Finite Group Databasebeta

← #14424594

Subgroups — #14424594

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic
2C5×#5825C211yesmaximal, characteristic, complemented
3C22×#6661C211yesmaximal, characteristic, complemented
4C2×#91307C211yesmaximal, characteristic, complemented
5#11751335C211yesmaximal, characteristic, complemented
6#11748555C214yesmaximal, complemented
7#11748528C214yesmaximal, complemented
8#11748399C211yesmaximal, characteristic, complemented
9#11748364C211yesmaximal, characteristic, complemented
10#10615142—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C3×#4150—24no—
14C3×#4150—24no—
15C2×C3×Q8×D5—21no—
16C2×C3×#711—22no—
17C2×C3×#711—21no—
18C2×C3×#709C2212yes—
19C2×C3×#709C2211yescharacteristic
20C22×C3×Dic10C2212yes—
21C22×C3×Dic10C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#944—21no—
25C5×#936—21no—
26C5×#935—22no—
27C5×#926C2211yescharacteristic
28C5×#924C2214yes—
29C2×#6661—24no—
30C2×#6661C2212yes—
31C2×#6661C2214yes—
32#91307—24no—
33C2×#6655C2212yes—
34#91114C2214yes—
35#90970C2212yes—
36#90970C2214yes—
37#90964C2212yes—
38#84117—51nomaximal, Hall
39C2×#4150D311yescharacteristic
40C5×#536—31no—
41C22×#689—31no—
42C2×#4088—31no—
43#65523—31no—
44#65339—34no—
45#65336—34no—
46#65293—31no—
47#65291—31no—
48C3×C5×#41—22no—
49C3×C5×#41—22no—
50C2×C3×C5×Q8D411yescharacteristic
51C2×C3×C5×D4D412yes—
52C2×C3×C5×D4D411yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C5×Dic3—21no—
56C2×C5×Dic6—22no—
57C2×C5×Dic6—22no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6C2312yes—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—21no—
62C22×C3×Dic5—22no—
63C22×C3×Dic5—21no—
64C3×Q8×D5—28no—
65C3×#711—216no—
66C3×#711—28no—
67C3×#709—22no—
68C3×#709—24no—
69C3×#709—24no—
70C3×#709D414yes—
71C2×C3×D20C2311yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—21no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10—21no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—24no—
78C2×C3×Dic10—24no—
79C2×C3×Dic10D414yes—
80C2×C3×Dic10C2311yescharacteristic
81C2×C3×Dic10C2312yes—
82#6710—22no—
83C2×C3⋊#168—22no—
84C2×C3⋊#168C2312yes—
85C2×C3⋊#168C2312yes—
86C5×#217—24no—
87C5×#217—21no—
88C5×C4⋊Dic3C2312yes—
89C5×Dic3⋊C4—24no—
90C4×C5×Dic3—21no—
91#6661—24no—
92#6661—28no—
93#6655—24no—
94C2×C3×2−1+4—51no—
95#5825D511yescharacteristic, complemented
96C2×#951—51no—
97C22×#216—51no—
98#5239—54no—
99#5234—51no—
100#5233—51no—
101#5228—54no—
102#5225—51no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×Q8—31no—
105#4150—24no—
106#4150—24no—
107C2×Q8×D5—21no—
108C2×#711—22no—
109C2×#711—21no—
110C2×#709C2×D312yes—
111C2×#709C2×D311yescharacteristic
112C22×Dic10C2×D312yes—
113C22×Dic10C2×D311yescharacteristic
114C5×C4⋊Q8—61no—
115C5×#124—61no—
116C5×#123—62no—
117C5×C22⋊Q8—34no—
118C5×#117—31no—
119C2×#689—34no—
120C2×#689—32no—
121C2×#689—64no—
