Finite Group Databasebeta

← #14326609

Subgroups — #14326609

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91766C211yesmaximal, characteristic
2C22×Dic3⋊Dic5C211yesmaximal, characteristic
3C2×#91528C211yesmaximal, characteristic
4C5×#4942C211yesmaximal, characteristic
5C3×#65232C211yesmaximal, characteristic
6Dic3×C22⋊Dic5C211yesmaximal, characteristic
7#11749473C211yesmaximal, characteristic
8#11748811C212yesmaximal, complemented
9#11748660C212yesmaximal, complemented
10#11748651C212yesmaximal, complemented
11#11748630C212yesmaximal, complemented
12#10605609—31nomaximal, Hall
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18C2×#6712C2212yes—
19C2×C4×Dic15C2212yes—
20#91766—24no—
21C2×C5×#217C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yes—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×Dic3⋊Dic5C418yescomplemented
25C2×Dic3⋊Dic5C2211yescharacteristic
26C2×Dic3⋊Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5C2211yescharacteristic
29C2×#6668C2212yes—
30#91528—24no—
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C5×C3⋊#95C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#74060—51nomaximal, Hall
40C22×C4⋊Dic5—31no—
41C2×#4023—31no—
42C2×#4023—31no—
43C5×#380—31no—
44C4×C22⋊Dic5—31no—
45C4⋊C4×Dic5—32no—
46#65262—32no—
47#65232—31no—
48#65232D311yescharacteristic
49#64943—32no—
50#64943—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×Dic15—22no—
54C22×Dic15—22no—
55C22×Dic15C2×C414yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×C5×Dic3—24no—
60C22×C5×Dic3C2×C414yes—
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C3×Dic5—22no—
65C22×C3×Dic5—22no—
66C22×C3×Dic5C2×C414yes—
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2311yescharacteristic
70C3×C5×C22⋊C4—22no—
71#6719D414yes—
72#6712—24no—
73C4×Dic15—24no—
74C5×#217—22no—
75C5×Dic3⋊C4—24no—
76C3×C22⋊Dic5—22no—
77Dic3⋊Dic5C2×C414yes—
78Dic3⋊Dic5C2×C414yes—
79Dic3⋊Dic5C2×C414yes—
80Dic3⋊Dic5C2×C414yes—
81#6668—24no—
82Dic3×Dic5—24no—
83Dic3×Dic5—24no—
84C2×#926—51no—
85C22×Dic3⋊C4—51no—
86C2×#877—51no—
87C3×#381—51no—
88#4943—51no—
89#4942D511yescharacteristic
90Dic3×C22⋊C4—51no—
91#4655—52no—
92#4652—52no—
93#4649—52no—
94#4647—52no—
95C23×C4×C5—31no—
96C23×Dic5—31no—
97C23×Dic5C2×D311yescharacteristic
98C2×C5×C4⋊C4—32no—
99C2×C5×C22⋊C4—31no—
100C2×C5×C22⋊C4C2×D311yescharacteristic
101C2×C22⋊Dic5—31no—
102C2×C22⋊Dic5C2×D311yescharacteristic
103C2×C4⋊Dic5—38no—
104C2×C4⋊Dic5—31no—
105C2×C4⋊Dic5—31no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5—31no—
108C2×#683—32no—
109C2×#683—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5—32no—
113#4023—64no—
114#4023—64no—
115C5×#95—32no—
116#3963—32no—
117#3963—32no—
118#3963—32no—
119#3963C2×D312yes—
120#3963C2×D312yes—
121#2344—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5C2411yescharacteristic
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×Dic15—28no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—22no—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15C22×C412yes—
139C2×Dic15C22×C412yes—
140C2×Dic15C2×D414yes—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—28no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3C22×C412yes—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3#4114yes—
149C2×C3×Dic5—28no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5C22×C412yes—
159C23×C3×C4—51no—
160C23×Dic3—51no—
161C23×Dic3C2×D511yescharacteristic
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4C2×D511yescharacteristic
164C2×#217—51no—
165C2×#217C2×D511yescharacteristic
166#926—104no—
167C2×C4⋊Dic3—52no—
168C2×Dic3⋊C4—58no—
169C2×Dic3⋊C4—51no—
170C2×Dic3⋊C4—51no—
171C2×Dic3⋊C4—51no—
172C2×Dic3⋊C4—51no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4C2×D512yes—
175C2×C4×Dic3—52no—
