Finite Group Databasebeta

← #14471839

Subgroups — #14471839

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756472C211yesmaximal, characteristic, complemented
2#11752648C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic
5#11749089C212yesmaximal, complemented
6#11748993C212yesmaximal, complemented
7#11748984C212yesmaximal, complemented
8#11748944C212yesmaximal, complemented
9C4×#6657C211yesmaximal, characteristic, complemented
10#11746963C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10613316—31nomaximal, Hall
13C3×C5×#127C2211yescharacteristic
14#91825—21no—
15#91825C2212yes—
16#91824—22no—
17D4×Dic15—21no—
18D4×Dic15C2212yes—
19C4×Dic30C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#686C2212yes—
23C3×C4×D20C2211yescharacteristic
24#91434C2212yes—
25#91421—22no—
26D5×C4⋊Dic3—21no—
27#91384C2212yes—
28#91360—21no—
29C2×#6657C2211yescharacteristic
30C5×#832C2212yes—
31C5×#832C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3964C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90988C2212yes—
36#90987C2211yescharacteristic
37#90983C2212yes—
38#90975C2212yes—
39#90974C2211yescharacteristic
40#90965C2211yescharacteristic
41#90951C2212yes—
42#80319—51nomaximal, Hall
43#66064—31no—
44#66047—31no—
45C5×#486—31no—
46#65380—31no—
47#65361D311yescharacteristic
48#65076—32no—
49#65057—32no—
50#65052—32no—
51#65045—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C22×Dic15—22no—
58C2×Dic30D411yescharacteristic
59C2×Dic30C2311yescharacteristic
60C2×C5×Dic6—21no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×D5×Dic3—22no—
64C3×C42×C5C2311yescharacteristic
65#6719—22no—
66#6719—22no—
67#6719—22no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71#6712D412yes—
72C4×Dic15—21no—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×#686—24no—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C2×C3×#168C2312yes—
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6665—22no—
85#6657—22no—
86#5713—51no—
87#5543—51no—
88C3×#459—51no—
89#5153—52no—
90Dic3×D8—52no—
91#5070D511yescharacteristic, complemented
92C4×#214—51no—
93#4850—51no—
94#4830—51no—
95#4768—52no—
96#4766—52no—
97C5×C4⋊Q8—31no—
98C5×#127C2×D311yescharacteristic
99#4092—62no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—61no—
105C2×#686C2×D312yes—
106C2×#677—31no—
107#4043—61no—
108#4039—32no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—31no—
114C5×#102—32no—
115C5×#102—32no—
116C4×C5×C8—31no—
117#3964C2×D312yes—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
125C4⋊#168C2×D311yescharacteristic
126#3361—151noSylow
127C23×C3×C5—22no—
128C22×C3×D5—21no—
129C3×C5×D4—22no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C3×C5×D4—81no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—82no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141Dic30—22no—
142Dic30—21no—
143Dic30—21no—
144C2×C5×Dic3—22no—
145C5×Dic6—81no—
146C2×C3×Dic5—21no—
147C3×D20—21no—
148C3×D20#4112yes—
149C3×C4×D5—42no—
150D5×Dic3—82no—
151C3×#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C2×C3×D8—52no—
155C3×#127C2×D511yescharacteristic
156C3×C4×D4—51no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—52no—
162D4×Dic3—101no—
163C2×#214—51no—
164C2×C4⋊Dic3—101no—
165#924—101no—
166#890—52no—
167#878—102no—
168#869C2×D511yescharacteristic
169C4×Dic6—51no—
170C4×Dic6—51no—
171C3×C4⋊C8—51no—
172C3×#102—52no—
173#832—51no—
174#832C2×D512yes—
175#832C2×D512yes—
176#818—52no—
177#816—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—51no—
181#808—51no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—61no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4C22×D312yes—
187C22×Dic5—62no—
188C2×D20C22×D311yescharacteristic
189C2×C4×D5—21no—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10—31no—
193C2×C5×C8—31no—
194C2×C5×C8—31no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201#686—24no—
202#685—21no—
203#685—62no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D311yescharacteristic
208#683—32no—
209#683—62no—
210#683—61no—
211C4×Dic5—32no—
212C4×Dic5—61no—
213C2×#168C22×D312yes—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—31no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—51no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C3×D5—22no—
231C2×C3×D5—41no—
232C2×C3×D5—41no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—41no—
240Dic15—41no—
241C3×Dic5—41no—
242C5×Dic3—42no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—51no—
246C2×C3×D4C22×D512yes—
247C22×C3×C4—101no—
248C22×Dic3—102no—
249C22×Dic3—102no—
250C2×Dic6—21no—
251C2×Dic6—51no—
252C2×Dic6—51no—
