Finite Group Databasebeta

← #14305915

Subgroups — #14305915

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#936C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic
3C2×C3×#3964C211yesmaximal, characteristic
4#11748861C211yesmaximal, characteristic, complemented
5C2×#90973C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7C2×#90953C211yesmaximal, characteristic, complemented
8#10602519—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#217—22no—
14C5×#936—22no—
15C5×#936C414yescomplemented
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C2×Dic3⋊Dic5—22no—
20#91116—22no—
21C3×#3964—22no—
22#90973—22no—
23#90972—22no—
24#90953—22no—
25#70159—51nomaximal, Hall
26C2×C5×#124—31no—
27C2×#3967—31no—
28C2×#3967—31no—
29C2×#3964—31no—
30C2×#3964D311yescharacteristic
31#65224—31no—
32C2×#3935—31no—
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C412yes—
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3D412yes—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6C2×C412yes—
50C22×C3×Dic5—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C5×#217—28no—
57C4×C5×Dic3C2×C412yes—
58C4×C5×Dic3D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168D412yes—
64Dic3⋊Dic5—44no—
65C2×#936D511yescharacteristic
66C2×C3×#102—51no—
67C2×#832—51no—
68C2×#816—51no—
69C2×#815—51no—
70#4975—51no—
71C2×#810—51no—
72C22×C5×Q8—31no—
73C22×C5×D4C2×D311yescharacteristic
74C5×#124—34no—
75C5×#124—62no—
76C2×C5×C22⋊C4—62no—
77C2×C42×C5—31no—
78C2×C4⋊Dic5—31no—
79C2×C4⋊Dic5—62no—
80C2×C4⋊Dic5C2×D311yescharacteristic
81C22×#168—31no—
82C22×#168C2×D311yescharacteristic
83#3967—62no—
84#3967—62no—
85#3964—22no—
86#3964—62no—
87#3935—62no—
88#1959—151noSylow
89C23×C3×C5—22no—
90C23×C3×C5—41no—
91C23×C3×C5—41no—
92C23×C3×C5—42no—
93C23×C3×C5—42no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×D4—22no—
96C3×C5×D4—22no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×Dic15—41no—
106C2×Dic15—42no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—22no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3C22⋊C414yes—
113C5×Dic6—22no—
114C5×Dic6—22no—
115C5×Dic6—41no—
116C5×Dic6—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—42no—
119C3⋊#168—22no—
120C3×#168—22no—
121C22×C3×D4C2×D511yescharacteristic
122C22×Dic6C2×D511yescharacteristic
123C22×C3×C8—51no—
124C2×C3×C4⋊C4—51no—
125C2×#217—22no—
126#936—22no—
127#936Dic514yescomplemented
128C2×C4⋊Dic3—51no—
129C2×Dic3⋊C4—102no—
130C2×C4×Dic3C2×D511yescharacteristic
131C22×C3⋊C8—51no—
132C3×#102—102no—
133#832—102no—
134#816—102no—
135#815—102no—
136#810—102no—
137C24×C5—21no—
138C2×C5×Q8—32no—
139C2×C5×Q8—61no—
140C2×C5×Q8—61no—
141C2×C5×Q8—61no—
142C2×C5×Q8—61no—
143C2×C5×Q8—61no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4C4×D312yes—
150C22×C4×C5—32no—
151C22×C4×C5—61no—
152C22×C4×C5C22×D311yescharacteristic
153C22×Dic5—21no—
154C22×Dic5—61no—
155C5×C22⋊C4—68no—
156C42×C5—32no—
157C42×C5—32no—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5—124no—
163C2×#168—21no—
164C2×#168—21no—
165C2×#168—32no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#168#6712yes—
169C2×#124—31no—
170C2×#103—151no—
171C2×#103—151no—
172C2×#102—51no—
173C2×#102—151no—
174C2×#97—151no—
175#384—151no—
176C22×C3×C5—42no—
177C22×C3×C5—44no—
178C22×C3×C5—82no—
179C22×C3×C5—81no—
180C22×C3×C5—81no—
181C22×C3×C5C2×C22⋊C411yescharacteristic
182C22×C3×C5#12411yescharacteristic
183C22×C3×C5#12711yescharacteristic
184C22×C3×C5AGL(1,ℤ/8)12yes—
185C22×C3×C5#13712yes—
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5#12111yescharacteristic
189C3×C4×C5#12111yescharacteristic
190Dic15—81no—
191C3×Dic5—81no—
192C5×Dic3—24no—
193C5×Dic3—42no—
194C24×C3—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4C2×Dic512yes—
201C22×C3×C4—101no—
202C22×C3×C4C22×D511yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—101no—
205C22×Dic3C22⋊D512yes—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6C2×Dic512yes—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217#217—28no—
218C4⋊Dic3—101no—
219C4⋊Dic3—101no—
220Dic3⋊C4—204no—
221C4×Dic3C2×Dic512yes—
222C4×Dic3C22⋊D512yes—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5—22no—
227C23×C5—41no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—41no—
231C23×C5D3×D411yescharacteristic
232C5×Q8—62no—
233C5×Q8—62no—
234C5×Q8—121no—
235C5×Q8—121no—
236C5×D4—22no—
237C5×D4—22no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—34no—
241C2×C4×C5—62no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5—121no—
