Finite Group Databasebeta

← #14301771

Subgroups — #14301771

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×#91390C211yesmaximal, characteristic
2C22×#6648C211yesmaximal, characteristic
3#11751088C211yesmaximal, characteristic
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5C2×#90971C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10599675—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6714—21no—
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×Dic3⋊Dic5—21no—
18C2×#6667—21no—
19#91390—22no—
20#91390C414yescomplemented
21C2×#6648—22no—
22C2×#6648—22no—
23C2×#6648—22no—
24#91115—21no—
25C3×#3942—22no—
26#90971—22no—
27#70270—51nomaximal, Hall
28C22×C8×D5—31no—
29C2×#4043—31no—
30C2×#3948—31no—
31#65276—31no—
32C2×#3942D311yescharacteristic, complemented
33C5×#340—31no—
34#64749—31no—
35C23×D15D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15D411yescharacteristic
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15C2×C412yes—
45C2×C4×D15D412yes—
46C22×C5×Dic3—21no—
47C22×C3×Dic5—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10—21no—
51C2×C3×Dic10—21no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2×C412yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56#6714—42no—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3C2×C412yes—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8D412yes—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168D412yes—
67Dic3⋊Dic5—24no—
68#6667—24no—
69#6648—28no—
70C2×#946—51no—
71C22×D3×C8—51no—
72C2×C3×#103—51no—
73C2×#835—51no—
74#4987—51no—
75#4551—51no—
76#4529D511yescharacteristic, complemented
77C22×C4×D5—31no—
78C22×Dic10C2×D311yescharacteristic
79C22×C5×C8—31no—
80C2×C5×C4⋊C4—31no—
81C2×C5×C4⋊C4C2×D311yescharacteristic
82C2×#685—61no—
83C2×#685—61no—
84C2×C4⋊Dic5—31no—
85C2×C4⋊Dic5—61no—
86C22×#168C2×D311yescharacteristic
87C2×C8×D5—62no—
88C2×C8×D5—62no—
89C2×C8×D5—62no—
90#4043—34no—
91#4043—62no—
92#3963—61no—
93#3948—62no—
94#3942—22no—
95#1892—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—21no—
101C22×D15C22⋊C412yes—
102C22×D15SD1612yes—
103C22×D15Q1612yes—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15C22⋊C412yes—
119C4×D15—22no—
120C4×D15—22no—
121C4×D15—22no—
122C4×D15—22no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C3×Dic10—22no—
130C3×Dic10—22no—
131C3×Dic10—41no—
132C3×Dic10—41no—
133C3×#168—22no—
134C5×C3⋊C8—22no—
135C22×C3×Q8—51no—
136C22×C4×D3—51no—
137C22×C3×C8—51no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139#946—54no—
140#946—102no—
141C2×(C2×D3)⋊C4—101no—
142C2×(C2×D3)⋊C4—101no—
143C2×C4⋊Dic3—51no—
144C2×C4⋊Dic3C2×D511yescharacteristic
145C2×Dic3⋊C4—101no—
146C22×C3⋊C8C2×D511yescharacteristic
147C2×D3×C8—102no—
148C2×D3×C8—102no—
149C2×D3×C8—102no—
150C3×#103—102no—
151#835—102no—
152C3⋊#95—101no—
153C23×D5—31no—
154C22×C4×C5—21no—
155C22×C4×C5—61no—
156C22×C4×C5C22×D311yescharacteristic
157C22×Dic5—21no—
158C22×Dic5—31no—
159C22×Dic5—61no—
160C2×C4×D5—32no—
161C2×C4×D5—32no—
162C2×C4×D5—61no—
163C2×C4×D5—61no—
164C2×C4×D5—61no—
165C2×C4×D5—61no—
166C2×Dic10—21no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10C4×D312yes—
172C2×C5×C8—32no—
173C2×C5×C8—61no—
174C2×C5×C8—61no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—32no—
178C5×C4⋊C4—61no—
179#685—64no—
180#685—122no—
181C4⋊Dic5—64no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168#6712yes—
187C8×D5—68no—
188C23×C8—151no—
189C2×C22⋊Q8—151no—
190C2×#103—51no—
191C2×#103—151no—
192#380—151no—
193#340—31no—
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×D15—22no—
