Finite Group Databasebeta

← #14299367

Subgroups — #14299367

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C2×C5×#807C211yesmaximal, characteristic, complemented
3#11748799C211yesmaximal, characteristic
4C2×#90988C211yesmaximal, characteristic, complemented
5C2×#90957C211yesmaximal, characteristic
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10601425—31nomaximal, Hall
9C22×C4×D15—21no—
10C22×C4×D15C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×#6712—21no—
14C4⋊C4×D15—22no—
15C4⋊C4×D15—22no—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C2×#6667—21no—
21C5×#807—22no—
22#90994—21no—
23#90988—22no—
24#90957C414yescomplemented
25#68874—51nomaximal, Hall
26C2×D5×C4⋊C4—31no—
27C2×C5×#107—31no—
28C2×#3952—31no—
29#65276—31no—
30C2×#3939—31no—
31#64771—31no—
32#64749D311yescharacteristic, complemented
33C23×D15D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×Dic15D411yescharacteristic
38C2×C4×D15—21no—
39C2×C4×D15—21no—
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15—24no—
43C2×C4×D15—42no—
44C2×C4×D15—42no—
45C2×C4×D15C2×C412yes—
46C2×C4×D15Q812yes—
47C22×C5×Dic3—21no—
48C22×C3×Dic5—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4D412yes—
51C4⋊Dic15—21no—
52C4⋊Dic15D412yes—
53#6712—24no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8C2×C412yescomplemented
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168C2×C412yescomplemented
64#6667—42no—
65C2×D3×C4⋊C4—51no—
66C2×(C2×D3)⋊C8—51no—
67C2×#818—51no—
68#4987—51no—
69C2×#807D511yescharacteristic, complemented
70C3×#340—51no—
71#4529—51no—
72C22×C4×D5—31no—
73C22×C4×D5—61no—
74C22×C5×C8—31no—
75C2×C5×C4⋊C4—31no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×#685—61no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C2×#683—61no—
81C22×#168C2×D311yescharacteristic
82D5×C4⋊C4—62no—
83D5×C4⋊C4—62no—
84C5×#107—62no—
85#3963—61no—
86#3952—34no—
87#3939—62no—
88#1852—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×D15—21no—
91C22×D15—21no—
92C22×D15—21no—
93C22×D15—21no—
94C22×D15C4⋊C412yes—
95C22×D15D812yes—
96C22×D15Q1612yes—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×Q811yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—22no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15C4⋊C412yes—
112C4×D15—22no—
113C4×D15—22no—
114C4×D15—22no—
115C4×D15—22no—
116C4×D15—48no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C3×#168—22no—
124C5×C3⋊C8—22no—
125C22×C4×D3—51no—
126C22×C4×D3—101no—
127C22×C3×C8—51no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×(C2×D3)⋊C4—101no—
131C2×C4⋊Dic3—51no—
132C2×C4⋊Dic3C2×D511yescharacteristic
133C2×Dic3⋊C4—101no—
134C22×C3⋊C8C2×D511yescharacteristic
135D3×C4⋊C4—102no—
136D3×C4⋊C4—102no—
137C3⋊#95—101no—
138(C2×D3)⋊C8—54no—
139#818—102no—
140#807—22no—
141C23×D5—31no—
142C22×C4×C5—21no—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—31no—
147C22×Dic5—61no—
148C2×C4×D5—32no—
149C2×C4×D5—32no—
150C2×C4×D5—61no—
151C2×C4×D5—61no—
152C2×C4×D5—61no—
153C2×C4×D5—61no—
154C2×C4×D5—64no—
155C2×C4×D5—122no—
156C2×C4×D5—122no—
157C2×C5×C8—32no—
158C2×C5×C8—61no—
159C2×C5×C8—61no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—61no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4D1212yes—
164#685—122no—
165C4⋊Dic5—21no—
166C4⋊Dic5—21no—
167C4⋊Dic5—32no—
168C4⋊Dic5—61no—
169#683—64no—
170C2×#168—21no—
171C2×#168—21no—
172C2×#168C4×D312yescomplemented
173C22×C4⋊C4—151no—
174C2×#107—31no—
175C2×#107—151no—
176C2×C22⋊C8—151no—
177#380—151no—
178#340—51no—
179#340—151no—
180C22×C3×C5C2×C4⋊C411yescharacteristic
181C22×C3×C5#12011yescharacteristic
182C22×C3×C5#12311yescharacteristic
183C22×C3×C5C2×D811yescharacteristic