245C2×C4×C5—121no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C2×Dic5—42no—
253C2×Dic5—41no—
254C2×Dic5—122no—
255C2×Dic5—121no—
256#168—22no—
257#168—62no—
258C22×Q8—31no—
259C22×D4D3×D511yescharacteristic
260C22×C8—51no—
261C22×C8—151no—
262#124—34no—
263#124—62no—
264C2×C4⋊C4—51no—
265C2×C4⋊C4—151no—
266C2×C4⋊C4—302no—
267C2×C22⋊C4—62no—
268C2×C42—31no—
269#103—302no—
270#103—302no—
271#102—102no—
272#102—302no—
273#97—302no—
274C2×C3×C5—82no—
275C2×C3×C5#39011yescharacteristic
276C2×C3×C5#41712yes—
277C2×C3×C5#48912yes—
278C2×C3×C5#49611yescharacteristic
279C2×C3×C5#49711yescharacteristic
280C23×C3—22no—
281C23×C3—42no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—42no—
285C23×C3C2×C22⋊D511yescharacteristic
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—41no—
289C3×D4—41no—
290C2×C3×C4—201no—
291C2×C3×C4—202no—
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4#71111yescharacteristic
295C2×C3×C4#71111yescharacteristic
296C2×C3×C4C22×Dic511yescharacteristic
297C2×C3×C4C2×C22⋊D511yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—201no—
304C2×Dic3—202no—
305C2×Dic3C22⋊Dic514yes—
306Dic6—22no—
307Dic6—22no—
308Dic6—41no—
309Dic6—41no—
310C3×C8—102no—
311C3⋊C8—102no—
312C22×C5—42no—
313C22×C5—44no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5—82no—
317C22×C5D3×C22⋊C411yescharacteristic
318C22×C5#88511yescharacteristic
319C22×C5#91112yes—
320C22×C5#91512yes—
321C22×C5#94011yescharacteristic
322C4×C5—64no—
323C4×C5—122no—
324C4×C5#67⋊C411yescharacteristic
325C4×C5#88411yescharacteristic
326C4×C5C4×#6711yescharacteristic
327C4×C5#93911yescharacteristic
328Dic5—81no—
329Dic5—241no—
330C24—21no—
331C2×Q8—32no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4D3×Dic512yes—
343C22×C4—32no—
344C22×C4—61no—
345C22×C4—101no—
346C22×C4—301no—
347C22×C4C2×D3×D511yescharacteristic
348C2×C8—52no—
349C2×C8—101no—
350C2×C8—101no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C4⋊C4—101no—
355C4⋊C4—101no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—68no—
360C42—32no—
361C42—32no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3—42no—
364C22×C3—44no—
365C22×C3—82no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3#408211yescharacteristic
369C22×C3#408611yescharacteristic
370C22×C3#409512yes—
371C22×C3#409712yes—
372C22×C3C2×C22⋊Dic511yescharacteristic
373C3×C4—401no—
374C3×C4D4×Dic511yescharacteristic
375C3×C4D4×Dic511yescharacteristic
376C3×C4#408411yescharacteristic
377C3×C4#408411yescharacteristic
378Dic3—24no—
379Dic3—42no—
380Dic3—401no—
381C2×C5—82no—
382C2×C5#476512yes—
383C2×C5#477112yes—
384C2×C5#495711yescharacteristic
385C2×C5#515411yescharacteristic
386C2×C5#516711yescharacteristic
387C23—22no—
388C23—42no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23D3×C22⋊D511yescharacteristic
393Q8—62no—
394Q8—62no—
395Q8—121no—
396Q8—121no—
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—34no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—202no—
408C2×C4—201no—
409C2×C4—602no—
410C2×C4—601no—
411C2×C4#678011yescharacteristic
412C2×C4C2×D3×Dic511yescharacteristic
413C2×C4#678211yescharacteristic
414C2×C4D5×#6711yescharacteristic
415C2×C4D3×C22⋊D511yescharacteristic
416C2×C4#679011yescharacteristic
417C8—102no—
418C8—302no—
419C2×C3—82no—
420C2×C3#6534412yes—
421C2×C3#6534711yescharacteristic
422C2×C3#6534911yescharacteristic
423C2×C3#6551011yescharacteristic
424C2×C3#6552112yes—
425C5#7015911yescharacteristic, complemented, Sylow
426C22—44no—
427C22—42no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22#9148012yes—
432C22#9148612yes—
433C22#9152511yescharacteristic
434C22D3×C22⋊Dic511yescharacteristic
435C22#9156711yescharacteristic
436C4—64no—
437C4—122no—
438C4—401no—
439C4—1201no—
440C4#9154911yescharacteristic
441C4Dic5×#6711yescharacteristic
442C4#9155711yescharacteristic
443C4#67⋊Dic511yescharacteristic
444C3#1060251911yescharacteristic, complemented, Sylow
445C2—82no—
446C2#1174894512yes—
447C2#1174895512yes—
448C2#1174909811yescharacteristic
449C2#1174911011yescharacteristic
450C2#1174948211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748861C2semidirect
5. C2×#90973C2semidirect
6. C2×#90972C2semidirect
7. C2×#90953C2semidirect
15. C5×#936C4semidirect
127. #936Dic5semidirect
362. C3×C5#1959semidirect
425. C5#70159semidirect
444. C3#10602519semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9362
C2×#911162
C2×C3×#39642
#117488612
C2×#909732
C2×#909722
C2×#909532
#106025193
#701595