Finite Group Databasebeta

← #14323155

Subgroups — #14323155

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic5×D12C211yesmaximal, characteristic
2#11751073C211yesmaximal, characteristic, complemented
3C5×#4988C211yesmaximal, characteristic
4C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5#11748887C212yesmaximal, complemented
6#11748880C212yesmaximal, complemented
7#11748858C211yesmaximal, characteristic, complemented
8#11748797C211yesmaximal, characteristic
9#11748715C212yesmaximal, complemented
10#11748714C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10608026—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6712C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×#6669C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29Dic5×D12C418yescomplemented
30#91115C2212yes—
31C3×#3963C2212yes—
32#90994C2211yescharacteristic
33#90994C2211yescharacteristic
34#90994C2211yescharacteristic
35#90994C2211yescharacteristic
36#90994C2212yes—
37#73761—51nomaximal, Hall
38C2×D4×Dic5—31no—
39C5×#390—31no—
40#65510—31no—
41C4⋊C4×Dic5D311yescharacteristic, complemented
42#65262—31no—
43#65234—32no—
44#65233—32no—
45#65232—32no—
46#65231—32no—
47#65221—31no—
48#65217—31no—
49C23×C5×D3C2312yes—
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2311yescharacteristic
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×C5×Dic3C2311yescharacteristic
56C22×C5×Dic3C2311yescharacteristic
57C2×C5×D12—22no—
58C2×C5×D12—22no—
59C2×C5×D12C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C2×D3×Dic5—42no—
64C2×D3×Dic5—42no—
65C2×D3×Dic5C2×C418yes—
66C3×C5×C4⋊C4—22no—
67C4⋊Dic15C2×C414yes—
68#6712—42no—
69C4×Dic15—22no—
70C5×(C2×D3)⋊C4—42no—
71C5×(C2×D3)⋊C4—42no—
72C4×C5×Dic3—22no—
73C3×C4⋊Dic5—22no—
74C3×C4×Dic5—42no—
75C3×C4×Dic5C2×C414yes—
76#6669—42no—
77(C2×D3)⋊Dic5—42no—
78(C2×D3)⋊Dic5—42no—
79(C2×D3)⋊Dic5C2×C418yes—
80C2×C4×D12—51no—
81C3×C4×C4⋊C4—51no—
82#4988—51no—
83#4988D511yescharacteristic
84#4972—51no—
85#4972—51no—
86#4940—52no—
87#4940—52no—
88#4932—51no—
89#4667—52no—
90#4664—52no—
91C22×C5×D4—31no—
92C23×Dic5—32no—
93C2×C5×C4⋊C4C2×D311yescharacteristic
94C2×C5×C22⋊C4—32no—
95C2×C5×C22⋊C4—32no—
96C2×C42×C5—31no—
97C2×C22⋊Dic5—32no—
98C2×C22⋊Dic5—32no—
99C2×C22⋊Dic5—32no—
100D4×Dic5—38no—
101C2×C4⋊Dic5—31no—
102C2×C4⋊Dic5C2×D311yescharacteristic
103C2×#683—32no—
104C2×#683—32no—
105C2×C4×Dic5—31no—
106C2×C4×Dic5C2×D312yes—
107C2×C4×Dic5C2×D311yescharacteristic
108#3963—32no—
109#3963—32no—
110#3963—31no—
111#3963—31no—
112#3963—31no—
113#3963—31no—
114#3963C2×D312yes—
115#2319—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×C5×D3—22no—
118C22×C5×D3—22no—
119C22×C5×D3—22no—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3—22no—
123C22×C5×D3C22×C414yes—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5#4112yes—
129C2×C3×C4×C5#4112yes—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15C22×C414yes—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C5×D12—28no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22×C412yes—
154C2×C3×Dic5C22×C412yes—
155D3×Dic5—48no—
156C22×D12C2×D511yescharacteristic
157C22×C4×D3—52no—
158C2×C3×C4⋊C4—51no—
159C2×C3×C4⋊C4C2×D511yescharacteristic
160C2×C3×C42—51no—
161C2×C3×C42—52no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4—52no—
165C2×(C2×D3)⋊C4C2×D512yes—
166C2×(C2×D3)⋊C4C2×D512yes—
167C2×C4⋊Dic3—51no—
168C2×Dic3⋊C4—52no—
169C2×Dic3⋊C4—52no—
170C2×C4×Dic3—51no—
171C2×C4×Dic3C2×D511yescharacteristic
172C4×D12—58no—
173C3×#95—52no—
174C3⋊#95—52no—
175C3⋊#95—51no—
176C3⋊#95—52no—
177C3⋊#95—51no—
178C3⋊#95—51no—
179C3⋊#95—51no—
180C24×C5—32no—
181C2×C5×D4—34no—
182C2×C5×D4—62no—
183C2×C5×D4—62no—
184C22×C4×C5—31no—
185C22×C4×C5—31no—
186C22×C4×C5C22×D312yes—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—32no—
