Finite Group Databasebeta

← #14305895

Subgroups — #14305895

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×#91364C211yesmaximal, characteristic
2C2×#91094C211yesmaximal, characteristic, complemented
3C5×#4975C211yesmaximal, characteristic, complemented
4C2×C3×#3941C211yesmaximal, characteristic
5C2×#90975C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic
7C2×#90953C211yesmaximal, characteristic, complemented
8#10600374—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×Dic3⋊C4—22no—
15C2×C4×C5×Dic3C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×#6665—22no—
18#91364—22no—
19#91364C414yescomplemented
20#91094—22no—
21C3×#3941—22no—
22#90975—22no—
23#90964—22no—
24#90953—22no—
25#70159—51nomaximal, Hall
26C2×#4021—31no—
27C5×#384—31no—
28C2×#3942—31no—
29C2×#3942—31no—
30C2×#3941—31no—
31C2×#3941D311yescharacteristic
32C2×#3935—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30C2×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—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C5×C4⋊Dic3—21no—
57C5×C4⋊Dic3—21no—
58C5×Dic3⋊C4—44no—
59C4×C5×Dic3C2×C412yes—
60C4×C5×Dic3D412yes—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168D412yes—
64#6665—28no—
65C2×#936—51no—
66C2×C3×#102—51no—
67C2×#832—51no—
68C2×#816—51no—
69C2×#815—51no—
70#4975D511yescharacteristic, complemented
71C2×#810—51no—
72C22×D20C2×D311yescharacteristic
73C22×Dic10—31no—
74C2×C5×C4⋊C4—31no—
75C2×C5×C4⋊C4—62no—
76C2×C5×C4⋊C4C2×D311yescharacteristic
77C2×C42×C5—31no—
78C2×#685—62no—
79C22×#168—31no—
80C22×#168C2×D311yescharacteristic
81#4021—34no—
82#4021—62no—
83#3942—62no—
84#3942—62no—
85#3941—22no—
86#3941—62no—
87#3935—62no—
88#1959—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—22no—
91C22×C3×D5—41no—
92C22×C3×D5—41no—
93C22×C3×D5—42no—
94C22×C3×D5—42no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106Dic30—22no—
107Dic30—22no—
108Dic30—41no—
109Dic30—41no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—42no—
114C2×C5×Dic3C22⋊C414yes—
115C3×D20—22no—
116C3×D20—22no—
117C3×D20—41no—
118C3×D20—41no—
119C3⋊#168—22no—
120C3×#168—22no—
121C22×C3×D4—51no—
122C22×Dic6—51no—
123C22×C3×C8—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×#217—102no—
126#936—54no—
127#936—102no—
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—22no—
130C2×C4×Dic3C2×D511yescharacteristic
131C22×C3⋊C8—51no—
132C3×#102—102no—
133#832—102no—
134#816—102no—
135#815—102no—
136#810—102no—
137C23×D5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—32no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—61no—
143C2×D20—21no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20C4×D312yes—
149C2×Dic10—32no—
150C2×Dic10—61no—
151C2×Dic10—61no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—61no—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—124no—
160C42×C5—32no—
161C42×C5—32no—
162#685—68no—
163C2×#168—21no—
164C2×#168—21no—
165C2×#168—32no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#168#6712yes—
169C2×#124—151no—
170C2×#103—151no—
171C2×#103—151no—
172C2×#102—51no—
173C2×#102—151no—
174C2×#97—151no—
175#384—31no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C22×C3×C5#12411yescharacteristic
178C22×C3×C5#12711yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)12yes—
180C22×C3×C5#13712yes—
181C2×C3×D5—42no—
182C2×C3×D5—44no—
183C2×C3×D5—82no—
184C2×C3×D5—81no—
185C2×C3×D5—81no—
186C3×C4×C5—81no—
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12111yescharacteristic
190C3×C4×C5#12111yescharacteristic
191Dic15—42no—
192C5×Dic3—24no—
193C5×Dic3—81no—
194C24×C3—101no—
195C2×C3×D4—52no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C22×C3×C4—21no—
202C22×C3×C4C22×D511yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—101no—
205C22×Dic3C22⋊D512yes—
206C2×Dic6—52no—
207C2×Dic6—101no—
208C2×Dic6—101no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217#217—108no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220Dic3⋊C4—44no—
221C4×Dic3C4×D512yes—
222C4×Dic3D2012yes—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5D3×D411yescharacteristic
227C22×D5—22no—
228C22×D5—41no—
229C22×D5—42no—
230C22×D5—42no—
231C22×D5—41no—
232C2×C4×C5—34no—
233C2×C4×C5—42no—
234C2×C4×C5—41no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—122no—
238C2×C4×C5—121no—
239C2×C4×C5C2×C4×D311yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C2×C4×C5#23711yescharacteristic
244C2×C4×C5C2×#6711yescharacteristic
245C2×Dic5—62no—
246C2×Dic5—121no—
247C2×Dic5—121no—
248D20—22no—
249D20—22no—
