Finite Group Databasebeta

← #14301787

Subgroups — #14301787

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#946C211yesmaximal, characteristic
2C22×D3×#168C211yesmaximal, characteristic
3C2×#91119C211yesmaximal, characteristic, complemented
4C2×C3×#3967C211yesmaximal, characteristic, complemented
5#11748786C211yesmaximal, characteristic
6#11745981C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10602489—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C4×C5×D3C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C5×#946—22no—
14C5×#946C414yescomplemented
15C2×C5×(C2×D3)⋊C4—21no—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C2×C5×Dic3⋊C4—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C2×(C2×D3)⋊Dic5—21no—
21C2×D3×#168—22no—
22C2×D3×#168—22no—
23C2×D3×#168—22no—
24#91119—22no—
25C3×#3967—22no—
26#90994—21no—
27#70270—51nomaximal, Hall
28C2×C5×C22⋊Q8—31no—
29C23×#168—31no—
30C2×#3967—31no—
31C2×#3967D311yescharacteristic, complemented
32#65501—31no—
33#64749—31no—
34#64749—31no—
35C23×C5×D3D411yescharacteristic
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8C2×C412yes—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15—21no—
45C22×C5×Dic3—21no—
46C22×C5×Dic3D411yescharacteristic
47C2×C4×C5×D3—21no—
48C2×C4×C5×D3—21no—
49C2×C4×C5×D3—21no—
50C2×C4×C5×D3—21no—
51C2×C4×C5×D3C2×C412yes—
52C2×C4×C5×D3D412yes—
53C22×C3×Dic5—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168D412yes—
59C5×(C2×D3)⋊C4—24no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3C2×C412yes—
62C5×Dic3⋊C4—24no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C2×C3×#168D412yes—
68(C2×D3)⋊Dic5—42no—
69D3×#168—28no—
70C2×#946D511yescharacteristic
71C22×D3×C8—51no—
72C2×C3×#103—51no—
73C2×#835—51no—
74#4987—51no—
75#4551—51no—
76#4529—51no—
77C22×C5×Q8C2×D311yescharacteristic
78C23×C4×C5—31no—
79C5×C22⋊Q8—34no—
80C5×C22⋊Q8—62no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4—61no—
83C2×C5×C22⋊C4—61no—
84C2×C22⋊Dic5—61no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C22×#168—31no—
88C22×#168—62no—
89C22×#168—62no—
90C22×#168—62no—
91C22×#168C2×D311yescharacteristic
92#3967—22no—
93#3967—62no—
94#3963—61no—
95#1892—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—21no—
100C22×C5×D3—21no—
101C22×C5×D3C22⋊C412yes—
102C22×C5×D3SD1612yes—
103C22×C5×D3Q1612yes—
104C3×C5×Q8—22no—
105C3×C5×Q8—22no—
106C3×C5×Q8—41no—
107C3×C5×Q8—41no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—22no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3C22⋊C412yes—
126C4×C5×D3—22no—
127C4×C5×D3—22no—
128C4×C5×D3—22no—
129C4×C5×D3—22no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C3⋊#168—22no—
134C3×#168—22no—
135C22×C3×Q8C2×D511yescharacteristic
136C22×C4×D3C2×D511yescharacteristic
137C22×C3×C8—51no—
138C2×C3×C4⋊C4—51no—
139#946—22no—
140#946Dic514yescomplemented
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—101no—
143C2×C4⋊Dic3—51no—
144C2×C4⋊Dic3C2×D511yescharacteristic
145C2×Dic3⋊C4—21no—
146C22×C3⋊C8—51no—
147C2×D3×C8—102no—
148C2×D3×C8—102no—
149C2×D3×C8—102no—
150C3×#103—102no—
151#835—102no—
152C3⋊#95—101no—
153C24×C5—31no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8C4×D312yes—
160C22×C4×C5—21no—
161C22×C4×C5—31no—
162C22×C4×C5—32no—
163C22×C4×C5—32no—
164C22×C4×C5—61no—
165C22×C4×C5—61no—
166C22×C4×C5—61no—
167C22×C4×C5—61no—
168C22×C4×C5—61no—
169C22×C4×C5C22×D311yescharacteristic
170C22×Dic5—21no—
171C22×Dic5—61no—
172C5×C4⋊C4—32no—
173C5×C4⋊C4—64no—
174C5×C4⋊C4—61no—
175C5×C22⋊C4—64no—
176C22⋊Dic5—122no—
177C4⋊Dic5—21no—
178C4⋊Dic5—21no—
179C4⋊Dic5—61no—
180C4⋊Dic5—61no—
181C2×#168—21no—
182C2×#168—21no—
183C2×#168—32no—
184C2×#168—68no—
