Finite Group Databasebeta

← #14424542

Subgroups — #14424542

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×C5×2−1+4C211yesmaximal, characteristic
2#11756584C211yesmaximal, characteristic, complemented
3C2×#91840C211yesmaximal, characteristic, complemented
4C22×#6718C211yesmaximal, characteristic, complemented
5#11751340C214yesmaximal, complemented
6#11751335C211yesmaximal, characteristic, complemented
7#11751334C211yesmaximal, characteristic, complemented
8#11751329C214yesmaximal, complemented
9#11751326C211yesmaximal, characteristic, complemented
10#10615848—31nomaximal, Hall
11C3×C5×2−1+4—24no—
12C3×C5×2−1+4—24no—
13C2×C3×C5×#41—22no—
14C2×C3×C5×#41—21no—
15C2×C3×C5×#41C2212yes—
16C2×C3×C5×#41C2211yescharacteristic
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×Q8—21no—
19C22×C3×C5×Q8C2212yes—
20C22×C3×C5×Q8C2211yescharacteristic
21C22×Dic30C2211yescharacteristic
22#91840—24no—
23#91833—21no—
24C2×#6718—24no—
25C2×#6718C2214yes—
26C2×#6718C2212yes—
27#91825—21no—
28#91824—22no—
29C2×#6716C2212yes—
30#91815C2211yescharacteristic
31#91813C2214yes—
32C2×#6710C2211yescharacteristic
33C22×C3⋊#168C2211yescharacteristic
34#91119C2214yes—
35#91119C2212yes—
36#91116C2212yes—
37#91114C2214yes—
38#84117—51nomaximal, Hall
39C2×C5×2−1+4D311yescharacteristic
40#66159—31no—
41C2×#4097—31no—
42C22×#689—31no—
43#65528—34no—
44#65523—31no—
45#65522—31no—
46#65517—34no—
47#65514—31no—
48C3×C5×#41—216no—
49C3×C5×#41—28no—
50C3×C5×#41—24no—
51C3×C5×#41—24no—
52C3×C5×#41—22no—
53C3×C5×#41—22no—
54C3×C5×#41—22no—
55C3×C5×#41D414yes—
56C2×C3×C5×Q8—28no—
57C2×C3×C5×Q8—24no—
58C2×C3×C5×Q8—24no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8—21no—
61C2×C3×C5×Q8—22no—
62C2×C3×C5×Q8D414yes—
63C2×C3×C5×Q8D411yescharacteristic
64C2×C3×C5×Q8C2311yescharacteristic
65C2×C3×C5×Q8C2312yes—
66C2×C3×C5×D4—22no—
67C2×C3×C5×D4—21no—
68C2×C3×C5×D4D412yes—
69C2×C3×C5×D4D411yescharacteristic
70C2×C3×C5×D4C2311yescharacteristic
71C22×C3×C4×C5—22no—
72C22×C3×C4×C5—21no—
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—21no—
75C22×C3×C4×C5C2312yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15—21no—
78C2×Dic30—22no—
79C2×Dic30—22no—
80C2×Dic30—21no—
81C2×Dic30C2312yes—
82#6719—24no—
83#6719—21no—
84#6718—28no—
85#6718—24no—
86#6716—24no—
87C4⋊Dic15C2312yes—
88#6712—24no—
89C4×Dic15—21no—
90#6710—22no—
91C2×C3⋊#168—22no—
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2312yes—
94C2×C3×2−1+4D511yescharacteristic
95#5825—51no—
96C2×#951—51no—
97C22×#216—51no—
98#5239—54no—
99#5234—51no—
100#5233—51no—
101#5228—54no—
102#5225—51no—
103C5×2−1+4—24no—
104C5×2−1+4—24no—
105C2×C5×#41—22no—
106C2×C5×#41—21no—
107C2×C5×#41C2×D312yes—
108C2×C5×#41C2×D311yescharacteristic
109C2×C5×#41C2×D311yescharacteristic
110C22×C5×Q8—21no—
111C22×C5×Q8C2×D312yes—
112C22×C5×Q8C2×D311yescharacteristic
113C22×Dic10—31no—
114#4097—64no—
115#4090—61no—
116C2×#689—34no—
117C2×#689—32no—
