Finite Group Databasebeta

← #14417275

Subgroups — #14417275

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91840C211yesmaximal, characteristic
2C5×#5827C211yesmaximal, characteristic
3#11754213C211yesmaximal, characteristic, complemented
4C3×#65522C211yesmaximal, characteristic
5#11749260C212yesmaximal, complemented
6#11749257C212yesmaximal, complemented
7#11749014C212yesmaximal, complemented
8#11749011C212yesmaximal, complemented
9#11748472C211yesmaximal, characteristic, complemented
10C2×#90975C211yesmaximal, characteristic, complemented
11#11748323C211yesmaximal, characteristic, complemented
12#10614302—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15#91840C418yescomplemented
16C2×#6718C2212yes—
17C2×#6716C2212yes—
18C2×#6710C2211yescharacteristic
19C5×Q8×Dic3C2212yes—
20C5×D4×Dic3—22no—
21C5×D4×Dic3C2212yes—
22C5×#926—21no—
23C5×#926C2211yescharacteristic
24C2×C5×C4⋊Dic3—21no—
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C3×#4072C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28#91532—22no—
29#91340C2212yes—
30#91340C2212yes—
31#91333—21no—
32#91333—21no—
33C3×#3967C2211yescharacteristic
34C3×#3967C2211yescharacteristic
35C3×#3964C2211yescharacteristic
36C3×#3964C2211yescharacteristic
37#90989C2212yes—
38#90986C2212yes—
39#90975C2212yes—
40#90975C2212yes—
41#90953C2212yes—
42Dic3×#168C2212yes—
43#78821—51nomaximal, Hall
44C5×#520—31no—
45C2×#4097—31no—
46#65850—31no—
47#65522D311yescharacteristic
48#65319—32no—
49C4×#689—32no—
50#65307—32no—
51C4×#687—32no—
52#65286—31no—
53C2×#3942—31no—
54#65253—31no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yes—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—21no—
63C2×Dic30—21no—
64C2×Dic30—22no—
65C2×Dic30C2×C414yescomplemented
66C2×Dic30C2312yes—
67C22×C5×Dic3—21no—
68C22×C5×Dic3—22no—
69#6718C2×C418yescomplemented
70#6716C2×C418yescomplemented
71#6710C2×C414yescomplemented
72C2×C3⋊#168C2312yes—
73C5×#217—22no—
74C5×#217D412yes—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3—22no—
77C5×C4⋊Dic3D411yescharacteristic
78C5×C4⋊Dic3D411yescharacteristic
79C5×C4⋊Dic3C2312yes—
80C4×C5×Dic3—22no—
81C4×C5×Dic3C2312yes—
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4×Dic5—21no—
86C2×C3×#168—22no—
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89#6669—22no—
90#6669—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#5827D511yescharacteristic
94C2×#951—51no—
95#5516—51no—
96C3×#416—51no—
97C2×#816—51no—
98#5101—51no—
99#4995—51no—
100#4790—52no—
101#4789—52no—
102#4758—52no—
103#4757—52no—
104C2×C5×#41C2×D311yescharacteristic
105C22×Dic10—31no—
106C4×C5×Q8—32no—
107C4×C5×D4—32no—
108C4×C5×D4—62no—
109C5×#117—31no—
110C5×#117—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113#4097—38no—
114C2×#689—32no—
115C2×#687—32no—
116#4072C2×D311yescharacteristic
117C2×#681—31no—
118C22×#168C2×D311yescharacteristic
119#4033—61no—
120#4033—61no—
121#4023—62no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124#3967C2×D311yescharacteristic
125#3967C2×D311yescharacteristic
126#3964C2×D311yescharacteristic
127#3964C2×D311yescharacteristic
128#3942—32no—
129#3942—32no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2947—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C3×C5×Q8—21no—
138C3×C5×Q8C22×C412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C22×C412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—24no—
149C2×Dic15—22no—
150Dic30—24no—
151Dic30—22no—
152Dic30C22×C414yes—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—82no—
155C2×C5×Dic3—81no—
156C2×C5×Dic3C2×D412yes—
157C2×C5×Dic3C2×D412yes—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C3⋊#168C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C2×C3×#41C2×D511yescharacteristic
164C22×Dic6—51no—
165C22×C3×C8—51no—
166C3×#117—51no—
167#951—58no—
168Q8×Dic3C2×D512yes—
169C2×#216—52no—
170D4×Dic3—22no—
171D4×Dic3C2×D512yes—
172C2×#214—52no—
173#926—21no—
174#926C2×D511yescharacteristic
175C2×C4⋊Dic3—21no—
176C2×C4⋊Dic3C2×D511yescharacteristic
177C2×#208—51no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#103—51no—
184C3×#103—51no—
185C3×#102—51no—
186C3×#102—51no—
187#816—52no—
188#816—52no—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C5×#41—22no—
194C5×#41C4×D314yes—
195C2×C5×Q8C22×D311yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4C22×D311yescharacteristic
198C22×C4×C5—21no—
199C22×C4×C5—62no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—61no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C5×C4⋊C4—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4—61no—
212C5×C22⋊C4—32no—
213C5×C22⋊C4—62no—
214C42×C5—32no—
215C42×C5—62no—
216C22⋊Dic5—21no—
217#689—38no—
218#687—38no—
219C4⋊Dic5C22×D311yescharacteristic
220C4⋊Dic5C22×D311yescharacteristic
221#683—62no—
222#683—62no—
223C4×Dic5—21no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226#681—34no—
227C2×#168—22no—
228C2×#168—32no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231C2×#137—151no—
232#520—31no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—51no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C4×D412yes—
248C22×C3×C5C22×D411yescharacteristic
249C3×C4×C5—22no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—24no—
254C3×Dic5—41no—
255C3×Dic5—41no—
256C5×Dic3—22no—
257C5×Dic3—22no—
258C5×Dic3—42no—
