Finite Group Databasebeta

← #14323056

Subgroups — #14323056

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×D12C211yesmaximal, characteristic
2#11751038C211yesmaximal, characteristic, complemented
3C3×#65225C211yesmaximal, characteristic, complemented
4#11748901C212yesmaximal
5#11748897C212yesmaximal, complemented
6D3×#3963C211yesmaximal, characteristic, complemented
7#11748782C211yesmaximal, characteristic, complemented
8#11748777C211yesmaximal, characteristic, complemented
9#11748719C211yesmaximal, characteristic, complemented
10#11748682C212yesmaximal, complemented
11#11748675C212yesmaximal, complemented
12#10614055—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C5×(C2×D3)⋊C4C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C4×C5×D12C418yescomplemented
22C2×C3×C4⋊Dic5C2212yes—
23C2×Dic3⋊Dic5C2212yes—
24C2×(C2×D3)⋊Dic5C2212yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×Dic3×Dic5C2212yes—
28#91115C2211yescharacteristic
29#91115C2212yes—
30#91115C2212yes—
31#91115C2211yescharacteristic
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#74226—51nomaximal, Hall
38C2×C4×C5×D4—31no—
39#65509—32no—
40#65501—31no—
41#65500—31no—
42C4×C22⋊Dic5—31no—
43C2×#3963—31no—
44#65270—32no—
45#65240—32no—
46#65239—32no—
47#65226—31no—
48#65225D311yescharacteristic, complemented
49C23×C5×D3C2311yescharacteristic
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C2×C5×D12—24no—
59C2×C5×D12C2×C414yes—
60C2×C4×C5×D3—42no—
61C2×C4×C5×D3—42no—
62C2×C4×C5×D3C2×C414yes—
63C2×C4×C5×D3C2×C414yescomplemented
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2312yes—
66C2×D3×Dic5—24no—
67C2×D3×Dic5—42no—
68C2×D3×Dic5—42no—
69C3×C42×C5C2×C414yescomplemented
70C5×(C2×D3)⋊C4C2×C414yes—
71C5×(C2×D3)⋊C4C2×C414yescomplemented
72C5×C4⋊Dic3C2×C414yescomplemented
73C3×C4⋊Dic5—42no—
74Dic3⋊Dic5—42no—
75(C2×D3)⋊Dic5—24no—
76(C2×D3)⋊Dic5—42no—
77(C2×D3)⋊Dic5—42no—
78Dic3×Dic5—42no—
79C2×C4×D12D511yescharacteristic
80C3×#382—51no—
81#4990—52no—
82#4989—52no—
83#4937—51no—
84#4667—51no—
85#4666—51no—
86#4665—52no—
87#4664—51no—
88D3×#95—51no—
89#4653—52no—
90C22×C5×D4—31no—
91C23×C4×C5—31no—
92C23×C4×C5—31no—
93C23×Dic5—32no—
94C4×C5×D4—38no—
95C2×C5×C4⋊C4—31no—
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C42×C5C2×D311yescharacteristic
99C2×C22⋊Dic5—32no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5—32no—
102C2×C4⋊Dic5—32no—
103C2×C4⋊Dic5C2×D312yes—
104C2×C4×Dic5—32no—
105#3963—32no—
106#3963—31no—
107#3963—31no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963C2×D311yescharacteristic
112#3963C2×D311yescharacteristic
113#3963C2×D312yes—
114#2318—151noSylow
115C23×C3×C5C2411yescharacteristic
116C22×C5×D3—21no—
117C22×C5×D3—22no—
118C22×C5×D3—21no—
119C22×C5×D3—22no—
120C22×C5×D3—21no—
121C22×C5×D3—22no—
122C22×C5×D3—21no—
123C22×C5×D3C22×C412yes—
124C22×C5×D3C22×C412yes—
125C22×C5×D3#4114yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3C22×C412yes—
142C2×C5×Dic3C22×C412yes—
143C5×D12—28no—
144C4×C5×D3—44no—
145C4×C5×D3—44no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152D3×Dic5—48no—
153C22×D12C2×D511yescharacteristic
154C22×C4×D3—52no—
155C22×C4×D3C2×D511yescharacteristic
156C22×C4×D3C2×D511yescharacteristic
157C2×C3×C4⋊C4—52no—
158C2×C3×C42C2×D511yescharacteristic
159C2×(C2×D3)⋊C4—52no—
160C2×(C2×D3)⋊C4—52no—
161C2×(C2×D3)⋊C4—52no—
162C2×(C2×D3)⋊C4C2×D511yescharacteristic
163C2×(C2×D3)⋊C4C2×D511yescharacteristic
164C2×C4⋊Dic3C2×D511yescharacteristic
165C2×Dic3⋊C4—52no—
166C2×C4×Dic3—52no—
167C4×D12Dic518yescomplemented
168C3×#95—52no—
169C3×#95—51no—
170C3×#95—51no—
171C3⋊#95—52no—
172C3⋊#95—51no—
173C3⋊#95—51no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C24×C5—31no—
178C24×C5—31no—
179C2×C5×D4—34no—
180C2×C5×D4—64no—
181C22×C4×C5—31no—
182C22×C4×C5—31no—