189C22×Dic5—38no—
190C22×Dic5—31no—
191C22×Dic5—31no—
192C22×Dic5—122no—
193C22×Dic5—122no—
194C22×Dic5C22×D312yes—
195C22×Dic5C22×D311yescharacteristic
196C22×Dic5C22×D311yescharacteristic
197C5×C4⋊C4—22no—
198C5×C22⋊C4—122no—
199C5×C22⋊C4—122no—
200C42×C5—62no—
201C22⋊Dic5—38no—
202C22⋊Dic5—122no—
203C22⋊Dic5—122no—
204C4⋊Dic5—22no—
205C4⋊Dic5—34no—
206#683—122no—
207#683—122no—
208C4×Dic5—42no—
209C4×Dic5—62no—
210C4×Dic5C4×D314yes—
211C2×C4×D4—151no—
212#390—31no—
213#390—151no—
214#389—151no—
215#389—151no—
216#388—152no—
217#388—152no—
218#381—152no—
219#380—152no—
220C4×C4⋊C4—51no—
221#376—151no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C2×#4111yescharacteristic
224C22×C3×C5C2×#4111yescharacteristic
225C22×C3×C5H(5,𝔽2)11yescharacteristic
226C22×C3×C5H(5,𝔽2)11yescharacteristic
227C22×C3×C5H(5,𝔽2)11yescharacteristic
228C22×C3×C52−1+411yescharacteristic
229C2×C5×D3—24no—
230C2×C5×D3—24no—
231C2×C5×D3—24no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C3×C4×C5—42no—
237C3×C4×C5#11714yes—
238Dic15—24no—
239Dic15—41no—
240Dic15—41no—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—42no—
244C5×Dic3—41no—
245C5×Dic3—41no—
246C23×D3C22×D512yes—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—52no—
250C22×C3×C4C22×D512yes—
251C22×C3×C4C22×D511yescharacteristic
252C22×Dic3—52no—
253C22×Dic3—51no—
254C22×Dic3—51no—
255C22×Dic3C22×D511yescharacteristic
256C22×Dic3C22×D511yescharacteristic
257C2×D12—22no—
258C2×D12—22no—
259C2×D12C4×D514yes—
260C2×C4×D3—58no—
261C2×C4×D3—202no—
262C2×C4×D3—202no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—102no—
265C3×C42—54no—
266C3×C42—202no—
267(C2×D3)⋊C4—42no—
268(C2×D3)⋊C4—42no—
269(C2×D3)⋊C4—58no—
270(C2×D3)⋊C4—202no—
271(C2×D3)⋊C4—202no—
272C4⋊Dic3—54no—
273Dic3⋊C4—202no—
274Dic3⋊C4—202no—
275C4×Dic3—22no—
276C4×Dic3—102no—
277C23×C5—34no—
278C23×C5—62no—
279C23×C5—62no—
280C23×C5—62no—
281C23×C5—62no—
282C23×C5—62no—
283C23×C5—62no—
284C23×C5C23×D311yescharacteristic
285C5×D4—68no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5—61no—
295C2×C4×C5C2×C4×D312yes—
296C2×C4×C5#23512yes—
297C2×C4×C5#23512yes—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—34no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5—128no—
315C2×Dic5C2×C4×D312yes—
316C2×Dic5C2×C4×D312yes—
317C22×D4—31no—
318C23×C4—152no—
319C4×D4—158no—
320C2×C4⋊C4—51no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4—152no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4D3×D511yescharacteristic
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—152no—
328C2×C22⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C42—31no—
331C2×C42—51no—
332C2×C42—52no—
333C2×C42—151no—
334#95—52no—
335#95—151no—
336#95—151no—
337#95—151no—
338#95—151no—
339#95—152no—
340#95—152no—
341C2×C3×C5C2×#11711yescharacteristic
342C2×C3×C5#51811yescharacteristic
343C2×C3×C5#52011yescharacteristic
344C2×C3×C5#54011yescharacteristic
345C2×C3×C5#54011yescharacteristic
346C2×C3×C5#54211yescharacteristic
347C2×C3×C5#54211yescharacteristic
348C5×D3—44no—
349C23×C3C23×D511yescharacteristic
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3C2×C4×D514yes—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—52no—
361C2×C3×C4—52no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—102no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4C2×C4×D512yes—
370C2×C3×C4#71112yes—
371C2×C3×C4#71112yes—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—54no—
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C2×Dic3—101no—
387D12—28no—
388C4×D3—208no—
389C22×C5—64no—
390C22×C5—64no—
391C22×C5—64no—
392C22×C5—122no—
393C22×C5—122no—
394C22×C5—122no—
395C22×C5—122no—
396C22×C5C22×C4×D311yescharacteristic
397C22×C5C2×#23511yescharacteristic
398C22×C5C2×#23511yescharacteristic
