Finite Group Databasebeta

← #14435504

Subgroups — #14435504

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
3C5×#4926C211yesmaximal, characteristic, complemented
4#11748556C211yesmaximal, characteristic, complemented
5#11748532C211yesmaximal, characteristic
6#11748454C211yesmaximal, characteristic
7#11748414C211yesmaximal, characteristic, complemented
8#11747091C212yesmaximal, complemented
9#11747065C212yesmaximal, complemented
10#11747054C212yesmaximal, complemented
11#11746944C212yesmaximal, complemented
12#10611088—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15#91819C2211yescharacteristic
16#91818—21no—
17C4×#1220—21no—
18#91813C2211yescharacteristic
19#91765—21no—
20#91764C2211yescharacteristic
21C4×D60C2211yescharacteristic
22#91761—21no—
23#91759C2211yescharacteristic
24C4×Dic30C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×#683—21no—
27C2×C3×C4×Dic5—21no—
28C3×C4×Dic10—21no—
29C3×C4×Dic10—21no—
30C3×C4×Dic10C2212yes—
31C3×C4×Dic10C2212yes—
32C2×#6662C2212yes—
33C2×#6658C2212yes—
34C5×#830C2211yescharacteristic
35C5×#830C2211yescharacteristic
36C5×C4⋊(C3⋊C8)C2212yes—
37C5×#803C2212yes—
38#90990C2212yes—
39#90987C2212yes—
40#90974C2212yes—
41#90971C2212yes—
42#90971C2212yes—
43#90968C2212yes—
44#82445—51nomaximal, Hall
45#65813—31no—
46C2×C4×Dic10D311yescharacteristic, complemented
47C5×#432—31no—
48#65134—32no—
49#65118—32no—
50#65028—31no—
51#65027—31no—
52#65024—31no—
53#65011—31no—
54#65005—32no—
55#64999—32no—
56C22×C3×C4×C5D411yescharacteristic
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2311yescharacteristic
63C22×C3×Dic5—21no—
64C22×C3×Dic5—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—24no—
67C2×C3×Dic10C2312yes—
68C3×C42×C5D411yescharacteristic
69C3×C42×C5D411yescharacteristic
70C3×C42×C5C2311yescharacteristic
71C3×C42×C5C2311yescharacteristic
72#6719—21no—
73#6714—21no—
74#6714—21no—
75#6714—21no—
76#6714—21no—
77C4⋊Dic15C2311yescharacteristic
78C4⋊Dic15C2311yescharacteristic
79#6712—21no—
80#6712—21no—
81#6712—21no—
82#6712—21no—
83C4×Dic15—21no—
84C2×C5×C3⋊C8C2312yes—
85C2×C5×C3⋊C8C2312yes—
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C3×#683—22no—
89C3×#683—22no—
90C3×C4×Dic5—22no—
91C3×C4×Dic5—22no—
92#6662—24no—
93#6658—24no—
94C2×C3×C4×Q8—51no—
95#5479—51no—
96#5228—51no—
97#5227—51no—
98#5030—52no—
99#5028—52no—
100#5026—52no—
101#5022—52no—
102#4970—51no—
103#4968—51no—
104#4926D511yescharacteristic, complemented
105C22×Dic10C2×D311yescharacteristic
106C2×C42×C5C2×D311yescharacteristic
107#4076—31no—
108#4075—61no—
109C4×C22⋊D5—61no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111#4070—31no—
112C2×#683—21no—
113C2×C4×Dic5—21no—
114C2×Dic20—32no—
115C2×#677—32no—
116#4022—61no—
117#4021—31no—
118C4×D20—31no—
119#4018—61no—
120#4016—31no—
121C4×Dic10—21no—
122C4×Dic10—21no—
123C4×Dic10—31no—
124C4×Dic10C2×D312yes—
125C4×Dic10C2×D312yes—
126C5×C4⋊C8—32no—
127C5×C22⋊C8—31no—
128C5×C22⋊C8—31no—
129C5×#97—32no—
130#3953—32no—
131#3950—32no—
132#3949—32no—
133#3948—32no—
134#3948—32no—
135#3948—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148#1220—42no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15—21no—
152D60—22no—
153C4×D15—42no—
154Dic30—22no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—42no—
159C3×Dic10—24no—
160C3×Dic10—22no—
161C3×Dic10#4114yes—
162C5×C3⋊C8—22no—
163C5×C3⋊C8—22no—
164C22×C3×Q8—51no—
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C2×C3×C4⋊C4—51no—
