Finite Group Databasebeta

← #14435447

Subgroups — #14435447

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#11754415C211yesmaximal, characteristic
2C2×#91333C211yesmaximal, characteristic, complemented
3#11750839C211yesmaximal, characteristic
4C5×#4722C211yesmaximal, characteristic, complemented
5C3×#65008C211yesmaximal, characteristic, complemented
6#11748565C211yesmaximal, characteristic, complemented
7#11748374C211yesmaximal, characteristic
8#11747858C212yesmaximal, complemented
9#11747857C212yesmaximal, complemented
10#11747835C212yesmaximal, complemented
11#11747778C212yesmaximal, complemented
12#10613186—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14#91819C2211yescharacteristic
15C2×#6706C2212yes—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C5×#924C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19#91552—21no—
20#91546—21no—
21C2×#6669—21no—
22C2×Dic3×Dic5—21no—
23#91418C2211yescharacteristic
24#91402—21no—
25#91388C2211yescharacteristic
26#91387—21no—
27#91375C2211yescharacteristic
28#91333—21no—
29#91333—21no—
30#91333C2212yes—
31#91333C2212yes—
32Dic5×Dic6C2211yescharacteristic
33C2×#6663C2212yes—
34C3×C5×C22⋊C8C2211yescharacteristic
35#91100C2212yes—
36C5×#818C2212yes—
37C5×#816C2212yes—
38C3×C22⋊#168C2211yescharacteristic
39C3×#3947C2212yes—
40C3×#3946C2212yes—
41#90985C2212yes—
42#90975C2212yes—
43#90969C2212yes—
44#79357—51nomaximal, Hall
45#65958—31no—
46C2×#4033—31no—
47C5×#484—31no—
48#65339—31no—
49#65257—31no—
50#65178—32no—
51#65166—32no—
52#65087—32no—
53#65078—32no—
54#65027—31no—
55#65008D311yescharacteristic, complemented
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59C2×D60C2311yescharacteristic
60C2×Dic30—21no—
61C2×Dic30—24no—
62C2×Dic30C2312yes—
63C22×C5×Dic3—21no—
64C2×C5×Dic6C2311yescharacteristic
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×#1200—21no—
68C2×C3×C5×C8C2312yes—
69#6714—21no—
70C4⋊Dic15C2311yescharacteristic
71#6706—24no—
72C5×#217—21no—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×C4⋊Dic3C2312yes—
76C5×Dic3⋊C4—21no—
77C3×C4×Dic5D411yescharacteristic
78C3×C4×Dic5D411yescharacteristic
79C3×C4×Dic5C2311yescharacteristic
80C3×C4×Dic5C2311yescharacteristic
81C2×C3×#168C2312yes—
82Dic3⋊Dic5—21no—
83Dic3⋊Dic5—21no—
84#6669—22no—
85#6669—22no—
86#6669—21no—
87#6667—21no—
88#6667—21no—
89#6667—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#4738—51no—
101#4735—51no—
102#4722D511yescharacteristic, complemented
103#4716—52no—
104#4710—52no—
105C22×Dic10—31no—
106C5×C22⋊Q8—31no—
107C2×C5×C4⋊C4—31no—
108#4093—31no—
109Q8×Dic5—31no—
110C2×#689—32no—
111#4076—31no—
112C2×#683—61no—
113C2×C4×Dic5—61no—
114C2×C4×Dic5C2×D311yescharacteristic
115C2×#677—32no—
116#4044—61no—
117#4039—31no—
118#4038—61no—
119#4036—31no—
120#4033—32no—
121#4033—32no—
122#4033—61no—
123#4033—61no—
124#4032—61no—
125#4027—61no—
126C5×#107—32no—
127C5×#103—32no—
128C5×C22⋊C8C2×D311yescharacteristic
129C22⋊#168C2×D311yescharacteristic
130#3948—32no—
131#3947C2×D312yes—
132#3946C2×D312yes—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142#1220—42no—
143C2×Dic15—24no—
144C2×Dic15—22no—
145C2×Dic15—21no—
146D60—22no—
147Dic30—24no—
148Dic30—22no—
149Dic30#4114yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—42no—
154C5×Dic6—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161#1200—42no—
162C3×C5×C8—22no—
163C3×#168—22no—
164C22×Dic6—51no—
165C2×C3×C42—51no—
166#930—51no—
167#929—101no—
168C4×#67—101no—
169C2×C4⋊Dic3C2×D511yescharacteristic
170#924C2×D511yescharacteristic
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—101no—
173C2×Dic12—52no—
174C2×#204—52no—
175#876—101no—
176#875—51no—
177C4×D12—51no—
178#872—101no—
179#870—51no—
180C4×Dic6—51no—
181C4×Dic6—52no—
182C4×Dic6—52no—
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#818C2×D512yes—
191#817—52no—
192#816—52no—
193#816—52no—
194#816C2×D512yes—
195C2×C5×Q8—31no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C22×Dic5—61no—
200C22×Dic5D1211yescharacteristic
201C22×Dic5D1211yescharacteristic
202C2×D20—31no—
203C2×C4×D5—61no—
204C2×Dic10—32no—
205C2×Dic10—64no—
206C2×Dic10—61no—
207C2×C5×C8C22×D312yes—
208C5×C4⋊C4—32no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C22⋊C4—61no—
213#689—64no—
214#685—61no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—31no—
219C4⋊Dic5—61no—
220C4⋊Dic5—61no—
221#683—61no—
222#683—62no—
223#683—62no—
224C4×Dic5—61no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5D1211yescharacteristic
228C4×Dic5D1211yescharacteristic
229C4×Dic5C22×D311yescharacteristic
230C4×Dic5C22×D311yescharacteristic
231C2×#168C22×D312yes—
232#677—64no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—31no—