399C22×C5#100411yescharacteristic
400C22×C5#100711yescharacteristic
401C22×C5#100911yescharacteristic
402C22×C5#100911yescharacteristic
403C4×C5—42no—
404C4×C5—121no—
405C4×C5—121no—
406C4×C5#87214yes—
407Dic5—22no—
408Dic5—22no—
409Dic5—42no—
410Dic5—64no—
411Dic5—121no—
412Dic5—121no—
413C24—32no—
414C2×D4—34no—
415C2×D4—62no—
416C2×D4—62no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—51no—
420C22×C4—51no—
421C22×C4—52no—
422C22×C4—158no—
423C22×C4—152no—
424C22×C4—151no—
425C22×C4—151no—
426C22×C4—602no—
427C22×C4—602no—
428C22×C4C2×D3×D512yes—
429C22×C4C2×D3×D511yescharacteristic
430C4⋊C4—22no—
431C4⋊C4—102no—
432C4⋊C4—154no—
433C4⋊C4—602no—
434C4⋊C4—602no—
435C22⋊C4—122no—
436C22⋊C4—122no—
437C22⋊C4—158no—
438C22⋊C4—602no—
439C22⋊C4—602no—
440C42—54no—
441C42—62no—
442C42—202no—
443C42—302no—
444C3×C5#231911yescharacteristic, complemented, Hall
445C22×C3C22×C4×D511yescharacteristic
446C22×C3C2×#71111yescharacteristic
447C22×C3C2×#71111yescharacteristic
448C22×C3#414411yescharacteristic
449C22×C3#414411yescharacteristic
450C22×C3#414911yescharacteristic
451C22×C3#415011yescharacteristic
452C2×D3—24no—
453C2×D3—24no—
454C2×D3—24no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C3×C4—42no—
460C3×C4—102no—
461C3×C4—102no—
462C3×C4—202no—
463C3×C4#402314yes—
464Dic3—41no—
465Dic3—41no—
466Dic3—104no—
467Dic3—201no—
468Dic3—201no—
469C2×C5—124no—
470C2×C5C2×#87211yescharacteristic
471C2×C5#550411yescharacteristic
472C2×C5#552111yescharacteristic
473C2×C5#556211yescharacteristic
474C2×C5#556211yescharacteristic
475C2×C5#558211yescharacteristic
476C2×C5#558211yescharacteristic
477C23—34no—
478C23—62no—
479C23—62no—
480C23—62no—
481C23—62no—
482C23—62no—
483C23—62no—
484C23C22×D3×D511yescharacteristic
485D4—68no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—101no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—154no—
505C2×C4—302no—
506C2×C4—302no—
507C2×C4—301no—
508C2×C4—301no—
509C2×C4—301no—
510C2×C4—301no—
511C2×C4—301no—
512C2×C4—301no—
513C2×C4—608no—
514C2×C4#677212yes—
515C2×C4C4×D3×D512yes—
516C2×C4#678212yes—
517C2×C3C2×#402311yescharacteristic
518C2×C3#6587911yescharacteristic
519C2×C3#6588011yescharacteristic
520C2×C3#6593711yescharacteristic
521C2×C3#6595311yescharacteristic
522C2×C3#6601611yescharacteristic
523C2×C3#6605311yescharacteristic
524D3—44no—
525C5#7376111yescharacteristic, complemented, Sylow
526C22—64no—
527C22—64no—
528C22—64no—
529C22—122no—
530C22—122no—
531C22—122no—
532C22—122no—
533C22C2×#677211yescharacteristic
534C22C2×C4×D3×D511yescharacteristic
535C22#9202511yescharacteristic
536C22#9202711yescharacteristic
537C22#9203011yescharacteristic
538C22#9203511yescharacteristic
539C22C2×#678211yescharacteristic
540C4—42no—
541C4—102no—
542C4—102no—
543C4—121no—
544C4—121no—
545C4—202no—
546C4—304no—
547C4—601no—
548C4—601no—
549C4#9139814yes—
550C3#1060802611yescharacteristic, complemented, Sylow
551C2—124no—
552C2#1175337611yescharacteristic
553C2#1175367111yescharacteristic
554C2#1175381511yescharacteristic
555C2#1175383711yescharacteristic
556C2C2×#9139811yescharacteristic
557C2#1175491711yescharacteristic
558C2#1175522111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2319
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751073C2semidirect
4. C3×C4⋊C4×Dic5C2semidirect
5. #11748887C2semidirect
6. #11748880C2semidirect
7. #11748858C2semidirect
9. #11748715C2semidirect
10. #11748714C2semidirect
11. #11748611C2semidirect
29. Dic5×D12C4semidirect
41. C4⋊C4×Dic5D3semidirect
444. C3×C5#2319semidirect
525. C5#73761semidirect
550. C3#10608026semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×D122
#117510732
C5×#49882
C3×C4⋊C4×Dic52
#117488872
#117488802
#117488582
#117487972
#117487152
#117487142
#117486112
#106080263
#737615