Finite Group Databasebeta

← #14323031

Subgroups — #14323031

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×#67C211yesmaximal, characteristic
2C2×#91115C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4#11749517C212yesmaximal, complemented
5#11749501C212yesmaximal
6#11748782C211yesmaximal, characteristic, complemented
7#11748777C211yesmaximal, characteristic, complemented
8#11748747C212yesmaximal, complemented
9#11748618C211yesmaximal, characteristic, complemented
10#11748600C211yesmaximal, characteristic, complemented
11#11748573C212yesmaximal, complemented
12#10614055—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2212yes—
15C22×C5×#67C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C2×C5×#217C2211yescharacteristic
18C4×C5×#67C418yescomplemented
19C2×C5×(C2×D3)⋊C4C2211yescharacteristic
20C2×C5×Dic3⋊C4C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C4×Dic5C2212yes—
24C2×Dic3⋊Dic5C2212yes—
25C2×Dic3⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28#91115C2211yescharacteristic
29#91115C2212yes—
30#91115C2211yescharacteristic
31C3×#3963C2211yescharacteristic
32C3×#3963C2211yescharacteristic
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73568—51nomaximal, Hall
38C2×C4×C5×D4—31no—
39#65509—32no—
40#65501—31no—
41#65500—31no—
42C4×C22⋊Dic5D311yescharacteristic, complemented
43C2×#3963—31no—
44#65270—32no—
45#65240—32no—
46#65239—32no—
47#65226—31no—
48#65225—31no—
49C24×C3×C5C2311yescharacteristic
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—24no—
56C22×Dic15—42no—
57C22×Dic15—42no—
58C22×Dic15C2312yes—
59C22×Dic15C2312yes—
60C2×C5×#67—24no—
61C2×C5×#67C2×C414yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—42no—
66C2×C4×C5×D3C2×C414yescomplemented
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2312yes—
69C5×#217C2×C414yes—
70C5×(C2×D3)⋊C4C2×C414yescomplemented
71C5×Dic3⋊C4C2×C414yescomplemented
72C4×C5×Dic3C2×C414yescomplemented
73C3×C22⋊Dic5—24no—
74C3×C4×Dic5—42no—
75Dic3⋊Dic5—42no—
76Dic3⋊Dic5—42no—
77(C2×D3)⋊Dic5—42no—
78(C2×D3)⋊Dic5—42no—
79C2×C4×#67D511yescharacteristic
80C3×C4×C22⋊C4—51no—
81C2×C3⋊#95—51no—
82#4958—52no—
83#4946—52no—
84#4940—52no—
85#4933—52no—
86#4667—51no—
87#4664—51no—
88#4651—51no—
89#4650—51no—
90C22×C5×D4—31no—
91C23×C4×C5—31no—
92C23×C4×C5C2×D311yescharacteristic
93C23×Dic5—32no—
94C4×C5×D4—38no—
95C2×C5×C4⋊C4—31no—
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C42×C5—31no—
99C2×C22⋊Dic5—32no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5C2×D312yes—
102C2×C4⋊Dic5—32no—
103C2×C4⋊Dic5—32no—
104C2×C4×Dic5C2×D312yes—
105#3963—31no—
106#3963—31no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963C2×D311yescharacteristic
113#3963C2×D311yescharacteristic
114#2318—151noSylow
115C23×C3×C5—21no—
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5#4114yes—
120C23×C3×C5C2411yescharacteristic
121C22×C5×D3—22no—
122C22×C5×D3—21no—
123C22×C5×D3—22no—
124C22×C5×D3—21no—
125C22×C5×D3C22×C412yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—44no—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—48no—
138C5×#67—28no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3C22×C412yes—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C4×C5×D3—44no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C23×C3×C4C2×D511yescharacteristic
154C22×#67C2×D511yescharacteristic
155C23×Dic3—52no—
156C22×C4×D3C2×D511yescharacteristic
157C2×C3×C22⋊C4—52no—
158C2×C3×C42—52no—
159C2×#217C2×D511yescharacteristic
160C4×#67Dic518yescomplemented
161C2×(C2×D3)⋊C4—52no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4C2×D511yescharacteristic
164C2×Dic3⋊C4—52no—
165C2×Dic3⋊C4—52no—
166C2×Dic3⋊C4C2×D511yescharacteristic
167C2×C4×Dic3C2×D511yescharacteristic
