Finite Group Databasebeta

← #14299459

Subgroups — #14299459

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91358C211yesmaximal, characteristic
2C2×#91092C211yesmaximal, characteristic, complemented
3C2×C5×#807C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5C2×#90955C211yesmaximal, characteristic
6#11745980C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10601426—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×#6665—21no—
18C2×Dic3×Dic5—21no—
19#91358—22no—
20#91358—22no—
21#91092—22no—
22C5×#807—22no—
23C3×#3963—21no—
24#90955C414yescomplemented
25#69506—51nomaximal, Hall
26C2×#4038—31no—
27C2×C5×#107—31no—
28C2×#3952—31no—
29#65276D311yescharacteristic
30C2×#3940—31no—
31#64771—31no—
32#64749—31no—
33C23×C3×D5D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C412yes—
45C2×C3×C4×D5Q812yes—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D412yes—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168C2×C412yes—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D412yes—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8C2×C412yes—
58C3×#685—42no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61#6665—24no—
62Dic3×Dic5—24no—
63C2×#926—51no—
64C3×#380—51no—
65C2×#830—51no—
66C2×#808—51no—
67C2×#807D511yescharacteristic, complemented
68#4529—51no—
69#4529—51no—
70C22×C4×D5C2×D311yescharacteristic
71C22×C5×C8—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×#685—21no—
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5C2×D311yescharacteristic
78C2×C4×Dic5—61no—
79C22×#168—31no—
80#4038—62no—
81#4038—62no—
82C5×#107—62no—
83#3963—21no—
84#3952—34no—
85#3940—62no—
86#1854—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5—21no—
89C22×C3×D5—21no—
90C22×C3×D5—21no—
91C22×C3×D5—21no—
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5C4⋊C412yes—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—22no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5C4⋊C412yes—
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3⋊#168—22no—
121C5×C3⋊C8—22no—
122C23×C3×C4—51no—
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C22⋊C4—101no—
126C2×#217—101no—
127#926—102no—
128#926—102no—
129C2×C4⋊Dic3—51no—
130C2×C4⋊Dic3C2×D511yescharacteristic
131C2×C4×Dic3—101no—
132C22×C3⋊C8—51no—
133C22×C3⋊C8C2×D511yescharacteristic
134C3×#95—101no—
135#830—54no—
136#808—102no—
137#807—22no—
138C23×D5#6711yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5—61no—
144C22×Dic5#6711yescharacteristic
145C2×C4×D5—21no—
146C2×C4×D5—21no—
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5Dic612yes—
150C2×C4×D5C4×D312yes—
151C2×C5×C8—32no—
152C2×C5×C8—61no—
153C2×C5×C8—61no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—32no—
157C5×C4⋊C4—61no—
158#685—42no—
159#685—64no—
160C4⋊Dic5—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5—32no—
163C4⋊Dic5—61no—
164C4×Dic5—64no—
165C2×#168—32no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#117—151no—
169C2×#107—31no—
170C2×#106—151no—
171C2×C22⋊C8—151no—
172#380—51no—
173#340—151no—
174#340—151no—
175C22×C3×C5C2×C4⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5#13711yescharacteristic
182C2×C3×D5—22no—
183C2×C3×D5—22no—
184C2×C3×D5—22no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5—81no—
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194Dic15—42no—
195C3×Dic5—22no—
196C3×Dic5—81no—
197C5×Dic3—42no—
198C24×C3—51no—
199C22×C3×C4—21no—
200C22×C3×C4—51no—
201C22×C3×C4—52no—
202C22×C3×C4—52no—
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C22×C3×C4—101no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—21no—
210C22×Dic3—101no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—101no—
214C3×C4⋊C4—101no—
215C3×C22⋊C4—202no—
216#217—104no—
217C4⋊Dic3—21no—
218C4⋊Dic3—52no—
219C4⋊Dic3—101no—
220C4⋊Dic3C22⋊D512yes—
221C4×Dic3—104no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—52no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8C4×D512yes—
228C23×C5C2×#6711yescharacteristic
229C22×D5—21no—
230C22×D5—21no—
231C22×D5—21no—
232C22×D5—21no—
233C22×D5—21no—
234C22×D5—21no—
235C22×D5Dic3⋊C412yes—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—62no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—41no—
251C2×Dic5—41no—
252C2×Dic5—41no—
253C2×Dic5—62no—
254C2×Dic5—121no—
255C2×Dic5—121no—
256C2×Dic5Dic3⋊C412yes—
257C4×D5—22no—
258C4×D5—22no—
259C4×D5—22no—
260C4×D5—22no—
261C5×C8—62no—
262#168—62no—
263C23×C4—51no—
264C22×C8—31no—
265C22×C8—151no—
266#117—302no—
267#117—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4D3×D511yescharacteristic
272C2×C22⋊C4—101no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—62no—
276#106—302no—
277C22⋊C8—154no—
278#95—101no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#42711yescharacteristic
281C2×C3×C5#42811yescharacteristic
282C2×C3×C5#44911yescharacteristic
283C2×C3×C5#45211yescharacteristic
284C2×C3×C5#48211yescharacteristic
