Finite Group Databasebeta

← #14435499

Subgroups — #14435499

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
1C5×#5479C211yesmaximal, characteristic
2C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
3#11751027C211yesmaximal, characteristic, complemented
4#11748555C211yesmaximal, characteristic, complemented
5#11748529C211yesmaximal, characteristic
6#11748471C211yesmaximal, characteristic, complemented
7#11748385C211yesmaximal, characteristic
8#11747089C212yesmaximal, complemented
9#11747061C212yesmaximal, complemented
10#11747050C212yesmaximal, complemented
11#11746919C212yesmaximal, complemented
12#10614884—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C5×#930C2211yescharacteristic
16C5×#929—21no—
17C4×C5×#67—21no—
18C5×#924C2211yescharacteristic
19C5×#876—21no—
20C5×#875C2211yescharacteristic
21C4×C5×D12C2211yescharacteristic
22C5×#872—21no—
23C5×#870C2211yescharacteristic
24C4×C5×Dic6C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×#683—21no—
27C2×C3×C4×Dic5—21no—
28C3×C4×Dic10—21no—
29C3×C4×Dic10—21no—
30C3×C4×Dic10C2212yes—
31C3×C4×Dic10C2212yes—
32C2×#6661C2212yes—
33C2×#6656C2212yes—
34#91114C2211yescharacteristic
35#91114C2211yescharacteristic
36C4⋊(C3⋊#168)C2212yes—
37#91087C2212yes—
38#90989C2212yes—
39#90986C2212yes—
40#90972C2212yes—
41#90970C2212yes—
42#90970C2212yes—
43#90966C2212yes—
44#82445—51nomaximal, Hall
45C5×#529—31no—
46C2×C4×Dic10D311yescharacteristic, complemented
47#65352—32no—
48#65343—32no—
49#65339—31no—
50#65333—31no—
51#65329—31no—
52#65323—31no—
53#65319—32no—
54#65307—32no—
55#65215—31no—
56C22×C3×C4×C5D411yescharacteristic
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C2×C5×#67—21no—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C5×Dic6C2311yescharacteristic
63C22×C3×Dic5—21no—
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10C2312yes—
68C3×C42×C5D411yescharacteristic
69C3×C42×C5D411yescharacteristic
70C3×C42×C5C2311yescharacteristic
71C3×C42×C5C2311yescharacteristic
72C2×C3⋊#168C2312yes—
73C2×C3⋊#168C2312yes—
74C5×#217—21no—
75C5×(C2×D3)⋊C4—21no—
76C5×(C2×D3)⋊C4—21no—
77C5×(C2×D3)⋊C4—21no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C5×Dic3⋊C4—21no—
82C5×Dic3⋊C4—21no—
83C5×Dic3⋊C4—21no—
84C5×Dic3⋊C4—21no—
85C4×C5×Dic3—21no—
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C3×#683—22no—
89C3×#683—22no—
90C3×C4×Dic5—22no—
91C3×C4×Dic5—22no—
92#6661—24no—
93#6656—24no—
94C2×C3×C4×Q8—51no—
95#5479D511yescharacteristic
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×Dic10C2×D311yescharacteristic
106C5×#126—61no—
107C5×#125—31no—
108C5×#124—31no—
109C5×#123—61no—
110C5×C22⋊Q8—31no—
111C5×#121—31no—
112C4×C5×Q8—31no—
113C4×C5×D4—31no—
114C4×C5×D4—61no—
115C5×#117—61no—
116C2×C42×C5C2×D311yescharacteristic
117C2×#689—32no—
118C2×#687—32no—
119C2×C4⋊Dic5C2×D311yescharacteristic
120C2×#683—21no—
121C2×C4×Dic5—21no—
122C4×Dic10—21no—
123C4×Dic10—21no—
124C4×Dic10C2×D312yes—
125C4×Dic10C2×D312yes—
126#3967—32no—
127#3964—32no—
128C22⋊#168—31no—
129C22⋊#168—31no—
130#3942—32no—
131#3942—32no—
132#3940—32no—
133#3939—32no—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C5×#67—42no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C5×D12—22no—
153C4×C5×D3—42no—
154C5×Dic6—22no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—42no—
159C3×Dic10—24no—
160C3×Dic10—22no—
161C3×Dic10#4114yes—
162C3⋊#168—22no—
163C3⋊#168—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—51no—
170C2×C3×C4⋊C4—101no—
171C2×C3×C42—101no—
172C2×C3×C42C2×D511yescharacteristic
173C2×#216—52no—
174C2×#215—52no—
175#930C2×D511yescharacteristic
176#929—21no—
177C4×#67—21no—
178#924C2×D511yescharacteristic
179#876—21no—
180#875C2×D511yescharacteristic
181C4×D12C2×D511yescharacteristic
182#872—21no—
183#870C2×D511yescharacteristic
184C4×Dic6C2×D511yescharacteristic
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—31no—
196C2×C5×D4—31no—
197C2×C5×D4—61no—
198C22×C4×C5—61no—
199C22×C4×C5#6711yescharacteristic
200C22×C4×C5#6711yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C22×Dic5—21no—
204C2×Dic10—21no—
205C2×Dic10—24no—
206C2×Dic10C22×D312yes—
207C5×C4⋊C4—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—61no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4—61no—
213C5×C22⋊C4—61no—
214C5×C22⋊C4—61no—
215C5×C22⋊C4—61no—
216C5×C22⋊C4—61no—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219C42×C5#6711yescharacteristic
220C42×C5#6711yescharacteristic
221C42×C5C22×D311yescharacteristic
222C42×C5C22×D311yescharacteristic
223#689—64no—
224#687—64no—
225C4⋊Dic5—21no—
226C4⋊Dic5C22×D312yes—
227#683—22no—
228#683—22no—
229C4×Dic5—22no—
230C4×Dic5—22no—
231C2×#168—32no—
232C2×#168—32no—
233#529—31no—
234C2×C4×Q8—51no—
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×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C3×C4×C5—21no—
252C3×C4×C5—21no—
253C3×C4×C5—21no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5C2×#4112yes—
257C3×Dic5—24no—
258C3×Dic5—42no—
259C5×Dic3—41no—
260C5×Dic3—41no—
261C5×Dic3—41no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C22×C3×C4—101no—
