Finite Group Databasebeta

← #14435441

Subgroups — #14435441

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
1C3×#65934C211yesmaximal, characteristic
2C2×#91333C211yesmaximal, characteristic, complemented
3#11751141C211yesmaximal, characteristic
4C5×#5034C211yesmaximal, characteristic
5#11749004C212yesmaximal, complemented
6#11749002C212yesmaximal, complemented
7#11748564C211yesmaximal, characteristic, complemented
8#11748461C211yesmaximal, characteristic, complemented
9#11748333C211yesmaximal, characteristic, complemented
10#11747286C212yesmaximal, complemented
11#11747269C212yesmaximal, complemented
12#10613042—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C3×C5×#121C2211yescharacteristic
15C2×#6716C2212yes—
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C3×#4082C2211yescharacteristic
18C3×#4081—21no—
19C3×D4×Dic5—21no—
20C3×D4×Dic5C2211yescharacteristic
21C3×#4070C2211yescharacteristic
22C2×C3×C4×Dic5C2211yescharacteristic
23C3×#4036C2211yescharacteristic
24C3×#4033C2211yescharacteristic
25C3×#4025—21no—
26C3×#4023—21no—
27C2×#6669—21no—
28C2×Dic3×Dic5—21no—
29#91333—21no—
30#91333—21no—
31#91333C2212yes—
32#91333C2212yes—
33C2×#6662C2212yes—
34#91114C2211yescharacteristic
35#91094C2212yes—
36C5×#832C2212yes—
37C5×#830C2211yescharacteristic
38C5×#808C2212yes—
39#90989C2212yes—
40#90982C2212yes—
41#90974C2212yes—
42#90970C2212yes—
43#90952C2212yes—
44#83153—51nomaximal, Hall
45#65934D311yescharacteristic
46C2×#4033—31no—
47C5×#481—31no—
48#65329—31no—
49#65259—31no—
50#65146—32no—
51#65142—32no—
52#65056—32no—
53#65046—32no—
54#65028—31no—
55#65008—31no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C2×Dic30—21no—
61C2×Dic30—24no—
62C2×Dic30C2312yes—
63C22×C5×Dic3—21no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×C3×Dic10C2311yescharacteristic
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C22⋊C4—21no—
70#6716—24no—
71C2×C3⋊#168C2312yes—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2312yes—
74C2×C5×C3⋊C8C2312yes—
75C3×C22⋊Dic5—21no—
76C3×C22⋊Dic5—21no—
77C3×C22⋊Dic5—21no—
78C3×C22⋊Dic5—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×#683—21no—
82C3×#683—21no—
83C3×#683—21no—
84C3×C4×Dic5—21no—
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5C2311yescharacteristic
88C3×C4×Dic5C2311yescharacteristic
89#6669—22no—
90#6669—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6662—24no—
94C3×#529—51no—
95C2×C4×Dic6—51no—
96#5063—52no—
97#5054—52no—
98#5050—51no—
99#5044—51no—
100#5040—51no—
101#5034D511yescharacteristic
102#5030—52no—
103#5018—52no—
104#4926—51no—
105C22×Dic10—31no—
106C5×#121C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108#4082C2×D311yescharacteristic
109#4081—21no—
110D4×Dic5—21no—
111D4×Dic5C2×D311yescharacteristic
112C2×#687—32no—
113#4070C2×D311yescharacteristic
114C2×#683—61no—
115C2×C4×Dic5—61no—
116C2×C4×Dic5C2×D311yescharacteristic
117C2×Dic20—32no—
118#4036C2×D311yescharacteristic
119#4033—32no—
120#4033—32no—
121#4033—61no—
122#4033—61no—
123#4033C2×D311yescharacteristic
124#4025—21no—
125#4023—21no—
126C5×#106—32no—
127C5×#102—32no—
128C5×C22⋊C8—31no—
129C22⋊#168—31no—
130#3948—32no—
131#3947—32no—
132#3946—32no—
133#3942—32no—
134#3942—32no—
135#3939—32no—
136#3117—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C3×C5×D4—22no—
140C3×C5×D4—42no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—24no—
146C2×Dic15—22no—
147Dic30—24no—
148Dic30—22no—
149Dic30#4114yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—42no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—41no—
156C2×C3×Dic5—42no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161C3×Dic10—22no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C22×Dic6—51no—
