Finite Group Databasebeta

← #14424612

Subgroups — #14424612

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
2C2×C5×#951C211yesmaximal, characteristic, complemented
3#11754251C211yesmaximal, characteristic, complemented
4C22×#6661C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749290C214yesmaximal, complemented
7#11749047C214yesmaximal, complemented
8#11748400C211yesmaximal, characteristic, complemented
9#11748343C211yesmaximal, characteristic, complemented
10#10615714—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C3×#4150—24no—
14C3×#4150—24no—
15C2×C3×Q8×D5C2212yes—
16C2×C3×#711—22no—
17C2×C3×#711C2212yes—
18C2×C3×#709—21no—
19C2×C3×#709C2211yescharacteristic
20C22×C3×Dic10—21no—
21C22×C3×Dic10C2211yescharacteristic
22#91815C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#951—24no—
25C2×C5×#216C2212yes—
26C2×C5×#214C2212yes—
27C2×C5×#208C2211yescharacteristic
28#91536—22no—
29#91385—21no—
30#91368—21no—
31#91359C2214yes—
32C2×#6661—24no—
33C2×#6661C2214yes—
34#91119C2212yes—
35#91116C2212yes—
36#90971C2214yes—
37#90955C2214yes—
38#84117—51nomaximal, Hall
39C2×#4150D311yescharacteristic
40C2×C5×#137—31no—
41#66150—31no—
42C22×#689—31no—
43#65522—31no—
44#65475—34no—
45#65462—34no—
46#65418—31no—
47#65409—31no—
48C3×C5×#41—22no—
49C3×C5×#41D414yes—
50C2×C3×C5×Q8C2311yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2311yescharacteristic
53C22×C3×C4×C5—21no—
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⋊D5D412yes—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—22no—
64C3×Q8×D5—24no—
65C3×Q8×D5—24no—
66C3×#711—216no—
67C3×#711—24no—
68C3×#711—24no—
69C3×#709—28no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20D411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5C2312yes—
75C2×C3×Dic10—28no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10D411yescharacteristic
80C2×C3×Dic10D414yes—
81C2×C3×Dic10C2312yes—
82#6719—21no—
83C4⋊Dic15C2312yes—
84C4×Dic15—21no—
85C2×C3⋊#168—22no—
86C2×C3⋊#168C2312yes—
87C5×#216—24no—
88C5×#214—24no—
89C5×#208—22no—
90C2×C5×C3⋊C8C2312yes—
91#6669—24no—
92#6665—24no—
93#6661—28no—
94C2×C3×2−1+4—51no—
95#5825—51no—
96C2×#951D511yescharacteristic, complemented
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×D5C2×D312yes—
108C2×#711—22no—
109C2×#711C2×D312yes—
110C2×#709—21no—
111C2×#709C2×D311yescharacteristic
112C22×Dic10—21no—
113C22×Dic10C2×D311yescharacteristic
114C5×#137—64no—
115C2×C5×Q16—32no—
116C2×C5×SD16—32no—
117C2×C5×M16—31no—
118#4093—61no—
119#4092—34no—
120#4090—61no—
121C2×#689—34no—
122C2×#689—64no—
123#4075—62no—
124#4072—31no—
125C22×#168—31no—
126#3967—32no—
127#3964—32no—
128#3952—34no—
129#3948—34no—
130#3011—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×C3×D5C2×D412yes—
134C3×C5×Q8—21no—
135C3×C5×Q8C2×D412yes—
136C3×C5×D4—24no—
137C3×C5×D4—21no—
138C3×C5×D4C2×D412yes—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—42no—
148C5×Dic6—22no—
149C5×Dic6—22no—
150C5×Dic6—42no—
151C3×C22⋊D5—28no—
152C3×C22⋊D5—24no—
153C2×C3×Dic5—28no—
154C2×C3×Dic5—24no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5C2×D412yes—
157C3×D20—22no—
158C3×C4×D5—28no—
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161C3×Dic10—28no—
162C3×Dic10—22no—
163C3×Dic10—24no—
164C3×Dic10—22no—
165C3×Dic10C2×D414yes—
166C3⋊#168—22no—
167C5×C3⋊C8—22no—
168C3×2−1+4—104no—
169C3×2−1+4—104no—
170C2×C3×#41—51no—
171C2×C3×#41—52no—
172C2×C3×#41—101no—
173C2×C3×#41—102no—
174C2×C3×#41C2×D511yescharacteristic
175C22×C3×Q8—52no—
176C22×C3×Q8—51no—
177C22×C3×Q8—101no—
178C22×Dic6C2×D511yescharacteristic
179#951—24no—
180#944—101no—
181C2×#216—54no—
182C2×#216—104no—
183C2×#216C2×D512yes—
