Finite Group Databasebeta

← #14435468

Subgroups — #14435468

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
1C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
2#11754422C211yesmaximal, characteristic
3#11751329C211yesmaximal, characteristic, complemented
4C3×#65516C211yesmaximal, characteristic
5#11749334C212yesmaximal, complemented
6#11749325C212yesmaximal, complemented
7#11749260C212yesmaximal, complemented
8#11749234C212yesmaximal, complemented
9#11748464C211yesmaximal, characteristic, complemented
10#11748372C211yesmaximal, characteristic
11#11748337C211yesmaximal, characteristic, complemented
12#10614176—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6718C2212yes—
15#91813C2211yescharacteristic
16C5×Q8×Dic3—21no—
17C5×Q8×Dic3—21no—
18C5×Q8×Dic3C2212yes—
19C5×Q8×Dic3C2212yes—
20C2×C5×C4⋊Dic3—21no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C4×C5×Dic3—21no—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×#688C2212yes—
25C3×#4076C2211yescharacteristic
26Dic3×C22⋊D5—21no—
27#91536—21no—
28Dic3×D20C2211yescharacteristic
29#91393—21no—
30#91381C2211yescharacteristic
31#91364C2211yescharacteristic
32#91363—21no—
33#91340C2211yescharacteristic
34#91119C2212yes—
35#91114C2211yescharacteristic
36C3×#3967C2212yes—
37C3×C22⋊#168C2211yescharacteristic
38#90988C2212yes—
39#90986C2212yes—
40Dic3⋊#168C2212yes—
41#90975C2212yes—
42#90964C2212yes—
43#90953C2212yes—
44#80031—51nomaximal, Hall
45C2×C4×C5×Q8—31no—
46#65813—31no—
47#65517—31no—
48#65516D311yescharacteristic
49#65319—32no—
50#65317—32no—
51#65315—32no—
52#65311—32no—
53#65259—31no—
54#65257—31no—
55#65215—31no—
56C2×C3×C5×Q8—24no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×Dic30C2311yescharacteristic
62C22×C5×Dic3—21no—
63C22×C5×Dic3D411yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C2×C3×C22⋊D5—21no—
66C2×C3×D20C2311yescharacteristic
67C2×D5×Dic3—21no—
68#6719—21no—
69#6718—24no—
70C4⋊Dic15C2311yescharacteristic
71#6712—21no—
72C2×C3⋊#168C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3—22no—
75C5×C4⋊Dic3—22no—
76C5×C4⋊Dic3C2312yes—
77C4×C5×Dic3—22no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3D411yescharacteristic
81C4×C5×Dic3C2311yescharacteristic
82C4×C5×Dic3C2311yescharacteristic
83C3×#688—24no—
84C3×#685—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C2×C3×#168C2312yes—
87#6669—21no—
88#6669—21no—
89#6668—21no—
90#6665—21no—
91#6665—21no—
92#6665—21no—
93Dic3×Dic5—21no—
94C2×Q8×Dic3D511yescharacteristic, complemented
95#5600—51no—
96C3×#448—51no—
97#5228—51no—
98#5166—52no—
99#5164—52no—
100#5034—51no—
101#4796—52no—
102#4789—52no—
103#4722—51no—
104#4719—51no—
105C22×C5×Q8C2×D311yescharacteristic
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—31no—
113C2×C42×C5—61no—
114C2×#689—32no—
115C2×#688C2×D312yes—
116#4076C2×D311yescharacteristic
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#3967C2×D312yes—
128C22⋊#168—31no—
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3939—32no—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C3×D5—21no—
139C3×C5×Q8—24no—
140C3×C5×Q8—22no—
141C3×C5×Q8#4114yes—
142C2×C3×C4×C5—24no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—21no—
148C2×Dic15—21no—
149Dic30—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—41no—
153C2×C5×Dic3—42no—
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C2×C5×Dic3C2×D411yescharacteristic
