Finite Group Databasebeta

← #14302457

Subgroups — #14302457

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#908C211yesmaximal, characteristic
2#11754503C211yesmaximal, characteristic, complemented
3#11748625C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5#11748386C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7C3×#64777C211yesmaximal, characteristic, complemented
8#10602882—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#908—22no—
15C5×#908—22no—
16C2×C5×D24C412yescomplemented
17C2×C5×#204C412yescomplemented
18C3×#4072C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20D3×C22⋊Dic5—22no—
21#91435—22no—
22Dic5×D12—22no—
23#90996—22no—
24#90979—22no—
25#90966—22no—
26#68704—51nomaximal, Hall
27C2×C5×AGL(1,ℤ/8)—31no—
28#66132—31no—
29#65529—31no—
30#65525—31no—
31#65504—31no—
32#64777D311yescharacteristic, complemented
33#64776—31no—
34C23×C5×D3—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C5×#67—21no—
37C5×#235—21no—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235—21no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12C2×C412yes—
45C2×C5×D12C2×C411yescharacteristic, complemented
46C2×C5×D12D412yes—
47C2×C5×D12D412yes—
48C2×C4×C5×D3—21no—
49C2×C5×Dic6C2×C411yescharacteristic, complemented
50C2×D3×Dic5—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8C2×C412yescomplemented
54#6719D412yes—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57#6710—21no—
58#6710—21no—
59C2×C3⋊#168—21no—
60C5×D24—24no—
61C5×#204—24no—
62C3×C22⋊Dic5—21no—
63C3×C22⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5D412yes—
68(C2×D3)⋊Dic5—24no—
69C2×#908D511yescharacteristic
70#5521—51no—
71#5006—51no—
72#5005—51no—
73#5001—51no—
74C3×H(3,ℤ/4)—51no—
75#4556—51no—
76C2×C5×#41—31no—
77C22×C5×D4—31no—
78C5×AGL(1,ℤ/8)—62no—
79C5×AGL(1,ℤ/8)—62no—
80C2×C5×SD16—32no—
81C2×C5×D8—32no—
82C2×C5×M16C2×D311yescharacteristic
83C2×C22⋊Dic5—62no—
84D4×Dic5—62no—
85D4×Dic5—62no—
86#4072—31no—
87#4072C2×D311yescharacteristic
88#4072C2×D311yescharacteristic
89C2×#681—31no—
90#3969—62no—
91#3966—62no—
92#3964—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—22no—
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—21no—
99C22×C5×D3—82no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—22no—
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—21no—
110C5×D12—21no—
111C5×D12—22no—
112C5×D12—21no—
113C5×D12—22no—
114C5×D12—22no—
115C5×D12C22⋊C414yes—
116C4×C5×D3—41no—
117C4×C5×D3—41no—
118C5×Dic6—21no—
119C5×Dic6—21no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—41no—
122D3×Dic5—84no—
123C3×C5×C8—22no—
124C3⋊#168—41no—
125C2×#235C2×D511yescharacteristic
126C22×D12C2×D511yescharacteristic
127C2×C3×M16C2×D511yescharacteristic
128C3×#117—51no—
129C3×#117—51no—
130#926—51no—
131C2×#208—51no—
132#908—22no—
133#908—22no—
134C2×D24Dic512yescomplemented
135C2×#204Dic512yescomplemented
136#893—102no—
137D3×C22⋊C4—102no—
138C4×D12—102no—
139#809—102no—
140#806—102no—
141#805—102no—
142C24×C5—61no—
143C5×#41—61no—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C2×C5×Q8—31no—
148C2×C5×D4—32no—
149C2×C5×D4—31no—
150C2×C5×D4—32no—
151C2×C5×D4—32no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C22×C4×C5—61no—
157C22×C4×C5C22×D311yescharacteristic
158C22×Dic5—64no—
159C5×SD16—64no—
160C5×D8—64no—
161C5×M16—21no—
