Finite Group Databasebeta

← #14472160

Subgroups — #14472160

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#11752482C211yesmaximal, characteristic, complemented
2#11752480C211yesmaximal, characteristic
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic
5C3×#64970C211yesmaximal, characteristic, complemented
6#11747979C212yesmaximal
7#11747877C212yesmaximal, complemented
8#11747865C212yesmaximal
9#11747828C212yesmaximal, complemented
10#11747099C211yesmaximal, characteristic, complemented
11#11746900C211yesmaximal, characteristic
12#10611354—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C2×C5×#204C2211yescharacteristic
15C4×C5×D12C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91389—21no—
20#91384C2212yes—
21#91370C2212yes—
22#91365—21no—
23#91346—22no—
24#91344C2212yes—
25#91341—22no—
26#91338—21no—
27#91331C2212yes—
28Dic3×Dic10—21no—
29C2×#6661C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#817C2211yescharacteristic
36C5×#816C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90989C2212yes—
40#90970C2212yes—
41#90966C2212yes—
42#81625—51nomaximal, Hall
43#65904—31no—
44#65876—31no—
45C4×C5×SD16—31no—
46#65455—32no—
47#65320—31no—
48#65296—31no—
49#65146—32no—
50#65079—32no—
51#65057—32no—
52#64970D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2312yes—
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15D411yescharacteristic
64#6712D412yes—
65C4×Dic15C2312yes—
66C2×C3⋊#168C2312yes—
67C5×(C2×D3)⋊C4—21no—
68C5×C4⋊Dic3C2311yescharacteristic
69C5×C4⋊Dic3C2311yescharacteristic
70C5×Dic3⋊C4—21no—
71C4×C5×Dic3—21no—
72C5×#204—22no—
73C3×C4⋊Dic5—21no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2312yes—
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79#6668—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6661—24no—
86#5732—51no—
87#5721—51no—
88C3×#487—51no—
89#5090—51no—
90#5087—51no—
91#4800—52no—
92#4799—52no—
93#4798—52no—
94#4790—52no—
95C4×#204D511yescharacteristic
96C8×Dic6—51no—
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4—31no—
100Q8×Dic5—32no—
101C2×#689—32no—
102#4082—32no—
103#4072—61no—
104#4070—61no—
105#4036—32no—
106#4036—62no—
107#4033—32no—
108#4025—62no—
109#4015—61no—
110#4015C2×D311yescharacteristic
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3948C2×D312yes—
120#3948C2×D312yes—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
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—21no—
136C2×C5×Dic3—21no—
137C5×D12—21no—
138C5×D12—21no—
139C4×C5×D3—42no—
140C5×Dic6—21no—
141C5×Dic6#4112yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C3×Dic10—22no—
145C3×Dic10—22no—
146C3×Dic10—42no—
147C3×C5×C8—21no—
148C3×C5×C8—21no—
149C3⋊#168—22no—
150C3×C4⋊Q8—51no—
151C3×C4⋊Q8—51no—
152#947—52no—
153Q8×Dic3—52no—
154Q8×Dic3—101no—
155#944—101no—
156C2×#216—52no—
157C2×#204C2×D511yescharacteristic
158#898—102no—
159#897—101no—
160#892—101no—
161#890—52no—
162#889—102no—
163#887—52no—
164C4×D12C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#103—52no—
168C3×#103—52no—
169C3×C4×C8C2×D511yescharacteristic
170#835—52no—
171#821C2×D511yescharacteristic
172#817C2×D511yescharacteristic
173#816C2×D511yescharacteristic
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—52no—
177#807—52no—
178C4⋊(C3⋊C8)—51no—
179C2×C5×Q8—31no—
180C2×C5×D4—31no—
181C22×C4×C5—61no—
182C2×Dic10—21no—
183C2×Dic10—31no—
184C2×Dic10C22×D312yes—
185C5×SD16—62no—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—31no—
189C5×C4⋊C4—31no—
190C5×C4⋊C4—61no—
191C5×C22⋊C4—61no—
192C42×C5—61no—
193C42×C5C22×D311yescharacteristic
194C22⋊Dic5—62no—
195C22⋊Dic5—62no—
196#689—64no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—31no—
201C4⋊Dic5—62no—
202C4⋊Dic5—62no—
203C4⋊Dic5C22×D312yes—
204#683—32no—
205#683—62no—
206#683—62no—
207C4×Dic5—32no—
208C4×Dic5—62no—
209C4×Dic5—62no—
210C2×#168—32no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—51no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—31no—
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—42no—
233C3×Dic5—42no—
234C5×Dic3—22no—
235C5×Dic3—41no—
236C5×Dic3—41no—
237C2×C3×Q8—52no—
238C2×C3×Q8—101no—
239C2×D12C22×D511yescharacteristic
240C2×C4×D3—21no—
