Finite Group Databasebeta

← #14435500

Subgroups — #14435500

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×C4×Dic30C211yesmaximal, characteristic, complemented
2C5×#5479C211yesmaximal, characteristic
3C3×#65215C211yesmaximal, characteristic, complemented
4#11748565C211yesmaximal, characteristic, complemented
5#11748553C211yesmaximal, characteristic
6#11748467C211yesmaximal, characteristic, complemented
7#11748379C211yesmaximal, characteristic
8#11747093C212yesmaximal, complemented
9#11747056C212yesmaximal, complemented
10#11746967C212yesmaximal, complemented
11#11746884C212yesmaximal, complemented
12#10614884—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6712—21no—
17C2×C4×Dic15—21no—
18C4×Dic30—21no—
19C4×Dic30—21no—
20C4×Dic30C2212yes—
21C4×Dic30C2212yes—
22C5×#930C2211yescharacteristic
23C5×#929—21no—
24C4×C5×#67—21no—
25C5×#924C2211yescharacteristic
26C5×#876—21no—
27C5×#875C2211yescharacteristic
28C4×C5×D12C2211yescharacteristic
29C5×#872—21no—
30C5×#870C2211yescharacteristic
31C4×C5×Dic6C2211yescharacteristic
32C2×#6663C2212yes—
33C2×#6659C2212yes—
34C3×C22⋊#168C2211yescharacteristic
35C3×C22⋊#168C2211yescharacteristic
36C3×C4⋊#168C2212yes—
37C3×#3935C2212yes—
38#90988C2212yes—
39#90985C2212yes—
40#90975C2212yes—
41#90975C2212yes—
42#90973C2212yes—
43#90967C2212yes—
44#79357—51nomaximal, Hall
45C5×#529—31no—
46C2×C4×Dic10—31no—
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#65215D311yescharacteristic, complemented
56C22×C3×C4×C5D411yescharacteristic
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×Dic15—21no—
61C2×Dic30—21no—
62C2×Dic30—24no—
63C2×Dic30C2312yes—
64C2×C5×#67—21no—
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C2×C5×Dic6C2311yescharacteristic
68C3×C42×C5D411yescharacteristic
69C3×C42×C5D411yescharacteristic
70C3×C42×C5C2311yescharacteristic
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74#6712—22no—
75#6712—22no—
76C4×Dic15—22no—
77C4×Dic15—22no—
78C5×#217—21no—
79C5×(C2×D3)⋊C4—21no—
80C5×(C2×D3)⋊C4—21no—
81C5×(C2×D3)⋊C4—21no—
82C5×(C2×D3)⋊C4—21no—
83C5×C4⋊Dic3C2311yescharacteristic
84C5×C4⋊Dic3C2311yescharacteristic
85C5×Dic3⋊C4—21no—
86C5×Dic3⋊C4—21no—
87C5×Dic3⋊C4—21no—
88C5×Dic3⋊C4—21no—
89C4×C5×Dic3—21no—
90C2×C3×#168C2312yes—
91C2×C3×#168C2312yes—
92#6663—24no—
93#6659—24no—
94#5479D511yescharacteristic
95C2×C4×Dic6—51no—
96C3×#432—51no—
97#4845—52no—
98#4829—52no—
99#4739—51no—
100#4738—51no—
101#4735—51no—
102#4722—51no—
103#4716—52no—
104#4710—52no—
105C22×Dic10—31no—
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⋊Dic5—31no—
120C2×#683—61no—
121C2×C4×Dic5—61no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C4×Dic10—61no—
125C4×Dic10—61no—
126#3967—32no—
127#3964—32no—
128C22⋊#168C2×D311yescharacteristic
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3942—32no—
132#3940—32no—
133#3939—32no—
134C4⋊#168C2×D312yes—
135#3935C2×D312yes—
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
148C2×Dic15—24no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—42no—
152Dic30—24no—
153Dic30—22no—
154Dic30#4114yes—
155C5×#67—42no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C5×D12—22no—
160C4×C5×D3—42no—
161C5×Dic6—22no—
162C3×#168—22no—
163C3×#168—22no—
164C22×Dic6—51no—
165C2×C3×C42C2×D511yescharacteristic
166#930C2×D511yescharacteristic
167#929—21no—
168C4×#67—21no—
169C2×C4⋊Dic3—51no—
170#924C2×D511yescharacteristic
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—101no—
173C2×Dic12—52no—
174C2×#204—52no—
175#876—21no—
176#875C2×D511yescharacteristic
177C4×D12C2×D511yescharacteristic
178#872—21no—
179#870C2×D511yescharacteristic
180C4×Dic6—52no—
181C4×Dic6—52no—
182C4×Dic6—101no—
183C4×Dic6—101no—
184C4×Dic6C2×D511yescharacteristic
185C3×C4⋊C8—52no—
186C3×C22⋊C8—51no—
187C3×C22⋊C8—51no—
188C3×#97—52no—
189#821—52no—
190#818—52no—
191#817—52no—
192#816—52no—
193#816—52no—
194#816—52no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C2×C5×D4—61no—
198C22×C4×C5—61no—
199C22×C4×C5D1211yescharacteristic
200C22×C4×C5D1211yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—61no—
203C22×Dic5—61no—
204C2×Dic10—32no—
205C2×Dic10—64no—
206C2×Dic10—61no—
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×C5D1211yescharacteristic
220C42×C5D1211yescharacteristic
221C42×C5C22×D311yescharacteristic
222C42×C5C22×D311yescharacteristic
223#689—64no—
224#687—64no—
225C4⋊Dic5—32no—
226C4⋊Dic5—61no—
227#683—62no—
228#683—62no—
229C4×Dic5—62no—
230C4×Dic5—62no—
231C2×#168C22×D312yes—
232C2×#168C22×D312yes—
233#529—31no—
234C2×C4×Q8—151no—
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—51no—
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—
257Dic15—24no—
258Dic15—42no—
259C5×Dic3—41no—
260C5×Dic3—41no—
261C5×Dic3—41no—
262C22×C3×C4C22⋊D511yescharacteristic
263C22×C3×C4C22⋊D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—101no—
