Finite Group Databasebeta

← #14435442

Subgroups — #14435442

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#11754410C211yesmaximal, characteristic
2C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
3#11750823C211yesmaximal, characteristic, complemented
4C5×#4738C211yesmaximal, characteristic
5C3×#65008C211yesmaximal, characteristic, complemented
6#11748561C211yesmaximal, characteristic, complemented
7#11748379C211yesmaximal, characteristic
8#11747961C212yesmaximal, complemented
9#11747855C212yesmaximal, complemented
10#11747835C212yesmaximal, complemented
11#11747769C212yesmaximal, complemented
12#10611762—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15#91813C2211yescharacteristic
16C5×#930C2211yescharacteristic
17C2×C5×#204C2212yes—
18C2×C3×C4×Dic5C2211yescharacteristic
19Dic5×#67—21no—
20C2×Dic3⋊Dic5—21no—
21#91539—21no—
22C2×Dic3×Dic5—21no—
23Dic5×D12C2211yescharacteristic
24#91398—21no—
25#91388C2211yescharacteristic
26#91373C2211yescharacteristic
27#91372—21no—
28#91333C2211yescharacteristic
29Dic5×Dic6—21no—
30Dic5×Dic6—21no—
31Dic5×Dic6C2212yes—
32Dic5×Dic6C2212yes—
33C2×#6663C2212yes—
34C3×C5×C22⋊C8C2211yescharacteristic
35#91102C2212yes—
36#91100C2212yes—
37C5×#816C2212yes—
38C3×C22⋊#168C2211yescharacteristic
39C3×#3947C2212yes—
40C3×#3946C2212yes—
41#90985C2212yes—
42#90973C2212yes—
43#90967C2212yes—
44#79357—51nomaximal, Hall
45C2×Q8×Dic5—31no—
46#65934—31no—
47C5×#448—31no—
48#65517—31no—
49#65455—32no—
50#65453—32no—
51#65323—31no—
52#65085—32no—
53#65078—32no—
54#65011—31no—
55#65008D311yescharacteristic, complemented
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C2×Dic30C2311yescharacteristic
59C2×C5×#67—21no—
60C22×C5×Dic3—21no—
61C2×C5×D12C2311yescharacteristic
62C2×C5×Dic6—21no—
63C2×C5×Dic6—24no—
64C2×C5×Dic6C2312yes—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×D3×Dic5—21no—
68C2×C3×C5×C8C2312yes—
69#6719—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73#6712—21no—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×#204—24no—
77C3×C4×Dic5D411yescharacteristic
78C3×C4×Dic5D411yescharacteristic
79C3×C4×Dic5C2311yescharacteristic
80C3×C4×Dic5C2311yescharacteristic
81C2×C3×#168C2312yes—
82Dic3⋊Dic5—22no—
83Dic3⋊Dic5—22no—
84Dic3⋊Dic5—21no—
85#6669—21no—
86#6669—21no—
87(C2×D3)⋊Dic5—21no—
88(C2×D3)⋊Dic5—21no—
89(C2×D3)⋊Dic5—21no—
90Dic3×Dic5—21no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6663—24no—
94#5479—51no—
95C2×C4×Dic6—51no—
96C3×#432—51no—
97#4845—52no—
98#4829—52no—
99#4739—51no—
100#4738D511yescharacteristic
101#4735—51no—
102#4722—51no—
103#4716—52no—
104#4710—52no—
105C22×C5×Q8—31no—
106C2×C5×SD16—32no—
107C5×#121—31no—
108Q8×Dic5—32no—
109Q8×Dic5—32no—
110Q8×Dic5—61no—
111Q8×Dic5—61no—
112C2×#689—32no—
113#4082—31no—
114#4081—61no—
115D4×Dic5—31no—
116D4×Dic5—61no—
117C2×C4⋊Dic5—31no—
118C2×C4⋊Dic5—61no—
119#4070—31no—
120C2×C4×Dic5—61no—
121C2×C4×Dic5C2×D311yescharacteristic
122#4036—31no—
123#4033—31no—
124#4025—61no—
125#4023—61no—
126C5×#103—32no—
127C5×C22⋊C8C2×D311yescharacteristic
128#3967—32no—
129#3964—32no—
130C22⋊#168C2×D311yescharacteristic
131#3950—32no—
132#3948—32no—
133#3947C2×D312yes—
134#3946C2×D312yes—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15—42no—
146Dic30—22no—
147C5×#67—42no—
148C2×C5×Dic3—24no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—21no—
151C5×D12—22no—
152C5×Dic6—24no—
153C5×Dic6—22no—
154C5×Dic6#4114yes—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161D3×Dic5—42no—
162C3×C5×C8—22no—
