Finite Group Databasebeta

← #14282855

Subgroups — #14282855

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5627C211yesmaximal, characteristic
2#11748719C211yesmaximal, characteristic, complemented
3D3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10602500—31nomaximal, Hall
9C2×C5×#239C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12C5×#946C411yescharacteristic, complemented
13C5×#930C2211yescharacteristic
14C5×#895C411yescharacteristic, complemented
15C5×#894—21no—
16C5×#893—21no—
17C5×#892C411yescharacteristic, complemented
18C5×#882—21no—
19C5×#67⋊C4—21no—
20C2×(C2×D3)⋊Dic5—21no—
21C2×Dic3×Dic5—21no—
22C2×D3×#168—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27(C2×D3)⋊#168—21no—
28#68333—51nomaximal, Hall
29C5×#525—31no—
30C4×C22⋊Dic5—31no—
31C2×C22⋊#168—31no—
32#64758—31no—
33#64758D311yescharacteristic, complemented
34#64757—31no—
35#64757—31no—
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C22×C5×Dic3D411yescharacteristic
42C5×#239—42no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12C2×C411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—42no—
48C2×C4×C5×D3C2×C411yescharacteristic
49C2×C4×C5×D3C2×C411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C22×C3×Dic5—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C2×C3⋊#168—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×C4⋊Dic3C2×C411yescharacteristic
62C5×Dic3⋊C4—21no—
63C4×C5×Dic3—21no—
64C2×C3×#168—21no—
65(C2×D3)⋊Dic5—24no—
66Dic3×Dic5—42no—
67D3×#168—42no—
68#5627D511yescharacteristic
69D3×C22⋊C8—51no—
70#4666—51no—
71C3×#328—51no—
72#4538—51no—
73#4470—51no—
74#4451—51no—
75C2×C5×#41—31no—
76C23×C4×C5—31no—
77C5×#123—61no—
78C5×C22⋊Q8—31no—
79C5×C22⋊Q8C2×D311yescharacteristic
80C5×#121—31no—
81C5×#121—31no—
82C5×#120—61no—
83C4×C5×D4—61no—
84C4×C5×D4—61no—
85C5×#117—31no—
86C2×C22⋊Dic5—61no—
87C2×C4×Dic5—61no—
88C22×#168—61no—
89#3963—31no—
90#3963C2×D311yescharacteristic
91C22⋊#168—31no—
92C22⋊#168—61no—
93C22⋊#168C2×D311yescharacteristic
94#1501—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—22no—
99C22×C5×D3—21no—
100C22×C5×D3—41no—
101C22×C5×D3C22⋊C411yescharacteristic
102C22×C5×D3C22⋊C411yescharacteristic
103C3×C5×Q8—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C5×#67—41no—
113C5×#67—41no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3C22⋊C411yescharacteristic
117C2×C5×Dic3C22⋊C411yescharacteristic
118C5×D12—41no—
119C5×D12—42no—
120C5×D12—42no—
121C4×C5×D3—22no—
122C4×C5×D3—22no—
123C4×C5×D3—41no—
124C4×C5×D3—41no—
125C4×C5×D3—42no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5—41no—
129C3⋊#168—41no—
130C3×#168—41no—
131C2×#239Dic511yescharacteristic, complemented
132C22×C4×D3C2×D511yescharacteristic
133C3×C22⋊Q8C2×D511yescharacteristic
134#946Dic511yescharacteristic, complemented
135#930C2×D511yescharacteristic
136C2×(C2×D3)⋊C4—101no—
137C2×C4×Dic3—101no—
138C2×D3×C8—101no—
139#895Dic511yescharacteristic, complemented
140#894—21no—
141#893—21no—
142#892Dic511yescharacteristic, complemented
143#882—21no—
144#67⋊C4—21no—
145C3×C22⋊C8—51no—
146C3×#95—51no—
147C3⋊#95—51no—
148#830—51no—
149(C2×D3)⋊C8—101no—
150C24×C5—31no—
151C5×#41—122no—
152C2×C5×Q8C4×D311yescharacteristic
153C2×C5×D4—31no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—61no—
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—61no—
163C22×C4×C5—122no—
164C22×C4×C5C22×D311yescharacteristic
165C22×Dic5—21no—
166C22×Dic5—61no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—31no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4C4×D311yescharacteristic