184C22×C3×C5C2×Q1611yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C22×C3×C5#13711yescharacteristic
187C2×D15—22no—
188C2×D15—22no—
189C2×D15—22no—
190C2×D15—22no—
191C2×D15—22no—
192C2×D15—22no—
193C2×D15#10714yescomplemented
194C3×C4×C5—42no—
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C22⋊Q811yescharacteristic
198C3×C4×C5C22⋊Q811yescharacteristic
199Dic15—22no—
200Dic15—42no—
201C3×Dic5—81no—
202C5×Dic3—81no—
203C23×D3—51no—
204C22×C3×C4—21no—
205C22×C3×C4—101no—
206C22×C3×C4C22×D511yescharacteristic
207C22×Dic3—21no—
208C22×Dic3—51no—
209C22×Dic3—101no—
210C2×C4×D3—52no—
211C2×C4×D3—52no—
212C2×C4×D3—101no—
213C2×C4×D3—101no—
214C2×C4×D3—101no—
215C2×C4×D3—101no—
216C2×C4×D3—104no—
217C2×C4×D3—202no—
218C2×C4×D3—202no—
219C2×C3×C8—52no—
220C2×C3×C8—101no—
221C2×C3×C8—101no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—101no—
224C3×C4⋊C4—101no—
225C3×C4⋊C4C22⋊D512yes—
226(C2×D3)⋊C4—202no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—52no—
230C4⋊Dic3—101no—
231Dic3⋊C4—104no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8C4×D512yescomplemented
235C23×C5D3×D411yescharacteristic
236C22×D5—32no—
237C22×D5—32no—
238C22×D5—32no—
239C22×D5—61no—
240C22×D5—61no—
241C22×D5—61no—
242C22×D5—61no—
243C2×C4×C5—22no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—121no—
247C2×C4×C5—121no—
248C2×C4×C5—121no—
249C2×C4×C5C2×C4×D311yescharacteristic
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5D3×Q811yescharacteristic
255C2×Dic5—32no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—61no—
260C2×Dic5—61no—
261C2×Dic5—62no—
262C2×Dic5—121no—
263C2×Dic5—121no—
264C4×D5—62no—
265C4×D5—62no—
266C4×D5—62no—
267C4×D5—62no—
268C4×D5—128no—
269C5×C8—62no—
270#168—22no—
271C23×C4—151no—
272C23×C4—301no—
273C22×C8—31no—
274C22×C8—51no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—51no—
277C2×C4⋊C4—151no—
278C2×C4⋊C4—302no—
279C2×C4⋊C4—301no—
280C2×C4⋊C4—302no—
281C2×C4⋊C4D3×D511yescharacteristic
282C2×C22⋊C4—301no—
283#107—62no—
284#107—302no—
285C22⋊C8—154no—
286#95—301no—
287C2×C3×C5#38511yescharacteristic
288C2×C3×C5C2×#10711yescharacteristic
289C2×C3×C5#42811yescharacteristic
290C2×C3×C5#44711yescharacteristic
291C2×C3×C5#45111yescharacteristic
292C2×C3×C5#48011yescharacteristic
293C2×C3×C5#48411yescharacteristic
294D15—24no—
295C23×C3D4×D511yescharacteristic
296C22×D3—52no—
297C22×D3—52no—
298C22×D3—52no—
299C22×D3—101no—
300C22×D3—101no—
301C22×D3—101no—
302C22×D3—101no—
303C2×C3×C4—22no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4#70911yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4Q8×D511yescharacteristic
313C2×C3×C4#71311yescharacteristic
314C2×C3×C4C2×C22⋊D511yescharacteristic
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—52no—
319C2×Dic3—101no—
320C2×Dic3—101no—
321C2×Dic3—102no—
322C2×Dic3—201no—
323C2×Dic3—201no—
324C4×D3—102no—
325C4×D3—102no—
326C4×D3—102no—
327C4×D3—102no—
328C4×D3—208no—
329C3×C8—102no—
330C3⋊C8—22no—
331C22×C5#88211yescharacteristic
332C22×C5#88311yescharacteristic
333C22×C5D3×C4⋊C411yescharacteristic
334C22×C5D3×D811yescharacteristic
335C22×C5#91411yescharacteristic
336C22×C5#91511yescharacteristic
337C22×C5D3×Q1611yescharacteristic
338C2×D5—34no—
339C2×D5—62no—
340C2×D5—62no—
341C2×D5—62no—
342C2×D5—62no—
343C2×D5—62no—
344C2×D5—62no—
345C4×C5—42no—
346C4×C5—241no—
347C4×C5C4×D1211yescharacteristic
348C4×C5#67⋊C411yescharacteristic
349C4×C5#89611yescharacteristic
350C4×C5#89711yescharacteristic
351Dic5—62no—
352Dic5—81no—
353Dic5—122no—
354C24—151no—
355C22×C4—21no—
356C22×C4—61no—
357C22×C4—101no—
358C22×C4—151no—
359C22×C4—152no—
360C22×C4—152no—
361C22×C4—304no—
