Finite Group Databasebeta

← #14308854

Subgroups — #14308854

Order 1920.

588 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×#91384C211yesmaximal, characteristic, complemented
2C2×C5×#821C211yesmaximal, characteristic
3#11748797C211yesmaximal, characteristic
4C2×#90966C211yesmaximal, characteristic
5#11746371C211yesmaximal, characteristic, complemented
6C3×#64771C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10600957—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×Dic3⋊Dic5—21no—
17C2×#6668—21no—
18C2×(C2×D3)⋊Dic5—21no—
19C2×(C2×D3)⋊Dic5—21no—
20#91384—22no—
21#91384—22no—
22C5×#821—22no—
23#90966—22no—
24#68899—51nomaximal, Hall
25C2×#4036—31no—
26C2×C5×#102—31no—
27#65510—31no—
28C2×#3964—31no—
29#64771D311yescharacteristic, complemented
30#64770—31no—
31#64749—31no—
32C23×C5×D3—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15D411yescharacteristic
35C22×Dic15D411yescharacteristic
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×D12Q812yes—
43C22×C3×Dic5—21no—
44C22×C3×Dic5—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C4×Dic15—21no—
49C4×Dic15—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D412yes—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D412yes—
59Dic3⋊Dic5—24no—
60#6668—24no—
61(C2×D3)⋊Dic5—42no—
62(C2×D3)⋊Dic5—42no—
63C2×#890—51no—
64C2×#821D511yescharacteristic
65#4988—51no—
66C2×#809—51no—
67C3×#340—51no—
68#4550—51no—
69#4529—51no—
70C22×C5×D4—31no—
71C22×C5×C8C2×D311yescharacteristic
72C2×C5×C4⋊C4—31no—
73C2×C22⋊Dic5—61no—
74C2×C22⋊Dic5—61no—
75C2×C4⋊Dic5—61no—
76C2×C4⋊Dic5C2×D311yescharacteristic
77C2×C4⋊Dic5C2×D311yescharacteristic
78C2×#683—61no—
79C2×C4×Dic5—31no—
80C22×#168—31no—
81#4036—62no—
82#4036—62no—
83C5×#102—62no—
84#3964—62no—
85#2025—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C5×D3—22no—
88C22×C5×D3—41no—
89C22×C5×D3—41no—
90C22×C5×D3—41no—
91C22×C5×D3—41no—
92C22×C5×D3—41no—
93C22×C5×D3—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×Q811yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C5×D12—22no—
110C5×D12—22no—
111C5×D12—41no—
112C5×D12—41no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C3×C5×C8—41no—
120C3⋊#168—41no—
121C22×D12C2×D511yescharacteristic
122C22×C3×C8C2×D511yescharacteristic
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4—51no—
125C2×(C2×D3)⋊C4—101no—
126C2×(C2×D3)⋊C4—101no—
127C2×C4⋊Dic3—101no—
128C2×C4⋊Dic3C2×D511yescharacteristic
129C2×Dic3⋊C4—101no—
130C2×C4×Dic3—51no—
131C22×C3⋊C8—51no—
132#890—102no—
133#890—102no—
134#821—22no—
135#809—102no—
136C24×C5—61no—
137C2×C5×D4—32no—
138C2×C5×D4—61no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C2×C5×D4—61no—
142C2×C5×D4—61no—
143C22×C4×C5—61no—
144C22×C4×C5C22×D311yescharacteristic
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—31no—
148C22×Dic5—31no—
149C2×C5×C8—21no—
150C2×C5×C8—21no—
151C2×C5×C8—21no—
152C5×C4⋊C4—32no—
153C5×C4⋊C4—61no—
154C22⋊Dic5—122no—
155C22⋊Dic5—122no—
156C4⋊Dic5—21no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C4⋊Dic5—64no—
160C4⋊Dic5D1212yes—
161#683—64no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#125—151no—
168C2×#102—31no—
169C2×#102—151no—
170#390—151no—
171#340—51no—
172#340—151no—
173#336—151no—
174C22×C3×C5#12011yescharacteristic
175C22×C3×C5C22⋊Q811yescharacteristic
