Finite Group Databasebeta

← #14472174

Subgroups — #14472174

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
1#11752480C211yesmaximal, characteristic
2#11752477C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4846C211yesmaximal, characteristic
5C3×#65138C211yesmaximal, characteristic, complemented
6#11747979C212yesmaximal
7#11747883C212yesmaximal, complemented
8#11747878C212yesmaximal, complemented
9#11747837C212yesmaximal
10C4×#6656C211yesmaximal, characteristic
11#11746924C211yesmaximal, characteristic, complemented
12#10612725—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C2×C3×Dic20C2212yes—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91384C2212yes—
20#91376—21no—
21#91370C2212yes—
22#91365—21no—
23#91341—22no—
24#91338—21no—
25#91335—22no—
26Dic5×Dic6—21no—
27#91331C2212yes—
28#91331C2212yes—
29C2×#6656C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#821C2212yes—
35C5×#818C2212yes—
36C3×#3948C2212yes—
37#90986C2211yescharacteristic
38#90970C2212yes—
39#90970C2211yescharacteristic
40#90970C2212yes—
41#90966C2211yescharacteristic
42#80463—51nomaximal, Hall
43#66055—31no—
44#65876—31no—
45C5×#474—31no—
46#65382—31no—
47C4×#687—31no—
48#65166—32no—
49#65162—32no—
50#65138D311yescharacteristic, complemented
51#65119—31no—
52#65057—32no—
53#65056—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6—21no—
58C2×C3×Dic10C2312yes—
59C2×C3×Dic10C2311yescharacteristic
60C2×C3×C5×C8C2312yes—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15D411yescharacteristic
63#6712D412yes—
64C4×Dic15C2312yes—
65C2×C3⋊#168C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×(C2×D3)⋊C4—21no—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3C2312yes—
70C5×C4⋊Dic3C2311yescharacteristic
71C3×C4⋊Dic5—21no—
72C3×C4⋊Dic5—21no—
73C3×C4⋊Dic5C2311yescharacteristic
74C3×#683—21no—
75C3×C4×Dic5—21no—
76C3×Dic20—24no—
77Dic3⋊Dic5—22no—
78#6668—22no—
79#6668—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6656—22no—
86#5732—51no—
87#5570—51no—
88C3×#462—51no—
89#5185—52no—
90Dic3×Q16—52no—
91#5079—51no—
92C4×#215—51no—
93#4846D511yescharacteristic
94#4830—51no—
95#4800—52no—
96#4796—52no—
97C5×C4⋊Q8—31no—
98C4×C5×D4—31no—
99Q8×Dic5—61no—
100#4090—61no—
101#4082—32no—
102C2×#687—31no—
103#4072—61no—
104#4070—61no—
105C2×Dic20C2×D312yes—
106#4036—32no—
107#4035—62no—
108#4033—32no—
109#4033—32no—
110#4025—62no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#107—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102—32no—
117#3964—31no—
118#3948C2×D312yes—
119#3946—32no—
120C8×Dic5—32no—
121#3942—31no—
122#3942—32no—
123#3942—32no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C22×C5×D3—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C2×D412yes—
132C2×Dic15C2×D412yes—
133Dic30—22no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3—22no—
136C5×D12—21no—
137C5×D12—21no—
138C4×C5×D3—42no—
139C5×Dic6—42no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—21no—
143C3×Dic10—21no—
144C3×Dic10—22no—
145C3×Dic10—22no—
146C3×Dic10#4112yes—
147C3×C5×C8—22no—
148C3⋊#168—21no—
149C3⋊#168—21no—
150C2×C3×Q16—52no—
151C3×C4⋊Q8—51no—
152C3×C4×Q8—51no—
153#947—52no—
154Q8×Dic3—52no—
155Q8×Dic3—52no—
156C2×#215—51no—
157#898—102no—
158#897—101no—
159#892—101no—
160#890—52no—
161#890—102no—
162C4×D12C2×D511yescharacteristic
163#869—101no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—101no—
167C3×C4⋊C8C2×D511yescharacteristic
168C3×#103—52no—
169#835—51no—
170#835—52no—
171#835—52no—
172#821C2×D512yes—
173#818C2×D512yes—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—51no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—61no—
180C2×C5×D4—31no—
181C22×C4×C5—61no—
182C2×Dic10—31no—
183C2×Dic10C22×D312yes—
184C2×Dic10C22×D311yescharacteristic
185C2×C5×C8C22×D312yes—
186C5×C4⋊C4—31no—
187C5×C4⋊C4—32no—
188C5×C4⋊C4—61no—
189C5×C22⋊C4—61no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—62no—
192C22⋊Dic5—62no—
193#687—62no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—31no—
197C4⋊Dic5—62no—
198C4⋊Dic5C22×D311yescharacteristic
199#683—21no—
200#683—32no—
201#683—62no—
202#683—62no—
203#683—62no—
204C4×Dic5—21no—
205C4×Dic5—32no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C2×#168—31no—
209C2×#168—31no—
210Dic20—24no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—31no—
217#464—152no—
218#462—51no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C5×D3—41no—
