Finite Group Databasebeta

← #14307504

Subgroups — #14307504

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4024C211yesmaximal, characteristic
2#11749506C211yesmaximal, characteristic
3Dic5×#217C211yesmaximal, characteristic
4#11746347C211yesmaximal, characteristic
5C5×#4526C211yesmaximal, characteristic
6#11746019C211yesmaximal, characteristic
7#11746019C211yesmaximal, characteristic
8#10599748—31nomaximal, Hall
9C23×C3×Dic5C2211yescharacteristic
10C22×C3×Dic10C411yescharacteristic, complemented
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×C3×C4⋊Dic5C411yescharacteristic, complemented
18C2×C3×#683C411yescharacteristic, complemented
19C2×C3×#683C411yescharacteristic, complemented
20C3×#4024—21no—
21C3×#4024—21no—
22C3×#4024—21no—
23C3×#4024—21no—
24C2×#6668—21no—
25C2×Dic3×Dic5—21no—
26#90994—21no—
27#90994—21no—
28#71701—51nomaximal, Hall
29C2×#4024D311yescharacteristic
30#65231—31no—
31C22⋊C4×Dic5—31no—
32C5×#342—31no—
33#64747—31no—
34#64747—31no—
35#64746—31no—
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×Dic15—21no—
40C22×Dic15—21no—
41C22×C5×Dic3—21no—
42C22×C5×Dic3—21no—
43C22×C3×Dic5—42no—
44C22×C3×Dic5C2×C411yescharacteristic
45C22×C3×Dic5C2×C411yescharacteristic
46C22×C3×Dic5C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C22×C3×Dic5D411yescharacteristic
49C22×C3×Dic5D411yescharacteristic
50C22×C3×Dic5D411yescharacteristic
51C22×C3×Dic5D411yescharacteristic
52C2×C3×Dic10—21no—
53C2×C3×Dic10—21no—
54C2×C3×Dic10—42no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57#6719—21no—
58#6719—21no—
59#6719—21no—
60#6719Q812yescomplemented
61C5×#217—21no—
62C5×#217—21no—
63C5×#217—21no—
64C5×#217Q812yescomplemented
65C3×C22⋊Dic5—21no—
66C3×C22⋊Dic5—21no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×#683—21no—
70C3×#683—21no—
71C3×#683—21no—
72C3×#683—21no—
73#6668—42no—
74Dic3×Dic5—42no—
75C2×C3×C22⋊Q8—51no—
76#5212—51no—
77C4×#217—51no—
78#4526—51no—
79#4526—51no—
80#4526—51no—
81#4526D511yescharacteristic
82C23×Dic5C2×D311yescharacteristic
83C22×Dic10Dic311yescharacteristic, complemented
84C2×C5×C22⋊C4—31no—
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4C2×D311yescharacteristic
87C2×C22⋊Dic5—31no—
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5C2×D311yescharacteristic
90C2×C4⋊Dic5Dic311yescharacteristic, complemented
91C2×#683—61no—
92C2×#683Dic311yescharacteristic, complemented
93C2×#683Dic311yescharacteristic, complemented
94C2×C4×Dic5—61no—
95#4024—21no—
96#4024—21no—
97#4024—21no—
98#4024—21no—
99#3963—61no—
100#3963—61no—
101#1996—151noSylow
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5C2×Q811yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—21no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×Dic15—41no—
121C2×C5×Dic3—22no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C2×C5×Dic3—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—21no—
131C2×C3×Dic5—21no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C2×C3×Dic5—41no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C2×C3×Dic5C22⋊C411yescharacteristic
138C2×C3×Dic5C22⋊C411yescharacteristic
139C2×C3×Dic5C22⋊C411yescharacteristic
140C2×C3×Dic5C22⋊C411yescharacteristic
141C3×Dic10—42no—
142C3×Dic10—42no—
143C22×C3×Q8—51no—
144C23×C3×C4—51no—
145C3×C22⋊Q8—101no—
146C3×C22⋊Q8—101no—
147C3×C22⋊Q8—101no—
148C3×C22⋊Q8—101no—
149C2×C3×C4⋊C4—51no—
150C2×C3×C4⋊C4—51no—
151C2×C3×C4⋊C4—51no—
152C2×C3×C22⋊C4—51no—
153C2×C3×C22⋊C4C2×D511yescharacteristic
154C2×#217—51no—
155C2×#217—51no—
156C2×#217C2×D511yescharacteristic
157C2×#217C2×D511yescharacteristic
158C2×C4⋊Dic3—101no—
159C2×C4×Dic3—101no—
160C3⋊#95—101no—
161C3⋊#95—101no—
162C24×C5C22×D311yescharacteristic
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5C2×Dic311yescharacteristic
166C22×C4×C5C2×Dic311yescharacteristic
167C22×Dic5—42no—
168C22×Dic5—61no—
169C22×Dic5—61no—
170C22×Dic5C2×Dic311yescharacteristic
171C22×Dic5C2×Dic311yescharacteristic
172C22×Dic5C2×Dic311yescharacteristic
173C22×Dic5C2×Dic311yescharacteristic