176C22×C3×C5#12411yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C2×C5×D3—42no—
182C2×C5×D3—42no—
183C2×C5×D3—42no—
184C2×C5×D3—81no—
185C2×C5×D3—81no—
186C2×C5×D3—81no—
187C2×C5×D3—81no—
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5#12411yescharacteristic
191C3×C4×C5#12411yescharacteristic
192Dic15—41no—
193Dic15—41no—
194C3×Dic5—42no—
195C3×Dic5—81no—
196C5×Dic3—42no—
197C23×D3—21no—
198C22×C3×C4—101no—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—51no—
203C22×Dic3—51no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12Dic1012yes—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C3×C4⋊C4—52no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217(C2×D3)⋊C4—202no—
218(C2×D3)⋊C4—202no—
219C4⋊Dic3—21no—
220C4⋊Dic3—104no—
221C4⋊Dic3C22⋊D512yes—
222Dic3⋊C4—104no—
223C4×Dic3—101no—
224C4×Dic3—101no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5—62no—
229C23×C5—121no—
230C23×C5—121no—
231C23×C5—121no—
232C23×C5—121no—
233C23×C5—121no—
234C23×C5—121no—
235C23×C5D3×D411yescharacteristic
236C5×D4—62no—
237C5×D4—62no—
238C5×D4—121no—
239C5×D4—121no—
240C2×C4×C5—62no—
241C2×C4×C5—121no—
242C2×C4×C5—121no—
243C2×C4×C5C2×D1211yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5D3×Q811yescharacteristic
249C2×Dic5—22no—
250C2×Dic5—41no—
251C2×Dic5—41no—
252C2×Dic5—41no—
253C2×Dic5—41no—
254C2×Dic5—41no—
255C2×Dic5—61no—
256C2×Dic5—61no—
257C2×Dic5—61no—
258C2×Dic5—61no—
259C2×Dic5—61no—
260C2×Dic5—61no—
261C5×C8—41no—
262#168—121no—
263C22×D4—31no—
264C22×C8—151no—
265C22×C8D3×D511yescharacteristic
266#125—302no—
267#125—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—301no—
273C2×C22⋊C4—301no—
274C2×C22⋊C4—301no—
275C2×C42—151no—
276#102—62no—
277#102—302no—
278C2×C3×C5#39311yescharacteristic
279C2×C3×C5#44911yescharacteristic
280C2×C3×C5#44911yescharacteristic
281C2×C3×C5#47811yescharacteristic
282C2×C3×C5#47811yescharacteristic
283C2×C3×C5#48811yescharacteristic
284C2×C3×C5#49011yescharacteristic
285C5×D3—82no—
286C23×C3D4×D511yescharacteristic
287C22×D3—22no—
288C22×D3—41no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C2×C3×C4—102no—
295C2×C3×C4—201no—
296C2×C3×C4—201no—
297C2×C3×C4—201no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4C2×Dic1011yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—101no—
310C2×Dic3—101no—
311C2×Dic3—101no—
312C2×Dic3—101no—
313C2×Dic3—101no—
314C2×Dic3—101no—
315D12—22no—
316D12—22no—
317D12—41no—
318D12—41no—
319C3×C8—41no—
320C3⋊C8—201no—
321C22×C5—122no—
322C22×C5—122no—
323C22×C5—122no—
324C22×C5—241no—
325C22×C5—241no—
326C22×C5—241no—
327C22×C5—241no—
328C22×C5#88211yescharacteristic
329C22×C5#88511yescharacteristic
330C22×C5#89611yescharacteristic
331C22×C5#91111yescharacteristic
332C22×C5#91411yescharacteristic
333C22×C5#91611yescharacteristic
334C22×C5#91911yescharacteristic
335C4×C5—122no—
336C4×C5#87511yescharacteristic
337C4×C5#88511yescharacteristic
338C4×C5#89611yescharacteristic
339C4×C5#89711yescharacteristic
340Dic5—42no—
341Dic5—81no—
342Dic5—121no—
343Dic5—121no—
344C24—61no—
345C2×D4—32no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—61no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—301no—
361C2×C8—301no—
362C2×C8—301no—
363C4⋊C4—32no—
364C4⋊C4—52no—
365C4⋊C4—61no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—101no—
