Finite Group Databasebeta

← #14435420

Subgroups — #14435420

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2#11756238C211yesmaximal, characteristic
3#11751329C211yesmaximal, characteristic, complemented
4#11751328C211yesmaximal, characteristic
5#11751131C212yesmaximal, complemented
6#11751129C212yesmaximal, complemented
7#11751127C212yesmaximal, complemented
8#11751123C212yesmaximal, complemented
9#11751071C211yesmaximal, characteristic, complemented
10#11751069C211yesmaximal, characteristic
11#11751027C211yesmaximal, characteristic, complemented
12#10614176—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C3×C4×C5×Q8—21no—
15C3×C4×C5×Q8—21no—
16C3×C4×C5×Q8C2212yes—
17C3×C4×C5×Q8C2212yes—
18C2×C3×C5×C4⋊C4—21no—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C42×C5—21no—
21C2×C3×C42×C5C2211yescharacteristic
22C2×#6718C2212yes—
23C2×#6717C2212yes—
24#91819C2211yescharacteristic
25#91818—21no—
26C4×#1220—21no—
27#91813C2211yescharacteristic
28#91765—21no—
29#91764C2211yescharacteristic
30C4×D60C2211yescharacteristic
31#91761—21no—
32#91759C2211yescharacteristic
33C4×Dic30C2211yescharacteristic
34#91119C2212yes—
35#91119C2212yes—
36#91114C2211yescharacteristic
37#91114C2211yescharacteristic
38#91094C2212yes—
39#91093C2212yes—
40#91092C2212yes—
41#91091C2212yes—
42C4⋊(C3⋊#168)C2212yes—
43#91087C2212yes—
44#82445—51nomaximal, Hall
45C2×C4×C5×Q8D311yescharacteristic, complemented
46#65813—31no—
47#65517—31no—
48#65516—31no—
49#65319—32no—
50#65317—32no—
51#65315—32no—
52#65311—32no—
53#65259—31no—
54#65257—31no—
55#65215—31no—
56C2×C3×C5×Q8—24no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5D411yescharacteristic
62C22×C3×C4×C5D411yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—22no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C42×C5—22no—
73C3×C42×C5—22no—
74C3×C42×C5D411yescharacteristic
75C3×C42×C5D411yescharacteristic
76C3×C42×C5C2311yescharacteristic
77C3×C42×C5C2311yescharacteristic
78#6719—21no—
79#6718—24no—
80#6717—24no—
81#6714—21no—
82#6714—21no—
83#6714—21no—
84#6714—21no—
85C4⋊Dic15C2311yescharacteristic
86C4⋊Dic15C2311yescharacteristic
87#6712—21no—
88#6712—21no—
89#6712—21no—
90#6712—21no—
91C4×Dic15—21no—
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2312yes—
94C2×C3×C4×Q8D511yescharacteristic, complemented
95#5479—51no—
96#5228—51no—
97#5227—51no—
98#5030—52no—
99#5028—52no—
100#5026—52no—
101#5022—52no—
102#4970—51no—
103#4968—51no—
104#4926—51no—
105C22×C5×Q8C2×D311yescharacteristic
106C4×C5×Q8—21no—
107C4×C5×Q8—21no—
108C4×C5×Q8C2×D312yes—
109C4×C5×Q8C2×D312yes—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4C2×D311yescharacteristic
112C2×C42×C5—21no—
113C2×C42×C5C2×D311yescharacteristic
114C2×#689—32no—
115C2×#688—32no—
116#4076—31no—
117#4075—61no—
118C4×C22⋊D5—61no—
119#4070—31no—
120#4022—61no—
121#4021—31no—
122C4×D20—31no—
123#4018—61no—
124#4016—31no—
125C4×Dic10—31no—
126#3967—32no—
127#3967—32no—
128C22⋊#168—31no—
129C22⋊#168—31no—
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3939—32no—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C3×C5×Q8—24no—
140C3×C5×Q8—22no—
141C3×C5×Q8#4114yes—
142C2×C3×C4×C5—24no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—41no—
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2411yescharacteristic
155#1220—42no—
156C2×Dic15—21no—
157C2×Dic15—21no—
158C2×Dic15—21no—
159D60—22no—
160C4×D15—42no—
161Dic30—22no—
162C3⋊#168—22no—
163C3⋊#168—22no—
164C22×C3×Q8C2×D511yescharacteristic
165C3×C4×Q8—21no—
166C3×C4×Q8—21no—
167C3×C4×Q8C2×D512yes—
168C3×C4×Q8C2×D512yes—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C42—21no—
172C2×C3×C42C2×D511yescharacteristic
173C2×#216—52no—
174C2×#215—52no—
175#930—51no—
176#929—101no—
177C4×#67—101no—
178#924—51no—
179#876—101no—
180#875—51no—
181C4×D12—51no—
182#872—101no—
183#870—51no—
184C4×Dic6—51no—
185#835—52no—
186#835—52no—
187#830—51no—
188#830—51no—
189#810—52no—
190#809—52no—
191#808—52no—
192#807—52no—
193C4⋊(C3⋊C8)—52no—
194#803—52no—
195C2×C5×Q8—24no—
196C2×C5×Q8—21no—
197C2×C5×Q8C22×D312yes—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5#6711yescharacteristic
201C22×C4×C5#6711yescharacteristic
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—61no—
204C2×D20—31no—
205C2×C4×D5—61no—
206C2×Dic10—31no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C22×D312yes—
211C42×C5—22no—
212C42×C5—22no—
213C42×C5#6711yescharacteristic
214C42×C5#6711yescharacteristic
215C42×C5C22×D311yescharacteristic
216C42×C5C22×D311yescharacteristic
217C22⋊Dic5—61no—
218#689—64no—
219#688—64no—
220#685—61no—
221#685—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—31no—
225C4⋊Dic5—31no—
226#683—61no—
227#683—61no—
228#683—61no—
229#683—61no—
230C4×Dic5—61no—
231C2×#168—32no—
232C2×#168—32no—
233#529—151no—
234C2×C4×Q8D1511yescharacteristic, complemented
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—151no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C3×C4×C5—24no—
252C3×C4×C5—21no—
253C3×C4×C5—21no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5—21no—
257C3×C4×C5—42no—
