Finite Group Databasebeta

← #14417284

Subgroups — #14417284

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#11754513C211yesmaximal, characteristic
3#11754211C211yesmaximal, characteristic, complemented
4#11751222C211yesmaximal, characteristic, complemented
5C3×#65411C211yesmaximal, characteristic, complemented
6C2×#90973C211yesmaximal, characteristic, complemented
7#11748388C211yesmaximal, characteristic
8#11747856C212yesmaximal, complemented
9Dic5×Dic12C212yesmaximal, complemented
10#11747769C212yesmaximal, complemented
11Dic5×#204C212yesmaximal, complemented
12#10615696—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C5×#909C418yescomplemented
19C2×C5×Dic12C2212yes—
20C2×C5×#204C2212yes—
21C3×#4072C2211yescharacteristic
22C22×C3×#168C2211yescharacteristic
23#67⋊Dic5—22no—
24#91529—22no—
25D3×C4⋊Dic5—21no—
26Dic5×D12C2212yes—
27#91344—21no—
28#91344—21no—
29#91338—21no—
30Dic5×Dic6C2212yes—
31Dic5×Dic6C2212yes—
32Dic5×Dic6C2212yes—
33#91102C2212yes—
34#91101C2212yes—
35C3×#3947C2212yes—
36C3×C8×Dic5C2212yes—
37#90973C2211yescharacteristic
38#90973C2212yes—
39#90973C2211yescharacteristic
40#90973C2212yes—
41#90967C2211yescharacteristic
42#90967C2211yescharacteristic
43#78571—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#65411D311yescharacteristic, complemented
54#65410—31no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×C5×#67—21no—
58C22×C5×Dic3—21no—
59C5×#235—22no—
60C5×#235C2×C414yes—
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6C2×C414yescomplemented
66C2×C5×Dic6C2312yes—
67C2×C5×Dic6C2311yescharacteristic
68C2×D3×Dic5—22no—
69C3×C5×M16C2×C414yescomplemented
70C2×C3×C5×C8C2312yes—
71#6719—21no—
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C4×Dic15—21no—
77C5×Dic12C2×C418yescomplemented
78C5×#204C2×C418yescomplemented
79C3×C22⋊Dic5D412yes—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5D411yescharacteristic
82C3×C4×Dic5C2312yes—
83C2×C3×#168—22no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
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#5523—51no—
95#5516—51no—
96C3×#405—51no—
97#5121—51no—
98#5113—51no—
99C2×#816—51no—
100#4716—52no—
101#4710—52no—
102C4×Dic12—52no—
103C4×#204—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—62no—
119#4072—61no—
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—31no—
122C2×C4⋊Dic5—61no—
123C22×#168C2×D311yescharacteristic
124#3967—32no—
125#3967—32no—
126#3967—31no—
127#3967—31no—
128#3964—31no—
129#3964—31no—
130#3950—32no—
131#3949—32no—
132#3947C2×D312yes—
133C8×Dic5C2×D312yes—
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×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—81no—
145C5×#67—24no—
146C2×C5×Dic3—24no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—21no—
149C5×D12—21no—
150C5×D12C22×C412yes—
151C4×C5×D3—24no—
152C5×Dic6—24no—
153C5×Dic6—22no—
154C5×Dic6—21no—
155C5×Dic6C22×C414yes—
156C5×Dic6C22×C412yes—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159D3×Dic5—82no—
160C3×C5×C8C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C2×#235C2×D511yescharacteristic
164C22×Dic6C2×D511yescharacteristic
165C2×C3×M16C2×D511yescharacteristic
166C22×C3×C8—51no—
167C3×#117—51no—
168#926—51no—
169C2×C4⋊Dic3—51no—
170#909Dic518yescomplemented
171C2×Dic12C2×D512yes—
172C2×#204C2×D512yes—
173#892—101no—
174D3×C4⋊C4—101no—
175#887—101no—
176#887—101no—
177#67⋊C4—102no—
178#877—102no—
179C4×D12—52no—
180C4×Dic6—52no—
181C4×Dic6—52no—
182C4×Dic6—52no—
183C3×#97—52no—
184C3×C4×C8—52no—
185#821—51no—
186#821—51no—
187#818—52no—
188#817—52no—
189#816—52no—
190#816—51no—
191#816—52no—
192#816—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—61no—
206C22×Dic5—62no—
207C5×Q16—38no—
208C5×SD16—38no—
209C5×M16C4×D314yescomplemented
210C2×C5×C8C22×D312yes—
211C22⋊Dic5—61no—
212C22⋊Dic5—62no—
213C22⋊Dic5D1212yes—
214C4⋊Dic5—31no—
215C4⋊Dic5—32no—
216C4⋊Dic5—31no—
217C4⋊Dic5—61no—
218C4⋊Dic5—62no—
219C4⋊Dic5—62no—
220C4⋊Dic5—62no—
221C4⋊Dic5D1211yescharacteristic
222C4⋊Dic5D1211yescharacteristic
223C4×Dic5—61no—
224C4×Dic5—62no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5C22×D312yes—
228C2×#168—22no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231C2×#137—31no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—151no—
241#405—51no—
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—42no—
253Dic15—41no—
254Dic15—41no—
255C3×Dic5—22no—
256C3×Dic5—22no—
257C5×Dic3—24no—
258C5×Dic3—22no—
259C22×C3×C4C22×D511yescharacteristic
260C2×#67—21no—
261C22×Dic3—21no—
262C22×Dic3—101no—
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×C8—51no—
