Finite Group Databasebeta

← #14413461

Subgroups — #14413461

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#11756263C211yesmaximal, characteristic
2#11754506C211yesmaximal, characteristic
3C2×#91291C211yesmaximal, characteristic
4C2×C5×#808C211yesmaximal, characteristic, complemented
5C3×#65253C211yesmaximal, characteristic, complemented
6#11748459C211yesmaximal, characteristic, complemented
7#11748451C211yesmaximal, characteristic, complemented
8#11747459C212yesmaximal, complemented
9#11747457C212yesmaximal, complemented
10#11747441C212yesmaximal, complemented
11#11747439C212yesmaximal, complemented
12#10610847—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C4×#1220—22no—
16#91815C2211yescharacteristic
17#91782—21no—
18#91781C2212yes—
19C4⋊C4×D15C2212yes—
20#91776—21no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91556—22no—
26#91437C2212yes—
27#91418—21no—
28#91347C2212yes—
29#91333—21no—
30C2×#6651C2212yes—
31#91291C418yescomplemented
32C2×#6648C2212yes—
33C5×#808C2212yes—
34C5×#808C2212yes—
35C3×#3940C2212yes—
36C3×#3939C2212yes—
37#90990C2211yescharacteristic
38#90990C2211yescharacteristic
39#90988C2212yes—
40#90987C2211yescharacteristic
41#90987C2211yescharacteristic
42#90985C2212yes—
43#79209—51nomaximal, Hall
44C2×#4047—31no—
45#65838—31no—
46#65838—31no—
47C2×C5×#106—31no—
48#65395—31no—
49#65253—31no—
50#65253D311yescharacteristic, complemented
51#65150—32no—
52#65150—32no—
53#65149—32no—
54D5×#106—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220D412yes—
58#6817C2×C414yes—
59#6817Q814yes—
60C2×D60D411yescharacteristic
61C2×C4×D15—22no—
62C2×C4×D15C2312yes—
63C2×Dic30D411yescharacteristic
64C22×C5×Dic3—21no—
65C2×#1200—22no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68#6719—21no—
69#6714—22no—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712—22no—
73C4×Dic15—21no—
74C4×Dic15—22no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C2×C5×C3⋊C8C2×C414yescomplemented
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4×Dic5—21no—
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#4998—51no—
97C2×#808D511yescharacteristic, complemented
98#4881—52no—
99#4880—52no—
100#4861—52no—
101D3×#106—52no—
102C2×#709—31no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C4×C22⋊D5—62no—
107C4×C22⋊D5—62no—
108#4072—31no—
109#4072C2×D311yescharacteristic
110C2×#681C2×D311yescharacteristic
111#4047—38no—
112C2×#676—32no—
113C2×C8×D5—32no—
114#4039—61no—
115#4039—61no—
116#4038—32no—
117#4038—32no—
118D5×C4⋊C4—32no—
119D5×C4⋊C4—32no—
120#4033—61no—
121#4033—61no—
122C5×#106—32no—
123C5×#106—32no—
124#3950—31no—
125#3950—31no—
126#3949—31no—
127#3949—31no—
128#3940—32no—
129#3940C2×D312yes—
130#3939—32no—
131#3939C2×D312yes—
132#2912—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×D15C2×D412yes—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—81no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×Q812yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220C4⋊C418yes—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15C2×D412yes—
145D60C4⋊C414yes—
146C4×D15—82no—
147C4×D15C22×C414yes—
148C4×D15C2×Q814yes—
149Dic30C4⋊C414yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—81no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154#1200—82no—
155C3×#168C22×C414yes—
156C5×C3⋊C8C22×C412yes—
157C5×C3⋊C8C22×C412yes—
158C2×#235—51no—
159C2×C3×M16—51no—
160C3×#117—51no—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C4×#67—102no—
163#926—51no—
164C2×C4⋊Dic3C2×D511yescharacteristic
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#808—51no—
183#808—51no—
184#808C2×D512yes—
185#808C2×D512yes—
186#807—51no—
187#807—51no—
188C22×C4×C5—21no—
189C22×C4×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—32no—
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—21no—
203C5×C4⋊C4—32no—
204C5×C4⋊C4—61no—
205C5×C4⋊C4C22×D312yes—
206C22⋊Dic5—21no—
207C22⋊Dic5—61no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—31no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D311yescharacteristic
214#683—62no—
215#683—62no—
216C4×Dic5—21no—
217C4×Dic5—62no—
218C4×Dic5—62no—
219C4×Dic5—61no—
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—152no—
232#427—151no—
233C2×#106—31no—
234C2×#106—152no—
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—42no—
243C3×C4×C5C2×C4⋊C412yes—
244C3×C4×C5C23×C411yescharacteristic
245C3×C4×C5C22×Q811yescharacteristic
246Dic15—41no—
247Dic15—41no—
248Dic15C2×C4⋊C414yes—
249C3×Dic5—41no—
250C3×Dic5—41no—
251C5×Dic3—42no—
252C22×C3×C4—21no—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67—52no—