176C2×C4×Dic3—52no—
177C2×C4×Dic3—52no—
178#877—104no—
179C3×#95—52no—
180C3×#95—52no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C3⋊#95C2×D512yes—
185C24×C5C22×D311yescharacteristic
186C22×C4×C5—31no—
187C22×C4×C5—34no—
188C22×C4×C5—31no—
189C22×C4×C5—32no—
190C22×C4×C5—64no—
191C22×C4×C5C22×D312yes—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—34no—
195C22×Dic5—32no—
196C22×Dic5—31no—
197C22×Dic5—31no—
198C22×Dic5—62no—
199C22×Dic5—62no—
200C22×Dic5C4×D314yes—
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C22×Dic5C22×D311yescharacteristic
204C5×C4⋊C4—64no—
205C5×C22⋊C4—22no—
206C5×C22⋊C4—62no—
207C22⋊Dic5—22no—
208C22⋊Dic5—34no—
209C4⋊Dic5—34no—
210C4⋊Dic5—34no—
211C4⋊Dic5—34no—
212C4⋊Dic5—34no—
213#683—64no—
214#683—64no—
215C4×Dic5—64no—
216C4×Dic5—64no—
217C4×Dic5—64no—
218C2×#117—151no—
219C2×#117—151no—
220C22×C4⋊C4—151no—
221#389—152no—
222#387—152no—
223#387—152no—
224#381—51no—
225#381—151no—
226#380—31no—
227C4×C4⋊C4—152no—
228C4×C22⋊C4—151no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5C4×D414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C2×#4112yes—
237C22×C3×C5C2×#4111yescharacteristic
238C22×C3×C52−1+412yes—
239C3×C4×C5—42no—
240Dic15—22no—
241Dic15—22no—
242Dic15—24no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—42no—
246C5×Dic3—22no—
247C5×Dic3—42no—
248C5×Dic3#11714yescomplemented
249C24×C3C22×D511yescharacteristic
250C22×C3×C4—54no—
251C22×C3×C4—51no—
252C22×C3×C4—51no—
253C22×C3×C4—52no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C22×C3×C4C22×D512yes—
257C22×Dic3—24no—
258C22×Dic3—54no—
259C22×Dic3—51no—
260C22×Dic3—51no—
261C22×Dic3—52no—
262C22×Dic3—102no—
263C22×Dic3—102no—
264C22×Dic3C4×D514yes—
265C22×Dic3C22×D512yes—
266C22×Dic3C22×D511yescharacteristic
267C22×Dic3C22×D511yescharacteristic
268C3×C22⋊C4—22no—
269C3×C22⋊C4—102no—
270#217—22no—
271#217—54no—
272C4⋊Dic3—104no—
273Dic3⋊C4—24no—
274Dic3⋊C4—54no—
275Dic3⋊C4—54no—
276Dic3⋊C4—54no—
277Dic3⋊C4—54no—
278Dic3⋊C4—104no—
279C4×Dic3—104no—
280C4×Dic3—104no—
281C4×Dic3—104no—
282C23×C5—22no—
283C23×C5—22no—
284C23×C5C2×C4×D312yes—
285C23×C5D3×D412yes—
286C23×C5#23712yes—
287C23×C5C23×D311yescharacteristic
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—32no—
292C2×C4×C5—34no—
293C2×C4×C5—32no—
294C2×C4×C5—68no—
295C2×C4×C5—62no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×Dic5—28no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—32no—
308C2×Dic5—32no—
309C2×Dic5—34no—
310C2×Dic5—68no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315C2×Dic5—62no—
316C2×Dic5—62no—
317C2×Dic5C2×C4×D312yes—
318C2×Dic5C2×C4×D312yes—
319C23×C4—31no—
320C23×C4—51no—
321C23×C4—151no—
322#117—304no—
323#117—304no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—151no—
326C2×C4⋊C4—151no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4—151no—
329C2×C4⋊C4—158no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—51no—
334C2×C22⋊C4—151no—
335C2×C22⋊C4D3×D511yescharacteristic
336C2×C42—152no—
337C2×C42—152no—
338C2×C42—152no—
339#95—32no—
340#95—52no—
341#95—52no—
342#95—152no—
343#95—152no—
344#95—152no—
345C2×C3×C5—24no—
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5C2×C4×D411yescharacteristic
348C2×C3×C5#51911yescharacteristic
349C2×C3×C5#54712yes—
350C2×C3×C5#55212yes—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3C2×C4×D512yes—
354C23×C3D4×D512yes—
355C23×C3#71312yes—
356C23×C3C23×D511yescharacteristic
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—52no—
361C2×C3×C4—52no—
362C2×C3×C4—101no—
363C2×C3×C4—101no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—108no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×Dic3—22no—
371C2×Dic3—28no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—52no—
376C2×Dic3—52no—
377C2×Dic3—54no—
