Finite Group Databasebeta

← #14308858

Subgroups — #14308858

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
2#11751089C211yesmaximal, characteristic
3C2×#90969C211yesmaximal, characteristic
4C2×#90968C211yesmaximal, characteristic
5C5×#4529C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745968C211yesmaximal, characteristic, complemented
8#10599692—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6714—21no—
12C2×#6714—21no—
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C2×Dic3⋊Dic5—21no—
19C2×#6668—21no—
20#91384—22no—
21#91384—22no—
22#90969—22no—
23#90968—22no—
24#68899—51nomaximal, Hall
25C2×#4036—31no—
26C2×#3953—31no—
27#65277—31no—
28C2×#3941—31no—
29C5×#340—31no—
30#64770—31no—
31#64749D311yescharacteristic, complemented
32C23×D15—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15D411yescharacteristic
36C22×Dic15D411yescharacteristic
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60Q812yes—
43C22×C5×Dic3—21no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47#6714—42no—
48#6714—42no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D412yes—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5D412yes—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61Dic3⋊Dic5—24no—
62#6668—24no—
63C2×#890—51no—
64C2×#821—51no—
65#4988—51no—
66C2×#809—51no—
67C3×#340—51no—
68#4550—51no—
69#4529D511yescharacteristic, complemented
70C22×D20—31no—
71C22×C5×C8—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×#685—61no—
75C2×#685—61no—
76C2×C4⋊Dic5—61no—
77C2×C4⋊Dic5C2×D311yescharacteristic
78C2×#683—61no—
79C2×C4×Dic5—31no—
80C22×#168C2×D311yescharacteristic
81#4036—62no—
82#4036—62no—
83#3953—62no—
84#3941—62no—
85#2025—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×D15—22no—
88C22×D15—41no—
89C22×D15—41no—
90C22×D15—41no—
91C22×D15—41no—
92C22×D15—41no—
93C22×D15—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×Q811yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109D60—22no—
110D60—22no—
111D60—41no—
112D60—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—41no—
118C2×C3×Dic5—41no—
119C3×#168—41no—
120C5×C3⋊C8—41no—
121C22×D12—51no—
122C22×C3×C8—51no—
123C2×C3×C4⋊C4—51no—
124C2×C3×C4⋊C4C2×D511yescharacteristic
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⋊C8C2×D511yescharacteristic
132#890—102no—
133#890—102no—
134#821—102no—
135#809—102no—
136C23×D5—61no—
137C22×C4×C5—21no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—21no—
141C22×Dic5—31no—
142C22×Dic5—31no—
143C2×D20—32no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×D20—61no—
148C2×D20—61no—
149C2×C5×C8—61no—
150C2×C5×C8—61no—
151C2×C5×C8—61no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—21no—
154C5×C4⋊C4—32no—
155C5×C4⋊C4—61no—
156#685—122no—
157#685—122no—
158C4⋊Dic5—21no—
159C4⋊Dic5—64no—
160C4⋊Dic5D1212yes—
161#683—64no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164C2×#168—21no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#125—151no—
168C2×#102—151no—
169C2×#102—151no—
170#390—151no—
171#340—31no—
172#340—51no—
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×D15—42no—
182C2×D15—42no—
183C2×D15—42no—
184C2×D15—81no—
185C2×D15—81no—
186C2×D15—81no—
187C2×D15—81no—
188C3×C4×C5—81no—
189C3×C4×C5C22⋊Q811yescharacteristic
190C3×C4×C5C22⋊Q811yescharacteristic
191C3×C4×C5#12411yescharacteristic
192C3×C4×C5#12411yescharacteristic
193Dic15—41no—
194Dic15—41no—
195C3×Dic5—42no—
196C5×Dic3—42no—
197C23×D3—101no—
198C22×C3×C4—21no—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—51no—
203C22×Dic3—51no—
204C2×D12—52no—
205C2×D12—101no—
206C2×D12—101no—
207C2×D12—101no—
208C2×D12—101no—
209C2×D12—101no—
210C2×C3×C8—101no—
211C2×C3×C8—101no—
212C2×C3×C8—101no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—52no—
216C3×C4⋊C4—101no—
217(C2×D3)⋊C4—202no—
218(C2×D3)⋊C4—202no—
219C4⋊Dic3—21no—
220C4⋊Dic3—104no—
221C4⋊Dic3D2012yes—
222Dic3⋊C4—104no—
223C4×Dic3—101no—
224C4×Dic3—101no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C23×C5D3×D411yescharacteristic
229C22×D5—62no—
230C22×D5—121no—
231C22×D5—121no—
232C22×D5—121no—
233C22×D5—121no—
234C22×D5—121no—
235C22×D5—121no—
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×D1211yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5D3×Q811yescharacteristic
248C2×Dic5—22no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251C2×Dic5—61no—
252C2×Dic5—61no—
253C2×Dic5—61no—
254C2×Dic5—61no—
255C2×Dic5—61no—
256C2×Dic5—61no—
257D20—62no—
258D20—62no—
259D20—121no—
260D20—121no—
261C5×C8—121no—
262#168—41no—
263C22×D4—151no—
264C22×C8—31no—
265C22×C8—51no—
266#125—302no—