163C3×#168—22no—
164C22×Dic6C2×D511yescharacteristic
165C2×C3×C42—51no—
166#930C2×D511yescharacteristic
167#929—101no—
168C4×#67—101no—
169C2×C4⋊Dic3—51no—
170#924—51no—
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—101no—
173C2×Dic12—52no—
174C2×#204C2×D512yes—
175#876—101no—
176#875—51no—
177C4×D12—51no—
178#872—101no—
179#870—51no—
180C4×Dic6—52no—
181C4×Dic6—52no—
182C4×Dic6—51no—
183C4×Dic6—101no—
184C4×Dic6—101no—
185C3×C4⋊C8—52no—
186C3×C22⋊C8—51no—
187C3×C22⋊C8C2×D511yescharacteristic
188C3×#97—52no—
189#821—52no—
190#818—52no—
191#817—52no—
192#816—52no—
193#816—52no—
194#816C2×D512yes—
195C2×C5×Q8—32no—
196C2×C5×Q8—64no—
197C2×C5×Q8—61no—
198C2×C5×D4—31no—
199C2×C5×D4—61no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—61no—
203C22×Dic5—61no—
204C22×Dic5D1211yescharacteristic
205C22×Dic5D1211yescharacteristic
206C2×Dic10—31no—
207C5×SD16—64no—
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—31no—
210C5×C22⋊C4—61no—
211C22⋊Dic5—61no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214C22⋊Dic5—61no—
215#689—64no—
216C4⋊Dic5—32no—
217C4⋊Dic5—31no—
218C4⋊Dic5—61no—
219C4⋊Dic5—61no—
220C4⋊Dic5—62no—
221C4⋊Dic5—62no—
222#683—61no—
223#683—61no—
224#683—61no—
225C4×Dic5—61no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5D1211yescharacteristic
229C4×Dic5D1211yescharacteristic
230C4×Dic5C22×D311yescharacteristic
231C4×Dic5C22×D311yescharacteristic
232C2×#168C22×D312yes—
233#529—151no—
234C2×C4×Q8—151no—
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—31no—
241#441—152no—
242#440—152no—
243#432—51no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C3×C4×C5—21no—
252C3×C4×C5C2×#4112yes—
253Dic15—41no—
254Dic15—41no—
255Dic15—42no—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—21no—
260C5×Dic3—24no—
261C5×Dic3—41no—
262C22×C3×C4—51no—
263C22×C3×C4—51no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—21no—
267C22×Dic3—101no—
268C2×D12C22×D511yescharacteristic
269C2×C4×D3—101no—
270C2×Dic6—21no—
271C2×Dic6—24no—
272C2×Dic6—51no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—52no—
275C2×C3×C8C22×D512yes—
276C3×C42—51no—
277C3×C42—51no—
278C3×C42—51no—
279C3×C42—51no—
280#217—101no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284(C2×D3)⋊C4—101no—
285C4⋊Dic3—51no—
286C4⋊Dic3—52no—
287C4⋊Dic3—101no—
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—101no—
290Dic3⋊C4—101no—
291Dic3⋊C4—102no—
292Dic3⋊C4—102no—
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295C4×Dic3—102no—
296C4×Dic3—102no—
297C4×Dic3—101no—
298Dic12—104no—
299#204—24no—
300C23×C5—61no—
301C23×C5C2×D1211yescharacteristic
302C5×Q8—34no—
303C5×Q8—64no—
304C5×Q8—62no—
305C5×D4—62no—
306C5×D4—122no—
307C2×C4×C5—22no—
308C2×C4×C5—64no—
309C2×C4×C5—62no—
310C2×C4×C5—61no—
311C2×C4×C5C2×D1211yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—62no—
316C2×Dic5—61no—
317C2×Dic5—61no—
318C2×Dic5—122no—
319C2×Dic5—122no—
320C2×Dic5C2×D1211yescharacteristic
321C2×Dic5C2×D1211yescharacteristic
322C2×Dic5C2×D1211yescharacteristic
323C2×Dic5C2×D1211yescharacteristic
324Dic10—62no—
325C5×C8—22no—
326#168—22no—
327C22×Q8—31no—
328C2×Q16—152no—
329C2×SD16—32no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—31no—
336C4×Q8—151no—
337C4×Q8—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—301no—
346C2×C42—51no—
347C2×C42—301no—
348#107—152no—
349#106—152no—
350C4⋊C8—52no—
351#103—32no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—51no—
356C22⋊C8D3×D511yescharacteristic
