Finite Group Databasebeta

← #14424614

Subgroups — #14424614

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×C5×#1010C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3#11754255C211yesmaximal, characteristic, complemented
4C22×#6661C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749304C214yesmaximal, complemented
7#11749059C214yesmaximal, complemented
8#11748409C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615848—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1010—24no—
13C5×#1010—24no—
14C2×C5×D3×Q8C2212yes—
15C2×C5×#237—22no—
16C2×C5×#237C2212yes—
17C2×C5×#235—21no—
18C2×C5×#235C2211yescharacteristic
19C22×C5×Dic6—21no—
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×Dic10C2211yescharacteristic
22#91815C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C3×#4097—24no—
25C2×C3×#689C2212yes—
26C2×C3×#687C2212yes—
27C2×C3×#681C2211yescharacteristic
28#91539—22no—
29#91385—21no—
30#91370—21no—
31#91369C2214yes—
32C2×#6661—24no—
33C2×#6661C2214yes—
34#91119C2212yes—
35#91116C2212yes—
36#90973C2214yes—
37(C2×D3)⋊#168C2214yes—
38#83983—51nomaximal, Hall
39C2×C5×2−1+4—31no—
40#66159—31no—
41C2×#4097D311yescharacteristic, complemented
42C22×#689—31no—
43#65528—34no—
44#65523—31no—
45#65522—31no—
46#65517—34no—
47#65514—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
55C2×C5×#67—22no—
56C2×C5×#67D412yes—
57C22×C5×Dic3—21no—
58C22×C5×Dic3—22no—
59C5×D3×Q8—24no—
60C5×D3×Q8—24no—
61C5×#237—216no—
62C5×#237—24no—
63C5×#237—24no—
64C5×#235—28no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12D411yescharacteristic
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3C2312yes—
70C2×C5×Dic6—28no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6—22no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6D411yescharacteristic
75C2×C5×Dic6D414yes—
76C2×C5×Dic6C2312yes—
77C22×C3×Dic5—21no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—22no—
80C2×C3×Dic10—21no—
81C2×C3×Dic10C2312yes—
82#6719—21no—
83C4⋊Dic15C2312yes—
84C4×Dic15—21no—
85C2×C3⋊#168—22no—
86C2×C3⋊#168C2312yes—
87C3×#689—24no—
88C3×#687—24no—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91#6669—24no—
92(C2×D3)⋊Dic5—24no—
93#6661—28no—
94C2×#1010D511yescharacteristic
95C2×C3×#137—51no—
96#5816—51no—
97C22×#216—51no—
98#5233—51no—
99#5186—54no—
100#5173—54no—
101#5129—51no—
102#5120—51no—
103C5×2−1+4—64no—
104C5×2−1+4—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—61no—
108C2×C5×#41—62no—
109C2×C5×#41C2×D311yescharacteristic
110C22×C5×Q8—32no—
111C22×C5×Q8—31no—
112C22×C5×Q8—61no—
113C22×Dic10C2×D311yescharacteristic
114#4097—24no—
115#4090—61no—
116C2×#689—34no—
117C2×#689—64no—
118C2×#689C2×D312yes—
119#4082—61no—
120#4081—62no—
121C2×#687C2×D312yes—
122#4072—31no—
123#4070—34no—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126#3967—32no—
127#3967—34no—
128#3964—32no—
129C22⋊#168—34no—
130#3011—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×C5×D3C2×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—
146C5×#67—28no—
147C5×#67—24no—
148C2×C5×Dic3—28no—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3C2×D412yes—
152C5×D12—22no—
153C4×C5×D3—28no—
154C4×C5×D3—22no—
155C4×C5×D3—22no—
156C5×Dic6—28no—
157C5×Dic6—22no—
158C5×Dic6—24no—
159C5×Dic6—22no—
160C5×Dic6C2×D414yes—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—42no—
163C3×Dic10—22no—
164C3×Dic10—22no—
165C3×Dic10—42no—
166C3⋊#168—22no—
167C3×#168—22no—
168C2×C3×#41C2×D511yescharacteristic
169C22×C3×Q8—51no—
170#1010—24no—
171#1010—24no—
172C2×D3×Q8C2×D512yes—
173C2×#237—22no—
174C2×#237C2×D512yes—
175C2×#235—21no—
