Finite Group Databasebeta

← #14305894

Subgroups — #14305894

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×#91374C211yesmaximal, characteristic
2C2×#91093C211yesmaximal, characteristic
3C5×#4975C211yesmaximal, characteristic, complemented
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5C2×#90970C211yesmaximal, characteristic, complemented
6C2×#90969C211yesmaximal, characteristic
7C2×#90953C211yesmaximal, characteristic, complemented
8#10600374—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
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×#6667—22no—
18#91374—22no—
19#91374C414yescomplemented
20#91093—22no—
21C3×#3942—22no—
22#90970—22no—
23#90969—22no—
24#90953—22no—
25#70227—51nomaximal, Hall
26C2×#4021—31no—
27C5×#384—31no—
28C2×#3942—31no—
29C2×#3942D311yescharacteristic, complemented
30C2×#3941—31no—
31C2×#3941—31no—
32C2×#3935—31no—
33C23×D15—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60C2×C412yes—
42C22×C5×Dic3—21no—
43C22×C5×Dic3D412yes—
44C22×C3×Dic5—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10—21no—
49C2×C3×Dic10—21no—
50C2×C3×Dic10C2×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#6667—28no—
65C2×#947—51no—
66C2×C3×#103—51no—
67C2×#835—51no—
68C2×#821—51no—
69C2×#815—51no—
70#4975D511yescharacteristic, complemented
71C2×#809—51no—
72C22×D20—31no—
73C22×Dic10C2×D311yescharacteristic
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—22no—
84#3942—62no—
85#3941—62no—
86#3941—62no—
87#3935—62no—
88#1959—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×D15—22no—
91C22×D15—41no—
92C22×D15—41no—
93C22×D15—42no—
94C22×D15—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
103D60—22no—
104D60—22no—
105D60—41no—
106D60—41no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—42no—
111C2×C5×Dic3C22⋊C414yes—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C3×Dic10—22no—
116C3×Dic10—22no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3⋊#168—22no—
120C3×#168—22no—
121C22×C3×Q8—51no—
122C22×D12—51no—
123C22×C3×C8—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
125#947—54no—
126#947—102no—
127C2×(C2×D3)⋊C4—102no—
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—22no—
130C2×C4×Dic3C2×D511yescharacteristic
131C22×C3⋊C8—51no—
132C3×#103—102no—
133#835—102no—
134#821—102no—
135#815—102no—
136#809—102no—
137C23×D5—61no—
138C22×C4×C5—21no—
139C22×C4×C5—32no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C2×D20—32no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×D20—61no—
148C2×D20—61no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10C4×D312yes—
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—51no—
171C2×#103—151no—
172C2×#102—151no—
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×D15—42no—
182C2×D15—44no—
183C2×D15—82no—
184C2×D15—81no—
185C2×D15—81no—
186C3×C4×C5—81no—
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5#12111yescharacteristic
190C3×C4×C5#12111yescharacteristic
191C3×Dic5—42no—
192C5×Dic3—24no—
193C5×Dic3—81no—
194C23×D3—101no—
195C2×C3×Q8—52no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×Q8—101no—
199C2×C3×Q8—101no—
200C2×C3×Q8—101no—
201C22×C3×C4—21no—
202C22×C3×C4—101no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—21no—
205C22×Dic3C22⋊D512yes—
206C2×D12—52no—
207C2×D12—101no—
208C2×D12—101no—
209C2×D12—101no—
210C2×D12—101no—
211C2×D12—101no—
212C2×C3×C8—52no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217(C2×D3)⋊C4—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—62no—
228C22×D5—121no—
229C22×D5—122no—
230C22×D5—122no—
231C22×D5—121no—
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—22no—
246C2×Dic5—41no—
247C2×Dic5—41no—
248D20—62no—
249D20—62no—
250D20—121no—
251D20—121no—
252Dic10—22no—
253Dic10—22no—
254Dic10—41no—