267#125—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—301no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4D3×D511yescharacteristic
273C2×C22⋊C4—301no—
274C2×C22⋊C4—301no—
275C2×C42—151no—
276#102—302no—
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
285D15—82no—
286C23×C3D4×D511yescharacteristic
287C22×D3—102no—
288C22×D3—201no—
289C22×D3—201no—
290C22×D3—201no—
291C22×D3—201no—
292C22×D3—201no—
293C22×D3—201no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—102no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4C2×D2011yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4Q8×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—102no—
316D12—102no—
317D12—201no—
318D12—201no—
319C3×C8—201no—
320C3⋊C8—41no—
321C22×C5#88211yescharacteristic
322C22×C5#88511yescharacteristic
323C22×C5#89611yescharacteristic
324C22×C5#91111yescharacteristic
325C22×C5#91411yescharacteristic
326C22×C5#91611yescharacteristic
327C22×C5#91911yescharacteristic
328C2×D5—122no—
329C2×D5—122no—
330C2×D5—122no—
331C2×D5—241no—
332C2×D5—241no—
333C2×D5—241no—
334C2×D5—241no—
335C4×C5—81no—
336C4×C5—122no—
337C4×C5#87511yescharacteristic
338C4×C5#88511yescharacteristic
339C4×C5#89611yescharacteristic
340C4×C5#89711yescharacteristic
341Dic5—42no—
342Dic5—121no—
343Dic5—121no—
344C24—301no—
345C2×D4—152no—
346C2×D4—301no—
347C2×D4—301no—
348C2×D4—301no—
349C2×D4—301no—
350C2×D4—301no—
351C22×C4—21no—
352C22×C4—61no—
353C22×C4—101no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—101no—
361C2×C8—101no—
362C2×C8—101no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—32no—
366C4⋊C4—52no—
367C4⋊C4—61no—
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#402811yescharacteristic
377C22×C3#403111yescharacteristic
378C22×C3#404211yescharacteristic
379C22×C3#405711yescharacteristic
380C22×C3#406011yescharacteristic
381C22×C3#406211yescharacteristic
382C22×C3#406511yescharacteristic
383C2×D3—202no—
384C2×D3—202no—
385C2×D3—202no—
386C2×D3—401no—
387C2×D3—401no—
388C2×D3—401no—
389C2×D3—401no—
390C3×C4—81no—
391C3×C4—202no—
392C3×C4#402111yescharacteristic
393C3×C4#403111yescharacteristic
394C3×C4#404211yescharacteristic
395C3×C4#404311yescharacteristic
396Dic3—42no—
397Dic3—201no—
398Dic3—201no—
399C2×C5#467311yescharacteristic
400C2×C5#476411yescharacteristic
401C2×C5#478111yescharacteristic
402C2×C5#480011yescharacteristic
403C2×C5#481011yescharacteristic
404C2×C5#487111yescharacteristic
405C2×C5#489111yescharacteristic
406D5—242no—
407C23—302no—
408C23—601no—
409C23—601no—
410C23—601no—
411C23—601no—
412C23—601no—
413C23—601no—
414C23#679011yescharacteristic
415D4—302no—
416D4—302no—
417D4—601no—
418D4—601no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—62no—
423C2×C4—102no—
424C2×C4—121no—
425C2×C4—121no—
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×C4D15⋊Q811yescharacteristic
435C2×C4#677111yescharacteristic
436C2×C4D5×D1211yescharacteristic
437C2×C4D3×D2011yescharacteristic
438C2×C4#677911yescharacteristic
439C2×C4#678211yescharacteristic
440C8—121no—
441C8—201no—
442C2×C3#6496211yescharacteristic
443C2×C3#6505311yescharacteristic
444C2×C3#6507011yescharacteristic
445C2×C3#6508911yescharacteristic
446C2×C3#6510011yescharacteristic
447C2×C3#6516011yescharacteristic
448C2×C3#6518011yescharacteristic
449D3—402no—
450C5#6889911yescharacteristic, complemented, Sylow
451C22—602no—
452C22—602no—
453C22—602no—
454C22—1201no—
455C22—1201no—
456C22—1201no—
457C22—1201no—
458C22#9137711yescharacteristic
459C22#9147611yescharacteristic
460C22#9149811yescharacteristic
461C22#9150011yescharacteristic
462C22#9152111yescharacteristic
463C22#9152311yescharacteristic
464C22#9152611yescharacteristic
465C4—81no—
466C4—122no—
467C4—202no—
468C4—601no—
469C4—601no—
470C4#9135011yescharacteristic
471C4#9135311yescharacteristic
472C4#9141911yescharacteristic
473C4#9142911yescharacteristic
474C3#1059969211yescharacteristic, complemented, Sylow
475C2—1202no—
476C2#1174718511yescharacteristic
477C2#1174718611yescharacteristic
478C2#1174751811yescharacteristic
479C2#1174752011yescharacteristic
480C2#1174857911yescharacteristic
481C2#1174909011yescharacteristic
482C2#1174919011yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2025
LCSG ▷ C22×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
1. C2×#91384C2semidirect
5. C5×#4529C2semidirect
6. C3×#64749C2semidirect
7. #11745968C2semidirect
31. #64749D3semidirect
69. #4529D5semidirect
375. C3×C5#2025semidirect
450. C5#68899semidirect
474. C3#10599692semidirect

Maximal subgroups

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

subgroupindex
C2×#913842
#117510892
C2×#909692
C2×#909682
C5×#45292
C3×#647492
#117459682
#105996923
#688995