Finite Group Databasebeta

← #14417279

Subgroups — #14417279

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
1#11756275C211yesmaximal, characteristic, complemented
2#11754499C211yesmaximal, characteristic
3C2×#91313C211yesmaximal, characteristic
4C5×#4995C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic
6C2×#90975C211yesmaximal, characteristic, complemented
7#11748324C211yesmaximal, characteristic, complemented
8#11747274C212yesmaximal, complemented
9#11747271C212yesmaximal, complemented
10#11747228C212yesmaximal, complemented
11#11747227C212yesmaximal, complemented
12#10610933—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17#91776C2212yes—
18#91776C2212yes—
19#91766—22no—
20C4×Dic30—21no—
21C4×Dic30—21no—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C5×#208C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25Dic3×C22⋊D5—22no—
26#91434C2212yes—
27D5×C4⋊Dic3—21no—
28#91358—21no—
29#91331C2212yes—
30C2×#6662C2212yes—
31#91313C418yescomplemented
32C2×#6657C2212yes—
33C5×#808C2212yes—
34C5×#807C2212yes—
35C3×#3942C2211yescharacteristic
36C3×#3942C2211yescharacteristic
37C3×#3941C2211yescharacteristic
38C3×#3941C2211yescharacteristic
39#90975C2212yes—
40#90975C2212yes—
41#90954C2212yes—
42#90951C2212yes—
43#78821—51nomaximal, Hall
44C2×#4055—31no—
45#65850—31no—
46#65838—31no—
47C5×#428—31no—
48#65411—31no—
49#65291D311yescharacteristic
50C2×#3942—31no—
51#65178—32no—
52#65162—32no—
53#65142—32no—
54#65141—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×Dic30—21no—
58C2×Dic30—22no—
59C2×Dic30C2×C414yescomplemented
60C2×Dic30C2312yes—
61C22×C5×Dic3—21no—
62C2×C3×C22⋊D5—21no—
63C3×#709—22no—
64C3×#709C2×C414yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10C2311yescharacteristic
68C2×D5×Dic3—22no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73#6719D412yes—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15D411yescharacteristic
76#6712—22no—
77#6712—22no—
78C4×Dic15—22no—
79C4×Dic15—22no—
80C4×Dic15C2312yes—
81C5×C4⋊Dic3—21no—
82C5×C4⋊Dic3C2312yes—
83C5×#208C2×C414yescomplemented
84C2×C5×C3⋊C8C2312yes—
85C2×C3×#168—22no—
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88#6668—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6662C2×C418yescomplemented
92#6657C2×C418yescomplemented
93#5827—51no—
94C2×#951—51no—
95#5516—51no—
96C3×#416—51no—
97C2×#816—51no—
98#5101—51no—
99#4995D511yescharacteristic, complemented
100#4790—52no—
101#4789—52no—
102#4758—52no—
103#4757—52no—
104C2×#709C2×D311yescharacteristic
105C22×Dic10—31no—
106C2×C5×M16—31no—
107C5×#117C2×D311yescharacteristic
108C2×C5×C4⋊C4—31no—
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168C2×D311yescharacteristic
112#4055—38no—
113C2×Dic20—32no—
114C2×#677—32no—
115#4039—32no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4033—32no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#107—32no—
125C5×#106—32no—
126#3947—32no—
127C8×Dic5—32no—
128#3942—32no—
129#3942—32no—
130#3942C2×D311yescharacteristic
131#3942C2×D311yescharacteristic
132#3941C2×D311yescharacteristic
133#3941C2×D311yescharacteristic
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—24no—
144C2×Dic15—22no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147Dic30—24no—
148Dic30—22no—
149Dic30C22×C414yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—81no—
152C3×C22⋊D5—24no—
153C2×C3×Dic5—21no—
154C3×D20—21no—
155C3×D20C22×C412yes—
156C3×C4×D5—24no—
157C3×Dic10—21no—
158C3×Dic10C22×C412yes—
159D5×Dic3—82no—
160C3×#168—21no—
161C3×#168—21no—
162C5×C3⋊C8C22×C414yes—
163C2×C3×#41—51no—
164C22×Dic6—51no—
165C22×C3×C8—51no—
166C3×#117C2×D511yescharacteristic
167#951—58no—
168Q8×Dic3—52no—
169C2×#216—52no—
170D4×Dic3—52no—
171D4×Dic3—102no—
172C2×#214—52no—
173#926—51no—
174#926—101no—
175C2×C4⋊Dic3—101no—
176C2×C4⋊Dic3C2×D511yescharacteristic
177C2×#208C2×D511yescharacteristic
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#808C2×D512yes—
192#807C2×D512yes—
193C22×C4×C5—61no—
194C22×C4×C5C22×D311yescharacteristic
195C2×C22⋊D5—21no—
196C22×Dic5—61no—
197#709—22no—
198#709C4×D314yes—
199C2×D20C22×D311yescharacteristic
200C2×C4×D5—21no—
201C2×C4×D5—62no—
202C2×Dic10—34no—
203C2×Dic10—32no—
204C2×Dic10—61no—
205C2×Dic10—62no—
206C2×Dic10C22×D311yescharacteristic
207C5×M16—34no—
208C2×C5×C8—32no—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C42×C5—21no—
215C22⋊Dic5—32no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219#683—62no—
220#683—62no—
221#683—62no—
222C4×Dic5—32no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C2×#168—22no—
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D311yescharacteristic
229Dic20—38no—
230#677—38no—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—31no—
239#416—51no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C3×D5—22no—
247C2×C3×D5—41no—
248C2×C3×D5—41no—
249C3×C4×C5—41no—
250C3×C4×C5—41no—
251C3×C4×C5C4×D412yes—
252C3×C4×C5C23×C411yescharacteristic
253C3×C4×C5C2×#4111yescharacteristic
254Dic15—24no—
255Dic15—22no—
256Dic15—22no—
257C3×Dic5—22no—
258C5×Dic3—42no—
259C3×#41—54no—