176C2×#235C2×D511yescharacteristic
177C22×Dic6—21no—
178C22×Dic6C2×D511yescharacteristic
179C3×#137—104no—
180C2×C3×Q16—52no—
181C2×C3×SD16—52no—
182C2×C3×M16—51no—
183#947—101no—
184#946—54no—
185#944—101no—
186C2×#216—54no—
187C2×#216—104no—
188#929—102no—
189#926—51no—
190C22×C3⋊C8—51no—
191#835—52no—
192#832—52no—
193(C2×D3)⋊C8—54no—
194#816—54no—
195C5×#41—22no—
196C5×#41—68no—
197C5×#41—64no—
198C5×#41—616no—
199C5×#41—64no—
200C5×#41—62no—
201C5×#41—62no—
202C5×#41#6714yes—
203C2×C5×Q8—31no—
204C2×C5×Q8—34no—
205C2×C5×Q8—32no—
206C2×C5×Q8—62no—
207C2×C5×Q8—68no—
208C2×C5×Q8—64no—
209C2×C5×Q8—64no—
210C2×C5×Q8—61no—
211C2×C5×Q8—62no—
212C2×C5×Q8C22×D311yescharacteristic
213C2×C5×D4—21no—
214C2×C5×D4—32no—
215C2×C5×D4—31no—
216C2×C5×D4—62no—
217C2×C5×D4C22×D311yescharacteristic
218C22×C4×C5—21no—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—21no—
225C2×Dic10—22no—
226C2×Dic10—22no—
227C2×Dic10—21no—
228C2×Dic10C22×D312yes—
229C22⋊Dic5—64no—
230C22⋊Dic5—61no—
231#689—24no—
232#689—68no—
233#687—24no—
234C4⋊Dic5—32no—
235#683—64no—
236C4×Dic5—61no—
237#681—22no—
238C2×#168—32no—
239C2×#168—62no—
240C2×#168C22×D312yes—
241C2×2−1+4—31no—
242C2×#137—51no—
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×C5×D3—22no—
256C2×C5×D3—24no—
257C3×C4×C5—22no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—42no—
262C3×Dic5—42no—
263C5×Dic3—22no—
264C5×Dic3—24no—
265C3×#41—22no—
266C3×#41C22⋊D514yes—
267C2×C3×Q8—52no—
268C2×C3×Q8—101no—
269C2×C3×Q8—102no—
270C2×C3×Q8—102no—
271C2×C3×Q8C22×D511yescharacteristic
272C2×C3×D4—21no—
273C2×C3×D4C22×D511yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—101no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—22no—
278C2×#67C22⋊D512yes—
279C22×Dic3—21no—
280C22×Dic3—22no—
281D3×Q8—24no—
282D3×Q8—24no—
283#237—216no—
284#237—24no—
285#237—24no—
286#235—28no—
287#235—22no—
288#235—22no—
289C2×D12C22⋊D511yescharacteristic
290C2×C4×D3—22no—
291C2×C4×D3C22×D512yes—
292C2×Dic6—28no—
293C2×Dic6—21no—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6C22⋊D511yescharacteristic
297C2×Dic6C22⋊D514yes—
298C2×Dic6C22×D512yes—
299C3×Q16—104no—
300C3×SD16—104no—
301C3×M16—102no—
302C2×C3×C8—52no—
303#217—101no—
304#216—108no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—52no—
307Dic3⋊C4—104no—
308C4×Dic3—101no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—102no—
311C23×C5—21no—
312C23×C5—32no—
313C23×C5D3×D411yescharacteristic
314C5×Q8—21no—
315C5×Q8—34no—
316C5×Q8—68no—
317C5×Q8—62no—
318C5×Q8—64no—
319C5×Q8—62no—
320C5×Q8C2×#6712yes—
321C5×D4—24no—
322C5×D4—21no—
323C5×D4—68no—
324C5×D4—64no—
325C5×D4—62no—
326C5×D4C2×#6712yes—
327C2×C4×C5—21no—
328C2×C4×C5—24no—
329C2×C4×C5—32no—
330C2×C4×C5—68no—
331C2×C4×C5—68no—
332C2×C4×C5—64no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5D3×D411yescharacteristic
337C2×C4×C5D3×D412yes—
338C2×C4×C5C2×#6712yes—
339C2×C4×C5C23×D311yescharacteristic
340C2×Dic5—22no—
341C2×Dic5—42no—
342C2×Dic5—62no—
343Dic10—22no—
344Dic10—22no—
345Dic10—42no—
346#168—22no—
347#168—62no—
3482−1+4—64no—
3492−1+4—64no—
350C2×#41—31no—
351C2×#41—32no—
352C2×#41—61no—
353C2×#41—62no—
354C2×#41D3×D511yescharacteristic
355C22×Q8—32no—
356C22×Q8—31no—
357C22×Q8—51no—
358C22×Q8—61no—
359#137—104no—
360C2×Q16—52no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—52no—
364C2×M16—51no—
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—
379C5×D3—42no—
380C23×C3—21no—
381C23×C3C2×C22⋊D511yescharacteristic
382C22×D3C2×C22⋊D512yes—
383C3×Q8—21no—
384C3×Q8—102no—
385C3×Q8—102no—
386C3×Q8—202no—
387C3×Q8C2×C22⋊D512yes—
388C3×D4—24no—
389C3×D4—21no—
390C3×D4C2×C22⋊D512yes—
