Finite Group Databasebeta

← #14323542

Subgroups — #14323542

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic
2C2×D4×Dic15C211yesmaximal, characteristic
3C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic
5#11751312C211yesmaximal, characteristic, complemented
6#11751085C212yesmaximal, complemented
7#11751081C212yesmaximal, complemented
8#11751052C212yesmaximal, complemented
9#11751051C212yesmaximal, complemented
10#11751051C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
12#10614567—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C23×Dic15C2211yescharacteristic
17C23×Dic15C2211yescharacteristic
18C3×C5×#123C418yescomplemented
19C2×C3×C5×C4⋊C4C2212yes—
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×#6719C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2212yes—
26D4×Dic15—24no—
27C2×C4⋊Dic15—24no—
28C2×C4⋊Dic15C2212yes—
29C2×C4⋊Dic15C2212yes—
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32C2×C4×Dic15C2211yescharacteristic
33C2×C4×Dic15C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#82836—51nomaximal, Hall
40C2×C5×#123D311yescharacteristic
41C2×D4×Dic5—31no—
42C22×C4⋊Dic5—31no—
43#65509—31no—
44#65500—31no—
45#65274—32no—
46#65270—32no—
47#65240—32no—
48#65239—31no—
49#65239—32no—
50C22⋊C4×Dic5—31no—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5C2×C414yescomplemented
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×Dic15—22no—
63C22×Dic15—22no—
64C22×Dic15—42no—
65C22×Dic15—42no—
66C22×Dic15—42no—
67C22×Dic15D414yes—
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2312yes—
70C22×Dic15C2312yes—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C3×C5×C4⋊C4C2×C418yescomplemented
75C3×C5×C22⋊C4C2×C414yescomplemented
76C3×C5×C22⋊C4C2×C418yescomplemented
77#6719—22no—
78#6719—22no—
79#6719—22no—
80#6719—42no—
81C4⋊Dic15—24no—
82C4⋊Dic15—24no—
83C4⋊Dic15—22no—
84C4⋊Dic15—42no—
85C4×Dic15—22no—
86C4×Dic15—42no—
87C2×C3×#123D511yescharacteristic
88C2×D4×Dic3—51no—
89C22×C4⋊Dic3—51no—
90#5220—51no—
91#5211—51no—
92#4984—52no—
93#4980—52no—
94#4951—52no—
95#4950—52no—
96#4950—51no—
97Dic3×C22⋊C4—51no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5C2×D311yescharacteristic
100C23×Dic5—31no—
101C23×Dic5—31no—
102C23×Dic5—31no—
103C5×#123Dic318yescomplemented
104C2×C5×C4⋊C4C2×D312yes—
105C2×C5×C22⋊C4C2×D311yescharacteristic
106C2×C5×C22⋊C4C2×D312yes—
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5—31no—
109C2×C22⋊Dic5—31no—
110C2×C22⋊Dic5—32no—
111D4×Dic5—64no—
112C2×C4⋊Dic5—32no—
113C2×C4⋊Dic5—32no—
114C2×C4⋊Dic5—31no—
115C2×C4⋊Dic5—32no—
116C2×C4⋊Dic5—64no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2322—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5C22×C412yes—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5#4112yes—
135C23×C3×C5C2411yescharacteristic
136C3×C5×D4—28no—
137C2×C3×C4×C5—28no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C414yes—
145C2×C3×C4×C5C22×C414yes—
146C2×C3×C4×C5C22×C412yes—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—21no—
150C2×Dic15—22no—
151C2×Dic15—21no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—44no—
160C2×Dic15—44no—
161C2×Dic15—44no—
162C2×Dic15C2×D412yes—
163C2×Dic15C2×D412yes—
164C22×C3×D4C2×D511yescharacteristic
165C23×C3×C4C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3—51no—
168C23×Dic3—51no—
169C3×#123Dic518yescomplemented
170C2×C3×C4⋊C4C2×D512yes—
171C2×C3×C22⋊C4C2×D511yescharacteristic
172C2×C3×C22⋊C4C2×D512yes—
173C2×#217—51no—
174C2×#217—51no—
175C2×#217—51no—
176C2×#217—52no—
177D4×Dic3—104no—
178C2×C4⋊Dic3—52no—
179C2×C4⋊Dic3—52no—
180C2×C4⋊Dic3—51no—
181C2×C4⋊Dic3—52no—
182C2×C4⋊Dic3—104no—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5C22×D311yescharacteristic
191C24×C5C22×D311yescharacteristic
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4C2×Dic314yes—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5C2×Dic314yescomplemented
198C22×C4×C5C22×D312yes—
199C22×C4×C5C22×D312yes—