259C3×#41—22no—
260C3×#41C4×D514yes—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4C22×D511yescharacteristic
264C22×C3×C4—21no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—22no—
268C22×Dic3—101no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—101no—
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—51no—
278C3×C22⋊C4—101no—
279C3×C42—101no—
280#217—22no—
281#217C22⋊D512yes—
282#216—58no—
283#214—58no—
284C4⋊Dic3—21no—
285C4⋊Dic3—22no—
286C4⋊Dic3C22⋊D511yescharacteristic
287C4⋊Dic3C22⋊D511yescharacteristic
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—22no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208—54no—
296C2×C3⋊C8—52no—
297C23×C5—21no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—21no—
300C5×Q8C2×C4×D312yes—
301C5×D4—24no—
302C5×D4—21no—
303C5×D4C2×C4×D312yes—
304C2×C4×C5—21no—
305C2×C4×C5—24no—
306C2×C4×C5—32no—
307C2×C4×C5—32no—
308C2×C4×C5—62no—
309C2×C4×C5—242no—
310C2×C4×C5—241no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23712yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—64no—
318C2×Dic5—62no—
319Dic10—34no—
320Dic10—64no—
321Dic10—62no—
322#168—21no—
323#168—21no—
324#168—34no—
325C2×#41D3×D511yescharacteristic
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8—51no—
332C4×Q8—32no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—32no—
338C4×D4—62no—
339#117—31no—
340#117—51no—
341#117—61no—
342#117—302no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—61no—
345#107—152no—
346#106—152no—
347#103—51no—
348#103—51no—
349#103—152no—
350#103—152no—
351#102—51no—
352#102—51no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5—42no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#57711yescharacteristic
359C2×C3×C5#57811yescharacteristic
360C23×C3—21no—
361C23×C3C2×C22⋊D511yescharacteristic
362C3×Q8—21no—
363C3×Q8C2×C4×D512yes—
364C3×D4—24no—
365C3×D4—21no—
366C3×D4C2×C4×D512yes—
367C2×C3×C4—21no—
368C2×C3×C4—24no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4#70912yes—
373C2×C3×C4C2×C22⋊D511yescharacteristic
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—22no—
376C2×Dic3—82no—
377C2×Dic3—81no—
378C2×Dic3—102no—
379C2×Dic3—104no—
380C2×Dic3C2×C22⋊D512yes—
381C2×Dic3C2×C22⋊D512yes—
382Dic6—54no—
383Dic6—102no—
384Dic6—104no—
385C3×C8—101no—
386C3×C8—101no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—22no—
391C22×C5—41no—
392C22×C5—41no—
393C22×C5#67⋊C412yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—22no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—122no—
399C4×C5#67⋊C412yes—
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×#23711yescharacteristic
402Dic5—41no—
403Dic5—41no—
404Dic5—64no—
405#41—22no—
406#41#120014yes—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—302no—
410C2×Q8—301no—
411C2×Q8C2×D3×D511yescharacteristic
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—21no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—51no—
423C2×C8—51no—
424C2×C8—102no—
425C2×C8—152no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—51no—
430C4⋊C4—51no—
431C4⋊C4—62no—
432C4⋊C4—61no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—32no—
436C22⋊C4—62no—
437C22⋊C4—101no—
438C42—32no—
439C42—62no—
440C42—101no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3C4×C22⋊D512yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C3×C4—22no—
452C3×C4—201no—
453C3×C4—201no—
454C3×C4C4×C22⋊D512yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#70911yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—42no—
460Dic3—104no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#577011yescharacteristic
465C2×C5#577111yescharacteristic
466C23—21no—
467C23D3×C22⋊D511yescharacteristic
468Q8—21no—
469Q8—154no—
470Q8—302no—
471Q8—304no—
472Q8C2×#120012yes—
473D4—24no—
474D4—21no—
475D4C2×#120012yes—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—62no—
481C2×C4—101no—
482C2×C4—101no—
483C2×C4—242no—
484C2×C4—241no—
485C2×C4—302no—
486C2×C4—304no—
487C2×C4#677912yes—
488C2×C4C2×#120012yes—
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8—154no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3C2×C4×C22⋊D511yescharacteristic
497C2×C3#6617011yescharacteristic
498C2×C3#6617211yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22#9155612yes—
506C22C2×D3×C22⋊D511yescharacteristic
507C4—22no—
508C4—62no—
509C4—62no—
510C4—122no—
511C4—201no—
512C4—201no—
513C4—304no—
514C4#9155612yes—
515C4C2×#677911yescharacteristic
516C4C22×#120011yescharacteristic
517C3#1061430211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2#1175534611yescharacteristic
521C2#1175534711yescharacteristic
522C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #11754213C2semidirect
5. #11749260C2semidirect
6. #11749257C2semidirect
7. #11749014C2semidirect
8. #11749011C2semidirect
9. #11748472C2semidirect
10. C2×#90975C2semidirect
11. #11748323C2semidirect
15. #91840C4semidirect
65. C2×Dic30C2×C4semidirect
69. #6718C2×C4semidirect
70. #6716C2×C4semidirect
71. #6710C2×C4semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10614302semidirect

Maximal subgroups

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

subgroupindex
C2×#918402
C5×#58272
#117542132
C3×#655222
#117492602
#117492572
#117490142
#117490112
#117484722
C2×#909752
#117483232
#106143023
#788215