Finite Group Databasebeta

← #14417269

Subgroups — #14417269

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#11754509C211yesmaximal, characteristic
2#11754213C211yesmaximal, characteristic, complemented
3C2×#91313C211yesmaximal, characteristic
4C2×#91100C211yesmaximal, characteristic, complemented
5C5×#5101C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic
7#11748455C211yesmaximal, characteristic, complemented
8#11747832C212yesmaximal, complemented
9#11747831C212yesmaximal, complemented
10#11747742C212yesmaximal, complemented
11#11747739C212yesmaximal, complemented
12#10610302—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#91559—22no—
21#91532—22no—
22Dic3×D20C2212yes—
23D5×C4⋊Dic3—21no—
24#91358—21no—
25#91340C2212yes—
26#91340C2212yes—
27#91333—21no—
28#91333—21no—
29Dic3×Dic10C2212yes—
30C2×#6662C2212yes—
31#91313C418yescomplemented
32C2×#6657C2212yes—
33#91100C2212yes—
34#91100C2212yes—
35C5×#815C2212yes—
36C5×C8×Dic3C2212yes—
37C3×#3953C2211yescharacteristic
38C3×#3953C2211yescharacteristic
39C3×#3948C2211yescharacteristic
40C3×#3948C2211yescharacteristic
41#90990C2212yes—
42#90987C2212yes—
43#78821—51nomaximal, Hall
44C2×#4055—31no—
45#65857—31no—
46#65850—31no—
47C5×#405—31no—
48#65410—31no—
49#65402D311yescharacteristic
50C2×#3948—31no—
51#65005—32no—
52#64999—32no—
53C4×Dic20—32no—
54C4×#677—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C22×Dic15—21no—
58C2×Dic30—21no—
59C2×Dic30—22no—
60C2×Dic30C2×C414yescomplemented
61C2×Dic30C2312yes—
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—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C5×#217D412yes—
75C5×C4⋊Dic3D411yescharacteristic
76C5×C4⋊Dic3D411yescharacteristic
77C4×C5×Dic3C2312yes—
78C5×#208C2×C414yescomplemented
79C2×C5×C3⋊C8C2312yes—
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4×Dic5—21no—
84#6669—22no—
85#6669—22no—
86#6668—22no—
87#6665—22no—
88Dic3×Dic5—22no—
89Dic3×Dic5—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#5101D511yescharacteristic, complemented
99#4995—51no—
100#4790—52no—
101#4789—52no—
102#4758—52no—
103#4757—52no—
104C2×#709C2×D311yescharacteristic
105C22×Dic10—31no—
106C2×C5×M16—31no—
107C22×C5×C8C2×D311yescharacteristic
108C5×#117—31no—
109#4072C2×D311yescharacteristic
110C2×C4⋊Dic5—31no—
111#4055—38no—
112C2×Dic20—32no—
113C2×#677—32no—
114#4038—61no—
115D5×C4⋊C4—61no—
116#4033—61no—
117#4033—61no—
118#4027—62no—
119#4023—62no—
120C4×D20—32no—
121C4×Dic10—32no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C5×#97—32no—
125C4×C5×C8—32no—
126#3953C2×D311yescharacteristic
127#3953C2×D311yescharacteristic
128#3950—32no—
129#3949—32no—
130#3948—32no—
131#3948—32no—
132#3948C2×D311yescharacteristic
133#3948C2×D311yescharacteristic
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—24no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—81no—
145Dic30—24no—
146Dic30—22no—
147Dic30C22×C414yes—
148C2×C5×Dic3C2×D412yes—
149C2×C5×Dic3C2×D412yes—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C3×D20—21no—
155C3×D20C22×C412yes—
156C3×C4×D5—24no—
157C3×Dic10—21no—
158C3×Dic10C22×C412yes—
159D5×Dic3—82no—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C5×C3⋊C8C22×C414yes—
163C2×C3×#41—51no—
164C22×Dic6—51no—
165C22×C3×C8C2×D511yescharacteristic
166C3×#117—51no—
167#951—58no—
168Q8×Dic3—52no—
169C2×#216—52no—
170D4×Dic3—52no—
171D4×Dic3—102no—
172C2×#214—52no—
173#926—101no—
174#926C2×D511yescharacteristic
175C2×C4⋊Dic3—51no—
176C2×C4⋊Dic3—101no—
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#815C2×D512yes—
190C8×Dic3C2×D512yes—
191#808—52no—
192#807—52no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—21no—
195C22×Dic5—61no—
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—22no—
209C2×C5×C8—32no—
210C2×C5×C8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212C5×C4⋊C4—31no—
213C5×C4⋊C4—31no—
214C5×C22⋊C4—32no—
215C42×C5—32no—
216C22⋊Dic5—21no—
217#685—62no—
218C4⋊Dic5—32no—
219C4⋊Dic5—61no—
220C4⋊Dic5C22×D311yescharacteristic
221C4⋊Dic5C22×D311yescharacteristic
222#683—62no—
223#683—62no—
224#683—62no—
225C4×Dic5—21no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
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—151no—
239#416—51no—
240C2×#103—151no—
241#405—31no—
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×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—24no—
253Dic15—42no—
254C3×Dic5—22no—
255C3×Dic5—41no—
256C3×Dic5—41no—
257C5×Dic3—22no—
258C5×Dic3—22no—
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—101no—
267C22×Dic3—101no—
268C22×Dic3—102no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C2×C3×C8—22no—
274C2×C3×C8C22×D511yescharacteristic
275C2×C3×C8C22×D511yescharacteristic
276C3×C4⋊C4—51no—
277C3×C4⋊C4—51no—
278C3×C22⋊C4—101no—