165C3×#126—101no—
166C3×#125—51no—
167C3×#124—51no—
168C3×#123—101no—
169C3×C22⋊Q8—51no—
170C3×#121C2×D511yescharacteristic
171C3×C4×Q8—51no—
172C3×C4×D4—51no—
173C3×C4×D4—101no—
174C3×#117—101no—
175C2×C3×C42—51no—
176C2×#216—52no—
177C2×#214—52no—
178C2×C4⋊Dic3C2×D511yescharacteristic
179C2×Dic3⋊C4—101no—
180C2×C4×Dic3—101no—
181C4×Dic6—52no—
182C4×Dic6—52no—
183C4×Dic6—101no—
184C4×Dic6—101no—
185#835—52no—
186#832C2×D512yes—
187#830—51no—
188#830C2×D511yescharacteristic
189#810—52no—
190#810—52no—
191#808C2×D512yes—
192#807—52no—
193C4⋊(C3⋊C8)—52no—
194#803—52no—
195C2×C5×D4—21no—
196C2×C5×D4C22×D311yescharacteristic
197C22×C4×C5—61no—
198C22×C4×C5C22×D311yescharacteristic
199C22×Dic5—21no—
200C22×Dic5—61no—
201C22×Dic5#6711yescharacteristic
202C22×Dic5#6711yescharacteristic
203C2×Dic10—32no—
204C2×Dic10—64no—
205C2×Dic10—61no—
206C2×Dic10C22×D311yescharacteristic
207C2×C5×C8—32no—
208C5×C4⋊C4—32no—
209C5×C4⋊C4—61no—
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C22⋊C4—21no—
212C22⋊Dic5—21no—
213C22⋊Dic5—21no—
214C22⋊Dic5—21no—
215C22⋊Dic5—21no—
216#687—64no—
217C4⋊Dic5—21no—
218C4⋊Dic5C22×D311yescharacteristic
219#683—21no—
220#683—21no—
221#683—21no—
222#683—62no—
223#683—62no—
224C4×Dic5—21no—
225C4×Dic5—62no—
226C4×Dic5—62no—
227C4×Dic5#6711yescharacteristic
228C4×Dic5#6711yescharacteristic
229C4×Dic5C22×D311yescharacteristic
230C4×Dic5C22×D311yescharacteristic
231C2×#168—32no—
232Dic20—64no—
233#529—51no—
234C2×C4×Q8—151no—
235#484—151no—
236#481—31no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—151no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5#13712yes—
250C22×C3×C5C22×D411yescharacteristic
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×#4112yes—
254Dic15—24no—
255C3×Dic5—21no—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—41no—
260C3×Dic5—41no—
261C5×Dic3—42no—
262C2×C3×Q8—51no—
263C2×C3×D4—21no—
264C2×C3×D4C22×D511yescharacteristic
265C22×C3×C4—51no—
266C22×C3×C4—51no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—101no—
271C2×Dic6—52no—
272C2×Dic6—104no—
273C2×Dic6—101no—
274C3×C4⋊C4—51no—
275C3×C4⋊C4—101no—
276C3×C4⋊C4—101no—
277C3×C4⋊C4—101no—
278C3×C4⋊C4—101no—
279C3×C4⋊C4C22×D511yescharacteristic
280C3×C22⋊C4—21no—
281C3×C22⋊C4—101no—
282C3×C22⋊C4—101no—
283C3×C22⋊C4—101no—
284C3×C22⋊C4—101no—
285C3×C42—51no—
286C3×C42—51no—
287C3×C42—51no—
288C3×C42—51no—
289C3×C42—101no—
290#216—104no—
291#214—104no—
292C4⋊Dic3—21no—
293C4⋊Dic3C22×D512yes—
294Dic3⋊C4—102no—
295Dic3⋊C4—102no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8C22×D512yes—
300C23×C5—21no—
301C23×C5C2×#6711yescharacteristic
302C5×D4—22no—
303C5×D4—42no—
304C2×C4×C5—22no—
305C2×C4×C5—21no—
306C2×C4×C5—62no—
307C2×C4×C5—122no—
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C2×Dic5—22no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—41no—
314C2×Dic5—42no—
315C2×Dic5—64no—
316C2×Dic5—62no—
317C2×Dic5C2×#6711yescharacteristic
318C2×Dic5C2×#6711yescharacteristic
319C2×Dic5C2×#6711yescharacteristic
320C2×Dic5C2×#6711yescharacteristic
321Dic10—22no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325C5×C8—62no—
326#168—62no—
327C22×Q8—151no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—101no—
331#125—51no—
332#124—51no—
333#123—101no—
334C22⋊Q8—51no—
335#121D3×D511yescharacteristic
336C4×Q8—51no—
337C4×Q8—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—51no—
342C4×D4—101no—
343#117—101no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—301no—
346C2×C42—51no—
347C2×C42—301no—
348#107—152no—
349#106—32no—
350C4⋊C8—152no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—32no—