266C22×C3×C4—101no—
267C22×C3×C4C22⋊D511yescharacteristic
268C22×C3×C4C22⋊D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271C2×D12C22×D511yescharacteristic
272C2×C4×D3—21no—
273C2×Dic6C22×D511yescharacteristic
274C3×C4⋊C4—52no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4—101no—
278C3×C42—102no—
279C3×C42—102no—
280C3×C42C22⋊D511yescharacteristic
281C3×C42C22⋊D511yescharacteristic
282C3×C42C22×D511yescharacteristic
283C3×C42C22×D511yescharacteristic
284#217—21no—
285#216—104no—
286#215—104no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—21no—
290(C2×D3)⋊C4—21no—
291C4⋊Dic3C22×D511yescharacteristic
292C4⋊Dic3C22×D511yescharacteristic
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296Dic3⋊C4—21no—
297C4×Dic3—21no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8—52no—
300C23×C5—61no—
301C23×C5C2×#6711yescharacteristic
302C5×Q8—62no—
303C5×D4—62no—
304C5×D4—122no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—41no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—122no—
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C2×#6711yescharacteristic
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C2×Dic5—24no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—42no—
322Dic10—24no—
323Dic10—22no—
324Dic10#23514yes—
325#168—62no—
326#168—62no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—61no—
331#125—31no—
332#124—31no—
333#123—61no—
334C22⋊Q8—31no—
335#121—31no—
336C4×Q8—31no—
337C4×Q8—52no—
338C4×Q8—52no—
339C4×Q8—101no—
340C4×Q8—101no—
341C4×D4—31no—
342C4×D4—61no—
343#117—61no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C42—101no—
347C2×C42D3×D511yescharacteristic
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
362C5×D3—81no—
363C23×C3C2×C22⋊D511yescharacteristic
364C22×D3—21no—
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—41no—
371C2×C3×C4—104no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—202no—
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—42no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385D12—22no—
386C4×D3—42no—
387Dic6—22no—
388C3⋊C8—102no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—121no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5#94212yes—
396C22×C5C22×#6711yescharacteristic
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—21no—
402C4×C5—121no—
403C4×C5—121no—
404C4×C5—121no—
405C4×C5C2×#23512yes—
406Dic5—24no—
407Dic5—42no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—104no—
411C2×Q8—101no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4#120111yescharacteristic
418C22×C4#120111yescharacteristic
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—152no—
423C2×C8—152no—
424C4⋊C4—31no—
425C4⋊C4—31no—
426C4⋊C4—52no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—101no—
432C4⋊C4—102no—
433C4⋊C4—102no—
434C22⋊C4—61no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—61no—
439C42—61no—
440C42—102no—
441C42—102no—
442C42#120111yescharacteristic
443C42#120111yescharacteristic
444C42C2×D3×D511yescharacteristic
445C42C2×D3×D511yescharacteristic
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#409712yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—104no—
460C3×C4—202no—
461C3×C4D5×#4112yes—
462Dic3—41no—
463Dic3—41no—
464Dic3—41no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#579111yescharacteristic
468C2×C5C2×#94211yescharacteristic
469C2×C5#582211yescharacteristic
470C23—61no—
471C23C2×#120111yescharacteristic
472Q8—54no—
473Q8—62no—
474Q8—104no—
475Q8—102no—
476D4—62no—
477D4—122no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—104no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—122no—
488C2×C4—202no—
489C2×C4C2×#120111yescharacteristic
490C2×C4C2×#120111yescharacteristic
491C2×C4C2×#120111yescharacteristic
492C2×C4C2×#120111yescharacteristic
493C2×C4C2×#120111yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—302no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6615611yescharacteristic
499C2×C3C2×#409711yescharacteristic
500C2×C3#6616211yescharacteristic
501D3—81no—
502C5#8244511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9130912yes—
509C22C22×#120111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—104no—
516C4—121no—
517C4—121no—
518C4—121no—
519C4—202no—
520C4D5×#23512yes—
521C3#1061488411yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175413811yescharacteristic
525C2C2×#9130911yescharacteristic
526C2#1175456311yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radicalC5×#930C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic10C2semidirect
3. #11751027C2semidirect
4. #11748555C2semidirect
6. #11748471C2semidirect
8. #11747089C2semidirect
9. #11747061C2semidirect
10. #11747050C2semidirect
11. #11746919C2semidirect
46. C2×C4×Dic10D3semidirect
446. C3×C5#3117semidirect
502. C5#82445semidirect
521. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C5×#54792
C2×C3×C4×Dic102
#117510272
#117485552
#117485292
#117484712
#117483852
#117470892
#117470612
#117470502
#117469192
#106148843
#824455