Finite Group Databasebeta

← #14305902

Subgroups — #14305902

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×#91370C211yesmaximal, characteristic
2C2×#91099C211yesmaximal, characteristic, complemented
3C2×C5×#821C211yesmaximal, characteristic
4C2×C3×#3948C211yesmaximal, characteristic, complemented
5#11748866C211yesmaximal, characteristic, complemented
6C2×#90970C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic
8#10600952—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×#6669—22no—
17C2×(C2×D3)⋊Dic5—22no—
18#91370—22no—
19#91370C414yescomplemented
20#91099—22no—
21C5×#821—22no—
22C3×#3948—22no—
23#90970—22no—
24#90966—22no—
25#70227—51nomaximal, Hall
26C2×#4082—31no—
27C2×C5×#102—31no—
28C2×#3964—31no—
29C2×#3948D311yescharacteristic, complemented
30C2×#3947—31no—
31#65265—31no—
32C2×#3942—31no—
33C23×C5×D3—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15D412yes—
36C22×C5×Dic3—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12C2×C412yes—
43C22×C3×Dic5—21no—
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—
51C2×C3×C5×C8—21no—
52C2×C3×C5×C8—21no—
53C2×C3×C5×C8D412yes—
54C4×Dic15C2×C412yes—
55C4×Dic15D412yes—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168D412yes—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63#6669—44no—
64(C2×D3)⋊Dic5—28no—
65C2×#947—51no—
66C2×C3×#103—51no—
67C2×#835—51no—
68C2×#821D511yescharacteristic
69C2×#815—51no—
70#4975—51no—
71C2×#809—51no—
72C22×C5×D4—31no—
73C22×Dic10C2×D311yescharacteristic
74C22×C5×C8C2×D311yescharacteristic
75C2×C5×C4⋊C4—31no—
76C2×C22⋊Dic5—62no—
77#4082—34no—
78#4082—62no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80C2×#683—62no—
81C2×C4×Dic5—31no—
82C22×#168—31no—
83C5×#102—62no—
84#3964—62no—
85#3948—22no—
86#3947—62no—
87#3942—62no—
88#1959—151noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C5×D3—22no—
91C22×C5×D3—41no—
92C22×C5×D3—41no—
93C22×C5×D3—42no—
94C22×C5×D3—42no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×Dic15—22no—
102C2×Dic15—22no—
103C2×Dic15C22⋊C414yes—
104C2×C5×Dic3—41no—
105C2×C5×Dic3—42no—
106C5×D12—22no—
107C5×D12—22no—
108C5×D12—41no—
109C5×D12—41no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—42no—
115C3×Dic10—22no—
116C3×Dic10—22no—
117C3×Dic10—41no—
118C3×Dic10—41no—
119C3×C5×C8—22no—
120C3⋊#168—22no—
121C22×C3×Q8—51no—
122C22×D12C2×D511yescharacteristic
123C22×C3×C8C2×D511yescharacteristic
124C2×C3×C4⋊C4—51no—
125#947—54no—
126#947—102no—
127C2×(C2×D3)⋊C4—102no—
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—102no—
130C2×C4×Dic3—51no—
131C22×C3⋊C8—51no—
132C3×#103—102no—
133#835—102no—
134#821—22no—
135#815—102no—
136#809—102no—
137C24×C5—61no—
138C2×C5×D4—32no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C2×C5×D4—61no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—32no—
149C2×Dic10—21no—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10C4×D312yes—
155C2×C5×C8—21no—
156C2×C5×C8—21no—
157C2×C5×C8#6712yes—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—61no—
160C22⋊Dic5—68no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163#683—124no—
164C4×Dic5—32no—
165C4×Dic5—32no—
166C2×#168—32no—
167C2×#168—61no—
168C2×#168—61no—
169C2×#124—151no—
170C2×#103—51no—
171C2×#103—151no—
172C2×#102—31no—
173C2×#102—151no—
174C2×#97—151no—
175#384—151no—
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×C5×D3—42no—
182C2×C5×D3—44no—
183C2×C5×D3—82no—
184C2×C5×D3—81no—
185C2×C5×D3—81no—
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5C4×D411yescharacteristic
188C3×C4×C5#12111yescharacteristic
189C3×C4×C5#12111yescharacteristic
190Dic15—24no—
191C3×Dic5—42no—
192C3×Dic5—81no—
193C5×Dic3—81no—
194C23×D3—21no—
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—101no—
202C22×C3×C4—101no—
203C22×C3×C4C22×D511yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—52no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C4×D512yes—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8C22⋊D512yes—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217(C2×D3)⋊C4—108no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220Dic3⋊C4—204no—
221C4×Dic3—52no—
222C4×Dic3—52no—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—101no—
225C2×C3⋊C8—101no—
226C23×C5—62no—
227C23×C5—121no—
228C23×C5—122no—
229C23×C5—122no—
230C23×C5—121no—
231C23×C5D3×D411yescharacteristic
232C5×D4—62no—
233C5×D4—62no—
234C5×D4—121no—
235C5×D4—121no—
236C2×C4×C5—122no—
237C2×C4×C5—121no—
238C2×C4×C5C2×C4×D311yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5#23711yescharacteristic
243C2×C4×C5C2×#6711yescharacteristic