170C2×C3×C4⋊C4—101no—
171C2×C3×C42—101no—
172C2×C3×C42C2×D511yescharacteristic
173C2×#216—52no—
174C2×#215—52no—
175#930—51no—
176#929—101no—
177C4×#67—101no—
178#924—51no—
179#876—101no—
180#875—51no—
181C4×D12—51no—
182#872—101no—
183#870—51no—
184C4×Dic6—51no—
185#835—52no—
186#835—52no—
187#830C2×D511yescharacteristic
188#830C2×D511yescharacteristic
189#810—52no—
190#809—52no—
191#808—52no—
192#807—52no—
193C4⋊(C3⋊C8)C2×D512yes—
194#803C2×D512yes—
195C22×C4×C5#6711yescharacteristic
196C22×C4×C5#6711yescharacteristic
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C2×D20—31no—
202C2×C4×D5—61no—
203C2×Dic10—21no—
204C2×Dic10—24no—
205C2×Dic10—31no—
206C2×Dic10C22×D312yes—
207C2×C5×C8—32no—
208C2×C5×C8—32no—
209C42×C5#6711yescharacteristic
210C42×C5#6711yescharacteristic
211C42×C5C22×D311yescharacteristic
212C42×C5C22×D311yescharacteristic
213C22⋊Dic5—61no—
214#685—61no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5C22×D312yes—
222#683—22no—
223#683—22no—
224#683—61no—
225#683—61no—
226#683—61no—
227#683—61no—
228C4×Dic5—22no—
229C4×Dic5—22no—
230C4×Dic5—61no—
231Dic20—64no—
232#677—64no—
233#529—151no—
234C2×C4×Q8—51no—
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—151no—
241#441—152no—
242#440—152no—
243#432—31no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C3×C4×C5—21no—
252C3×C4×C5—21no—
253C3×C4×C5—21no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5C2×#4112yes—
257Dic15—41no—
258Dic15—41no—
259Dic15—41no—
260C3×Dic5—24no—
261C3×Dic5—42no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C22×C3×C4—101no—
266C22×C3×C4—101no—
267C22×C3×C4D2011yescharacteristic
268C22×C3×C4D2011yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C2×D12—51no—
272C2×C4×D3—101no—
273C2×Dic6—51no—
274C3×C4⋊C4—52no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4—101no—
278C3×C42—102no—
279C3×C42—102no—
280C3×C42D2011yescharacteristic
281C3×C42D2011yescharacteristic
282C3×C42C22×D511yescharacteristic
283C3×C42C22×D511yescharacteristic
284#217—101no—
285#216—104no—
286#215—104no—
287(C2×D3)⋊C4—101no—
288(C2×D3)⋊C4—101no—
289(C2×D3)⋊C4—101no—
290(C2×D3)⋊C4—101no—
291C4⋊Dic3—51no—
292C4⋊Dic3—51no—
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C2×C3⋊C8C22×D512yes—
299C2×C3⋊C8C22×D512yes—
300C23×C5C2×#6711yescharacteristic
301C22×D5—61no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—41no—
305C2×C4×C5C2×#6711yescharacteristic
306C2×C4×C5C2×#6711yescharacteristic
307C2×C4×C5C2×#6711yescharacteristic
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C2×#6711yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—122no—
312C2×Dic5—24no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—42no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319D20—62no—
320C4×D5—122no—
321Dic10—24no—
322Dic10—22no—
323Dic10—62no—
324Dic10#23514yes—
325C5×C8—62no—
326C5×C8—62no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—151no—
336C4×Q8—52no—
337C4×Q8—52no—
338C4×Q8—101no—
339C4×Q8—101no—
340C4×Q8—151no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C42—101no—
347C2×C42D3×D511yescharacteristic
348#107—152no—
349#106—152no—
350C4⋊C8—32no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—31no—
356C22⋊C8—31no—
357#97—32no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362D15—81no—
363C23×C3C2×D2011yescharacteristic
364C22×D3—101no—
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—41no—
