Finite Group Databasebeta

← #14471698

Subgroups — #14471698

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#11752648C211yesmaximal, characteristic, complemented
2#11752480C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4842C211yesmaximal, characteristic, complemented
5C3×#65130C211yesmaximal, characteristic, complemented
6#11747979C212yesmaximal, complemented
7#11747877C212yesmaximal, complemented
8#11747806C212yesmaximal, complemented
9#11747751C212yesmaximal
10C4×#6652C211yesmaximal, characteristic
11#11746924C211yesmaximal, characteristic, complemented
12#10612818—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C2×C3×#677C2212yes—
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91434C2212yes—
20#91421—22no—
21D5×C4⋊Dic3—21no—
22#91384C2212yes—
23#91370C2212yes—
24#91365—21no—
25#91360—21no—
26#91341—22no—
27#91338—21no—
28#91331C2212yes—
29C2×#6652C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#821C2212yes—
35C5×#817C2212yes—
36C3×#3948C2212yes—
37#90989C2211yescharacteristic
38#90970C2212yes—
39#90970C2212yes—
40#90966C2211yescharacteristic
41#90964C2211yescharacteristic
42#80415—51nomaximal, Hall
43#66064—31no—
44#65876—31no—
45C5×#476—31no—
46#65382—31no—
47C4×#686—31no—
48#65146—32no—
49#65141—32no—
50#65130D311yescharacteristic, complemented
51#65119—31no—
52#65076—32no—
53#65057—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6—21no—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×Dic10C2312yes—
61C2×D5×Dic3—22no—
62C2×C3×C5×C8C2312yes—
63C3×C42×C5C2311yescharacteristic
64C4⋊Dic15D411yescharacteristic
65#6712D412yes—
66C4×Dic15C2312yes—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×(C2×D3)⋊C4—21no—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3C2312yes—
72C5×C4⋊Dic3C2311yescharacteristic
73C3×#685—21no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#677—24no—
78Dic3⋊Dic5—22no—
79#6668—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83#6665—22no—
84Dic3×Dic5—22no—
85#6652—22no—
86#5732—51no—
87#5543—51no—
88C3×#461—51no—
89#5165—52no—
90Dic3×SD16—52no—
91#5079—51no—
92C4×#213—51no—
93#4842D511yescharacteristic, complemented
94#4830—51no—
95#4800—52no—
96#4799—52no—
97C5×C4⋊Q8—31no—
98C4×C5×D4—31no—
99#4092—62no—
100#4082—32no—
101C2×#686—31no—
102#4072—61no—
103#4070—61no—
104C2×#677C2×D312yes—
105#4043—61no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4033—32no—
110#4025—62no—
111C4×D20C2×D311yescharacteristic
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C5×#106—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102—32no—
117#3964—31no—
118#3948C2×D312yes—
119#3946—32no—
120C8×Dic5—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3939—31no—
125C4×#168—31no—
126#3360—151noSylow
127C22×C5×D3—21no—
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134Dic30—22no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—22no—
137C5×D12—21no—
138C5×D12—21no—
139C4×C5×D3—42no—
140C5×Dic6—81no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20#4112yes—
145C3×C4×D5—42no—
146C3×Dic10—22no—
147C3×Dic10—22no—
148D5×Dic3—82no—
149C3×C5×C8—22no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C2×C3×SD16—52no—
153C3×C4⋊Q8—51no—
154C3×C4×D4—51no—
155#947—52no—
156Q8×Dic3—52no—
157D4×Dic3—52no—
158C2×#213—51no—
159C2×C4⋊Dic3—101no—
160#924—101no—
161#898—102no—
162#897—101no—
163#892—101no—
164#890—52no—
165#878—102no—
166C4×D12C2×D511yescharacteristic
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C3×C4⋊C8C2×D511yescharacteristic
170C3×#103—52no—
171#835—52no—
172#835—52no—
173#832—51no—
174#821C2×D512yes—
175#817C2×D512yes—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8—51no—
181C2×C5×Q8—61no—
182C2×C5×D4—31no—
183C22×C4×C5—61no—
184C2×D20C22×D311yescharacteristic
185C2×C4×D5—21no—
186C2×C4×D5—62no—
187C2×Dic10—31no—
188C2×Dic10C22×D312yes—
189C2×C5×C8C22×D312yes—
190C5×C4⋊C4—31no—
191C5×C4⋊C4—32no—
192C5×C4⋊C4—61no—
193C5×C22⋊C4—61no—
194C42×C5C22×D311yescharacteristic
195C22⋊Dic5—62no—
196C22⋊Dic5—62no—
197#686—62no—
198#685—21no—
199#685—62no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—31no—
203C4⋊Dic5—62no—
204C4⋊Dic5C22×D311yescharacteristic
205#683—32no—
206#683—62no—
207#683—62no—
208C4×Dic5—32no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212#677—24no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—31no—
219#463—152no—
220#461—51no—
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×C5×D3—41no—
226C2×C5×D3—41no—
227C2×C5×D3—41no—
228C2×C3×D5—22no—
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—22no—
236Dic15—22no—
237C3×Dic5—42no—
238C3×Dic5—41no—
239C5×Dic3—41no—
240C5×Dic3—42no—
241C2×C3×Q8—52no—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×D12C22×D511yescharacteristic