162C5×M16—21no—
163C2×C5×C8C4×D312yescomplemented
164C22⋊Dic5—21no—
165C22⋊Dic5—21no—
166C22⋊Dic5—32no—
167C22⋊Dic5—64no—
168C4⋊Dic5—21no—
169C4⋊Dic5—21no—
170C4⋊Dic5—61no—
171C4×Dic5—21no—
172C4×Dic5—61no—
173C4×Dic5D1212yes—
174#681—61no—
175#681—61no—
176C2×#168—61no—
177C2×AGL(1,ℤ/8)—31no—
178#518—151no—
179#421—151no—
180#418—151no—
181#410—151no—
182#344—151no—
183H(3,ℤ/4)—51no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×C5×D3—24no—
189C2×C5×D3—44no—
190C2×C5×D3—41no—
191C2×C5×D3—82no—
192C2×C5×D3—82no—
193C2×C5×D3—81no—
194C3×C4×C5C2×C22⋊C411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12111yescharacteristic
197C3×C4×C5#12311yescharacteristic
198Dic15—42no—
199C3×Dic5—42no—
200C3×Dic5—81no—
201C5×Dic3—41no—
202C23×D3—21no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—21no—
205#235—21no—
206#235—21no—
207#235—21no—
208#235—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C2×Dic512yes—
213C2×D12C2×Dic511yescharacteristic, complemented
214C2×D12C22⋊D512yes—
215C2×D12C22⋊D512yes—
216C2×C4×D3—21no—
217C2×C4×D3—104no—
218C2×Dic6C2×Dic511yescharacteristic, complemented
219C3×M16—21no—
220C3×M16—21no—
221C2×C3×C8C2×Dic512yescomplemented
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227C3×C42—101no—
228#217—52no—
229(C2×D3)⋊C4—104no—
230C4⋊Dic3—101no—
231C4×Dic3—101no—
232#208—101no—
233#208—101no—
234C2×C3⋊C8—101no—
235D24—24no—
236#204—24no—
237C23×C5—62no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—61no—
241C23×C5—242no—
242C23×C5D3×D411yescharacteristic
243C5×Q8—61no—
244C5×Q8—61no—
245C5×D4—34no—
246C5×D4—62no—
247C5×D4—61no—
248C5×D4—61no—
249C5×D4—62no—
250C5×D4—62no—
251C5×D4—121no—
252C5×D4—121no—
253C2×C4×C5—61no—
254C2×C4×C5—121no—
255C2×C4×C5—121no—
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5C2×D1211yescharacteristic
258C2×C4×C5#23511yescharacteristic
259C2×C4×C5D3×D411yescharacteristic
260C2×C4×C5D3×D411yescharacteristic
261C2×C4×C5#23911yescharacteristic
262C2×Dic5—22no—
263C2×Dic5—41no—
264C2×Dic5—62no—
265C2×Dic5—244no—
266C5×C8—22no—
267#168—121no—
268C2×#41—31no—
269C22×D4—31no—
270AGL(1,ℤ/8)—62no—
271AGL(1,ℤ/8)—62no—
272C2×SD16—32no—
273C2×D8—32no—
274C2×M16—151no—
275C2×M16D3×D511yescharacteristic
276C4×D4—302no—
277C4×D4—302no—
278#117—51no—
279#117—51no—
280#117—151no—
281C2×C22⋊C4—302no—
282#104—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289C5×D3—44no—
290C5×D3—81no—
291C23×C3D4×D511yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—21no—
296C22×D3—82no—
297C2×C3×C4—102no—
298C2×C3×C4—201no—
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4#71111yescharacteristic
301C2×C3×C4#71111yescharacteristic
302C2×C3×C4C22×Dic511yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304C2×C3×C4C2×C22⋊D511yescharacteristic
305#67—41no—
306#67—41no—
307C2×Dic3—21no—
308C2×Dic3—102no—
309D12—21no—
310D12—22no—
311D12—21no—
312D12—22no—
313D12—22no—
314D12C22⋊Dic514yes—
315C4×D3—41no—
316C4×D3—41no—
317C4×D3—404no—
318Dic6—21no—
319Dic6—21no—
320C3×C8—22no—
321C3⋊C8—201no—
322C22×C5—41no—
323C22×C5—64no—
324C22×C5—124no—
325C22×C5—121no—
326C22×C5—242no—
327C22×C5—242no—
328C22×C5—241no—
329C22×C5#88211yescharacteristic
330C22×C5#88411yescharacteristic
331C22×C5#89311yescharacteristic
332C4×C5—121no—
333C4×C5C4×D1211yescharacteristic
334C4×C5D3×C22⋊C411yescharacteristic