357#97—52no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C5×D3—81no—
363C23×C3D4×D511yescharacteristic
364C22×D3—21no—
365C2×C3×C4—22no—
366C2×C3×C4—51no—
367C2×C3×C4—51no—
368C2×C3×C4—51no—
369C2×C3×C4—51no—
370C2×C3×C4—102no—
371C2×C3×C4—201no—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4C23×D511yescharacteristic
374#67—42no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—102no—
379C2×Dic3—101no—
380C2×Dic3—101no—
381C2×Dic3—202no—
382D12—22no—
383C4×D3—202no—
384Dic6—24no—
385Dic6—22no—
386Dic6—102no—
387Dic6#71114yes—
388C3×C8—22no—
389C3×C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—121no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5#90912yes—
396C22×C5C22×D1211yescharacteristic
397C4×C5—21no—
398C4×C5—64no—
399C4×C5—121no—
400C4×C5D3×#4112yes—
401Dic5—21no—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—121no—
406Dic5—122no—
407Dic5—121no—
408C2×Q8—32no—
409C2×Q8—64no—
410C2×Q8—61no—
411C2×Q8—151no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—61no—
417C22×C4—301no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—64no—
422C2×C8—52no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—31no—
425C4⋊C4—152no—
426C4⋊C4—151no—
427C4⋊C4—302no—
428C4⋊C4—302no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—61no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—302no—
444C42—302no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#406112yes—
450C22×C3C2×D4×D511yescharacteristic
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—101no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—101no—
459C3×C4C2×#71112yes—
460Dic3—24no—
461Dic3—41no—
462Dic3—201no—
463Dic3—202no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#552411yescharacteristic
468C2×C5C2×#90911yescharacteristic
469C2×C5#574811yescharacteristic
470C23—61no—
471C23D5×D1211yescharacteristic
472Q8—34no—
473Q8—64no—
474Q8—62no—
475Q8—302no—
476D4—62no—
477D4—122no—
478C2×C4—22no—
479C2×C4—51no—
480C2×C4—51no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—64no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—102no—
487C2×C4—201no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—301no—
491C2×C4—602no—
492C2×C4—602no—
493C2×C4D5×D1211yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—22no—
496C8—102no—
497C2×C3—22no—
498C2×C3#6592011yescharacteristic
499C2×C3C2×#406111yescharacteristic
500C2×C3#6611111yescharacteristic
501D3—81no—
502C5#7935711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9126012yes—
509C22C2×D5×D1211yescharacteristic
510C4—21no—
511C4—64no—
512C4—101no—
513C4—101no—
514C4—101no—
515C4—101no—
516C4—121no—
517C4—602no—
518C4—601no—
519C4—601no—
520C4D3×#71112yes—
521C3#1061176211yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175287111yescharacteristic
525C2C2×#9126011yescharacteristic
526C2#1175402111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC5×#930C22
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×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. C2×Dic5×Dic6C2semidirect
3. #11750823C2semidirect
5. C3×#65008C2semidirect
6. #11748561C2semidirect
8. #11747961C2semidirect
9. #11747855C2semidirect
10. #11747835C2semidirect
11. #11747769C2semidirect
55. #65008D3semidirect
446. C3×C5#3117semidirect
502. C5#79357semidirect
521. C3#10611762semidirect

Maximal subgroups

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

subgroupindex
#117544102
C2×Dic5×Dic62
#117508232
C5×#47382
C3×#650082
#117485612
#117483792
#117479612
#117478552
#117478352
#117477692
#106117623
#793575