Finite Group Databasebeta

← #14323627

Subgroups — #14323627

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×Dic5×#67C211yesmaximal, characteristic
2C22×#6669C211yesmaximal, characteristic, complemented
3C2×#91543C211yesmaximal, characteristic
4#11751044C211yesmaximal, characteristic, complemented
5C5×#4958C211yesmaximal, characteristic
6C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
7#11749511C211yesmaximal, characteristic, complemented
8#11748893C212yesmaximal, complemented
9#11748802C212yesmaximal, complemented
10#11748714C212yesmaximal, complemented
11#11748648C212yesmaximal, complemented
12#10606395—31nomaximal, Hall
13C23×Dic15C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×D3×Dic5C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C2×C3×C4×Dic5C2212yes—
23Dic5×#67—24no—
24C2×Dic3⋊Dic5C2211yescharacteristic
25C2×#6669—24no—
26C2×#6669C2212yes—
27C2×#6669C2212yes—
28#91543C418yescomplemented
29C2×#6668C2212yes—
30C2×#6668C2212yes—
31C2×(C2×D3)⋊Dic5C2211yescharacteristic
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×Dic3×Dic5C2211yescharacteristic
34#91115C2212yes—
35#91115C2212yes—
36C5×C3⋊#95C2212yes—
37C3×#3963C2212yes—
38#90994C2212yes—
39#73446—51nomaximal, Hall
40C2×#4081—31no—
41C2×D4×Dic5—31no—
42C22×#683—31no—
43C5×#386—31no—
44#65499—31no—
45#65235—32no—
46#65233—32no—
47#65232—31no—
48C22⋊C4×Dic5D311yescharacteristic, complemented
49#64941—32no—
50#64936—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×Dic15—22no—
55C22×Dic15—22no—
56C22×Dic15C2×C414yescomplemented
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2311yescharacteristic
59C22×Dic15C2312yes—
60C2×C5×#67—22no—
61C2×C5×#67—22no—
62C2×C5×#67C2×C414yes—
63C22×C5×Dic3—22no—
64C22×C5×Dic3—42no—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2311yescharacteristic
67C22×C3×Dic5—42no—
68C22×C3×Dic5D414yes—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×D3×Dic5—22no—
73C2×D3×Dic5—42no—
74C3×C5×C22⋊C4—22no—
75#6719—22no—
76C5×(C2×D3)⋊C4—42no—
77C3×C22⋊Dic5C2×C414yescomplemented
78C3×C4×Dic5—42no—
79Dic3⋊Dic5—22no—
80#6669—24no—
81#6669—24no—
82#6668—42no—
83#6668C2×C418yescomplemented
84(C2×D3)⋊Dic5—22no—
85(C2×D3)⋊Dic5C2×C418yescomplemented
86Dic3×Dic5—22no—
87C2×C4×#67—51no—
88C22×Dic3⋊C4—51no—
89C2×#886—51no—
90C3×C4×C22⋊C4—51no—
91#4958D511yescharacteristic
92#4950—51no—
93#4943—51no—
94#4940—52no—
95#4928—52no—
96#4668—52no—
97#4653—52no—
98C22×C5×D4—31no—
99C23×C4×C5—31no—
100C23×Dic5—31no—
101C23×Dic5—31no—
102C23×Dic5C2×D311yescharacteristic
103C2×C5×C22⋊C4—32no—
104C2×C5×C22⋊C4C2×D311yescharacteristic
105C2×C22⋊Dic5—32no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4081—38no—
110D4×Dic5—64no—
111C2×C4⋊Dic5—31no—
112C2×#683—32no—
113C2×#683—32no—
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—64no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5C2×D312yes—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2322—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5C2411yescharacteristic
131C22×C5×D3—21no—
132C22×C5×D3—21no—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×Dic15—28no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15C22×C414yes—
147C5×#67—28no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—44no—
154C2×C5×Dic3C22×C412yes—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—44no—
160C2×C3×Dic5C22×C414yes—
161C2×C3×Dic5C2×D412yes—
162C2×C3×Dic5C2×D412yes—
163D3×Dic5—44no—
164C23×C3×C4—51no—
165C22×#67C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3C2×D511yescharacteristic
168C22×C4×D3—51no—
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4C2×D511yescharacteristic
171C2×C3×C42—52no—
172C2×#217—51no—
173C4×#67—104no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—51no—
176C2×(C2×D3)⋊C4C2×D512yes—
177C2×C4⋊Dic3—52no—
178C2×C4⋊Dic3—52no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4—51no—
181C2×Dic3⋊C4—52no—
182C2×Dic3⋊C4—104no—
