Finite Group Databasebeta

← #14417185

Subgroups — #14417185

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#11756586C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic
3#11756275C211yesmaximal, characteristic, complemented
4C3×C5×#416C211yesmaximal, characteristic
5C2×#91100C211yesmaximal, characteristic, complemented
6#11751202C211yesmaximal, characteristic, complemented
7#11751096C211yesmaximal, characteristic, complemented
8#11750891C212yesmaximal, complemented
9#11750890C212yesmaximal, complemented
10#11750859C212yesmaximal, complemented
11#11750858C212yesmaximal, complemented
12#10610552—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91840C418yescomplemented
18Q8×Dic15C2212yes—
19C2×#6718C2212yes—
20D4×Dic15—22no—
21D4×Dic15C2212yes—
22C2×#6716C2212yes—
23#91815—21no—
24#91815C2211yescharacteristic
25C2×C4⋊Dic15—21no—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×#6710C2211yescharacteristic
28#91776C2212yes—
29#91776C2212yes—
30#91766—22no—
31C4×Dic30—21no—
32C4×Dic30—21no—
33C3×C5×#103C2211yescharacteristic
34C3×C5×#103C2211yescharacteristic
35C3×C5×#102C2211yescharacteristic
36C3×C5×#102C2211yescharacteristic
37#91100C2212yes—
38#91100C2212yes—
39#91099C2212yes—
40C8×Dic15C2212yes—
41#91092C2212yes—
42#91091C2212yes—
43#78821—51nomaximal, Hall
44#66161—31no—
45C2×#4097—31no—
46#65850—31no—
47C5×#416D311yescharacteristic
48C2×#3948—31no—
49#65390—31no—
50#65284—31no—
51#65079—32no—
52#65078—32no—
53#65047—32no—
54#65046—32no—
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—
63C22×Dic15—21no—
64C22×Dic15—22no—
65C2×Dic30—21no—
66C2×Dic30—22no—
67C2×Dic30C2×C414yescomplemented
68C2×Dic30C2312yes—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C22⋊C4—21no—
75C3×C42×C5—21no—
76#6719—22no—
77#6719D412yes—
78#6718C2×C418yescomplemented
79#6716C2×C418yescomplemented
80C4⋊Dic15—21no—
81C4⋊Dic15—22no—
82C4⋊Dic15D411yescharacteristic
83C4⋊Dic15D411yescharacteristic
84C4⋊Dic15C2312yes—
85#6712—22no—
86#6712—22no—
87C4×Dic15—22no—
88C4×Dic15—22no—
89C4×Dic15—22no—
90C4×Dic15C2312yes—
91#6710C2×C414yescomplemented
92C2×C3⋊#168C2312yes—
93#5827—51no—
94C2×#951—51no—
95#5516—51no—
96C3×#416D511yescharacteristic
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—
106C22×C5×C8C2×D311yescharacteristic
107C5×#117C2×D311yescharacteristic
108#4097—38no—
109Q8×Dic5—32no—
110C2×#689—32no—
111D4×Dic5—32no—
112D4×Dic5—62no—
113C2×#687—32no—
114#4072—31no—
115#4072—61no—
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—61no—
118C2×#681—31no—
119#4033—32no—
120#4033—32no—
121#4023—62no—
122C4×Dic10—61no—
123C4×Dic10—61no—
124C5×#103C2×D311yescharacteristic
125C5×#103C2×D311yescharacteristic
126C5×#102C2×D311yescharacteristic
127C5×#102C2×D311yescharacteristic
128#3948—32no—
129#3948—32no—
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—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×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5#4112yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—24no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—82no—
154C2×Dic15—81no—
155C2×Dic15C2×D412yes—
156C2×Dic15C2×D412yes—
157Dic30—24no—
158Dic30—22no—
159Dic30C22×C414yes—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C3⋊#168C22×C414yes—
163C2×C3×#41C2×D511yescharacteristic
164C22×Dic6—51no—
165C22×C3×C8C2×D511yescharacteristic
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—51no—
176C2×C4⋊Dic3—101no—
177C2×#208—51no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#103C2×D511yescharacteristic
184C3×#103C2×D511yescharacteristic
185C3×#102C2×D511yescharacteristic
186C3×#102C2×D511yescharacteristic
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×C5C22×D311yescharacteristic
200C22×Dic5—62no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C2×C5×C8—22no—
208C2×C5×C8C22×D311yescharacteristic
209C2×C5×C8C22×D311yescharacteristic
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C22⋊C4—21no—
213C42×C5—21no—
214C22⋊Dic5—32no—
215C22⋊Dic5—62no—
216#689—38no—
217#687—38no—
218C4⋊Dic5—31no—
219C4⋊Dic5—31no—
220C4⋊Dic5—32no—
221C4⋊Dic5—62no—
222C4⋊Dic5—61no—
223#683—62no—
224#683—62no—
225C4×Dic5—32no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
229#681—34no—
230C2×#168—32no—
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#416D1511yescharacteristic
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×C5—41no—
251C3×C4×C5—41no—
252C3×C4×C5C4×D412yes—
253C3×C4×C5C23×C411yescharacteristic
254C3×C4×C5C2×#4111yescharacteristic
255Dic15—24no—
256Dic15—22no—
257Dic15—22no—
258Dic15—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—102no—
267C22×Dic3—101no—
268C22×Dic3—101no—