184#936—101no—
185#935—102no—
186C2×#214C2×D512yes—
187#926—51no—
188#924—54no—
189C2×#208C2×D511yescharacteristic
190C22×C3⋊C8—51no—
191#835—52no—
192#835—54no—
193#832—52no—
194#830—54no—
195C5×#41—22no—
196C5×#41#6714yes—
197C2×C5×Q8—32no—
198C2×C5×Q8—61no—
199C2×C5×Q8—62no—
200C2×C5×Q8—62no—
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4—21no—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—22no—
208C2×C22⋊D5#6712yes—
209C22×Dic5—21no—
210C22×Dic5—22no—
211Q8×D5—24no—
212Q8×D5—24no—
213#711—216no—
214#711—24no—
215#711—24no—
216#709—28no—
217#709—22no—
218#709—22no—
219C2×D20#6711yescharacteristic
220C2×C4×D5—22no—
221C2×C4×D5C22×D312yes—
222C2×Dic10—28no—
223C2×Dic10—21no—
224C2×Dic10—22no—
225C2×Dic10—22no—
226C2×Dic10#6711yescharacteristic
227C2×Dic10#6714yes—
228C2×Dic10C22×D312yes—
229C5×Q16—64no—
230C5×SD16—64no—
231C5×M16—62no—
232C2×C5×C8—32no—
233C22⋊Dic5—61no—
234#689—68no—
235#685—64no—
236C4⋊Dic5—32no—
237#683—64no—
238C4×Dic5—61no—
239C2×#168—32no—
240C2×#168—62no—
241C2×2−1+4—51no—
242C2×#137—31no—
243C22×Q16—151no—
244#536—151no—
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—42no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×C3×D5—22no—
256C2×C3×D5—24no—
257C3×C4×C5—22no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—42no—
262C3×Dic5—22no—
263C3×Dic5—24no—
264C5×Dic3—42no—
265C3×#41—22no—
266C3×#41—108no—
267C3×#41—104no—
268C3×#41—1016no—
269C3×#41—104no—
270C3×#41—102no—
271C3×#41—102no—
272C3×#41C22⋊D514yes—
273C2×C3×Q8—51no—
274C2×C3×Q8—54no—
275C2×C3×Q8—52no—
276C2×C3×Q8—102no—
277C2×C3×Q8—108no—
278C2×C3×Q8—104no—
279C2×C3×Q8—104no—
280C2×C3×Q8—101no—
281C2×C3×Q8—102no—
282C2×C3×Q8C22×D511yescharacteristic
283C2×C3×D4—21no—
284C2×C3×D4—52no—
285C2×C3×D4—51no—
286C2×C3×D4—102no—
287C2×C3×D4C22×D511yescharacteristic
288C22×C3×C4—21no—
289C22×C3×C4—52no—
290C22×C3×C4—102no—
291C22×C3×C4—102no—
292C22×C3×C4—101no—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—21no—
295C2×Dic6—22no—
296C2×Dic6—22no—
297C2×Dic6—21no—
298C2×Dic6C22×D512yes—
299#217—104no—
300#217—101no—
301#216—24no—
302#216—108no—
303#214—24no—
304C4⋊Dic3—52no—
305Dic3⋊C4—104no—
306C4×Dic3—101no—
307#208—22no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—102no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—21no—
312C23×C5C2×#6711yescharacteristic
313C22×D5C2×#6712yes—
314C5×Q8—21no—
315C5×Q8—62no—
316C5×Q8—62no—
317C5×Q8—122no—
318C5×Q8C2×#6712yes—
319C5×D4—24no—
320C5×D4—21no—
321C5×D4C2×#6712yes—
322C2×C4×C5—21no—
323C2×C4×C5—24no—
324C2×C4×C5—62no—
325C2×C4×C5—122no—
326C2×C4×C5C2×#6712yes—
327C2×C4×C5C2×#6711yescharacteristic
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—28no—
331C22⋊D5—24no—
332C2×Dic5—28no—
333C2×Dic5—24no—
334C2×Dic5—22no—
335C2×Dic5—62no—
336C2×Dic5C2×#6712yes—
337D20—22no—
338C4×D5—28no—
339C4×D5—22no—
340C4×D5—22no—
341Dic10—28no—
342Dic10—22no—
343Dic10—24no—
344Dic10—22no—
345Dic10C2×#6714yes—
346C5×C8—62no—
347#168—62no—
3482−1+4—104no—
3492−1+4—104no—
350C2×#41—51no—
351C2×#41—52no—
352C2×#41—101no—
353C2×#41—102no—
354C2×#41D3×D511yescharacteristic
355C22×Q8—31no—
356C22×Q8—52no—
357C22×Q8—51no—
358C22×Q8—101no—
359#137—64no—
360C2×Q16—32no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—32no—
364C2×M16—31no—
365C22×C8—151no—
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—151no—
371#103—154no—
372#103—152no—
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—21no—
381C23×C3—52no—
382C23×C3D4×D511yescharacteristic
383C3×Q8—21no—
384C3×Q8—54no—
385C3×Q8—108no—
386C3×Q8—102no—
387C3×Q8—102no—
388C3×Q8—104no—
389C3×Q8C2×C22⋊D512yes—
390C3×D4—24no—
391C3×D4—21no—
392C3×D4—108no—
393C3×D4—104no—
