Finite Group Databasebeta

← #14471681

Subgroups — #14471681

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#11752657C211yesmaximal, characteristic, complemented
2#11752507C211yesmaximal, characteristic, complemented
3#11750782C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×C4×D40C211yesmaximal, characteristic
6#11747970C212yesmaximal, complemented
7#11747874C212yesmaximal, complemented
8#11747756C212yesmaximal
9#11747739C212yesmaximal, complemented
10#11747062C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611657—31nomaximal, Hall
13#91758C2211yescharacteristic
14#91758C2211yescharacteristic
15C4×C5×Dic6C2211yescharacteristic
16C2×C3×D40C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19#91431—22no—
20Dic3×D20C2212yes—
21D5×C4⋊Dic3—21no—
22#91381C2212yes—
23#91364C2212yes—
24#91362—22no—
25#91359—21no—
26#91359—21no—
27#91358—21no—
28#91340C2212yes—
29C2×#6657C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91100C2212yes—
32#91100C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3953C2211yescharacteristic
38C3×#3950C2211yescharacteristic
39#90987C2212yes—
40#90974C2212yes—
41#90965C2212yes—
42#79568—51nomaximal, Hall
43#65918—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65133—32no—
47#65131—31no—
48#65130—31no—
49#65118—32no—
50#64986—32no—
51C4×D40D311yescharacteristic
52C4×#677—32no—
53#64970—31no—
54C2×Dic30—21no—
55C2×Dic30C2312yes—
56C2×C5×Dic6D411yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5—21no—
61C2×D5×Dic3—22no—
62C2×C3×C5×C8C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15—21no—
66C4⋊Dic15—21no—
67C4⋊Dic15—21no—
68C4⋊Dic15C2312yes—
69C5×C4⋊Dic3D411yescharacteristic
70C5×Dic3⋊C4D412yes—
71C4×C5×Dic3C2312yes—
72C2×C5×C3⋊C8C2312yes—
73C3×#685—21no—
74C3×#685—21no—
75C3×C4⋊Dic5C2311yescharacteristic
76C3×C4⋊Dic5C2311yescharacteristic
77C3×D40—22no—
78#6669—22no—
79#6669—22no—
80#6668—22no—
81#6665—22no—
82#6665—22no—
83#6665—22no—
84Dic3×Dic5—22no—
85#6657—24no—
86#5543—51no—
87#5542—51no—
88C3×C4×D8—51no—
89#5153—52no—
90#5019—51no—
91#5008—51no—
92#4877—52no—
93#4768—52no—
94#4758—52no—
95#4681—51no—
96C8×Dic6D511yescharacteristic, complemented
97C4×C5×Q8—31no—
98#4092—61no—
99#4092—61no—
100C2×D40C2×D311yescharacteristic
101C2×#677—32no—
102#4044—62no—
103#4042—62no—
104#4038—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107C4×D20—32no—
108C4×D20C2×D311yescharacteristic
109C4×D20C2×D311yescharacteristic
110#4016—32no—
111#4015—31no—
112#4015—31no—
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3953—32no—
119#3953C2×D311yescharacteristic
120#3953C2×D311yescharacteristic
121#3950C2×D311yescharacteristic
122#3949—32no—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3360—151noSylow
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—22no—
134Dic30—22no—
135Dic30—22no—
136Dic30—81no—
137C2×C5×Dic3C2×D412yes—
138C2×C5×Dic3C2×D412yes—
139C5×Dic6—22no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C3×D20—21no—
143C3×D20—21no—
144C3×D20—21no—
145C3×D20#4112yes—
146C3×C4×D5—42no—
147C3×C4×D5—42no—
148D5×Dic3—82no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C5×C3⋊C8—22no—
152C2×C3×D8—51no—
153C3×C4×D4—51no—
154C3×C4×D4—51no—
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×Dic6C2×D511yescharacteristic
169C3×#107—51no—
170C3×#102—51no—
171C3×#102—51no—
172C3×C4×C8C2×D511yescharacteristic
173#832—52no—
174#816—52no—
175#816—52no—
176Dic3⋊C8C2×D512yes—
177C8×Dic3C2×D512yes—
178#810—52no—
179#808—52no—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C2×C5×Q8—31no—
182C2×D20C22×D311yescharacteristic
183C2×D20C22×D311yescharacteristic
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—62no—
187C2×Dic10—32no—
188C2×Dic10—61no—
189C2×C5×C8—32no—
190C2×C5×C8C22×D311yescharacteristic
191C2×C5×C8C22×D311yescharacteristic
192C5×C4⋊C4—32no—
193C5×C4⋊C4—31no—
194C42×C5—32no—
195C42×C5C22×D311yescharacteristic
196#685—21no—
197#685—21no—
198#685—62no—
199#685—62no—
200#685—62no—
201C4⋊Dic5—32no—
202C4⋊Dic5—61no—
203C4⋊Dic5—61no—
204C4⋊Dic5—61no—
205C4⋊Dic5C22×D311yescharacteristic
206C4⋊Dic5C22×D311yescharacteristic
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—62no—
211D40—22no—
212#677—64no—
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—31no—
222C4×SD16—152no—
223C4×D8—51no—
224C22×C3×C5C22×D411yescharacteristic
225C2×C3×D5—22no—
226C2×C3×D5—41no—
227C2×C3×D5—41no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—21no—
232C3×C4×C5#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—42no—
236Dic15—42no—
237C3×Dic5—41no—
238C3×Dic5—41no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C2×C3×D4—51no—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×C3×C4—101no—
245C22×Dic3—102no—
246C2×Dic6—52no—
247C2×Dic6—101no—
248C2×Dic6D2011yescharacteristic