203C2×D15—22no—
204C2×D15—22no—
205C2×D15—22no—
206C2×D15—22no—
207C2×D15—22no—
208C2×D15#10314yescomplemented
209C3×C4×C5—81no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—22no—
215Dic15—81no—
216C3×Dic5—42no—
217C5×Dic3—42no—
218C23×D3—51no—
219C2×C3×Q8—52no—
220C2×C3×Q8—101no—
221C2×C3×Q8—101no—
222C2×C3×Q8—101no—
223C2×C3×Q8—101no—
224C2×C3×Q8—101no—
225C22×C3×C4—21no—
226C22×C3×C4—101no—
227C22×C3×C4C22×D511yescharacteristic
228C22×Dic3—21no—
229C22×Dic3—51no—
230C22×Dic3—101no—
231C2×C4×D3—52no—
232C2×C4×D3—52no—
233C2×C4×D3—101no—
234C2×C4×D3—101no—
235C2×C4×D3—101no—
236C2×C4×D3—101no—
237C2×C3×C8—52no—
238C2×C3×C8—101no—
239C2×C3×C8—101no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242(C2×D3)⋊C4—104no—
243(C2×D3)⋊C4—202no—
244C4⋊Dic3—21no—
245C4⋊Dic3—101no—
246C4⋊Dic3—101no—
247C4⋊Dic3C4×D512yes—
248Dic3⋊C4—104no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8D2012yes—
252D3×C8—108no—
253C23×C5D3×D411yescharacteristic
254C22×D5—32no—
255C22×D5—32no—
256C22×D5—32no—
257C22×D5—61no—
258C22×D5—61no—
259C22×D5—61no—
260C22×D5—61no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—62no—
265C2×C4×C5—121no—
266C2×C4×C5—121no—
267C2×C4×C5C2×C4×D311yescharacteristic
268C2×C4×C5#23511yescharacteristic
269C2×C4×C5D3×D411yescharacteristic
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5#23711yescharacteristic
272C2×C4×C5C2×#6711yescharacteristic
273C2×Dic5—22no—
274C2×Dic5—32no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—61no—
278C2×Dic5—61no—
279C2×Dic5—121no—
280C2×Dic5—121no—
281C2×Dic5—121no—
282C4×D5—62no—
283C4×D5—62no—
284C4×D5—62no—
285C4×D5—62no—
286Dic10—22no—
287Dic10—22no—
288Dic10—41no—
289Dic10—41no—
290C5×C8—62no—
291#168—22no—
292C22×Q8—51no—
293C23×C4—151no—
294C22×C8—31no—
295C22×C8—51no—
296C22×C8—302no—
297C22×C8—302no—
298C22×C8—302no—
299C22⋊Q8—154no—
300C22⋊Q8—302no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—151no—
303C2×C4⋊C4—301no—
304C2×C4⋊C4D3×D511yescharacteristic
305C2×C22⋊C4—301no—
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
317D15—24no—
318C23×C3D4×D511yescharacteristic
319C22×D3—52no—
320C22×D3—52no—
321C22×D3—52no—
322C22×D3—101no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—101no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—201no—
329C3×Q8—201no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—102no—
334C2×C3×C4—201no—
335C2×C3×C4—201no—
336C2×C3×C4C2×C4×D511yescharacteristic
337C2×C3×C4C2×D2011yescharacteristic
338C2×C3×C4#70911yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4#71311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3—201no—
351C4×D3—102no—
352C4×D3—102no—
353C4×D3—102no—
354C4×D3—102no—
355C3×C8—102no—
356C3⋊C8—22no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5D3×SD1611yescharacteristic
360C22×C5#91611yescharacteristic
361C22×C5D3×Q1611yescharacteristic
362C22×C5#91911yescharacteristic
363C22×C5#93811yescharacteristic
364C2×D5—34no—
365C2×D5—62no—
366C2×D5—62no—
367C2×D5—62no—
368C2×D5—62no—
369C2×D5—62no—
370C2×D5—62no—
371C4×C5—81no—
372C4×C5—122no—
373C4×C5#67⋊C411yescharacteristic
374C4×C5#88311yescharacteristic
375C4×C5C4×#6711yescharacteristic
376C4×C5#93711yescharacteristic
377Dic5—42no—
378Dic5—62no—
379Dic5—241no—
380C24—151no—
381C2×Q8—52no—
382C2×Q8—101no—
383C2×Q8—101no—
384C2×Q8—101no—
385C2×Q8—101no—
386C2×Q8—101no—
387C22×C4—21no—
388C22×C4—61no—
389C22×C4—101no—
390C22×C4—151no—
391C22×C4—152no—
392C22×C4—152no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4—301no—
396C22×C4—301no—
397C22×C4—301no—