394C3×D4—102no—
395C3×D4C2×C22⋊D512yes—
396C2×C3×C4—21no—
397C2×C3×C4—24no—
398C2×C3×C4—52no—
399C2×C3×C4—108no—
400C2×C3×C4—108no—
401C2×C3×C4—102no—
402C2×C3×C4—104no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4D4×D512yes—
406C2×C3×C4D4×D511yescharacteristic
407C2×C3×C4C2×C22⋊D512yes—
408C2×C3×C4C23×D511yescharacteristic
409C2×Dic3—22no—
410C2×Dic3—42no—
411C2×Dic3—102no—
412Dic6—22no—
413Dic6—22no—
414Dic6—42no—
415C3⋊C8—22no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—42no—
420C22×C5#95312yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—24no—
423C2×D5—22no—
424C4×C5—22no—
425C4×C5—122no—
426C4×C5#95312yes—
427C4×C5C22×#6711yescharacteristic
428C4×C5C22×#6711yescharacteristic
429Dic5—22no—
430Dic5—24no—
431Dic5—122no—
432#41—22no—
433#41—108no—
434#41—104no—
435#41—1016no—
436#41—104no—
437#41—102no—
438#41—102no—
439#41#120114yes—
440C2×Q8—32no—
441C2×Q8—51no—
442C2×Q8—54no—
443C2×Q8—52no—
444C2×Q8—61no—
445C2×Q8—62no—
446C2×Q8—62no—
447C2×Q8—102no—
448C2×Q8—108no—
449C2×Q8—104no—
450C2×Q8—104no—
451C2×Q8—102no—
452C2×Q8—101no—
453C2×Q8C2×D3×D511yescharacteristic
454C2×D4—21no—
455C2×D4—52no—
456C2×D4—51no—
457C2×D4—102no—
458C2×D4C2×D3×D511yescharacteristic
459C22×C4—21no—
460C22×C4—52no—
461C22×C4—61no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—101no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—64no—
467Q16—308no—
468SD16—64no—
469M16—62no—
470C2×C8—32no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—152no—
474C4⋊C4—304no—
475C22⋊C4—304no—
476C22⋊C4—301no—
477C42—301no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—42no—
482C22×C3—104no—
483C22×C3—102no—
484C22×C3#408312yes—
485C22×C3C2×D4×D511yescharacteristic
486C3×C4—22no—
487C3×C4—102no—
488C3×C4—104no—
489C3×C4#408312yes—
490C3×C4C2×D4×D511yescharacteristic
491C3×C4C22×C22⋊D511yescharacteristic
492Dic3—42no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5#583812yes—
497C2×C5C2×#95311yescharacteristic
498D5—42no—
499C23—21no—
500C23—52no—
501C23D5×#6711yescharacteristic
502Q8—21no—
503Q8—54no—
504Q8—62no—
505Q8—62no—
506Q8—108no—
507Q8—102no—
508Q8—102no—
509Q8—104no—
510Q8—122no—
511Q8C2×#120112yes—
512D4—24no—
513D4—21no—
514D4—108no—
515D4—104no—
516D4—102no—
517D4C2×#120112yes—
518C2×C4—21no—
519C2×C4—24no—
520C2×C4—52no—
521C2×C4—62no—
522C2×C4—108no—
523C2×C4—108no—
524C2×C4—102no—
525C2×C4—104no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—122no—
529C2×C4—302no—
530C2×C4C2×#120112yes—
531C2×C4D5×#6712yes—
532C2×C4D5×#6711yescharacteristic
533C2×C4C22×D3×D511yescharacteristic
534C8—62no—
535C8—302no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3—202no—
539C2×C3#6611312yes—
540C2×C3C2×#408311yescharacteristic
541C5#8411711yescharacteristic, complemented, Sylow
542C22—22no—
543C22—22no—
544C22—42no—
545C22—104no—
546C22—102no—
547C22#9156312yes—
548C22C2×D5×#6711yescharacteristic
549C4—22no—
550C4—102no—
551C4—104no—
552C4—122no—
553C4—602no—
554C4#9156312yes—
555C4C22×#120111yescharacteristic
556C4C2×D5×#6711yescharacteristic
557C3#1061571411yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—202no—
561C2#1175533612yes—
562C2C2×#9156311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C5×#951C2semidirect
3. #11754251C2semidirect
4. C22×#6661C2semidirect
5. #11751334C2semidirect
6. #11749290C2semidirect
7. #11749047C2semidirect
8. #11748400C2semidirect
9. #11748343C2semidirect
96. C2×#951D5semidirect
478. C3×C5#3011semidirect
541. C5#84117semidirect
557. C3#10615714semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×C5×#9512
#117542512
C22×#66612
#117513342
#117492902
#117490472
#117484002
#117483432
#106157143
#841175