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×C5C2×#4112yes—
253Dic15—24no—
254Dic15—41no—
255C3×Dic5—21no—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C5×Dic3—41no—
260C5×Dic3—41no—
261C5×Dic3—42no—
262C22×C3×C4—51no—
263C22×C3×C4—51no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—21no—
267C22×Dic3—101no—
268C2×D12—51no—
269C2×C4×D3—101no—
270C2×Dic6—52no—
271C2×Dic6—104no—
272C2×Dic6—101no—
273C2×Dic6C22×D511yescharacteristic
274C2×C3×C8—52no—
275C2×C3×C8C22×D512yes—
276C3×C42—51no—
277C3×C42—51no—
278C3×C42—51no—
279C3×C42—51no—
280#217—21no—
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⋊Dic3C22×D511yescharacteristic
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—21no—
290Dic3⋊C4—102no—
291Dic3⋊C4—102no—
292Dic3⋊C4—101no—
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295C4×Dic3—102no—
296C4×Dic3—102no—
297C4×Dic3—101no—
298Dic12—104no—
299#204—104no—
300C23×C5C2×D1211yescharacteristic
301C22×D5—61no—
302C5×Q8—62no—
303C2×C4×C5—22no—
304C2×C4×C5—62no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5—122no—
308C2×C4×C5C2×D1211yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—122no—
311C2×Dic5—22no—
312C2×Dic5—41no—
313C2×Dic5—64no—
314C2×Dic5—62no—
315C2×Dic5—61no—
316C2×Dic5C2×D1211yescharacteristic
317C2×Dic5C2×D1211yescharacteristic
318C2×Dic5C2×D1211yescharacteristic
319C2×Dic5C2×D1211yescharacteristic
320D20—62no—
321C4×D5—122no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325C5×C8—22no—
326#168—22no—
327C22×Q8—151no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—31no—
335#121—151no—
336C4×Q8—152no—
337C4×Q8—152no—
338C4×Q8—151no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—301no—
346C2×C42—51no—
347C2×C42—301no—
348#107—32no—
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
362D15—81no—
363C23×C3D4×D511yescharacteristic
364C22×D3—101no—
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—202no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—42no—
379C2×Dic3—104no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382D12—102no—
383C4×D3—202no—
384Dic6—22no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
388C3×C8—22no—
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—121no—
399C4×C5—122no—
400C4×C5—121no—
401C4×C5D3×#4112yes—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—21no—
406Dic5—64no—
407Dic5—121no—
408C2×Q8—31no—
409C2×Q8—152no—
410C2×Q8—304no—
411C2×Q8—301no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—61no—
417C22×C4—301no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—52no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4—302no—
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#406412yes—
450C22×C3C2×D4×D511yescharacteristic
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—21no—
455C3×C4—101no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—101no—
459C3×C4D5×#4112yes—
460Dic3—41no—
461Dic3—42no—
462Dic3—41no—
463Dic3—104no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#552411yescharacteristic
467C2×C5C2×#90911yescharacteristic
468C2×C5#574811yescharacteristic
469D5—241no—
470C23—301no—
471C23D5×D1211yescharacteristic
472Q8—62no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—51no—
480C2×C4—51no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—102no—
487C2×C4—122no—
488C2×C4—201no—
489C2×C4—304no—
490C2×C4—302no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D5×D1211yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—22no—
496C8—102no—
497C2×C3—22no—
498C2×C3#6599011yescharacteristic
499C2×C3C2×#406411yescharacteristic
500C2×C3#6610711yescharacteristic
501D3—401no—
502C5#7935711yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9126112yes—
509C22C2×D5×D1211yescharacteristic
510C4—21no—
511C4—101no—
512C4—101no—
513C4—101no—
514C4—101no—
515C4—122no—
516C4—121no—
517C4—121no—
518C4—304no—
519C4—601no—
520C4#9202412yes—
521C3#1061318611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175287211yescharacteristic
525C2C2×#9126111yescharacteristic
526C2#1175402211yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radical#91819C22
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×#91333C2semidirect
4. C5×#4722C2semidirect
5. C3×#65008C2semidirect
6. #11748565C2semidirect
8. #11747858C2semidirect
9. #11747857C2semidirect
10. #11747835C2semidirect
11. #11747778C2semidirect
55. #65008D3semidirect
102. #4722D5semidirect
446. C3×C5#3117semidirect
502. C5#79357semidirect
521. C3#10613186semidirect

Maximal subgroups

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

subgroupindex
#117544152
C2×#913332
#117508392
C5×#47222
C3×#650082
#117485652
#117483742
#117478582
#117478572
#117478352
#117477782
#106131863
#793575