Finite Group Databasebeta

← #14472148

Subgroups — #14472148

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5570C211yesmaximal, characteristic, complemented
2#11752483C211yesmaximal, characteristic
3C4×#6717C211yesmaximal, characteristic
4C3×#65320C211yesmaximal, characteristic, complemented
5#11749326C212yesmaximal
6Dic3×#689C212yesmaximal, complemented
7#11747379C212yesmaximal
8#11747295C212yesmaximal, complemented
9#11746966C211yesmaximal, characteristic
10#11746924C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615420—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14C2×#6717C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×Q8×Dic3C2212yes—
17C5×#890—22no—
18C5×#890C2212yes—
19C5×#869—21no—
20C5×#869C2211yescharacteristic
21C4×C5×Dic6—21no—
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#689C2212yes—
24C3×#4015C2211yescharacteristic
25#91383—21no—
26#91374C2212yes—
27#91347—21no—
28#91345—22no—
29Dic3×Dic10C2212yes—
30#91119C2211yescharacteristic
31#91093C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3942C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90988C2212yes—
37Dic3⋊#168C2212yes—
38#90970C2212yes—
39#90970C2212yes—
40#90969C2212yes—
41Dic3×#168C2212yes—
42#80463—51nomaximal, Hall
43C5×#557—31no—
44#65918—31no—
45#65382—31no—
46#65376—31no—
47#65357—32no—
48#65352—32no—
49#65320D311yescharacteristic, complemented
50C4×#689—32no—
51#65317—32no—
52C4×#688—31no—
53Q8×#168—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×Dic10C2312yes—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4C2311yescharacteristic
62C3×C42×C5—21no—
63C3×C42×C5C2311yescharacteristic
64#6717—22no—
65#6714—21no—
66C4⋊Dic15C2311yescharacteristic
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3—22no—
71C5×C4⋊Dic3—22no—
72C5×C4⋊Dic3D411yescharacteristic
73C5×C4⋊Dic3C2312yes—
74C5×Dic3⋊C4—22no—
75C5×Dic3⋊C4D412yes—
76C4×C5×Dic3—22no—
77C4×C5×Dic3C2312yes—
78C3×#689—24no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C2×C3×#168C2312yes—
82#6668—22no—
83#6667—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#5732—51no—
87#5570D511yescharacteristic, complemented
88C3×#462—51no—
89#5185—52no—
90Dic3×Q16—52no—
91#5079—51no—
92C4×#215—51no—
93#4846—51no—
94#4830—51no—
95#4800—52no—
96#4796—52no—
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8—61no—
99C5×#125—32no—
100C5×#125—62no—
101C4×C5×Q8—31no—
102C4×C5×Q8—32no—
103C4×C5×Q8—61no—
104C4×C5×Q8C2×D311yescharacteristic
105#4092—61no—
106C2×#689C2×D312yes—
107C2×#688—31no—
108#4044—62no—
109#4038—61no—
110#4021—32no—
111C4×D20—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10—32no—
114#3967—31no—
115#3942—32no—
116#3942—32no—
117#3942C2×D312yes—
118#3941—31no—
119#3941—32no—
120#3940—31no—
121#3939—32no—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3364—151noSylow
127C22×D15—21no—
128C3×C5×Q8—21no—
129C3×C5×Q8#4112yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×Dic6—22no—
143C5×Dic6—42no—
144C2×C3×Dic5—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3⋊#168—21no—
148C3⋊#168—21no—
149C3×#168—22no—
150C2×C3×Q16—52no—
151C3×C4⋊Q8—51no—
152C3×C4×Q8C2×D511yescharacteristic
153#947—52no—
154Q8×Dic3—52no—
155Q8×Dic3C2×D512yes—
156C2×#215—51no—
157#898—102no—
158#897—101no—
159#892—101no—
160#890—22no—
161#890C2×D512yes—
162C4×D12—51no—
163#869—21no—
164#869C2×D511yescharacteristic
165C4×Dic6—21no—
166C4×Dic6C2×D511yescharacteristic
167C3×C4⋊C8—51no—
168C3×#103—52no—
169#835—51no—
170#835—52no—
171#835—52no—
172#821—52no—
173#818—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—51no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—31no—
180C2×C5×Q8—61no—
181C2×C5×Q8C22×D311yescharacteristic
182C2×D20—31no—
183C2×C4×D5—61no—
184C2×Dic10C22×D312yes—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—31no—
187C5×C4⋊C4—32no—
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C5×C4⋊C4—62no—
191C5×C4⋊C4—62no—
192C5×C4⋊C4—61no—
193C5×C4⋊C4C22×D311yescharacteristic
194C42×C5—21no—
195C42×C5—32no—
196C42×C5—62no—
197C42×C5C22×D311yescharacteristic
198#689—24no—
199#688—62no—
200#685—62no—
201#685—62no—
202#685—61no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4⋊Dic5—31no—
206#683—62no—
207C4×Dic5—62no—
208C2×#168—31no—
209C2×#168—31no—
210C2×#168C22×D312yes—
211#557—31no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—51no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—22no—
227C3×C4×C5—21no—
228C3×C4×C5—41no—
229C3×C4×C5#13512yes—
230C3×C4×C5C2×#4111yescharacteristic
231C3×C4×C52−1+411yescharacteristic
232Dic15—41no—