355C22⋊C8—31no—
356C22⋊C8—151no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5—81no—
360C2×C3×C5#52511yescharacteristic
361C2×C3×C5C2×#13711yescharacteristic
362C2×C3×C5#57511yescharacteristic
363C23×C3—21no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—102no—
366C3×D4—22no—
367C3×D4—42no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—51no—
371C2×C3×C4—51no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—102no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—201no—
378C2×C3×C4—202no—
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381C2×Dic3—22no—
382C2×Dic3—42no—
383C2×Dic3—104no—
384C2×Dic3—102no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
388C3⋊C8—22no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—41no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5#95112yes—
396C22×C5C22×#6711yescharacteristic
397C4×C5—21no—
398C4×C5—41no—
399C4×C5—122no—
400C4×C5D3×#4112yes—
401Dic5—21no—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—41no—
406Dic5—41no—
407Dic5—64no—
408C2×Q8—51no—
409C2×Q8—152no—
410C2×Q8—304no—
411C2×Q8—301no—
412C2×D4—21no—
413C2×D4C2×D3×D511yescharacteristic
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—61no—
417C22×C4—101no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—32no—
423C2×C8—152no—
424C4⋊C4—32no—
425C4⋊C4—51no—
426C4⋊C4—61no—
427C4⋊C4—101no—
428C4⋊C4—101no—
429C4⋊C4—101no—
430C4⋊C4—101no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4C2×D3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—101no—
436C22⋊C4—101no—
437C22⋊C4—101no—
438C22⋊C4—101no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—101no—
444C42—302no—
445C42—302no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3#406112yes—
453C22×C3C2×D4×D511yescharacteristic
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—201no—
461C3×C4—201no—
462C3×C4D5×#4112yes—
463Dic3—42no—
464Dic3—104no—
465C2×C5—22no—
466C2×C5—81no—
467C2×C5#582211yescharacteristic
468C2×C5C2×#95111yescharacteristic
469C2×C5#582811yescharacteristic
470C23—21no—
471C23D5×#6711yescharacteristic
472Q8—102no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—22no—
477D4—42no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—51no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—62no—
485C2×C4—102no—
486C2×C4—101no—
487C2×C4—101no—
488C2×C4—122no—
489C2×C4—201no—
490C2×C4—202no—
491C2×C4—304no—
492C2×C4—302no—
493C2×C4D5×#6711yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—62no—
496C8—302no—
497C2×C3—22no—
498C2×C3—81no—
499C2×C3#6599011yescharacteristic
500C2×C3C2×#406111yescharacteristic
501C2×C3#6610711yescharacteristic
502C5#8315311yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22#9148412yes—
509C22C2×D5×#6711yescharacteristic
510C4—21no—
511C4—41no—
512C4—101no—
513C4—101no—
514C4—101no—
515C4—101no—
516C4—122no—
517C4—201no—
518C4—201no—
519C4—304no—
520C4#9202412yes—
521C3#1061304211yescharacteristic, complemented, Sylow
522C2—22no—
523C2—81no—
524C2C2×#9148411yescharacteristic
525C2#1175480011yescharacteristic
526C2#1175534311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#91333C2semidirect
5. #11749004C2semidirect
6. #11749002C2semidirect
7. #11748564C2semidirect
8. #11748461C2semidirect
9. #11748333C2semidirect
10. #11747286C2semidirect
11. #11747269C2semidirect
446. C3×C5#3117semidirect
502. C5#83153semidirect
521. C3#10613042semidirect

Maximal subgroups

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

subgroupindex
C3×#659342
C2×#913332
#117511412
C5×#50342
#117490042
#117490022
#117485642
#117484612
#117483332
#117472862
#117472692
#106130423
#831535