Finite Group Databasebeta

← #14305968

Subgroups — #14305968

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91458C211yesmaximal, characteristic
2C2×#91093C211yesmaximal, characteristic, complemented
3C5×#4977C211yesmaximal, characteristic, complemented
4C2×C3×#3941C211yesmaximal, characteristic, complemented
5C2×#90969C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic, complemented
7C2×#90953C211yesmaximal, characteristic, complemented
8#10600346—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C22×#1202—22no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17#91458—22no—
18#91458C414yescomplemented
19#91093—22no—
20C5×C3⋊#95—22no—
21C3×#3941—22no—
22#90969—22no—
23#90964—22no—
24#90953—22no—
25#70160—51nomaximal, Hall
26C2×#4020—31no—
27C5×#382—31no—
28C2×#3941—31no—
29C2×#3941—31no—
30C2×#3941—31no—
31C2×#3941D311yescharacteristic, complemented
32C2×#3935—31no—
33C23×D15—21no—
34C23×C3×D5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60C2×C412yes—
43C22×C5×Dic3—21no—
44C22×C5×Dic3D412yes—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20C2×C412yes—
51C2×#1202—28no—
52C2×#1202—44no—
53C2×#1202—44no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168D412yescomplemented
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3C2×C412yes—
62C4×C5×Dic3D412yes—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C2×C3×#168D412yescomplemented
66C2×#940—51no—
67C2×C3×#102—51no—
68C2×#832—51no—
69C2×#821—51no—
70C2×#815—51no—
71#4977D511yescharacteristic, complemented
72C2×#809—51no—
73C22×D20—31no—
74C22×D20—62no—
75C22×D20C2×D311yescharacteristic
76C2×C5×C4⋊C4—31no—
77C2×C5×C4⋊C4C2×D311yescharacteristic
78C2×C42×C5—31no—
79C22×#168—31no—
80C22×#168C2×D311yescharacteristic
81#4020—34no—
82#4020—62no—
83C5×#95—62no—
84#3941—22no—
85#3941—62no—
86#3941—62no—
87#3941—62no—
88#3935—62no—
89#1961—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×D15—22no—
92C22×D15—41no—
93C22×D15—41no—
94C22×D15—42no—
95C22×D15—42no—
96C22×C3×D5—22no—
97C22×C3×D5—41no—
98C22×C3×D5—41no—
99C22×C3×D5—42no—
100C22×C3×D5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—42no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109D60—22no—
110D60—22no—
111D60—41no—
112D60—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—42no—
117C2×C5×Dic3C22⋊C414yes—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—41no—
121C3×D20—41no—
122#1202—416no—
123C3⋊#168—22no—
124C3×#168—22no—
125C22×C3×D4—51no—
126C22×#67—102no—
127C22×D12—51no—
128C22×C3×C8—51no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130#940—54no—
131#940—102no—
132C2×C4⋊Dic3C2×D511yescharacteristic
133C2×C4×Dic3C2×D511yescharacteristic
134C22×C3⋊C8—51no—
135C3×#102—102no—
136#832—102no—
137C3⋊#95—22no—
138#821—102no—
139#815—102no—
140#809—102no—
141C23×D5—21no—
142C23×D5—61no—
143C22×C4×C5—21no—
144C22×C4×C5—32no—
145C22×C4×C5—61no—
146C22×C4×C5C22×D311yescharacteristic
147C2×D20—21no—
148C2×D20—21no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20—21no—
152C2×D20—32no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—61no—
157C2×D20—68no—
158C2×D20—61no—
159C2×D20—124no—
160C2×D20—124no—
161C2×D20C4×D312yes—
162C5×C4⋊C4—21no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C42×C5—32no—
167C42×C5—32no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—32no—
171C2×#168—61no—
172C2×#168—61no—
173C2×#168#6712yescomplemented
174C2×#127—151no—
175C2×#102—51no—
176C2×#102—151no—