398C22×C4C2×D3×D511yescharacteristic
399C2×C8—32no—
400C2×C8—52no—
401C2×C8—61no—
402C2×C8—61no—
403C2×C8—101no—
404C2×C8—101no—
405C2×C8—308no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—32no—
409C4⋊C4—61no—
410C4⋊C4—304no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C22⋊C4—304no—
414C22⋊C4—602no—
415C3×C5#189211yescharacteristic, complemented, Hall
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#403011yescharacteristic
418C22×C3#404111yescharacteristic
419C22×C3#405811yescharacteristic
420C22×C3D5×SD1611yescharacteristic
421C22×C3#406211yescharacteristic
422C22×C3D5×Q1611yescharacteristic
423C2×D3—54no—
424C2×D3—102no—
425C2×D3—102no—
426C2×D3—102no—
427C2×D3—102no—
428C2×D3—102no—
429C2×D3—102no—
430C3×C4—81no—
431C3×C4—202no—
432C3×C4C4×D2011yescharacteristic
433C3×C4#402811yescharacteristic
434C3×C4#403911yescharacteristic
435C3×C4#404011yescharacteristic
436Dic3—42no—
437Dic3—102no—
438Dic3—401no—
439C2×C5D3×#10311yescharacteristic
440C2×C5#480411yescharacteristic
441C2×C5#480711yescharacteristic
442C2×C5#481311yescharacteristic
443C2×C5#495611yescharacteristic
444C2×C5#517111yescharacteristic
445C2×C5#518811yescharacteristic
446D5—64no—
447C23—152no—
448C23—152no—
449C23—152no—
450C23—301no—
451C23—301no—
452C23—301no—
453C23—301no—
454C23#679011yescharacteristic
455Q8—102no—
456Q8—102no—
457Q8—201no—
458Q8—201no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—62no—
463C2×C4—102no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—152no—
467C2×C4—201no—
468C2×C4—201no—
469C2×C4—301no—
470C2×C4—301no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—601no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4#677311yescharacteristic
479C2×C4C4×D3×D511yescharacteristic
480C2×C4D3×D2011yescharacteristic
481C2×C4#677711yescharacteristic
482C2×C4#677911yescharacteristic
483C2×C4D5×#6711yescharacteristic
484C8—62no—
485C8—102no—
486C2×C3#6495411yescharacteristic
487C2×C3#6506111yescharacteristic
488C2×C3#6506711yescharacteristic
489C2×C3D5×#10311yescharacteristic
490C2×C3#6510211yescharacteristic
491C2×C3#6515311yescharacteristic
492C2×C3#6517611yescharacteristic
493D3—104no—
494C5#7027011yescharacteristic, complemented, Sylow
495C22—154no—
496C22—302no—
497C22—302no—
498C22—302no—
499C22—302no—
500C22—302no—
501C22—302no—
502C22#9145911yescharacteristic
503C22#9147311yescharacteristic
504C22#9148711yescharacteristic
505C22#9149911yescharacteristic
506C22#9151111yescharacteristic
507C22#9152311yescharacteristic
508C22#9153311yescharacteristic
509C4—81no—
510C4—122no—
511C4—202no—
512C4—302no—
513C4—1201no—
514C4#9135611yescharacteristic
515C4#9139511yescharacteristic
516C4#9144411yescharacteristic
517C4#9147411yescharacteristic
518C3#1059967511yescharacteristic, complemented, Sylow
519C2—304no—
520C2#1174735711yescharacteristic
521C2#1174735911yescharacteristic
522C2#1174749011yescharacteristic
523C2#1174750811yescharacteristic
524C2#1174870011yescharacteristic
525C2#1174905311yescharacteristic
526C2#1174929911yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1892
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3942C2semidirect
5. C2×#90971C2semidirect
6. C5×#4529C2semidirect
7. #11745981C2semidirect
20. #91390C4semidirect
32. C2×#3942D3semidirect
76. #4529D5semidirect
208. C2×D15#103semidirect
415. C3×C5#1892semidirect
494. C5#70270semidirect
518. C3#10599675semidirect

Maximal subgroups

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

subgroupindex
C2×#913902
C22×#66482
#117510882
C2×C3×#39422
C2×#909712
C5×#45292
#117459812
#105996753
#702705