Finite Group Databasebeta

← #14435445

Subgroups — #14435445

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#11754440C211yesmaximal, characteristic
2C2×#91340C211yesmaximal, characteristic, complemented
3#11750839C211yesmaximal, characteristic
4C5×#4719C211yesmaximal, characteristic, complemented
5C3×#65011C211yesmaximal, characteristic, complemented
6#11748564C211yesmaximal, characteristic, complemented
7#11748454C211yesmaximal, characteristic
8#11747874C212yesmaximal, complemented
9#11747872C212yesmaximal, complemented
10#11747832C212yesmaximal, complemented
11#11747800C212yesmaximal, complemented
12#10611088—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14#91819C2211yescharacteristic
15C2×#6706C2212yes—
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C3×#4070C2211yescharacteristic
19#91556—21no—
20C2×#6669—21no—
21#91542—21no—
22C2×Dic3×Dic5—21no—
23#91428C2211yescharacteristic
24#91403—21no—
25#91381C2211yescharacteristic
26#91380—21no—
27#91374C2211yescharacteristic
28#91340—21no—
29#91340—21no—
30#91340C2212yes—
31#91340C2212yes—
32Dic3×Dic10C2211yescharacteristic
33C2×#6662C2212yes—
34C3×C5×C22⋊C8C2211yescharacteristic
35#91100C2212yes—
36C5×#830C2211yescharacteristic
37C5×#815C2212yes—
38C5×Dic3⋊C8C2212yes—
39C3×#3950C2212yes—
40C3×#3948C2212yes—
41#90987C2212yes—
42#90974C2212yes—
43#90968C2212yes—
44#81455—51nomaximal, Hall
45#65813—31no—
46C2×C4×Dic10—31no—
47C5×#432—31no—
48#65134—32no—
49#65118—32no—
50#65028—31no—
51#65027—31no—
52#65024—31no—
53#65011D311yescharacteristic, complemented
54#65005—32no—
55#64999—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59C2×D60C2311yescharacteristic
60C2×Dic30—21no—
61C2×Dic30—24no—
62C2×Dic30C2312yes—
63C22×C5×Dic3D411yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C22×C3×Dic5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×#1200—21no—
68C2×C3×C5×C8C2312yes—
69#6714—21no—
70C4⋊Dic15C2311yescharacteristic
71#6706—24no—
72C4×C5×Dic3D411yescharacteristic
73C4×C5×Dic3D411yescharacteristic
74C4×C5×Dic3C2311yescharacteristic
75C4×C5×Dic3C2311yescharacteristic
76C2×C5×C3⋊C8C2312yes—
77C3×C22⋊Dic5—21no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2311yescharacteristic
80C3×C4⋊Dic5C2312yes—
81C3×#683—21no—
82#6669—22no—
83#6669—22no—
84#6669—21no—
85#6668—21no—
86#6668—21no—
87#6667—21no—
88#6667—21no—
89#6667—21no—
90Dic3×Dic5—21no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6662—24no—
94#5624—51no—
95C2×#887—51no—
96C3×#484—51no—
97#5050—51no—
98#4968—51no—
99#4889—52no—
100#4877—52no—
101#4798—52no—
102#4789—52no—
103#4738—51no—
104#4719D511yescharacteristic, complemented
105C22×Dic10—31no—
106C2×C42×C5—31no—
107#4076—31no—
108#4075—61no—
109C4×C22⋊D5—61no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111#4070C2×D311yescharacteristic
112C2×#683—61no—
113C2×C4×Dic5—61no—
114C2×Dic20—32no—
115C2×#677—32no—
116#4022—61no—
117#4021—31no—
118C4×D20—31no—
119#4018—61no—
120#4016—31no—
121C4×Dic10—31no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C4×Dic10—61no—
125C4×Dic10—61no—
126C5×C4⋊C8—32no—
127C5×C22⋊C8—31no—
128C5×C22⋊C8C2×D311yescharacteristic
129C5×#97—32no—
130#3953—32no—
131#3950C2×D312yes—
132#3949—32no—
133#3948—32no—
134#3948—32no—
135#3948C2×D312yes—
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—41no—
