Finite Group Databasebeta

← #14306002

Subgroups — #14306002

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×#91109C211yesmaximal, characteristic, complemented
3C2×C5×#825C211yesmaximal, characteristic, complemented
4C3×#65407C211yesmaximal, characteristic, complemented
5C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
6C2×#90980C211yesmaximal, characteristic, complemented
7C2×#90978C211yesmaximal, characteristic, complemented
8#10601149—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91566—22no—
17C2×Dic3×Dic5—22no—
18#91451C411yescharacteristic, complemented
19C4×#1203—22no—
20#91376C411yescharacteristic, complemented
21#91375C411yescharacteristic, complemented
22#91373C411yescharacteristic, complemented
23#91109—22no—
24C5×#825—22no—
25C3×#3946—22no—
26#90980—22no—
27#90978—22no—
28#70512—51nomaximal, Hall
29#66166—31no—
30C2×C5×#104—31no—
31C2×#3969—31no—
32C2×#3957—31no—
33#65407D311yescharacteristic, complemented
34C42×Dic5—31no—
35C2×#3937—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—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—
47C22×C5×Dic3—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C2×C5×D12C2×C411yescharacteristic
53C2×C4×C5×D3—21no—
54C2×C5×Dic6C2×C411yescharacteristic
55C22×C3×Dic5D412yes—
56C2×#1203—22no—
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C4×Dic15—21no—
61C4×Dic15D412yescomplemented
62C4×C5×Dic3—21no—
63C4×C5×Dic3D412yescomplemented
64C3×C4×Dic5C2×C411yescharacteristic
65C3×C4×Dic5C2×C411yescharacteristic
66C3×C4×Dic5D412yes—
67C3×#681—21no—
68C3×#681—21no—
69C2×C3×#168—21no—
70#6668—22no—
71#6667—22no—
72(C2×D3)⋊Dic5—22no—
73Dic3×Dic5—28no—
74#5477—51no—
75C3×#423—51no—
76C2×#825—51no—
77C2×#825—51no—
78C2×#825—51no—
79C2×#825D511yescharacteristic, complemented
80C42×Dic3—51no—
81C2×C5×#41—31no—
82C2×#709—31no—
83C2×C5×M16C2×D311yescharacteristic
84C2×C42×C5—31no—
85#4093—31no—
86#4090—31no—
87#4086—31no—
88#4085—62no—
89#4082—31no—
90C4×C22⋊D5—62no—
91C2×C4×Dic5—31no—
92C2×C4×Dic5—62no—
93C2×C4×Dic5C2×D311yescharacteristic
94C2×#681C2×D311yescharacteristic
95C5×#104—62no—
96#3969—62no—
97#3957—62no—
98#3946—22no—
99#3937—62no—
100#1962—151noSylow
101C23×C3×C5C2×D411yescharacteristic
102C22×D15—21no—
103C22×C5×D3—21no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110#1220—41no—
111#1220—41no—
112C2×Dic15—24no—
113C2×Dic15—22no—
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—24no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—21no—
126C5×D12—21no—
127C5×D12—21no—
128C4×C5×D3—41no—
129C4×C5×D3—41no—
130C5×Dic6—21no—
131C5×Dic6—21no—
132C2×C3×Dic5—24no—
133C2×C3×Dic5C22⋊C412yes—
134C2×C3×Dic5C22⋊C412yes—
135#1203—44no—
136C3×C5×C8—41no—
137C3×#168—41no—
138C2×#235—51no—
139C2×#235C2×D511yescharacteristic
140C2×C3×M16—51no—
141C2×C3×M16C2×D511yescharacteristic
142C2×C3×C42—51no—
143#930—102no—
144C2×C4×Dic3—51no—
145C2×C4×Dic3—102no—
146C2×C4×Dic3C2×D511yescharacteristic
147#875—51no—
148#875—51no—
149#874—51no—
150C4×D12—102no—
151#869—51no—
152C3×C4⋊C8—102no—
153#825—22no—
154#825—102no—
155#825—102no—
156#825—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—61no—
165C22×C4×C5—61no—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—61no—
168C2×C22⋊D5—62no—
169C22×Dic5—61no—
170C22×Dic5D1212yes—
171#709—61no—
172#709—61no—
173#709—61no—
174#709—61no—
175C2×D20—31no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C42×C5—32no—
182C42×C5—61no—
183C22⋊Dic5—62no—
184#685—62no—
185#683—62no—
186C4×Dic5—32no—
187C4×Dic5—68no—
188C4×Dic5—61no—
189C4×Dic5C4×D311yescharacteristic
190C4×Dic5C4×D311yescharacteristic
191C4×Dic5#6712yes—
192#681—21no—
193#681—21no—
194C2×#168—21no—
195#532—151no—
196#423—51no—
197C2×#104—31no—
198C2×#104—151no—
199C2×#104—151no—
200C2×#104—151no—
201C43—151no—
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×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12411yescharacteristic
213C3×C4×C5#12711yescharacteristic
214Dic15—24no—
215Dic15—41no—
216C3×Dic5—22no—
217C3×Dic5#10414yescomplemented
218C5×Dic3—24no—
219C5×Dic3—41no—
220C22×C3×C4—52no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C2×#67—101no—
224C22×Dic3—21no—
225C22×Dic3—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×M16—21no—
242C3×M16—21no—
243C3×M16—101no—
244C3×M16—101no—
245C2×C3×C8—21no—
246C2×C3×C8—101no—
247C3×C42—51no—
248C3×C42—51no—
249C3×C42—52no—
250(C2×D3)⋊C4—102no—
251(C2×D3)⋊C4—102no—
252C4⋊Dic3—102no—
253C4×Dic3—21no—
254C4×Dic3—52no—
255C4×Dic3—108no—
256C4×Dic3—101no—
257C4×Dic3C22⋊D512yescomplemented
