Finite Group Databasebeta

← #14299490

Subgroups — #14299490

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×#91781C211yesmaximal, characteristic
2C2×C5×#808C211yesmaximal, characteristic, complemented
3#11748799C211yesmaximal, characteristic
4C2×#90988C211yesmaximal, characteristic, complemented
5C2×#90957C211yesmaximal, characteristic
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10601373—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6714—21no—
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4×Dic15—21no—
14#91781—22no—
15#91781—22no—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C2×#6667—21no—
21C5×#808—22no—
22#90994—21no—
23#90988—22no—
24#90957C414yescomplemented
25#68877—51nomaximal, Hall
26C2×#4038—31no—
27C2×C5×#106—31no—
28C2×#3952—31no—
29#65276—31no—
30C2×#3939—31no—
31#64771—31no—
32#64749D311yescharacteristic, complemented
33C23×D15D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×Dic15D411yescharacteristic
38C2×C4×D15—21no—
39C2×C4×D15—21no—
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15C2×C412yes—
43C2×C4×D15Q812yes—
44C22×C5×Dic3—21no—
45C22×C3×Dic5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D412yes—
48#6714—24no—
49C4⋊Dic15—21no—
50C4⋊Dic15D412yes—
51C4×Dic15—24no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8C2×C412yes—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168C2×C412yes—
62#6667—42no—
63C2×#892—51no—
64C2×(C2×D3)⋊C8—51no—
65C2×#818—51no—
66#4987—51no—
67C2×#808D511yescharacteristic, complemented
68C3×#340—51no—
69#4529—51no—
70C22×C4×D5—31no—
71C22×C5×C8—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×#685—61no—
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5C2×D311yescharacteristic
78C2×C4×Dic5—61no—
79C22×#168C2×D311yescharacteristic
80#4038—62no—
81#4038—62no—
82C5×#106—62no—
83#3963—61no—
84#3952—34no—
85#3939—62no—
86#1854—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×D15—21no—
89C22×D15—21no—
90C22×D15—21no—
91C22×D15—21no—
92C22×D15—21no—
93C22×D15—21no—
94C22×D15C4⋊C412yes—
95C2×C3×C4×C5—22no—
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—21no—
105C2×Dic15—21no—
106C2×Dic15—22no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×Dic15C4⋊C412yes—
110C4×D15—22no—
111C4×D15—22no—
112C4×D15—22no—
113C4×D15—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C3×#168—22no—
121C5×C3⋊C8—22no—
122C22×C4×D3—51no—
123C22×C3×C8—51no—
124C2×C3×C4⋊C4—51no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×(C2×D3)⋊C4—101no—
127C2×(C2×D3)⋊C4—101no—
128C2×C4⋊Dic3—51no—
129C2×C4⋊Dic3C2×D511yescharacteristic
130C2×C4×Dic3—101no—
131C22×C3⋊C8C2×D511yescharacteristic
132#892—102no—
133#892—102no—
134C3⋊#95—101no—
135(C2×D3)⋊C8—54no—
136#818—102no—
137#808—22no—
138C23×D5—31no—
139C22×C4×C5—21no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5—31no—
144C22×Dic5—61no—
145C2×C4×D5—32no—
146C2×C4×D5—32no—
147C2×C4×D5—61no—
148C2×C4×D5—61no—
149C2×C4×D5—61no—
150C2×C4×D5—61no—
151C2×C5×C8—32no—
152C2×C5×C8—61no—
153C2×C5×C8—61no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4—61no—
157C5×C4⋊C4D1212yes—
158#685—64no—
159#685—122no—
160C4⋊Dic5—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5—32no—
163C4⋊Dic5—61no—
164C4×Dic5—64no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168C4×D312yes—
168C2×#117—151no—
169C2×#107—151no—
170C2×#106—31no—
171C2×C22⋊C8—151no—
172#380—151no—
173#340—51no—
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×D15—22no—
183C2×D15—22no—
184C2×D15—22no—
185C2×D15—41no—
186C2×D15—41no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—42no—
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194Dic15—22no—
195Dic15—42no—
196C3×Dic5—81no—
197C5×Dic3—81no—
198C23×D3—51no—
199C22×C3×C4—21no—
200C22×C3×C4—101no—
201C22×C3×C4C22×D511yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—51no—
204C22×Dic3—101no—
205C2×C4×D3—52no—
206C2×C4×D3—52no—
207C2×C4×D3—101no—
208C2×C4×D3—101no—
209C2×C4×D3—101no—
210C2×C4×D3—101no—
211C2×C3×C8—52no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4C22⋊D512yes—
218(C2×D3)⋊C4—104no—
219(C2×D3)⋊C4—202no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—52no—
223C4⋊Dic3—101no—
224C4×Dic3—104no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8C4×D512yes—
228C23×C5D3×D411yescharacteristic
229C22×D5—32no—
230C22×D5—61no—
231C22×D5—61no—
232C22×D5—61no—
233C22×D5—61no—
234C22×D5—61no—
235C22×D5—61no—
236C2×C4×C5—22no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5C2×D1211yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5D3×Q811yescharacteristic
248C2×Dic5—32no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251C2×Dic5—41no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254C2×Dic5—62no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257C4×D5—62no—
258C4×D5—62no—
259C4×D5—62no—
260C4×D5—62no—
261C5×C8—62no—
262#168—22no—
263C23×C4—151no—
264C22×C8—31no—
265C22×C8—51no—
