Finite Group Databasebeta

← #14435502

Subgroups — #14435502

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×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C3×#65215C211yesmaximal, characteristic, complemented
4#11748561C211yesmaximal, characteristic, complemented
5#11748544C211yesmaximal, characteristic
6#11748464C211yesmaximal, characteristic, complemented
7#11748374C211yesmaximal, characteristic
8#11747102C212yesmaximal, complemented
9#11747093C212yesmaximal, complemented
10#11747058C212yesmaximal, complemented
11#11746965C212yesmaximal, complemented
12#10614176—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
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×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4—21no—
27C2×C4×C5×Dic3—21no—
28C4×C5×Dic6—21no—
29C4×C5×Dic6—21no—
30C4×C5×Dic6C2212yes—
31C4×C5×Dic6C2212yes—
32C2×#6663C2212yes—
33C2×#6660C2212yes—
34C3×C22⋊#168C2211yescharacteristic
35C3×C22⋊#168C2211yescharacteristic
36C3×C4⋊#168C2212yes—
37C3×#3935C2212yes—
38#90988C2212yes—
39#90985C2212yes—
40#90975C2212yes—
41#90973C2212yes—
42#90973C2212yes—
43#90969C2212yes—
44#79357—51nomaximal, Hall
45C2×C4×C5×Q8—31no—
46#65813—31no—
47#65517—31no—
48#65516—31no—
49#65319—32no—
50#65317—32no—
51#65315—32no—
52#65311—32no—
53#65259—31no—
54#65257—31no—
55#65215D311yescharacteristic, complemented
56C22×C3×C4×C5D411yescharacteristic
57C22×C3×C4×C5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2311yescharacteristic
63C22×C5×Dic3—21no—
64C22×C5×Dic3—21no—
65C2×C5×Dic6—21no—
66C2×C5×Dic6—24no—
67C2×C5×Dic6C2312yes—
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—
84C5×C4⋊Dic3—21no—
85C5×C4⋊Dic3C2312yes—
86C5×Dic3⋊C4—22no—
87C5×Dic3⋊C4—22no—
88C4×C5×Dic3—22no—
89C4×C5×Dic3—22no—
90C2×C3×#168C2312yes—
91C2×C3×#168C2312yes—
92#6663—24no—
93#6660—24no—
94#5479—51no—
95C2×C4×Dic6D511yescharacteristic, complemented
96C3×#432—51no—
97#4845—52no—
98#4829—52no—
99#4739—51no—
100#4738—51no—
101#4735—51no—
102#4722—51no—
103#4716—52no—
104#4710—52no—
105C22×C5×Q8—31no—
106C4×C5×Q8—32no—
107C4×C5×Q8—32no—
108C4×C5×Q8—61no—
109C4×C5×Q8—61no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C4⋊C4—61no—
112C2×C42×C5—61no—
113C2×C42×C5C2×D311yescharacteristic
114C2×#689—32no—
115C2×#688—32no—
116#4076—31no—
117#4075—61no—
118C4×C22⋊D5—61no—
119#4070—31no—
120#4022—61no—
121#4021—31no—
122C4×D20—31no—
123#4018—61no—
124#4016—31no—
125C4×Dic10—31no—
126#3967—32no—
127#3967—32no—
128C22⋊#168C2×D311yescharacteristic
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3939—32no—
134C4⋊#168C2×D312yes—
135#3935C2×D312yes—
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×C5×Dic3—24no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—42no—
159C5×Dic6—24no—
160C5×Dic6—22no—
161C5×Dic6#4114yes—
162C3×#168—22no—
163C3×#168—22no—
164C22×Dic6C2×D511yescharacteristic
165C2×C3×C42C2×D511yescharacteristic
166#930—51no—
167#929—101no—
168C4×#67—101no—
169C2×C4⋊Dic3C2×D511yescharacteristic
170#924—51no—
171C2×Dic3⋊C4—21no—
172C2×C4×Dic3—21no—
173C2×Dic12—52no—
174C2×#204—52no—
175#876—101no—
176#875—51no—
177C4×D12—51no—
178#872—101no—
179#870—51no—
180C4×Dic6—21no—
181C4×Dic6—21no—
182C4×Dic6—51no—
183C4×Dic6C2×D512yes—
184C4×Dic6C2×D512yes—
185C3×C4⋊C8—52no—
186C3×C22⋊C8—51no—
187C3×C22⋊C8—51no—
188C3×#97—52no—
189#821—52no—
190#818—52no—
191#817—52no—
192#816—52no—
193#816—52no—
194#816—52no—
195C2×C5×Q8—32no—
196C2×C5×Q8—64no—
197C2×C5×Q8—61no—
198C22×C4×C5—61no—
199C22×C4×C5—61no—
200C22×C4×C5D1211yescharacteristic
201C22×C4×C5D1211yescharacteristic
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—61no—
204C2×D20—31no—
205C2×C4×D5—61no—
206C2×Dic10—31no—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—61no—
209C5×C4⋊C4—62no—
210C5×C4⋊C4—62no—
211C42×C5—62no—
212C42×C5—62no—
213C42×C5D1211yescharacteristic
214C42×C5D1211yescharacteristic
215C42×C5C22×D311yescharacteristic
216C42×C5C22×D311yescharacteristic
217C22⋊Dic5—61no—
218#689—64no—
219#688—64no—
220#685—61no—
221#685—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—31no—
225C4⋊Dic5—31no—
226#683—61no—
227#683—61no—
228#683—61no—
229#683—61no—
230C4×Dic5—61no—
231C2×#168C22×D312yes—
232C2×#168C22×D312yes—
233#529—151no—
234C2×C4×Q8—31no—
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—51no—
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—
260C5×Dic3—24no—
261C5×Dic3—42no—
262C22×C3×C4C22⋊D511yescharacteristic
263C22×C3×C4C22⋊D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C2×D12—51no—
269C2×C4×D3—101no—
270C2×Dic6—21no—
271C2×Dic6—24no—
272C2×Dic6—51no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—52no—
275C2×C3×C8—52no—
276C3×C42C22⋊D511yescharacteristic
277C3×C42C22⋊D511yescharacteristic
278C3×C42C22×D511yescharacteristic
279C3×C42C22×D511yescharacteristic
280#217—101no—