244C2×Dic5—22no—
245C2×Dic5—34no—
246C2×Dic5—41no—
247C2×Dic5—41no—
248C2×Dic5—42no—
249C2×Dic5—41no—
250C2×Dic5—62no—
251C2×Dic5—62no—
252Dic10—22no—
253Dic10—22no—
254Dic10—41no—
255Dic10—41no—
256C5×C8—22no—
257#168—62no—
258C22×Q8—51no—
259C22×D4—31no—
260C22×C8—151no—
261C22×C8D3×D511yescharacteristic
262#124—154no—
263#124—302no—
264C2×C4⋊C4—31no—
265C2×C4⋊C4—51no—
266C2×C4⋊C4—302no—
267C2×C22⋊C4—302no—
268C2×C42—151no—
269#103—102no—
270#103—302no—
271#102—62no—
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
279C5×D3—82no—
280C23×C3D4×D511yescharacteristic
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—42no—
284C22×D3—42no—
285C22×D3—41no—
286C3×Q8—102no—
287C3×Q8—102no—
288C3×Q8—201no—
289C3×Q8—201no—
290C2×C3×C4—102no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4—202no—
294C2×C3×C4—201no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—42no—
302C2×Dic3—41no—
303C2×Dic3—54no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306D12—22no—
307D12—22no—
308D12—41no—
309D12—41no—
310C3×C8—22no—
311C3⋊C8—102no—
312C22×C5—122no—
313C22×C5—124no—
314C22×C5—241no—
315C22×C5—241no—
316C22×C5—242no—
317C22×C5D3×C22⋊C411yescharacteristic
318C22×C5#88511yescharacteristic
319C22×C5#91412yes—
320C22×C5#91812yes—
321C22×C5#94011yescharacteristic
322C4×C5—241no—
323C4×C5#67⋊C411yescharacteristic
324C4×C5#88411yescharacteristic
325C4×C5C4×#6711yescharacteristic
326C4×C5#93911yescharacteristic
327Dic5—42no—
328Dic5—64no—
329Dic5—81no—
330C24—61no—
331C2×Q8—52no—
332C2×Q8—101no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×D4—32no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C2×D4—61no—
343C22×C4—61no—
344C22×C4—101no—
345C22×C4—101no—
346C22×C4—152no—
347C22×C4C2×D3×D511yescharacteristic
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—152no—
351C2×C8—301no—
352C2×C8—301no—
353C2×C8#120112yes—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—101no—
357C4⋊C4—101no—
358C4⋊C4—604no—
359C22⋊C4—308no—
360C42—152no—
361C42—152no—
362C3×C5#195911yescharacteristic, complemented, Hall
363C22×C3D5×C22⋊C411yescharacteristic
364C22×C3#403111yescharacteristic
365C22×C3#405712yes—
366C22×C3#406112yes—
367C22×C3#408611yescharacteristic
368C2×D3—44no—
369C2×D3—42no—
370C2×D3—82no—
371C2×D3—81no—
372C2×D3—81no—
373C3×C4—202no—
374C3×C4—401no—
375C3×C4#402711yescharacteristic
376C3×C4#403011yescharacteristic
377C3×C4C4×C22⋊D511yescharacteristic
378C3×C4#408511yescharacteristic
379Dic3—81no—
380Dic3—104no—
381C2×C5—242no—
382C2×C5#479412yes—
383C2×C5#480312yes—
384C2×C5#495711yescharacteristic
385C2×C5#517611yescharacteristic
386C2×C5#519011yescharacteristic
387C23—62no—
388C23—121no—
389C23—121no—
390C23—122no—
391C23—122no—
392C23#677711yescharacteristic
393Q8—102no—
394Q8—102no—
395Q8—201no—
396Q8—201no—
397D4—62no—
398D4—62no—
399D4—121no—
400D4—121no—
401C2×C4—102no—
402C2×C4—121no—
403C2×C4—122no—
404C2×C4—154no—
405C2×C4—201no—
406C2×C4—201no—
407C2×C4—201no—
408C2×C4—202no—
409C2×C4—302no—
410C2×C4—302no—
411C2×C4#677111yescharacteristic
412C2×C4C4×D3×D511yescharacteristic
413C2×C4#677711yescharacteristic
414C2×C4#678011yescharacteristic
415C2×C4C2×#120111yescharacteristic
416C2×C4#679011yescharacteristic
417C8—22no—
418C8—302no—
419C2×C3#6505412yes—
420C2×C3#6506012yes—
421C2×C3#6524611yescharacteristic
422C2×C3#6544311yescharacteristic
423C2×C3#6545611yescharacteristic
424D3—82no—
425C5#7022711yescharacteristic, complemented, Sylow
426C22—124no—
427C22—122no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#9125712yes—
432C22#9128012yes—
433C22#9146311yescharacteristic
434C22#9146411yescharacteristic
435C22#9147311yescharacteristic
436C4—202no—
437C4—241no—
438C4—304no—
439C4—401no—
440C4C4×#120111yescharacteristic
441C4#9144211yescharacteristic
442C4#9146111yescharacteristic
443C4#9157111yescharacteristic
444C3#1060095211yescharacteristic, complemented, Sylow
445C2—242no—
446C2#1174797512yes—
447C2#1174798311yescharacteristic
448C2#1174801311yescharacteristic
449C2#1174814612yes—
450C2#1174891511yescharacteristic
subgroupG/H
centerC23#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1959
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91099C2semidirect
4. C2×C3×#3948C2semidirect
5. #11748866C2semidirect
6. C2×#90970C2semidirect
19. #91370C4semidirect
29. C2×#3948D3semidirect
362. C3×C5#1959semidirect
425. C5#70227semidirect
444. C3#10600952semidirect

Maximal subgroups

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

subgroupindex
C2×#913702
C2×#910992
C2×C5×#8212
C2×C3×#39482
#117488662
C2×#909702
C2×#909662
#106009523
#702275