183C22×C4×C5—34no—
184C22×C4×C5—34no—
185C22×C4×C5—122no—
186C22×C4×C5—122no—
187C22×C4×C5C22×D311yescharacteristic
188C22×C4×C5C22×D311yescharacteristic
189C22×C4×C5C22×D311yescharacteristic
190C22×Dic5—32no—
191C22×Dic5—32no—
192C22×Dic5—64no—
193C22×Dic5—122no—
194C22×Dic5—122no—
195C22×Dic5C22×D312yes—
196C22×Dic5C22×D312yes—
197C5×C4⋊C4—34no—
198C5×C22⋊C4—34no—
199C5×C22⋊C4—34no—
200C42×C5C4×D314yescomplemented
201C22⋊Dic5—64no—
202C22⋊Dic5—122no—
203C22⋊Dic5—122no—
204C4⋊Dic5—42no—
205C4⋊Dic5—122no—
206C4×Dic5—122no—
207C2×C4×D4—31no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—151no—
213#382—51no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—151no—
217C2×#95—151no—
218C22×C3×C5C23×C411yescharacteristic
219C22×C3×C5C2×#4112yes—
220C22×C3×C5H(5,𝔽2)12yes—
221C22×C3×C5H(5,𝔽2)11yescharacteristic
222C22×C3×C52−1+411yescharacteristic
223C2×C5×D3—22no—
224C2×C5×D3—22no—
225C2×C5×D3—24no—
226C2×C5×D3—24no—
227C2×C5×D3—22no—
228C2×C5×D3—22no—
229C2×C5×D3—22no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3#11714yes—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—22no—
236Dic15—42no—
237Dic15—42no—
238C3×Dic5—42no—
239C3×Dic5—42no—
240C5×Dic3—22no—
241C5×Dic3—22no—
242C23×D3C22×D511yescharacteristic
243C23×D3C22×D511yescharacteristic
244C22×C3×C4—52no—
245C22×C3×C4—52no—
246C22×C3×C4C22×D511yescharacteristic
247C22×C3×C4C22×D511yescharacteristic
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—52no—
250C22×Dic3—52no—
251C22×Dic3C22×D511yescharacteristic
252C22×Dic3C22×D511yescharacteristic
253C2×D12—24no—
254C2×D12C2×Dic514yes—
255C2×C4×D3—42no—
256C2×C4×D3—42no—
257C2×C4×D3—104no—
258C2×C4×D3—202no—
259C2×C4×D3—202no—
260C2×C4×D3C2×Dic514yes—
261C2×C4×D3C2×Dic514yescomplemented
262C3×C4⋊C4—202no—
263C3×C42C2×Dic514yescomplemented
264(C2×D3)⋊C4—104no—
265(C2×D3)⋊C4—202no—
266(C2×D3)⋊C4—202no—
267(C2×D3)⋊C4C2×Dic514yes—
268(C2×D3)⋊C4C2×Dic514yescomplemented
269C4⋊Dic3C2×Dic514yescomplemented
270Dic3⋊C4—202no—
271C4×Dic3—202no—
272C23×C5—32no—
273C23×C5—34no—
274C23×C5—32no—
275C23×C5—61no—
276C23×C5—61no—
277C23×C5—62no—
278C23×C5—61no—
279C23×C5—61no—
280C23×C5—62no—
281C23×C5—62no—
282C23×C5C23×D311yescharacteristic
283C5×D4—68no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—32no—
289C2×C4×C5—32no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—124no—
293C2×C4×C5—124no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5C2×C4×D312yes—
296C2×C4×C5C2×C4×D312yes—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5—62no—
309C2×Dic5—128no—
310C22×D4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—152no—
314C4×D4—38no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—52no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—31no—
320C2×C22⋊C4—152no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C42—152no—
324C2×C42D3×D511yescharacteristic
325#95—51no—
326#95—51no—
327#95—52no—
328#95—152no—
329#95—152no—
330#95—151no—
331#95—151no—
332#95—152no—
333#95—152no—
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#51811yescharacteristic
336C2×C3×C5#52011yescharacteristic
337C2×C3×C5#53812yes—
338C2×C3×C5#53912yes—
339C5×D3—24no—
340C5×D3—42no—
341C23×C3C23×D511yescharacteristic
342C22×D3—22no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3#70914yes—
350C22×D3C22×Dic512yes—
351C22×D3C22×Dic512yes—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4C22×Dic512yes—
363C2×C3×C4C22×Dic512yes—
364C2×C3×C4C22×Dic512yes—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—102no—
368C2×Dic3—102no—
369C2×Dic3—102no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3C22×Dic512yes—
374C2×Dic3C22×Dic512yes—
375D12—28no—
376C4×D3—44no—
377C4×D3—44no—
378C4×D3—208no—
379C22×C5—34no—
380C22×C5—64no—
381C22×C5—64no—
382C22×C5—62no—
383C22×C5—62no—