378C2×Dic3—101no—
379C2×Dic3—101no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382C2×Dic3—101no—
383C2×Dic3—102no—
384C2×Dic3—108no—
385C2×Dic3C2×C4×D512yes—
386C2×Dic3C2×C4×D512yes—
387C2×Dic3#71114yes—
388C22×C5—24no—
389C22×C5—24no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5#67⋊C414yes—
393C22×C5C22×C4×D311yescharacteristic
394C22×C5C2×D3×D411yescharacteristic
395C22×C5C2×#23711yescharacteristic
396C22×C5D3×#4112yes—
397C22×C5#101012yes—
398C4×C5—34no—
399C4×C5—42no—
400C4×C5—62no—
401C4×C5—122no—
402Dic5—22no—
403Dic5—22no—
404Dic5—42no—
405Dic5—64no—
406Dic5—62no—
407Dic5—62no—
408C24C2×D3×D511yescharacteristic
409C22×C4—31no—
410C22×C4—34no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—54no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—52no—
417C22×C4—64no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—154no—
421C22×C4—151no—
422C22×C4—151no—
423C22×C4—152no—
424C22×C4—302no—
425C22×C4—302no—
426C22×C4C2×D3×D512yes—
427C4⋊C4—64no—
428C4⋊C4—154no—
429C4⋊C4—154no—
430C4⋊C4—154no—
431C4⋊C4—154no—
432C4⋊C4—304no—
433C4⋊C4—304no—
434C22⋊C4—22no—
435C22⋊C4—62no—
436C22⋊C4—102no—
437C22⋊C4—154no—
438C42—304no—
439C42—304no—
440C42—304no—
441C3×C5#234411yescharacteristic, complemented, Hall
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3#403914yes—
447C22×C3C22×C4×D511yescharacteristic
448C22×C3C2×D4×D511yescharacteristic
449C22×C3C2×#71112yes—
450C22×C3C2×#71311yescharacteristic
451C22×C3#415012yes—
452C3×C4—42no—
453C3×C4—102no—
454C3×C4—102no—
455C3×C4—202no—
456Dic3—22no—
457Dic3—42no—
458Dic3—102no—
459Dic3—102no—
460Dic3—104no—
461Dic3#402314yescomplemented
462C2×C5—24no—
463C2×C5C2×#67⋊C411yescharacteristic
464C2×C5#551611yescharacteristic
465C2×C5D3×#11711yescharacteristic
466C2×C5#565012yes—
467C2×C5#565512yes—
468C23—22no—
469C23—22no—
470C23#676612yes—
471C23C4×D3×D512yes—
472C23#679012yes—
473C23C22×D3×D511yescharacteristic
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—32no—
478C2×C4—34no—
479C2×C4—32no—
480C2×C4—52no—
481C2×C4—52no—
482C2×C4—68no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—108no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—101no—
491C2×C4—101no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—152no—
496C2×C4—152no—
497C2×C4—154no—
498C2×C4—308no—
499C2×C4—301no—
500C2×C4—301no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—301no—
504C2×C4—301no—
505C2×C3—24no—
506C2×C3C2×#402311yescharacteristic
507C2×C3C2×#403911yescharacteristic
508C2×C3#6585011yescharacteristic
509C2×C3#6594512yes—
510C2×C3#6597612yes—
511C5#7406011yescharacteristic, complemented, Sylow
512C22—24no—
513C22—24no—
514C22—22no—
515C22—22no—
516C22#9139614yes—
517C22C2×#676611yescharacteristic
518C22C2×C4×D3×D511yescharacteristic
519C22#9202012yes—
520C22D3×#71112yes—
521C22C2×#679011yescharacteristic
522C4—34no—
523C4—42no—
524C4—62no—
525C4—102no—
526C4—102no—
527C4—122no—
528C4—202no—
529C4—302no—
530C4—302no—
531C4—304no—
532C3#1060560911yescharacteristic, complemented, Sylow
533C2—24no—
534C2D3×#402311yescharacteristic
535C2#1175298412yes—
536C2#1175318711yescharacteristic
537C2C2×#9139611yescharacteristic
538C2#1175482512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2344
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #11748811C2semidirect
9. #11748660C2semidirect
10. #11748651C2semidirect
11. #11748630C2semidirect
24. C2×Dic3⋊Dic5C4semidirect
248. C5×Dic3#117semidirect
441. C3×C5#2344semidirect
461. Dic3#4023semidirect
511. C5#74060semidirect
532. C3#10605609semidirect

Maximal subgroups

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

subgroupindex
C2×#917662
C22×Dic3⋊Dic52
C2×#915282
C5×#49422
C3×#652322
Dic3×C22⋊Dic52
#117494732
#117488112
#117486602
#117486512
#117486302
#106056093
#740605