Finite Group Databasebeta

← #14417287

Subgroups — #14417287

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×#91798C211yesmaximal, characteristic
2#11754496C211yesmaximal, characteristic
3#11754213C211yesmaximal, characteristic, complemented
4C5×#5122C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6#11748411C211yesmaximal, characteristic
7C2×#90974C211yesmaximal, characteristic, complemented
8#11747876C212yesmaximal, complemented
9#11747873C212yesmaximal, complemented
10#11747800C212yesmaximal, complemented
11#11747789C212yesmaximal, complemented
12#10610302—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91798C418yescomplemented
17C2×Dic60C2212yes—
18C2×#6706C2212yes—
19C5×#926C2211yescharacteristic
20C22×C5×C3⋊C8C2211yescharacteristic
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23#91552—22no—
24#91532—22no—
25#91437—21no—
26#91428C2212yes—
27#91347—21no—
28#91340C2212yes—
29#91340C2212yes—
30#91340C2212yes—
31#91333—21no—
32#91333—21no—
33C5×#815C2212yes—
34C5×C8×Dic3C2212yes—
35C3×#3950C2212yes—
36C3×#3949C2212yes—
37#90974C2211yescharacteristic
38#90974C2212yes—
39#90974C2211yescharacteristic
40#90974C2212yes—
41#90968C2211yescharacteristic
42#90968C2211yescharacteristic
43#79202—51nomaximal, Hall
44C2×#4055—31no—
45#65857—31no—
46#65850—31no—
47C5×#405—31no—
48#65410D311yescharacteristic, complemented
49#65402—31no—
50C2×#3948—31no—
51#65005—32no—
52#64999—32no—
53C4×Dic20—32no—
54C4×#677—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57C22×Dic15—21no—
58#6817—22no—
59#6817C2×C414yes—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30—21no—
63C2×Dic30—22no—
64C2×Dic30C2×C414yescomplemented
65C2×Dic30C2312yes—
66C2×Dic30C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×#1200—22no—
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71Dic60C2×C418yescomplemented
72#6706C2×C418yescomplemented
73C5×#217D412yes—
74C5×C4⋊Dic3D411yescharacteristic
75C5×C4⋊Dic3D411yescharacteristic
76C4×C5×Dic3C2312yes—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4×Dic5—21no—
86#6669—22no—
87#6669—22no—
88#6669—22no—
89#6667—22no—
90Dic3×Dic5—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C2×#909—51no—
94#5516—51no—
95#5504—51no—
96C3×#428—51no—
97#5122D511yescharacteristic, complemented
98#5002—51no—
99C2×#810—51no—
100#4889—52no—
101#4873—52no—
102#4853—52no—
103#4852—52no—
104C2×#709—31no—
105C22×Dic10—31no—
106C2×C5×M16C2×D311yescharacteristic
107C22×C5×C8—31no—
108C5×#117—31no—
109#4072C2×D311yescharacteristic
110C2×C4⋊Dic5C2×D311yescharacteristic
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#3953—31no—
127#3953—31no—
128#3950C2×D312yes—
129#3949C2×D312yes—
130#3948—32no—
131#3948—32no—
132#3948—31no—
133#3948—31no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141#1220—24no—
142C2×Dic15—24no—
143C2×Dic15—22no—
144C2×Dic15—21no—
145D60—21no—
146D60C22×C412yes—
147C4×D15—24no—
148Dic30—24no—
149Dic30—22no—
150Dic30—21no—
151Dic30C22×C414yes—
152Dic30C22×C412yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—81no—
159#1200—82no—
160C3×C5×C8C22×C414yes—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—21no—
163C2×#235—51no—
164C22×Dic6—51no—
165C2×C3×M16C2×D511yescharacteristic
166C3×#117—51no—
167C2×C3×C4⋊C4—51no—
168C4×#67—102no—
169#926C2×D511yescharacteristic
170C22×C3⋊C8C2×D511yescharacteristic
171#909—58no—
172C2×Dic12—52no—
173C2×#204—52no—
174#893—52no—
175#892—101no—
176D3×C4⋊C4—101no—
177#887—52no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#107—52no—
184C3×#106—52no—
185#815C2×D512yes—
186C8×Dic3C2×D512yes—
187#810—51no—
188#810—52no—
189#810—52no—
190#810—51no—
191#809—51no—
192#809—51no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—61no—
195C22×Dic5—21no—
196C22×Dic5—61no—
197#709—34no—
198#709—62no—
199C2×D20—31no—
200C2×C4×D5—61no—
201C2×C4×D5—62no—
202C2×Dic10—34no—
203C2×Dic10—32no—
204C2×Dic10—31no—
205C2×Dic10—61no—
206C2×Dic10—62no—
207C5×M16C4×D314yescomplemented
208C2×C5×C8—31no—
209C2×C5×C8—31no—
210C2×C5×C8—62no—
211C2×C5×C8C22×D312yes—
212C5×C4⋊C4—31no—
213C5×C4⋊C4—31no—
214C5×C22⋊C4—32no—
215C42×C5—32no—
216C22⋊Dic5—21no—
217#685—62no—
218C4⋊Dic5—21no—
219C4⋊Dic5C22×D312yes—
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—51no—
239#416—151no—
240C2×#103—151no—
241#405—31no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—24no—
253Dic15—22no—
254C3×Dic5—42no—
255C3×Dic5—41no—
256C3×Dic5—41no—
257C5×Dic3—22no—
258C5×Dic3—22no—
259C22×C3×C4—101no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—101no—
262C22×Dic3—101no—
263#235—54no—
264#235—102no—
265C2×D12—51no—
266C2×C4×D3—101no—
267C2×C4×D3—102no—
268C2×Dic6—54no—
269C2×Dic6—52no—
270C2×Dic6—51no—
271C2×Dic6—101no—
272C2×Dic6—102no—
273C3×M16C4×D514yescomplemented
274C2×C3×C8C22×D512yes—
275C3×C4⋊C4—51no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—52no—
278C3×C4⋊C4—101no—
279C3×C22⋊C4—101no—
280C3×C42—101no—