122#4088—64no—
123C2×#688—32no—
124C2×#681—31no—
125C22×#168—31no—
126C22⋊#168—34no—
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3011—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×C3×D5—21no—
134C3×C5×Q8—22no—
135C3×C5×D4—24no—
136C3×C5×D4—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—42no—
147C5×Dic6—22no—
148C5×Dic6—22no—
149C5×Dic6—42no—
150C3×C22⋊D5—28no—
151C3×C22⋊D5—24no—
152C2×C3×Dic5—28no—
153C2×C3×Dic5—24no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—22no—
156C3×D20—21no—
157C3×D20C2×D412yes—
158C3×C4×D5—28no—
159C3×C4×D5—24no—
160C3×Dic10—28no—
161C3×Dic10—24no—
162C3×Dic10—22no—
163C3×Dic10—21no—
164C3×Dic10C2×D412yes—
165C3×Dic10C2×D414yes—
166C3⋊#168—22no—
167C3⋊#168—22no—
168C3×2−1+4—104no—
169C3×2−1+4—104no—
170C2×C3×#41—51no—
171C2×C3×#41—52no—
172C2×C3×#41—102no—
173C2×C3×#41—101no—
174C2×C3×#41C2×D511yescharacteristic
175C22×C3×Q8—51no—
176C22×C3×Q8—52no—
177C22×C3×Q8—101no—
178C22×Dic6C2×D511yescharacteristic
179#951—104no—
180#944—21no—
181C2×#216—52no—
182C2×#216—54no—
183C2×#216—104no—
184#936—21no—
185#935—22no—
186C2×#214—52no—
187#926C2×D511yescharacteristic
188#924C2×D514yes—
189C2×#208—51no—
190C22×C3⋊C8—51no—
191#835—54no—
192#835—52no—
193#832—52no—
194#830—54no—
195C5×#41—22no—
196C5×#41—22no—
197C2×C5×Q8—32no—
198C2×C5×Q8—61no—
199C2×C5×Q8—62no—
200C2×C5×Q8—62no—
201C2×C5×Q8#6711yescharacteristic
202C2×C5×D4#6712yes—
203C2×C5×D4#6711yescharacteristic
204C22×C4×C5—61no—
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—22no—
208C2×C22⋊D5—21no—
209C22×Dic5—22no—
210C22×Dic5—21no—
211Q8×D5—28no—
212#711—216no—
213#711—28no—
214#709—22no—
215#709—24no—
216#709—24no—
217#709#6714yes—
218C2×D20C22×D311yescharacteristic
219C2×C4×D5—22no—
220C2×C4×D5—21no—
221C2×Dic10—22no—
222C2×Dic10—21no—
223C2×Dic10—22no—
224C2×Dic10—24no—
225C2×Dic10—24no—
226C2×Dic10#6714yes—
227C2×Dic10C22×D311yescharacteristic
228C2×Dic10C22×D312yes—
229C5×C4⋊C4—32no—
230C5×C4⋊C4—64no—
231C5×C22⋊C4—61no—
232C5×C22⋊C4—64no—
233C42×C5—61no—
234#689—64no—
235#689—68no—
236#688—64no—
237#681—62no—
238C2×#168—32no—
239C2×#168—32no—
240C2×#168—62no—
241C2×2−1+4—51no—
242C2×#137—151no—
243C22×Q16—151no—
244#536—31no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—151no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—24no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×C3×D5—22no—
256C2×C3×D5—42no—
257C3×C4×C5—22no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261C3×Dic5—22no—
262C3×Dic5—24no—
263C5×Dic3—42no—
264C5×Dic3—42no—
265C3×#41—22no—
266C3×#41—22no—
267C3×#41—54no—
268C3×#41—104no—
269C3×#41—104no—
270C3×#41—1016no—
271C3×#41—108no—
272C3×#41—102no—
273C2×C3×Q8—54no—
274C2×C3×Q8—52no—
275C2×C3×Q8—51no—
276C2×C3×Q8—104no—
277C2×C3×Q8—104no—
278C2×C3×Q8—108no—
279C2×C3×Q8—102no—
280C2×C3×Q8—102no—
281C2×C3×Q8—101no—
282C2×C3×Q8C22⋊D511yescharacteristic
