Finite Group Databasebeta

← #14417285

Subgroups — #14417285

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×C5×#909C211yesmaximal, characteristic
2#11754492C211yesmaximal, characteristic
3#11754211C211yesmaximal, characteristic, complemented
4#11751223C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7#11748382C211yesmaximal, characteristic
8#11747888C212yesmaximal, complemented
9#11747886C212yesmaximal, complemented
10#11747816C212yesmaximal, complemented
11#11747807C212yesmaximal, complemented
12#10615696—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C5×#909C418yescomplemented
19C2×C5×Dic12C2212yes—
20C2×C5×#204C2212yes—
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23Dic5×#67—22no—
24#91529—22no—
25#91435C2212yes—
26D3×C4⋊Dic5—21no—
27#91344C2212yes—
28#91344C2212yes—
29#91344C2212yes—
30#91338—21no—
31Dic5×Dic6—21no—
32Dic5×Dic6—21no—
33#91099C2212yes—
34C8×Dic15C2212yes—
35C3×#3950C2212yes—
36C3×#3949C2212yes—
37#90972C2211yescharacteristic
38#90972C2211yescharacteristic
39#90972C2212yes—
40#90972C2212yes—
41#90966C2211yescharacteristic
42#90966C2211yescharacteristic
43#79202—51nomaximal, Hall
44C2×C5×#137—31no—
45#66161—31no—
46#66146—31no—
47#65522—31no—
48C2×#3967—31no—
49#65473—32no—
50Q16×Dic5—32no—
51#65453—32no—
52SD16×Dic5—32no—
53#65411—31no—
54#65410D311yescharacteristic, complemented
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C22×C5×Dic3—21no—
58C5×#235—22no—
59C5×#235C2×C414yes—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C5×Dic6—21no—
63C2×C5×Dic6—22no—
64C2×C5×Dic6C2×C414yescomplemented
65C2×C5×Dic6C2312yes—
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×D3×Dic5—22no—
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71#6719D412yes—
72C4⋊Dic15D411yescharacteristic
73C4⋊Dic15D411yescharacteristic
74C4×Dic15C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×Dic12C2×C418yescomplemented
79C5×#204C2×C418yescomplemented
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4×Dic5—21no—
86Dic3⋊Dic5—22no—
87Dic3⋊Dic5—22no—
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93C2×#909D511yescharacteristic
94#5516—51no—
95#5504—51no—
96C3×#428—51no—
97#5122—51no—
98#5002—51no—
99C2×#810—51no—
100#4889—52no—
101#4873—52no—
102#4853—52no—
103#4852—52no—
104C2×C5×#41—31no—
105C22×C5×Q8—31no—
106C5×#137—38no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C2×C5×M16C2×D311yescharacteristic
110Q8×Dic5—32no—
111Q8×Dic5—32no—
112Q8×Dic5—32no—
113Q8×Dic5—61no—
114Q8×Dic5—61no—
115D4×Dic5—32no—
116D4×Dic5—62no—
117#4072—31no—
118#4072—61no—
119#4072—62no—
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168—31no—
124#3967—32no—
125#3967—32no—
126#3967—31no—
127#3967—31no—
128#3964—31no—
129#3964—31no—
130#3950C2×D312yes—
131#3949C2×D312yes—
132#3947—32no—
133C8×Dic5—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C5×D3—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143C5×#67—24no—
144C2×C5×Dic3—24no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—21no—
147C5×D12—21no—
148C5×D12C22×C412yes—
149C4×C5×D3—24no—
150C5×Dic6—24no—
151C5×Dic6—22no—
152C5×Dic6—21no—
153C5×Dic6C22×C414yes—
154C5×Dic6C22×C412yes—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—81no—
159D3×Dic5—82no—
160C3×C5×C8C22×C414yes—
161C3⋊#168—21no—
162C3⋊#168—21no—
163C2×#235C2×D511yescharacteristic
164C22×Dic6C2×D511yescharacteristic
