Finite Group Databasebeta

← #14471593

Subgroups — #14471593

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#11756302C211yesmaximal, characteristic, complemented
2#11756301C211yesmaximal, characteristic, complemented
3C3×C4×C5×D8C211yesmaximal, characteristic
4#11751254C212yesmaximal
5#11751120C211yesmaximal, characteristic, complemented
6#11751109C211yesmaximal, characteristic, complemented
7#11750978C212yesmaximal, complemented
8#11750869C212yesmaximal, complemented
9#11750859C212yesmaximal, complemented
10#11750782C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10611299—31nomaximal, Hall
13C2×C3×C5×D8C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91825C2212yes—
17D4×Dic15C2212yes—
18C2×#6716C2212yes—
19#91815—21no—
20C2×C4⋊Dic15—21no—
21#91813—21no—
22#91813—21no—
23#91779C2212yes—
24#91776C2212yes—
25#91768—22no—
26#91767—22no—
27#91758C2211yescharacteristic
28#91758C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#107C2211yescharacteristic
31C3×C5×#102C2211yescharacteristic
32C3×C5×#102C2211yescharacteristic
33C3×C4×C5×C8C2211yescharacteristic
34#91116C2212yes—
35#91100C2212yes—
36#91100C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91094C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79568—51nomaximal, Hall
43#65877—31no—
44#65876—31no—
45C4×C5×D8D311yescharacteristic
46#65442—32no—
47#65308—31no—
48#65297—31no—
49#65166—32no—
50#65057—32no—
51#65047—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×Dic15—22no—
59C2×Dic30—21no—
60C2×Dic30D411yescharacteristic
61C2×Dic30C2312yes—
62C3×C5×D8—22no—
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C5×C22⋊C4—21no—
68C3×C5×C22⋊C4—21no—
69C3×C42×C5C2311yescharacteristic
70#6719—22no—
71#6719—22no—
72#6719—22no—
73#6716—24no—
74C4⋊Dic15—21no—
75C4⋊Dic15—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15—22no—
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15C2312yes—
80#6712—22no—
81#6712—22no—
82#6712D412yes—
83C4×Dic15—22no—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2312yes—
86#5543—51no—
87#5542—51no—
88C3×C4×D8D511yescharacteristic
89#5153—52no—
90#5019—51no—
91#5008—51no—
92#4877—52no—
93#4768—52no—
94#4758—52no—
95#4681—51no—
96C8×Dic6—51no—
97C2×C5×D8C2×D311yescharacteristic
98C4×C5×D4C2×D311yescharacteristic
99C4×C5×D4C2×D311yescharacteristic
100#4082—32no—
101D4×Dic5—32no—
102C2×#687—32no—
103#4072—61no—
104C2×C4⋊Dic5—61no—
105#4070—61no—
106#4070—61no—
107#4036—32no—
108#4033—32no—
109#4025—62no—
110#4024—62no—
111#4015—31no—
112#4015—31no—
113C4×Dic10—31no—
114C5×#107C2×D311yescharacteristic
115C5×#102C2×D311yescharacteristic
116C5×#102C2×D311yescharacteristic
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3948—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3940—32no—
125C4⋊#168—31no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C3×C5×D4—21no—
130C3×C5×D4—21no—
131C3×C5×D4—21no—
132C3×C5×D4#4112yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—82no—
143C2×Dic15C2×D412yes—
144C2×Dic15C2×D412yes—
145Dic30—22no—
146Dic30—22no—
147Dic30—22no—
148Dic30—81no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C3⋊#168—22no—
152C2×C3×D8C2×D511yescharacteristic
153C3×C4×D4C2×D511yescharacteristic
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#869—51no—
168C4×Dic6—51no—
169C3×#107C2×D511yescharacteristic
170C3×#102C2×D511yescharacteristic
171C3×#102C2×D511yescharacteristic
172C3×C4×C8C2×D511yescharacteristic
173#832—52no—
174#816—52no—
175#816—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#810—52no—
179#808—52no—
180C4⋊(C3⋊C8)—51no—
181C2×C5×D4C22×D311yescharacteristic
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×Dic5—62no—
186C2×Dic10—31no—
187C2×Dic10—32no—
188C2×Dic10—61no—
189C5×D8—22no—
190C2×C5×C8C22×D311yescharacteristic
191C2×C5×C8C22×D311yescharacteristic
192C5×C4⋊C4C22×D311yescharacteristic
193C5×C4⋊C4C22×D311yescharacteristic
194C5×C22⋊C4—21no—
195C5×C22⋊C4—21no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—62no—
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200#687—64no—
201C4⋊Dic5—31no—
202C4⋊Dic5—32no—
203C4⋊Dic5—62no—
204C4⋊Dic5—61no—
205C4⋊Dic5—61no—
206C4⋊Dic5—61no—
207#683—32no—
208#683—62no—
209#683—62no—
210C4×Dic5—32no—
211C4×Dic5—62no—
212C2×#168—32no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8D1511yescharacteristic
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5C22×D411yescharacteristic
231C3×C4×C5—21no—
232C3×C4×C5—41no—
233C3×C4×C5—41no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—42no—
240Dic15—42no—
241C2×C3×D4C22×D511yescharacteristic
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×Dic3—102no—
246C2×Dic6—51no—
247C2×Dic6—52no—