185C2×#168—61no—
186C2×#168—61no—
187C2×#168#6712yes—
188C23×C8—151no—
189C2×C22⋊Q8—31no—
190C2×#103—51no—
191C2×#103—151no—
192#380—151no—
193#340—151no—
194#340—151no—
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C22×C3×C5#12111yescharacteristic
197C22×C3×C5#12111yescharacteristic
198C22×C3×C5C2×SD1611yescharacteristic
199C22×C3×C5C2×Q1611yescharacteristic
200C22×C3×C5#13511yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C2×C5×D3—22no—
203C2×C5×D3—22no—
204C2×C5×D3—22no—
205C2×C5×D3—22no—
206C2×C5×D3—22no—
207C2×C5×D3—22no—
208C2×C5×D3#10314yescomplemented
209C3×C4×C5—42no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—81no—
215C3×Dic5—81no—
216C5×Dic3—22no—
217C5×Dic3—42no—
218C23×D3C22⋊D511yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C2×Dic512yes—
225C22×C3×C4—21no—
226C22×C3×C4—101no—
227C22×C3×C4C22×D511yescharacteristic
228C22×Dic3—21no—
229C22×Dic3—101no—
230C22×Dic3C22⋊D511yescharacteristic
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3C2×Dic512yes—
236C2×C4×D3C22⋊D512yes—
237C2×C3×C8—52no—
238C2×C3×C8—101no—
239C2×C3×C8—101no—
240C3×C4⋊C4—101no—
241C3×C4⋊C4—101no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—202no—
244C4⋊Dic3—21no—
245C4⋊Dic3—101no—
246C4⋊Dic3—101no—
247C4⋊Dic3C2×Dic512yes—
248Dic3⋊C4—24no—
249C2×C3⋊C8—52no—
250C2×C3⋊C8—101no—
251C2×C3⋊C8—101no—
252D3×C8—108no—
253C23×C5—32no—
254C23×C5—32no—
255C23×C5—32no—
256C23×C5—61no—
257C23×C5—61no—
258C23×C5—61no—
259C23×C5—61no—
260C23×C5D3×D411yescharacteristic
261C5×Q8—22no—
262C5×Q8—22no—
263C5×Q8—41no—
264C5×Q8—41no—
265C2×C4×C5—22no—
266C2×C4×C5—32no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—62no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5#23711yescharacteristic
283C2×C4×C5C2×#6711yescharacteristic
284C2×Dic5—41no—
285C2×Dic5—41no—
286C2×Dic5—41no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C2×Dic5—121no—
290#168—22no—
291#168—62no—
292C22×Q8D3×D511yescharacteristic
293C23×C4—31no—
294C22×C8—51no—
295C22×C8—151no—
296C22×C8—302no—
297C22×C8—302no—
298C22×C8—302no—
299C22⋊Q8—34no—
300C22⋊Q8—62no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—51no—
303C2×C4⋊C4—61no—
304C2×C4⋊C4—151no—
305C2×C22⋊C4—61no—
306C2×C22⋊C4—301no—
307#103—102no—
308#103—302no—
309#95—301no—
310C2×C3×C5#38611yescharacteristic
311C2×C3×C5C2×#10311yescharacteristic
312C2×C3×C5#41611yescharacteristic
313C2×C3×C5#46511yescharacteristic
314C2×C3×C5#46511yescharacteristic
315C2×C3×C5#46711yescharacteristic
316C2×C3×C5#46711yescharacteristic
317C5×D3—24no—
318C23×C3C2×C22⋊D511yescharacteristic
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3#68812yes—
324C22×D3#68912yes—
325C22×D3C22⋊Dic512yes—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—41no—
329C3×Q8—41no—
330C2×C3×C4—22no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—201no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4#71111yescharacteristic
339C2×C3×C4#71111yescharacteristic
340C2×C3×C4C22×Dic511yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3C22⋊Dic512yes—
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—22no—
354C4×D3—22no—
355C3×C8—102no—
356C3⋊C8—102no—
357C22×C5—34no—
358C22×C5—62no—
359C22×C5—62no—
360C22×C5—62no—
361C22×C5—62no—
362C22×C5—62no—
363C22×C5—62no—
364C22×C5D3×C22⋊C411yescharacteristic
365C22×C5#88411yescharacteristic
366C22×C5D3×SD1611yescharacteristic
367C22×C5#91611yescharacteristic
368C22×C5D3×Q1611yescharacteristic
369C22×C5#91911yescharacteristic
370C22×C5#93811yescharacteristic
371C4×C5—42no—
372C4×C5—62no—
373C4×C5—122no—
374C4×C5#67⋊C411yescharacteristic
375C4×C5#88311yescharacteristic
376C4×C5C4×#6711yescharacteristic
377C4×C5#93711yescharacteristic
