Finite Group Databasebeta

← #14281251

Subgroups — #14281251

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91350C211yesmaximal, characteristic
2C3×#65007C211yesmaximal, characteristic, complemented
3#11748333C211yesmaximal, characteristic, complemented
4#11746289C211yesmaximal, characteristic, complemented
5C5×#4468C211yesmaximal, characteristic, complemented
6#11745950C211yesmaximal, characteristic, complemented
7#11745949C211yesmaximal, characteristic, complemented
8#10598897—31nomaximal, Hall
9C22×#1204C411yescharacteristic
10C22×#1203C411yescharacteristic
11C2×#6714C2211yescharacteristic
12C2×C5×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×C4×Dic5C2211yescharacteristic
14C2×#6667C411yescharacteristic
15C2×(C2×D3)⋊Dic5C411yescharacteristic
16#91350—21no—
17#91350—21no—
18#91350—21no—
19#91350—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21#91114C2211yescharacteristic
22C5×#830C2211yescharacteristic
23C3×C22⋊#168C2211yescharacteristic
24C3×#3946—21no—
25C3×C8×Dic5—21no—
26#90982—21no—
27#90952—21no—
28#70784—51nomaximal, Hall
29C2×#4031—31no—
30#65008—31no—
31#65007D311yescharacteristic, complemented
32C5×#323—31no—
33#64745—31no—
34#64688—31no—
35#64688—31no—
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×#1204—21no—
44C2×#1204—21no—
45C2×#1204—42no—
46C2×#1203—21no—
47C2×#1203—21no—
48C2×#1203—42no—
49C2×C3×C5×C8—21no—
50#6714—21no—
51#6714—21no—
52C2×C3⋊#168—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C2×C5×C3⋊C8—21no—
56C3×C4×Dic5D411yescharacteristic
57C3×C4×Dic5D411yescharacteristic
58C3×C4×Dic5D411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C2×C3×#168—21no—
61#6667—21no—
62#6667—21no—
63(C2×D3)⋊Dic5—21no—
64(C2×D3)⋊Dic5—21no—
65C2×#875—51no—
66C3×#431—51no—
67#4926—51no—
68#4468—51no—
69#4468—51no—
70#4468—51no—
71#4468D511yescharacteristic, complemented
72C22×C22⋊D5—31no—
73C22×Dic10—31no—
74C2×C5×C22⋊C4—31no—
75C2×C22⋊Dic5—31no—
76C2×#685—31no—
77C2×#685—31no—
78C2×C4×Dic5C2×D311yescharacteristic
79#4031—61no—
80#4031—61no—
81#4031—61no—
82#4031—61no—
83C5×C22⋊C8—31no—
84C5×C22⋊C8C2×D311yescharacteristic
85C22⋊#168—31no—
86C22⋊#168C2×D311yescharacteristic
87#3947—61no—
88#3946—21no—
89#3946—61no—
90C8×Dic5—21no—
91#1469—151noSylow
92C23×C3×C5C22×C411yescharacteristic
93C22×D15—21no—
94C22×D15—21no—
95C22×D15—21no—
96C22×D15—41no—
97C22×D15—41no—
98C22×C5×D3—21no—
99C22×C5×D3—21no—
100C22×C5×D3—21no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—41no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C2×C3×Dic5C22⋊C411yescharacteristic
116C2×C3×Dic5C22⋊C411yescharacteristic
117#1204—42no—
118#1204—42no—
119#1203—42no—
120#1203—42no—
121C3×C5×C8—41no—
122C3⋊#168—41no—
123C3×#168—41no—
124C5×C3⋊C8—41no—
125C22×D12—51no—
126C22×Dic6—51no—
127C2×C3×C42—51no—
128C2×(C2×D3)⋊C4—51no—
129C2×(C2×D3)⋊C4—51no—
130C2×(C2×D3)⋊C4—51no—
131C2×(C2×D3)⋊C4C2×D511yescharacteristic
132#875—101no—
133#875—101no—
134#875—101no—
135#875—101no—
136C3×C4⋊C8—101no—
137C3×C22⋊C8—51no—
138C3×C22⋊C8C2×D511yescharacteristic
139C3×C4×C8—101no—
140#830—51no—
141#830C2×D511yescharacteristic
142C4⋊(C3⋊C8)—101no—
143#803—101no—
144C24×C5—31no—
145C23×D5—31no—
146C22×C4×C5—31no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—122no—
151C22×Dic5—31no—
152C22×Dic5C4×D311yescharacteristic
153C22×Dic5C4×D311yescharacteristic
154C2×Dic10—61no—