283C2×C3×D4—51no—
284C2×C3×D4—102no—
285C2×C3×D4—101no—
286C2×C3×D4C22⋊D512yes—
287C2×C3×D4C22⋊D511yescharacteristic
288C22×C3×C4—102no—
289C22×C3×C4—101no—
290C22×C3×C4—102no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—21no—
295C2×Dic6—22no—
296C2×Dic6—22no—
297C2×Dic6—21no—
298C2×Dic6C22×D512yes—
299#217—24no—
300#217—21no—
301#216—108no—
302#216—104no—
303#214—104no—
304C4⋊Dic3C22×D512yes—
305Dic3⋊C4—24no—
306C4×Dic3—21no—
307#208—102no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—102no—
311C23×C5C2×#6712yes—
312C23×C5C2×#6711yescharacteristic
313C22×D5—21no—
314C5×Q8—22no—
315C5×Q8—62no—
316C5×Q8—62no—
317C5×Q8—122no—
318C5×D4—24no—
319C5×D4—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—62no—
323C2×C4×C5—62no—
324C2×C4×C5—122no—
325C2×C4×C5C2×#6712yes—
326C2×C4×C5C2×#6711yescharacteristic
327C2×C4×C5C2×#6712yes—
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—28no—
331C22⋊D5—24no—
332C2×Dic5—28no—
333C2×Dic5—24no—
334C2×Dic5—21no—
335C2×Dic5—22no—
336D20—21no—
337D20C2×#6712yes—
338C4×D5—28no—
339C4×D5—24no—
340Dic10—28no—
341Dic10—24no—
342Dic10—22no—
343Dic10—21no—
344Dic10C2×#6712yes—
345Dic10C2×#6714yes—
346#168—62no—
347#168—62no—
3482−1+4—104no—
3492−1+4—104no—
350C2×#41—51no—
351C2×#41—52no—
352C2×#41—102no—
353C2×#41—101no—
354C2×#41D3×D511yescharacteristic
355C22×Q8—31no—
356C22×Q8—51no—
357C22×Q8—52no—
358C22×Q8—101no—
359#137—304no—
360C2×Q16—154no—
361C2×Q16—152no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—151no—
365C22×C8—151no—
366C4⋊Q8—61no—
367#124—61no—
368#123—62no—
369C22⋊Q8—34no—
370#117—31no—
371#103—152no—
372#103—154no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5—42no—
377C2×C3×C5C2×#12011yescharacteristic
378C2×C3×C5#57812yes—
379C3×D5—42no—
380C23×C3—101no—
381C23×C3C2×C22⋊D512yes—
382C23×C3C2×C22⋊D511yescharacteristic
383C3×Q8—22no—
384C3×Q8—54no—
385C3×Q8—52no—
386C3×Q8—108no—
387C3×Q8—102no—
388C3×Q8—101no—
389C3×Q8—104no—
390C3×D4—24no—
391C3×D4—22no—
392C3×D4—52no—
393C3×D4—108no—
394C3×D4—104no—
395C3×D4—101no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—108no—
399C2×C3×C4—108no—
400C2×C3×C4—102no—
401C2×C3×C4—101no—
402C2×C3×C4—104no—
403C2×C3×C4—104no—
404C2×C3×C4D4×D512yes—
405C2×C3×C4D4×D512yes—
406C2×C3×C4C2×C22⋊D512yes—
407C2×C3×C4C2×C22⋊D511yescharacteristic
408C2×C3×C4C23×D511yescharacteristic
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—42no—
412Dic6—22no—
413Dic6—22no—
414Dic6—42no—
415C3⋊C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—24no—
419C22×C5—22no—
420C22×C5#95312yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—22no—
423C2×D5—42no—
424C4×C5—22no—
425C4×C5—122no—
426C4×C5—122no—
427C4×C5#95312yes—
428C4×C5C22×#6711yescharacteristic
429C4×C5C22×#6711yescharacteristic
430Dic5—22no—
431Dic5—24no—
432#41—22no—
433#41—22no—
434#41—54no—
435#41—104no—
436#41—104no—