253C3×D8—104no—
254C2×C3×C8—52no—
255C3×C4⋊C4—51no—
256C3×C22⋊C4—101no—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#217—102no—
262#214—102no—
263C4⋊Dic3—21no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3—102no—
267C4⋊Dic3C22×D512yes—
268Dic3⋊C4—52no—
269Dic3⋊C4—102no—
270Dic3⋊C4—101no—
271C4×Dic3—52no—
272C4×Dic3—101no—
273C2×C3⋊C8C22×D511yescharacteristic
274C2×C3⋊C8C22×D511yescharacteristic
275C23×C5—22no—
276C22×D5—21no—
277C5×Q8—241no—
278C5×D4—22no—
279C5×D4—22no—
280C5×D4—42no—
281C5×D4—81no—
282C2×C4×C5—62no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—32no—
288C2×Dic5—32no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291C2×Dic5—242no—
292D20—21no—
293D20#23712yes—
294C4×D5—42no—
295C4×D5—242no—
296Dic10—62no—
297Dic10—61no—
298Dic10—61no—
299C5×C8—61no—
300C5×C8—61no—
301#168—22no—
302C2×SD16—151no—
303C2×D8—52no—
304C4⋊Q8—31no—
305#127D3×D511yescharacteristic
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—151no—
313C4×Q8—151no—
314C4×D4—51no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—51no—
322C4⋊C8—152no—
323#103—152no—
324#103—151no—
325#102—32no—
326#102—32no—
327#102—52no—
328#102—151no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5—82no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335C3×D5—42no—
336C23×C3—22no—
337C23×C3—101no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—42no—
341C3×D4—52no—
342C3×D4—81no—
343C3×D4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—202no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—52no—
351C2×Dic3—52no—
352C2×Dic3—101no—
353C2×Dic3—101no—
354C2×Dic3—402no—
355C2×Dic3—402no—
356Dic6—81no—
357Dic6—102no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—102no—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—22no—
368C2×D5—41no—
369C2×D5—41no—
370C4×C5—21no—
371C4×C5—122no—
372C4×C5#91212yes—
373C4×C5C2×#23711yescharacteristic
374C4×C5#101011yescharacteristic
375Dic5—41no—
376Dic5—62no—
377Dic5—62no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—61no—
381C2×Q8—151no—
382C2×Q8—151no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—51no—
386C2×D4C2×D3×D512yes—
387C22×C4—101no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—302no—
391D8—104no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—52no—
395C4⋊C4—32no—
396C4⋊C4—51no—
397C4⋊C4—61no—
398C4⋊C4—151no—
399C4⋊C4—152no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—101no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—152no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—102no—
417C22×C3—201no—
418C22×C3—201no—
419C22×C3C2×D4×D511yescharacteristic
420C3×C4—21no—
421C3×C4—201no—
422C3×C4#406212yes—
423C3×C4D5×#4111yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—42no—
426Dic3—102no—
427Dic3—102no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—82no—
431C2×C5#559811yescharacteristic
432C2×C5C2×#91211yescharacteristic
433C2×C5#577411yescharacteristic
434D5—42no—
435C23—22no—
436C23—101no—
437Q8—241no—
438Q8—302no—
439Q8—301no—
440Q8—301no—
441D4—22no—
442D4—22no—
443D4—42no—
444D4—52no—
445D4—81no—
446D4—101no—
447C2×C4—62no—
448C2×C4—101no—
449C2×C4—152no—
450C2×C4—152no—
451C2×C4—202no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—102no—
462C2×C3—82no—
463C2×C3—202no—
464C2×C3#6601111yescharacteristic
465C2×C3#6609111yescharacteristic
466C2×C3C2×#406211yescharacteristic
467C5#8031911yescharacteristic, complemented, Sylow
468C22—42no—
469C22—42no—
470C22—42no—
471C22—102no—
472C22—201no—
473C22—201no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—122no—
477C4—201no—
478C4—302no—
479C4—302no—
480C4—601no—
481C4—601no—
482C4#9149712yes—
483C4#9202011yescharacteristic
484C4D5×#23711yescharacteristic
485C3#1061331611yescharacteristic, complemented, Sylow
486C2—82no—
487C2—202no—
488C2#1175470411yescharacteristic
489C2C2×#9149711yescharacteristic
490C2#1175481611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC3×#65361C2
hypercenter#127D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11756472C2semidirect
2. #11752648C2semidirect
3. C5×#5070C2semidirect
5. #11749089C2semidirect
6. #11748993C2semidirect
7. #11748984C2semidirect
8. #11748944C2semidirect
9. C4×#6657C2semidirect
10. #11746963C2semidirect
11. #11746855C2semidirect
91. #5070D5semidirect
412. C3×C5#3361semidirect
467. C5#80319semidirect
485. C3#10613316semidirect

Maximal subgroups

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

subgroupindex
#117564722
#117526482
C5×#50702
C3×#653612
#117490892
#117489932
#117489842
#117489442
C4×#66572
#117469632
#117468552
#106133163
#803195