Finite Group Databasebeta

← #14300633

Subgroups — #14300633

Order 1920.

720 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×#91835C211yesmaximal, characteristic
2C2×#91781C211yesmaximal, characteristic
3C2×C3×C5×#103C211yesmaximal, characteristic, complemented
4C2×#91119C211yesmaximal, characteristic, complemented
5C2×#91104C211yesmaximal, characteristic
6#11746372C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10601062—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C22×C4×D15C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13#91835—22no—
14#91835C414yescomplemented
15C2×#6714—21no—
16C2×#6714—21no—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×#6712—21no—
20C2×C4×Dic15—21no—
21C22×C3⋊#168C2211yescharacteristic
22#91781—22no—
23#91781—22no—
24C3×C5×#103—22no—
25#91119—22no—
26#91104—22no—
27#70269—51nomaximal, Hall
28C2×#4092—31no—
29C2×#4038—31no—
30C2×C5×#103D311yescharacteristic, complemented
31C2×#3967—31no—
32C2×#3952—31no—
33#64771—31no—
34#64749—31no—
35C23×D15D411yescharacteristic
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×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C22×Dic15—21no—
47C22×Dic15D411yescharacteristic
48C2×C4×D15—21no—
49C2×C4×D15—21no—
50C2×C4×D15—21no—
51C2×C4×D15—21no—
52C2×C4×D15C2×C412yes—
53C2×C4×D15D412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4D412yes—
59#6714—24no—
60#6714—24no—
61C4⋊Dic15—21no—
62C4⋊Dic15—21no—
63C4⋊Dic15C2×C412yes—
64C4⋊Dic15D412yes—
65#6712—24no—
66C4×Dic15—24no—
67C2×C3⋊#168—21no—
68C2×C3⋊#168—21no—
69C2×C3⋊#168—21no—
70C2×#946—51no—
71C2×#892—51no—
72C2×C3×#103D511yescharacteristic, complemented
73C2×#835—51no—
74C2×(C2×D3)⋊C8—51no—
75#4551—51no—
76#4529—51no—
77C22×C5×Q8C2×D311yescharacteristic
78C22×C4×D5—31no—
79C22×C5×C8C2×D311yescharacteristic
80C2×C5×C4⋊C4C2×D311yescharacteristic
81#4092—34no—
82#4092—62no—
83C2×#685—61no—
84C2×#685—61no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5—31no—
87C2×#683—61no—
88C2×C4×Dic5—61no—
89C22×#168—31no—
90#4038—62no—
91#4038—62no—
92C5×#103—22no—
93#3967—62no—
94#3952—62no—
95#1873—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—21no—
102C22×D15—21no—
103C22×D15C22⋊C412yes—
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—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×Dic15—21no—
121C2×Dic15—21no—
122C2×Dic15—22no—
123C2×Dic15—22no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×Dic15—41no—
127C2×Dic15—41no—
128C2×Dic15C22⋊C412yes—
129C4×D15—22no—
130C4×D15—22no—
131C4×D15—22no—
132C4×D15—22no—
133C3×C5×C8—41no—
134C3⋊#168—41no—
135C22×C3×Q8C2×D511yescharacteristic
136C22×C4×D3—51no—
137C22×C3×C8C2×D511yescharacteristic
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⋊Dic3—51no—
145C2×Dic3⋊C4—101no—
146C2×C4×Dic3—101no—
147C22×C3⋊C8—51no—
148#892—102no—
149#892—102no—
150C3×#103—22no—
151#835—102no—
152(C2×D3)⋊C8—102no—
153C23×D5—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—21no—
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—31no—
164C22×Dic5—61no—
165C22×Dic5—61no—
166C2×C4×D5—32no—
167C2×C4×D5—32no—
168C2×C4×D5—61no—
169C2×C4×D5—61no—
170C2×C4×D5—61no—
171C2×C4×D5—61no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4#6712yes—
177#685—64no—
178#685—64no—
179C4⋊Dic5—32no—
180C4⋊Dic5—32no—
181C4⋊Dic5—61no—
182C4⋊Dic5—61no—
183#683—64no—
184C4×Dic5—64no—
185C2×#168—61no—
186C2×#168—61no—
187C2×#168—61no—
188C2×C22⋊Q8—151no—
189C2×#117—151no—
190C2×#103—151no—
191C2×#103D1511yescharacteristic, complemented
192C2×C22⋊C8—151no—
193#340—151no—
194#340—151no—