246C2×C4×D3—21no—
247C2×Dic6—21no—
248C2×Dic6—51no—
249C3×SD16—104no—
250C2×C3×C8C22×D512yes—
251C3×C4⋊C4—51no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4—101no—
254C3×C22⋊C4—101no—
255C3×C42C22×D511yescharacteristic
256#217—102no—
257#213—102no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3—102no—
264C4⋊Dic3—102no—
265C4⋊Dic3C22×D511yescharacteristic
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273C23×C5—61no—
274C22×D5—21no—
275C5×Q8—241no—
276C5×D4—61no—
277C5×D4—61no—
278C2×C4×C5—61no—
279C2×C4×C5—62no—
280C2×C4×C5—122no—
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—22no—
285C2×Dic5—21no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288D20—21no—
289D20#23712yes—
290C4×D5—42no—
291C4×D5—242no—
292Dic10—22no—
293Dic10—22no—
294Dic10—62no—
295C5×C8—22no—
296#168—61no—
297#168—61no—
298C2×SD16—52no—
299C2×D8—151no—
300C4⋊Q8—31no—
301C4⋊Q8—51no—
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—31no—
311C4×D4—51no—
312C4×D4—152no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—32no—
317C4⋊C8—152no—
318C4⋊C8D3×D511yescharacteristic
319#103—52no—
320#103—152no—
321#103—152no—
322#102—32no—
323#102—151no—
324#102—151no—
325C4×C8—152no—
326C4×C8—151no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330C3×D5—42no—
331C5×D3—81no—
332C23×C3—101no—
333C22×D3—21no—
334C3×Q8—102no—
335C3×Q8—102no—
336C3×D4—52no—
337C3×D4—101no—
338C2×C3×C4—102no—
339C2×C3×C4—101no—
340C2×C3×C4—202no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—52no—
347C2×Dic3—52no—
348C2×Dic3—402no—
349D12—21no—
350D12—21no—
351C4×D3—42no—
352Dic6—81no—
353Dic6—102no—
354C3×C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—121no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—22no—
362C2×D5—41no—
363C2×D5—41no—
364C4×C5—21no—
365C4×C5—121no—
366C4×C5—122no—
367C4×C5#91612yes—
368C4×C5C2×#23711yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—41no—
371Dic5—42no—
372Dic5—62no—
373Dic5—62no—
374C2×Q8—52no—
375C2×Q8—61no—
376C2×Q8—151no—
377C2×D4—31no—
378C2×D4—51no—
379C22×C4—61no—
380C22×C4—101no—
381C22×C4—302no—
382SD16—104no—
383D8—302no—
384C2×C8—151no—
385C2×C8—151no—
386C2×C8C2×D3×D512yes—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—51no—
390C4⋊C4—61no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—151no—
394C4⋊C4—152no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C22⋊C4—61no—
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—102no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3C2×D4×D511yescharacteristic
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C3×C4—21no—
415C3×C4—201no—
416C3×C4—202no—
417C3×C4#406212yes—
418C3×C4#414711yescharacteristic
419C3×C4D5×#4111yescharacteristic
420Dic3—41no—
421Dic3—42no—
422Dic3—102no—
423Dic3—102no—
424C2×C5—241no—
425C2×C5#559811yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5#577811yescharacteristic
428D5—42no—
429C23—61no—
430C23—101no—
431Q8—102no—
432Q8—102no—
433Q8—241no—
434Q8—302no—
435D4—52no—
436D4—61no—
437D4—61no—
438D4—101no—
439C2×C4—61no—
440C2×C4—62no—
441C2×C4—102no—
442C2×C4—101no—
443C2×C4—122no—
444C2×C4—152no—
445C2×C4—152no—
446C2×C4—202no—
447C2×C4—1202no—
448C2×C4#677711yescharacteristic
449C2×C4#677711yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—22no—
452C8—301no—
453C8—301no—
454C2×C3—202no—
455C2×C3#6596711yescharacteristic
456C2×C3C2×#406211yescharacteristic
457C2×C3#6610911yescharacteristic
458D3—81no—
459C5#8041511yescharacteristic, complemented, Sylow
460C22—102no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—201no—
465C22—201no—
466C22C2×#677711yescharacteristic
467C4—21no—
468C4—121no—
469C4—122no—
470C4—201no—
471C4—202no—
472C4—302no—
473C4—302no—
474C4#9127612yes—
475C4D5×#23711yescharacteristic
476C4#9202811yescharacteristic
477C3#1061281811yescharacteristic, complemented, Sylow
478C2—202no—
479C2—241no—
480C2#1175369811yescharacteristic
481C2C2×#9127611yescharacteristic
482C2#1175403911yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6652C22
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. #11752648C2semidirect
2. #11752480C2semidirect
3. #11750931C2semidirect
4. C5×#4842C2semidirect
5. C3×#65130C2semidirect
6. #11747979C2semidirect
7. #11747877C2semidirect
8. #11747806C2semidirect
11. #11746924C2semidirect
50. #65130D3semidirect
93. #4842D5semidirect
406. C3×C5#3360semidirect
459. C5#80415semidirect
477. C3#10612818semidirect

Maximal subgroups

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

subgroupindex
#117526482
#117524802
#117509312
C5×#48422
C3×#651302
#117479792
#117478772
#117478062
#117477512
C4×#66522
#117469242
#106128183
#804155