279C3×C42—101no—
280#217—102no—
281#217D2012yes—
282#216—58no—
283#214—58no—
284C4⋊Dic3—52no—
285C4⋊Dic3—101no—
286C4⋊Dic3—102no—
287C4⋊Dic3D2011yescharacteristic
288C4⋊Dic3D2011yescharacteristic
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208C4×D514yescomplemented
296C2×C3⋊C8C22×D512yes—
297C23×C5D3×D411yescharacteristic
298C22×D5—21no—
299C2×C4×C5—32no—
300C2×C4×C5—32no—
301C2×C4×C5C2×C4×D312yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23712yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—24no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—64no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—241no—
313D20—21no—
314D20C2×C4×D312yes—
315C4×D5—24no—
316C4×D5—242no—
317Dic10—21no—
318Dic10—34no—
319Dic10—64no—
320Dic10—62no—
321Dic10C2×C4×D312yes—
322C5×C8—21no—
323C5×C8—21no—
324C5×C8—34no—
325C2×#41—51no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—31no—
331C22×C8D3×D511yescharacteristic
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—31no—
340#117—51no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
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—32no—
354C4×C8—32no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C3×D5—42no—
360C23×C3—101no—
361C23×C3C2×D2011yescharacteristic
362C3×Q8—52no—
363C3×Q8—101no—
364C3×D4—52no—
365C3×D4—104no—
366C3×D4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—104no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4C2×D2011yescharacteristic
373C2×C3×C4#70912yes—
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—102no—
376C2×Dic3—104no—
377C2×Dic3—102no—
378C2×Dic3—402no—
379C2×Dic3—401no—
380C2×Dic3C2×D2012yes—
381C2×Dic3C2×D2012yes—
382Dic6—54no—
383Dic6—102no—
384Dic6—104no—
385C3×C8—21no—
386C3×C8—21no—
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—62no—
396C4×C5—62no—
397C4×C5#67⋊C412yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23711yescharacteristic
400Dic5—22no—
401Dic5—41no—
402Dic5—41no—
403Dic5—64no—
404Dic5—122no—
405#41—54no—
406#41—102no—
407C2×Q8—51no—
408C2×Q8—154no—
409C2×Q8—152no—
410C2×Q8—301no—
411C2×Q8—302no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—101no—
415C22×C4—302no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—34no—
422C2×C8—22no—
423C2×C8—32no—
424C2×C8C2×D3×D511yescharacteristic
425C2×C8C2×D3×D511yescharacteristic
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—51no—
429C4⋊C4—51no—
430C4⋊C4—152no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—301no—
435C22⋊C4—32no—
436C22⋊C4—101no—
437C22⋊C4—302no—
438C42—32no—
439C42—101no—
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×C3C4×D2012yes—
450C22×C3C22×D2011yescharacteristic
451C3×C4—102no—
452C3×C4—201no—
453C3×C4—201no—
454C3×C4C4×D2012yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#70911yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—104no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#577011yescharacteristic
464C2×C5#577111yescharacteristic
465D5—42no—
466C23—101no—
467C23D3×D2011yescharacteristic
468Q8—52no—
469Q8—101no—
470Q8—154no—
471Q8—304no—
472Q8—302no—
473D4—52no—
474D4—104no—
475D4—101no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—101no—
479C2×C4—104no—
480C2×C4—101no—
481C2×C4—101no—
482C2×C4—304no—
483C2×C4—302no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4C4×D3×D512yes—
488C2×C4D3×D2011yescharacteristic
489C2×C4#677912yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—34no—
494C2×C3—22no—
495C2×C3—202no—
496C2×C3C2×C4×D2011yescharacteristic
497C2×C3#6608511yescharacteristic
498C2×C3#6608711yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—102no—
503C22—201no—
504C22—201no—
505C22#9139512yes—
506C22C2×D3×D2011yescharacteristic
507C4—62no—
508C4—62no—
509C4—102no—
510C4—201no—
511C4—201no—
512C4—304no—
513C4—602no—
514C4#9139512yes—
515C4C2×C4×D3×D511yescharacteristic
516C4C2×#677911yescharacteristic
517C3#1061030211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—202no—
520C2#1175397211yescharacteristic
521C2#1175400311yescharacteristic
522C2C2×#9139511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754213C2semidirect
4. C2×#91100C2semidirect
5. C5×#5101C2semidirect
7. #11748455C2semidirect
8. #11747832C2semidirect
9. #11747831C2semidirect
10. #11747742C2semidirect
11. #11747739C2semidirect
31. #91313C4semidirect
60. C2×Dic30C2×C4semidirect
78. C5×#208C2×C4semidirect
91. #6662C2×C4semidirect
92. #6657C2×C4semidirect
98. #5101D5semidirect
295. #208C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10610302semidirect

Maximal subgroups

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

subgroupindex
#117545092
#117542132
C2×#913132
C2×#911002
C5×#51012
C3×#654022
#117484552
#117478322
#117478312
#117477422
#117477392
#106103023
#788215