Finite Group Databasebeta

← #14323621

Subgroups — #14323621

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91824C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic
3C22×#6669C211yesmaximal, characteristic, complemented
4C5×#5220C211yesmaximal, characteristic
5#11749512C211yesmaximal, characteristic, complemented
6#11749508C212yesmaximal, complemented
7#11749480C212yesmaximal, complemented
8Dic5×#217C211yesmaximal, characteristic, complemented
9#11749473C211yesmaximal, characteristic, complemented
10#11748824C212yesmaximal, complemented
11#11748676C212yesmaximal, complemented
12#10606395—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C2×#6719C2211yescharacteristic
19C2×#6719C2212yes—
20#91824C418yescomplemented
21C2×#6712C2212yes—
22C2×C5×#217C2211yescharacteristic
23C2×C5×#217C2212yes—
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C3×D4×Dic5—24no—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×#6669—24no—
30C2×#6669C2212yes—
31C2×#6669C2212yes—
32C2×#6669C2212yes—
33C2×Dic3×Dic5C2212yes—
34C5×C3⋊#95C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82326—51nomaximal, Hall
40C2×#4081—31no—
41C2×D4×Dic5D311yescharacteristic
42C22×#683—31no—
43C5×#386—31no—
44#65499—31no—
45#65235—32no—
46#65233—32no—
47#65232—31no—
48C22⋊C4×Dic5—31no—
49#64941—32no—
50#64936—32no—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—22no—
58C22×Dic15—22no—
59C22×Dic15C2×C414yescomplemented
60C22×Dic15C2312yes—
61C22×Dic15C2312yes—
62C22×C5×Dic3—22no—
63C22×C5×Dic3—42no—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2312yes—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—42no—
68C22×C3×Dic5—42no—
69C22×C3×Dic5D414yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74#6719C2×C414yescomplemented
75#6719C2×C418yescomplemented
76#6712C2×C418yescomplemented
77C5×#217—22no—
78C5×#217—42no—
79C3×C22⋊Dic5—22no—
80C3×C22⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82C3×C4×Dic5—22no—
83#6669—24no—
84#6669—24no—
85#6669—42no—
86Dic3×Dic5—42no—
87C2×C3×C4×D4—51no—
88C2×#935—51no—
89C22×Dic3⋊C4—51no—
90#5220D511yescharacteristic
91#5210—52no—
92C4×#217—51no—
93#4976—52no—
94#4946—51no—
95#4945—52no—
96#4943—51no—
97#4933—52no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5—31no—
100C23×Dic5—31no—
101C23×Dic5C2×D311yescharacteristic
102C23×Dic5C2×D311yescharacteristic
103C2×C5×C22⋊C4—31no—
104C2×C5×C22⋊C4—32no—
105C2×C22⋊Dic5—31no—
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5C2×D311yescharacteristic
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4081—38no—
110D4×Dic5—24no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—32no—
113C2×#683—32no—
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—64no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5C2×D311yescharacteristic
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2322—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5C22×C412yes—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5#4112yes—
135C23×C3×C5C2411yescharacteristic
136C3×C5×D4—28no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C412yes—
140C2×Dic15—28no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15C22×C414yes—
146C2×Dic15C22×C414yes—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—44no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—44no—
161C2×C3×Dic5—44no—
162C2×C3×Dic5C2×D412yes—
163C2×C3×Dic5C2×D412yes—
164C22×C3×D4C2×D511yescharacteristic
165C23×C3×C4—51no—
166C23×C3×C4—51no—
167C23×Dic3—51no—
168C23×Dic3C2×D511yescharacteristic
169C3×C4×D4—104no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C22⋊C4—51no—
172C2×C3×C22⋊C4—51no—
173C2×C3×C42—51no—
174C2×#217—52no—
175C2×#217—51no—
176C2×#217C2×D511yescharacteristic
177C2×#217C2×D512yes—
178#935—58no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4—52no—