200C22×C4×C5C22×D311yescharacteristic
201C22×Dic5—31no—
202C22×Dic5—31no—
203C22×Dic5—34no—
204C22×Dic5—31no—
205C22×Dic5—32no—
206C22×Dic5—32no—
207C22×Dic5—31no—
208C22×Dic5—62no—
209C22×Dic5—62no—
210C22×Dic5—122no—
211C22×Dic5—122no—
212C22×Dic5—122no—
213C5×C4⋊C4C2×Dic318yescomplemented
214C5×C22⋊C4C2×Dic314yescomplemented
215C5×C22⋊C4C2×Dic318yescomplemented
216C22⋊Dic5—62no—
217C22⋊Dic5—62no—
218C22⋊Dic5—62no—
219C22⋊Dic5—122no—
220C4⋊Dic5—64no—
221C4⋊Dic5—64no—
222C4⋊Dic5—62no—
223C4⋊Dic5—122no—
224C4×Dic5—62no—
225C4×Dic5—122no—
226C2×#123D1511yescharacteristic
227C2×C4×D4—151no—
228C22×C4⋊C4—151no—
229#389—152no—
230#388—152no—
231#387—152no—
232#386—151no—
233#385—152no—
234#385—151no—
235#381—151no—
236C4×C22⋊C4—151no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—24no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C4×D414yes—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D411yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5H(5,𝔽2)12yes—
251C22×C3×C52−1+412yes—
252C3×C4×C5—24no—
253C3×C4×C5—22no—
254C3×C4×C5—24no—
255Dic15—22no—
256Dic15—22no—
257Dic15—42no—
258Dic15—41no—
259Dic15—41no—
260Dic15—42no—
261C24×C3C22×D511yescharacteristic
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4C2×Dic514yes—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4C2×Dic514yescomplemented
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C22×C3×C4C22×D512yes—
272C22×Dic3—51no—
273C22×Dic3—51no—
274C22×Dic3—54no—
275C22×Dic3—51no—
276C22×Dic3—52no—
277C22×Dic3—52no—
278C22×Dic3—51no—
279C22×Dic3—102no—
280C22×Dic3—102no—
281C22×Dic3—202no—
282C22×Dic3—202no—
283C22×Dic3—202no—
284C3×C4⋊C4C2×Dic518yescomplemented
285C3×C22⋊C4C2×Dic514yescomplemented
286C3×C22⋊C4C2×Dic518yescomplemented
287#217—102no—
288#217—102no—
289#217—102no—
290#217—202no—
291C4⋊Dic3—104no—
292C4⋊Dic3—104no—
293C4⋊Dic3—102no—
294C4⋊Dic3—202no—
295C4×Dic3—102no—
296C4×Dic3—202no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5D3×D412yes—
304C23×C5#23712yes—
305C23×C5C22×Dic312yes—
306C23×C5C22×Dic312yes—
307C23×C5C23×D311yescharacteristic
308C5×D4—28no—
309C2×C4×C5—28no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5C22×Dic314yes—
317C2×C4×C5C22×Dic314yes—
318C2×C4×C5C22×Dic312yes—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—61no—
324C2×Dic5—62no—
325C2×Dic5—61no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—124no—
334C2×Dic5—124no—
335C2×Dic5—124no—
336C22×D4C2×D1511yescharacteristic
337C23×C4—151no—
338C23×C4—151no—
339C23×C4—151no—
340C23×C4C2×D1511yescharacteristic
341#123Dic1518yescomplemented
342C4×D4—304no—
343C2×C4⋊C4—152no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4—152no—
347C2×C4⋊C4—304no—
348C2×C4⋊C4C2×D1512yes—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C22⋊C4—151no—
352C2×C22⋊C4—152no—
353C2×C22⋊C4C2×D1511yescharacteristic
354C2×C22⋊C4C2×D1512yes—
355C2×C42—151no—
356C2×C42—152no—
357#95—152no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5#52012yes—
366C2×C3×C5#53411yescharacteristic
367C2×C3×C5#53611yescharacteristic
368C2×C3×C5#53912yes—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3D4×D512yes—
376C23×C3#71112yes—
377C23×C3C22×Dic512yes—
378C23×C3C22×Dic512yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—28no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—28no—
388C2×C3×C4C22×Dic514yes—
389C2×C3×C4C22×Dic514yes—
390C2×C3×C4C22×Dic512yes—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—101no—
396C2×Dic3—102no—
397C2×Dic3—101no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—204no—
406C2×Dic3—204no—
407C2×Dic3—204no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—24no—
412C22×C5—22no—
413C22×C5—24no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5—42no—
417C22×C5D4×Dic314yes—
418C22×C5C2×D3×D411yescharacteristic
419C22×C5C2×#23711yescharacteristic
420C22×C5#100912yes—
421C22×C5#101012yes—
422C22×C5C23×Dic311yescharacteristic
423C4×C5—24no—
424C4×C5—22no—