233C3×Dic5—42no—
234C5×Dic3—22no—
235C5×Dic3—22no—
236C5×Dic3—42no—
237C2×C3×Q8—52no—
238C2×C3×Q8C22×D511yescharacteristic
239C2×D12—51no—
240C2×C4×D3—101no—
241C2×Dic6—21no—
242C2×Dic6C22⋊D511yescharacteristic
243C3×Q16—104no—
244C2×C3×C8—52no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C42—21no—
250C3×C42C22×D511yescharacteristic
251#215—102no—
252(C2×D3)⋊C4—101no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—21no—
256C4⋊Dic3—22no—
257C4⋊Dic3—22no—
258C4⋊Dic3—51no—
259C4⋊Dic3—102no—
260C4⋊Dic3C22⋊D511yescharacteristic
261C4⋊Dic3C22×D512yes—
262Dic3⋊C4—22no—
263Dic3⋊C4C22⋊D512yes—
264C4×Dic3—22no—
265C4×Dic3—102no—
266C4×Dic3C22×D512yes—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—51no—
269C22×D5—61no—
270C5×Q8—21no—
271C5×Q8—62no—
272C5×Q8—122no—
273C5×Q8#23712yes—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5—62no—
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5C23×D311yescharacteristic
282C2×Dic5—22no—
283C2×Dic5—61no—
284D20—61no—
285D20—61no—
286C4×D5—122no—
287Dic10—22no—
288Dic10—22no—
289#168—22no—
290#168—61no—
291#168—61no—
292C2×Q16—52no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—51no—
296C4⋊Q8—61no—
297#126—302no—
298#125—32no—
299#125—62no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—32no—
304C4×Q8—61no—
305C4×Q8—152no—
306C4×Q8D3×D511yescharacteristic
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—51no—
312C4⋊C8—152no—
313#103—52no—
314#103—152no—
315#103—152no—
316#103—151no—
317#102—152no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—21no—
327C3×Q8—102no—
328C3×Q8—102no—
329C3×Q8#71312yes—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—102no—
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×C3×C4C2×C22⋊D511yescharacteristic
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—101no—
338C2×Dic3C2×C22⋊D512yes—
339C2×Dic3C2×C22⋊D512yes—
340D12—101no—
341D12—101no—
342C4×D3—202no—
343Dic6—22no—
344Dic6—42no—
345C3×C8—102no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—22no—
354C4×C5—41no—
355C4×C5—62no—
356C4×C5—62no—
357C4×C5—122no—
358C4×C5#91912yes—
359C4×C5C2×#23711yescharacteristic
360C4×C5#101011yescharacteristic
361Dic5—42no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—52no—
365C2×Q8—61no—
366C2×Q8C2×D3×D511yescharacteristic
367C2×D4—151no—
368C22×C4—301no—
369Q16—104no—
370SD16—302no—
371C2×C8—52no—
372C2×C8—151no—
373C2×C8—151no—
374C4⋊C4—21no—
375C4⋊C4—31no—
376C4⋊C4—32no—
377C4⋊C4—32no—
378C4⋊C4—62no—
379C4⋊C4—62no—
380C4⋊C4—62no—
381C4⋊C4—61no—
382C4⋊C4—101no—
383C4⋊C4—101no—
384C4⋊C4—151no—
385C4⋊C4—302no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—21no—
391C42—32no—
392C42—62no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C22×C22⋊D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—41no—
403C3×C4—202no—
404C3×C4#409612yes—
405C3×C4C2×#71311yescharacteristic
406C3×C4#414711yescharacteristic
407Dic3—22no—
408Dic3—22no—
409Dic3—42no—
410Dic3—201no—
411C2×C5#559811yescharacteristic
412C2×C5C2×#91911yescharacteristic
413C2×C5#577911yescharacteristic
414D5—241no—
415C23—301no—
416Q8—21no—
417Q8—62no—
418Q8—102no—
419Q8—102no—
420Q8—122no—
421Q8#676612yes—
422D4—301no—
423D4—301no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—32no—
427C2×C4—32no—
428C2×C4—62no—
429C2×C4—102no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4D3×C22⋊D511yescharacteristic
433C2×C4D3×C22⋊D511yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—102no—
436C8—301no—
437C8—301no—
438C2×C3#6615111yescharacteristic
439C2×C3C2×#409611yescharacteristic
440C2×C3#6617211yescharacteristic
441D3—401no—
442C5#8046311yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D3×C22⋊D511yescharacteristic
447C4—21no—
448C4—22no—
449C4—41no—
450C4—62no—
451C4—62no—
452C4—122no—
453C4—202no—
454C4—601no—
455C4#9151912yes—
456C4C2×#676611yescharacteristic
457C4#9200011yescharacteristic
458C3#1061542011yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175434411yescharacteristic
461C2C2×#9151911yescharacteristic
462C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5570C2semidirect
4. C3×#65320C2semidirect
6. Dic3×#689C2semidirect
8. #11747295C2semidirect
10. #11746924C2semidirect
11. #11746857C2semidirect
49. #65320D3semidirect
87. #5570D5semidirect
395. C3×C5#3364semidirect
442. C5#80463semidirect
458. C3#10615420semidirect

Maximal subgroups

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

subgroupindex
C5×#55702
#117524832
C4×#67172
C3×#653202
#117493262
Dic3×#6892
#117473792
#117472952
#117469662
#117469242
#117468572
#106154203
#804635