Finite Group Databasebeta

← #14435443

Subgroups — #14435443

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#11754460C211yesmaximal, characteristic
2C2×#91344C211yesmaximal, characteristic, complemented
3#11750820C211yesmaximal, characteristic, complemented
4C5×#4738C211yesmaximal, characteristic
5C3×#65011C211yesmaximal, characteristic, complemented
6#11748559C211yesmaximal, characteristic, complemented
7#11748385C211yesmaximal, characteristic
8#11747887C212yesmaximal, complemented
9#11747865C212yesmaximal, complemented
10#11747829C212yesmaximal, complemented
11#11747816C212yesmaximal, complemented
12#10611762—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C5×#930C2211yescharacteristic
16C2×C5×#204C2212yes—
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C3×#4070C2211yescharacteristic
19#67⋊Dic5—21no—
20C2×Dic3⋊Dic5—21no—
21#91543—21no—
22C2×Dic3×Dic5—21no—
23#91435C2211yescharacteristic
24#91400—21no—
25#91384C2211yescharacteristic
26#91370C2211yescharacteristic
27#91367—21no—
28#91344—21no—
29#91344—21no—
30#91344C2212yes—
31#91344C2212yes—
32#91331C2211yescharacteristic
33C2×#6661C2212yes—
34C3×C5×C22⋊C8C2211yescharacteristic
35#91114C2211yescharacteristic
36#91099C2212yes—
37#91098C2212yes—
38C5×#816C2212yes—
39C3×#3950C2212yes—
40C3×#3948C2212yes—
41#90986C2212yes—
42#90972C2212yes—
43#90966C2212yes—
44#81455—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#65011D311yescharacteristic, complemented
55#65008—31no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15D411yescharacteristic
58C22×Dic15D411yescharacteristic
59C2×C5×#67—21no—
60C22×C5×Dic3—21no—
61C2×C5×D12C2311yescharacteristic
62C2×C5×Dic6—21no—
63C2×C5×Dic6—24no—
64C2×C5×Dic6C2312yes—
65C22×C3×Dic5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×D3×Dic5—21no—
68C2×C3×C5×C8C2312yes—
69C4×Dic15D411yescharacteristic
70C4×Dic15D411yescharacteristic
71C4×Dic15C2311yescharacteristic
72C4×Dic15C2311yescharacteristic
73C2×C3⋊#168C2312yes—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×#204—24no—
77C3×C22⋊Dic5—21no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2311yescharacteristic
80C3×C4⋊Dic5C2312yes—
81C3×#683—21no—
82Dic3⋊Dic5—22no—
83Dic3⋊Dic5—22no—
84Dic3⋊Dic5—21no—
85#6668—21no—
86#6668—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#6661—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#4738D511yescharacteristic
104#4719—51no—
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—61no—
118C2×C4⋊Dic5C2×D311yescharacteristic
119#4070C2×D311yescharacteristic
120C2×C4×Dic5—31no—
121C2×C4×Dic5—61no—
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⋊#168—31no—
131#3950C2×D312yes—
132#3948C2×D312yes—
133#3947—32no—
134#3946—32no—
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—41no—
144C2×Dic15C2×D411yescharacteristic
145C2×Dic15C2×D411yescharacteristic
146C2×Dic15C2×D411yescharacteristic
147C2×Dic15C2×D411yescharacteristic
148C5×#67—42no—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—21no—
152C5×D12—22no—
153C5×Dic6—24no—
154C5×Dic6—22no—
155C5×Dic6#4114yes—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—42no—
160C3×Dic10—22no—
161D3×Dic5—42no—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C22×Dic6C2×D511yescharacteristic
165C3×C22⋊Q8—51no—
166C2×C3×C4⋊C4—51no—
167#947—51no—
168Q8×Dic3—51no—
169C2×#216—52no—
170#930C2×D511yescharacteristic
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—51no—
173C2×C4×Dic3—101no—
174C2×#204C2×D512yes—
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#830—51no—
189#816C2×D512yes—
190#815—52no—
191Dic3⋊C8—52no—
192#810—52no—
193#809—52no—
194#808—52no—
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—21no—
203C22×Dic5—31no—
204C22×Dic5—31no—
205C22×Dic5—61no—
206C2×Dic10C22×D311yescharacteristic
207C5×SD16—64no—
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—31no—
210C5×C22⋊C4—61no—
211C22⋊Dic5—21no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214C22⋊Dic5—61no—
215#689—64no—
216C4⋊Dic5—21no—
217C4⋊Dic5—61no—
218C4⋊Dic5—62no—
219C4⋊Dic5—62no—
220C4⋊Dic5C22×D312yes—
221C4⋊Dic5C22×D311yescharacteristic
222#683—21no—
223#683—61no—
224#683—61no—
225C4×Dic5—31no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—61no—
230C4×Dic5—62no—
231C4×Dic5—62no—
232C2×#168—32no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—51no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—31no—
241#441—152no—
242#440—152no—
243#432—151no—
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—21no—
254Dic15—21no—
255Dic15—21no—
256Dic15—21no—
257C3×Dic5—41no—
258C3×Dic5—41no—
259C3×Dic5—42no—