174C22×Dic5#6711yescharacteristic
175C22×Dic5#6711yescharacteristic
176C22×Dic5#6711yescharacteristic
177C22×Dic5#6711yescharacteristic
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10—42no—
181C5×C22⋊C4—21no—
182C5×C22⋊C4—21no—
183C5×C22⋊C4—32no—
184C5×C22⋊C4—61no—
185C5×C22⋊C4—61no—
186C5×C22⋊C4—61no—
187C22⋊Dic5—21no—
188C22⋊Dic5—21no—
189C22⋊Dic5—32no—
190C22⋊Dic5—61no—
191C22⋊Dic5—61no—
192C22⋊Dic5—61no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195#683—21no—
196#683—21no—
197#683—21no—
198#683—21no—
199#683—122no—
200C4×Dic5—122no—
201C2×C22⋊Q8—51no—
202#380—151no—
203C4×C22⋊C4—151no—
204#342—31no—
205#342—151no—
206#342—151no—
207#342—151no—
208C22×C3×C5—21no—
209C22×C3×C5—21no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—21no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×Q811yescharacteristic
220C22×C3×C5C4×Q811yescharacteristic
221C22×C3×C5C22⋊Q811yescharacteristic
222C22×C3×C5C22⋊Q811yescharacteristic
223C22×C3×C5#12411yescharacteristic
224C22×C3×C5C4⋊Q811yescharacteristic
225C3×C4×C5—41no—
226C3×C4×C5—41no—
227Dic15—42no—
228Dic15—81no—
229C3×Dic5—21no—
230C3×Dic5—21no—
231C3×Dic5—21no—
232C3×Dic5—41no—
233C3×Dic5—41no—
234C3×Dic5#9912yes—
235C5×Dic3—42no—
236C5×Dic3—81no—
237C24×C3C22×D511yescharacteristic
238C2×C3×Q8—101no—
239C2×C3×Q8—101no—
240C2×C3×Q8—202no—
241C22×C3×C4—51no—
242C22×C3×C4—51no—
243C22×C3×C4—51no—
244C22×C3×C4—51no—
245C22×C3×C4—51no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—202no—
250C22×C3×C4C4×D511yescharacteristic
251C22×C3×C4C4×D511yescharacteristic
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—101no—
255C22×Dic3—101no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4—101no—
258C3×C4⋊C4—101no—
259C3×C4⋊C4—101no—
260C3×C4⋊C4—101no—
261C3×C4⋊C4—101no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—101no—
265C3×C22⋊C4—101no—
266#217—21no—
267#217—21no—
268#217—21no—
269#217—52no—
270#217—101no—
271#217—101no—
272#217—101no—
273#217Dic1012yescomplemented
274C4⋊Dic3—202no—
275C4×Dic3—202no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5D3×Q811yescharacteristic
279C23×C5D3×Q811yescharacteristic
280C23×C5#23911yescharacteristic
281C23×C5#23911yescharacteristic
282C23×C5C22×Dic311yescharacteristic
283C23×C5C2×#6711yescharacteristic
284C23×C5C2×#6711yescharacteristic
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—62no—
290C2×C4×C5—121no—
291C2×C4×C5—121no—
292C2×C4×C5—121no—
293C2×C4×C5—121no—
294C2×C4×C5—121no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—62no—
306C2×Dic5—121no—
307C2×Dic5—121no—
308C2×Dic5—121no—
309C2×Dic5—121no—
310C2×Dic5—121no—
311C2×Dic5#21711yescharacteristic
312C2×Dic5#21711yescharacteristic
313C2×Dic5#21711yescharacteristic
314C2×Dic5#21711yescharacteristic
315Dic10—42no—
316Dic10—42no—
317C22×Q8—51no—
318C23×C4—51no—
319C22⋊Q8—101no—
320C22⋊Q8—101no—
321C22⋊Q8—101no—
322C22⋊Q8—101no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—51no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—301no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—51no—
330C2×C22⋊C4—151no—
331C2×C22⋊C4—151no—
332C2×C22⋊C4D3×D511yescharacteristic
333C2×C42—301no—
334#95—301no—
335#95—301no—
336C2×C3×C5—21no—
337C2×C3×C5—21no—
338C2×C3×C5—21no—
339C2×C3×C5—21no—
340C2×C3×C5—21no—
341C2×C3×C5—21no—
342C2×C3×C5#39111yescharacteristic
343C2×C3×C5C2×#9911yescharacteristic
344C2×C3×C5#41011yescharacteristic
345C23×C3—41no—
346C23×C3—41no—
347C23×C3C2×Dic1011yescharacteristic
348C23×C3C2×C4×D511yescharacteristic
349C23×C3#70911yescharacteristic
350C23×C3D4×D511yescharacteristic
351C23×C3D4×D511yescharacteristic
352C23×C3#71111yescharacteristic
353C23×C3Q8×D511yescharacteristic
354C3×Q8—202no—
355C3×Q8—202no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—51no—
361C2×C3×C4—51no—
362C2×C3×C4—51no—
363C2×C3×C4—51no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4—102no—
367C2×C3×C4—101no—
368C2×C3×C4—101no—
369C2×C3×C4—201no—
370C2×C3×C4—201no—
371C2×C3×C4—201no—
372C2×C3×C4—201no—
373C2×C3×C4—201no—