171C5×C22⋊C4—21no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174C5×C22⋊C4—61no—
175C5×C22⋊C4—61no—
176C42×C5—61no—
177C22⋊Dic5—64no—
178C4×Dic5—122no—
179C2×#168—21no—
180C2×#168—61no—
181C2×#168—122no—
182#525—31no—
183C2×C22⋊C8—151no—
184C4×C22⋊C4—151no—
185#328—51no—
186#328—151no—
187#327—151no—
188#327—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5#13511yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C2×C5×D3—21no—
195C2×C5×D3—21no—
196C2×C5×D3—21no—
197C2×C5×D3—21no—
198C2×C5×D3—21no—
199C2×C5×D3—42no—
200C2×C5×D3—42no—
201C2×C5×D3—41no—
202C2×C5×D3—41no—
203C2×C5×D3—41no—
204C2×C5×D3#10412yes—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—41no—
208C3×C4×C5—41no—
209Dic15—42no—
210C3×Dic5—42no—
211C5×Dic3—21no—
212C5×Dic3—41no—
213C5×Dic3#9912yes—
214C23×D3C22⋊D511yescharacteristic
215C2×C3×Q8C2×Dic511yescharacteristic
216C22×C3×C4—101no—
217C22×C3×C4C22×D511yescharacteristic
218C2×#67—21no—
219C22×Dic3—101no—
220C22×Dic3C22⋊D511yescharacteristic
221#239—42no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12C2×Dic511yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—42no—
227C2×C4×D3C2×Dic511yescharacteristic
228C2×C4×D3C2×Dic511yescharacteristic
229C2×C4×D3C22⋊D511yescharacteristic
230C2×C4×D3C22⋊D511yescharacteristic
231C2×C3×C8—101no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4C2×Dic511yescharacteristic
234C3×C22⋊C4—21no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—104no—
240C4⋊Dic3C2×Dic511yescharacteristic
241Dic3⋊C4—21no—
242C4×Dic3—21no—
243C4×Dic3—202no—
244C2×C3⋊C8—101no—
245D3×C8—202no—
246C23×C5—31no—
247C23×C5—31no—
248C23×C5—62no—
249C23×C5—61no—
250C23×C5—61no—
251C23×C5—61no—
252C23×C5—121no—
253C23×C5D3×D411yescharacteristic
254C5×Q8—41no—
255C5×D4—121no—
256C5×D4—122no—
257C5×D4—122no—
258C5×D4—121no—
259C5×D4—121no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—31no—
263C2×C4×C5—31no—
264C2×C4×C5—41no—
265C2×C4×C5—62no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—122no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×Dic5—22no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—62no—
278C2×Dic5—121no—
279C2×Dic5—121no—
280#168—41no—
281#168—121no—
282C2×#41—31no—
283C23×C4—31no—
284C22×C8—301no—
285#123—61no—
286C22⋊Q8—31no—
287C22⋊Q8D3×D511yescharacteristic
288#121—31no—
289#121—31no—
290#120—61no—
291C4×D4—61no—
292C4×D4—61no—
293#117—31no—
294C2×C22⋊C4—301no—
295C2×C42—301no—
296C22⋊C8—51no—
297C22⋊C8—151no—
298C22⋊C8—301no—
299#95—51no—
300#95—151no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5C2×#9911yescharacteristic
304C2×C3×C5#41611yescharacteristic
305C2×C3×C5C2×#10411yescharacteristic
306C5×D3—22no—
307C5×D3—41no—
308C5×D3—81no—
309C23×C3C2×C22⋊D511yescharacteristic
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—22no—
313C22×D3—21no—
314C22×D3—41no—
315C22×D3C22⋊Dic511yescharacteristic
316C22×D3C22⋊Dic511yescharacteristic
317C3×Q8—41no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—102no—
322C2×C3×C4—201no—
323C2×C3×C4—201no—
324C2×C3×C4C22×Dic511yescharacteristic
325C2×C3×C4C2×C22⋊D511yescharacteristic
326#67—41no—
327#67—41no—
328C2×Dic3—22no—
329C2×Dic3—21no—
330C2×Dic3—102no—
331C2×Dic3—201no—
332C2×Dic3—201no—
333C2×Dic3C22⋊Dic511yescharacteristic
334C2×Dic3C22⋊Dic511yescharacteristic
335D12—41no—
336D12—42no—
337D12—42no—
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—42no—
343C3×C8—201no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—32no—
348C22×C5—61no—
349C22×C5—61no—
