Finite Group Databasebeta

← #14299444

Subgroups — #14299444

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic
2C2×C3×C5×#106C211yesmaximal, characteristic, complemented
3C2×#91104C211yesmaximal, characteristic
4#11751088C211yesmaximal, characteristic
5C2×#91091C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10601373—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×#6714—21no—
14C2×#6714—21no—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15—21no—
18C22×C3⋊#168C2211yescharacteristic
19#91781—22no—
20#91781—22no—
21C3×C5×#106—22no—
22#91115—21no—
23#91104C414yescomplemented
24#91091—22no—
25#70580—51nomaximal, Hall
26C2×#4038—31no—
27C2×C5×#106D311yescharacteristic, complemented
28C2×#3952—31no—
29#65276—31no—
30C2×#3939—31no—
31#64771—31no—
32#64749—31no—
33C23×D15D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
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×D15Q812yes—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8C2×C412yes—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4D412yes—
53#6714—24no—
54#6714—42no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15D412yes—
59C4×Dic15—24no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168C2×C412yes—
63C2×#892—51no—
64C2×C3×#106D511yescharacteristic, complemented
65C2×(C2×D3)⋊C8—51no—
66#4987—51no—
67C2×#807—51no—
68#4551—51no—
69#4529—51no—
70C22×C4×D5—31no—
71C22×C5×C8C2×D311yescharacteristic
72C2×C5×C4⋊C4C2×D311yescharacteristic
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×#685—61no—
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—31no—
78C2×C4×Dic5—61no—
79C22×#168—31no—
80#4038—62no—
81#4038—62no—
82C5×#106—22no—
83#3963—61no—
84#3952—34no—
85#3939—62no—
86#1854—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×D15—21no—
89C22×D15—21no—
90C22×D15—21no—
91C22×D15—21no—
92C22×D15—21no—
93C22×D15—21no—
94C22×D15C4⋊C412yes—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—22no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×Dic15C4⋊C412yes—
116C4×D15—22no—
117C4×D15—22no—
118C4×D15—22no—
119C4×D15—22no—
120C3×C5×C8—22no—
121C3⋊#168—22no—
122C22×C4×D3—51no—
123C22×C3×C8C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×(C2×D3)⋊C4—101no—
127C2×(C2×D3)⋊C4—101no—
128C2×C4⋊Dic3—51no—
129C2×C4⋊Dic3—51no—
130C2×C4×Dic3—101no—
131C22×C3⋊C8—51no—
132#892—102no—
133#892—102no—
134C3×#106—22no—
135C3⋊#95—101no—
136(C2×D3)⋊C8—54no—
137#807—102no—
138C23×D5—31no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—31no—
143C22×Dic5—61no—
144C22×Dic5—61no—
145C2×C4×D5—32no—
146C2×C4×D5—32no—
147C2×C4×D5—61no—
148C2×C4×D5—61no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8C4×D312yes—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4#6712yes—
158#685—64no—
159#685—122no—
160C4⋊Dic5—32no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164C4×Dic5—64no—
165C2×#168—32no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#117—151no—
169C2×#107—151no—
170C2×#106D1511yescharacteristic, complemented
171C2×C22⋊C8—151no—
172#380—151no—
173#340—151no—
174#340—151no—
175C22×C3×C5C2×C4⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5#13711yescharacteristic
182C2×D15—22no—
183C2×D15—22no—
184C2×D15—22no—
185C2×D15—41no—
186C2×D15—41no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—42no—
190C3×C4×C5—81no—