258C3×C4×C5C2×#4112yes—
259Dic15—41no—
260Dic15—41no—
261Dic15—41no—
262C2×C3×Q8—24no—
263C2×C3×Q8—21no—
264C2×C3×Q8C22×D512yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C22⋊D511yescharacteristic
268C22×C3×C4C22⋊D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C2×D12—51no—
272C2×C4×D3—101no—
273C2×Dic6—51no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D512yes—
278C3×C42—22no—
279C3×C42—22no—
280C3×C42C22⋊D511yescharacteristic
281C3×C42C22⋊D511yescharacteristic
282C3×C42C22×D511yescharacteristic
283C3×C42C22×D511yescharacteristic
284#217—101no—
285#216—104no—
286#215—104no—
287(C2×D3)⋊C4—101no—
288(C2×D3)⋊C4—101no—
289(C2×D3)⋊C4—101no—
290(C2×D3)⋊C4—101no—
291C4⋊Dic3—51no—
292C4⋊Dic3—51no—
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8—52no—
300C23×C5C2×#6711yescharacteristic
301C22×D5—61no—
302C5×Q8—24no—
303C5×Q8—22no—
304C5×Q8#23514yes—
305C2×C4×C5—24no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—41no—
311C2×C4×C5—42no—
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—122no—
319C2×Dic5—61no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322D20—62no—
323C4×D5—122no—
324Dic10—62no—
325#168—62no—
326#168—62no—
327C22×Q8C2×D1511yescharacteristic
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—151no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—151no—
339C4×Q8C2×D1512yes—
340C4×Q8C2×D1512yes—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C2×D1511yescharacteristic
346C2×C42—21no—
347C2×C42C2×D1511yescharacteristic
348#107—152no—
349#106—152no—
350C4⋊C8—152no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—151no—
356C22⋊C8—151no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362D15—81no—
363C23×C3C2×C22⋊D511yescharacteristic
364C22×D3—101no—
365C3×Q8—24no—
366C3×Q8—22no—
367C3×Q8#70914yes—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4C2×C22⋊D511yescharacteristic
376C2×C3×C4C2×C22⋊D511yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C2×C22⋊D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—202no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385D12—102no—
386C4×D3—202no—
387Dic6—102no—
388C3⋊C8—102no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#94212yes—
393C22×C5C22×#6711yescharacteristic
394C2×D5—121no—
395C2×D5—121no—
396C2×D5—121no—
397C4×C5—24no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—21no—
402C4×C5—21no—
403C4×C5—42no—
404C4×C5C2×#23512yes—
405Dic5—121no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8—151no—
411C2×Q8C22×D1512yes—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—301no—
417C22×C4#122011yescharacteristic
418C22×C4#122011yescharacteristic
419C22×C4C22×D1511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—152no—
423C2×C8—152no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—151no—
428C4⋊C4—151no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4C22×D1512yes—
434C22⋊C4—301no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—22no—
440C42—22no—
441C42—301no—
442C42#122011yescharacteristic
443C42#122011yescharacteristic
444C42C22×D1511yescharacteristic
445C42C22×D1511yescharacteristic
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#408812yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—42no—
461C3×C4C2×#70912yes—
462Dic3—201no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#579111yescharacteristic
467C2×C5C2×#94211yescharacteristic
468C2×C5#582211yescharacteristic
469D5—241no—
470C23—301no—
471C23C2×#122011yescharacteristic
472Q8—24no—
473Q8—22no—
474Q8—302no—
475Q8#681714yes—
476D4—302no—
477D4—602no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—301no—
488C2×C4—602no—
489C2×C4C2×#122011yescharacteristic
490C2×C4C2×#122011yescharacteristic
491C2×C4C2×#122011yescharacteristic
492C2×C4C2×#122011yescharacteristic
493C2×C4C2×#122011yescharacteristic
494C2×C4C23×D1511yescharacteristic
495C8—302no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6612511yescharacteristic
499C2×C3C2×#408811yescharacteristic
500C2×C3#6615611yescharacteristic
501D3—401no—
502C5#8244511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9183112yes—
509C22C22×#122011yescharacteristic
510C4—24no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—601no—
518C4—601no—
519C4—601no—
520C4C2×#681712yes—
521C3#1061417611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175655011yescharacteristic
525C2C2×#9183111yescharacteristic
526C2#1175658111yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C4×C5×Q8C2
socleC22×C3×C5C22×D4
prime radical#91819C22
hypercenterC2×C4×Q8D15
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
3. #11751329C2semidirect
5. #11751131C2semidirect
6. #11751129C2semidirect
7. #11751127C2semidirect
8. #11751123C2semidirect
9. #11751071C2semidirect
11. #11751027C2semidirect
45. C2×C4×C5×Q8D3semidirect
94. C2×C3×C4×Q8D5semidirect
234. C2×C4×Q8D15semidirect
446. C3×C5#3117semidirect
502. C5#82445semidirect
521. C3#10614176semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
#117562382
#117513292
#117513282
#117511312
#117511292
#117511272
#117511232
#117510712
#117510692
#117510272
#106141763
#824455