Finite Group Databasebeta

← #14301769

Subgroups — #14301769

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×#91369C211yesmaximal, characteristic
2C22×D3×#168C211yesmaximal, characteristic
3C5×#4987C211yesmaximal, characteristic
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5C2×#90970C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10600307—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×#6669—21no—
18C2×(C2×D3)⋊Dic5—21no—
19#91369—22no—
20#91369C414yescomplemented
21C2×D3×#168—22no—
22C2×D3×#168—22no—
23C2×D3×#168—22no—
24C5×C3⋊#95—21no—
25C3×#3942—22no—
26#90970—22no—
27#70270—51nomaximal, Hall
28C2×#4070—31no—
29C23×#168—31no—
30C5×#380—31no—
31C2×#3942—31no—
32C2×#3942D311yescharacteristic, complemented
33#64749—31no—
34#64749—31no—
35C23×C5×D3D411yescharacteristic
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C22×C5×Dic3D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3C2×C412yes—
46C2×C4×C5×D3D412yes—
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—
56C4⋊Dic15—21no—
57C4⋊Dic15C2×C412yes—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168D412yes—
61C5×(C2×D3)⋊C4—42no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—21no—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168D412yes—
67#6669—24no—
68(C2×D3)⋊Dic5—24no—
69D3×#168—28no—
70C2×#946—51no—
71C22×D3×C8—51no—
72C2×C3×#103—51no—
73C2×#835—51no—
74#4987D511yescharacteristic
75#4551—51no—
76#4529—51no—
77C23×C4×C5—31no—
78C22×Dic10C2×D311yescharacteristic
79C2×C5×C4⋊C4—31no—
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×C5×C22⋊C4—61no—
82C2×C22⋊Dic5—61no—
83C2×C4⋊Dic5—31no—
84#4070—34no—
85#4070—62no—
86C2×#683—61no—
87C22×#168—31no—
88C22×#168—62no—
89C22×#168—62no—
90C22×#168—62no—
91C22×#168C2×D311yescharacteristic
92C5×#95—61no—
93#3942—22no—
94#3942—62no—
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—
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—22no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3C22⋊C412yes—
122C4×C5×D3—22no—
123C4×C5×D3—22no—
124C4×C5×D3—22no—
125C4×C5×D3—22no—
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—
134C3×#168—22no—
135C22×C3×Q8—51no—
136C22×C4×D3C2×D511yescharacteristic
137C22×C3×C8—51no—
138C2×C3×C4⋊C4C2×D511yescharacteristic
139#946—54no—
140#946—102no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—101no—
143C2×C4⋊Dic3—51no—
144C2×C4⋊Dic3C2×D511yescharacteristic
145C2×Dic3⋊C4—101no—
146C22×C3⋊C8—51no—
147C2×D3×C8—102no—
148C2×D3×C8—102no—
149C2×D3×C8—102no—
150C3×#103—102no—
151#835—102no—
152C3⋊#95—21no—
153C24×C5—31no—
154C22×C4×C5—21no—
155C22×C4×C5—31no—
156C22×C4×C5—32no—
157C22×C4×C5—32no—
158C22×C4×C5—61no—
159C22×C4×C5—61no—
160C22×C4×C5—61no—
161C22×C4×C5—61no—
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C22×Dic5—21no—
165C22×Dic5—61no—
166C2×Dic10—21no—
167C2×Dic10—21no—
168C2×Dic10—21no—
169C2×Dic10—21no—
170C2×Dic10—21no—
171C2×Dic10C4×D312yes—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—61no—
175C5×C4⋊C4—61no—
176C5×C22⋊C4—122no—
177C22⋊Dic5—64no—
178C4⋊Dic5—32no—
179C4⋊Dic5—61no—
180#683—64no—
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—151no—
190C2×#103—51no—
191C2×#103—151no—
192#380—31no—
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—81no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—42no—
215C3×Dic5—42no—
216C5×Dic3—22no—
217C5×Dic3—81no—
218C23×D3C22⋊D511yescharacteristic
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—101no—
230C22×Dic3C22⋊D511yescharacteristic
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3C4×D512yes—
236C2×C4×D3D2012yes—
237C2×C3×C8—52no—
238C2×C3×C8—101no—
239C2×C3×C8—101no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242(C2×D3)⋊C4—42no—
243(C2×D3)⋊C4—104no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—52no—
247C4⋊Dic3—101no—
248Dic3⋊C4—104no—
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
261C2×C4×C5—32no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5—41no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—121no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5C2×C4×D311yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5#23711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×Dic5—22no—