157C2×C5×Dic3C2×D411yescharacteristic
158C3×C22⋊D5—42no—
159C2×C3×Dic5—21no—
160C3×D20—22no—
161D5×Dic3—42no—
162C3⋊#168—22no—
163C3×#168—22no—
164C22×C3×Q8C2×D511yescharacteristic
165C2×C3×SD16—52no—
166C3×#121—51no—
167Q8×Dic3—21no—
168Q8×Dic3—21no—
169Q8×Dic3C2×D512yes—
170Q8×Dic3C2×D512yes—
171C2×#216—52no—
172#936—51no—
173#935—101no—
174D4×Dic3—51no—
175D4×Dic3—101no—
176C2×C4⋊Dic3—21no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178#924—51no—
179C2×C4×Dic3—21no—
180C2×C4×Dic3C2×D511yescharacteristic
181#890—51no—
182#887—51no—
183#879—101no—
184#877—101no—
185C3×#103—52no—
186C3×C22⋊C8—51no—
187#835—52no—
188#832—52no—
189#830—51no—
190#818—52no—
191#816—52no—
192#815—52no—
193Dic3⋊C8—52no—
194#808—52no—
195C2×C5×Q8—24no—
196C2×C5×Q8—21no—
197C2×C5×Q8C22×D312yes—
198C22×C4×C5—21no—
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—61no—
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—21no—
204C2×D20C22×D311yescharacteristic
205C2×C4×D5—61no—
206C2×Dic10—31no—
207C5×C4⋊C4—32no—
208C5×C4⋊C4—62no—
209C5×C4⋊C4—62no—
210C5×C4⋊C4—61no—
211C42×C5—31no—
212C42×C5—31no—
213C42×C5—31no—
214C42×C5—31no—
215C42×C5—62no—
216C42×C5—62no—
217C22⋊Dic5—61no—
218#689—64no—
219#688—24no—
220#685—21no—
221#685—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—31no—
225C4⋊Dic5C22×D311yescharacteristic
226#683—61no—
227#683—61no—
228#683—61no—
229#683—61no—
230C4×Dic5—61no—
231C2×#168—32no—
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—51no—
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×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C3×C4×C5—24no—
252C3×C4×C5—21no—
253C3×C4×C5C2×#4112yes—
254Dic15—41no—
255Dic15—41no—
256C3×Dic5—41no—
257C5×Dic3—21no—
258C5×Dic3—21no—
259C5×Dic3—21no—
260C5×Dic3—21no—
261C5×Dic3—42no—
262C2×C3×Q8—24no—
263C2×C3×Q8—21no—
264C2×C3×Q8C22×D512yes—
265C2×C3×D4—51no—
266C2×C3×D4—101no—
267C22×C3×C4—21no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—101no—
271C22×Dic3C22⋊D511yescharacteristic
272C22×Dic3C22⋊D511yescharacteristic
273C2×Dic6—51no—
274C3×SD16—104no—
275C2×C3×C8—52no—
276C3×C4⋊C4—51no—
277C3×C22⋊C4—101no—
278#217—101no—
279#217—101no—
280#217—101no—
281#217—101no—
282#216—104no—
283C4⋊Dic3—21no—
284C4⋊Dic3—22no—
285C4⋊Dic3—22no—
286C4⋊Dic3—51no—
287C4⋊Dic3—101no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—101no—
290Dic3⋊C4—101no—
291Dic3⋊C4—101no—
292C4×Dic3—22no—
293C4×Dic3—22no—
294C4×Dic3—101no—
295C4×Dic3C22⋊D511yescharacteristic
296C4×Dic3C22⋊D511yescharacteristic
297C4×Dic3C22×D511yescharacteristic
298C4×Dic3C22×D511yescharacteristic
299C2×C3⋊C8—52no—
300C23×C5D3×D411yescharacteristic
301C22×D5—21no—
302C5×Q8—24no—
303C5×Q8—22no—
304C5×Q8#23714yes—
305C2×C4×C5—24no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—31no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—121no—
315C2×C4×C5—122no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—42no—
319C2×Dic5—21no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322D20—22no—
323C4×D5—122no—
324Dic10—62no—
325#168—22no—
326#168—62no—
327C22×Q8D3×D511yescharacteristic
328C2×Q16—152no—
329C2×SD16—52no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—51no—
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—31no—
347C2×C42—61no—
348#107—152no—
349#106—152no—
350C4⋊C8—152no—