177C2×#102—151no—
178C2×#102—151no—
179C2×#97—151no—
180#382—31no—
181C22×C3×C5C2×C22⋊C411yescharacteristic
182C22×C3×C5#12411yescharacteristic
183C22×C3×C5#12711yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)12yes—
185C22×C3×C5AGL(1,ℤ/8)12yes—
186C2×D15—42no—
187C2×D15—44no—
188C2×D15—82no—
189C2×D15—81no—
190C2×D15—81no—
191C2×C3×D5—42no—
192C2×C3×D5—44no—
193C2×C3×D5—82no—
194C2×C3×D5—81no—
195C2×C3×D5—81no—
196C3×C4×C5—81no—
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C4×D411yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201C5×Dic3—24no—
202C5×Dic3—81no—
203C24×C3—101no—
204C23×D3—101no—
205C2×C3×D4—52no—
206C2×C3×D4—101no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C2×C3×D4—101no—
211C22×C3×C4—21no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—108no—
214C2×#67—204no—
215C2×#67—204no—
216C22×Dic3—21no—
217C22×Dic3C22⋊D512yes—
218C2×D12—52no—
219C2×D12—101no—
220C2×D12—101no—
221C2×D12—101no—
222C2×D12—101no—
223C2×D12—101no—
224C2×C3×C8—52no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4×Dic3C4×D512yes—
232C4×Dic3D2012yes—
233C2×C3⋊C8—52no—
234C2×C3⋊C8—101no—
235C2×C3⋊C8—101no—
236C23×C5D3×D411yescharacteristic
237C22×D5—22no—
238C22×D5—41no—
239C22×D5—42no—
240C22×D5—42no—
241C22×D5—41no—
242C22×D5—62no—
243C22×D5—121no—
244C22×D5—122no—
245C22×D5—122no—
246C22×D5—121no—
247C2×C4×C5—34no—
248C2×C4×C5—42no—
249C2×C4×C5—41no—
250C2×C4×C5—62no—
251C2×C4×C5—62no—
252C2×C4×C5—122no—
253C2×C4×C5—121no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5#23511yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5#23711yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260D20—22no—
261D20—22no—
262D20—41no—
263D20—41no—
264D20—62no—
265D20—62no—
266D20—1216no—
267D20—121no—
268D20—121no—
269#168—22no—
270#168—62no—
271C22×D4—51no—
272C22×D4—151no—
273C22×D4—302no—
274C22×C8—51no—
275C22×C8—151no—
276#127—154no—
277#127—302no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4D3×D511yescharacteristic
280C2×C42—31no—
281#102—102no—
282#102—302no—
283#102—302no—
284#102—302no—
285#97—302no—
286#95—62no—
287C2×C3×C5#39011yescharacteristic
288C2×C3×C5#41812yes—
289C2×C3×C5#49012yes—
290C2×C3×C5#49611yescharacteristic
291C2×C3×C5#49611yescharacteristic
292D15—82no—
293C3×D5—82no—
294C23×C3—102no—
295C23×C3—201no—
296C23×C3—201no—
297C23×C3—202no—
298C23×C3—202no—
299C23×C3C2×C22⋊D511yescharacteristic
300C22×D3—102no—
301C22×D3—201no—
302C22×D3—201no—
303C22×D3—202no—
304C22×D3—202no—
305C3×D4—102no—
306C3×D4—102no—
307C3×D4—201no—
308C3×D4—201no—
309C2×C3×C4—41no—
310C2×C3×C4—42no—
311C2×C3×C4C2×C4×D511yescharacteristic
312C2×C3×C4C2×D2011yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×C3×C4#71311yescharacteristic
316C2×C3×C4#71311yescharacteristic
317#67—2016no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—41no—
321C2×Dic3—42no—
322C2×Dic3#68514yes—
323D12—102no—
324D12—102no—
325D12—201no—
326D12—201no—
327C3×C8—102no—
328C3⋊C8—102no—
329C22×C5D3×C22⋊C411yescharacteristic
330C22×C5#88511yescharacteristic
331C22×C5#91112yes—
332C22×C5#91412yes—
333C22×C5#94011yescharacteristic
334C2×D5—42no—
335C2×D5—44no—
336C2×D5—81no—
337C2×D5—81no—
338C2×D5—82no—
339C2×D5—122no—
340C2×D5—124no—
341C2×D5—241no—
342C2×D5—241no—
343C2×D5—242no—
344C4×C5—64no—
345C4×C5—81no—
346C4×C5—241no—
347C4×C5#67⋊C411yescharacteristic
348C4×C5#88411yescharacteristic
349C4×C5C4×#6711yescharacteristic
350C4×C5#93911yescharacteristic
351C24—101no—