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C4×D411yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194C3×C4×C5C22⋊Q811yescharacteristic
195Dic15—22no—
196Dic15—42no—
197Dic15—81no—
198C23×D3—51no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4C22×D511yescharacteristic
202C22×Dic3—51no—
203C22×Dic3—101no—
204C22×Dic3—101no—
205C2×C4×D3—52no—
206C2×C4×D3—52no—
207C2×C4×D3—101no—
208C2×C4×D3—101no—
209C2×C4×D3—101no—
210C2×C4×D3—101no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8C4×D512yes—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4C22⋊D512yes—
218(C2×D3)⋊C4—104no—
219(C2×D3)⋊C4—202no—
220C4⋊Dic3—52no—
221C4⋊Dic3—101no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224C4×Dic3—104no—
225C2×C3⋊C8—52no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5D3×D411yescharacteristic
229C22×D5—32no—
230C22×D5—61no—
231C22×D5—61no—
232C22×D5—61no—
233C22×D5—61no—
234C22×D5—61no—
235C22×D5—61no—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×Q811yescharacteristic
246C2×C4×C5#23911yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C2×Dic5—32no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—62no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257C4×D5—62no—
258C4×D5—62no—
259C4×D5—62no—
260C4×D5—62no—
261C5×C8—22no—
262#168—62no—
263C23×C4—151no—
264C22×C8—151no—
265C22×C8C2×D1511yescharacteristic
266#117—302no—
267#117—302no—
268C2×C4⋊C4—151no—
269C2×C4⋊C4—151no—
270C2×C4⋊C4C2×D1511yescharacteristic
271C2×C4⋊C4C2×D1511yescharacteristic
272C2×C22⋊C4—301no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—302no—
276#106—22no—
277C22⋊C8—154no—
278#95—301no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#42711yescharacteristic
281C2×C3×C5#42811yescharacteristic
282C2×C3×C5#44911yescharacteristic
283C2×C3×C5#45211yescharacteristic
284C2×C3×C5#48211yescharacteristic
285C2×C3×C5#48511yescharacteristic
286D15—42no—
287C23×C3D4×D511yescharacteristic
288C22×D3—52no—
289C22×D3—101no—
290C22×D3—101no—
291C22×D3—101no—
292C22×D3—101no—
293C22×D3—101no—
294C22×D3—101no—
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4Q8×D511yescharacteristic
305C2×C3×C4#71311yescharacteristic
306C2×C3×C4C2×C22⋊D511yescharacteristic
307C2×Dic3—52no—
308C2×Dic3—101no—
309C2×Dic3—101no—
310C2×Dic3—102no—
311C2×Dic3—201no—
312C2×Dic3—201no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315C2×Dic3—201no—
316C4×D3—102no—
317C4×D3—102no—
318C4×D3—102no—
319C4×D3—102no—
320C3×C8—22no—
321C3⋊C8—102no—
322C22×C5D3×C4⋊C411yescharacteristic
323C22×C5#89411yescharacteristic
324C22×C5#91411yescharacteristic
325C22×C5#91511yescharacteristic
326C22×C5#91611yescharacteristic
327C22×C5#91611yescharacteristic
328C22×C5#93711yescharacteristic
329C2×D5—62no—
330C2×D5—62no—
331C2×D5—62no—
332C2×D5—121no—
333C2×D5—121no—
334C2×D5—121no—
335C2×D5—121no—
336C4×C5—42no—
337C4×C5—81no—
338C4×C5#89311yescharacteristic
339C4×C5#89611yescharacteristic
340C4×C5C4×#6711yescharacteristic
341C4×C5#94611yescharacteristic
342Dic5—62no—
343Dic5—122no—
344Dic5—241no—
345C24—151no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—151no—
349C22×C4—152no—
350C22×C4—152no—
351C22×C4—301no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4—301no—
355C22×C4—301no—
356C22×C4—301no—
357C22×C4C22×D1511yescharacteristic
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—152no—
361C2×C8—301no—
362C2×C8—301no—