437#41—1016no—
438#41—108no—
439#41—102no—
440C2×Q8—32no—
441C2×Q8—54no—
442C2×Q8—52no—
443C2×Q8—51no—
444C2×Q8—61no—
445C2×Q8—62no—
446C2×Q8—62no—
447C2×Q8—104no—
448C2×Q8—104no—
449C2×Q8—108no—
450C2×Q8—102no—
451C2×Q8—101no—
452C2×Q8—102no—
453C2×Q8#120111yescharacteristic
454C2×D4—51no—
455C2×D4—102no—
456C2×D4—101no—
457C2×D4#120112yes—
458C2×D4#120111yescharacteristic
459C22×C4—61no—
460C22×C4—102no—
461C22×C4—101no—
462C22×C4—102no—
463C22×C4—101no—
464C22×C4C2×D3×D512yes—
465C22×C4C2×D3×D511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—302no—
470C2×C8—152no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—32no—
474C4⋊C4—64no—
475C22⋊C4—61no—
476C22⋊C4—64no—
477C42—61no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—24no—
482C22×C3—102no—
483C22×C3—202no—
484C22×C3#408312yes—
485C22×C3C22×C22⋊D511yescharacteristic
486C3×C4—22no—
487C3×C4—104no—
488C3×C4—102no—
489C3×C4#408312yes—
490C3×C4C2×D4×D511yescharacteristic
491C3×C4C2×D4×D511yescharacteristic
492Dic3—42no—
493Dic3—42no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5#583812yes—
497C2×C5C2×#95311yescharacteristic
498D5—42no—
499C23—101no—
500C23C2×#120112yes—
501C23C2×#120111yescharacteristic
502Q8—22no—
503Q8—54no—
504Q8—52no—
505Q8—62no—
506Q8—62no—
507Q8—108no—
508Q8—102no—
509Q8—101no—
510Q8—104no—
511Q8—122no—
512D4—24no—
513D4—22no—
514D4—52no—
515D4—108no—
516D4—104no—
517D4—101no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—108no—
523C2×C4—108no—
524C2×C4—102no—
525C2×C4—101no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—122no—
529C2×C4C2×#120112yes—
530C2×C4C2×#120111yescharacteristic
531C2×C4D5×#6712yes—
532C2×C4D5×#6712yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—302no—
535C8—302no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3—202no—
539C2×C3C2×#408311yescharacteristic
540C2×C3#6617212yes—
541C5#8411711yescharacteristic, complemented, Sylow
542C22—22no—
543C22—24no—
544C22—22no—
545C22—102no—
546C22—202no—
547C22#9156312yes—
548C22C22×#120111yescharacteristic
549C4—22no—
550C4—104no—
551C4—102no—
552C4—122no—
553C4—122no—
554C4#9156312yes—
555C4C2×D5×#6711yescharacteristic
556C4C2×D5×#6711yescharacteristic
557C3#1061514211yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—202no—
561C2#1175530212yes—
562C2C2×#9156311yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4150C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×#5825C2semidirect
3. C22×#6661C2semidirect
4. C2×#91307C2semidirect
5. #11751335C2semidirect
6. #11748555C2semidirect
7. #11748528C2semidirect
8. #11748399C2semidirect
9. #11748364C2semidirect
95. #5825D5semidirect
478. C3×C5#3011semidirect
541. C5#84117semidirect
557. C3#10615142semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C5×#58252
C22×#66612
C2×#913072
#117513352
#117485552
#117485282
#117483992
#117483642
#106151423
#841175