168C3×#95—51no—
169C3×#95—51no—
170C3⋊#95—51no—
171C3⋊#95—51no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C24×C5—31no—
178C24×C5C22×D311yescharacteristic
179C2×C5×D4—34no—
180C2×C5×D4—64no—
181C22×C4×C5—31no—
182C22×C4×C5—31no—
183C22×C4×C5—31no—
184C22×C4×C5—34no—
185C22×C4×C5—42no—
186C22×C4×C5—122no—
187C22×C4×C5C4×D314yes—
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×C5—34no—
201C22⋊Dic5—24no—
202C22⋊Dic5—122no—
203C22⋊Dic5—122no—
204C4⋊Dic5—122no—
205C4⋊Dic5—122no—
206C4×Dic5—42no—
207C2×C4×D4—31no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—151no—
213#382—151no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—51no—
217C2×#95—151no—
218C22×C3×C5—22no—
219C22×C3×C5—22no—
220C22×C3×C5—24no—
221C22×C3×C5—24no—
222C22×C3×C5#11714yes—
223C22×C3×C5C23×C411yescharacteristic
224C22×C3×C5C2×#4112yes—
225C22×C3×C5H(5,𝔽2)12yes—
226C22×C3×C5H(5,𝔽2)11yescharacteristic
227C22×C3×C52−1+411yescharacteristic
228C2×C5×D3—22no—
229C2×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235Dic15—42no—
236Dic15—42no—
237C3×Dic5—42no—
238C3×Dic5—42no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C5×Dic3—22no—
242C24×C3C22×D511yescharacteristic
243C23×D3C22×D511yescharacteristic
244C22×C3×C4—42no—
245C22×C3×C4—52no—
246C22×C3×C4—52no—
247C22×C3×C4C2×Dic514yes—
248C22×C3×C4C22×D511yescharacteristic
249C22×C3×C4C22×D511yescharacteristic
250C2×#67—24no—
251C2×#67C2×Dic514yes—
252C22×Dic3—52no—
253C22×Dic3—52no—
254C22×Dic3—104no—
255C22×Dic3—202no—
256C22×Dic3—202no—
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D511yescharacteristic
259C22×Dic3C22×D511yescharacteristic
260C2×C4×D3—42no—
261C2×C4×D3C2×Dic514yescomplemented
262C3×C22⋊C4—104no—
263C3×C42—202no—
264#217C2×Dic514yes—
265(C2×D3)⋊C4—202no—
266(C2×D3)⋊C4—202no—
267(C2×D3)⋊C4C2×Dic514yescomplemented
268Dic3⋊C4—202no—
269Dic3⋊C4—202no—
270Dic3⋊C4C2×Dic514yescomplemented
271C4×Dic3C2×Dic514yescomplemented
272C23×C5—22no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—32no—
276C23×C5—62no—
277C23×C5—62no—
278C23×C5—61no—
279C23×C5—61no—
280C23×C5C2×C4×D312yes—
281C23×C5#23514yes—
282C23×C5C23×D311yescharacteristic
283C5×D4—68no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—32no—
287C2×C4×C5—32no—
288C2×C4×C5—32no—
289C2×C4×C5—44no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5—124no—
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—152no—
313C23×C4D3×D511yescharacteristic
314C4×D4—38no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—152no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—31no—
320C2×C22⋊C4—52no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C42—31no—
324C2×C42—52no—
325#95—51no—
326#95—51no—
327#95—152no—
328#95—152no—
329#95—152no—
330#95—152no—
331#95—151no—
332#95—151no—
333#95—152no—
334C2×C3×C5—24no—
335C2×C3×C5C2×#11711yescharacteristic
336C2×C3×C5#51811yescharacteristic
337C2×C3×C5#52011yescharacteristic
338C2×C3×C5#53812yes—
339C2×C3×C5#53912yes—
340C5×D3—42no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3#70914yes—
345C23×C3C22×Dic512yes—
346C23×C3C23×D511yescharacteristic
347C22×D3—22no—
348C22×D3—22no—
349C22×D3—21no—
350C22×D3—21no—
351C22×D3C22×Dic512yes—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—44no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4C22×Dic512yes—
362C2×C3×C4C22×Dic512yes—
363#67—28no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—102no—
369C2×Dic3—102no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—208no—
375C2×Dic3C22×Dic512yes—
376C2×Dic3C22×Dic512yes—
377C2×Dic3C22×Dic512yes—
378C4×D3—44no—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5—24no—
382C22×C5—24no—
383C22×C5—62no—
384C22×C5—62no—
385C22×C5—62no—
386C22×C5—122no—