258C23×C5—61no—
259C23×C5C2×D1211yescharacteristic
260C22×D5—61no—
261C5×Q8—61no—
262C5×Q8—61no—
263C5×D4—61no—
264C5×D4—61no—
265C5×D4—121no—
266C5×D4—121no—
267C2×C4×C5—64no—
268C2×C4×C5—62no—
269C2×C4×C5—61no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23911yescharacteristic
276C2×C4×C5#23911yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—121no—
279C22⋊D5—121no—
280C22⋊D5—124no—
281C2×Dic5—24no—
282C2×Dic5—64no—
283C2×Dic5—62no—
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—41no—
294#168—41no—
295C2×#41—31no—
296C2×#41—151no—
297C2×M16—51no—
298C2×M16D3×D511yescharacteristic
299C4⋊Q8—151no—
300#127—151no—
301#124—151no—
302#124—151no—
303#121—302no—
304C4×D4—302no—
305C2×C42—31no—
306C2×C42—51no—
307C2×C42—151no—
308C2×C42—302no—
309C4⋊C8—102no—
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—52no—
324C2×C3×C4—52no—
325C2×C3×C4—104no—
326C2×C3×C4C2×C4×D511yescharacteristic
327C2×C3×C4#70911yescharacteristic
328C2×C3×C4D4×D511yescharacteristic
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4#71111yescharacteristic
331C2×C3×C4C2×C22⋊D511yescharacteristic
332#67—41no—
333#67—41no—
334#67—201no—
335#67—201no—
336C2×Dic3—24no—
337C2×Dic3—22no—
338C2×Dic3—21no—
339C2×Dic3—104no—
340C2×Dic3—102no—
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×C5#89511yescharacteristic
361C22×C5#89511yescharacteristic
362C22×C5C2×(C2×D3)⋊C411yescharacteristic
363C2×D5—122no—
364C2×D5—121no—
365C4×C5—64no—
366C4×C5—121no—
367C4×C5#89311yescharacteristic
368C4×C5#89311yescharacteristic
369C4×C5#94011yescharacteristic
370C4×C5#94711yescharacteristic
371Dic5—22no—
372Dic5—64no—
373Dic5—121no—
374Dic5#82514yescomplemented
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—52no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—301no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—21no—
397M16—21no—
398M16—101no—
399M16—101no—
400C2×C8—21no—
401C2×C8—101no—
402C4⋊C4—302no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C42—32no—
406C42—51no—
407C42—51no—
408C42—52no—
409C42—61no—
410C42—152no—
411C42—308no—
412C42—301no—
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—54no—
423C3×C4—102no—
424C3×C4#402711yescharacteristic
425C3×C4#403111yescharacteristic
426C3×C4C4×C22⋊D511yescharacteristic
427C3×C4#408611yescharacteristic
428Dic3—24no—
429Dic3—41no—
430Dic3—104no—
431Dic3—201no—
432C2×C5—21no—
433C2×C5—21no—
434C2×C5—241no—
435C2×C5#498811yescharacteristic
436C2×C5C2×#82512yes—
437D5—241no—
438C23—61no—
439C23—301no—
440C23D5×D1211yescharacteristic
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—52no—
455C2×C4—52no—
456C2×C4—64no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—104no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—304no—
463C2×C4—302no—
464C2×C4—301no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4#676811yescharacteristic
468C2×C4#676911yescharacteristic
469C2×C4C4×D3×D511yescharacteristic
470C2×C4D5×#6711yescharacteristic
471C2×C4D3×C22⋊D511yescharacteristic
472C2×C4#679011yescharacteristic
473C8—41no—
474C8—201no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3D5×#10412yes—
478C2×C3#6524611yescharacteristic
479D3—81no—
480D3—401no—
481C5#7051211yescharacteristic, complemented, Sylow
482C22—22no—
483C22—121no—
484C22—122no—
485C22—601no—
486C22—602no—
487C22#9141611yescharacteristic
488C22#9142011yescharacteristic
489C22D5×(C2×D3)⋊C411yescharacteristic
490C4—54no—
491C4—64no—
492C4—102no—
493C4—121no—
494C4—304no—
495C4—601no—
496C4#9132611yescharacteristic
497C4#9140611yescharacteristic
498C4#9144611yescharacteristic
499C4#9156711yescharacteristic
500C3#1060114911yescharacteristic, complemented, Sylow
501C2—21no—
502C2—21no—
503C2—241no—
504C2—1201no—
505C2D5×#82512yes—
506C2#1174890911yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754572C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1962
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91109C2semidirect
3. C2×C5×#825C2semidirect
4. C3×#65407C2semidirect
5. C4×Dic3×Dic5C2semidirect
6. C2×#90980C2semidirect
7. C2×#90978C2semidirect
18. #91451C4semidirect
20. #91376C4semidirect
21. #91375C4semidirect
22. #91373C4semidirect
33. #65407D3semidirect
61. C4×Dic15D4semidirect
63. C4×C5×Dic3D4semidirect
79. C2×#825D5semidirect
217. C3×Dic5#104semidirect
257. C4×Dic3C22⋊D5semidirect
374. Dic5#825semidirect
413. C3×C5#1962semidirect
481. C5#70512semidirect
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×#911092
C2×C5×#8252
C3×#654072
C4×Dic3×Dic52
C2×#909802
C2×#909782
#106011493
#705125