Finite Group Databasebeta

← #14306005

Subgroups — #14306005

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754572C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic, complemented
4C3×C42×Dic5C211yesmaximal, characteristic, complemented
5#11748431C211yesmaximal, characteristic, complemented
6C2×#90981C211yesmaximal, characteristic, complemented
7C2×#90979C211yesmaximal, characteristic, complemented
8#10601149—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×C4×Dic5—22no—
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17#91566—22no—
18#91451C411yescharacteristic, complemented
19C4×#1203—22no—
20#91376C411yescharacteristic, complemented
21#91375C411yescharacteristic, complemented
22#91373C411yescharacteristic, complemented
23#91089—22no—
24C5×#805—22no—
25#90982—22no—
26#90981—22no—
27#90979—22no—
28#69395—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104—31no—
31C2×#3969—31no—
32C2×#3957—31no—
33#65407—31no—
34C42×Dic5D311yescharacteristic, complemented
35C2×#3937—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42#6817—21no—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×Dic30C2×C411yescharacteristic
46C2×C5×#67—21no—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C2×C5×D12C2×C411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C5×Dic6C2×C411yescharacteristic
54C22×C3×Dic5—21no—
55C22×C3×Dic5D412yes—
56C2×#1203—22no—
57C3×C42×C5—21no—
58C3×C42×C5D412yescomplemented
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×C4×Dic5—28no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5C2×C411yescharacteristic
68C3×C4×Dic5C2×C411yescharacteristic
69C3×C4×Dic5D412yes—
70C3×C4×Dic5D412yescomplemented
71#6668—22no—
72#6667—22no—
73(C2×D3)⋊Dic5—22no—
74#5477—51no—
75C3×C43—51no—
76C2×#805—51no—
77C2×#805—51no—
78C2×#805—51no—
79C2×#805D511yescharacteristic, complemented
80#4924—51no—
81C2×C5×#41—31no—
82C2×#709—31no—
83C2×C5×M16—31no—
84C2×C42×C5C2×D311yescharacteristic
85#4093—31no—
86#4090—31no—
87#4086—31no—
88#4085—62no—
89#4082—31no—
90C4×C22⋊D5—62no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5C2×D311yescharacteristic
93C2×C4×Dic5C2×D311yescharacteristic
94C2×#681—31no—
95C5×#104—62no—
96#3969—62no—
97#3957—62no—
98#3946—62no—
99#3937—62no—
100#1962—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×C5×D3—21no—
104C2×C3×C4×C5—24no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112#1220—41no—
113#1220—41no—
114C2×Dic15—21no—
115D60—21no—
116D60—21no—
117C4×D15—41no—
118C4×D15—41no—
119Dic30—21no—
120Dic30—21no—
121C5×#67—41no—
122C5×#67—41no—
123C2×C5×Dic3—21no—
124C5×D12—21no—
125C5×D12—21no—
126C4×C5×D3—41no—
127C4×C5×D3—41no—
128C5×Dic6—21no—
129C5×Dic6—21no—
130C2×C3×Dic5—24no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—24no—
133C2×C3×Dic5C22⋊C412yes—
134C2×C3×Dic5C22⋊C412yes—
135#1203—44no—
136C3⋊#168—41no—
137C5×C3⋊C8—41no—
138C2×#235—51no—
139C2×#235C2×D511yescharacteristic
140C2×C3×C42—51no—
141C2×C3×C42—51no—
142C2×C3×C42—102no—
143C2×C3×C42C2×D511yescharacteristic
144#930—102no—
145C2×#208—51no—
146C2×#208C2×D511yescharacteristic
147#875—51no—
148#875—51no—
149#874—51no—
150C4×D12—102no—
151#869—51no—
152#805—22no—
153#805—102no—
154#805—102no—
155#805—102no—
156C4⋊(C3⋊C8)—102no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C5×#41—61no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—61no—
164C22×C4×C5—21no—
165C22×C4×C5—61no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—61no—
168C2×C22⋊D5—62no—
169C22×Dic5—21no—
170C22×Dic5#6712yes—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C42×C5—21no—
182C42×C5D1212yescomplemented