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C2×C3×Dic5—22no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—42no—
160C3×Dic10—22no—
161#1200—42no—
162C3×C5×C8—22no—
163C5×C3⋊C8—22no—
164C22×Dic6—51no—
165C3×C22⋊Q8—51no—
166C2×C3×C4⋊C4—51no—
167#947—51no—
168Q8×Dic3—51no—
169C2×#216—52no—
170#930—51no—
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—101no—
173C2×C4×Dic3C2×D511yescharacteristic
174C2×#204—52no—
175#898—101no—
176#893—51no—
177#892—101no—
178#890—51no—
179#887—52no—
180#887—52no—
181#887—101no—
182#887—101no—
183#886—101no—
184#67⋊C4—101no—
185C3×#107—52no—
186C3×#103—52no—
187C3×C22⋊C8C2×D511yescharacteristic
188#830C2×D511yescharacteristic
189#816—52no—
190#815C2×D512yes—
191Dic3⋊C8C2×D512yes—
192#810—52no—
193#809—52no—
194#808—52no—
195C22×C4×C5—31no—
196C22×C4×C5—31no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C22×Dic5—21no—
200C22×Dic5—61no—
201C2×D20—31no—
202C2×C4×D5—61no—
203C2×Dic10—32no—
204C2×Dic10—64no—
205C2×Dic10—61no—
206C2×Dic10C22×D311yescharacteristic
207C2×C5×C8—32no—
208C2×C5×C8C22×D312yes—
209C42×C5—31no—
210C42×C5—31no—
211C42×C5—31no—
212C42×C5—31no—
213C22⋊Dic5—21no—
214#685—61no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—21no—
219C4⋊Dic5—31no—
220C4⋊Dic5C22×D311yescharacteristic
221C4⋊Dic5C22×D312yes—
222#683—21no—
223#683—61no—
224#683—61no—
225#683—62no—
226#683—62no—
227#683—61no—
228C4×Dic5—62no—
229C4×Dic5—62no—
230C4×Dic5—61no—
231Dic20—64no—
232#677—64no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—51no—
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×C5C2×#4112yes—
253Dic15—24no—
254Dic15—41no—
255C3×Dic5—41no—
256C3×Dic5—41no—
257C3×Dic5—42no—
258C5×Dic3—21no—
259C5×Dic3—21no—
260C5×Dic3—21no—
261C5×Dic3—21no—
262C2×C3×Q8—51no—
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—101no—
267C22×Dic3D2011yescharacteristic
268C22×Dic3D2011yescharacteristic
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×Dic6—52no—
272C2×Dic6—104no—
273C2×Dic6—101no—
274C2×C3×C8C22×D512yes—
275C3×C4⋊C4—52no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—101no—
278C3×C4⋊C4—101no—
279C3×C22⋊C4—101no—
280#216—104no—
281(C2×D3)⋊C4—101no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284(C2×D3)⋊C4—101no—
285C4⋊Dic3—51no—
286C4⋊Dic3—101no—
287C4⋊Dic3—101no—
288Dic3⋊C4—101no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—101no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3D2011yescharacteristic
295C4×Dic3D2011yescharacteristic
296C4×Dic3C22×D511yescharacteristic
297C4×Dic3C22×D511yescharacteristic
298C2×C3⋊C8C22×D512yes—
299#204—104no—
300C23×C5D3×D411yescharacteristic
301C22×D5—61no—
302C2×C4×C5—22no—
303C2×C4×C5—31no—
304C2×C4×C5—31no—
305C2×C4×C5—31no—
306C2×C4×C5—31no—
307C2×C4×C5—62no—
308C2×C4×C5—121no—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—122no—
312C2×Dic5—22no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—42no—
316C2×Dic5—64no—
317C2×Dic5—62no—
318C2×Dic5—61no—
319D20—62no—
320C4×D5—122no—
321Dic10—22no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325C5×C8—22no—
326C5×C8—62no—
327C22×Q8—151no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—51no—
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—51no—
345C2×C4⋊C4—301no—
346C2×C42—31no—
347C2×C42—301no—
348#107—52no—
349#106—152no—
350C4⋊C8—32no—
351#103—52no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—31no—