281#217D2012yes—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3D2011yescharacteristic
284C4⋊Dic3D2011yescharacteristic
285Dic3⋊C4—102no—
286Dic3⋊C4—102no—
287Dic3⋊C4—102no—
288C4×Dic3—102no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3C22×D512yes—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295Dic12—58no—
296#204—58no—
297C23×C5D3×D411yescharacteristic
298C22×D5—61no—
299C2×C4×C5—32no—
300C2×C4×C5—32no—
301C2×C4×C5C2×C4×D312yes—
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23912yes—
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—64no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—22no—
309C2×Dic5—64no—
310C2×Dic5—62no—
311C2×Dic5—61no—
312C2×Dic5—81no—
313D20—32no—
314D20—61no—
315C4×D5—64no—
316C4×D5—242no—
317Dic10—34no—
318Dic10—32no—
319Dic10—64no—
320Dic10—62no—
321Dic10—61no—
322C5×C8—61no—
323C5×C8—61no—
324C5×C8C2×C4×D314yes—
325C2×#41—151no—
326C22×Q8—151no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16D3×D511yescharacteristic
331C22×C8—31no—
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—51no—
344C2×C4⋊C4—301no—
345#107—52no—
346#106—52no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—32no—
354C4×C8—32no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3C2×D2011yescharacteristic
361C22×D3—101no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—102no—
365C2×C3×C4—401no—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4C2×D2011yescharacteristic
368C2×C3×C4#70912yes—
369C2×C3×C4C23×D511yescharacteristic
370#67—104no—
371C2×Dic3—102no—
372C2×Dic3—101no—
373C2×Dic3—104no—
374C2×Dic3C2×D2012yes—
375C2×Dic3C2×D2012yes—
376D12—52no—
377D12—101no—
378C4×D3—104no—
379C4×D3—402no—
380Dic6—54no—
381Dic6—52no—
382Dic6—102no—
383Dic6—101no—
384Dic6—104no—
385C3×C8C2×C4×D514yes—
386C3⋊C8—21no—
387C3⋊C8—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#89312yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—62no—
396C4×C5—62no—
397C4×C5#89312yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23911yescharacteristic
400Dic5—42no—
401Dic5—41no—
402Dic5—41no—
403Dic5—64no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—154no—
408C2×Q8—152no—
409C2×Q8—151no—
410C2×Q8—302no—
411C2×Q8—301no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—101no—
415C22×C4—302no—
416C22×C4—301no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16#120014yescomplemented
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—62no—
425C2×C8C2×D3×D512yes—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—51no—
429C4⋊C4—51no—
430C4⋊C4—52no—
431C4⋊C4—101no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
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×C3C4×D2012yes—
447C22×C3C22×D2011yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—202no—
452C3×C4—201no—
453C3×C4—201no—
454C3×C4C4×D2012yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#70911yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—104no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#89311yescharacteristic
463C2×C5#577511yescharacteristic
464C2×C5#577911yescharacteristic
465D5—122no—
466C23—301no—
467C23D3×D2011yescharacteristic
468Q8—154no—
469Q8—152no—
470Q8—304no—
471Q8—302no—
472Q8—301no—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—101no—
479C2×C4—101no—
480C2×C4—102no—
481C2×C4—304no—
482C2×C4—301no—
483C2×C4—302no—
484C2×C4—304no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4#676912yes—
488C2×C4D3×D2011yescharacteristic
489C2×C4C2×#120012yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—61no—
492C8—61no—
493C8C2×#120014yes—
494C2×C3—22no—
495C2×C3C2×C4×D2011yescharacteristic
496C2×C3#6608511yescharacteristic
497C2×C3#6608711yescharacteristic
498D3—202no—
499C5#7920211yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9142812yes—
506C22C2×D3×D2011yescharacteristic
507C4—62no—
508C4—62no—
509C4—202no—
510C4—201no—
511C4—201no—
512C4—302no—
513C4—304no—
514C4#9142812yes—
515C4C2×#676911yescharacteristic
516C4C22×#120011yescharacteristic
517C3#1061030211yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175403011yescharacteristic
521C2#1175404211yescharacteristic
522C2C2×#9142811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #11754213C2semidirect
4. C5×#5122C2semidirect
5. C3×#65410C2semidirect
7. C2×#90974C2semidirect
8. #11747876C2semidirect
9. #11747873C2semidirect
10. #11747800C2semidirect
11. #11747789C2semidirect
16. #91798C4semidirect
48. #65410D3semidirect
64. C2×Dic30C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
71. Dic60C2×C4semidirect
72. #6706C2×C4semidirect
97. #5122D5semidirect
207. C5×M16C4×D3semidirect
273. C3×M16C4×D5semidirect
421. M16#1200semidirect
443. C3×C5#2947semidirect
499. C5#79202semidirect
517. C3#10610302semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
#117544962
#117542132
C5×#51222
C3×#654102
#117484112
C2×#909742
#117478762
#117478732
#117478002
#117477892
#106103023
#792025