378Dic5—81no—
379Dic5—241no—
380C24—31no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8D3×Dic512yes—
387C22×C4—21no—
388C22×C4—31no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—101no—
397C22×C4—301no—
398C22×C4C2×D3×D511yescharacteristic
399C2×C8—52no—
400C2×C8—101no—
401C2×C8—101no—
402C2×C8—152no—
403C2×C8—308no—
404C2×C8—301no—
405C2×C8—301no—
406C4⋊C4—32no—
407C4⋊C4—64no—
408C4⋊C4—61no—
409C4⋊C4—101no—
410C4⋊C4—101no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C22⋊C4—64no—
414C22⋊C4—602no—
415C3×C5#189211yescharacteristic, complemented, Hall
416C22×C3#408511yescharacteristic
417C22×C3#408511yescharacteristic
418C22×C3C2×#68811yescharacteristic
419C22×C3C2×#68911yescharacteristic
420C22×C3#409611yescharacteristic
421C22×C3#409611yescharacteristic
422C22×C3C2×C22⋊Dic511yescharacteristic
423C2×D3—22no—
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—22no—
428C2×D3—22no—
429C2×D3#396714yescomplemented
430C3×C4—42no—
431C3×C4—401no—
432C3×C4D4×Dic511yescharacteristic
433C3×C4D4×Dic511yescharacteristic
434C3×C4#408111yescharacteristic
435C3×C4#408311yescharacteristic
436Dic3—22no—
437Dic3—42no—
438Dic3—401no—
439C2×C5—64no—
440C2×C5D3×#10311yescharacteristic
441C2×C5#480411yescharacteristic
442C2×C5#480711yescharacteristic
443C2×C5#481311yescharacteristic
444C2×C5#495611yescharacteristic
445C2×C5#517111yescharacteristic
446C2×C5#518811yescharacteristic
447C23—32no—
448C23—32no—
449C23—32no—
450C23—61no—
451C23—61no—
452C23—61no—
453C23—61no—
454C23D3×C22⋊D511yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459C2×C4—22no—
460C2×C4—32no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—201no—
473C2×C4—201no—
474C2×C4—201no—
475C2×C4—601no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4#678011yescharacteristic
479C2×C4C2×D3×Dic511yescharacteristic
480C2×C4#678211yescharacteristic
481C2×C4D5×#6711yescharacteristic
482C2×C4D3×C22⋊D511yescharacteristic
483C2×C4#679011yescharacteristic
484C8—102no—
485C8—302no—
486C2×C3#6533711yescharacteristic
487C2×C3#6533711yescharacteristic
488C2×C3#6534011yescharacteristic
489C2×C3#6534011yescharacteristic
490C2×C3#6550911yescharacteristic
491C2×C3C2×#396711yescharacteristic
492C2×C3#6552211yescharacteristic
493D3—24no—
494C5#7027011yescharacteristic, complemented, Sylow
495C22—34no—
496C22—62no—
497C22—62no—
498C22—62no—
499C22—62no—
500C22—62no—
501C22—62no—
502C22D3×#68811yescharacteristic
503C22D3×#68911yescharacteristic
504C22#9151711yescharacteristic
505C22#9151911yescharacteristic
506C22D3×C22⋊Dic511yescharacteristic
507C22#9155811yescharacteristic
508C22#9156511yescharacteristic
509C4—42no—
510C4—62no—
511C4—122no—
512C4—401no—
513C4—1201no—
514C4Dic5×#6711yescharacteristic
515C4#9155511yescharacteristic
516C4#67⋊Dic511yescharacteristic
517C4#9157711yescharacteristic
518C3#1060248911yescharacteristic, complemented, Sylow
519C2—64no—
520C2D3×#396711yescharacteristic
521C2#1174921111yescharacteristic
522C2#1174927411yescharacteristic
523C2#1174928011yescharacteristic
524C2#1174929611yescharacteristic
525C2#1174930111yescharacteristic
526C2#1174951911yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1892
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#91119C2semidirect
4. C2×C3×#3967C2semidirect
6. #11745981C2semidirect
7. #11745979C2semidirect
14. C5×#946C4semidirect
31. C2×#3967D3semidirect
140. #946Dic5semidirect
208. C2×C5×D3#103semidirect
415. C3×C5#1892semidirect
429. C2×D3#3967semidirect
494. C5#70270semidirect
518. C3#10602489semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9462
C22×D3×#1682
C2×#911192
C2×C3×#39672
#117487862
#117459812
#117459792
#106024893
#702705