281C2×Dic5—41no—
282C2×Dic5—41no—
283C2×Dic5—62no—
284C2×Dic5—121no—
285C2×Dic5—121no—
286Dic10—22no—
287Dic10—22no—
288Dic10—41no—
289Dic10—41no—
290#168—22no—
291#168—62no—
292C22×Q8—51no—
293C23×C4—31no—
294C22×C8—51no—
295C22×C8—151no—
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—61no—
306C2×C22⋊C4—301no—
307#103—102no—
308#103—302no—
309#95—61no—
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#68512yes—
324C22×D3#68712yes—
325C22×D3#68912yes—
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×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71111yescharacteristic
341C2×C3×C4#71111yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—102no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3#68512yes—
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—62no—
372C4×C5—81no—
373C4×C5—241no—
374C4×C5#67⋊C411yescharacteristic
375C4×C5#88311yescharacteristic
376C4×C5C4×#6711yescharacteristic
377C4×C5#93711yescharacteristic
378Dic5—42no—
379Dic5—122no—
380C24—31no—
381C2×Q8—52no—
382C2×Q8—101no—
383C2×Q8—101no—
384C2×Q8—101no—
385C2×Q8—101no—
386C2×Q8—101no—
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—21no—
407C4⋊C4—21no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—152no—
411C4⋊C4—304no—
412C4⋊C4—301no—
413C22⋊C4—122no—
414C22⋊C4—304no—
415C3×C5#189211yescharacteristic, complemented, Hall
416C22×C3C2×#68511yescharacteristic
417C22×C3C2×#68711yescharacteristic
418C22×C3#408511yescharacteristic
419C22×C3#408511yescharacteristic
420C22×C3C2×#68911yescharacteristic
421C22×C3#409611yescharacteristic
422C22×C3#409611yescharacteristic
423C2×D3—22no—
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—22no—
428C2×D3—22no—
429C2×D3#394214yescomplemented
430C3×C4—81no—
431C3×C4—202no—
432C3×C4#402711yescharacteristic
433C3×C4#402711yescharacteristic
434C3×C4#402811yescharacteristic
435C3×C4#403211yescharacteristic
436Dic3—22no—
437Dic3—81no—
438Dic3—202no—
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—102no—
456Q8—102no—
457Q8—201no—
458Q8—201no—
459C2×C4—32no—
460C2×C4—41no—
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—102no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—201no—
474C2×C4—201no—
475C2×C4—302no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4#677211yescharacteristic
479C2×C4C4×D3×D511yescharacteristic
480C2×C4D3×D2011yescharacteristic
481C2×C4#677711yescharacteristic
482C2×C4#678011yescharacteristic
483C2×C4D5×#6711yescharacteristic
484C8—102no—
485C8—302no—
486C2×C3#6524711yescharacteristic
487C2×C3C2×#394211yescharacteristic
488C2×C3#6529111yescharacteristic
489C2×C3#6533011yescharacteristic
490C2×C3#6533011yescharacteristic
491C2×C3#6534011yescharacteristic
492C2×C3#6534011yescharacteristic
493D3—24no—
494C5#7027011yescharacteristic, complemented, Sylow
495C22—34no—
496C22—62no—
497C22—62no—
498C22—62no—
499C22—62no—
500C22—62no—
501C22—62no—
502C22#9145311yescharacteristic
503C22D3×#68511yescharacteristic
504C22D3×#68711yescharacteristic
505C22#9149511yescharacteristic
506C22D3×#68911yescharacteristic
507C22#9151911yescharacteristic
508C22#9156511yescharacteristic
509C4—62no—
510C4—81no—
511C4—202no—
512C4—241no—
513C4—602no—
514C4#9144011yescharacteristic
515C4#9144211yescharacteristic
516C4#9145711yescharacteristic
517C4#9147411yescharacteristic
518C3#1060030711yescharacteristic, complemented, Sylow
519C2—64no—
520C2#1174735211yescharacteristic
521C2#1174735311yescharacteristic
522C2D3×#394211yescharacteristic
523C2#1174750411yescharacteristic
524C2#1174891111yescharacteristic
525C2#1174905011yescharacteristic
526C2#1174929611yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
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×#90970C2semidirect
6. #11746350C2semidirect
7. #11745981C2semidirect
20. #91369C4semidirect
32. C2×#3942D3semidirect
208. C2×C5×D3#103semidirect
415. C3×C5#1892semidirect
429. C2×D3#3942semidirect
494. C5#70270semidirect
518. C3#10600307semidirect

Maximal subgroups

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

subgroupindex
C2×#913692
C22×D3×#1682
C5×#49872
C2×C3×#39422
C2×#909702
#117463502
#117459812
#106003073
#702705