155C2×Dic10—61no—
156C2×Dic10—122no—
157C2×C5×C8—21no—
158C2×C5×C8—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C22⋊Dic5—61no—
162C22⋊Dic5—61no—
163#685—61no—
164#685—61no—
165#685—61no—
166#685—61no—
167C4×Dic5D1211yescharacteristic
168C4×Dic5D1211yescharacteristic
169C4×Dic5#6711yescharacteristic
170C4×Dic5#6711yescharacteristic
171C2×#168—21no—
172C2×#168—61no—
173C2×#124—151no—
174#432—151no—
175#431—51no—
176#323—31no—
177#323—151no—
178#323—151no—
179#323—151no—
180C22×C3×C5—21no—
181C22×C3×C5—21no—
182C22×C3×C5C2×C22⋊C411yescharacteristic
183C22×C3×C5#13111yescharacteristic
184C22×C3×C5#13111yescharacteristic
185C2×D15—41no—
186C2×D15—41no—
187C2×D15—41no—
188C2×D15—81no—
189C2×D15—81no—
190C2×C5×D3—41no—
191C2×C5×D3—41no—
192C2×C5×D3—41no—
193C2×C5×D3—81no—
194C2×C5×D3—81no—
195C3×C4×C5—21no—
196C3×C4×C5—21no—
197Dic15—41no—
198C3×Dic5—21no—
199C3×Dic5—21no—
200C3×Dic5—21no—
201C3×Dic5#10012yes—
202C5×Dic3—41no—
203C23×D3—51no—
204C23×D3C4×D511yescharacteristic
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4C22×D511yescharacteristic
208C22×Dic3—51no—
209C22×Dic3C4×D511yescharacteristic
210C2×D12—101no—
211C2×D12—101no—
212C2×D12—202no—
213C2×Dic6—101no—
214C2×Dic6—101no—
215C2×Dic6—202no—
216C2×C3×C8—21no—
217C2×C3×C8—101no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42—51no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—101no—
225(C2×D3)⋊C4—101no—
226(C2×D3)⋊C4—101no—
227(C2×D3)⋊C4—101no—
228(C2×D3)⋊C4—101no—
229(C2×D3)⋊C4—101no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—101no—
232C23×C5—61no—
233C23×C5—61no—
234C23×C5—61no—
235C23×C5—121no—
236C23×C5—121no—
237C23×C5C2×C4×D311yescharacteristic
238C22×D5—61no—
239C22×D5—61no—
240C22×D5—61no—
241C22×D5—121no—
242C22×D5—121no—
243C2×C4×C5—41no—
244C2×C4×C5—61no—
245C2×C4×C5—121no—
246C2×C4×C5C2×D1211yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C22⋊D5—122no—
249C22⋊D5—122no—
250C2×Dic5—21no—
251C2×Dic5—21no—
252C2×Dic5—22no—
253C2×Dic5—61no—
254C2×Dic5—121no—
255C2×Dic5(C2×D3)⋊C411yescharacteristic
256C2×Dic5(C2×D3)⋊C411yescharacteristic
257C2×Dic5(C2×D3)⋊C411yescharacteristic
258C2×Dic5(C2×D3)⋊C411yescharacteristic
259Dic10—122no—
260Dic10—122no—
261C5×C8—41no—
262C5×C8—121no—
263#168—41no—
264#168—121no—
265C22×Q8—151no—
266C22×D4—151no—
267#124—301no—
268#124—301no—
269#124—301no—
270#124—301no—
271C2×C22⋊C4—31no—
272C2×C22⋊C4—151no—
273C2×C22⋊C4—151no—
274C2×C22⋊C4—151no—
275C2×C42—51no—
276C4⋊C8—101no—
277C4⋊C8—301no—
278C22⋊C8—31no—
279C22⋊C8—51no—
280C22⋊C8—151no—
281C22⋊C8D3×D511yescharacteristic
282#97—301no—
283C4×C8—101no—
284C2×C3×C5—21no—
285C2×C3×C5—21no—
286C2×C3×C5#40811yescharacteristic
287C2×C3×C5#41011yescharacteristic
288C2×C3×C5C2×#10011yescharacteristic
289D15—81no—
290C5×D3—81no—
291C23×C3C2×C4×D511yescharacteristic
292C22×D3—21no—
293C22×D3—21no—
294C22×D3—21no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—101no—
298C22×D3—101no—
299C22×D3—101no—
300C22×D3—201no—
301C22×D3—201no—
302C2×C3×C4—41no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—102no—
308C2×C3×C4—101no—
309C2×C3×C4—101no—
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—101no—
315C2×Dic3—201no—
316D12—202no—
317D12—202no—
318Dic6—202no—
319Dic6—202no—
320C3×C8—41no—
321C3×C8—201no—
322C3⋊C8—41no—
323C3⋊C8—201no—
324C22×C5—21no—
325C22×C5—21no—
326C22×C5—121no—
327C22×C5—121no—