255Dic10—41no—
256#168—22no—
257#168—62no—
258C22×Q8—51no—
259C22×D4—151no—
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—102no—
270#103—302no—
271#102—302no—
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
279D15—82no—
280C23×C3C2×C22⋊D511yescharacteristic
281C22×D3—102no—
282C22×D3—202no—
283C22×D3—201no—
284C22×D3—202no—
285C22×D3—201no—
286C3×Q8—102no—
287C3×Q8—102no—
288C3×Q8—201no—
289C3×Q8—201no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—102no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71311yescharacteristic
300C2×C3×C4#71311yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—42no—
304C2×Dic3—41no—
305C2×Dic3#68514yes—
306D12—102no—
307D12—102no—
308D12—201no—
309D12—201no—
310C3×C8—102no—
311C3⋊C8—102no—
312C22×C5D3×C22⋊C411yescharacteristic
313C22×C5#88511yescharacteristic
314C22×C5#91412yes—
315C22×C5#91812yes—
316C22×C5#94011yescharacteristic
317C2×D5—122no—
318C2×D5—124no—
319C2×D5—241no—
320C2×D5—241no—
321C2×D5—242no—
322C4×C5—64no—
323C4×C5—81no—
324C4×C5—241no—
325C4×C5#67⋊C411yescharacteristic
326C4×C5#88411yescharacteristic
327C4×C5C4×#6711yescharacteristic
328C4×C5#93911yescharacteristic
329Dic5—42no—
330C24—301no—
331C2×Q8—52no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×D4—152no—
338C2×D4—301no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C22×C4—21no—
344C22×C4—32no—
345C22×C4—61no—
346C22×C4—101no—
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×C3C2×#68511yescharacteristic
364C22×C3#407812yes—
365C22×C3#408611yescharacteristic
366C22×C3#408812yes—
367C22×C3#409311yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—401no—
371C2×D3—401no—
372C2×D3—402no—
373C3×C4—81no—
374C3×C4—202no—
375C3×C4#403911yescharacteristic
376C3×C4#403911yescharacteristic
377C3×C4#404111yescharacteristic
378C3×C4#404111yescharacteristic
379Dic3—24no—
380Dic3—81no—
381C2×C5#479412yes—
382C2×C5#480312yes—
383C2×C5#495711yescharacteristic
384C2×C5#517611yescharacteristic
385C2×C5#519011yescharacteristic
386D5—242no—
387C23—302no—
388C23—601no—
389C23—602no—
390C23—602no—
391C23—601no—
392C23D3×C22⋊D511yescharacteristic
393Q8—102no—
394Q8—102no—
395Q8—201no—
396Q8—201no—
397D4—302no—
398D4—302no—
399D4—601no—
400D4—601no—
401C2×C4—34no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—102no—
407C2×C4—122no—
408C2×C4—121no—
409C2×C4—201no—
410C2×C4—201no—
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#6525512yes—
420C2×C3#6527711yescharacteristic
421C2×C3#6536311yescharacteristic
422C2×C3#6537511yescharacteristic
423C2×C3#6537812yes—
424D3—402no—
425C5#7022711yescharacteristic, complemented, Sylow
426C22—602no—
427C22—604no—
428C22—1202no—
429C22—1201no—
430C22—1201no—
431C22#9145511yescharacteristic
432C22D3×#68511yescharacteristic
433C22#9149612yes—
434C22#9152012yes—
435C22#9156711yescharacteristic
436C4—64no—
437C4—81no—
438C4—202no—
439C4—241no—
440C4#9139611yescharacteristic
441C4#9140911yescharacteristic
442C4#9144411yescharacteristic
443C4#9145911yescharacteristic
444C3#1060037411yescharacteristic, complemented, Sylow
445C2—1202no—
446C2#1174738012yes—
447C2#1174750512yes—
448C2#1174891311yescharacteristic
449C2#1174907611yescharacteristic
450C2#1174932411yescharacteristic
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×D60C22
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
3. C5×#4975C2semidirect
4. C2×C3×#3942C2semidirect
5. C2×#90970C2semidirect
7. C2×#90953C2semidirect
19. #91374C4semidirect
29. C2×#3942D3semidirect
70. #4975D5semidirect
362. C3×C5#1959semidirect
425. C5#70227semidirect
444. C3#10600374semidirect

Maximal subgroups

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

subgroupindex
C2×#913742
C2×#910932
C5×#49752
C2×C3×#39422
C2×#909702
C2×#909692
C2×#909532
#106003743
#702275