Finite Group Databasebeta

← #14321721

Subgroups — #14321721

Order 1920.

1376 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
1C22×C4×C5×Dic3C211yesmaximal, characteristic, complemented
2C2×Dic3×C22⋊D5C211yesmaximal, characteristic
3C2×#91536C211yesmaximal, characteristic
4#11751311C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic
6Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
7#11749472C211yesmaximal, characteristic, complemented
8Dic3×#685C212yesmaximal, complemented
9#11748808C212yesmaximal, complemented
10#11748706C212yesmaximal, complemented
11#11748645C212yesmaximal, complemented
12C4×#4075—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C22⋊D5C2211yescharacteristic
17C22×D5×Dic3C2211yescharacteristic
18C2×#6719C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×#6712C2212yes—
21C2×C4×C5×Dic3—24no—
22C2×C4×C5×Dic3C2212yes—
23C2×C4×C5×Dic3C2212yes—
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×#685C2212yes—
26Dic3×C22⋊D5—24no—
27C2×#6669C2212yes—
28C2×#6668C2211yescharacteristic
29#91536C418yescomplemented
30C2×#6665C2211yescharacteristic
31C2×#6665C2212yes—
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2211yescharacteristic
34#91115C2212yes—
35C3×#3963C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#74661—51nomaximal, Hall
40C22×C42×C5—31no—
41C2×#4075—31no—
42C2×C4×C22⋊D5—31no—
43#65502D311yescharacteristic
44#65500—31no—
45#65499—31no—
46C4×C22⋊Dic5—31no—
47#65229—32no—
48C4×#685—32no—
49#65222—32no—
50C4×#683—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—24no—
55C22×C3×C4×C5C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3—24no—
62C22×C5×Dic3C2×C414yescomplemented
63C22×C5×Dic3D414yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5—22no—
69C2×C3×C22⋊D5C2×C414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C2×D5×Dic3—22no—
73C2×D5×Dic3—24no—
74#6719—22no—
75#6719C2×C414yescomplemented
76#6712—24no—
77C4×C5×Dic3—24no—
78C4×C5×Dic3—24no—
79C3×C22⋊Dic5—22no—
80C3×#685—24no—
81#6669C2×C418yescomplemented
82#6668—22no—
83#6665—22no—
84#6665C2×C418yescomplemented
85Dic3×Dic5—22no—
86Dic3×Dic5—24no—
87C2×#935—51no—
88C2×D4×Dic3—51no—
89C22×C4×Dic3D511yescharacteristic, complemented
90C3×#386—51no—
91#5210—51no—
92#4945—52no—
93#4943—51no—
94Dic3×C22⋊C4—51no—
95Dic3×C22⋊C4—52no—
96#4655—52no—
97#4649—52no—
98C23×C4×C5—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5C2×D311yescharacteristic
102C22×C4×D5—31no—
103C2×C42×C5—32no—
104C2×C42×C5—32no—
105C2×C42×C5—64no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4075—38no—
110C4×C22⋊D5—64no—
111C2×#685—32no—
112C2×#685—31no—
113C2×#685C2×D312yes—
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—31no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124C4×#123—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×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—21no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—28no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5#4114yes—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15C22×C414yes—
147C2×C5×Dic3—28no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—28no—
152C2×C5×Dic3C22×C414yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3#4114yes—
156C3×C22⋊D5—28no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5C22×C412yes—
163D5×Dic3—44no—
164C22×C3×D4—51no—
165C23×C3×C4C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3C2×D511yescharacteristic
168C23×Dic3C2×D511yescharacteristic
169C2×C3×C22⋊C4—51no—
170C2×C3×C22⋊C4—52no—
171C2×#217—51no—
172C2×#217—52no—
173C2×#217—51no—
174C2×#217—51no—
175#935—58no—
176D4×Dic3—104no—
177C2×C4⋊Dic3—51no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—24no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—52no—
183C2×C4×Dic3C2×D512yes—
184C2×C4×Dic3C2×D512yes—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5C22×D311yescharacteristic
191C23×D5C22×D311yescharacteristic
192C22×C4×C5—22no—