181C2×Dic3⋊C4—52no—
182C2×Dic3⋊C4—52no—
183C2×Dic3⋊C4—104no—
184C2×C4×Dic3—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95C2×D512yes—
190C24×C5C22×D311yescharacteristic
191C24×C5C22×D311yescharacteristic
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4C4×D314yes—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5—62no—
198C22×C4×C5—122no—
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—22no—
201C22×Dic5—34no—
202C22×Dic5—32no—
203C22×Dic5—32no—
204C22×Dic5—42no—
205C22×Dic5—42no—
206C22×Dic5—62no—
207C22×Dic5—62no—
208C22×Dic5#6714yes—
209C22×Dic5C22×D311yescharacteristic
210C22×Dic5C22×D311yescharacteristic
211C22×Dic5C22×D311yescharacteristic
212C22×Dic5C22×D311yescharacteristic
213C5×C22⋊C4—62no—
214C5×C22⋊C4—122no—
215C22⋊Dic5—22no—
216C22⋊Dic5—22no—
217C22⋊Dic5—34no—
218C22⋊Dic5—38no—
219C4⋊Dic5—22no—
220#683—38no—
221#683—64no—
222#683—64no—
223#683—122no—
224C4×Dic5—22no—
225C4×Dic5—122no—
226C2×#123—151no—
227C2×C4×D4—51no—
228C22×C4⋊C4—151no—
229#389—152no—
230#388—152no—
231#387—152no—
232#386—31no—
233#385—152no—
234#385—151no—
235#381—151no—
236C4×C22⋊C4—151no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—24no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C4×D414yes—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D411yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5H(5,𝔽2)12yes—
251C22×C3×C52−1+412yes—
252C3×C4×C5—22no—
253Dic15—24no—
254Dic15—24no—
255C3×Dic5—22no—
256C3×Dic5—22no—
257C3×Dic5—41no—
258C3×Dic5—41no—
259C5×Dic3—42no—
260C5×Dic3—42no—
261C24×C3C22×D511yescharacteristic
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4C4×D514yes—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C22×C3×C4—54no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—102no—
272C22×C3×C4—202no—
273C22×C3×C4—202no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—22no—
276C22×Dic3—42no—
277C22×Dic3—54no—
278C22×Dic3—52no—
279C22×Dic3—52no—
280C22×Dic3—102no—
281C22×Dic3—102no—
282C22×Dic3C22×D512yes—
283C22×Dic3C22×D512yes—
284C3×C4⋊C4—102no—
285C3×C22⋊C4—102no—
286C3×C22⋊C4—102no—
287C3×C42—102no—
288#217—22no—
289#217—42no—
290#217—54no—
291#217—58no—
292Dic3⋊C4—58no—
293Dic3⋊C4—104no—
294Dic3⋊C4—104no—
295Dic3⋊C4—202no—
296C4×Dic3—202no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5—21no—
303C23×C5C2×C4×D312yes—
304C23×C5C2×C4×D312yes—
305C23×C5#23512yes—
306C23×C5C2×#6712yes—
307C23×C5C23×D311yescharacteristic
308C5×D4—28no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—124no—
318C2×C4×C5C2×C4×D312yes—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—34no—
326C2×Dic5—34no—
327C2×Dic5—44no—
328C2×Dic5—44no—
329C2×Dic5—68no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5C2×#6712yes—
335C2×Dic5C2×#6712yes—
336C22×D4D3×D511yescharacteristic
337C23×C4—31no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—151no—
341#123—158no—
342C4×D4—104no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C4⋊C4—152no—
348C2×C4⋊C4—304no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—152no—
355C2×C42—51no—
356C2×C42—152no—
357#95—32no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5#52012yes—
366C2×C3×C5#53411yescharacteristic
367C2×C3×C5#53611yescharacteristic
368C2×C3×C5#53912yes—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3C2×C4×D512yes—
376C23×C3C2×C4×D512yes—
377C23×C3D4×D512yes—
378C23×C3#71112yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—28no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—52no—
384C2×C3×C4—52no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—101no—
388C2×C3×C4—101no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—204no—
392C2×C3×C4—204no—
393C2×C3×C4C2×C4×D512yes—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—44no—
401C2×Dic3—54no—