391C2×C3×C4—21no—
392C2×C3×C4—24no—
393C2×C3×C4—102no—
394C2×C3×C4—202no—
395C2×C3×C4C2×C22⋊D512yes—
396C2×C3×C4C2×C22⋊D511yescharacteristic
397C2×C3×C4C2×C22⋊D512yes—
398C2×C3×C4C23×D511yescharacteristic
399#67—28no—
400#67—24no—
401C2×Dic3—28no—
402C2×Dic3—24no—
403C2×Dic3—22no—
404C2×Dic3—102no—
405C2×Dic3C2×C22⋊D512yes—
406D12—22no—
407C4×D3—28no—
408C4×D3—22no—
409C4×D3—22no—
410Dic6—28no—
411Dic6—22no—
412Dic6—24no—
413Dic6—22no—
414Dic6C2×C22⋊D514yes—
415C3×C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—42no—
420C22×C5—64no—
421C22×C5—62no—
422C22×C5#93712yes—
423C22×C5C2×D3×D411yescharacteristic
424C4×C5—22no—
425C4×C5—62no—
426C4×C5—64no—
427C4×C5#93712yes—
428C4×C5C2×D3×D411yescharacteristic
429C4×C5C22×#6711yescharacteristic
430Dic5—42no—
431Dic5—122no—
432#41—22no—
433#41—68no—
434#41—64no—
435#41—616no—
436#41—64no—
437#41—62no—
438#41—62no—
439#41#120114yes—
440C2×Q8—31no—
441C2×Q8—34no—
442C2×Q8—32no—
443C2×Q8—52no—
444C2×Q8—62no—
445C2×Q8—68no—
446C2×Q8—64no—
447C2×Q8—64no—
448C2×Q8—62no—
449C2×Q8—61no—
450C2×Q8—101no—
451C2×Q8—102no—
452C2×Q8—102no—
453C2×Q8C2×D3×D511yescharacteristic
454C2×D4—21no—
455C2×D4—32no—
456C2×D4—31no—
457C2×D4—62no—
458C2×D4C2×D3×D511yescharacteristic
459C22×C4—21no—
460C22×C4—32no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—61no—
464C22×C4—101no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—104no—
467Q16—308no—
468SD16—104no—
469M16—102no—
470C2×C8—52no—
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#409912yes—
483C22×C3C22×C22⋊D511yescharacteristic
484C2×D3—24no—
485C2×D3—22no—
486C3×C4—22no—
487C3×C4—202no—
488C3×C4#409912yes—
489C3×C4C22×C22⋊D511yescharacteristic
490C3×C4C22×C22⋊D511yescharacteristic
491Dic3—22no—
492Dic3—24no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5—122no—
497C2×C5#577912yes—
498C2×C5C2×#93711yescharacteristic
499C23—21no—
500C23—32no—
501C23D3×C22⋊D511yescharacteristic
502Q8—21no—
503Q8—34no—
504Q8—68no—
505Q8—62no—
506Q8—62no—
507Q8—64no—
508Q8—102no—
509Q8—102no—
510Q8—202no—
511Q8C2×#120112yes—
512D4—24no—
513D4—21no—
514D4—68no—
515D4—64no—
516D4—62no—
517D4C2×#120112yes—
518C2×C4—21no—
519C2×C4—24no—
520C2×C4—32no—
521C2×C4—68no—
522C2×C4—68no—
523C2×C4—62no—
524C2×C4—64no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—102no—
528C2×C4—202no—
529C2×C4—302no—
530C2×C4C2×#120112yes—
531C2×C4D3×C22⋊D512yes—
532C2×C4D3×C22⋊D511yescharacteristic
533C2×C4C22×D3×D511yescharacteristic
534C8—102no—
535C8—302no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3#6617212yes—
539C2×C3C2×#409911yescharacteristic
540D3—42no—
541C5#8398311yescharacteristic, complemented, Sylow
542C22—22no—
543C22—22no—
544C22—42no—
545C22—64no—
546C22—62no—
547C22#9156812yes—
548C22C2×D3×C22⋊D511yescharacteristic
549C4—22no—
550C4—62no—
551C4—64no—
552C4—202no—
553C4—602no—
554C4#9156812yes—
555C4C22×#120111yescharacteristic
556C4C2×D3×C22⋊D511yescharacteristic
557C3#1061584811yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—122no—
561C2#1175534112yes—
562C2C2×#9156811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1010C2
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×C3×#4097C2semidirect
3. #11754255C2semidirect
4. C22×#6661C2semidirect
5. #11751334C2semidirect
6. #11749304C2semidirect
7. #11749059C2semidirect
8. #11748409C2semidirect
9. #11748347C2semidirect
41. C2×#4097D3semidirect
478. C3×C5#3011semidirect
541. C5#83983semidirect
557. C3#10615848semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
C2×C3×#40972
#117542552
C22×#66612
#117513342
#117493042
#117490592
#117484092
#117483472
#106158483
#839835