Finite Group Databasebeta

← #14471662

Subgroups — #14471662

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756301C211yesmaximal, characteristic, complemented
2#11752648C211yesmaximal, characteristic, complemented
3C5×#5008C211yesmaximal, characteristic, complemented
4C3×C4×#686C211yesmaximal, characteristic
5#11748984C212yesmaximal
6#11748944C212yesmaximal, complemented
7#11747227C212yesmaximal, complemented
8#11747184C212yesmaximal, complemented
9#11747062C211yesmaximal, characteristic, complemented
10#11746930C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612818—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14#91825C2212yes—
15#91815—21no—
16#91813—21no—
17#91776C2212yes—
18#91768—22no—
19#91758C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#686C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91434C2212yes—
25#91421—22no—
26D5×C4⋊Dic3—21no—
27#91384C2212yes—
28#91360—21no—
29C2×#6657C2212yes—
30C5×#832C2212yes—
31C5×#808C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3964C2211yescharacteristic
34C3×#3941C2211yescharacteristic
35C3×#3939C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90975C2212yes—
39#90975C2212yes—
40#90974C2212yes—
41#90951C2212yes—
42#79568—51nomaximal, Hall
43#66064—31no—
44#65876—31no—
45C5×#476—31no—
46#65382—31no—
47C4×#686D311yescharacteristic
48#65146—32no—
49#65141—32no—
50#65130—31no—
51#65119—31no—
52#65076—32no—
53#65057—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30D411yescharacteristic
57C2×Dic30C2312yes—
58C2×C5×Dic6—21no—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×D5×Dic3—22no—
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C22⋊C4—21no—
64C3×C42×C5C2311yescharacteristic
65#6719—22no—
66#6719—22no—
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15D411yescharacteristic
70#6712—22no—
71#6712D412yes—
72C4×Dic15—22no—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8C2312yes—
77C3×#686—22no—
78C3×#685—21no—
79C3×C4⋊Dic5C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6665—22no—
85#6657—24no—
86#5543—51no—
87#5542—51no—
88C3×C4×D8—51no—
89#5153—52no—
90#5019—51no—
91#5008D511yescharacteristic, complemented
92#4877—52no—
93#4768—52no—
94#4758—52no—
95#4681—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8—31no—
98C4×C5×D4C2×D311yescharacteristic
99#4092—62no—
100#4082—32no—
101C2×#686C2×D311yescharacteristic
102#4072—61no—
103#4070—61no—
104C2×#677—32no—
105#4043—61no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4033—32no—
110#4025—62no—
111C4×D20C2×D311yescharacteristic
112#4015—31no—
113C4×Dic10—31no—
114C5×#106—32no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3964C2×D311yescharacteristic
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—32no—
122#3942—32no—
123#3941C2×D311yescharacteristic
124#3939C2×D311yescharacteristic
125C4×#168C2×D311yescharacteristic
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×C3×D5—21no—
129C3×C5×D4—21no—
130C3×C5×D4—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139Dic30—22no—
140Dic30—22no—
141Dic30—22no—
142C2×C5×Dic3—22no—
143C5×Dic6—81no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148D5×Dic3—82no—
149C3×#168—21no—
150C3×#168—21no—
151C5×C3⋊C8—22no—
152C2×C3×D8—51no—
153C3×C4×D4—51no—
154C3×C4×D4C2×D511yescharacteristic
155#936—52no—
156D4×Dic3—52no—
157C2×#214—52no—
158#926—101no—
159C2×C4⋊Dic3—101no—
160#924—101no—
161#924—101no—
162#890—52no—
163#887—52no—
164#879—102no—
165#878—102no—
166#869—51no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C3×#107—51no—
170C3×#102—51no—
171C3×#102—51no—
172C3×C4×C8—51no—
173#832C2×D512yes—
174#816—52no—
175#816—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#810—52no—
179#808C2×D512yes—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C2×C5×Q8—61no—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C2×D20C22×D311yescharacteristic
185C2×C4×D5—21no—
186C2×C4×D5—62no—
187C2×Dic10—31no—
188C2×Dic10—32no—
189C2×C5×C8—32no—
190C5×C4⋊C4—32no—
191C5×C4⋊C4—61no—
192C5×C4⋊C4C22×D311yescharacteristic
193C5×C22⋊C4—21no—
194C42×C5C22×D311yescharacteristic
195C22⋊Dic5—62no—
196C22⋊Dic5—62no—
197#686—22no—
198#685—21no—
199#685—62no—
200C4⋊Dic5—31no—
201C4⋊Dic5—62no—
202C4⋊Dic5—61no—
203C4⋊Dic5—61no—
204C4⋊Dic5C22×D311yescharacteristic
205#683—32no—
206#683—62no—
207#683—62no—
208C4×Dic5—32no—
209C4×Dic5—62no—
210C2×#168C22×D311yescharacteristic
211C2×#168C22×D311yescharacteristic
212#677—64no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—31no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—51no—
224C22×C3×C5—41no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×C3×D5—22no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5#13512yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—22no—
237Dic15—22no—
238Dic15—42no—
239C3×Dic5—41no—
240C5×Dic3—42no—