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C22×C3×C5#12011yescharacteristic
197C22×C3×C5#12311yescharacteristic
198C22×C3×C5#13511yescharacteristic
199C22×C3×C5#13511yescharacteristic
200C22×C3×C5#13711yescharacteristic
201C22×C3×C5#13711yescharacteristic
202C2×D15—22no—
203C2×D15—22no—
204C2×D15—22no—
205C2×D15—41no—
206C2×D15—41no—
207C2×D15—41no—
208C2×D15—41no—
209C3×C4×C5—42no—
210C3×C4×C5—42no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12111yescharacteristic
215Dic15—22no—
216Dic15—42no—
217Dic15—42no—
218C23×D3—51no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C4×D512yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4C22×D511yescharacteristic
228C22×Dic3—51no—
229C22×Dic3—101no—
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—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4C22⋊D512yes—
242(C2×D3)⋊C4—104no—
243(C2×D3)⋊C4—104no—
244C4⋊Dic3—52no—
245C4⋊Dic3—52no—
246C4⋊Dic3—101no—
247C4⋊Dic3—101no—
248Dic3⋊C4—104no—
249C4×Dic3—104no—
250C2×C3⋊C8—101no—
251C2×C3⋊C8—101no—
252C2×C3⋊C8—101no—
253C23×C5D3×D411yescharacteristic
254C22×D5—32no—
255C22×D5—61no—
256C22×D5—61no—
257C22×D5—61no—
258C22×D5—61no—
259C22×D5—61no—
260C22×D5—61no—
261C5×Q8—22no—
262C5×Q8—22no—
263C5×Q8—41no—
264C5×Q8—41no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—32no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—121no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285C2×Dic5—121no—
286C4×D5—62no—
287C4×D5—62no—
288C4×D5—62no—
289C4×D5—62no—
290C5×C8—41no—
291#168—121no—
292C22×Q8C2×D1511yescharacteristic
293C23×C4—151no—
294C22×C8—151no—
295C22×C8C2×D1511yescharacteristic
296C22⋊Q8—154no—
297C22⋊Q8—302no—
298#117—302no—
299#117—302no—
300C2×C4⋊C4—151no—
301C2×C4⋊C4—151no—
302C2×C4⋊C4—301no—
303C2×C4⋊C4C2×D1511yescharacteristic
304C2×C22⋊C4—301no—
305C2×C22⋊C4—301no—
306C2×C42—301no—
307#103—22no—
308#103—302no—
309C22⋊C8—302no—
310C2×C3×C5#38611yescharacteristic
311C2×C3×C5#41611yescharacteristic
312C2×C3×C5#41911yescharacteristic
313C2×C3×C5#45211yescharacteristic
314C2×C3×C5#45211yescharacteristic
315C2×C3×C5#48511yescharacteristic
316C2×C3×C5#48511yescharacteristic
317D15—42no—
318C23×C3D4×D511yescharacteristic
319C22×D3—52no—
320C22×D3—101no—
321C22×D3—101no—
322C22×D3—101no—
323C22×D3—101no—
324C22×D3—101no—
325C22×D3—101no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—41no—
329C3×Q8—41no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4C2×C4×D511yescharacteristic
337C2×C3×C4#70911yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71111yescharacteristic
341C2×C3×C4C2×C22⋊D511yescharacteristic
342C2×Dic3—52no—
343C2×Dic3—101no—
344C2×Dic3—101no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3—201no—
351C4×D3—102no—
352C4×D3—102no—
353C4×D3—102no—
354C4×D3—102no—
355C3×C8—41no—
356C3⋊C8—201no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88311yescharacteristic
359C22×C5#91511yescharacteristic
360C22×C5#91611yescharacteristic
361C22×C5#91811yescharacteristic
362C22×C5#91911yescharacteristic
363C22×C5#93711yescharacteristic
364C2×D5—62no—
365C2×D5—62no—
366C2×D5—62no—
367C2×D5—121no—
368C2×D5—121no—
369C2×D5—121no—
370C2×D5—121no—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5#67⋊C411yescharacteristic
374C4×C5#88411yescharacteristic
375C4×C5C4×#6711yescharacteristic
376C4×C5#93811yescharacteristic
377Dic5—62no—
378Dic5—122no—
379Dic5—122no—
380C24—151no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8C4×D1512yes—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—151no—
390C22×C4—152no—
391C22×C4—152no—
392C22×C4—301no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4—301no—