248C2×Dic6—101no—
249C3×D8—22no—
250C2×C3×C8C22×D511yescharacteristic
251C2×C3×C8C22×D511yescharacteristic
252C3×C4⋊C4C22×D511yescharacteristic
253C3×C4⋊C4C22×D511yescharacteristic
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#217—102no—
259#217—102no—
260#214—104no—
261C4⋊Dic3—51no—
262C4⋊Dic3—52no—
263C4⋊Dic3—102no—
264C4⋊Dic3—101no—
265C4⋊Dic3—101no—
266C4⋊Dic3—101no—
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C4×Dic3—52no—
271C4×Dic3—102no—
272C2×C3⋊C8—52no—
273C23×C5—21no—
274C23×C5—21no—
275C5×D4—21no—
276C5×D4—21no—
277C5×D4—21no—
278C5×D4#23512yes—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—62no—
289C2×Dic5—62no—
290C2×Dic5—242no—
291Dic10—62no—
292Dic10—62no—
293Dic10—62no—
294Dic10—241no—
295C5×C8—21no—
296C5×C8—21no—
297#168—62no—
298C2×SD16—152no—
299C2×D8C2×D1511yescharacteristic
300C4⋊Q8—151no—
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—152no—
311C4×D4C2×D1511yescharacteristic
312C4×D4C2×D1511yescharacteristic
313#117—301no—
314C2×C4⋊C4—301no—
315#107C2×D1511yescharacteristic
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8—151no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—152no—
323#102C2×D1511yescharacteristic
324#102C2×D1511yescharacteristic
325C4×C8—152no—
326C4×C8C2×D1511yescharacteristic
327C2×C3×C5—42no—
328C2×C3×C5—81no—
329C2×C3×C5#54811yescharacteristic
330C2×C3×C5C2×#13511yescharacteristic
331C2×C3×C5#57711yescharacteristic
332C23×C3—21no—
333C23×C3—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4#70912yes—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—52no—
346C2×Dic3—52no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3—402no—
350Dic6—102no—
351Dic6—102no—
352Dic6—102no—
353Dic6—401no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5—41no—
361C22×C5—41no—
362C22×C5—41no—
363C22×C5C2×D3×D411yescharacteristic
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—41no—
367C4×C5#91212yes—
368C4×C5C2×#23511yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—62no—
371Dic5—62no—
372Dic5—122no—
373Dic5—122no—
374C2×Q8—151no—
375C2×Q8—152no—
376C2×Q8—301no—
377C2×D4C22×D1511yescharacteristic
378C2×D4C22×D1511yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—302no—
382SD16—304no—
383D8—22no—
384C2×C8—152no—
385C2×C8C22×D1511yescharacteristic
386C2×C8C22×D1511yescharacteristic
387C4⋊C4—151no—
388C4⋊C4—152no—
389C4⋊C4—152no—
390C4⋊C4—302no—
391C4⋊C4—302no—
392C4⋊C4—302no—
393C4⋊C4—301no—
394C4⋊C4—301no—
395C4⋊C4—301no—
396C4⋊C4C22×D1511yescharacteristic
397C4⋊C4C22×D1511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C42—152no—
404C42—302no—
405C42C22×D1511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3C2×D4×D511yescharacteristic
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4#405812yes—
418C3×C4C2×#70911yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—102no—
421Dic3—102no—
422Dic3—202no—
423Dic3—202no—
424C2×C5—42no—
425C2×C5—81no—
426C2×C5#555211yescharacteristic
427C2×C5C2×#91211yescharacteristic
428C2×C5#577011yescharacteristic
429C23—21no—
430C23—21no—
431Q8—302no—
432Q8—302no—
433Q8—302no—
434Q8—1201no—
435D4—21no—
436D4—21no—
437D4—21no—
438D4#681712yes—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—302no—
446C2×C4—302no—
447C2×C4—1202no—
448C2×C4D4×D1511yescharacteristic
449C2×C4D4×D1511yescharacteristic
450C2×C4C23×D1511yescharacteristic
451C8—21no—
452C8—21no—
453C8—302no—
454C2×C3—42no—
455C2×C3—81no—
456C2×C3#6588611yescharacteristic
457C2×C3C2×#405811yescharacteristic
458C2×C3#6610411yescharacteristic
459C5#7956811yescharacteristic, complemented, Sylow
460C22—22no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22C2×D4×D1511yescharacteristic
467C4—21no—
468C4—41no—
469C4—41no—
470C4—302no—
471C4—302no—
472C4—602no—
473C4—602no—
474C4#9180112yes—
475C4C2×#681711yescharacteristic
476C4#9210111yescharacteristic
477C3#1061129911yescharacteristic, complemented, Sylow
478C2—42no—
479C2—81no—
480C2#1175631111yescharacteristic
481C2C2×#9180111yescharacteristic
482C2#1175652911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D8C22
hypercenterC4×D8D15
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11756302C2semidirect
2. #11756301C2semidirect
5. #11751120C2semidirect
6. #11751109C2semidirect
7. #11750978C2semidirect
8. #11750869C2semidirect
9. #11750859C2semidirect
10. #11750782C2semidirect
11. C8×Dic30C2semidirect
406. C3×C5#3360semidirect
459. C5#79568semidirect
477. C3#10611299semidirect

Maximal subgroups

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

subgroupindex
#117563022
#117563012
C3×C4×C5×D82
#117512542
#117511202
#117511092
#117509782
#117508692
#117508592
#117507822
C8×Dic302
#106112993
#795685