165C2×C3×M16C2×D511yescharacteristic
166C3×#117—51no—
167C2×C3×C4⋊C4—51no—
168C4×#67—102no—
169#926—51no—
170C22×C3⋊C8—51no—
171#909Dic518yescomplemented
172C2×Dic12C2×D512yes—
173C2×#204C2×D512yes—
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#815—52no—
186C8×Dic3—52no—
187#810—51no—
188#810—52no—
189#810—52no—
190#810—51no—
191#809—51no—
192#809—51no—
193C5×#41—34no—
194C5×#41—62no—
195C2×C5×Q8—34no—
196C2×C5×Q8—32no—
197C2×C5×Q8—31no—
198C2×C5×Q8—61no—
199C2×C5×Q8—62no—
200C2×C5×D4—31no—
201C2×C5×D4—61no—
202C22×C4×C5—61no—
203C22×C4×C5—61no—
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—62no—
207C5×Q16—38no—
208C5×SD16—38no—
209C5×M16C4×D314yescomplemented
210C2×C5×C8C22×D312yes—
211C22⋊Dic5—21no—
212C22⋊Dic5—32no—
213C22⋊Dic5—62no—
214C4⋊Dic5—21no—
215C4⋊Dic5—31no—
216C4⋊Dic5—31no—
217C4⋊Dic5—62no—
218C4⋊Dic5—62no—
219C4⋊Dic5—62no—
220C4⋊Dic5C22×D311yescharacteristic
221C4⋊Dic5C22×D312yes—
222C4⋊Dic5C22×D311yescharacteristic
223C4×Dic5—21no—
224C4×Dic5—32no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C2×#168—31no—
229C2×#168—31no—
230C2×#168—62no—
231C2×#137—31no—
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—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—22no—
253Dic15—22no—
254C3×Dic5—42no—
255C3×Dic5—41no—
256C3×Dic5—41no—
257C5×Dic3—24no—
258C5×Dic3—22no—
259C22×C3×C4—101no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—21no—
262C22×Dic3—21no—
263#235—22no—
264#235C2×Dic514yes—
265C2×D12C22×D511yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—102no—
268C2×Dic6—21no—
269C2×Dic6—22no—
270C2×Dic6C2×Dic514yescomplemented
271C2×Dic6C22×D512yes—
272C2×Dic6C22×D511yescharacteristic
273C3×M16C2×Dic514yescomplemented
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#217—52no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—51no—
284C4⋊Dic3—51no—
285Dic3⋊C4—102no—
286Dic3⋊C4—102no—
287Dic3⋊C4—102no—
288C4×Dic3—52no—
289C4×Dic3—102no—
290C4×Dic3—102no—
291C4×Dic3—102no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—51no—
294C2×C3⋊C8—102no—
295Dic12C2×Dic518yescomplemented
296#204C2×Dic518yescomplemented
297C23×C5—61no—
298C23×C5D3×D411yescharacteristic
299C5×Q8—34no—
300C5×Q8—32no—
301C5×Q8—64no—
302C5×Q8—62no—
303C5×Q8—61no—
304C5×D4—32no—
305C5×D4—64no—
306C5×D4—61no—
307C2×C4×C5—64no—
308C2×C4×C5—61no—
309C2×C4×C5—62no—
310C2×C4×C5—64no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5#23912yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—32no—
319C2×Dic5—32no—
320C2×Dic5—81no—
321C2×Dic5—242no—
322C5×C8C2×C4×D314yes—
323#168—61no—
324#168—61no—
325C2×#41—31no—
326C22×Q8—31no—
327#137—38no—
328C2×Q16—32no—
329C2×SD16—32no—
330C2×M16D3×D511yescharacteristic
331C22×C8—151no—
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—151no—
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—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C5×D3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—21no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—102no—
365C2×C3×C4—401no—
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4#71112yes—
368C2×C3×C4C22×Dic512yes—
369C2×C3×C4C23×D511yescharacteristic
370#67—24no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373C2×Dic3—24no—
374C2×Dic3—52no—
375C2×Dic3—52no—
376D12—21no—
377D12C22×Dic512yes—
378C4×D3—24no—
379C4×D3—402no—