350C22×C5—61no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5—122no—
354C22×C5—122no—
355C22×C5—121no—
356C22×C5—121no—
357C22×C5—121no—
358C22×C5D3×C22⋊C411yescharacteristic
359C22×C5#91611yescharacteristic
360C22×C5#91911yescharacteristic
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—32no—
364C4×C5—41no—
365C4×C5—41no—
366C4×C5—61no—
367C4×C5—121no—
368Dic5—42no—
369Dic5—122no—
370C24—31no—
371#41—122no—
372C2×Q8D3×Dic511yescharacteristic
373C2×D4—31no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—61no—
383C22×C4—101no—
384C22×C4—122no—
385C22×C4—301no—
386C22×C4C2×D3×D511yescharacteristic
387C2×C8—101no—
388C2×C8—301no—
389C2×C8—602no—
390C4⋊C4—21no—
391C4⋊C4—31no—
392C4⋊C4—61no—
393C4⋊C4D3×Dic511yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—61no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—304no—
400C42—61no—
401C42—602no—
402C3×C5#150111yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3#409611yescharacteristic
406C22×C3#409611yescharacteristic
407C22×C3C2×C22⋊Dic511yescharacteristic
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—41no—
416C2×D3—41no—
417C2×D3—41no—
418C2×D3#396912yes—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—202no—
424Dic3—21no—
425Dic3—41no—
426Dic3—202no—
427Dic3#396612yes—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—62no—
431C2×C5—121no—
432C2×C5—241no—
433C2×C5D3×#9911yescharacteristic
434C2×C5#480411yescharacteristic
435C2×C5D3×#10411yescharacteristic
436C23—31no—
437C23—31no—
438C23—62no—
439C23—61no—
440C23—61no—
441C23—61no—
442C23—121no—
443C23D3×C22⋊D511yescharacteristic
444Q8—41no—
445D4—121no—
446D4—122no—
447D4—122no—
448D4—121no—
449D4—121no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—41no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—102no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—122no—
463C2×C4—201no—
464C2×C4—201no—
465C2×C4—302no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4C2×D3×Dic511yescharacteristic
469C2×C4D3×C22⋊D511yescharacteristic
470C8—201no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3C2×#396611yescharacteristic
475C2×C3#6552211yescharacteristic
476C2×C3C2×#396911yescharacteristic
477D3—22no—
478D3—41no—
479D3—81no—
480C5#6833311yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—32no—
484C22—61no—
485C22—61no—
486C22—61no—
487C22—61no—
488C22—61no—
489C22—122no—
490C22—122no—
491C22—121no—
492C22—121no—
493C22—121no—
494C22#9151711yescharacteristic
495C22#9151911yescharacteristic
496C22D3×C22⋊Dic511yescharacteristic
497C4—21no—
498C4—21no—
499C4—32no—
500C4—41no—
501C4—41no—
502C4—61no—
503C4—121no—
504C4—202no—
505C4—602no—
506C3#1060250011yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—62no—
510C2—121no—
511C2—241no—
512C2D3×#396611yescharacteristic
513C2#1174921111yescharacteristic
514C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5627C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11748719C2semidirect
3. D3×C22⋊#168C2semidirect
4. #11746359C2semidirect
5. C3×#64758C2semidirect
6. #11745957C2semidirect
7. #11745956C2semidirect
9. C2×C5×#239C4semidirect
12. C5×#946C4semidirect
14. C5×#895C4semidirect
17. C5×#892C4semidirect
33. #64758D3semidirect
131. C2×#239Dic5semidirect
134. #946Dic5semidirect
139. #895Dic5semidirect
142. #892Dic5semidirect
402. C3×C5#1501semidirect
480. C5#68333semidirect
506. C3#10602500semidirect

Maximal subgroups

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

subgroupindex
C5×#56272
#117487192
D3×C22⋊#1682
#117463592
C3×#647582
#117459572
#117459562
#106025003
#683335