384C22×C5—62no—
385C22×C5—62no—
386C22×C5—62no—
387C22×C5—122no—
388C22×C5—122no—
389C22×C5C22×C4×D311yescharacteristic
390C22×C5#100411yescharacteristic
391C22×C5#100711yescharacteristic
392C22×C5D3×#4112yes—
393C22×C5#100912yes—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—62no—
398C4×C5—62no—
399Dic5—42no—
400Dic5—42no—
401Dic5—122no—
402Dic5—122no—
403C24—31no—
404C24—31no—
405C2×D4—34no—
406C2×D4—64no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—34no—
410C22×C4—34no—
411C22×C4—52no—
412C22×C4—52no—
413C22×C4—122no—
414C22×C4—122no—
415C22×C4—152no—
416C22×C4—152no—
417C22×C4—304no—
418C22×C4—602no—
419C22×C4—602no—
420C22×C4C2×D3×D511yescharacteristic
421C22×C4C2×D3×D511yescharacteristic
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—34no—
424C4⋊C4—202no—
425C4⋊C4—602no—
426C22⋊C4—34no—
427C22⋊C4—34no—
428C22⋊C4—304no—
429C22⋊C4—602no—
430C22⋊C4—602no—
431C42—602no—
432C42D3×Dic514yescomplemented
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3C2×#70912yes—
435C22×C3#414412yes—
436C22×C3#414911yescharacteristic
437C22×C3#415011yescharacteristic
438C22×C3C23×Dic511yescharacteristic
439C2×D3—22no—
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—22no—
443C2×D3—22no—
444C2×D3—22no—
445C2×D3—22no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3#407214yes—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—202no—
453C3×C4—202no—
454Dic3—22no—
455Dic3—22no—
456Dic3—202no—
457Dic3—202no—
458C2×C5—64no—
459C2×C5—122no—
460C2×C5#550411yescharacteristic
461C2×C5D3×#11711yescharacteristic
462C2×C5#552111yescharacteristic
463C2×C5#567812yes—
464C2×C5#569212yes—
465C23—34no—
466C23—32no—
467C23—32no—
468C23—61no—
469C23—61no—
470C23—62no—
471C23—61no—
472C23—62no—
473C23—61no—
474C23—62no—
475C23C22×D3×D511yescharacteristic
476D4—68no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—124no—
492C2×C4—124no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—608no—
500C2×C4C2×D3×Dic512yes—
501C2×C4C2×D3×Dic512yes—
502C2×C4C2×D3×Dic512yes—
503C2×C3#6589412yes—
504C2×C3#6589812yes—
505C2×C3C2×#407211yescharacteristic
506C2×C3#6613211yescharacteristic
507C2×C3#6616111yescharacteristic
508D3—24no—
509D3—42no—
510C5#7422611yescharacteristic, complemented, Sylow
511C22—34no—
512C22—62no—
513C22—64no—
514C22—64no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—122no—
520C22—122no—
521C22#9200411yescharacteristic
522C22D3×#70912yes—
523C22#9201711yescharacteristic
524C22#9201812yes—
525C22C22×D3×Dic511yescharacteristic
526C4—22no—
527C4—22no—
528C4—22no—
529C4—62no—
530C4—62no—
531C4—202no—
532C4—202no—
533C4—602no—
534C4—602no—
535C3#1061405511yescharacteristic, complemented, Sylow
536C2—64no—
537C2—122no—
538C2#1175261112yes—
539C2#1175276312yes—
540C2D3×#407211yescharacteristic
541C2#1175449211yescharacteristic
542C2#1175450311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2318
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751038C2semidirect
3. C3×#65225C2semidirect
5. #11748897C2semidirect
6. D3×#3963C2semidirect
7. #11748782C2semidirect
8. #11748777C2semidirect
9. #11748719C2semidirect
10. #11748682C2semidirect
11. #11748675C2semidirect
21. C4×C5×D12C4semidirect
48. #65225D3semidirect
63. C2×C4×C5×D3C2×C4semidirect
69. C3×C42×C5C2×C4semidirect
71. C5×(C2×D3)⋊C4C2×C4semidirect
72. C5×C4⋊Dic3C2×C4semidirect
167. C4×D12Dic5semidirect
200. C42×C5C4×D3semidirect
261. C2×C4×D3C2×Dic5semidirect
263. C3×C42C2×Dic5semidirect
268. (C2×D3)⋊C4C2×Dic5semidirect
269. C4⋊Dic3C2×Dic5semidirect
432. C42D3×Dic5semidirect
433. C3×C5#2318semidirect
510. C5#74226semidirect
535. C3#10614055semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D122
#117510382
C3×#652252
#117489012
#117488972
D3×#39632
#117487822
#117487772
#117487192
#117486822
#117486752
#106140553
#742265