193C22×C4×C5—24no—
194C22×C4×C5—31no—
195C22×C4×C5—34no—
196C22×C4×C5—34no—
197C22×C4×C5—32no—
198C22×C4×C5—31no—
199C22×C4×C5—64no—
200C22×C4×C5—62no—
201C22×C4×C5—62no—
202C22×C4×C5C22×D312yes—
203C2×C22⋊D5—22no—
204C2×C22⋊D5—22no—
205C2×C22⋊D5C4×D314yes—
206C22×Dic5—32no—
207C22×Dic5—31no—
208C22×Dic5—31no—
209C22×Dic5C22×D312yes—
210C22×Dic5C22×D311yescharacteristic
211C2×C4×D5—64no—
212C2×C4×D5—62no—
213C42×C5—64no—
214C42×C5—64no—
215C22⋊Dic5—22no—
216C22⋊Dic5—34no—
217C22⋊Dic5—62no—
218#685—24no—
219#685—38no—
220#685—62no—
221#683—38no—
222#683—62no—
223#683—64no—
224C4×Dic5—64no—
225C4×Dic5—62no—
226C2×#123—151no—
227C2×C4×D4—151no—
228C22×C42—31no—
229#388—152no—
230#387—152no—
231#386—51no—
232#385—151no—
233#381—151no—
234C4×C4⋊C4—152no—
235C4×C22⋊C4—152no—
236C4×C22⋊C4—151no—
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×C5C2×#4112yes—
246C22×C3×C5C2×#4112yes—
247C2×C3×D5—22no—
248C2×C3×D5—24no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C2×C3×D5—42no—
252C3×C4×C5—24no—
253Dic15—24no—
254Dic15—41no—
255Dic15—41no—
256C3×Dic5—22no—
257C3×Dic5—42no—
258C5×Dic3—24no—
259C5×Dic3—22no—
260C5×Dic3#12314yescomplemented
261C24×C3—51no—
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—54no—
264C2×C3×D4—102no—
265C2×C3×D4—102no—
266C22×C3×C4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—51no—
269C22×C3×C4—52no—
270C22×C3×C4C22×D512yes—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—24no—
274C22×Dic3—52no—
275C22×Dic3—51no—
276C22×Dic3—51no—
277C22×Dic3—104no—
278C22×Dic3—102no—
279C22×Dic3C4×D514yescomplemented
280C22×Dic3C22⋊D514yes—
281C22×Dic3C22×D512yes—
282C22×Dic3C22×D511yescharacteristic
283C22×Dic3C22×D511yescharacteristic
284C3×C22⋊C4—102no—
285C3×C22⋊C4—104no—
286#217—54no—
287#217—58no—
288#217—102no—
289#217—102no—
290C4⋊Dic3—102no—
291Dic3⋊C4—58no—
292Dic3⋊C4—104no—
293C4×Dic3—24no—
294C4×Dic3—24no—
295C4×Dic3—104no—
296C4×Dic3—102no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5C2×C4×D312yes—
300C23×C5D3×D412yes—
301C23×C5#23712yes—
302C23×C5C23×D311yescharacteristic
303C22×D5—21no—
304C22×D5—22no—
305C22×D5—21no—
306C22×D5—22no—
307C22×D5C2×C4×D312yes—
308C2×C4×C5—28no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—34no—
313C2×C4×C5—34no—
314C2×C4×C5—32no—
315C2×C4×C5—68no—
316C2×C4×C5—68no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5#23714yes—
321C22⋊D5—28no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—34no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—61no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5C2×C4×D312yes—
335C4×D5—124no—
336C22×D4—51no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—151no—
340C23×C4D3×D511yescharacteristic
341#123—158no—
342C4×D4—304no—
343C2×C4⋊C4—152no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—152no—
346C2×C22⋊C4—51no—
347C2×C22⋊C4—52no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C22⋊C4—151no—
352C2×C42—32no—
353C2×C42—32no—
354C2×C42—64no—
355C2×C42—151no—
356C2×C42—152no—
357#95—52no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4112yes—
365C2×C3×C5C2×#12311yescharacteristic
366C2×C3×C5#52511yescharacteristic
367C2×C3×C5#52912yes—
368C3×D5—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—52no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—101no—
375C23×C3—101no—
376C23×C3C2×C4×D512yes—
377C23×C3#70912yes—
378C23×C3C2×C22⋊D512yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—108no—
381C2×C3×C4—28no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—52no—
385C2×C3×C4—101no—
386C2×C3×C4—101no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4#70914yes—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—28no—
395C2×Dic3—28no—
396C2×Dic3—54no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—101no—
402C2×Dic3—101no—
403C2×Dic3—204no—
404C2×Dic3C2×C4×D514yes—
405C2×Dic3#70914yes—
406C2×Dic3C2×C22⋊D512yes—
407C2×Dic3C2×C22⋊D512yes—
408C22×C5—22no—
409C22×C5—24no—
410C22×C5—22no—
411C22×C5—24no—