402C2×Dic3—54no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—108no—
408C22×C5—24no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—22no—
412C22×C5—22no—
413C22×C5—24no—
414C22×C5—41no—
415C22×C5—42no—
416C22×C5—41no—
417C22×C5C4×#6714yes—
418C22×C5C22×C4×D311yescharacteristic
419C22×C5C2×#23511yescharacteristic
420C22×C5#100412yes—
421C22×C5#101012yes—
422C22×C5C22×#6711yescharacteristic
423C4×C5—22no—
424C4×C5—122no—
425C4×C5—122no—
426Dic5—22no—
427Dic5—22no—
428Dic5—41no—
429Dic5—41no—
430Dic5—64no—
431Dic5—64no—
432C24C2×D3×D511yescharacteristic
433C24C2×D3×D511yescharacteristic
434C2×D4—22no—
435C2×D4—22no—
436C2×D4#120014yes—
437C22×C4—32no—
438C22×C4—32no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—54no—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—62no—
445C22×C4—102no—
446C22×C4—122no—
447C22×C4—154no—
448C22×C4—152no—
449C22×C4—152no—
450C22×C4—202no—
451C22×C4—202no—
452C22×C4—302no—
453C22×C4—302no—
454C22×C4C2×D3×D511yescharacteristic
455C4⋊C4—102no—
456C4⋊C4—158no—
457C4⋊C4—304no—
458C4⋊C4—304no—
459C4⋊C4—602no—
460C22⋊C4—62no—
461C22⋊C4—102no—
462C22⋊C4—102no—
463C22⋊C4—122no—
464C22⋊C4—154no—
465C22⋊C4—158no—
466C42—102no—
467C42—602no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3#402714yes—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×D4×D511yescharacteristic
481C22×C3C2×#71111yescharacteristic
482C22×C3#414412yes—
483C22×C3#415012yes—
484C3×C4—22no—
485C3×C4—102no—
486C3×C4—102no—
487C3×C4—201no—
488C3×C4—201no—
489Dic3—42no—
490Dic3—42no—
491Dic3—104no—
492Dic3—104no—
493C2×C5—24no—
494C2×C5—42no—
495C2×C5#554612yes—
496C2×C5#556412yes—
497C2×C5C2×C4×#6711yescharacteristic
498C2×C5#580411yescharacteristic
499C2×C5#582511yescharacteristic
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—21no—
505C23—21no—
506C23#678212yes—
507C23C2×#120012yes—
508C23C2×#120012yes—
509C23D5×#6712yes—
510C23C22×D3×D511yescharacteristic
511D4—28no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—52no—
515C2×C4—52no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—124no—
529C2×C4—154no—
530C2×C4—154no—
531C2×C4—204no—
532C2×C4—204no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—308no—
538C2×C4C2×#120012yes—
539C2×C3—24no—
540C2×C3—42no—
541C2×C3C2×#402711yescharacteristic
542C2×C3#6588012yes—
543C2×C3#6592311yescharacteristic
544C2×C3#6593612yes—
545C2×C3#6598211yescharacteristic
546C5#8232611yescharacteristic, complemented, Sylow
547C22—24no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—24no—
553C22—42no—
554C22—41no—
555C22—41no—
556C22#9155214yes—
557C22#9202012yes—
558C22#9202512yes—
559C22C2×#678211yescharacteristic
560C22C22×#120011yescharacteristic
561C22C2×D5×#6711yescharacteristic
562C4—22no—
563C4—102no—
564C4—102no—
565C4—122no—
566C4—122no—
567C4—201no—
568C4—201no—
569C4—304no—
570C4—304no—
571C3#1060639511yescharacteristic, complemented, Sylow
572C2—24no—
573C2—42no—
574C2#1175491512yes—
575C2#1175491612yes—
576C2#1175493211yescharacteristic
577C2#1175500711yescharacteristic
578C2C2×#9155211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
Fitting, prime radicalC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C22×#6669C2semidirect
5. #11749512C2semidirect
6. #11749508C2semidirect
7. #11749480C2semidirect
8. Dic5×#217C2semidirect
9. #11749473C2semidirect
10. #11748824C2semidirect
11. #11748676C2semidirect
20. #91824C4semidirect
59. C22×Dic15C2×C4semidirect
74. #6719C2×C4semidirect
75. #6719C2×C4semidirect
76. #6712C2×C4semidirect
468. C3×C5#2322semidirect
546. C5#82326semidirect
571. C3#10606395semidirect

Maximal subgroups

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

subgroupindex
C2×#918242
C2×C3×D4×Dic52
C22×#66692
C5×#52202
#117495122
#117495082
#117494802
Dic5×#2172
#117494732
#117488242
#117486762
#106063953
#823265