260C3×#41—102no—
261C2×C3×Q8—51no—
262C2×C3×D4—51no—
263C2×C3×D4—101no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—102no—
268C22×Dic3—101no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4C22×D511yescharacteristic
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C22⋊C4—21no—
279C3×C42—21no—
280#217—52no—
281#217—102no—
282#216—58no—
283#214—58no—
284C4⋊Dic3—21no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—52no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295#208C4×D514yescomplemented
296C2×C3⋊C8C22×D512yes—
297C23×C5D3×D411yescharacteristic
298C22×D5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—62no—
302C2×C4×C5—241no—
303C2×C4×C5C2×C4×D312yes—
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5#23712yes—
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—24no—
308C2×Dic5—21no—
309C2×Dic5—32no—
310C2×Dic5—32no—
311C2×Dic5—64no—
312C2×Dic5—62no—
313D20—21no—
314D20C2×C4×D312yes—
315C4×D5—24no—
316C4×D5—242no—
317Dic10—21no—
318Dic10—34no—
319Dic10—64no—
320Dic10—62no—
321Dic10C2×C4×D312yes—
322C5×C8—34no—
323#168—21no—
324#168—21no—
325C2×#41—51no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—31no—
331C22×C8—51no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—151no—
340#117—302no—
341#117—301no—
342#117D3×D511yescharacteristic
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—32no—
346#106—32no—
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×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C3×D5—42no—
360C23×C3—101no—
361C23×C3D4×D511yescharacteristic
362C3×Q8—52no—
363C3×Q8—101no—
364C3×D4—52no—
365C3×D4—104no—
366C3×D4—101no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—101no—
370C2×C3×C4—104no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71312yes—
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—22no—
376C2×Dic3—52no—
377C2×Dic3—52no—
378C2×Dic3—81no—
379C2×Dic3—102no—
380C2×Dic3—104no—
381C2×Dic3—402no—
382Dic6—54no—
383Dic6—102no—
384Dic6—104no—
385C3×C8—101no—
386C3×C8—101no—
387C3⋊C8C2×C4×D514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#67⋊C412yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—22no—
393C2×D5—41no—
394C2×D5—41no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—122no—
398C4×C5#67⋊C412yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23711yescharacteristic
401Dic5—22no—
402Dic5—64no—
403Dic5—62no—
404Dic5—62no—
405#41—54no—
406#41—102no—
407C2×Q8—51no—
408C2×Q8—154no—
409C2×Q8—152no—
410C2×Q8—302no—
411C2×Q8—301no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—34no—
422C2×C8—32no—
423C2×C8—51no—
424C2×C8—51no—
425C2×C8—102no—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4C2×D3×D511yescharacteristic
434C4⋊C4C2×D3×D511yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—21no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—102no—
447C22×C3—201no—
448C22×C3—201no—
449C22×C3#403912yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—102no—
454C3×C4#403912yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#71311yescharacteristic
457Dic3—42no—
458Dic3—104no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#577011yescharacteristic
464C2×C5#577111yescharacteristic
465D5—42no—
466C23—101no—
467C23#679011yescharacteristic
468Q8—52no—
469Q8—101no—
470Q8—154no—
471Q8—304no—
472Q8—302no—
473D4—52no—
474D4—104no—
475D4—101no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—62no—
479C2×C4—101no—
480C2×C4—104no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—241no—
484C2×C4—304no—
485C2×C4—302no—
486C2×C4—1202no—
487C2×C4#676612yes—
488C2×C4C4×D3×D512yes—
489C2×C4#679011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—34no—
492C8—101no—
493C8—101no—
494C2×C3—22no—
495C2×C3—202no—
496C2×C3C2×#403911yescharacteristic
497C2×C3#6610911yescharacteristic
498C2×C3#6611311yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—102no—
503C22—201no—
504C22—201no—
505C22#9139612yes—
506C22C2×#679011yescharacteristic
507C4—41no—
508C4—41no—
509C4—102no—
510C4—122no—
511C4—304no—
512C4—302no—
513C4—302no—
514C4#9139612yes—
515C4C2×#676611yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061093311yescharacteristic, complemented, Sylow
518C2—22no—
519C2—202no—
520C2C2×#9139611yescharacteristic
521C2#1175533311yescharacteristic
522C2#1175535011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2947
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
1. #11756275C2semidirect
4. C5×#4995C2semidirect
6. C2×#90975C2semidirect
7. #11748324C2semidirect
8. #11747274C2semidirect
9. #11747271C2semidirect
10. #11747228C2semidirect
11. #11747227C2semidirect
31. #91313C4semidirect
59. C2×Dic30C2×C4semidirect
83. C5×#208C2×C4semidirect
91. #6662C2×C4semidirect
92. #6657C2×C4semidirect
99. #4995D5semidirect
295. #208C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10610933semidirect

Maximal subgroups

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

subgroupindex
#117562752
#117544992
C2×#913132
C5×#49952
C3×#652912
C2×#909752
#117483242
#117472742
#117472712
#117472282
#117472272
#106109333
#788215