285C2×C3×C5#48511yescharacteristic
286C3×D5—42no—
287C23×C3—52no—
288C23×C3—101no—
289C23×C3—101no—
290C23×C3—101no—
291C23×C3—101no—
292C23×C3—101no—
293C23×C3—101no—
294C23×C3D4×D511yescharacteristic
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—52no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—102no—
302C2×C3×C4—102no—
303C2×C3×C4—102no—
304C2×C3×C4—102no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4Q8×D511yescharacteristic
312C2×C3×C4#71311yescharacteristic
313C2×C3×C4C2×C22⋊D511yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—102no—
318C2×Dic3—201no—
319C2×Dic3—201no—
320C3⋊C8—22no—
321C3⋊C8—102no—
322C22×C5C2×Dic3⋊C411yescharacteristic
323C22×C5#93211yescharacteristic
324C22×C5#93511yescharacteristic
325C22×C5#93711yescharacteristic
326C22×C5#94211yescharacteristic
327C22×C5#95011yescharacteristic
328C22×C5#95011yescharacteristic
329C2×D5—22no—
330C2×D5—22no—
331C2×D5—22no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5—41no—
336C4×C5—81no—
337C4×C5—122no—
338C4×C5#87811yescharacteristic
339C4×C5#87811yescharacteristic
340C4×C5#67⋊C411yescharacteristic
341C4×C5#67⋊C411yescharacteristic
342Dic5—22no—
343Dic5—81no—
344Dic5—122no—
345C24—51no—
346C22×C4—21no—
347C22×C4—51no—
348C22×C4—52no—
349C22×C4—52no—
350C22×C4—61no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—101no—
355C22×C4—101no—
356C22×C4—301no—
357C22×C4C2×D3×D511yescharacteristic
358C2×C8—32no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8—152no—
362C2×C8—301no—
363C2×C8—301no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—32no—
367C4⋊C4—61no—
368C4⋊C4—101no—
369C4⋊C4—101no—
370C4⋊C4—152no—
371C4⋊C4—301no—
372C22⋊C4—202no—
373C22⋊C4—304no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3—102no—
377C22×C3—102no—
378C22×C3—102no—
379C22×C3—201no—
380C22×C3—201no—
381C22×C3—201no—
382C22×C3—201no—
383C22×C3D5×C4⋊C411yescharacteristic
384C22×C3#404011yescharacteristic
385C22×C3#405711yescharacteristic
386C22×C3#405811yescharacteristic
387C22×C3#406411yescharacteristic
388C22×C3#406511yescharacteristic
389C22×C3#408311yescharacteristic
390C3×C4—81no—
391C3×C4—102no—
392C3×C4—401no—
393C3×C4#403911yescharacteristic
394C3×C4#404211yescharacteristic
395C3×C4C4×C22⋊D511yescharacteristic
396C3×C4#409211yescharacteristic
397Dic3—42no—
398Dic3—202no—
399C2×C5#494611yescharacteristic
400C2×C5#496411yescharacteristic
401C2×C5#499811yescharacteristic
402C2×C5#503511yescharacteristic
403C2×C5#503711yescharacteristic
404C2×C5#504511yescharacteristic
405C2×C5#504711yescharacteristic
406D5—42no—
407C23—52no—
408C23—101no—
409C23—101no—
410C23—101no—
411C23—101no—
412C23—101no—
413C23—101no—
414C23D5×#6711yescharacteristic
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—52no—
419C2×C4—62no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—102no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—102no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—201no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—302no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4D5×Dic611yescharacteristic
435C2×C4#676511yescharacteristic
436C2×C4#676611yescharacteristic
437C2×C4C4×D3×D511yescharacteristic
438C2×C4D3×C22⋊D511yescharacteristic
439C2×C4#679011yescharacteristic
440C8—62no—
441C8—302no—
442C2×C3—202no—
443C2×C3#6516911yescharacteristic
444C2×C3#6517011yescharacteristic
445C2×C3#6517411yescharacteristic
446C2×C3#6517711yescharacteristic
447C2×C3#6527811yescharacteristic
448C2×C3#6544711yescharacteristic
449C2×C3#6547611yescharacteristic
450C5#6950611yescharacteristic, complemented, Sylow
451C22—102no—
452C22—102no—
453C22—102no—
454C22—201no—
455C22—201no—
456C22—201no—
457C22—201no—
458C22D5×Dic3⋊C411yescharacteristic
459C22#9140711yescharacteristic
460C22#9148911yescharacteristic
461C22#9149011yescharacteristic
462C22#9151511yescharacteristic
463C22#9151611yescharacteristic
464C22#9157711yescharacteristic
465C4—81no—
466C4—102no—
467C4—122no—
468C4—401no—
469C4—602no—
470C4#9139611yescharacteristic
471C4#9142111yescharacteristic
472C4#9143111yescharacteristic
473C4#9144111yescharacteristic
474C3#1060142611yescharacteristic, complemented, Sylow
475C2—202no—
476C2#1174720411yescharacteristic
477C2#1174720611yescharacteristic
478C2#1174743211yescharacteristic
479C2#1174745211yescharacteristic
480C2#1174889111yescharacteristic
481C2#1174915911yescharacteristic
482C2#1174940611yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1854
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×#91092C2semidirect
3. C2×C5×#807C2semidirect
6. #11745980C2semidirect
7. #11745979C2semidirect
24. #90955C4semidirect
67. C2×#807D5semidirect
375. C3×C5#1854semidirect
450. C5#69506semidirect
474. C3#10601426semidirect

Maximal subgroups

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

subgroupindex
C2×#913582
C2×#910922
C2×C5×#8072
C3×#652762
C2×#909552
#117459802
#117459792
#106014263
#695065