Finite Group Databasebeta

← #14435543

Subgroups — #14435543

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×#4033C211yesmaximal, characteristic, complemented
2#11754415C211yesmaximal, characteristic
3#11751069C211yesmaximal, characteristic
4C5×#4970C211yesmaximal, characteristic, complemented
5#11748555C211yesmaximal, characteristic, complemented
6#11748532C211yesmaximal, characteristic
7#11748333C211yesmaximal, characteristic, complemented
8#11747391C212yesmaximal, complemented
9#11747372C212yesmaximal, complemented
10#11747262C212yesmaximal, complemented
11#11747224C212yesmaximal, complemented
12#10613186—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15#91819C2211yescharacteristic
16C5×#924C2211yescharacteristic
17C2×C3×#683—21no—
18C2×C3×C4×Dic5—21no—
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×#4033—21no—
21C3×#4033—21no—
22C3×#4033C2212yes—
23C3×#4033C2212yes—
24#91552—21no—
25#91546—21no—
26#91418C2211yescharacteristic
27#91402—21no—
28#91388C2211yescharacteristic
29#91387—21no—
30#91375C2211yescharacteristic
31Dic5×Dic6C2211yescharacteristic
32C2×#6661C2212yes—
33C2×#6658C2212yes—
34#91114C2211yescharacteristic
35#91093C2212yes—
36#91092C2212yes—
37C5×#830C2211yescharacteristic
38C5×#810C2212yes—
39C5×#807C2212yes—
40#90982C2212yes—
41#90971C2212yes—
42#90970C2212yes—
43#90952C2212yes—
44#82445—51nomaximal, Hall
45#65958—31no—
46C2×#4033D311yescharacteristic, complemented
47C5×#484—31no—
48#65339—31no—
49#65257—31no—
50#65178—32no—
51#65166—32no—
52#65087—32no—
53#65078—32no—
54#65027—31no—
55#65008—31no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C2×D60C2311yescharacteristic
60C2×C5×Dic6C2311yescharacteristic
61C22×C3×Dic5—21no—
62C22×C3×Dic5D411yescharacteristic
63C22×C3×Dic5D411yescharacteristic
64C2×C3×Dic10—21no—
65C2×C3×Dic10—24no—
66C2×C3×Dic10C2312yes—
67C2×#1200—21no—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2312yes—
70#6714—21no—
71C4⋊Dic15C2311yescharacteristic
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×#683—22no—
78C3×#683—22no—
79C3×C4×Dic5—22no—
80C3×C4×Dic5—22no—
81C3×C4×Dic5D411yescharacteristic
82C3×C4×Dic5D411yescharacteristic
83C3×C4×Dic5C2311yescharacteristic
84C3×C4×Dic5C2311yescharacteristic
85Dic3⋊Dic5—21no—
86Dic3⋊Dic5—21no—
87#6669—21no—
88#6667—21no—
89#6667—21no—
90#6667—21no—
91Dic3×Dic5—21no—
92#6661—24no—
93#6658—24no—
94C2×C3×C4×Q8—51no—
95#5479—51no—
96#5228—51no—
97#5227—51no—
98#5030—52no—
99#5028—52no—
100#5026—52no—
101#5022—52no—
102#4970D511yescharacteristic, complemented
103#4968—51no—
104#4926—51no—
105C22×Dic10C2×D311yescharacteristic
106C5×C22⋊Q8—31no—
107C2×C5×C4⋊C4C2×D311yescharacteristic
108#4093—31no—
109Q8×Dic5—31no—
110C2×#689—32no—
111#4076—31no—
112C2×#683—21no—
113C2×C4×Dic5—21no—
114C2×C4×Dic5C2×D311yescharacteristic
115C2×#677—32no—
116#4044—61no—
117#4039—31no—
118#4038—61no—
119#4036—31no—
120#4033—21no—
121#4033—21no—
122#4033C2×D312yes—
123#4033C2×D312yes—
124#4032—61no—
125#4027—61no—
126C5×#107—32no—
127C5×#103—32no—
128C5×C22⋊C8—31no—
129C22⋊#168—31no—
130#3948—32no—
131#3947—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—42no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144#1220—42no—
145C2×Dic15—21no—
146D60—22no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C5×Dic6—22no—
150C2×C3×Dic5—24no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—41no—
154C2×C3×Dic5C2×D411yescharacteristic
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C3×Dic10—24no—
159C3×Dic10—22no—
160C3×Dic10#4114yes—
161#1200—42no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C22×C3×Q8—51no—
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C2×C3×C4⋊C4—101no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C42—51no—
172C2×C3×C42—101no—
173C2×#216—52no—
174C2×#215—52no—
175#930—51no—
176#929—101no—
177C4×#67—101no—
178#924C2×D511yescharacteristic
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#830C2×D511yescharacteristic
189#810C2×D512yes—
190#809—52no—
191#808—52no—
192#807C2×D512yes—
193C4⋊(C3⋊C8)—52no—
194#803—52no—
195C2×C5×Q8—31no—
196C22×C4×C5—21no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C22×Dic5—21no—
200C22×Dic5#6711yescharacteristic
201C22×Dic5#6711yescharacteristic
202C2×D20—31no—
203C2×C4×D5—61no—
204C2×Dic10—21no—
205C2×Dic10—24no—
206C2×Dic10C22×D312yes—
207C2×C5×C8—32no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4C22×D312yes—
212C5×C22⋊C4—61no—
213#689—64no—
214#685—61no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—31no—
219C4⋊Dic5—61no—
220C4⋊Dic5—61no—
221#683—22no—
222#683—22no—
223#683—61no—
224C4×Dic5—22no—
225C4×Dic5—22no—
226C4×Dic5—61no—
227C4×Dic5#6711yescharacteristic
228C4×Dic5#6711yescharacteristic
229C4×Dic5C22×D311yescharacteristic
230C4×Dic5C22×D311yescharacteristic
231C2×#168—32no—
232#677—64no—
