Finite Group Databasebeta

← #14313454

Subgroups — #14313454

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756564C211yesmaximal, characteristic
2C2×C3×C5×#99C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4#11746295C212yesmaximal, complemented
5#11746294C212yesmaximal, complemented
6#10600812—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6817C411yescharacteristic, complemented
9C2×C3×C5×C22⋊C4—21no—
10#91842—21no—
11#91842—21no—
12C2×#6719—21no—
13#91829C411yescharacteristic, complemented
14#91829C2211yescharacteristic
15#91827—21no—
16#91827—21no—
17#91825C411yescharacteristic, complemented
18#91825C2211yescharacteristic
19#91815C411yescharacteristic, complemented
20C3×C5×#99—21no—
21C3×C5×#99C2212yes—
22#91118—21no—
23#91118C2212yes—
24#70019—51nomaximal, Hall
25#66139—31no—
26C2×C5×#99D311yescharacteristic, complemented
27C2×#3966—31no—
28#64694—32no—
29#64693—32no—
30C24×C3×C5D411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C2×C3×C5×D4—41no—
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4C2311yescharacteristic
38C22×C3×C4×C5—41no—
39C22×C3×C4×C5C2×C411yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45C22×Dic15—41no—
46#6817—41no—
47#6817—41no—
48C2×D60C2×C411yescharacteristic, complemented
49C2×C4×D15—21no—
50C2×Dic30C2×C411yescharacteristic, complemented
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—41no—
53#6719—21no—
54#6719—21no—
55#6719—21no—
56#6719—21no—
57#6719—21no—
58#6719—22no—
59#6719—41no—
60C4⋊Dic15—21no—
61C4×Dic15C2×C411yescharacteristic, complemented
62C4×Dic15C2×C411yescharacteristic, complemented
63#5805—51no—
64C2×C3×#99D511yescharacteristic, complemented
65C2×#834—51no—
66#4474—52no—
67#4473—52no—
68C22×C5×D4C2×D311yescharacteristic
69C2×#709—31no—
70C2×C5×C22⋊C4—21no—
71#4099—61no—
72#4099—61no—
73C2×C22⋊Dic5—61no—
74#4086—31no—
75#4086—31no—
76#4084—61no—
77#4084—61no—
78#4082—31no—
79#4082—31no—
80#4072—31no—
81C5×#99—21no—
82C5×#99C2×D312yes—
83#3966—32no—
84#3966—61no—
85#2127—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C2×D411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C3×C5×D4—41no—
99C3×C5×D4—41no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—42no—
105C2×C3×C4×C5—82no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C22×C411yescharacteristic
108#1220—41no—
109#1220—41no—
110#1220—81no—
111#1220—81no—
112#1220—81no—
113#1220—81no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15—21no—
117C2×Dic15—42no—
118C2×Dic15—82no—
119D60—41no—
120C4×D15—42no—
121Dic30—41no—
122C22×C3×D4C2×D511yescharacteristic
123C2×#235—51no—
124C2×C3×C22⋊C4—21no—
125#953—101no—
126#953—101no—
127C2×#217—101no—
128#940—51no—
129#940—51no—
130#938—101no—
131#938—101no—
132#936—51no—
133#936—51no—
134#926—51no—
135C3×#99—21no—
136C3×#99C2×D512yes—
137#834—52no—
138#834—101no—
139C24×C5D1211yescharacteristic
140C24×C5#6711yescharacteristic
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4C4×D311yescharacteristic
144C2×C5×D4D1211yescharacteristic
145C2×C5×D4#6711yescharacteristic
146C2×C5×D4C22×D311yescharacteristic
147C22×C4×C5—41no—
148C22×C4×C5C4×D311yescharacteristic
149C2×C22⋊D5—61no—
150C2×C22⋊D5—61no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C2×C22⋊D5—61no—
154C22×Dic5—121no—
155#709—121no—
156#709—121no—
157C2×D20—31no—
158C2×C4×D5—61no—
159C2×Dic10—31no—
160C5×C22⋊C4—22no—
161C5×C22⋊C4—41no—
162C22⋊Dic5—61no—
163C22⋊Dic5—61no—
164C22⋊Dic5—61no—
165C22⋊Dic5—61no—