362C22×C4—301no—
363C22×C4—301no—
364C22×C4—301no—
365C22×C4—301no—
366C22×C4—301no—
367C22×C4—602no—
368C22×C4—602no—
369C22×C4C2×D3×D511yescharacteristic
370C2×C8—32no—
371C2×C8—52no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—101no—
375C2×C8—101no—
376C4⋊C4—21no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—152no—
382C4⋊C4—304no—
383C4⋊C4—301no—
384C4⋊C4#120312yes—
385C22⋊C4—602no—
386C3×C5#185211yescharacteristic, complemented, Hall
387C22×C3D5×C4⋊C411yescharacteristic
388C22×C3#404011yescharacteristic
389C22×C3D5×D811yescharacteristic
390C22×C3#405711yescharacteristic
391C22×C3D5×Q1611yescharacteristic
392C22×C3#406411yescharacteristic
393C22×C3#408311yescharacteristic
394C2×D3—54no—
395C2×D3—102no—
396C2×D3—102no—
397C2×D3—102no—
398C2×D3—102no—
399C2×D3—102no—
400C2×D3—102no—
401C3×C4—42no—
402C3×C4—401no—
403C3×C4#403911yescharacteristic
404C3×C4#404211yescharacteristic
405C3×C4C4×C22⋊D511yescharacteristic
406C3×C4#409211yescharacteristic
407Dic3—81no—
408Dic3—102no—
409Dic3—202no—
410C2×C5#466811yescharacteristic
411C2×C5#477311yescharacteristic
412C2×C5#477411yescharacteristic
413C2×C5#480911yescharacteristic
414C2×C5#481111yescharacteristic
415C2×C5#486111yescharacteristic
416C2×C5D3×#10711yescharacteristic
417D5—64no—
418C23—152no—
419C23—152no—
420C23—152no—
421C23—301no—
422C23—301no—
423C23—301no—
424C23—301no—
425C23#679011yescharacteristic
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—152no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—301no—
437C2×C4—301no—
438C2×C4—302no—
439C2×C4—302no—
440C2×C4—302no—
441C2×C4—302no—
442C2×C4—302no—
443C2×C4—608no—
444C2×C4—601no—
445C2×C4—601no—
446C2×C4#676611yescharacteristic
447C2×C4D15⋊Q811yescharacteristic
448C2×C4#677111yescharacteristic
449C2×C4C4×D3×D511yescharacteristic
450C2×C4C2×#120311yescharacteristic
451C2×C4#679011yescharacteristic
452C8—62no—
453C8—102no—
454C2×C3D5×#10711yescharacteristic
455C2×C3#6517011yescharacteristic
456C2×C3#6517111yescharacteristic
457C2×C3#6517311yescharacteristic
458C2×C3#6527811yescharacteristic
459C2×C3#6544511yescharacteristic
460C2×C3#6547511yescharacteristic
461D3—104no—
462C5#6887411yescharacteristic, complemented, Sylow
463C22—154no—
464C22—302no—
465C22—302no—
466C22—302no—
467C22—302no—
468C22—302no—
469C22—302no—
470C22#9135411yescharacteristic
471C22#9140411yescharacteristic
472C22#9148111yescharacteristic
473C22#9150011yescharacteristic
474C22#9151111yescharacteristic
475C22#9152211yescharacteristic
476C22#9157311yescharacteristic
477C4—42no—
478C4—241no—
479C4—302no—
480C4—401no—
481C4—602no—
482C4#9137711yescharacteristic
483C4#9138311yescharacteristic
484C4#9139611yescharacteristic
485C4C4×#120311yescharacteristic
486C3#1060142511yescharacteristic, complemented, Sylow
487C2—304no—
488C2#1174733011yescharacteristic
489C2#1174736511yescharacteristic
490C2#1174743811yescharacteristic
491C2#1174745811yescharacteristic
492C2#1174873111yescharacteristic
493C2#1174904111yescharacteristic
494C2#1174930811yescharacteristic
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#1852
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
2. C2×C5×#807C2semidirect
4. C2×#90988C2semidirect
6. C3×#64749C2semidirect
7. #11745980C2semidirect
24. #90957C4semidirect
32. #64749D3semidirect
58. C2×C5×C3⋊C8C2×C4semidirect
63. C2×C3×#168C2×C4semidirect
69. C2×#807D5semidirect
172. C2×#168C4×D3semidirect
193. C2×D15#107semidirect
234. C2×C3⋊C8C4×D5semidirect
386. C3×C5#1852semidirect
462. C5#68874semidirect
486. C3#10601425semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×C5×#8072
#117487992
C2×#909882
C2×#909572
C3×#647492
#117459802
#106014253
#688745