183C22⋊Dic5—62no—
184#685—62no—
185#683—62no—
186C4×Dic5—28no—
187C4×Dic5—21no—
188C4×Dic5C4×D311yescharacteristic
189C4×Dic5C4×D311yescharacteristic
190C4×Dic5D1212yes—
191C4×Dic5D1212yescomplemented
192#681—61no—
193#681—61no—
194C2×#168—61no—
195#532—151no—
196#423—151no—
197C2×#104—31no—
198C2×#104—151no—
199C2×#104—151no—
200C2×#104—151no—
201C43—51no—
202C22×C3×C5—22no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×D15—41no—
207C2×D15—42no—
208C2×C5×D3—41no—
209C2×C5×D3—42no—
210C3×C4×C5—24no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12411yescharacteristic
214C3×C4×C5#12711yescharacteristic
215Dic15—41no—
216C3×Dic5—24no—
217C3×Dic5—22no—
218C3×Dic5#10414yescomplemented
219C5×Dic3—41no—
220C22×C3×C4—21no—
221C22×C3×C4—52no—
222C22×C3×C4—101no—
223C22×C3×C4C22×D511yescharacteristic
224C2×#67—21no—
225C2×#67—101no—
226#235—21no—
227#235—21no—
228#235—21no—
229#235—21no—
230#235—101no—
231#235—101no—
232#235—101no—
233#235—101no—
234C2×D12—51no—
235C2×D12—102no—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3—21no—
238C2×C4×D3—101no—
239C2×Dic6—51no—
240C2×Dic6C4×D511yescharacteristic
241C3×C42—21no—
242C3×C42—51no—
243C3×C42—51no—
244C3×C42—52no—
245C3×C42—52no—
246C3×C42—108no—
247C3×C42—101no—
248C3×C42C22⋊D512yescomplemented
249(C2×D3)⋊C4—102no—
250(C2×D3)⋊C4—102no—
251C4⋊Dic3—102no—
252#208—21no—
253#208—21no—
254#208—101no—
255#208—101no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—101no—
258C23×C5—61no—
259C23×C5C2×#6711yescharacteristic
260C22×D5—61no—
261C5×Q8—61no—
262C5×Q8—61no—
263C5×D4—61no—
264C5×D4—61no—
265C5×D4—121no—
266C5×D4—121no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—61no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5C2×D1211yescharacteristic
274C2×C4×C5C2×D1211yescharacteristic
275C2×C4×C5C2×D1211yescharacteristic
276C2×C4×C5#23511yescharacteristic
277C2×C4×C5#23511yescharacteristic
278C22⋊D5—121no—
279C22⋊D5—121no—
280C22⋊D5—124no—
281C2×Dic5—24no—
282C2×Dic5—22no—
283C2×Dic5—24no—
284C2×Dic5—61no—
285C2×Dic5(C2×D3)⋊C412yes—
286C2×Dic5(C2×D3)⋊C412yes—
287D20—61no—
288D20—61no—
289C4×D5—121no—
290C4×D5—121no—
291Dic10—61no—
292Dic10—61no—
293C5×C8—121no—
294#168—121no—
295C2×#41—31no—
296C2×#41—151no—
297C2×M16—31no—
298C2×M16—151no—
299C4⋊Q8—151no—
300#127—151no—
301#124—151no—
302#124—151no—
303#121—302no—
304C4×D4—302no—
305C2×C42—51no—
306C2×C42—51no—
307C2×C42—102no—
308C2×C42D3×D511yescharacteristic
309C4⋊C8—302no—
310#104—62no—
311#104—302no—
312#104—302no—
313#104—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#39011yescharacteristic
317C2×C3×C5C2×#10412yes—
318D15—81no—
319C5×D3—81no—
320C23×C3D4×D511yescharacteristic
321C22×D3—21no—
322C22×D3—101no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—52no—
326C2×C3×C4—52no—
327C2×C3×C4—104no—
328C2×C3×C4—104no—
329C2×C3×C4—102no—
330C2×C3×C4C2×C4×D511yescharacteristic
331C2×C3×C4#70911yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4#71111yescharacteristic
335C2×C3×C4C2×C22⋊D511yescharacteristic
336#67—41no—
337#67—41no—
338#67—201no—
339#67—201no—
340C2×Dic3—21no—
341C2×Dic3—101no—
342D12—21no—
343D12—21no—
344D12—101no—
345D12—101no—
346D12—204no—
347C4×D3—41no—
348C4×D3—41no—
349C4×D3—201no—
350C4×D3—201no—
351Dic6—21no—
352Dic6—21no—
353Dic6—101no—
354Dic6—101no—
355C3⋊C8—41no—
356C3⋊C8—201no—
357C22×C5—22no—
358C22×C5—122no—
359C22×C5—121no—
360C22×C5C2×(C2×D3)⋊C411yescharacteristic
361C22×C5#93011yescharacteristic
362C22×C5#93011yescharacteristic
363C2×D5—122no—
364C2×D5—121no—
365C4×C5—24no—
366C4×C5—121no—
367C4×C5C4×D1211yescharacteristic
368C4×C5C4×D1211yescharacteristic