118C2×#689—64no—
119#4082—61no—
120#4081—62no—
121C2×#687—32no—
122#4072—31no—
123#4070—34no—
124C2×#681—31no—
125C22×#168—31no—
126#3967—34no—
127#3967—32no—
128#3964—32no—
129C22⋊#168—34no—
130#3011—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D412yes—
133C23×C3×C5C2×D411yescharacteristic
134C3×C5×Q8—28no—
135C3×C5×Q8—24no—
136C3×C5×Q8—22no—
137C3×C5×Q8—21no—
138C3×C5×Q8—22no—
139C3×C5×Q8C2×D412yes—
140C3×C5×Q8C2×D414yes—
141C3×C5×D4—28no—
142C3×C5×D4—24no—
143C3×C5×D4—24no—
144C3×C5×D4—22no—
145C3×C5×D4—21no—
146C3×C5×D4C2×D412yes—
147C2×C3×C4×C5—28no—
148C2×C3×C4×C5—28no—
149C2×C3×C4×C5—24no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2411yescharacteristic
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15—42no—
163Dic30—22no—
164Dic30—22no—
165Dic30—42no—
166C3⋊#168—22no—
167C3⋊#168—22no—
168C3×2−1+4—24no—
169C3×2−1+4—24no—
170C2×C3×#41—22no—
171C2×C3×#41—21no—
172C2×C3×#41C2×D512yes—
173C2×C3×#41C2×D511yescharacteristic
174C2×C3×#41C2×D511yescharacteristic
175C22×C3×Q8—21no—
176C22×C3×Q8C2×D512yes—
177C22×C3×Q8C2×D511yescharacteristic
178C22×Dic6—51no—
179#951—104no—
180#944—101no—
181C2×#216—52no—
182C2×#216—54no—
183C2×#216—104no—
184#936—101no—
185#935—102no—
186C2×#214—52no—
187#926—51no—
188#924—54no—
189C2×#208—51no—
190C22×C3⋊C8—51no—
191#835—54no—
192#835—52no—
193#832—52no—
194#830—54no—
195C5×#41—216no—
196C5×#41—28no—
197C5×#41—24no—
198C5×#41—24no—
199C5×#41—22no—
200C5×#41—22no—
201C5×#41—22no—
202C5×#41#6714yes—
203C2×C5×Q8—28no—
204C2×C5×Q8—24no—
205C2×C5×Q8—24no—
206C2×C5×Q8—22no—
207C2×C5×Q8—21no—
208C2×C5×Q8—22no—
209C2×C5×Q8#6714yes—
210C2×C5×Q8#6711yescharacteristic
211C2×C5×Q8C22×D311yescharacteristic
212C2×C5×Q8C22×D312yes—
213C2×C5×D4—22no—
214C2×C5×D4—21no—
215C2×C5×D4#6712yes—
216C2×C5×D4#6711yescharacteristic
217C2×C5×D4C22×D311yescharacteristic
218C22×C4×C5—22no—
219C22×C4×C5—21no—
220C22×C4×C5—22no—
221C22×C4×C5—21no—
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—61no—
225C2×Dic10—32no—
226C2×Dic10—62no—
227C2×Dic10—62no—
228C2×Dic10—61no—
229C22⋊Dic5—64no—
230C22⋊Dic5—61no—
231#689—64no—
232#689—68no—
233#687—64no—
234C4⋊Dic5—32no—
235#683—64no—
236C4×Dic5—61no—
237#681—62no—
238C2×#168—32no—
239C2×#168—32no—
240C2×#168—62no—
241C2×2−1+4D1511yescharacteristic
242C2×#137—151no—
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—22no—
253C22×C3×C5—24no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C3×C4×C5—24no—
258C3×C4×C5—22no—
259C3×C4×C5—22no—
260C3×C4×C5#12012yes—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C22×D411yescharacteristic
263Dic15—42no—
264Dic15—42no—
265C3×#41—216no—
266C3×#41—28no—
267C3×#41—24no—
268C3×#41—24no—
269C3×#41—22no—
270C3×#41—22no—
271C3×#41—22no—
272C3×#41C22⋊D514yes—
273C2×C3×Q8—28no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C2×C3×Q8—22no—
277C2×C3×Q8—21no—
278C2×C3×Q8—22no—
279C2×C3×Q8C22⋊D514yes—
280C2×C3×Q8C22⋊D511yescharacteristic