396C22×C4—301no—
397C22×C4—301no—
398C22×C4C22×D1511yescharacteristic
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—301no—
403C2×C8—301no—
404C2×C8—301no—
405C4⋊C4—21no—
406C4⋊C4—152no—
407C4⋊C4—152no—
408C4⋊C4—304no—
409C4⋊C4—301no—
410C4⋊C4—301no—
411C4⋊C4#122012yes—
412C22⋊C4—304no—
413C22⋊C4—304no—
414C42—304no—
415C3×C5#187311yescharacteristic, complemented, Hall
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#402911yescharacteristic
418C22×C3#406111yescharacteristic
419C22×C3#406211yescharacteristic
420C22×C3#406411yescharacteristic
421C22×C3#406511yescharacteristic
422C22×C3#408311yescharacteristic
423C2×D3—102no—
424C2×D3—102no—
425C2×D3—102no—
426C2×D3—201no—
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4#402711yescharacteristic
433C3×C4#403011yescharacteristic
434C3×C4C4×C22⋊D511yescharacteristic
435C3×C4#408411yescharacteristic
436Dic3—102no—
437Dic3—202no—
438Dic3—202no—
439C2×C5#480211yescharacteristic
440C2×C5#480411yescharacteristic
441C2×C5#481411yescharacteristic
442C2×C5#481511yescharacteristic
443C2×C5#495611yescharacteristic
444C2×C5#517311yescharacteristic
445C2×C5#518711yescharacteristic
446D5—122no—
447C23—152no—
448C23—301no—
449C23—301no—
450C23—301no—
451C23—301no—
452C23—301no—
453C23—301no—
454C23D4×D1511yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—152no—
466C2×C4—301no—
467C2×C4—301no—
468C2×C4—302no—
469C2×C4—302no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—302no—
473C2×C4—302no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4C2×C4×D1511yescharacteristic
479C2×C4#681711yescharacteristic
480C2×C4D4×D1511yescharacteristic
481C2×C4D4×D1511yescharacteristic
482C2×C4#681911yescharacteristic
483C2×C4C2×#122011yescharacteristic
484C8—41no—
485C8—601no—
486C2×C3#6509111yescharacteristic
487C2×C3#6509311yescharacteristic
488C2×C3#6510311yescharacteristic
489C2×C3#6510411yescharacteristic
490C2×C3#6524511yescharacteristic
491C2×C3#6546211yescharacteristic
492C2×C3#6547611yescharacteristic
493D3—202no—
494C5#7026911yescharacteristic, complemented, Sylow
495C22—302no—
496C22—302no—
497C22—302no—
498C22—601no—
499C22—601no—
500C22—601no—
501C22—601no—
502C22C22⋊C4×D1511yescharacteristic
503C22#9177211yescharacteristic
504C22#9180411yescharacteristic
505C22#9180511yescharacteristic
506C22#9180711yescharacteristic
507C22#9180811yescharacteristic
508C22#9182611yescharacteristic
509C4—42no—
510C4—42no—
511C4—302no—
512C4—602no—
513C4—602no—
514C4#9177011yescharacteristic
515C4#9177311yescharacteristic
516C4C4×#122011yescharacteristic
517C4#9182711yescharacteristic
518C3#1060106211yescharacteristic, complemented, Sylow
519C2—602no—
520C2#1175090311yescharacteristic
521C2#1175090511yescharacteristic
522C2#1175091511yescharacteristic
523C2#1175091611yescharacteristic
524C2#1175105711yescharacteristic
525C2#1175127411yescharacteristic
526C2#1175128811yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#103C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenterC2×#103D15
hypocenterC3×C5#1873
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×C3×C5×#103C2semidirect
4. C2×#91119C2semidirect
6. #11746372C2semidirect
7. #11746350C2semidirect
14. #91835C4semidirect
30. C2×C5×#103D3semidirect
72. C2×C3×#103D5semidirect
191. C2×#103D15semidirect
415. C3×C5#1873semidirect
494. C5#70269semidirect
518. C3#10601062semidirect

Maximal subgroups

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

subgroupindex
C2×#918352
C2×#917812
C2×C3×C5×#1032
C2×#911192
C2×#911042
#117463722
#117463502
#106010623
#702695