351#103—52no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—51no—
356C22⋊C8—151no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C3×D5—81no—
363C23×C3—101no—
364C23×C3C2×C22⋊D511yescharacteristic
365C3×Q8—24no—
366C3×Q8—22no—
367C3×Q8#70914yes—
368C3×D4—102no—
369C3×D4—202no—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—101no—
374C2×C3×C4C2×C22⋊D511yescharacteristic
375C2×C3×C4C23×D511yescharacteristic
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—41no—
379C2×Dic3—42no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382C2×Dic3—202no—
383C2×Dic3C2×C22⋊D511yescharacteristic
384C2×Dic3C2×C22⋊D511yescharacteristic
385C2×Dic3C2×C22⋊D511yescharacteristic
386C2×Dic3C2×C22⋊D511yescharacteristic
387Dic6—102no—
388C3×C8—102no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#91512yes—
393C22×C5C2×D3×D411yescharacteristic
394C2×D5—41no—
395C2×D5—41no—
396C2×D5—41no—
397C4×C5—24no—
398C4×C5—21no—
399C4×C5—61no—
400C4×C5—61no—
401C4×C5—61no—
402C4×C5—61no—
403C4×C5—122no—
404C4×C5C2×#23712yes—
405Dic5—41no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8—151no—
411C2×Q8C2×D3×D512yes—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—104no—
422C2×C8—52no—
423C2×C8—152no—
424C4⋊C4—32no—
425C4⋊C4—51no—
426C4⋊C4—62no—
427C4⋊C4—62no—
428C4⋊C4—61no—
429C4⋊C4—151no—
430C4⋊C4—301no—
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—62no—
444C42—62no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3#408812yes—
453C22×C3C22×C22⋊D511yescharacteristic
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—201no—
457C3×C4C2×#70912yes—
458Dic3—21no—
459Dic3—21no—
460Dic3—21no—
461Dic3—21no—
462Dic3—42no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#558611yescharacteristic
467C2×C5C2×#91511yescharacteristic
468C2×C5#577711yescharacteristic
469D5—81no—
470C23—101no—
471C23D3×C22⋊D511yescharacteristic
472Q8—24no—
473Q8—22no—
474Q8—302no—
475Q8#677914yes—
476D4—102no—
477D4—202no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—101no—
488C2×C4—121no—
489C2×C4—122no—
490C2×C4—301no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D3×C22⋊D511yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—302no—
497C2×C3—22no—
498C2×C3—401no—
499C2×C3#6612511yescharacteristic
500C2×C3C2×#408811yescharacteristic
501C2×C3#6615611yescharacteristic
502C5#8003111yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22#9151812yes—
509C22C2×D3×C22⋊D511yescharacteristic
510C4—24no—
511C4—21no—
512C4—61no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—122no—
517C4—201no—
518C4—601no—
519C4—601no—
520C4C2×#677912yes—
521C3#1061417611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—401no—
524C2#1175509011yescharacteristic
525C2C2×#9151811yescharacteristic
526C2#1175538811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q8×Dic3C2semidirect
3. #11751329C2semidirect
5. #11749334C2semidirect
6. #11749325C2semidirect
7. #11749260C2semidirect
8. #11749234C2semidirect
9. #11748464C2semidirect
11. #11748337C2semidirect
94. C2×Q8×Dic3D5semidirect
446. C3×C5#3117semidirect
502. C5#80031semidirect
521. C3#10614176semidirect

Maximal subgroups

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

subgroupindex
C2×C5×Q8×Dic32
#117544222
#117513292
C3×#655162
#117493342
#117493252
#117492602
#117492342
#117484642
#117483722
#117483372
#106141763
#800315