281C2×C3×Q8C22×D511yescharacteristic
282C2×C3×Q8C22×D512yes—
283C2×C3×D4—22no—
284C2×C3×D4—21no—
285C2×C3×D4C22⋊D512yes—
286C2×C3×D4C22⋊D511yescharacteristic
287C2×C3×D4C22×D511yescharacteristic
288C22×C3×C4—22no—
289C22×C3×C4—21no—
290C22×C3×C4—22no—
291C22×C3×C4—21no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—101no—
295C2×Dic6—52no—
296C2×Dic6—102no—
297C2×Dic6—102no—
298C2×Dic6—101no—
299#217—104no—
300#217—101no—
301#216—108no—
302#216—104no—
303#214—104no—
304C4⋊Dic3—52no—
305Dic3⋊C4—104no—
306C4×Dic3—101no—
307#208—102no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—102no—
311C23×C5—21no—
312C23×C5C2×#6712yes—
313C23×C5C2×#6711yescharacteristic
314C5×Q8—28no—
315C5×Q8—24no—
316C5×Q8—22no—
317C5×Q8—21no—
318C5×Q8—22no—
319C5×Q8C2×#6712yes—
320C5×Q8C2×#6714yes—
321C5×D4—28no—
322C5×D4—24no—
323C5×D4—24no—
324C5×D4—22no—
325C5×D4—21no—
326C5×D4C2×#6712yes—
327C2×C4×C5—28no—
328C2×C4×C5—28no—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—24no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5C2×#6712yes—
336C2×C4×C5C2×#6711yescharacteristic
337C2×C4×C5C2×#6712yes—
338C2×C4×C5C2×#6712yes—
339C2×C4×C5C23×D311yescharacteristic
340C2×Dic5—62no—
341C2×Dic5—62no—
342C2×Dic5—122no—
343Dic10—62no—
344Dic10—62no—
345Dic10—122no—
346#168—62no—
347#168—62no—
3482−1+4—24no—
3492−1+4—24no—
350C2×#41—22no—
351C2×#41—21no—
352C2×#41C2×D1512yes—
353C2×#41C2×D1511yescharacteristic
354C2×#41C2×D1511yescharacteristic
355C22×Q8—21no—
356C22×Q8—151no—
357C22×Q8C2×D1512yes—
358C22×Q8C2×D1511yescharacteristic
359#137—304no—
360C2×Q16—154no—
361C2×Q16—152no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—151no—
365C22×C8—151no—
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—151no—
371#103—152no—
372#103—154no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5—42no—
377C2×C3×C5—42no—
378C2×C3×C5C2×#12011yescharacteristic
379C2×C3×C5#57812yes—
380C23×C3—21no—
381C23×C3C2×C22⋊D512yes—
382C23×C3C2×C22⋊D511yescharacteristic
383C3×Q8—28no—
384C3×Q8—24no—
385C3×Q8—22no—
386C3×Q8—21no—
387C3×Q8—22no—
388C3×Q8C2×C22⋊D512yes—
389C3×Q8C2×C22⋊D514yes—
390C3×D4—28no—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—22no—
394C3×D4—21no—
395C3×D4C2×C22⋊D512yes—
396C2×C3×C4—28no—
397C2×C3×C4—28no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4C2×C22⋊D512yes—
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C2×C22⋊D512yes—
407C2×C3×C4C2×C22⋊D512yes—
408C2×C3×C4C23×D511yescharacteristic
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3—202no—
412Dic6—102no—
413Dic6—102no—
414Dic6—202no—
415C3⋊C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—24no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—42no—
422C22×C5#95312yes—
423C22×C5C22×#6711yescharacteristic
424C4×C5—24no—
425C4×C5—22no—
426C4×C5—22no—
427C4×C5#95312yes—
428C4×C5C22×#6711yescharacteristic
429C4×C5C22×#6711yescharacteristic
430Dic5—122no—
431Dic5—122no—
432#41—216no—
