Finite Group Databasebeta

← #14299981

Subgroups — #14299981

Order 1920.

724 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×C3×C4×D20C211yesmaximal, characteristic
2C5×#4928C211yesmaximal, characteristic, complemented
3C2×#90989C211yesmaximal, characteristic, complemented
4C2×#90964C211yesmaximal, characteristic
5C2×#90964C211yesmaximal, characteristic
6#11746345C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10600418—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C2×C3×C42×C5C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×Dic3⋊C4—21no—
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C3×C4×D20—22no—
20C3×C4×D20—22no—
21C5×C3⋊#95—21no—
22#90989—22no—
23#90964—22no—
24#90964C414yescomplemented
25#71606—51nomaximal, Hall
26C2×C4×D20D311yescharacteristic
27C5×#389—31no—
28C2×#3941—31no—
29C2×#3941—31no—
30C2×#3939—31no—
31#64749—31no—
32#64744—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×C5×Dic3—21no—
38C22×C5×Dic3—21no—
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×D20D412yes—
45C2×C3×D20Q812yes—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168C2×C412yescomplemented
57C5×C4⋊Dic3—21no—
58C5×C4⋊Dic3—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3C2×C412yescomplemented
61C5×Dic3⋊C4—42no—
62C3×#685—24no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5D412yes—
65C2×C3×C4×D4—51no—
66C2×#832—51no—
67C2×#832—51no—
68C2×#807—51no—
69#4928D511yescharacteristic, complemented
70#4529—51no—
71#4524—51no—
72C22×D20C2×D311yescharacteristic
73C22×C4×D5—21no—
74C2×C5×C4⋊C4—31no—
75C2×C5×C4⋊C4—31no—
76C2×C5×C4⋊C4—61no—
77C2×C42×C5C2×D311yescharacteristic
78C2×#685—21no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C22×#168—31no—
81C22×#168—31no—
82C4×D20—22no—
83C4×D20—22no—
84C5×#95—61no—
85#3941—34no—
86#3941—62no—
87#3939—62no—
88#1862—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—22no—
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5D812yes—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×Q811yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C5×Dic3—22no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C2×C5×Dic3—41no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C4⋊C414yescomplemented
122C3×C4×D5—48no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C22×C3×D4—51no—
126C23×C3×C4—101no—
127C3×C4×D4—102no—
128C3×C4×D4—102no—
129C2×C3×C4⋊C4—51no—
130C2×C3×C22⋊C4—101no—
131C2×C3×C42C2×D511yescharacteristic
132C2×C4⋊Dic3C2×D511yescharacteristic
133C2×C4⋊Dic3C2×D511yescharacteristic
134C2×Dic3⋊C4—21no—
135C22×C3⋊C8—51no—
136C22×C3⋊C8—51no—
137#832—54no—
138#832—102no—
139C3⋊#95—21no—
140#807—102no—
141C23×D5—21no—
142C22×C4×C5—61no—
143C22×C4×C5—61no—
144C22×C4×C5#6711yescharacteristic
145C22×C4×C5#6711yescharacteristic
146C22×C4×C5C22×D311yescharacteristic
147C22×Dic5—21no—
148C2×D20—21no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20Dic612yes—
152C2×D20C4×D312yes—
153C2×D20#6712yes—
154C2×C4×D5—24no—
155C2×C4×D5—42no—
156C2×C4×D5—42no—
157C5×C4⋊C4—32no—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—61no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4—122no—
162C42×C5—21no—
163C42×C5—21no—
164#685—24no—
165C4⋊Dic5—21no—
166C4⋊Dic5#6712yes—
167C2×#168—32no—
168C2×#168—61no—
169C2×#168—61no—
170C2×#168—61no—
171C2×#168—61no—
172C2×#168—61no—
173C2×C4×D4—51no—
174C2×#107—151no—
175C2×#102—151no—
176C2×#102—151no—
177#389—31no—
178#340—151no—
179#336—151no—
180C22×C3×C5C4×D411yescharacteristic
181C22×C3×C5#12011yescharacteristic
182C22×C3×C5C22⋊Q811yescharacteristic
183C22×C3×C5C2×D811yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C22×C3×C5#13711yescharacteristic
187C2×C3×D5—24no—