249C3×D8—102no—
250C2×C3×C8C22×D511yescharacteristic
251C2×C3×C8C22×D511yescharacteristic
252C3×C4⋊C4—51no—
253C3×C4⋊C4—51no—
254C3×C22⋊C4—101no—
255C3×C22⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#217—102no—
259#217—102no—
260#214—104no—
261C4⋊Dic3—52no—
262C4⋊Dic3—101no—
263C4⋊Dic3—101no—
264C4⋊Dic3—101no—
265C4⋊Dic3—102no—
266C4⋊Dic3D2011yescharacteristic
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269Dic3⋊C4D2012yes—
270C4×Dic3—102no—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8C22×D512yes—
273C22×D5—21no—
274C22×D5—21no—
275C5×Q8—62no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285D20—21no—
286D20—21no—
287D20—21no—
288D20#23512yes—
289C4×D5—42no—
290C4×D5—42no—
291C4×D5—242no—
292Dic10—62no—
293Dic10—62no—
294Dic10—241no—
295C5×C8—21no—
296C5×C8—21no—
297C5×C8—62no—
298C2×SD16—152no—
299C2×D8—51no—
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—31no—
309C4×Q8—152no—
310C4×D4—51no—
311C4×D4—51no—
312C4×D4—152no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—51no—
316#106—152no—
317C4⋊C8—32no—
318C4⋊C8—31no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—51no—
323#102—51no—
324#102—152no—
325C4×C8—32no—
326C4×C8D3×D511yescharacteristic
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330C3×D5—42no—
331C3×D5—81no—
332C23×C3—101no—
333C23×C3—101no—
334C3×D4—52no—
335C3×D4—101no—
336C3×D4—101no—
337C3×D4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—202no—
341C2×C3×C4—202no—
342C2×C3×C4C2×D2011yescharacteristic
343C2×C3×C4C2×D2011yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—402no—
348C2×Dic3C2×D2012yes—
349C2×Dic3C2×D2012yes—
350Dic6—22no—
351Dic6—102no—
352Dic6—102no—
353Dic6—401no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—22no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—41no—
362C2×D5—41no—
363C2×D5—41no—
364C4×C5—21no—
365C4×C5—62no—
366C4×C5—62no—
367C4×C5#91212yes—
368C4×C5C2×#23511yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—41no—
371Dic5—41no—
372Dic5—122no—
373Dic5—122no—
374C2×Q8—31no—
375C2×Q8—152no—
376C2×Q8—301no—
377C2×D4—51no—
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—101no—
381C22×C4—302no—
382SD16—304no—
383D8—102no—
384C2×C8—32no—
385C2×C8C2×D3×D511yescharacteristic
386C2×C8C2×D3×D511yescharacteristic
387C4⋊C4—31no—
388C4⋊C4—32no—
389C4⋊C4—51no—
390C4⋊C4—51no—
391C4⋊C4—152no—
392C4⋊C4—302no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—301no—
396C4⋊C4—301no—
397C4⋊C4—301no—
398C22⋊C4—101no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—302no—
403C42—32no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—102no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3—201no—
411C22×C3—201no—
412C22×C3—201no—
413C22×C3C22×D2011yescharacteristic
414C3×C4—21no—
415C3×C4—201no—
416C3×C4—201no—
417C3×C4#405012yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—202no—
423Dic3—202no—
424C2×C5#555211yescharacteristic
425C2×C5C2×#91211yescharacteristic
426C2×C5#577011yescharacteristic
427D5—42no—
428D5—81no—
429C23—101no—
430C23—101no—
431Q8—62no—
432Q8—302no—
433Q8—302no—
434Q8—1201no—
435D4—52no—
436D4—101no—
437D4—101no—
438D4—101no—
439C2×C4—32no—
440C2×C4—32no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—202no—
444C2×C4—202no—
445C2×C4—302no—
446C2×C4—302no—
447C2×C4—1202no—
448C2×C4D3×D2011yescharacteristic
449C2×C4D3×D2011yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—21no—
452C8—21no—
453C8—62no—
454C2×C3—202no—
455C2×C3—401no—
456C2×C3#6591011yescharacteristic
457C2×C3C2×#405011yescharacteristic
458C2×C3#6608511yescharacteristic
459C5#7956811yescharacteristic, complemented, Sylow
460C22—102no—
461C22—201no—
462C22—201no—
463C22—201no—
464C22—201no—
465C22—201no—
466C22C2×D3×D2011yescharacteristic
467C4—21no—
468C4—62no—
469C4—62no—
470C4—201no—
471C4—201no—
472C4—602no—
473C4—602no—
474C4#9127312yes—
475C4#9200011yescharacteristic
476C4D5×#23511yescharacteristic
477C3#1061165711yescharacteristic, complemented, Sylow
478C2—202no—
479C2—401no—
480C2#1175254111yescharacteristic
481C2#1175397211yescharacteristic
482C2C2×#9127311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D40C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752657C2semidirect
2. #11752507C2semidirect
3. #11750782C2semidirect
4. C5×C8×Dic6C2semidirect
6. #11747970C2semidirect
7. #11747874C2semidirect
9. #11747739C2semidirect
10. #11747062C2semidirect
11. #11746881C2semidirect
96. C8×Dic6D5semidirect
406. C3×C5#3360semidirect
459. C5#79568semidirect
477. C3#10611657semidirect

Maximal subgroups

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

subgroupindex
#117526572
#117525072
#117507822
C5×C8×Dic62
C3×C4×D402
#117479702
#117478742
#117477562
#117477392
#117470622
#117468812
#106116573
#795685