412C22×C5#67⋊C414yes—
413C22×C5C22×C4×D311yescharacteristic
414C22×C5C2×D3×D411yescharacteristic
415C22×C5C2×#23711yescharacteristic
416C22×C5C2×#23712yes—
417C22×C5D3×#4112yes—
418C2×D5—22no—
419C2×D5—24no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—42no—
423C4×C5—24no—
424C4×C5—34no—
425C4×C5—62no—
426C4×C5—64no—
427Dic5—22no—
428Dic5—42no—
429Dic5—64no—
430Dic5—121no—
431Dic5—121no—
432C24—51no—
433C24C2×D3×D511yescharacteristic
434C2×D4—54no—
435C2×D4—102no—
436C2×D4—102no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—31no—
440C22×C4—34no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—31no—
444C22×C4—51no—
445C22×C4—52no—
446C22×C4—64no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—152no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—302no—
453C22×C4—304no—
454C22×C4C2×D3×D512yes—
455C4⋊C4—158no—
456C4⋊C4—302no—
457C4⋊C4—304no—
458C22⋊C4—102no—
459C22⋊C4—104no—
460C22⋊C4—158no—
461C22⋊C4—154no—
462C22⋊C4—302no—
463C22⋊C4—302no—
464C42—64no—
465C42—64no—
466C42—302no—
467C42—304no—
468C3×C5C4×#12311yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—104no—
474C22×C3—102no—
475C22×C3—202no—
476C22×C3—201no—
477C22×C3—201no—
478C22×C3C4×C22⋊D514yes—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3C2×#70912yes—
482C22×C3C2×#70912yes—
483C22×C3C22×C22⋊D511yescharacteristic
484C3×C4—24no—
485C3×C4—102no—
486C3×C4—202no—
487Dic3—24no—
488Dic3—22no—
489Dic3—104no—
490Dic3—201no—
491Dic3—201no—
492Dic3#407514yescomplemented
493C2×C5—24no—
494C2×C5C2×#67⋊C411yescharacteristic
495C2×C5C4×#23712yes—
496C2×C5#558611yescharacteristic
497C2×C5#560012yes—
498C2×C5D3×#12311yescharacteristic
499D5—42no—
500C23—22no—
501C23—22no—
502C23—52no—
503C23—101no—
504C23—102no—
505C23—102no—
506C23—101no—
507C23#676512yes—
508C23C4×D3×D512yes—
509C23D3×C22⋊D512yes—
510C23C22×D3×D511yescharacteristic
511D4—108no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—34no—
516C2×C4—32no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—52no—
520C2×C4—68no—
521C2×C4—68no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—101no—
526C2×C4—101no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—154no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—301no—
536C2×C4—301no—
537C2×C4—604no—
538C2×C4#677914yes—
539C2×C3—24no—
540C2×C3—202no—
541C2×C3C4×#70912yes—
542C2×C3#6581312yes—
543C2×C3C2×C4×C22⋊D511yescharacteristic
544C2×C3C2×#407511yescharacteristic
545C2×C3#6612511yescharacteristic
546C5#7466111yescharacteristic, complemented, Sylow
547C22—24no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—102no—
552C22—104no—
553C22—201no—
554C22—201no—
555C22—202no—
556C22#9144114yes—
557C22C2×#676511yescharacteristic
558C22C2×C4×D3×D511yescharacteristic
559C22D3×#70912yes—
560C22C2×#677912yes—
561C22C2×D3×C22⋊D511yescharacteristic
562C4—24no—
563C4—34no—
564C4—64no—
565C4—62no—
566C4—102no—
567C4—202no—
568C4—304no—
569C4—601no—
570C4—601no—
571C3C4×#407511yescharacteristic, complemented, Sylow
572C2—24no—
573C2—202no—
574C2C4×#677912yes—
575C2#1175442212yes—
576C2C2×#9144111yescharacteristic
577C2D3×#407511yescharacteristic
578C2#1175538811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#123
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×Dic3C2semidirect
4. #11751311C2semidirect
6. Dic3×C22⋊Dic5C2semidirect
7. #11749472C2semidirect
8. Dic3×#685C2semidirect
9. #11748808C2semidirect
10. #11748706C2semidirect
11. #11748645C2semidirect
29. #91536C4semidirect
62. C22×C5×Dic3C2×C4semidirect
75. #6719C2×C4semidirect
81. #6669C2×C4semidirect
84. #6665C2×C4semidirect
89. C22×C4×Dic3D5semidirect
260. C5×Dic3#123semidirect
279. C22×Dic3C4×D5semidirect
468. C3×C5C4×#123semidirect
492. Dic3#4075semidirect
546. C5#74661semidirect
571. C3C4×#4075semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×Dic32
C2×Dic3×C22⋊D52
C2×#915362
#117513112
C3×#655022
Dic3×C22⋊Dic52
#117494722
Dic3×#6852
#117488082
#117487062
#117486452
C4×#40753
#746615