387C22×C5—122no—
388C22×C5#87214yes—
389C22×C5C22×C4×D311yescharacteristic
390C22×C5C2×#23512yes—
391C22×C5#100412yes—
392C22×C5#100911yescharacteristic
393C22×C5#101011yescharacteristic
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—62no—
399Dic5—42no—
400Dic5—42no—
401Dic5—122no—
402Dic5—122no—
403C24—31no—
404C24C2×D3×D511yescharacteristic
405C2×D4—34no—
406C2×D4—64no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—34no—
411C22×C4—42no—
412C22×C4—52no—
413C22×C4—52no—
414C22×C4—122no—
415C22×C4—152no—
416C22×C4—152no—
417C22×C4—304no—
418C22×C4—602no—
419C22×C4—602no—
420C22×C4D3×Dic514yes—
421C22×C4C2×D3×D511yescharacteristic
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—34no—
424C4⋊C4—602no—
425C4⋊C4—602no—
426C22⋊C4—34no—
427C22⋊C4—34no—
428C22⋊C4—104no—
429C22⋊C4—602no—
430C22⋊C4—602no—
431C42—34no—
432C42—202no—
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3—22no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—22no—
438C22×C3#407214yes—
439C22×C3C2×#70912yes—
440C22×C3#414412yes—
441C22×C3#414911yescharacteristic
442C22×C3#415011yescharacteristic
443C22×C3C23×Dic511yescharacteristic
444C2×D3—22no—
445C2×D3—22no—
446C2×D3—22no—
447C2×D3—42no—
448C2×D3—42no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—202no—
452C3×C4—202no—
453Dic3—22no—
454Dic3—22no—
455Dic3—22no—
456Dic3—202no—
457Dic3—202no—
458C2×C5—24no—
459C2×C5—122no—
460C2×C5C2×#87211yescharacteristic
461C2×C5#548611yescharacteristic
462C2×C5#552311yescharacteristic
463C2×C5#556012yes—
464C2×C5#556412yes—
465C23—21no—
466C23—21no—
467C23—22no—
468C23—32no—
469C23—61no—
470C23—62no—
471C23—61no—
472C23—62no—
473C23#677114yes—
474C23C2×D3×Dic512yes—
475C23C22×D3×D511yescharacteristic
476D4—68no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—44no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—124no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—608no—
501C2×C4C2×D3×Dic512yes—
502C2×C4C2×D3×Dic512yes—
503C2×C3—24no—
504C2×C3#6589412yes—
505C2×C3#6589812yes—
506C2×C3C2×#407211yescharacteristic
507C2×C3#6613211yescharacteristic
508C2×C3#6616111yescharacteristic
509D3—42no—
510C5#7356811yescharacteristic, complemented, Sylow
511C22—22no—
512C22—24no—
513C22—24no—
514C22—22no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22—122no—
519C22—122no—
520C22#9137114yes—
521C22#9200111yescharacteristic
522C22C2×#677112yes—
523C22#9201911yescharacteristic
524C22C22×D3×Dic511yescharacteristic
525C22#9204912yes—
526C4—22no—
527C4—22no—
528C4—62no—
529C4—62no—
530C4—62no—
531C4—202no—
532C4—202no—
533C4—602no—
534C4—602no—
535C3#1061405511yescharacteristic, complemented, Sylow
536C2—24no—
537C2—122no—
538C2C2×#9137111yescharacteristic
539C2#1175451311yescharacteristic
540C2#1175459612yes—
541C2#1175459912yes—
542C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2318
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91115C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
4. #11749517C2semidirect
6. #11748782C2semidirect
7. #11748777C2semidirect
8. #11748747C2semidirect
9. #11748618C2semidirect
10. #11748600C2semidirect
11. #11748573C2semidirect
18. C4×C5×#67C4semidirect
42. C4×C22⋊Dic5D3semidirect
66. C2×C4×C5×D3C2×C4semidirect
70. C5×(C2×D3)⋊C4C2×C4semidirect
71. C5×Dic3⋊C4C2×C4semidirect
72. C4×C5×Dic3C2×C4semidirect
160. C4×#67Dic5semidirect
261. C2×C4×D3C2×Dic5semidirect
267. (C2×D3)⋊C4C2×Dic5semidirect
270. Dic3⋊C4C2×Dic5semidirect
271. C4×Dic3C2×Dic5semidirect
433. C3×C5#2318semidirect
510. C5#73568semidirect
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×#672
C2×#911152
C3×C4×C22⋊Dic52
#117495172
#117495012
#117487822
#117487772
#117487472
#117486182
#117486002
#117485732
#106140553
#735685