371C2×C3×C4—104no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—202no—
375C2×C3×C4C2×D2011yescharacteristic
376C2×C3×C4C2×D2011yescharacteristic
377C2×C3×C4C2×D2011yescharacteristic
378C2×C3×C4C2×D2011yescharacteristic
379C2×C3×C4C2×D2011yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—202no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385D12—102no—
386C4×D3—202no—
387Dic6—102no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#94212yes—
393C22×C5C22×#6711yescharacteristic
394C2×D5—121no—
395C2×D5—121no—
396C2×D5—121no—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—21no—
402C4×C5C2×#23512yes—
403Dic5—24no—
404Dic5—42no—
405Dic5—121no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—52no—
409C2×Q8—104no—
410C2×Q8—101no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—301no—
417C22×C4#120211yescharacteristic
418C22×C4#120211yescharacteristic
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—32no—
423C2×C8—32no—
424C4⋊C4—52no—
425C4⋊C4—101no—
426C4⋊C4—102no—
427C4⋊C4—102no—
428C4⋊C4—151no—
429C4⋊C4—151no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—301no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—102no—
440C42—102no—
441C42—301no—
442C42#120211yescharacteristic
443C42#120211yescharacteristic
444C42C2×D3×D511yescharacteristic
445C42C2×D3×D511yescharacteristic
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#405512yes—
450C22×C3C22×D2011yescharacteristic
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—104no—
460C3×C4—202no—
461C3×C4D5×#4112yes—
462Dic3—201no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#579111yescharacteristic
467C2×C5C2×#94211yescharacteristic
468C2×C5#582211yescharacteristic
469D5—241no—
470C23—301no—
471C23C2×#120211yescharacteristic
472Q8—54no—
473Q8—104no—
474Q8—102no—
475Q8—302no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—104no—
482C2×C4—102no—
483C2×C4—102no—
484C2×C4—202no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—301no—
488C2×C4—602no—
489C2×C4C2×#120211yescharacteristic
490C2×C4C2×#120211yescharacteristic
491C2×C4C2×#120211yescharacteristic
492C2×C4C2×#120211yescharacteristic
493C2×C4C2×#120211yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—62no—
496C8—62no—
497C2×C3—22no—
498C2×C3#6585811yescharacteristic
499C2×C3C2×#405511yescharacteristic
500C2×C3#6608211yescharacteristic
501D3—401no—
502C5#8244511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9131512yes—
509C22C22×#120211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—104no—
516C4—202no—
517C4—601no—
518C4—601no—
519C4—601no—
520C4D5×#23512yes—
521C3#1061108811yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175415411yescharacteristic
525C2C2×#9131511yescharacteristic
526C2#1175456411yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
prime radical#91819C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic10C2semidirect
3. C5×#4926C2semidirect
4. #11748556C2semidirect
7. #11748414C2semidirect
8. #11747091C2semidirect
9. #11747065C2semidirect
10. #11747054C2semidirect
11. #11746944C2semidirect
46. C2×C4×Dic10D3semidirect
104. #4926D5semidirect
446. C3×C5#3117semidirect
502. C5#82445semidirect
521. C3#10611088semidirect

Maximal subgroups

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

subgroupindex
#117562382
C2×C3×C4×Dic102
C5×#49262
#117485562
#117485322
#117484542
#117484142
#117470912
#117470652
#117470542
#117469442
#106110883
#824455