335C4×C5#89411yescharacteristic
336C4×C5#89511yescharacteristic
337Dic5—42no—
338Dic5—81no—
339Dic5—122no—
340C24—61no—
341#41—61no—
342#41—61no—
343#41—61no—
344#41—61no—
345C2×Q8—31no—
346C2×D4—32no—
347C2×D4—31no—
348C2×D4—32no—
349C2×D4—32no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C22×C4—61no—
355C22×C4—304no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—64no—
358D8—64no—
359M16—21no—
360M16—21no—
361M16—301no—
362M16—301no—
363C2×C8—301no—
364C2×C8D3×Dic512yescomplemented
365C4⋊C4—101no—
366C4⋊C4—101no—
367C4⋊C4—301no—
368C22⋊C4—101no—
369C22⋊C4—101no—
370C22⋊C4—152no—
371C22⋊C4—304no—
372C42—52no—
373C42—101no—
374C42—301no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3D4×Dic511yescharacteristic
378C22×C3#408311yescharacteristic
379C22×C3#408511yescharacteristic
380C2×D3—24no—
381C2×D3—44no—
382C2×D3—41no—
383C2×D3—82no—
384C2×D3—82no—
385C2×D3—81no—
386C3×C4—202no—
387C3×C4—401no—
388C3×C4D4×Dic511yescharacteristic
389C3×C4#408111yescharacteristic
390C3×C4#408511yescharacteristic
391C3×C4C2×C22⋊Dic511yescharacteristic
392Dic3—41no—
393Dic3—202no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—124no—
398C2×C5—241no—
399C2×C5#466511yescharacteristic
400C23—62no—
401C23—62no—
402C23—62no—
403C23—61no—
404C23—242no—
405C23#677711yescharacteristic
406Q8—61no—
407Q8—61no—
408D4—34no—
409D4—62no—
410D4—61no—
411D4—62no—
412D4—62no—
413D4—61no—
414D4—121no—
415D4—121no—
416C2×C4—61no—
417C2×C4—102no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—201no—
421C2×C4—302no—
422C2×C4—1204no—
423C2×C4#676811yescharacteristic
424C2×C4#677211yescharacteristic
425C2×C4D5×D1211yescharacteristic
426C2×C4C2×D3×Dic511yescharacteristic
427C2×C4D3×C22⋊D511yescharacteristic
428C2×C4D3×C22⋊D511yescharacteristic
429C8—22no—
430C8—601no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3#6550911yescharacteristic
435D3—44no—
436D3—81no—
437C5#6870411yescharacteristic, complemented, Sylow
438C22—41no—
439C22—64no—
440C22—124no—
441C22—121no—
442C22—242no—
443C22—242no—
444C22—241no—
445C22#9143511yescharacteristic
446C22#9145311yescharacteristic
447C22#9147511yescharacteristic
448C4—121no—
449C4—202no—
450C4—401no—
451C4—602no—
452C4Dic5×D1211yescharacteristic
453C4#9141611yescharacteristic
454C4#9142311yescharacteristic
455C4D3×C22⋊Dic511yescharacteristic
456C3#1060288211yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—124no—
461C2—241no—
462C2#1174890111yescharacteristic
subgroupG/H
centerC2#11748901
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C5×#908C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754503C2semidirect
3. #11748625C2semidirect
4. #11748425C2semidirect
5. #11748386C2semidirect
6. #11746377C2semidirect
7. C3×#64777C2semidirect
16. C2×C5×D24C4semidirect
17. C2×C5×#204C4semidirect
32. #64777D3semidirect
45. C2×C5×D12C2×C4semidirect
49. C2×C5×Dic6C2×C4semidirect
53. C2×C3×C5×C8C2×C4semidirect
134. C2×D24Dic5semidirect
135. C2×#204Dic5semidirect
163. C2×C5×C8C4×D3semidirect
213. C2×D12C2×Dic5semidirect
218. C2×Dic6C2×Dic5semidirect
221. C2×C3×C8C2×Dic5semidirect
364. C2×C8D3×Dic5semidirect
375. C3×C5#1904semidirect
437. C5#68704semidirect
456. C3#10602882semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9082
#117545032
#117486252
#117484252
#117483862
#117463772
C3×#647772
#106028823
#687045