52no—
336#107—152no—
337#107—152no—
338#107—152no—
339#106—31no—
340#106—31no—
341#106—52no—
342#106—152no—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57611yescharacteristic
346C2×C3×C5#57811yescharacteristic
347D15—24no—
348C23×C3D4×D511yescharacteristic
349C22×D3—52no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—102no—
353C2×C3×C4—401no—
354C2×C3×C4C2×C4×D512yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4Q8×D512yes—
357C2×C3×C4C23×D511yescharacteristic
358#67—58no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—52no—
362C2×Dic3—102no—
363C2×Dic3—401no—
364D12—54no—
365C4×D3—54no—
366C4×D3—54no—
367C4×D3—402no—
368C4×D3—402no—
369Dic6—54no—
370C3×C8—54no—
371C3⋊C8C2×C4×D512yes—
372C3⋊C8C2×C4×D512yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5D3×C4⋊C412yes—
376C22×C5C2×D3×D411yescharacteristic
377C2×D5—34no—
378C2×D5—62no—
379C2×D5—62no—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5D3×C4⋊C412yes—
385C4×C5C22×C4×D311yescharacteristic
386C4×C5C2×D3×Q811yescharacteristic
387Dic5—34no—
388Dic5—42no—
389Dic5—122no—
390#41—154no—
391#41—154no—
392C2×Q8—151no—
393C2×D4—152no—
394C2×D4—151no—
395C22×C4—101no—
396C22×C4—152no—
397C22×C4—302no—
398C22×C4—302no—
399C22×C4—301no—
400C22×C4C2×D3×D511yescharacteristic
401M16—54no—
402M16—158no—
403C2×C8—34no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—52no—
407C2×C8—158no—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—52no—
411C4⋊C4—101no—
412C4⋊C4—152no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C4⋊C4C2×D3×D511yescharacteristic
417C4⋊C4C2×D3×D511yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—61no—
420C22⋊C4—302no—
421C22⋊C4—302no—
422C42—21no—
423C42—61no—
424C42—302no—
425C42—302no—
426C3×C5#291311yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3D5×C4⋊C412yes—
430C22×C3C2×D4×D511yescharacteristic
431C2×D3—54no—
432C2×D3—102no—
433C2×D3—102no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—202no—
437C3×C4D5×C4⋊C412yes—
438C3×C4C22×C4×D511yescharacteristic
439C3×C4C2×Q8×D511yescharacteristic
440Dic3—41no—
441Dic3—41no—
442Dic3—54no—
443Dic3—202no—
444C2×C5—22no—
445C2×C5C2×D3×C4⋊C411yescharacteristic
446C2×C5#577411yescharacteristic
447C2×C5#577911yescharacteristic
448D5—64no—
449C23—152no—
450C23#679011yescharacteristic
451Q8—154no—
452D4—158no—
453D4—154no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—102no—
459C2×C4—152no—
460C2×C4—154no—
461C2×C4—154no—
462C2×C4—302no—
463C2×C4—401no—
464C2×C4—1202no—
465C2×C4—1202no—
466C2×C4—1201no—
467C2×C4D15⋊Q812yes—
468C2×C4C4×D3×D512yes—
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—32no—
472C8—32no—
473C8—54no—
474C2×C3—22no—
475C2×C3C2×D5×C4⋊C411yescharacteristic
476C2×C3#6610311yescharacteristic
477C2×C3#6610511yescharacteristic
478D3—104no—
479C5#7921011yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—154no—
483C22—302no—
484C22—302no—
485C22#9140412yes—
486C22C2×#679011yescharacteristic
487C4—41no—
488C4—41no—
489C4—121no—
490C4—121no—
491C4—154no—
492C4—202no—
493C4—602no—
494C4#9140412yes—
495C4C2×D15⋊Q811yescharacteristic
496C4C2×C4×D3×D511yescharacteristic
497C3#1061091011yescharacteristic, complemented, Sylow
498C2—22no—
499C2—304no—
500C2C2×#9140411yescharacteristic
501C2#1175533011yescharacteristic
502C2#1175535311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2913
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C5×#4998C2semidirect
5. C3×#65284C2semidirect
6. C2×#90990C2semidirect
7. #11748460C2semidirect
8. #11747459C2semidirect
9. #11747457C2semidirect
10. #11747440C2semidirect
11. #11747438C2semidirect
31. #91291C4semidirect
50. #65284D3semidirect
79. C2×C5×C3⋊C8C2×C4semidirect
84. C3×#681C2×C4semidirect
89. #6651C2×C4semidirect
90. #6648C2×C4semidirect
96. #4998D5semidirect
220. #681C4×D3semidirect
283. C2×C3⋊C8C4×D5semidirect
426. C3×C5#2913semidirect
479. C5#79210semidirect
497. C3#10610910semidirect

Maximal subgroups

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

subgroupindex
#117562822
#117544962
C2×#912912
C5×#49982
C3×#652842
C2×#909902
#117484602
#117474592
#117474572
#117474402
#117474382
#106109103
#792105