255C22×Dic3—21no—
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—21no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—51no—
268C3×C4⋊C4C22×D512yes—
269C3×C22⋊C4—101no—
270C3×C42—101no—
271#217—101no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—21no—
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3C22×D512yes—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—102no—
281C4×Dic3—102no—
282C4×Dic3—101no—
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—22no—
291C2×C4×C5—62no—
292C2×C4×C5—81no—
293C2×C4×C5—241no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×Q812yes—
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—38no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—32no—
302C2×Dic5—61no—
303C2×Dic5—61no—
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—302no—
323C4×D4—301no—
324C4×D4—302no—
325#117—51no—
326#117—152no—
327#117—151no—
328#117—152no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4D3×D511yescharacteristic
333#107—52no—
334#107—152no—
335#107—151no—
336#107—151no—
337#106—32no—
338#106—32no—
339#106—52no—
340#106—152no—
341#106—151no—
342#106—151no—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57711yescharacteristic
346C2×C3×C5#57711yescharacteristic
347D15—24no—
348C23×C3D4×D511yescharacteristic
349C22×D3—52no—
350C2×C3×C4—22no—
351C2×C3×C4—81no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4C2×C4×D512yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4Q8×D512yes—
357C2×C3×C4C23×D511yescharacteristic
358#67—58no—
359C2×Dic3—22no—
360C2×Dic3—52no—
361C2×Dic3—81no—
362C2×Dic3—101no—
363C2×Dic3—101no—
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—42no—
381C4×C5—122no—
382C4×C5D3×C4⋊C412yes—
383C4×C5C22×C4×D311yescharacteristic
384C4×C5C2×D3×Q811yescharacteristic
385Dic5—34no—
386Dic5—41no—
387Dic5—41no—
388Dic5—121no—
389Dic5—121no—
390#41—154no—
391#41—154no—
392C2×Q8—151no—
393C2×D4—152no—
394C2×D4—151no—
395C22×C4—21no—
396C22×C4—61no—
397C22×C4—152no—
398C22×C4—302no—
399C22×C4—302no—
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—21no—
409C4⋊C4—32no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—61no—
413C4⋊C4—151no—
414C4⋊C4—151no—
415C4⋊C4—302no—
416C4⋊C4—302no—
417C4⋊C4C2×D3×D512yes—
418C22⋊C4—101no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C42—101no—
423C42—302no—
424C42—302no—
425C42—301no—
426C3×C5#291211yescharacteristic, 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—42no—
435C3×C4—201no—
436C3×C4—201no—
437C3×C4D5×C4⋊C412yes—
438C3×C4C22×C4×D511yescharacteristic
439C3×C4C2×Q8×D511yescharacteristic
440Dic3—42no—
441Dic3—54no—
442Dic3—201no—
443Dic3—201no—
444C2×C5—22no—
445C2×C5C2×D3×C4⋊C411yescharacteristic
446C2×C5#577511yescharacteristic
447C2×C5#577811yescharacteristic
448D5—64no—
449C23—152no—
450C23#679011yescharacteristic
451Q8—154no—
452D4—158no—
453D4—154no—
454C2×C4—22no—
455C2×C4—62no—
456C2×C4—81no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—152no—
460C2×C4—154no—
461C2×C4—154no—
462C2×C4—241no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—1202no—
466C2×C4—1202no—
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#6609611yescharacteristic
477C2×C3#6609611yescharacteristic
478D3—104no—
479C5#7920911yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—154no—
483C22—302no—
484C22—302no—
485C22#9140412yes—
486C22C2×#679011yescharacteristic
487C4—42no—
488C4—122no—
489C4—154no—
490C4—201no—
491C4—201no—
492C4—601no—
493C4—601no—
494C4#9140412yes—
495C4C2×D15⋊Q811yescharacteristic
496C4C2×C4×D3×D511yescharacteristic
497C3#1061084711yescharacteristic, complemented, Sylow
498C2—22no—
499C2—304no—
500C2C2×#9140411yescharacteristic
501C2#1175472511yescharacteristic
502C2#1175509811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2912
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C5×#808C2semidirect
5. C3×#65253C2semidirect
6. #11748459C2semidirect
7. #11748451C2semidirect
8. #11747459C2semidirect
9. #11747457C2semidirect
10. #11747441C2semidirect
11. #11747439C2semidirect
31. #91291C4semidirect
50. #65253D3semidirect
77. C2×C5×C3⋊C8C2×C4semidirect
84. C3×#681C2×C4semidirect
89. #6651C2×C4semidirect
90. #6648C2×C4semidirect
97. C2×#808D5semidirect
220. #681C4×D3semidirect
283. C2×C3⋊C8C4×D5semidirect
426. C3×C5#2912semidirect
479. C5#79209semidirect
497. C3#10610847semidirect

Maximal subgroups

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

subgroupindex
#117562632
#117545062
C2×#912912
C2×C5×#8082
C3×#652532
#117484592
#117484512
#117474592
#117474572
#117474412
#117474392
#106108473
#792095