188C2×C3×D5—42no—
189C2×C3×D5—42no—
190C2×C3×D5—42no—
191C2×C3×D5—42no—
192C2×C3×D5—42no—
193C2×C3×D5—42no—
194C3×C4×C5—22no—
195C3×C4×C5—41no—
196C3×C4×C5C2×C4⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C22⋊Q811yescharacteristic
199C3×C4×C5#12311yescharacteristic
200C3×Dic5—42no—
201C5×Dic3—42no—
202C5×Dic3—81no—
203C24×C3—101no—
204C2×C3×D4—52no—
205C2×C3×D4—52no—
206C2×C3×D4—52no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C22×C3×C4—104no—
211C22×C3×C4—101no—
212C22×C3×C4—202no—
213C22×C3×C4—202no—
214C22×C3×C4C22⋊D511yescharacteristic
215C22×C3×C4C22⋊D511yescharacteristic
216C22×C3×C4C22×D511yescharacteristic
217C22×Dic3—21no—
218C22×Dic3—21no—
219C3×C4⋊C4—52no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—104no—
222C3×C42—21no—
223C3×C42—21no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3C4×D512yescomplemented
228Dic3⋊C4—42no—
229C2×C3⋊C8—52no—
230C2×C3⋊C8—101no—
231C2×C3⋊C8—101no—
232C2×C3⋊C8—101no—
233C2×C3⋊C8—101no—
234C2×C3⋊C8—101no—
235C23×C5C2×#6711yescharacteristic
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—41no—
240C22×D5—41no—
241C22×D5—41no—
242C22×D5—41no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—21no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—62no—
249C2×C4×C5—121no—
250C2×C4×C5—121no—
251C2×C4×C5—121no—
252C2×C4×C5—121no—
253C2×C4×C5—121no—
254C2×C4×C5#21312yes—
255C2×C4×C5C2×Dic611yescharacteristic
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5#23511yescharacteristic
258C2×C4×C5#23511yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260C2×C4×C5C2×#6711yescharacteristic
261C2×Dic5—22no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264D20—22no—
265D20—22no—
266D20—22no—
267D20Dic3⋊C414yescomplemented
268C4×D5—48no—
269#168—62no—
270#168—121no—
271C22×D4—51no—
272C23×C4—101no—
273C22×C8—151no—
274C22×C8—151no—
275C4×D4—102no—
276C4×D4—102no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—51no—
280C2×C4⋊C4—61no—
281C2×C22⋊C4—101no—
282C2×C42D3×D511yescharacteristic
283#107—302no—
284#102—154no—
285#102—302no—
286#95—61no—
287C2×C3×C5#38511yescharacteristic
288C2×C3×C5C4×D811yescharacteristic
289C2×C3×C5#44011yescharacteristic
290C2×C3×C5#44711yescharacteristic
291C2×C3×C5#45211yescharacteristic
292C2×C3×C5#47411yescharacteristic
293C2×C3×C5#47811yescharacteristic
294C3×D5—44no—
295C23×C3—102no—
296C23×C3—102no—
297C23×C3—102no—
298C23×C3—201no—
299C23×C3—201no—
300C23×C3—201no—
301C23×C3—201no—
302C23×C3C2×C22⋊D511yescharacteristic
303C3×D4—54no—
304C3×D4—102no—
305C3×D4—102no—
306C3×D4—102no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—102no—
313C2×C3×C4—208no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4#68612yes—
317C2×C3×C4C2×C4×D511yescharacteristic
318C2×C3×C4#70911yescharacteristic
319C2×C3×C4D4×D511yescharacteristic
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4Q8×D511yescharacteristic
322C2×C3×C4#71311yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C3⋊C8—102no—
330C3⋊C8—201no—
331C22×C5#92411yescharacteristic
332C22×C5C4×#6711yescharacteristic
333C22×C5C2×#21311yescharacteristic
334C22×C5#93211yescharacteristic
335C22×C5#95011yescharacteristic
336C22×C5#95111yescharacteristic
337C22×C5#95311yescharacteristic
338C2×D5—24no—
339C2×D5—42no—
340C2×D5—42no—
341C2×D5—42no—
342C2×D5—42no—
343C2×D5—42no—
344C2×D5—42no—
345C4×C5—22no—
346C4×C5—41no—
347C4×C5—122no—
348C4×C5—241no—
349C4×C5C2×Dic3⋊C411yescharacteristic
350C4×C5#92411yescharacteristic
351C4×C5C4×#6711yescharacteristic
352C4×C5#92911yescharacteristic
353Dic5—42no—
354C24—101no—
355C2×D4—52no—
356C2×D4—52no—
357C2×D4—52no—
358C2×D4—101no—
359C2×D4—101no—
360C2×D4—101no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—104no—