260C5×Dic3—24no—
261C5×Dic3—41no—
262C2×C3×Q8—51no—
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—21no—
267C22×Dic3—51no—
268C22×Dic3—51no—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—101no—
271C2×Dic6—21no—
272C2×Dic6—24no—
273C2×Dic6C22×D512yes—
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—21no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284(C2×D3)⋊C4—101no—
285C4⋊Dic3—101no—
286C4⋊Dic3—101no—
287C4⋊Dic3C22×D511yescharacteristic
288Dic3⋊C4—101no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—51no—
292C4×Dic3—51no—
293C4×Dic3—51no—
294C4×Dic3—51no—
295C4×Dic3—101no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C2×C3⋊C8—52no—
299#204—24no—
300C23×C5—61no—
301C23×C5D3×D411yescharacteristic
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×C5D3×D411yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C2×Dic5—22no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—31no—
319C2×Dic5—31no—
320C2×Dic5—42no—
321C2×Dic5—62no—
322C2×Dic5—122no—
323C2×Dic5—121no—
324Dic10—22no—
325C5×C8—22no—
326#168—62no—
327C22×Q8—31no—
328C2×Q16—152no—
329C2×SD16—32no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—51no—
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—51no—
345C2×C4⋊C4—301no—
346C2×C42—151no—
347C2×C42—301no—
348#107—52no—
349#106—152no—
350C4⋊C8—152no—
351#103—32no—
352#103—52no—
353#103—152no—
354#102—152no—
355C22⋊C8—151no—
356C22⋊C8D3×D511yescharacteristic
357#97—152no—
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—
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×C4D4×D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—42no—
374C2×Dic3—24no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—51no—
378C2×Dic3—51no—
379C2×Dic3—51no—
380C2×Dic3—51no—
381C2×Dic3—102no—
382C2×Dic3—201no—
383D12—22no—
384C4×D3—202no—
385Dic6—24no—
386Dic6—22no—
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#91812yes—
396C22×C5C2×D3×D411yescharacteristic
397C4×C5—21no—
398C4×C5—64no—
399C4×C5—121no—
400C4×C5D3×#4112yes—
401Dic5—41no—
402Dic5—42no—
403Dic5—41no—
404Dic5—61no—
405Dic5—61no—
406Dic5—61no—
407Dic5—61no—
408C2×Q8—32no—
409C2×Q8—51no—
410C2×Q8—64no—
411C2×Q8—61no—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—64no—
422C2×C8—152no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—31no—
425C4⋊C4—52no—
426C4⋊C4—51no—
427C4⋊C4—101no—
428C4⋊C4—101no—
429C4⋊C4—302no—
430C4⋊C4—302no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—61no—
435C22⋊C4—101no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—151no—
440C42—151no—
441C42—151no—
442C42—151no—
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—201no—
456C3×C4—202no—
457C3×C4—201no—
458C3×C4C2×#71112yes—
459Dic3—24no—
460Dic3—41no—
461Dic3—101no—
462Dic3—101no—
463Dic3—101no—
464Dic3—101no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#565611yescharacteristic
468C2×C5C2×#91811yescharacteristic
469C2×C5#577311yescharacteristic
470C23—61no—
471C23#677711yescharacteristic
472Q8—34no—
473Q8—64no—
474Q8—62no—
475Q8—102no—
476D4—62no—
477D4—122no—
478C2×C4—22no—
479C2×C4—64no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—102no—
483C2×C4—101no—
484C2×C4—101no—
485C2×C4—151no—
486C2×C4—151no—
487C2×C4—151no—
488C2×C4—151no—
489C2×C4—202no—
490C2×C4—302no—
491C2×C4—602no—
492C2×C4—601no—
493C2×C4#677711yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—22no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6592011yescharacteristic
499C2×C3C2×#406111yescharacteristic
500C2×C3#6611111yescharacteristic
501D3—81no—
502C5#8145511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9128012yes—
509C22C2×#677711yescharacteristic
510C4—21no—
511C4—64no—
512C4—121no—
513C4—202no—
514C4—201no—
515C4—201no—
516C4—301no—
517C4—301no—
518C4—301no—
519C4—301no—
520C4D3×#71112yes—
521C3#1061176211yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175288211yescharacteristic
525C2C2×#9128011yescharacteristic
526C2#1175403611yescharacteristic
subgroupG/H
centerC22C2×#6777
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×#91344C2semidirect
3. #11750820C2semidirect
5. C3×#65011C2semidirect
6. #11748559C2semidirect
8. #11747887C2semidirect
9. #11747865C2semidirect
10. #11747829C2semidirect
11. #11747816C2semidirect
54. #65011D3semidirect
446. C3×C5#3117semidirect
502. C5#81455semidirect
521. C3#10611762semidirect

Maximal subgroups

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

subgroupindex
#117544602
C2×#913442
#117508202
C5×#47382
C3×#650112
#117485592
#117483852
#117478872
#117478652
#117478292
#117478162
#106117623
#814555