166C22⋊Dic5—61no—
167C22⋊Dic5—62no—
168C22⋊Dic5—121no—
169C4⋊Dic5—61no—
170C4×Dic5—31no—
171C4×Dic5—31no—
172#535—151no—
173C2×#99—151no—
174C2×#99D1511yescharacteristic, complemented
175#354—152no—
176#353—152no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—21no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5—81no—
189C22×C3×C5—81no—
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5#9911yescharacteristic
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C2×D15—41no—
194C2×D15—41no—
195C2×D15—41no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198C3×C4×C5—82no—
199Dic15—41no—
200Dic15—41no—
201Dic15—41no—
202Dic15—82no—
203C24×C3D2011yescharacteristic
204C24×C3C22⋊D511yescharacteristic
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4C4×D511yescharacteristic
208C2×C3×D4D2011yescharacteristic
209C2×C3×D4C22⋊D511yescharacteristic
210C2×C3×D4C22×D511yescharacteristic
211C22×C3×C4—41no—
212C22×C3×C4C4×D511yescharacteristic
213C2×#67—101no—
214C2×#67—101no—
215C2×#67—101no—
216C2×#67—101no—
217C2×#67—101no—
218C22×Dic3—201no—
219#235—201no—
220#235—201no—
221C2×D12—51no—
222C2×C4×D3—101no—
223C2×Dic6—51no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—41no—
226#217—101no—
227#217—101no—
228#217—101no—
229#217—101no—
230#217—101no—
231#217—102no—
232#217—201no—
233C4⋊Dic3—101no—
234C4×Dic3—51no—
235C4×Dic3—51no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—21no—
240C23×C5—81no—
241C23×C5—81no—
242C23×C5(C2×D3)⋊C411yescharacteristic
243C23×C5(C2×D3)⋊C411yescharacteristic
244C23×C5(C2×D3)⋊C411yescharacteristic
245C23×C5C2×D1211yescharacteristic
246C23×C5C2×#6711yescharacteristic
247C22×D5—61no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—42no—
255C2×C4×C5—82no—
256C2×C4×C5(C2×D3)⋊C411yescharacteristic
257C2×C4×C5C2×C4×D311yescharacteristic
258C22⋊D5—121no—
259C22⋊D5—121no—
260C22⋊D5—241no—
261C22⋊D5—241no—
262C22⋊D5—241no—
263C22⋊D5—241no—
264C2×Dic5—61no—
265C2×Dic5—61no—
266C2×Dic5—61no—
267C2×Dic5—122no—
268C2×Dic5—242no—
269D20—121no—
270C4×D5—122no—
271Dic10—121no—
272C2×#41—151no—
273C22×D4C2×D1511yescharacteristic
274#127—151no—
275#127—151no—
276#124—151no—
277#124—151no—
278#121—301no—
279#121—301no—
280#120—301no—
281#120—301no—
282#117—151no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—301no—
285#99—21no—
286#99—152no—
287#99—301no—
288#99C2×D1512yes—
289C2×C3×C5—21no—
290C2×C3×C5—21no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5C2×#9911yescharacteristic
297D15—81no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3#68511yescharacteristic
305C23×C3#68511yescharacteristic
306C23×C3#68511yescharacteristic
307C23×C3C2×D2011yescharacteristic
308C23×C3C2×C22⋊D511yescharacteristic
309C22×D3—101no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—42no—
317C2×C3×C4—82no—
318C2×C3×C4#68511yescharacteristic
319C2×C3×C4C2×C4×D511yescharacteristic
320#67—201no—
321#67—201no—
322#67—401no—
323#67—401no—
324#67—401no—
325#67—401no—
326C2×Dic3—101no—
327C2×Dic3—101no—
328C2×Dic3—101no—
329C2×Dic3—202no—
330C2×Dic3—402no—
331D12—201no—
332C4×D3—202no—
333Dic6—201no—
334C22×C5—21no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—41no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—42no—
345C22×C5—81no—
346C22×C5—81no—
347C22×C5#80611yescharacteristic
348C22×C5#80611yescharacteristic
349C22×C5C2×(C2×D3)⋊C411yescharacteristic
350C2×D5—121no—
351C2×D5—121no—
352C2×D5—121no—
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—82no—