363C2×C8C4×D1512yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—152no—
368C4⋊C4—301no—
369C4⋊C4—301no—
370C4⋊C4—301no—
371C4⋊C4#122012yes—
372C22⋊C4—304no—
373C22⋊C4—602no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3D5×C4⋊C411yescharacteristic
377C22×C3#404011yescharacteristic
378C22×C3#406011yescharacteristic
379C22×C3#406111yescharacteristic
380C22×C3#406211yescharacteristic
381C22×C3#406211yescharacteristic
382C22×C3#408311yescharacteristic
383C2×D3—102no—
384C2×D3—102no—
385C2×D3—102no—
386C2×D3—201no—
387C2×D3—201no—
388C2×D3—201no—
389C2×D3—201no—
390C3×C4—42no—
391C3×C4—81no—
392C3×C4#403911yescharacteristic
393C3×C4#404211yescharacteristic
394C3×C4C4×C22⋊D511yescharacteristic
395C3×C4#409211yescharacteristic
396Dic3—102no—
397Dic3—202no—
398Dic3—401no—
399C2×C5#486011yescharacteristic
400C2×C5#486111yescharacteristic
401C2×C5#486611yescharacteristic
402C2×C5#486811yescharacteristic
403C2×C5#498911yescharacteristic
404C2×C5#517211yescharacteristic
405C2×C5#517311yescharacteristic
406D5—122no—
407C23—152no—
408C23—301no—
409C23—301no—
410C23—301no—
411C23—301no—
412C23—301no—
413C23—301no—
414C23D4×D1511yescharacteristic
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—152no—
422C2×C4—301no—
423C2×C4—301no—
424C2×C4—302no—
425C2×C4—302no—
426C2×C4—302no—
427C2×C4—302no—
428C2×C4—302no—
429C2×C4—601no—
430C2×C4—601no—
431C2×C4—601no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4C2×C4×D1511yescharacteristic
435C2×C4#681711yescharacteristic
436C2×C4D4×D1511yescharacteristic
437C2×C4Q8×D1511yescharacteristic
438C2×C4#682111yescharacteristic
439C2×C4C2×#122011yescharacteristic
440C8—22no—
441C8—302no—
442C2×C3#6514911yescharacteristic
443C2×C3#6515011yescharacteristic
444C2×C3#6515511yescharacteristic
445C2×C3#6515611yescharacteristic
446C2×C3#6527811yescharacteristic
447C2×C3#6546111yescharacteristic
448C2×C3#6546211yescharacteristic
449D3—202no—
450C5#7058011yescharacteristic, complemented, Sylow
451C22—302no—
452C22—302no—
453C22—302no—
454C22—601no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22C4⋊C4×D1511yescharacteristic
459C22#9178311yescharacteristic
460C22#9180311yescharacteristic
461C22#9180411yescharacteristic
462C22#9180511yescharacteristic
463C22#9180511yescharacteristic
464C22#9182611yescharacteristic
465C4—42no—
466C4—81no—
467C4—302no—
468C4—602no—
469C4—1201no—
470C4#9178211yescharacteristic
471C4#9178511yescharacteristic
472C4C4×#122011yescharacteristic
473C4#9183511yescharacteristic
474C3#1060137311yescharacteristic, complemented, Sylow
475C2—602no—
476C2#1175096111yescharacteristic
477C2#1175096211yescharacteristic
478C2#1175096711yescharacteristic
479C2#1175096911yescharacteristic
480C2#1175109011yescharacteristic
481C2#1175127311yescharacteristic
482C2#1175127411yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#106C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenterC2×#106D15
hypocenterC3×C5#1854
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#106C2semidirect
5. C2×#91091C2semidirect
6. #11746372C2semidirect
7. #11746350C2semidirect
23. #91104C4semidirect
27. C2×C5×#106D3semidirect
64. C2×C3×#106D5semidirect
170. C2×#106D15semidirect
375. C3×C5#1854semidirect
450. C5#70580semidirect
474. C3#10601373semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C3×C5×#1062
C2×#911042
#117510882
C2×#910912
#117463722
#117463502
#106013733
#705805