Finite Group Databasebeta

← #14321077

Subgroups — #14321077

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic15C211yesmaximal, characteristic
2C2×#91766C211yesmaximal, characteristic
3C2×#91766C211yesmaximal, characteristic
4C3×C5×#385C211yesmaximal, characteristic
5#11751311C211yesmaximal, characteristic
6#11751077C212yesmaximal, complemented
7C4⋊C4×Dic15C212yesmaximal, complemented
8#11751051C211yesmaximal, characteristic
9#11751047C211yesmaximal, characteristic
10#11750750C212yesmaximal, complemented
11#11750748C212yesmaximal, complemented
12#10606109—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2212yes—
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×#6719C2211yescharacteristic
21C2×C4⋊Dic15C2212yes—
22C2×#6712C2211yescharacteristic
23C2×#6712C2212yes—
24C2×#6712C2212yes—
25C2×#6712C2211yescharacteristic
26C2×#6712C2212yes—
27C2×C4×Dic15—24no—
28C2×C4×Dic15C2212yes—
29C2×C4×Dic15C2211yescharacteristic
30C2×C4×Dic15C2212yes—
31C2×C4×Dic15C2211yescharacteristic
32C2×C4×Dic15C2212yes—
33#91766—24no—
34#91766C418yescomplemented
35C3×C5×#95C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#74378—51nomaximal, Hall
40C22×C4×Dic5—31no—
41C2×#4023—31no—
42C2×#4023—31no—
43C5×#385D311yescharacteristic
44#65499—31no—
45C4⋊C4×Dic5—32no—
46#65261—32no—
47#65239—31no—
48#65235—31no—
49#64938—32no—
50#64936—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—24no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×Dic15—22no—
59C22×Dic15—24no—
60C22×Dic15C2×C414yes—
61C22×Dic15D414yes—
62C22×Dic15Q814yes—
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C3×C5×C4⋊C4—24no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4C2×C414yes—
72#6719—22no—
73#6719C2×C414yes—
74C4⋊Dic15—24no—
75#6712—24no—
76#6712—22no—
77#6712—22no—
78#6712—24no—
79#6712C2×C418yescomplemented
80C4×Dic15—22no—
81C4×Dic15—22no—
82C4×Dic15—24no—
83C4×Dic15—24no—
84C4×Dic15C2×C418yescomplemented
85C22×C4×Dic3—51no—
86C2×#877—51no—
87C2×#877—51no—
88C3×#385D511yescharacteristic
89#5210—51no—
90#4976—52no—
91Dic3×C4⋊C4—52no—
92#4950—51no—
93#4946—51no—
94#4649—52no—
95#4647—52no—
96C23×C4×C5C2×D311yescharacteristic
97C23×Dic5—31no—
98C23×Dic5—31no—
99C2×C5×C4⋊C4C2×D312yes—
100C2×C5×C22⋊C4C2×D311yescharacteristic
101C2×C5×C22⋊C4C2×D311yescharacteristic
102C2×C22⋊Dic5—31no—
103C2×C22⋊Dic5—31no—
104C2×C4⋊Dic5—32no—
105C2×#683—32no—
106C2×#683—31no—
107C2×#683—31no—
108C2×#683—32no—
109C2×#683—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—64no—
116#4023—38no—
117#4023—64no—
118C5×#95C2×D312yes—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#2296—151noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×Q812yes—
128C23×C3×C5C2411yescharacteristic
129C2×C3×C4×C5—28no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C414yes—
139C2×C3×C4×C5#4114yes—
140C2×Dic15—28no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—21no—
146C2×Dic15—21no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15C4⋊C4116yescomplemented
150C2×Dic15C22×C414yes—
151C2×Dic15C22×C412yes—
152C2×Dic15C22×C412yes—
153C2×Dic15C2×D412yes—
154C2×Dic15C2×D412yes—
155C2×Dic15C2×Q812yes—
156C2×Dic15C2×Q812yes—
157C2×Dic15#4114yes—
158C23×C3×C4C2×D511yescharacteristic
159C23×Dic3—51no—
160C23×Dic3—51no—
161C2×C3×C4⋊C4C2×D512yes—
162C2×C3×C22⋊C4C2×D511yescharacteristic
163C2×C3×C22⋊C4C2×D511yescharacteristic
164C2×#217—51no—
165C2×#217—51no—
166C2×C4⋊Dic3—52no—
167C2×Dic3⋊C4—52no—
168C2×Dic3⋊C4—51no—
169C2×Dic3⋊C4—52no—
170C2×Dic3⋊C4—52no—
171C2×Dic3⋊C4—51no—
172C2×C4×Dic3—52no—
173C2×C4×Dic3—52no—
174C2×C4×Dic3—51no—
175C2×C4×Dic3—52no—
176C2×C4×Dic3—51no—
177C2×C4×Dic3—104no—
178#877—58no—
179#877—104no—
180C3×#95C2×D512yes—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C24×C5C22×D311yescharacteristic