241C2×Dic6—51no—
242C2×Dic6C22×D511yescharacteristic
243C2×C3×C8C22×D511yescharacteristic
244C2×C3×C8C22×D511yescharacteristic
245C3×C4⋊C4—52no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4—101no—
249C3×C42C22×D511yescharacteristic
250#216—104no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—102no—
254C4⋊Dic3—51no—
255C4⋊Dic3—102no—
256C4⋊Dic3—102no—
257C4⋊Dic3C22×D511yescharacteristic
258C4⋊Dic3C22×D511yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—52no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263C4×Dic3—21no—
264C4×Dic3—52no—
265C4×Dic3—102no—
266C4×Dic3—102no—
267C2×C3⋊C8—52no—
268#204—22no—
269C23×C5—61no—
270C5×Q8—32no—
271C5×Q8—61no—
272C5×D4—61no—
273C5×D4—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5—122no—
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—32no—
284C2×Dic5—32no—
285Dic10—22no—
286Dic10—22no—
287Dic10—42no—
288Dic10—62no—
289C5×C8—21no—
290C5×C8—21no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—31no—
294C4⋊Q8—51no—
295C4⋊Q8—51no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—31no—
308#117—301no—
309#107—152no—
310#106—31no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—31no—
314#103—52no—
315#103—52no—
316#103—152no—
317#102—31no—
318#102—152no—
319C4×C8—152no—
320C4×C8D3×D511yescharacteristic
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C5×D3—81no—
325C22×D3—21no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—202no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4C23×D511yescharacteristic
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—52no—
338C2×Dic3—52no—
339D12—21no—
340D12—21no—
341C4×D3—42no—
342Dic6—21no—
343Dic6—102no—
344Dic6#70912yes—
345C3×C8—21no—
346C3×C8—21no—
347C3⋊C8—102no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—62no—
354C4×C5—121no—
355C4×C5—121no—
356C4×C5#91612yes—
357C4×C5D3×#4111yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—42no—
360Dic5—42no—
361Dic5—62no—
362Dic5—62no—
363C2×Q8—31no—
364C2×Q8—52no—
365C2×Q8—101no—
366C2×Q8—151no—
367C2×D4—31no—
368C22×C4—61no—
369Q16—304no—
370SD16—62no—
371C2×C8—152no—
372C2×C8C2×D3×D511yescharacteristic
373C2×C8C2×D3×D511yescharacteristic
374C4⋊C4—31no—
375C4⋊C4—31no—
376C4⋊C4—52no—
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—61no—
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—202no—
402C3×C4—202no—
403C3×C4#406212yes—
404C3×C4C2×#70911yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—22no—
407Dic3—41no—
408Dic3—41no—
409Dic3—102no—
410Dic3—102no—
411C2×C5—241no—
412C2×C5#567711yescharacteristic
413C2×C5C2×#91611yescharacteristic
414C2×C5#576611yescharacteristic
415C23—61no—
416Q8—32no—
417Q8—61no—
418Q8—102no—
419Q8—102no—
420Q8—202no—
421Q8—302no—
422D4—61no—
423D4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—102no—
428C2×C4—102no—
429C2×C4—122no—
430C2×C4—152no—
431C2×C4—152no—
432C2×C4#677711yescharacteristic
433C2×C4#677711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—21no—
436C8—21no—
437C8—302no—
438C2×C3#6588611yescharacteristic
439C2×C3C2×#406211yescharacteristic
440C2×C3#6610511yescharacteristic
441D3—81no—
442C5#8162511yescharacteristic, complemented, Sylow
443C22—121no—
444C22—121no—
445C22—121no—
446C22C2×#677711yescharacteristic
447C4—21no—
448C4—62no—
449C4—121no—
450C4—121no—
451C4—202no—
452C4—202no—
453C4—302no—
454C4—302no—
455C4#9127612yes—
456C4#9200111yescharacteristic
457C4D3×#70911yescharacteristic
458C3#1061135411yescharacteristic, complemented, Sylow
459C2—241no—
460C2#1175255511yescharacteristic
461C2C2×#9127611yescharacteristic
462C2#1175401111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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
1. #11752482C2semidirect
3. C8×Dic30C2semidirect
5. C3×#64970C2semidirect
7. #11747877C2semidirect
9. #11747828C2semidirect
10. #11747099C2semidirect
52. #64970D3semidirect
395. C3×C5#3364semidirect
442. C5#81625semidirect
458. C3#10611354semidirect

Maximal subgroups

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

subgroupindex
#117524822
#117524802
C8×Dic302
C4×C5×#2042
C3×#649702
#117479792
#117478772
#117478652
#117478282
#117470992
#117469002
#106113543
#816255