281(C2×D3)⋊C4—101no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284(C2×D3)⋊C4—101no—
285C4⋊Dic3—21no—
286C4⋊Dic3—51no—
287C4⋊Dic3—51no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—22no—
290Dic3⋊C4—22no—
291Dic3⋊C4—101no—
292Dic3⋊C4—101no—
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295C4×Dic3—22no—
296C4×Dic3—22no—
297C4×Dic3—101no—
298Dic12—104no—
299#204—104no—
300C23×C5C2×D1211yescharacteristic
301C22×D5—61no—
302C5×Q8—34no—
303C5×Q8—64no—
304C5×Q8—62no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—41no—
308C2×C4×C5—64no—
309C2×C4×C5—62no—
310C2×C4×C5—62no—
311C2×C4×C5—122no—
312C2×C4×C5C2×D1211yescharacteristic
313C2×C4×C5C2×D1211yescharacteristic
314C2×C4×C5C2×D1211yescharacteristic
315C2×C4×C5C2×D1211yescharacteristic
316C2×C4×C5C2×D1211yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—122no—
319C2×Dic5—61no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322D20—62no—
323C4×D5—122no—
324Dic10—62no—
325#168—22no—
326#168—22no—
327C22×Q8—31no—
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—32no—
337C4×Q8—32no—
338C4×Q8—61no—
339C4×Q8—61no—
340C4×Q8—151no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—61no—
346C2×C42—61no—
347C2×C42D3×D511yescharacteristic
348#107—152no—
349#106—152no—
350C4⋊C8—52no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—51no—
356C22⋊C8—51no—
357#97—52no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362D15—81no—
363C23×C3C2×C22⋊D511yescharacteristic
364C22×D3—101no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—41no—
368C2×C3×C4C2×C22⋊D511yescharacteristic
369C2×C3×C4C2×C22⋊D511yescharacteristic
370C2×C3×C4C2×C22⋊D511yescharacteristic
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×C3×C4C23×D511yescharacteristic
374#67—202no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—42no—
379C2×Dic3—101no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382D12—102no—
383C4×D3—202no—
384Dic6—24no—
385Dic6—22no—
386Dic6—102no—
387Dic6#70914yes—
388C3×C8—102no—
389C3×C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#90912yes—
393C22×C5C22×D1211yescharacteristic
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×C5—64no—
403C4×C5—122no—
404C4×C5D3×#4112yes—
405Dic5—121no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—32no—
409C2×Q8—64no—
410C2×Q8—61no—
411C2×Q8—151no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—301no—
417C22×C4#120311yescharacteristic
418C22×C4#120311yescharacteristic
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—52no—
423C2×C8—52no—
424C4⋊C4—32no—
425C4⋊C4—61no—
426C4⋊C4—62no—
427C4⋊C4—62no—
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—62no—
440C42—62no—
441C42—301no—
442C42#120311yescharacteristic
443C42#120311yescharacteristic
444C42C2×D3×D511yescharacteristic
445C42C2×D3×D511yescharacteristic
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#408812yes—
450C22×C3C22×C22⋊D511yescharacteristic
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×C4C2×#70912yes—
460Dic3—24no—
461Dic3—42no—
462Dic3—201no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#552411yescharacteristic
467C2×C5C2×#90911yescharacteristic
468C2×C5#574811yescharacteristic
469D5—241no—
470C23—301no—
471C23C2×#120311yescharacteristic
472Q8—34no—
473Q8—64no—
474Q8—62no—
475Q8—302no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—64no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—122no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—301no—
488C2×C4—602no—
489C2×C4C2×#120311yescharacteristic
490C2×C4C2×#120311yescharacteristic
491C2×C4C2×#120311yescharacteristic
492C2×C4C2×#120311yescharacteristic
493C2×C4C2×#120311yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—102no—
497C2×C3—22no—
498C2×C3#6612511yescharacteristic
499C2×C3C2×#408811yescharacteristic
500C2×C3#6615611yescharacteristic
501D3—401no—
502C5#7935711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9132112yes—
509C22C22×#120311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—64no—
516C4—122no—
517C4—601no—
518C4—601no—
519C4—601no—
520C4D3×#70912yes—
521C3#1061417611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175414511yescharacteristic
525C2C2×#9132111yescharacteristic
526C2#1175458411yescharacteristic
subgroupG/H
centerC22C22×#1203
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×C4×C5×Dic6C2semidirect
3. C3×#65215C2semidirect
4. #11748561C2semidirect
6. #11748464C2semidirect
8. #11747102C2semidirect
9. #11747093C2semidirect
10. #11747058C2semidirect
11. #11746965C2semidirect
55. #65215D3semidirect
95. C2×C4×Dic6D5semidirect
446. C3×C5#3117semidirect
502. C5#79357semidirect
521. C3#10614176semidirect

Maximal subgroups

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

subgroupindex
#117562382
C2×C4×C5×Dic62
C3×#652152
#117485612
#117485442
#117484642
#117483742
#117471022
#117470932
#117470582
#117469652
#106141763
#793575