183C2×C4×Dic3—51no—
184#886—58no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95C2×D512yes—
190C24×C5—31no—
191C24×C5C22×D311yescharacteristic
192C2×C5×D4—34no—
193C2×C5×D4—62no—
194C2×C5×D4—62no—
195C22×C4×C5—31no—
196C22×C4×C5—32no—
197C22×C4×C5—62no—
198C22×C4×C5—122no—
199C22×C4×C5C22×D312yes—
200C22×Dic5—34no—
201C22×Dic5—32no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204C22×Dic5—42no—
205C22×Dic5—62no—
206C22×Dic5—62no—
207C22×Dic5—62no—
208C22×Dic5—122no—
209C22×Dic5D1214yes—
210C22×Dic5C22×D312yes—
211C22×Dic5C22×D311yescharacteristic
212C22×Dic5C22×D311yescharacteristic
213C5×C22⋊C4—22no—
214C5×C22⋊C4—122no—
215C22⋊Dic5—38no—
216C22⋊Dic5—62no—
217C22⋊Dic5—62no—
218C22⋊Dic5C4×D314yescomplemented
219C4⋊Dic5—62no—
220#683—38no—
221#683—64no—
222#683—64no—
223#683—122no—
224C4×Dic5—42no—
225C4×Dic5—62no—
226C2×#123—151no—
227C2×C4×D4—151no—
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—51no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5C4×D414yes—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)12yes—
246C22×C3×C52−1+412yes—
247C2×C5×D3—22no—
248C2×C5×D3—24no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C2×C5×D3—42no—
252C3×C4×C5—42no—
253Dic15—24no—
254Dic15—41no—
255Dic15—41no—
256C3×Dic5—24no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C5×Dic3—22no—
260C5×Dic3—42no—
261C24×C3C22×D511yescharacteristic
262C23×D3C22×D511yescharacteristic
263C22×C3×C4—52no—
264C22×C3×C4—51no—
265C22×C3×C4—51no—
266C22×C3×C4—54no—
267C22×C3×C4—202no—
268C22×C3×C4C22×D512yes—
269C2×#67—22no—
270C2×#67—22no—
271C2×#67C4×D514yes—
272C22×Dic3—22no—
273C22×Dic3—42no—
274C22×Dic3—54no—
275C22×Dic3—52no—
276C22×Dic3—51no—
277C22×Dic3—51no—
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3C22×D512yes—
281C22×Dic3C22×D511yescharacteristic
282C2×C4×D3—102no—
283C2×C4×D3—202no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—54no—
286C3×C42—202no—
287#217—102no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—58no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—58no—
292C4⋊Dic3—202no—
293Dic3⋊C4—104no—
294Dic3⋊C4—104no—
295Dic3⋊C4—102no—
296C4×Dic3—102no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—32no—
300C23×C5—61no—
301C23×C5—61no—
302C23×C5—62no—
303C23×C5—62no—
304C23×C5C2×C4×D312yes—
305C23×C5C2×D1212yes—
306C23×C5#23512yes—
307C23×C5C23×D311yescharacteristic
308C5×D4—68no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—32no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—124no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—34no—
324C2×Dic5—44no—
325C2×Dic5—68no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—61no—
329C2×Dic5—61no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—124no—
333C2×Dic5C2×C4×D314yes—
334C2×Dic5C2×D1212yes—
335C2×Dic5C2×D1212yes—
336C22×D4—31no—
337C23×C4—31no—
338C23×C4—51no—
339C23×C4—151no—
340C23×C4—151no—
341#123—158no—
342C4×D4—304no—
343C2×C4⋊C4—152no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—151no—
347C2×C4⋊C4—152no—
348C2×C4⋊C4—304no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—152no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4D3×D511yescharacteristic
355C2×C42—52no—
356C2×C42—151no—
357#95—32no—
358#95—52no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5#52012yes—
365C2×C3×C5#53411yescharacteristic
366C2×C3×C5#53611yescharacteristic
367C2×C3×C5#53912yes—
368C5×D3—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3C2×C4×D512yes—
372C23×C3D4×D512yes—
373C23×C3#71112yes—
374C23×C3C23×D511yescharacteristic
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3C2×C4×D512yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—54no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—204no—
391#67—28no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—44no—
398C2×Dic3—54no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—108no—
402C2×Dic3—101no—