433#41—28no—
434#41—24no—
435#41—24no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41#122014yes—
440C2×Q8—28no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—152no—
447C2×Q8—301no—
448C2×Q8—302no—
449C2×Q8—302no—
450C2×Q8#122014yes—
451C2×Q8#122011yescharacteristic
452C2×Q8C22×D1511yescharacteristic
453C2×Q8C22×D1512yes—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4#122012yes—
457C2×D4#122011yescharacteristic
458C2×D4C22×D1511yescharacteristic
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—301no—
464C22×C4C22×D1512yes—
465C22×C4C22×D1511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—302no—
470C2×C8—152no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—152no—
474C4⋊C4—304no—
475C22⋊C4—301no—
476C22⋊C4—304no—
477C42—301no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—24no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—42no—
484C22×C3#409912yes—
485C22×C3C22×C22⋊D511yescharacteristic
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4#409912yes—
490C3×C4C22×C22⋊D511yescharacteristic
491C3×C4C22×C22⋊D511yescharacteristic
492Dic3—202no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5—42no—
497C2×C5#583812yes—
498C2×C5C2×#95311yescharacteristic
499C23—21no—
500C23C2×#122012yes—
501C23C2×#122011yescharacteristic
502Q8—28no—
503Q8—24no—
504Q8—22no—
505Q8—21no—
506Q8—22no—
507Q8—302no—
508Q8—302no—
509Q8—602no—
510Q8C2×#122012yes—
511Q8C2×#122014yes—
512D4—28no—
513D4—24no—
514D4—24no—
515D4—22no—
516D4—21no—
517D4C2×#122012yes—
518C2×C4—28no—
519C2×C4—28no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—602no—
529C2×C4C2×#122012yes—
530C2×C4C2×#122011yescharacteristic
531C2×C4C2×#122012yes—
532C2×C4C2×#122012yes—
533C2×C4C23×D1511yescharacteristic
534C8—302no—
535C8—302no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3—42no—
539C2×C3#6617212yes—
540C2×C3C2×#409911yescharacteristic
541C5#8411711yescharacteristic, complemented, Sylow
542C22—22no—
543C22—24no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22#9184212yes—
548C22C22×#122011yescharacteristic
549C4—24no—
550C4—22no—
551C4—22no—
552C4—602no—
553C4—602no—
554C4#9184212yes—
555C4C22×#122011yescharacteristic
556C4C22×#122011yescharacteristic
557C3#1061584811yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—42no—
561C2#1175659712yes—
562C2C2×#9184211yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC2×C3×C5×2−1+4C2
socleC22×C3×C5C22×D4
hypercenterC2×2−1+4D15
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
2. #11756584C2semidirect
3. C2×#91840C2semidirect
4. C22×#6718C2semidirect
5. #11751340C2semidirect
6. #11751335C2semidirect
7. #11751334C2semidirect
8. #11751329C2semidirect
9. #11751326C2semidirect
478. C3×C5#3011semidirect
541. C5#84117semidirect
557. C3#10615848semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
#117565842
C2×#918402
C22×#67182
#117513402
#117513352
#117513342
#117513292
#117513262
#106158483
#841175