224C2×C5×D3—41no—
225C2×C5×D3—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—22no—
232C3×Dic5—22no—
233C3×Dic5—42no—
234C3×Dic5—41no—
235C5×Dic3—42no—
236C5×Dic3—41no—
237C2×C3×Q8—51no—
238C2×C3×Q8—52no—
239C2×D12C22×D511yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6—21no—
242C2×Dic6—51no—
243C3×Q16—104no—
244C2×C3×C8C22×D512yes—
245C3×C4⋊C4—51no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4—101no—
249C3×C42—101no—
250C3×C42C22×D511yescharacteristic
251#215—102no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—21no—
256C4⋊Dic3—51no—
257C4⋊Dic3—102no—
258C4⋊Dic3—102no—
259C4⋊Dic3—102no—
260C4⋊Dic3C22×D511yescharacteristic
261C4⋊Dic3C22×D512yes—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264C4×Dic3—52no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—51no—
269C23×C5—61no—
270C5×Q8—122no—
271C5×D4—61no—
272C5×D4—61no—
273C2×C4×C5—61no—
274C2×C4×C5—62no—
275C2×C4×C5—122no—
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—22no—
282C2×Dic5—32no—
283C2×Dic5—32no—
284Dic10—21no—
285Dic10—22no—
286Dic10—22no—
287Dic10—62no—
288Dic10#23712yes—
289C5×C8—22no—
290#168—61no—
291#168—61no—
292C2×Q16—52no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—51no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—31no—
308#117—301no—
309#107—32no—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8D3×D511yescharacteristic
313#103—52no—
314#103—151no—
315#103—152no—
316#103—152no—
317#102—32no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C5×D3—81no—
325C22×D3—21no—
326C3×Q8—52no—
327C3×Q8—101no—
328C3×Q8—102no—
329C3×Q8—102no—
330C2×C3×C4—101no—
331C2×C3×C4—102no—
332C2×C3×C4—101no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4C23×D511yescharacteristic
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—52no—
339C2×Dic3—52no—
340D12—21no—
341D12—21no—
342C4×D3—42no—
343Dic6—42no—
344Dic6—102no—
345C3×C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—121no—
354C4×C5—122no—
355C4×C5#91912yes—
356C4×C5C2×#23711yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—22no—
359Dic5—41no—
360Dic5—42no—
361Dic5—62no—
362Dic5—62no—
363C2×Q8—51no—
364C2×Q8—52no—
365C2×Q8—61no—
366C2×Q8—151no—
367C2×D4—31no—
368C22×C4—61no—
369Q16—104no—
370SD16—302no—
371C2×C8—151no—
372C2×C8—151no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—32no—
375C4⋊C4—31no—
376C4⋊C4—51no—
377C4⋊C4—61no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—152no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C22⋊C4—61no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—101no—
391C42—152no—
392C42—302no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—102no—
402C3×C4—201no—
403C3×C4—202no—
404C3×C4#405812yes—
405C3×C4#414711yescharacteristic
406C3×C4D5×#4111yescharacteristic
407Dic3—42no—
408Dic3—41no—
409Dic3—102no—
410Dic3—102no—
411C2×C5—241no—
412C2×C5#559811yescharacteristic
413C2×C5C2×#91911yescharacteristic
414C2×C5#577911yescharacteristic
415C23—61no—
416Q8—52no—
417Q8—101no—
418Q8—102no—
419Q8—102no—
420Q8—122no—
421Q8—302no—
422D4—61no—
423D4—61no—
424C2×C4—61no—
425C2×C4—62no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—102no—
429C2×C4—122no—
430C2×C4—152no—
431C2×C4—152no—
432C2×C4#677711yescharacteristic
433C2×C4#677711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—22no—
436C8—301no—
437C8—301no—
438C2×C3#6596711yescharacteristic
439C2×C3C2×#405811yescharacteristic
440C2×C3#6611311yescharacteristic
441D3—81no—
442C5#8046311yescharacteristic, complemented, Sylow
443C22—121no—
444C22—121no—
445C22—121no—
446C22C2×#677711yescharacteristic
447C4—21no—
448C4—102no—
449C4—121no—
450C4—122no—
451C4—201no—
452C4—202no—
453C4—302no—
454C4—302no—
455C4#9127912yes—
456C4D5×#23711yescharacteristic
457C4#9202811yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—241no—
460C2#1175369811yescharacteristic
461C2C2×#9127911yescharacteristic
462C2#1175404311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3364
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
2. #11752477C2semidirect
3. #11750931C2semidirect
5. C3×#65138C2semidirect
7. #11747883C2semidirect
8. #11747878C2semidirect
11. #11746924C2semidirect
50. #65138D3semidirect
395. C3×C5#3364semidirect
442. C5#80463semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
#117524802
#117524772
#117509312
C5×#48462
C3×#651382
#117479792
#117478832
#117478782
#117478372
C4×#66562
#117469242
#106127253
#804635