275C2×C3×C8—51no—
276C2×C3×C8—102no—
277C2×C3×C8C22×D512yes—
278C3×C4⋊C4—51no—
279C3×C4⋊C4—51no—
280C3×C22⋊C4—52no—
281C3×C42—52no—
282#217—101no—
283(C2×D3)⋊C4—102no—
284C4⋊Dic3—52no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287C4⋊Dic3—101no—
288Dic3⋊C4—102no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—101no—
295Dic12C2×Dic518yescomplemented
296#204C2×Dic518yescomplemented
297C23×C5—61no—
298C23×C5C2×D1211yescharacteristic
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×C5C2×D1211yescharacteristic
313C2×C4×C5#23512yes—
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—62no—
318C2×Dic5—242no—
319C2×Dic5—241no—
320C2×Dic5C2×D1212yes—
321C2×Dic5C2×D1212yes—
322C5×C8C2×C4×D314yes—
323#168—21no—
324#168—21no—
325C2×#41—31no—
326C22×Q8—31no—
327#137—38no—
328C2×Q16—32no—
329C2×SD16—32no—
330C2×M16D3×D511yescharacteristic
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—51no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—152no—
348#103—152no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—52no—
354C4×C8—52no—
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—52no—
363C2×C3×C4—52no—
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4#71112yes—
366C2×C3×C4C22×Dic512yes—
367C2×C3×C4C23×D511yescharacteristic
368#67—24no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—24no—
372C2×Dic3—101no—
373C2×Dic3—101no—
374C2×Dic3—102no—
375C2×Dic3—401no—
376D12—21no—
377D12C22×Dic512yes—
378C4×D3—24no—
379C4×D3—402no—
380Dic6—22no—
381Dic6—21no—
382Dic6—24no—
383Dic6C22×Dic514yes—
384Dic6C22×Dic512yes—
385C3×C8—101no—
386C3×C8—101no—
387C3×C8C22×Dic514yes—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—62no—
391C22×C5—121no—
392C22×C5—121no—
393C22×C5C4×D1212yes—
394C22×C5C22×D1211yescharacteristic
395C4×C5—62no—
396C4×C5—64no—
397C4×C5C4×D1212yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23511yescharacteristic
400Dic5—22no—
401Dic5—22no—
402Dic5—121no—
403Dic5—122no—
404Dic5—121no—
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—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—38no—
420SD16—38no—
421M16D3×Dic514yescomplemented
422C2×C8—51no—
423C2×C8—51no—
424C2×C8—102no—
425C2×C8C2×D3×D512yes—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—152no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—301no—
435C22⋊C4—52no—
436C22⋊C4—302no—
437C22⋊C4—301no—
438C42—52no—
439C42—302no—
440C42—302no—
441C42—302no—
442C42—301no—
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—102no—
452C3×C4—102no—
453C3×C4D4×Dic512yes—
454C3×C4C2×#71111yescharacteristic
455C3×C4C23×Dic511yescharacteristic
456Dic3—24no—
457Dic3—22no—
458Dic3—202no—
459Dic3—201no—
460Dic3—201no—
461C2×C5—22no—
462C2×C5—122no—
463C2×C5C2×C4×D1211yescharacteristic
464C2×C5#575111yescharacteristic
465C2×C5#575311yescharacteristic
466C23—61no—
467C23D5×D1211yescharacteristic
468Q8—34no—
469Q8—32no—
470Q8—64no—
471Q8—62no—
472Q8—61no—
473D4—32no—
474D4—64no—
475D4—61no—
476C2×C4—52no—
477C2×C4—52no—
478C2×C4—64no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—64no—
482C2×C4—301no—
483C2×C4—301no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4#677212yes—
488C2×C4D5×D1211yescharacteristic
489C2×C4C2×D3×Dic512yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8C2×D3×Dic514yes—
494C2×C3—22no—
495C2×C3#6611211yescharacteristic
496C2×C3#6611311yescharacteristic
497C2×C3C2×D4×Dic511yescharacteristic
498D3—42no—
499C5#7857111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22Dic5×D1212yes—
506C22C2×D5×D1211yescharacteristic
507C4—62no—
508C4—64no—
509C4—102no—
510C4—102no—
511C4—602no—
512C4—601no—
513C4—601no—
514C4Dic5×D1212yes—
515C4C2×#677211yescharacteristic
516C4C22×D3×Dic511yescharacteristic
517C3#1061569611yescharacteristic, complemented, Sylow
518C2—22no—
519C2—122no—
520C2#1175402511yescharacteristic
521C2#1175404011yescharacteristic
522C2C2×Dic5×D1211yescharacteristic
subgroupG/H
centerC22C2×D5×D12
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. #11751222C2semidirect
5. C3×#65411C2semidirect
6. C2×#90973C2semidirect
8. #11747856C2semidirect
9. Dic5×Dic12C2semidirect
10. #11747769C2semidirect
11. Dic5×#204C2semidirect
18. C5×#909C4semidirect
53. #65411D3semidirect
65. C2×C5×Dic6C2×C4semidirect
69. C3×C5×M16C2×C4semidirect
77. C5×Dic12C2×C4semidirect
78. C5×#204C2×C4semidirect
170. #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#78571semidirect
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
#117545132
#117542112
#117512222
C3×#654112
C2×#909732
#117483882
#117478562
Dic5×Dic122
#117477692
Dic5×#2042
#106156963
#785715