403C2×Dic3—101no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3C2×C4×D512yes—
407C4×D3—204no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—24no—
412C22×C5—62no—
413C22×C5—64no—
414C22×C5—121no—
415C22×C5—121no—
416C22×C5—122no—
417C22×C5C4×D1214yes—
418C22×C5C22×C4×D311yescharacteristic
419C22×C5C22×D1211yescharacteristic
420C22×C5C2×#23511yescharacteristic
421C22×C5#100412yes—
422C22×C5#101012yes—
423C4×C5—42no—
424C4×C5—62no—
425C4×C5—122no—
426Dic5—22no—
427Dic5—22no—
428Dic5—24no—
429Dic5—64no—
430Dic5—121no—
431Dic5—121no—
432C24—31no—
433C24C2×D3×D511yescharacteristic
434C2×D4—34no—
435C2×D4—62no—
436C2×D4—62no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—51no—
440C22×C4—52no—
441C22×C4—51no—
442C22×C4—54no—
443C22×C4—62no—
444C22×C4—122no—
445C22×C4—154no—
446C22×C4—152no—
447C22×C4—151no—
448C22×C4—151no—
449C22×C4—202no—
450C22×C4—302no—
451C22×C4—302no—
452C22×C4—302no—
453C22×C4—602no—
454C22×C4C2×D3×D512yes—
455C4⋊C4—158no—
456C4⋊C4—304no—
457C4⋊C4—304no—
458C4⋊C4—302no—
459C4⋊C4—602no—
460C22⋊C4—22no—
461C22⋊C4—54no—
462C22⋊C4—122no—
463C22⋊C4—158no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C42—202no—
467C42—302no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—22no—
473C22×C3#402714yes—
474C22×C3C22×C4×D511yescharacteristic
475C22×C3C2×D4×D511yescharacteristic
476C22×C3C2×#71111yescharacteristic
477C22×C3#414412yes—
478C22×C3#415012yes—
479C2×D3—22no—
480C2×D3—24no—
481C2×D3—41no—
482C2×D3—42no—
483C2×D3—41no—
484C3×C4—42no—
485C3×C4—104no—
486C3×C4—102no—
487C3×C4—102no—
488Dic3—22no—
489Dic3—42no—
490Dic3—104no—
491Dic3—201no—
492Dic3—201no—
493C2×C5—24no—
494C2×C5—122no—
495C2×C5C2×C4×D1211yescharacteristic
496C2×C5#549311yescharacteristic
497C2×C5#552611yescharacteristic
498C2×C5#554612yes—
499C2×C5#556412yes—
500C23—22no—
501C23—22no—
502C23—32no—
503C23—61no—
504C23—62no—
505C23—62no—
506C23—61no—
507C23C4×D3×D512yes—
508C23D5×D1212yes—
509C23#678212yes—
510C23C22×D3×D511yescharacteristic
511D4—68no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—54no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—124no—
529C2×C4—154no—
530C2×C4—204no—
531C2×C4—308no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—301no—
535C2×C4—301no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—604no—
539C2×C3—24no—
540C2×C3C2×#402711yescharacteristic
541C2×C3#6588012yes—
542C2×C3#6592311yescharacteristic
543C2×C3#6593612yes—
544C2×C3#6598211yescharacteristic
545D3—42no—
546C5#7344611yescharacteristic, complemented, Sylow
547C22—22no—
548C22—24no—
549C22—24no—
550C22—22no—
551C22—62no—
552C22—64no—
553C22—121no—
554C22—122no—
555C22—121no—
556C22#9140514yes—
557C22C2×C4×D3×D511yescharacteristic
558C22C2×D5×D1211yescharacteristic
559C22#9202012yes—
560C22#9202512yes—
561C22C2×#678211yescharacteristic
562C4—42no—
563C4—62no—
564C4—102no—
565C4—102no—
566C4—104no—
567C4—122no—
568C4—304no—
569C4—601no—
570C4—601no—
571C3#1060639511yescharacteristic, complemented, Sylow
572C2—24no—
573C2—122no—
574C2#1175282112yes—
575C2#1175287411yescharacteristic
576C2#1175326311yescharacteristic
577C2C2×#9140511yescharacteristic
578C2#1175491512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6669C2semidirect
4. #11751044C2semidirect
6. C3×C22⋊C4×Dic5C2semidirect
7. #11749511C2semidirect
8. #11748893C2semidirect
9. #11748802C2semidirect
10. #11748714C2semidirect
11. #11748648C2semidirect
28. #91543C4semidirect
48. C22⋊C4×Dic5D3semidirect
56. C22×Dic15C2×C4semidirect
77. C3×C22⋊Dic5C2×C4semidirect
83. #6668C2×C4semidirect
85. (C2×D3)⋊Dic5C2×C4semidirect
218. C22⋊Dic5C4×D3semidirect
468. C3×C5#2322semidirect
546. C5#73446semidirect
571. C3#10606395semidirect

Maximal subgroups

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

subgroupindex
C2×Dic5×#672
C22×#66692
C2×#915432
#117510442
C5×#49582
C3×C22⋊C4×Dic52
#117495112
#117488932
#117488022
#117487142
#117486482
#106063953
#734465