328C22×C5—121no—
329C22×C5—241no—
330C22×C5—241no—
331C22×C5#90111yescharacteristic
332C22×C5#90111yescharacteristic
333C22×C5C2×(C2×D3)⋊C411yescharacteristic
334C2×D5—121no—
335C2×D5—121no—
336C2×D5—121no—
337C2×D5—241no—
338C2×D5—241no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—121no—
342Dic5—21no—
343Dic5—21no—
344Dic5—21no—
345Dic5—121no—
346Dic5#82312yes—
347C24—31no—
348C24—151no—
349C2×Q8—301no—
350C2×Q8—301no—
351C2×Q8—602no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—602no—
355C22×C4—31no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—151no—
359C22×C4C2×D3×D511yescharacteristic
360C2×C8—21no—
361C2×C8—61no—
362C2×C8—101no—
363C2×C8—301no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—301no—
367C22⋊C4—301no—
368C22⋊C4—301no—
369C22⋊C4—301no—
370C22⋊C4—301no—
371C22⋊C4—301no—
372C42—51no—
373C42—51no—
374C42—51no—
375C42—51no—
376C3×C5#146911yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#404711yescharacteristic
381C22×C3#405311yescharacteristic
382C2×D3—41no—
383C2×D3—41no—
384C2×D3—41no—
385C2×D3—81no—
386C2×D3—81no—
387C2×D3—201no—
388C2×D3—201no—
389C2×D3—201no—
390C2×D3—401no—
391C2×D3—401no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—52no—
395C3×C4—101no—
396C3×C4—101no—
397C3×C4—101no—
398Dic3—41no—
399Dic3—201no—
400C2×C5—21no—
401C2×C5—21no—
402C2×C5—241no—
403C2×C5#500611yescharacteristic
404C2×C5#511011yescharacteristic
405C2×C5C2×#82311yescharacteristic
406D5—241no—
407C23—61no—
408C23—61no—
409C23—61no—
410C23—121no—
411C23—121no—
412C23—301no—
413C23—301no—
414C23—301no—
415C23—601no—
416C23—601no—
417C23C4×D3×D511yescharacteristic
418Q8—602no—
419Q8—602no—
420D4—602no—
421D4—602no—
422C2×C4—41no—
423C2×C4—51no—
424C2×C4—51no—
425C2×C4—51no—
426C2×C4—51no—
427C2×C4—61no—
428C2×C4—102no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—121no—
432C2×C4—301no—
433C2×C4—601no—
434C2×C4D5×D1211yescharacteristic
435C2×C4D5×#6711yescharacteristic
436C8—41no—
437C8—121no—
438C8—201no—
439C8—601no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3#6501611yescharacteristic
443C2×C3#6502911yescharacteristic
444C2×C3D5×#10011yescharacteristic
445D3—81no—
446D3—401no—
447C5#7078411yescharacteristic, complemented, Sylow
448C22—21no—
449C22—21no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—241no—
454C22—241no—
455C22—601no—
456C22—601no—
457C22—601no—
458C22—1201no—
459C22—1201no—
460C22#9126511yescharacteristic
461C22#9126611yescharacteristic
462C22D5×(C2×D3)⋊C411yescharacteristic
463C4—21no—
464C4—21no—
465C4—52no—
466C4—101no—
467C4—101no—
468C4—101no—
469C4—121no—
470C4—601no—
471C3#1059889711yescharacteristic, complemented, Sylow
472C2—21no—
473C2—21no—
474C2—241no—
475C2—1201no—
476C2#1174712911yescharacteristic
477C2#1174813411yescharacteristic
478C2D5×#82311yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1469
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65007C2semidirect
3. #11748333C2semidirect
4. #11746289C2semidirect
5. C5×#4468C2semidirect
6. #11745950C2semidirect
7. #11745949C2semidirect
31. #65007D3semidirect
71. #4468D5semidirect
376. C3×C5#1469semidirect
447. C5#70784semidirect
471. C3#10598897semidirect

Maximal subgroups

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

subgroupindex
C2×#913502
C3×#650072
#117483332
#117462892
C5×#44682
#117459502
#117459492
#105988973
#707845