374C2×Dic3—22no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—102no—
381C2×Dic3—201no—
382C2×Dic3—201no—
383C2×Dic3—201no—
384C2×Dic3—201no—
385C2×Dic3—201no—
386C22×C5—21no—
387C22×C5—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5#94411yescharacteristic
397C22×C5Q8×Dic311yescharacteristic
398C22×C5Q8×Dic311yescharacteristic
399C22×C5#94611yescharacteristic
400C22×C5#94611yescharacteristic
401C22×C5#94711yescharacteristic
402C22×C5C2×#21711yescharacteristic
403C4×C5—41no—
404C4×C5—41no—
405C4×C5—122no—
406C4×C5—241no—
407Dic5—21no—
408Dic5—21no—
409Dic5—21no—
410Dic5—41no—
411Dic5—41no—
412Dic5—122no—
413Dic5—241no—
414Dic5#83412yes—
415C24C2×D3×D511yescharacteristic
416C2×Q8—101no—
417C2×Q8—101no—
418C2×Q8—202no—
419C22×C4—51no—
420C22×C4—51no—
421C22×C4—51no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—202no—
430C22×C4—301no—
431C22×C4—301no—
432C22×C4D5×Dic311yescharacteristic
433C22×C4D5×Dic311yescharacteristic
434C4⋊C4—101no—
435C4⋊C4—101no—
436C4⋊C4—101no—
437C4⋊C4—101no—
438C4⋊C4—101no—
439C4⋊C4—101no—
440C4⋊C4—602no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—32no—
444C22⋊C4—61no—
445C22⋊C4—61no—
446C22⋊C4—61no—
447C22⋊C4—101no—
448C22⋊C4—101no—
449C22⋊C4—152no—
450C22⋊C4—301no—
451C22⋊C4—301no—
452C22⋊C4—301no—
453C42—602no—
454C3×C5#199611yescharacteristic, complemented, Hall
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3C4×Dic1011yescharacteristic
466C22×C3#402411yescharacteristic
467C22×C3D5×C22⋊C411yescharacteristic
468C22×C3#403111yescharacteristic
469C22×C3#403311yescharacteristic
470C22×C3#403411yescharacteristic
471C22×C3#404211yescharacteristic
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—52no—
475C3×C4—101no—
476C3×C4—101no—
477C3×C4—101no—
478C3×C4—201no—
479C3×C4—201no—
480Dic3—42no—
481Dic3—81no—
482Dic3—202no—
483Dic3—401no—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—21no—
489C2×C5—21no—
490C2×C5C2×#83411yescharacteristic
491C2×C5#522911yescharacteristic
492C2×C5#524011yescharacteristic
493C23—41no—
494C23—41no—
495C23D3×Dic1011yescharacteristic
496C23#676811yescharacteristic
497C23#676911yescharacteristic
498C23D15⋊Q811yescharacteristic
499C23C2×D5×Dic311yescharacteristic
500C23D5×#6711yescharacteristic
501C23D5×#6711yescharacteristic
502Q8—202no—
503Q8—202no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—51no—
509C2×C4—51no—
510C2×C4—51no—
511C2×C4—51no—
512C2×C4—62no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—302no—
529C2×C4—601no—
530C2×C4—601no—
531C2×C4—601no—
532C2×C4—601no—
533C2×C4—601no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3#6493511yescharacteristic
541C2×C3#6502911yescharacteristic
542C2×C3D5×#9911yescharacteristic
543C5#7170111yescharacteristic, complemented, Sylow
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22#9132611yescharacteristic
555C22#9132711yescharacteristic
556C22Dic3×Dic1011yescharacteristic
557C22#9133111yescharacteristic
558C22#9141011yescharacteristic
559C22#9141111yescharacteristic
560C22D5×#21711yescharacteristic
561C4—41no—
562C4—41no—
563C4—52no—
564C4—101no—
565C4—101no—
566C4—101no—
567C4—122no—
568C4—201no—
569C4—201no—
570C4—241no—
571C4—602no—
572C4—1201no—
573C3#1059974811yescharacteristic, complemented, Sylow
574C2—21no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2#1174867211yescharacteristic
581C2D5×#83411yescharacteristic
582C2#1174917211yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radical, cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1996
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
10. C22×C3×Dic10C4semidirect
17. C2×C3×C4⋊Dic5C4semidirect
18. C2×C3×#683C4semidirect
19. C2×C3×#683C4semidirect
60. #6719Q8semidirect
64. C5×#217Q8semidirect
83. C22×Dic10Dic3semidirect
90. C2×C4⋊Dic5Dic3semidirect
92. C2×#683Dic3semidirect
93. C2×#683Dic3semidirect
273. #217Dic10semidirect
454. C3×C5#1996semidirect
543. C5#71701semidirect
573. C3#10599748semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40242
#117495062
Dic5×#2172
#117463472
C5×#45262
#117460192
#105997483
#717015