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⋊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—51no—
285C4⋊Dic3—51no—
286C4⋊Dic3—52no—
287C4⋊Dic3—102no—
288C4⋊Dic3—101no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—52no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—102no—
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—21no—
307C2×C4×C5—21no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5#23712yes—
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—32no—
313C2×Dic5—32no—
314C2×Dic5—64no—
315C2×Dic5—62no—
316C2×Dic5—62no—
317C2×Dic5—242no—
318C2×Dic5—241no—
319Dic10—34no—
320Dic10—64no—
321Dic10—62no—
322C5×C8—21no—
323C5×C8—21no—
324#168—34no—
325C2×#41C2×D1511yescharacteristic
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8C2×D1511yescharacteristic
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#117C2×D1511yescharacteristic
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—152no—
348#103—152no—
349#103C2×D1511yescharacteristic
350#103C2×D1511yescharacteristic
351#102C2×D1511yescharacteristic
352#102C2×D1511yescharacteristic
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×C3D4×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—21no—
370C2×C3×C4—21no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71112yes—
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—52no—
376C2×Dic3—52no—
377C2×Dic3—102no—
378C2×Dic3—104no—
379C2×Dic3—102no—
380C2×Dic3—402no—
381C2×Dic3—401no—
382Dic6—54no—
383Dic6—102no—
384Dic6—104no—
385C3×C8—21no—
386C3×C8—21no—
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—41no—
397C4×C5—41no—
398C4×C5#67⋊C412yes—
399C4×C5C22×C4×D311yescharacteristic
400C4×C5C2×#23711yescharacteristic
401Dic5—64no—
402Dic5—62no—
403Dic5—62no—
404Dic5—122no—
405#41—22no—
406#41C4×D1514yes—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—301no—
410C2×Q8—302no—
411C2×Q8C22×D1511yescharacteristic
412C2×D4—21no—
413C2×D4C22×D1511yescharacteristic
414C22×C4—21no—
415C22×C4—302no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4C22×D1511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—22no—
423C2×C8—152no—
424C2×C8C22×D1511yescharacteristic
425C2×C8C22×D1511yescharacteristic
426C4⋊C4—151no—
427C4⋊C4—151no—
428C4⋊C4—152no—
429C4⋊C4—302no—
430C4⋊C4—302no—
431C4⋊C4—302no—
432C4⋊C4—301no—
433C4⋊C4C22×D1511yescharacteristic
434C4⋊C4C22×D1511yescharacteristic
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—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3#402712yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4#402712yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#71111yescharacteristic
457Dic3—104no—
458Dic3—102no—
459Dic3—102no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5—42no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#577011yescharacteristic
465C2×C5#577111yescharacteristic
466C23—21no—
467C23D4×D1511yescharacteristic
468Q8—21no—
469Q8—154no—
470Q8—304no—
471Q8—302no—
472Q8C2×C4×D1512yes—
473D4—24no—
474D4—21no—
475D4C2×C4×D1512yes—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—152no—
481C2×C4—152no—
482C2×C4—304no—
483C2×C4—302no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4C2×C4×D1512yes—
488C2×C4D4×D1511yescharacteristic
489C2×C4#681912yes—
490C2×C4C23×D1511yescharacteristic
491C8—21no—
492C8—21no—
493C8—154no—
494C2×C3—22no—
495C2×C3—42no—
496C2×C3C2×#402711yescharacteristic
497C2×C3#6610411yescharacteristic
498C2×C3#6610511yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—22no—
503C22—41no—
504C22—41no—
505C22#9177012yes—
506C22C2×D4×D1511yescharacteristic
507C4—22no—
508C4—41no—
509C4—41no—
510C4—304no—
511C4—302no—
512C4—302no—
513C4—602no—
514C4#9177012yes—
515C4C22×C4×D1511yescharacteristic
516C4C2×#681911yescharacteristic
517C3#1061055211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—42no—
520C2C2×#9177011yescharacteristic
521C2#1175652911yescharacteristic
522C2#1175653011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#416C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4×C5C24
hypercenter#416D15
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
3. #11756275C2semidirect
5. C2×#91100C2semidirect
6. #11751202C2semidirect
7. #11751096C2semidirect
8. #11750891C2semidirect
9. #11750890C2semidirect
10. #11750859C2semidirect
11. #11750858C2semidirect
17. #91840C4semidirect
67. C2×Dic30C2×C4semidirect
78. #6718C2×C4semidirect
79. #6716C2×C4semidirect
91. #6710C2×C4semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10610552semidirect

Maximal subgroups

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

subgroupindex
#117565862
C2×#918402
#117562752
C3×C5×#4162
C2×#911002
#117512022
#117510962
#117508912
#117508902
#117508592
#117508582
#106105523
#788215