369C4⋊C4—304no—
370C4⋊C4—304no—
371C22⋊C4—602no—
372C22⋊C4—602no—
373C42—301no—
374C42—301no—
375C3×C5#202511yescharacteristic, complemented, Hall
376C22×C3#402411yescharacteristic
377C22×C3#403111yescharacteristic
378C22×C3#405711yescharacteristic
379C22×C3#405811yescharacteristic
380C22×C3#406011yescharacteristic
381C22×C3#406211yescharacteristic
382C22×C3#408311yescharacteristic
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—42no—
386C2×D3—81no—
387C2×D3—81no—
388C2×D3—81no—
389C2×D3—81no—
390C3×C4—202no—
391C3×C4—401no—
392C3×C4#402411yescharacteristic
393C3×C4#403111yescharacteristic
394C3×C4#407011yescharacteristic
395C3×C4#408211yescharacteristic
396Dic3—42no—
397Dic3—201no—
398Dic3—201no—
399C2×C5—242no—
400C2×C5#467311yescharacteristic
401C2×C5#476411yescharacteristic
402C2×C5#478111yescharacteristic
403C2×C5#480011yescharacteristic
404C2×C5#481011yescharacteristic
405C2×C5#487111yescharacteristic
406C2×C5#489111yescharacteristic
407C23—62no—
408C23—121no—
409C23—121no—
410C23—121no—
411C23—121no—
412C23—121no—
413C23—121no—
414C23#677711yescharacteristic
415D4—62no—
416D4—62no—
417D4—121no—
418D4—121no—
419C2×C4—62no—
420C2×C4—102no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4—201no—
427C2×C4—201no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4—301no—
433C2×C4—301no—
434C2×C4D3×Dic1011yescharacteristic
435C2×C4#677111yescharacteristic
436C2×C4D5×D1211yescharacteristic
437C2×C4#678011yescharacteristic
438C2×C4#678211yescharacteristic
439C2×C4D3×C22⋊D511yescharacteristic
440C8—41no—
441C8—601no—
442C2×C3#6505211yescharacteristic
443C2×C3#6505311yescharacteristic
444C2×C3#6505511yescharacteristic
445C2×C3#6505711yescharacteristic
446C2×C3#6523611yescharacteristic
447C2×C3#6544711yescharacteristic
448C2×C3#6546111yescharacteristic
449D3—82no—
450C5#6889911yescharacteristic, complemented, Sylow
451C22—122no—
452C22—122no—
453C22—122no—
454C22—241no—
455C22—241no—
456C22—241no—
457C22—241no—
458C22#9125711yescharacteristic
459C22#9125811yescharacteristic
460C22#9127611yescharacteristic
461C22#9127911yescharacteristic
462C22#9143611yescharacteristic
463C22#9146411yescharacteristic
464C22#9147511yescharacteristic
465C4—122no—
466C4—202no—
467C4—401no—
468C4—601no—
469C4—601no—
470C4#9135011yescharacteristic
471C4#9135211yescharacteristic
472C4#9141711yescharacteristic
473C4#9152511yescharacteristic
474C3#1060095711yescharacteristic, complemented, Sylow
475C2—242no—
476C2#1174781411yescharacteristic
477C2#1174781711yescharacteristic
478C2#1174797911yescharacteristic
479C2#1174801411yescharacteristic
480C2#1174815311yescharacteristic
481C2#1174815911yescharacteristic
482C2#1174875711yescharacteristic
subgroupG/H
centerC23#6777
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
hypercenterC22×C8D3×D5
hypocenterC3×C5#2025
LCSG ▷ C22×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
1. C2×#91384C2semidirect
5. #11746371C2semidirect
6. C3×#64771C2semidirect
7. #11745979C2semidirect
29. #64771D3semidirect
375. C3×C5#2025semidirect
450. C5#68899semidirect
474. C3#10600957semidirect

Maximal subgroups

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

subgroupindex
C2×#913842
C2×C5×#8212
#117487972
C2×#909662
#117463712
C3×#647712
#117459792
#106009573
#688995