241C2×C3×D4—51no—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×C3×C4—101no—
245C22×Dic3—102no—
246C2×Dic6—21no—
247C2×Dic6—51no—
248C2×Dic6—52no—
249C3×D8—102no—
250C2×C3×C8—51no—
251C2×C3×C8—51no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4C22×D511yescharacteristic
254C3×C22⋊C4—21no—
255C3×C22⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#217—102no—
259#217—102no—
260#214—104no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3—102no—
264C4⋊Dic3—101no—
265C4⋊Dic3—101no—
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C4×Dic3—52no—
271C4×Dic3—102no—
272C2×C3⋊C8C22×D512yes—
273C23×C5—21no—
274C22×D5—21no—
275C5×Q8—241no—
276C5×D4—21no—
277C5×D4—21no—
278C2×C4×C5—21no—
279C2×C4×C5—42no—
280C2×C4×C5—62no—
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—21no—
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—62no—
288D20—21no—
289D20#23512yes—
290C4×D5—42no—
291C4×D5—242no—
292Dic10—62no—
293Dic10—62no—
294Dic10—62no—
295C5×C8—62no—
296#168—21no—
297#168—21no—
298C2×SD16—152no—
299C2×D8—51no—
300C4⋊Q8—31no—
301C4⋊Q8—151no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—51no—
311C4×D4—152no—
312C4×D4D3×D511yescharacteristic
313#117—301no—
314C2×C4⋊C4—301no—
315#107—51no—
316#106—32no—
317C4⋊C8—31no—
318C4⋊C8—152no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—32no—
323#102—51no—
324#102—51no—
325C4×C8—51no—
326C4×C8—152no—
327C2×C3×C5—81no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331C3×D5—42no—
332C23×C3—21no—
333C23×C3—101no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—52no—
337C3×D4—101no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—101no—
341C2×C3×C4—202no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—52no—
347C2×Dic3—52no—
348C2×Dic3—102no—
349C2×Dic3—402no—
350Dic6—81no—
351Dic6—102no—
352Dic6—102no—
353Dic6—102no—
354C3×C8—101no—
355C3×C8—101no—
356C3⋊C8—22no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—22no—
362C2×D5—41no—
363C2×D5—41no—
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—122no—
367C4×C5#91212yes—
368C4×C5C2×#23511yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—41no—
371Dic5—62no—
372Dic5—62no—
373Dic5—122no—
374C2×Q8—61no—
375C2×Q8—151no—
376C2×Q8—152no—
377C2×D4—51no—
378C2×D4C2×D3×D511yescharacteristic
379C22×C4—21no—
380C22×C4—101no—
381C22×C4—302no—
382SD16—304no—
383D8—102no—
384C2×C8—32no—
385C2×C8—51no—
386C2×C8—51no—
387C4⋊C4—32no—
388C4⋊C4—51no—
389C4⋊C4—61no—
390C4⋊C4—151no—
391C4⋊C4—152no—
392C4⋊C4—302no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—301no—
396C4⋊C4—301no—
397C4⋊C4C2×D3×D511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C42—152no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—102no—
411C22×C3—201no—
412C22×C3—201no—
413C22×C3C2×D4×D511yescharacteristic
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—201no—
417C3×C4#406212yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—42no—
421Dic3—102no—
422Dic3—102no—
423Dic3—202no—
424C2×C5—81no—
425C2×C5#555211yescharacteristic
426C2×C5C2×#91211yescharacteristic
427C2×C5#577011yescharacteristic
428D5—42no—
429C23—21no—
430C23—101no—
431Q8—241no—
432Q8—302no—
433Q8—302no—
434Q8—302no—
435D4—21no—
436D4—21no—
437D4—52no—
438D4—101no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—62no—
442C2×C4—101no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—202no—
446C2×C4—302no—
447C2×C4—1202no—
448C2×C4#679011yescharacteristic
449C2×C4#679011yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—62no—
452C8—101no—
453C8—101no—
454C2×C3—81no—
455C2×C3—202no—
456C2×C3#6596711yescharacteristic
457C2×C3C2×#406211yescharacteristic
458C2×C3#6610911yescharacteristic
459C5#7956811yescharacteristic, complemented, Sylow
460C22—41no—
461C22—41no—
462C22—41no—
463C22—102no—
464C22—201no—
465C22—201no—
466C22C2×#679011yescharacteristic
467C4—21no—
468C4—41no—
469C4—122no—
470C4—201no—
471C4—302no—
472C4—302no—
473C4—602no—
474C4#9149712yes—
475C4#9200011yescharacteristic
476C4D5×#23511yescharacteristic
477C3#1061281811yescharacteristic, complemented, Sylow
478C2—81no—
479C2—202no—
480C2#1175436711yescharacteristic
481C2C2×#9149711yescharacteristic
482C2#1175533311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#686C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756301C2semidirect
2. #11752648C2semidirect
3. C5×#5008C2semidirect
6. #11748944C2semidirect
7. #11747227C2semidirect
8. #11747184C2semidirect
9. #11747062C2semidirect
10. #11746930C2semidirect
11. #11746851C2semidirect
91. #5008D5semidirect
406. C3×C5#3360semidirect
459. C5#79568semidirect
477. C3#10612818semidirect

Maximal subgroups

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

subgroupindex
#117563012
#117526482
C5×#50082
C3×C4×#6862
#117489842
#117489442
#117472272
#117471842
#117470622
#117469302
#117468512
#106128183
#795685