356Dic5—121no—
357Dic5—121no—
358Dic5—121no—
359Dic5—242no—
360C24D6011yescharacteristic
361C24#122011yescharacteristic
362#41—601no—
363#41—601no—
364C2×Q8—151no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—151no—
368C2×D4—301no—
369C2×D4—301no—
370C2×D4—301no—
371C2×D4—301no—
372C2×D4—301no—
373C2×D4C4×D1511yescharacteristic
374C2×D4D6011yescharacteristic
375C2×D4#122011yescharacteristic
376C2×D4C22×D1511yescharacteristic
377C22×C4—41no—
378C22×C4—301no—
379C22×C4—601no—
380C22×C4C4×D1511yescharacteristic
381C4⋊C4—301no—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—301no—
385C22⋊C4—301no—
386C22⋊C4—301no—
387C22⋊C4—301no—
388C22⋊C4—301no—
389C22⋊C4—302no—
390C22⋊C4—601no—
391C42—151no—
392C42—151no—
393C3×C5#212711yescharacteristic, complemented, Hall
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3#393811yescharacteristic
408C22×C3#393811yescharacteristic
409C22×C3C2×#68511yescharacteristic
410C2×D3—201no—
411C2×D3—201no—
412C2×D3—201no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—82no—
416Dic3—201no—
417Dic3—201no—
418Dic3—201no—
419Dic3—402no—
420C2×C5—21no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—41no—
424C2×C5—41no—
425C2×C5—41no—
426C2×C5—41no—
427C2×C5C2×#80611yescharacteristic
428D5—241no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—81no—
434C23—81no—
435C23—301no—
436C23#671411yescharacteristic
437C23#671411yescharacteristic
438C23#671411yescharacteristic
439C23C2×D6011yescharacteristic
440C23C2×#122011yescharacteristic
441Q8—601no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—601no—
447D4—601no—
448D4—601no—
449D4—1201no—
450D4—1201no—
451D4—1201no—
452D4—1201no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—301no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—602no—
461C2×C4—602no—
462C2×C4—1202no—
463C2×C4#671411yescharacteristic
464C2×C4C2×C4×D1511yescharacteristic
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3C2×#393811yescharacteristic
473D3—401no—
474C5#7001911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—42no—
485C22—42no—
486C22—81no—
487C22—81no—
488C22—601no—
489C22—601no—
490C22—601no—
491C22#9109011yescharacteristic
492C22#9109011yescharacteristic
493C22C2×#671411yescharacteristic
494C4—21no—
495C4—21no—
496C4—82no—
497C4—601no—
498C4—601no—
499C4—601no—
500C4—1202no—
501C3#1060081211yescharacteristic, complemented, Sylow
502C2—21no—
503C2—21no—
504C2—21no—
505C2—41no—
506C2—41no—
507C2—41no—
508C2—41no—
509C2—1201no—
510C2C2×#9109011yescharacteristic
subgroupG/H
centerC2C2×#91090
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C22×D15
FittingC2×C3×C5×#99C2
socleC2×C3×C5C2×#99
prime radical#11756564C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#99D15
hypocenterC3×C5#2127
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#99C2semidirect
3. C2×#91118C2semidirect
4. #11746295C2semidirect
5. #11746294C2semidirect
8. C2×#6817C4semidirect
13. #91829C4semidirect
17. #91825C4semidirect
19. #91815C4semidirect
26. C2×C5×#99D3semidirect
48. C2×D60C2×C4semidirect
50. C2×Dic30C2×C4semidirect
61. C4×Dic15C2×C4semidirect
62. C4×Dic15C2×C4semidirect
64. C2×C3×#99D5semidirect
174. C2×#99D15semidirect
393. C3×C5#2127semidirect
474. C5#70019semidirect
501. C3#10600812semidirect

Maximal subgroups

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

subgroupindex
#117565642
C2×C3×C5×#992
C2×#911182
#117462952
#117462942
#106008123
#700195