185C22×C4×C5—22no—
186C22×C4×C5—24no—
187C22×C4×C5C22×D311yescharacteristic
188C22×C4×C5C22×D311yescharacteristic
189C22×C4×C5C22×D312yes—
190C22×C4×C5C22×D312yes—
191C22×Dic5—34no—
192C22×Dic5—34no—
193C22×Dic5—34no—
194C22×Dic5—31no—
195C22×Dic5—31no—
196C22×Dic5—32no—
197C22×Dic5—32no—
198C22×Dic5—31no—
199C22×Dic5—31no—
200C22×Dic5—64no—
201C22×Dic5—62no—
202C5×C4⋊C4—24no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4C4×D314yes—
205C22⋊Dic5—34no—
206C22⋊Dic5—62no—
207C4⋊Dic5—64no—
208#683—38no—
209#683—62no—
210#683—62no—
211#683—64no—
212#683—64no—
213C4×Dic5—38no—
214C4×Dic5—62no—
215C4×Dic5—62no—
216C4×Dic5—64no—
217C4×Dic5—64no—
218C2×#117—151no—
219C2×#117—151no—
220C22×C42—151no—
221#389—152no—
222#389—152no—
223#385—151no—
224#385—151no—
225#385—151no—
226#385D1511yescharacteristic
227C4×C4⋊C4—152no—
228C4×C4⋊C4—152no—
229C22×C3×C5—24no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—24no—
233C22×C3×C5C2×C4⋊C414yes—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C22×D411yescharacteristic
236C22×C3×C5C22×Q811yescharacteristic
237C22×C3×C5C2×#4112yes—
238C22×C3×C5C2×#4112yes—
239C3×C4×C5—24no—
240C3×C4×C5—24no—
241C3×C4×C5—41no—
242C3×C4×C5—41no—
243Dic15—24no—
244Dic15—24no—
245Dic15—41no—
246Dic15—41no—
247Dic15C2×C4⋊C414yes—
248Dic15C2×C4⋊C414yes—
249C24×C3C22×D511yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—24no—
252C22×C3×C4C22×D511yescharacteristic
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D512yes—
255C22×C3×C4C22×D512yes—
256C22×Dic3—54no—
257C22×Dic3—54no—
258C22×Dic3—54no—
259C22×Dic3—51no—
260C22×Dic3—51no—
261C22×Dic3—52no—
262C22×Dic3—52no—
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3—104no—
266C22×Dic3—102no—
267C3×C4⋊C4—24no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4C4×D514yes—
270#217—54no—
271#217—102no—
272C4⋊Dic3—104no—
273Dic3⋊C4—58no—
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276Dic3⋊C4—104no—
277Dic3⋊C4—104no—
278C4×Dic3—58no—
279C4×Dic3—102no—
280C4×Dic3—102no—
281C4×Dic3—104no—
282C4×Dic3—104no—
283C23×C5—22no—
284C23×C5—22no—
285C23×C5C2×C4×D312yes—
286C23×C5D3×D412yes—
287C23×C5D3×Q812yes—
288C23×C5C23×D311yescharacteristic
289C2×C4×C5—28no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5C2×C4×D314yes—
299C2×C4×C5#23714yes—
300C2×Dic5—316no—
301C2×Dic5—32no—
302C2×Dic5—32no—
303C2×Dic5—32no—
304C2×Dic5—32no—
305C2×Dic5—32no—
306C2×Dic5—32no—
307C2×Dic5—34no—
308C2×Dic5—34no—
309C2×Dic5—68no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5—61no—
315C2×Dic5—61no—
316C2×Dic5—62no—
317C2×Dic5—62no—
318C23×C4—151no—
319C23×C4—151no—
320C23×C4C2×D1511yescharacteristic
321#117—158no—
322#117—304no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4—151no—
326C2×C4⋊C4—152no—
327C2×C4⋊C4—152no—
328C2×C4⋊C4—152no—
329C2×C4⋊C4C2×D1512yes—
330C2×C22⋊C4—151no—
331C2×C22⋊C4—151no—
332C2×C22⋊C4C2×D1511yescharacteristic
333C2×C22⋊C4C2×D1511yescharacteristic
334C2×C42—152no—
335C2×C42—151no—
336C2×C42—151no—
337C2×C42—152no—
338C2×C42—152no—
339C2×C42—304no—
340#95—152no—
341#95—152no—
342#95—152no—
343#95C2×D1512yes—
344C2×C3×C5—24no—
345C2×C3×C5C22×C4⋊C411yescharacteristic
346C2×C3×C5C4×#4112yes—
347C2×C3×C5#52511yescharacteristic
348C2×C3×C5#52511yescharacteristic
349C2×C3×C5#53312yes—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3C2×C4×D512yes—
353C23×C3D4×D512yes—
354C23×C3Q8×D512yes—
355C23×C3C23×D511yescharacteristic
356C2×C3×C4—28no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4C2×C4×D514yes—
366C2×C3×C4#71114yes—
367C2×Dic3—52no—
368C2×Dic3—52no—
369C2×Dic3—52no—
370C2×Dic3—52no—
371C2×Dic3—52no—
372C2×Dic3—52no—
373C2×Dic3—516no—
374C2×Dic3—54no—
375C2×Dic3—54no—