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—301no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—302no—
276#106—62no—
277C22⋊C8—154no—
278#95—301no—
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
286D15—42no—
287C23×C3D4×D511yescharacteristic
288C22×D3—52no—
289C22×D3—101no—
290C22×D3—101no—
291C22×D3—101no—
292C22×D3—101no—
293C22×D3—101no—
294C22×D3—101no—
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4Q8×D511yescharacteristic
305C2×C3×C4#71311yescharacteristic
306C2×C3×C4C2×C22⋊D511yescharacteristic
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—52no—
311C2×Dic3—101no—
312C2×Dic3—101no—
313C2×Dic3—102no—
314C2×Dic3—201no—
315C2×Dic3—201no—
316C4×D3—102no—
317C4×D3—102no—
318C4×D3—102no—
319C4×D3—102no—
320C3×C8—102no—
321C3⋊C8—22no—
322C22×C5#88211yescharacteristic
323C22×C5#88311yescharacteristic
324C22×C5D3×C4⋊C411yescharacteristic
325C22×C5#91211yescharacteristic
326C22×C5#91411yescharacteristic
327C22×C5#91511yescharacteristic
328C22×C5#91911yescharacteristic
329C2×D5—62no—
330C2×D5—62no—
331C2×D5—62no—
332C2×D5—121no—
333C2×D5—121no—
334C2×D5—121no—
335C2×D5—121no—
336C4×C5—42no—
337C4×C5—241no—
338C4×C5C4×D1211yescharacteristic
339C4×C5#67⋊C411yescharacteristic
340C4×C5#89611yescharacteristic
341C4×C5#89711yescharacteristic
342Dic5—62no—
343Dic5—81no—
344Dic5—122no—
345C24—151no—
346C22×C4—21no—
347C22×C4—61no—
348C22×C4—101no—
349C22×C4—151no—
350C22×C4—152no—
351C22×C4—152no—
352C22×C4—301no—
353C22×C4—301no—
354C22×C4—301no—
355C22×C4—301no—
356C22×C4—301no—
357C22×C4C2×D3×D511yescharacteristic
358C2×C8—32no—
359C2×C8—52no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—101no—
363C2×C8—101no—
364C4⋊C4—21no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—152no—
370C4⋊C4—301no—
371C4⋊C4#120312yes—
372C22⋊C4—304no—
373C22⋊C4—602no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3D5×C4⋊C411yescharacteristic
377C22×C3#404011yescharacteristic
378C22×C3#406011yescharacteristic
379C22×C3#406111yescharacteristic
380C22×C3#406211yescharacteristic
381C22×C3#406211yescharacteristic
382C22×C3#408311yescharacteristic
383C2×D3—102no—
384C2×D3—102no—
385C2×D3—102no—
386C2×D3—201no—
387C2×D3—201no—
388C2×D3—201no—
389C2×D3—201no—
390C3×C4—42no—
391C3×C4—401no—
392C3×C4#403911yescharacteristic
393C3×C4#404211yescharacteristic
394C3×C4C4×C22⋊D511yescharacteristic
395C3×C4#409211yescharacteristic
396Dic3—81no—
397Dic3—102no—
398Dic3—202no—
399C2×C5#466811yescharacteristic
400C2×C5#478311yescharacteristic
401C2×C5#478411yescharacteristic
402C2×C5#481011yescharacteristic
403C2×C5#481411yescharacteristic
404C2×C5#486111yescharacteristic
405C2×C5#488011yescharacteristic
406D5—122no—
407C23—152no—
408C23—301no—
409C23—301no—
410C23—301no—
411C23—301no—
412C23—301no—
413C23—301no—
414C23#679011yescharacteristic
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—152no—
422C2×C4—201no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—301no—
426C2×C4—301no—
427C2×C4—302no—
428C2×C4—302no—
429C2×C4—302no—
430C2×C4—302no—
431C2×C4—302no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4#676611yescharacteristic
435C2×C4D15⋊Q811yescharacteristic
436C2×C4#677111yescharacteristic
437C2×C4C4×D3×D511yescharacteristic
438C2×C4C2×#120311yescharacteristic
439C2×C4#679011yescharacteristic
440C8—62no—
441C8—102no—
442C2×C3#6514911yescharacteristic
443C2×C3#6515011yescharacteristic
444C2×C3#6515511yescharacteristic
445C2×C3#6515611yescharacteristic
446C2×C3#6527811yescharacteristic
447C2×C3#6546111yescharacteristic
448C2×C3#6546211yescharacteristic
449D3—202no—
450C5#6887711yescharacteristic, complemented, Sylow
451C22—302no—
452C22—302no—
453C22—302no—
454C22—601no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22#9135411yescharacteristic
459C22#9140411yescharacteristic
460C22#9148811yescharacteristic
461C22#9149711yescharacteristic
462C22#9150611yescharacteristic
463C22#9152311yescharacteristic
464C22#9157311yescharacteristic
465C4—42no—
466C4—241no—
467C4—302no—
468C4—401no—
469C4—602no—
470C4#9137711yescharacteristic
471C4#9138311yescharacteristic
472C4#9139611yescharacteristic
473C4C4×#120311yescharacteristic
474C3#1060137311yescharacteristic, complemented, Sylow
475C2—602no—
476C2#1174733611yescharacteristic
477C2#1174736611yescharacteristic
478C2#1174743911yescharacteristic
479C2#1174745911yescharacteristic
480C2#1174873111yescharacteristic
481C2#1174906111yescharacteristic
482C2#1174928911yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
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×C5×#808C2semidirect
4. C2×#90988C2semidirect
6. C3×#64749C2semidirect
7. #11745980C2semidirect
24. #90957C4semidirect
32. #64749D3semidirect
67. C2×#808D5semidirect
375. C3×C5#1854semidirect
450. C5#68877semidirect
474. C3#10601373semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C5×#8082
#117487992
C2×#909882
C2×#909572
C3×#647492
#117459802
#106013733
#688775