369C4×C5#87411yescharacteristic
370C4×C5#87511yescharacteristic
371Dic5—24no—
372Dic5—22no—
373Dic5—121no—
374Dic5#80514yescomplemented
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—301no—
380#41—301no—
381#41—301no—
382#41—301no—
383C2×Q8—31no—
384C2×Q8—151no—
385C2×D4—31no—
386C2×D4—61no—
387C2×D4—151no—
388C2×D4—302no—
389C2×D4—301no—
390C22×C4—21no—
391C22×C4—52no—
392C22×C4—61no—
393C22×C4—101no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—61no—
397M16—61no—
398M16—301no—
399M16—301no—
400C2×C8—61no—
401C2×C8—301no—
402C4⋊C4—302no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C42—21no—
406C42—51no—
407C42—51no—
408C42—52no—
409C42—52no—
410C42—108no—
411C42—101no—
412C42#120312yescomplemented
413C3×C5#196211yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#403011yescharacteristic
417C22×C3#408511yescharacteristic
418C2×D3—42no—
419C2×D3—41no—
420C2×D3—202no—
421C2×D3—201no—
422C3×C4—24no—
423C3×C4—54no—
424C3×C4—104no—
425C3×C4—102no—
426C3×C4#402711yescharacteristic
427C3×C4#403111yescharacteristic
428C3×C4C4×C22⋊D511yescharacteristic
429C3×C4#408611yescharacteristic
430Dic3—41no—
431Dic3—201no—
432C2×C5—21no—
433C2×C5—21no—
434C2×C5—241no—
435C2×C5C2×#80512yes—
436C2×C5#493911yescharacteristic
437D5—241no—
438C23—61no—
439C23—301no—
440C23D5×#6711yescharacteristic
441Q8—61no—
442Q8—61no—
443Q8—301no—
444Q8—301no—
445D4—61no—
446D4—61no—
447D4—121no—
448D4—121no—
449D4—301no—
450D4—301no—
451D4—604no—
452D4—601no—
453D4—601no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—52no—
457C2×C4—52no—
458C2×C4—61no—
459C2×C4—104no—
460C2×C4—104no—
461C2×C4—102no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—301no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4#677111yescharacteristic
468C2×C4C4×D3×D511yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4D5×D1211yescharacteristic
471C2×C4#678211yescharacteristic
472C2×C4C2×#120311yescharacteristic
473C8—121no—
474C8—601no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3D5×#10412yes—
478C2×C3#6524611yescharacteristic
479D3—81no—
480D3—401no—
481C5#6939511yescharacteristic, complemented, Sylow
482C22—22no—
483C22—122no—
484C22—121no—
485C22—602no—
486C22—601no—
487C22#9144811yescharacteristic
488C22D5×(C2×D3)⋊C411yescharacteristic
489C22#9156611yescharacteristic
490C4—24no—
491C4—54no—
492C4—104no—
493C4—102no—
494C4—121no—
495C4—601no—
496C4#9135011yescharacteristic
497C4#9140511yescharacteristic
498C4C4×#120311yescharacteristic
499C4#9145111yescharacteristic
500C3#1060114911yescharacteristic, complemented, Sylow
501C2—21no—
502C2—21no—
503C2—241no—
504C2—1201no—
505C2D5×#80512yes—
506C2#1174890811yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754572C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1962
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#91089C2semidirect
3. C2×C5×#805C2semidirect
4. C3×C42×Dic5C2semidirect
5. #11748431C2semidirect
6. C2×#90981C2semidirect
7. C2×#90979C2semidirect
18. #91451C4semidirect
20. #91376C4semidirect
21. #91375C4semidirect
22. #91373C4semidirect
34. C42×Dic5D3semidirect
58. C3×C42×C5D4semidirect
70. C3×C4×Dic5D4semidirect
79. C2×#805D5semidirect
182. C42×C5D12semidirect
191. C4×Dic5D12semidirect
218. C3×Dic5#104semidirect
248. C3×C42C22⋊D5semidirect
374. Dic5#805semidirect
412. C42#1203semidirect
413. C3×C5#1962semidirect
481. C5#69395semidirect
500. C3#10601149semidirect

Maximal subgroups

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

subgroupindex
#117545722
C2×#910892
C2×C5×#8052
C3×C42×Dic52
#117484312
C2×#909812
C2×#909792
#106011493
#693955