356C22⋊C8D3×D511yescharacteristic
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—102no—
366C2×C3×C4—22no—
367C2×C3×C4—102no—
368C2×C3×C4—101no—
369C2×C3×C4—101no—
370C2×C3×C4—202no—
371C2×C3×C4C2×D2011yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—202no—
374C2×Dic3—22no—
375C2×Dic3—41no—
376C2×Dic3—104no—
377C2×Dic3—102no—
378C2×Dic3—101no—
379C2×Dic3C2×D2011yescharacteristic
380C2×Dic3C2×D2011yescharacteristic
381C2×Dic3C2×D2011yescharacteristic
382C2×Dic3C2×D2011yescharacteristic
383D12—102no—
384C4×D3—202no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
388C3×C8—22no—
389C3⋊C8—22no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#91812yes—
393C22×C5C2×D3×D411yescharacteristic
394C2×D5—121no—
395C2×D5—121no—
396C2×D5—121no—
397C4×C5—21no—
398C4×C5—61no—
399C4×C5—61no—
400C4×C5—61no—
401C4×C5—61no—
402C4×C5D3×#4112yes—
403Dic5—41no—
404Dic5—41no—
405Dic5—42no—
406Dic5—64no—
407Dic5—121no—
408C2×Q8—51no—
409C2×Q8—152no—
410C2×Q8—304no—
411C2×Q8—301no—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—101no—
417C22×C4—301no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—32no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—52no—
425C4⋊C4—51no—
426C4⋊C4—101no—
427C4⋊C4—101no—
428C4⋊C4—151no—
429C4⋊C4—302no—
430C4⋊C4—302no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—101no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—302no—
444C42—302no—
445C42—301no—
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—201no—
456C3×C4—202no—
457C3×C4—201no—
458C3×C4D5×#4112yes—
459Dic3—21no—
460Dic3—21no—
461Dic3—21no—
462Dic3—21no—
463Dic3—104no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#565611yescharacteristic
467C2×C5C2×#91811yescharacteristic
468C2×C5#577311yescharacteristic
469D5—241no—
470C23—301no—
471C23D3×D2011yescharacteristic
472Q8—102no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—62no—
484C2×C4—102no—
485C2×C4—101no—
486C2×C4—101no—
487C2×C4—121no—
488C2×C4—202no—
489C2×C4—304no—
490C2×C4—302no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D3×D2011yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—22no—
496C8—62no—
497C2×C3—22no—
498C2×C3#6585811yescharacteristic
499C2×C3C2×#405511yescharacteristic
500C2×C3#6608211yescharacteristic
501D3—401no—
502C5#8145511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9126312yes—
509C22C2×D3×D2011yescharacteristic
510C4—21no—
511C4—61no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—202no—
516C4—201no—
517C4—201no—
518C4—304no—
519C4—601no—
520C4#9202412yes—
521C3#1061108811yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175287611yescharacteristic
525C2C2×#9126311yescharacteristic
526C2#1175402911yescharacteristic
subgroupG/H
centerC22C2×D3×D20
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×#91340C2semidirect
4. C5×#4719C2semidirect
5. C3×#65011C2semidirect
6. #11748564C2semidirect
8. #11747874C2semidirect
9. #11747872C2semidirect
10. #11747832C2semidirect
11. #11747800C2semidirect
53. #65011D3semidirect
104. #4719D5semidirect
446. C3×C5#3117semidirect
502. C5#81455semidirect
521. C3#10611088semidirect

Maximal subgroups

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

subgroupindex
#117544402
C2×#913402
#117508392
C5×#47192
C3×#650112
#117485642
#117484542
#117478742
#117478722
#117478322
#117478002
#106110883
#814555