380Dic6—22no—
381Dic6—21no—
382Dic6—24no—
383Dic6C22×Dic514yes—
384Dic6C22×Dic512yes—
385C3×C8C22×Dic514yes—
386C3⋊C8—101no—
387C3⋊C8—101no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5#89312yes—
394C22×C5C2×D3×D411yescharacteristic
395C4×C5—62no—
396C4×C5—64no—
397C4×C5#89312yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23911yescharacteristic
400Dic5—41no—
401Dic5—42no—
402Dic5—41no—
403Dic5—62no—
404Dic5—62no—
405#41—34no—
406#41—62no—
407C2×Q8—34no—
408C2×Q8—32no—
409C2×Q8—31no—
410C2×Q8—62no—
411C2×Q8—61no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—38no—
420SD16—38no—
421M16D3×Dic514yescomplemented
422C2×C8—151no—
423C2×C8—151no—
424C2×C8—302no—
425C2×C8C2×D3×D512yes—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—52no—
429C4⋊C4—101no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—101no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—101no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3D4×Dic512yes—
447C22×C3C2×D4×D511yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—202no—
452C3×C4—201no—
453C3×C4—201no—
454C3×C4D4×Dic512yes—
455C3×C4C2×#71111yescharacteristic
456C3×C4C23×Dic511yescharacteristic
457Dic3—24no—
458Dic3—22no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×#89311yescharacteristic
464C2×C5#577511yescharacteristic
465C2×C5#577911yescharacteristic
466C23—61no—
467C23#677711yescharacteristic
468Q8—34no—
469Q8—32no—
470Q8—64no—
471Q8—62no—
472Q8—61no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—64no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—64no—
480C2×C4—101no—
481C2×C4—101no—
482C2×C4—102no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4#676812yes—
488C2×C4#677711yescharacteristic
489C2×C4C2×D3×Dic512yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—301no—
492C8—301no—
493C8C2×D3×Dic514yes—
494C2×C3—22no—
495C2×C3#6611211yescharacteristic
496C2×C3#6611311yescharacteristic
497C2×C3C2×D4×Dic511yescharacteristic
498D3—42no—
499C5#7920211yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22#9143512yes—
506C22C2×#677711yescharacteristic
507C4—62no—
508C4—64no—
509C4—202no—
510C4—201no—
511C4—201no—
512C4—302no—
513C4—302no—
514C4#9143512yes—
515C4C2×#676811yescharacteristic
516C4C22×D3×Dic511yescharacteristic
517C3#1061569611yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2#1175403711yescharacteristic
521C2#1175404311yescharacteristic
522C2C2×#9143511yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
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. #11754211C2semidirect
4. #11751223C2semidirect
5. C3×#65410C2semidirect
6. C2×#90972C2semidirect
8. #11747888C2semidirect
9. #11747886C2semidirect
10. #11747816C2semidirect
11. #11747807C2semidirect
18. C5×#909C4semidirect
54. #65410D3semidirect
64. C2×C5×Dic6C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
78. C5×Dic12C2×C4semidirect
79. C5×#204C2×C4semidirect
171. #909Dic5semidirect
209. C5×M16C4×D3semidirect
270. C2×Dic6C2×Dic5semidirect
273. C3×M16C2×Dic5semidirect
295. Dic12C2×Dic5semidirect
296. #204C2×Dic5semidirect
421. M16D3×Dic5semidirect
443. C3×C5#2947semidirect
499. C5#79202semidirect
517. C3#10615696semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9092
#117544922
#117542112
#117512232
C3×#654102
C2×#909722
#117483822
#117478882
#117478862
#117478162
#117478072
#106156963
#792025