233#529—151no—
234C2×C4×Q8—51no—
235#484—31no—
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—21no—
252C3×C4×C5—42no—
253C3×C4×C5C2×#4112yes—
254Dic15—41no—
255C3×Dic5—24no—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—21no—
260C5×Dic3—41no—
261C5×Dic3—41no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C22×C3×C4—21no—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C2×D12—51no—
272C2×C4×D3—101no—
273C2×Dic6C22×D511yescharacteristic
274C3×C4⋊C4—21no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4C22×D512yes—
278C3×C42—51no—
279C3×C42—51no—
280C3×C42—51no—
281C3×C42—51no—
282C3×C42—102no—
283C3×C42—102no—
284#217—21no—
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⋊Dic3C22×D511yescharacteristic
293Dic3⋊C4—21no—
294Dic3⋊C4—101no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8C22×D512yes—
300C23×C5C2×#6711yescharacteristic
301C22×D5—61no—
302C5×Q8—62no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—42no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—122no—
311C2×Dic5—24no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—61no—
316C2×Dic5C2×#6711yescharacteristic
317C2×Dic5C2×#6711yescharacteristic
318C2×Dic5C2×#6711yescharacteristic
319C2×Dic5C2×#6711yescharacteristic
320D20—62no—
321C4×D5—122no—
322Dic10—24no—
323Dic10—22no—
324Dic10#23514yes—
325C5×C8—62no—
326#168—62no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—31no—
335#121—151no—
336C4×Q8—52no—
337C4×Q8—52no—
338C4×Q8—101no—
339C4×Q8—101no—
340C4×Q8—151no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4D3×D511yescharacteristic
346C2×C42—51no—
347C2×C42—101no—
348#107—32no—
349#106—152no—
350C4⋊C8—152no—
351#103—32no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—31no—
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×C3D4×D511yescharacteristic
364C22×D3—101no—
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—42no—
371C2×C3×C4—51no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—51no—
375C2×C3×C4—104no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—201no—
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—202no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—101no—
385D12—102no—
386C4×D3—202no—
387Dic6—22no—
388C3⋊C8—22no—
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—21no—
398C4×C5—42no—
399C4×C5—121no—
400C4×C5—121no—
401C4×C5C2×#23512yes—
402Dic5—24no—
403Dic5—21no—
404Dic5—21no—
405Dic5—21no—
406Dic5—21no—
407Dic5—121no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—104no—
411C2×Q8—101no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—101no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—32no—
423C2×C8—152no—
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—61no—
427C4⋊C4—102no—
428C4⋊C4—102no—
429C4⋊C4—151no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D512yes—
434C22⋊C4—61no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—102no—
444C42—102no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#406412yes—
450C22×C3C2×D4×D511yescharacteristic
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—104no—
461C3×C4D5×#4112yes—
462Dic3—41no—
463Dic3—41no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#579111yescharacteristic
467C2×C5C2×#94211yescharacteristic
468C2×C5#582211yescharacteristic
469D5—241no—
470C23—301no—
471C23D5×#6711yescharacteristic
472Q8—54no—
473Q8—62no—
474Q8—104no—
475Q8—102no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—104no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—201no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D5×#6711yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—62no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6599011yescharacteristic
499C2×C3C2×#406411yescharacteristic
500C2×C3#6610711yescharacteristic
501D3—401no—
502C5#8244511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9151512yes—
509C22C2×D5×#6711yescharacteristic
510C4—21no—
511C4—42no—
512C4—104no—
513C4—101no—
514C4—101no—
515C4—101no—
516C4—101no—
517C4—121no—
518C4—121no—
519C4—601no—
520C4D5×#23512yes—
521C3#1061318611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175431611yescharacteristic
525C2#1175469011yescharacteristic
526C2C2×#9151511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#91819C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4033C2semidirect
4. C5×#4970C2semidirect
5. #11748555C2semidirect
7. #11748333C2semidirect
8. #11747391C2semidirect
9. #11747372C2semidirect
10. #11747262C2semidirect
11. #11747224C2semidirect
46. C2×#4033D3semidirect
102. #4970D5semidirect
446. C3×C5#3117semidirect
502. C5#82445semidirect
521. C3#10613186semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40332
#117544152
#117510692
C5×#49702
#117485552
#117485322
#117483332
#117473912
#117473722
#117472622
#117472242
#106131863
#824455