250D20—41no—
251D20—41no—
252Dic10—62no—
253Dic10—62no—
254Dic10—121no—
255Dic10—121no—
256#168—22no—
257#168—62no—
258C22×Q8—151no—
259C22×D4—51no—
260C22×C8—51no—
261C22×C8—151no—
262#124—154no—
263#124—302no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—62no—
266C2×C4⋊C4D3×D511yescharacteristic
267C2×C22⋊C4—302no—
268C2×C42—31no—
269#103—302no—
270#103—302no—
271#102—102no—
272#102—302no—
273#97—302no—
274C2×C3×C5#39011yescharacteristic
275C2×C3×C5#41712yes—
276C2×C3×C5#48912yes—
277C2×C3×C5#49611yescharacteristic
278C2×C3×C5#49711yescharacteristic
279C3×D5—82no—
280C23×C3—102no—
281C23×C3—202no—
282C23×C3—201no—
283C23×C3—202no—
284C23×C3—201no—
285C23×C3C2×C22⋊D511yescharacteristic
286C3×D4—102no—
287C3×D4—102no—
288C3×D4—201no—
289C3×D4—201no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4C2×C4×D511yescharacteristic
293C2×C3×C4C2×D2011yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71311yescharacteristic
297C2×C3×C4#71311yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—42no—
301C2×Dic3—41no—
302C2×Dic3—102no—
303C2×Dic3—201no—
304C2×Dic3—201no—
305C2×Dic3#68514yes—
306Dic6—102no—
307Dic6—102no—
308Dic6—201no—
309Dic6—201no—
310C3×C8—102no—
311C3⋊C8—102no—
312C22×C5D3×C22⋊C411yescharacteristic
313C22×C5#88511yescharacteristic
314C22×C5#91112yes—
315C22×C5#91512yes—
316C22×C5#94011yescharacteristic
317C2×D5—42no—
318C2×D5—44no—
319C2×D5—81no—
320C2×D5—81no—
321C2×D5—82no—
322C4×C5—64no—
323C4×C5—81no—
324C4×C5—241no—
325C4×C5#67⋊C411yescharacteristic
326C4×C5#88411yescharacteristic
327C4×C5C4×#6711yescharacteristic
328C4×C5#93911yescharacteristic
329Dic5—122no—
330C24—101no—
331C2×Q8—152no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×D4—52no—
338C2×D4—101no—
339C2×D4—101no—
340C2×D4—101no—
341C2×D4—101no—
342C2×D4—101no—
343C22×C4—21no—
344C22×C4—32no—
345C22×C4—61no—
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—21no—
355C4⋊C4—21no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—124no—
359C22⋊C4—308no—
360C42—32no—
361C42—32no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3—204no—
364C22×C3—202no—
365C22×C3—401no—
366C22×C3—401no—
367C22×C3—402no—
368C22×C3C2×#68511yescharacteristic
369C22×C3#407812yes—
370C22×C3#408611yescharacteristic
371C22×C3#408812yes—
372C22×C3#409311yescharacteristic
373C3×C4—81no—
374C3×C4#403911yescharacteristic
375C3×C4#403911yescharacteristic
376C3×C4#404111yescharacteristic
377C3×C4#404111yescharacteristic
378Dic3—24no—
379Dic3—81no—
380Dic3—202no—
381C2×C5#476512yes—
382C2×C5#477112yes—
383C2×C5#495711yescharacteristic
384C2×C5#515411yescharacteristic
385C2×C5#516711yescharacteristic
386D5—82no—
387C23—102no—
388C23—201no—
389C23—202no—
390C23—202no—
391C23—201no—
392C23D3×C22⋊D511yescharacteristic
393Q8—302no—
394Q8—302no—
395Q8—601no—
396Q8—601no—
397D4—102no—
398D4—102no—
399D4—201no—
400D4—201no—
401C2×C4—34no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—122no—
407C2×C4—121no—
408C2×C4—302no—
409C2×C4—601no—
410C2×C4—601no—
411C2×C4#676611yescharacteristic
412C2×C4#677311yescharacteristic
413C2×C4C4×D3×D511yescharacteristic
414C2×C4D3×D2011yescharacteristic
415C2×C4D5×#6711yescharacteristic
416C2×C4#679011yescharacteristic
417C8—102no—
418C8—302no—
419C2×C3—402no—
420C2×C3#6525512yes—
421C2×C3#6527711yescharacteristic
422C2×C3#6536311yescharacteristic
423C2×C3#6537511yescharacteristic
424C2×C3#6537812yes—
425C5#7015911yescharacteristic, complemented, Sylow
426C22—202no—
427C22—204no—
428C22—402no—
429C22—401no—
430C22—401no—
431C22#9145511yescharacteristic
432C22D3×#68511yescharacteristic
433C22#9149412yes—
434C22#9151812yes—
435C22#9156711yescharacteristic
436C4—64no—
437C4—81no—
438C4—241no—
439C4—602no—
440C4#9139611yescharacteristic
441C4#9140911yescharacteristic
442C4#9144411yescharacteristic
443C4#9145911yescharacteristic
444C3#1060037411yescharacteristic, complemented, Sylow
445C2—402no—
446C2#1174737612yes—
447C2#1174750312yes—
448C2#1174891311yescharacteristic
449C2#1174907111yescharacteristic
450C2#1174931911yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1959
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×#91094C2semidirect
3. C5×#4975C2semidirect
5. C2×#90975C2semidirect
7. C2×#90953C2semidirect
19. #91364C4semidirect
70. #4975D5semidirect
362. C3×C5#1959semidirect
425. C5#70159semidirect
444. C3#10600374semidirect

Maximal subgroups

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

subgroupindex
C2×#913642
C2×#910942
C5×#49752
C2×C3×#39412
C2×#909752
C2×#909642
C2×#909532
#106003743
#701595