352C24—301no—
353C2×D4—52no—
354C2×D4—101no—
355C2×D4—101no—
356C2×D4—101no—
357C2×D4—101no—
358C2×D4—101no—
359C2×D4—152no—
360C2×D4—308no—
361C2×D4—301no—
362C2×D4—301no—
363C2×D4—301no—
364C2×D4—301no—
365C2×D4—301no—
366C2×D4—604no—
367C2×D4—604no—
368C22×C4—21no—
369C22×C4—32no—
370C22×C4—61no—
371C22×C4C2×D3×D511yescharacteristic
372C2×C8—52no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—152no—
376C2×C8—301no—
377C2×C8—301no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C42—32no—
383C42—32no—
384C3×C5#196111yescharacteristic, complemented, Hall
385C22×C3—204no—
386C22×C3—202no—
387C22×C3—401no—
388C22×C3—401no—
389C22×C3—402no—
390C22×C3C2×#68511yescharacteristic
391C22×C3#408611yescharacteristic
392C22×C3#409311yescharacteristic
393C22×C3#409512yes—
394C22×C3#409512yes—
395C2×D3—204no—
396C2×D3—202no—
397C2×D3—401no—
398C2×D3—401no—
399C2×D3—402no—
400C3×C4—81no—
401C3×C4#403911yescharacteristic
402C3×C4#403911yescharacteristic
403C3×C4#404111yescharacteristic
404C3×C4#404111yescharacteristic
405Dic3—24no—
406Dic3—81no—
407C2×C5#476412yes—
408C2×C5#477012yes—
409C2×C5#495711yescharacteristic
410C2×C5#515411yescharacteristic
411C2×C5#517611yescharacteristic
412D5—82no—
413D5—242no—
414C23—102no—
415C23—201no—
416C23—202no—
417C23—202no—
418C23—201no—
419C23—302no—
420C23—601no—
421C23—602no—
422C23—602no—
423C23—601no—
424C23D3×C22⋊D511yescharacteristic
425D4—102no—
426D4—102no—
427D4—201no—
428D4—201no—
429D4—302no—
430D4—302no—
431D4—6016no—
432D4—601no—
433D4—601no—
434C2×C4—34no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—122no—
440C2×C4—121no—
441C2×C4#676611yescharacteristic
442C2×C4#677311yescharacteristic
443C2×C4C4×D3×D511yescharacteristic
444C2×C4D3×D2011yescharacteristic
445C2×C4D5×#6711yescharacteristic
446C2×C4#679011yescharacteristic
447C8—102no—
448C8—302no—
449C2×C3—402no—
450C2×C3#6527711yescharacteristic
451C2×C3#6529012yes—
452C2×C3#6534711yescharacteristic
453C2×C3#6534711yescharacteristic
454C2×C3#6535612yes—
455D3—402no—
456C5#7016011yescharacteristic, complemented, Sylow
457C22—202no—
458C22—204no—
459C22—402no—
460C22—401no—
461C22—401no—
462C22—602no—
463C22—604no—
464C22—1202no—
465C22—1201no—
466C22—1201no—
467C22#9145511yescharacteristic
468C22D3×#68511yescharacteristic
469C22#9148012yes—
470C22#9150412yes—
471C22#9156711yescharacteristic
472C4—64no—
473C4—81no—
474C4—241no—
475C4#9139611yescharacteristic
476C4#9140911yescharacteristic
477C4#9144411yescharacteristic
478C4#9145911yescharacteristic
479C3#1060034611yescharacteristic, complemented, Sylow
480C2—402no—
481C2—1202no—
482C2#1174740512yes—
483C2#1174747712yes—
484C2#1174891311yescharacteristic
485C2#1174909811yescharacteristic
486C2#1174934211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×#91458C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1961
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×#91093C2semidirect
3. C5×#4977C2semidirect
4. C2×C3×#3941C2semidirect
5. C2×#90969C2semidirect
6. C2×#90964C2semidirect
7. C2×#90953C2semidirect
18. #91458C4semidirect
31. C2×#3941D3semidirect
58. C2×C3⋊#168D4semidirect
65. C2×C3×#168D4semidirect
71. #4977D5semidirect
173. C2×#168#67semidirect
384. C3×C5#1961semidirect
456. C5#70160semidirect
479. C3#10600346semidirect

Maximal subgroups

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

subgroupindex
C2×#914582
C2×#910932
C5×#49772
C2×C3×#39412
C2×#909692
C2×#909642
C2×#909532
#106003463
#701605