376C2×Dic3—108no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382C2×Dic3—101no—
383C2×Dic3—102no—
384C2×Dic3—102no—
385C22×C5—22no—
386C22×C5—24no—
387C22×C5—22no—
388C22×C5—24no—
389C22×C5D3×C4⋊C414yes—
390C22×C5C22×C4×D311yescharacteristic
391C22×C5C2×D3×D411yescharacteristic
392C22×C5C2×#23712yes—
393C22×C5C2×D3×Q811yescharacteristic
394C22×C5D3×#4112yes—
395C4×C5—24no—
396C4×C5—24no—
397C4×C5—41no—
398C4×C5—41no—
399Dic5—34no—
400Dic5—34no—
401Dic5—64no—
402Dic5—64no—
403Dic5—121no—
404Dic5—121no—
405C24C22×D1511yescharacteristic
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—154no—
409C22×C4—154no—
410C22×C4—154no—
411C22×C4—151no—
412C22×C4—151no—
413C22×C4—152no—
414C22×C4—152no—
415C22×C4—151no—
416C22×C4—151no—
417C22×C4—304no—
418C22×C4—302no—
419C22×C4C22×D1511yescharacteristic
420C22×C4C22×D1511yescharacteristic
421C22×C4C22×D1512yes—
422C22×C4C22×D1512yes—
423C4⋊C4—24no—
424C4⋊C4—158no—
425C4⋊C4—302no—
426C4⋊C4—302no—
427C4⋊C4—304no—
428C4⋊C4—304no—
429C4⋊C4—304no—
430C22⋊C4—22no—
431C22⋊C4—154no—
432C22⋊C4—302no—
433C22⋊C4C4×D1514yes—
434C42—158no—
435C42—304no—
436C42—304no—
437C42—302no—
438C42—302no—
439C3×C5#229611yescharacteristic, complemented, Hall
440C22×C3—24no—
441C22×C3—22no—
442C22×C3—24no—
443C22×C3—22no—
444C22×C3D5×C4⋊C414yes—
445C22×C3C22×C4×D511yescharacteristic
446C22×C3C2×D4×D511yescharacteristic
447C22×C3C2×#71112yes—
448C22×C3C2×Q8×D511yescharacteristic
449C22×C3D5×#4112yes—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—41no—
453C3×C4—41no—
454Dic3—54no—
455Dic3—54no—
456Dic3—104no—
457Dic3—104no—
458Dic3—201no—
459Dic3—201no—
460C2×C5—24no—
461C2×C5C2×D3×C4⋊C411yescharacteristic
462C2×C5C4×#23712yes—
463C2×C5#558611yescharacteristic
464C2×C5#562212yes—
465C2×C5#565611yescharacteristic
466C23—22no—
467C23—22no—
468C23C2×C4×D1512yes—
469C23D4×D1512yes—
470C23Q8×D1512yes—
471C23C23×D1511yescharacteristic
472C2×C4—28no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—1516no—
482C2×C4—152no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—152no—
486C2×C4—152no—
487C2×C4—152no—
488C2×C4—154no—
489C2×C4—154no—
490C2×C4—308no—
491C2×C4—302no—
492C2×C4—302no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4—301no—
496C2×C4—301no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4C2×C4×D1514yes—
500C2×C4#681914yes—
501C2×C3—24no—
502C2×C3C2×D5×C4⋊C411yescharacteristic
503C2×C3C4×#71112yes—
504C2×C3#6592011yescharacteristic
505C2×C3#6595612yes—
506C2×C3#6599011yescharacteristic
507C5#7437811yescharacteristic, complemented, Sylow
508C22—24no—
509C22—22no—
510C22—24no—
511C22—22no—
512C22C4⋊C4×D1514yes—
513C22C22×C4×D1511yescharacteristic
514C22C2×D4×D1511yescharacteristic
515C22C2×#681912yes—
516C22C2×Q8×D1511yescharacteristic
517C22#41×D1512yes—
518C4—24no—
519C4—24no—
520C4—41no—
521C4—41no—
522C4—154no—
523C4—154no—
524C4—304no—
525C4—304no—
526C4—601no—
527C4—601no—
528C3#1060610911yescharacteristic, complemented, Sylow
529C2—24no—
530C2C2×C4⋊C4×D1511yescharacteristic
531C2C4×#681912yes—
532C2#1175634511yescharacteristic
533C2#1175638112yes—
534C2#1175641511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#385C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenter#385D15
hypocenterC3×C5#2296
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
6. #11751077C2semidirect
7. C4⋊C4×Dic15C2semidirect
10. #11750750C2semidirect
11. #11750748C2semidirect
34. #91766C4semidirect
79. #6712C2×C4semidirect
84. C4×Dic15C2×C4semidirect
149. C2×Dic15C4⋊C4semidirect
439. C3×C5#2296semidirect
507. C5#74378semidirect
528. C3#10606109semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic152
C2×#917662
C3×C5×#3852
#117513112
#117510772
C4⋊C4×Dic152
#117510512
#117510472
#117507502
#117507482
#106061093
#743785