364C22×C4—101no—
365C22×C4—202no—
366C22×C4—202no—
367C22×C4#120111yescharacteristic
368C22×C4#120111yescharacteristic
369C22×C4C2×D3×D511yescharacteristic
370C2×C8—152no—
371C2×C8—301no—
372C2×C8—301no—
373C2×C8—301no—
374C2×C8—301no—
375C2×C8—301no—
376C4⋊C4—32no—
377C4⋊C4—52no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—101no—
382C4⋊C4—122no—
383C22⋊C4—104no—
384C42—21no—
385C42—21no—
386C3×C5#186211yescharacteristic, complemented, Hall
387C22×C3—104no—
388C22×C3—202no—
389C22×C3—202no—
390C22×C3—202no—
391C22×C3—202no—
392C22×C3—202no—
393C22×C3—202no—
394C22×C3C4×C22⋊D511yescharacteristic
395C22×C3C2×#68611yescharacteristic
396C22×C3#408311yescharacteristic
397C22×C3#408811yescharacteristic
398C22×C3#409211yescharacteristic
399C22×C3#409511yescharacteristic
400C22×C3#409611yescharacteristic
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—202no—
404C3×C4D5×C4⋊C411yescharacteristic
405C3×C4#403911yescharacteristic
406C3×C4#404011yescharacteristic
407C3×C4#404211yescharacteristic
408Dic3—42no—
409Dic3—81no—
410C2×C5#500711yescharacteristic
411C2×C5#500911yescharacteristic
412C2×C5C4×#21311yescharacteristic
413C2×C5#501811yescharacteristic
414C2×C5#521011yescharacteristic
415C2×C5#521711yescharacteristic
416C2×C5#523911yescharacteristic
417D5—44no—
418C23—102no—
419C23—102no—
420C23—102no—
421C23—201no—
422C23—201no—
423C23—201no—
424C23—201no—
425C23C2×#120111yescharacteristic
426D4—54no—
427D4—102no—
428D4—102no—
429D4—102no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—62no—
436C2×C4—102no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—208no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4#665212yes—
446C2×C4D5×Dic611yescharacteristic
447C2×C4#677111yescharacteristic
448C2×C4#677311yescharacteristic
449C2×C4C4×D3×D511yescharacteristic
450C2×C4D5×#6711yescharacteristic
451C2×C4D5×#6711yescharacteristic
452C8—302no—
453C8—601no—
454C2×C3—204no—
455C2×C3#6527811yescharacteristic
456C2×C3C4×#68611yescharacteristic
457C2×C3#6531511yescharacteristic
458C2×C3#6532511yescharacteristic
459C2×C3#6533611yescharacteristic
460C2×C3#6535511yescharacteristic
461C2×C3#6537611yescharacteristic
462C5#7160611yescharacteristic, complemented, Sylow
463C22—104no—
464C22—202no—
465C22—202no—
466C22—202no—
467C22—202no—
468C22—202no—
469C22—202no—
470C22C2×#665211yescharacteristic
471C22#9129711yescharacteristic
472C22#9129811yescharacteristic
473C22#9130711yescharacteristic
474C22#9135911yescharacteristic
475C22C4×#120111yescharacteristic
476C22#9156311yescharacteristic
477C4—22no—
478C4—41no—
479C4—122no—
480C4—202no—
481C4—241no—
482C4#9134811yescharacteristic
483C4#9134911yescharacteristic
484C4D5×Dic3⋊C411yescharacteristic
485C4#9144411yescharacteristic
486C3#1060041811yescharacteristic, complemented, Sylow
487C2—204no—
488C2#1174688611yescharacteristic
489C2#1174688711yescharacteristic
490C2C4×#665211yescharacteristic
491C2#1174704811yescharacteristic
492C2#1174851011yescharacteristic
493C2#1174852811yescharacteristic
494C2#1174870311yescharacteristic
subgroupG/H
centerC23C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1862
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C5×#4928C2semidirect
3. C2×#90989C2semidirect
6. #11746345C2semidirect
7. #11745979C2semidirect
24. #90964C4semidirect
56. C2×C3⋊#168C2×C4semidirect
60. C5×C4⋊Dic3C2×C4semidirect
69. #4928D5semidirect
121. C3×D20C4⋊C4semidirect
227. C4⋊Dic3C4×D5semidirect
267. D20Dic3⋊C4semidirect
386. C3×C5#1862semidirect
462. C5#71606semidirect
486. C3#10600418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C5×#49282
C2×#909892
C2×#909642
#117463452
#117459792
#106004183
#716065