425C4×C5—24no—
426Dic5—62no—
427Dic5—62no—
428Dic5—121no—
429Dic5—122no—
430Dic5—121no—
431Dic5—122no—
432C24C22×D1511yescharacteristic
433C24C22×D1511yescharacteristic
434C2×D4—22no—
435C2×D4—22no—
436C2×D4C2×Dic1514yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—151no—
440C22×C4—151no—
441C22×C4—154no—
442C22×C4—151no—
443C22×C4—152no—
444C22×C4—151no—
445C22×C4—152no—
446C22×C4—302no—
447C22×C4—302no—
448C22×C4—602no—
449C22×C4—602no—
450C22×C4—602no—
451C22×C4C2×Dic1514yescomplemented
452C22×C4C22×D1512yes—
453C22×C4C22×D1511yescharacteristic
454C22×C4C22×D1512yes—
455C4⋊C4—304no—
456C4⋊C4—304no—
457C4⋊C4—302no—
458C4⋊C4—602no—
459C4⋊C4C2×Dic1518yescomplemented
460C22⋊C4—302no—
461C22⋊C4—302no—
462C22⋊C4—302no—
463C22⋊C4—602no—
464C22⋊C4C2×Dic1514yescomplemented
465C22⋊C4C2×Dic1518yescomplemented
466C42—302no—
467C42—602no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3D4×Dic514yes—
479C22×C3C2×D4×D511yescharacteristic
480C22×C3C2×#71111yescharacteristic
481C22×C3#414912yes—
482C22×C3#415012yes—
483C22×C3C23×Dic511yescharacteristic
484C3×C4—24no—
485C3×C4—22no—
486C3×C4—24no—
487Dic3—102no—
488Dic3—102no—
489Dic3—201no—
490Dic3—202no—
491Dic3—201no—
492Dic3—202no—
493C2×C5—24no—
494C2×C5—42no—
495C2×C5#564811yescharacteristic
496C2×C5#565311yescharacteristic
497C2×C5#566512yes—
498C2×C5C2×D4×Dic311yescharacteristic
499C2×C5#582712yes—
500C23—22no—
501C23—22no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—22no—
506C23D4×D1512yes—
507C23#681912yes—
508C23C22×Dic1512yes—
509C23C22×Dic1512yes—
510C23C23×D1511yescharacteristic
511D4—28no—
512C2×C4—28no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—301no—
524C2×C4—301no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—604no—
534C2×C4—604no—
535C2×C4—604no—
536C2×C4C22×Dic1514yes—
537C2×C4C22×Dic1514yes—
538C2×C4C22×Dic1512yes—
539C2×C3—24no—
540C2×C3—42no—
541C2×C3#6598211yescharacteristic
542C2×C3#6598711yescharacteristic
543C2×C3#6599912yes—
544C2×C3C2×D4×Dic511yescharacteristic
545C2×C3#6616112yes—
546C5#8283611yescharacteristic, complemented, Sylow
547C22—24no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—22no—
552C22—24no—
553C22—41no—
554C22—41no—
555C22—42no—
556C22D4×Dic1514yes—
557C22C2×D4×D1511yescharacteristic
558C22C2×#681911yescharacteristic
559C22#9210012yes—
560C22#9210112yes—
561C22C23×Dic1511yescharacteristic
562C4—24no—
563C4—22no—
564C4—24no—
565C4—302no—
566C4—302no—
567C4—601no—
568C4—601no—
569C4—602no—
570C4—602no—
571C3#1061456711yescharacteristic, complemented, Sylow
572C2—24no—
573C2—42no—
574C2#1175640711yescharacteristic
575C2#1175641211yescharacteristic
576C2#1175642412yes—
577C2C2×D4×Dic1511yescharacteristic
578C2#1175658612yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×#123C2
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×#123D15
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic15C2semidirect
5. #11751312C2semidirect
6. #11751085C2semidirect
7. #11751081C2semidirect
8. #11751052C2semidirect
9. #11751051C2semidirect
10. #11751051C2semidirect
11. C22⋊C4×Dic15C2semidirect
18. C3×C5×#123C4semidirect
58. C22×C3×C4×C5C2×C4semidirect
74. C3×C5×C4⋊C4C2×C4semidirect
75. C3×C5×C22⋊C4C2×C4semidirect
76. C3×C5×C22⋊C4C2×C4semidirect
103. C5×#123Dic3semidirect
169. C3×#123Dic5semidirect
197. C22×C4×C5C2×Dic3semidirect
213. C5×C4⋊C4C2×Dic3semidirect
214. C5×C22⋊C4C2×Dic3semidirect
215. C5×C22⋊C4C2×Dic3semidirect
268. C22×C3×C4C2×Dic5semidirect
284. C3×C4⋊C4C2×Dic5semidirect
285. C3×C22⋊C4C2×Dic5semidirect
286. C3×C22⋊C4C2×Dic5semidirect
341. #123Dic15semidirect
451. C22×C4C2×Dic15semidirect
459. C4⋊C4C2×Dic15semidirect
464. C22⋊C4C2×Dic15semidirect
465. C22⋊C4C2×Dic15semidirect
468. C3×C5#2322semidirect
546. C5#82836semidirect
571. C3#10614567semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1232
C2×D4×Dic152
C22×C4⋊Dic152
#117513212
#117513122
#117510852
#117510812
#117510522
#117510512
C22⋊C4×Dic152
#106145673
#828365