267C22×Dic3—101no—
268C2×D12C22×D511yescharacteristic
269C2×C4×D3—21no—
270C2×Dic6—52no—
271C2×Dic6—104no—
272C2×Dic6—101no—
273C2×Dic6C22×D511yescharacteristic
274C2×C3×C8—52no—
275C2×C3×C8—52no—
276C3×C42C22⋊D511yescharacteristic
277C3×C42C22⋊D511yescharacteristic
278C3×C42C22×D511yescharacteristic
279C3×C42C22×D511yescharacteristic
280#217—21no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—21no—
285C4⋊Dic3—52no—
286C4⋊Dic3—101no—
287C4⋊Dic3C22×D511yescharacteristic
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—102no—
294Dic3⋊C4—102no—
295C4×Dic3—21no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298Dic12—104no—
299#204—104no—
300C23×C5—61no—
301C23×C5C2×D1211yescharacteristic
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×D1211yescharacteristic
313C2×C4×C5C2×D1211yescharacteristic
314C2×C4×C5C2×D1211yescharacteristic
315C2×C4×C5C2×D1211yescharacteristic
316C2×C4×C5C2×D1211yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C2×Dic5—64no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—122no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325#168—22no—
326#168—22no—
327C22×Q8—151no—
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—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—31no—
342C4×D4—61no—
343#117—61no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—301no—
346C2×C42—301no—
347C2×C42D3×D511yescharacteristic
348#107—152no—
349#106—152no—
350C4⋊C8—52no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—51no—
356C22⋊C8—51no—
357#97—52no—
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—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—41no—
368C2×C3×C4C2×C22⋊D511yescharacteristic
369C2×C3×C4C2×C22⋊D511yescharacteristic
370C2×C3×C4C2×C22⋊D511yescharacteristic
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×C3×C4C23×D511yescharacteristic
374#67—42no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—104no—
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—202no—
382D12—22no—
383C4×D3—42no—
384Dic6—22no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
388C3×C8—102no—
389C3×C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—121no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5#90912yes—
396C22×C5C22×D1211yescharacteristic
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×C5D3×#4112yes—
406Dic5—64no—
407Dic5—122no—
408C2×Q8—31no—
409C2×Q8—152no—
410C2×Q8—304no—
411C2×Q8—301no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—301no—
416C22×C4—301no—
417C22×C4#120311yescharacteristic
418C22×C4#120311yescharacteristic
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—52no—
423C2×C8—52no—
424C4⋊C4—31no—
425C4⋊C4—31no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—152no—
431C4⋊C4—301no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C22⋊C4—61no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—61no—
439C42—61no—
440C42—302no—
441C42—302no—
442C42#120311yescharacteristic
443C42#120311yescharacteristic
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×C4D5×#4112yes—
460Dic3—41no—
461Dic3—41no—
462Dic3—41no—
463Dic3—104no—
464Dic3—202no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#552411yescharacteristic
468C2×C5C2×#90911yescharacteristic
469C2×C5#574811yescharacteristic
470C23—61no—
471C23C2×#120311yescharacteristic
472Q8—62no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—62no—
477D4—122no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—122no—
485C2×C4—304no—
486C2×C4—302no—
487C2×C4—302no—
488C2×C4—602no—
489C2×C4C2×#120311yescharacteristic
490C2×C4C2×#120311yescharacteristic
491C2×C4C2×#120311yescharacteristic
492C2×C4C2×#120311yescharacteristic
493C2×C4C2×#120311yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—102no—
497C2×C3—22no—
498C2×C3#6615611yescharacteristic
499C2×C3C2×#409711yescharacteristic
500C2×C3#6616211yescharacteristic
501D3—81no—
502C5#7935711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9132212yes—
509C22C22×#120311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—121no—
516C4—121no—
517C4—121no—
518C4—304no—
519C4—602no—
520C4#9201612yes—
521C3#1061488411yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175414511yescharacteristic
525C2C2×#9132211yescharacteristic
526C2#1175459211yescharacteristic
subgroupG/H
centerC22C22×#1203
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
1. C2×C4×Dic30C2semidirect
3. C3×#65215C2semidirect
4. #11748565C2semidirect
6. #11748467C2semidirect
8. #11747093C2semidirect
9. #11747056C2semidirect
10. #11746967C2semidirect
11. #11746884C2semidirect
55. #65215D3semidirect
446. C3×C5#3117semidirect
502. C5#79357semidirect
521. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C5×#54792
C3×#652152
#117485652
#117485532
#117484672
#117483792
#117470932
#117470562
#117469672
#117468842
#106148843
#793575