Finite Group Databasebeta

← #14472170

Subgroups — #14472170

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#11752507C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3#11750950C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65135C211yesmaximal, characteristic
6#11747972C212yesmaximal
7#11747970C212yesmaximal
8#11747874C212yesmaximal, complemented
9#11747873C212yesmaximal, complemented
10C4×#6657C211yesmaximal, characteristic
11#11746921C211yesmaximal, characteristic, complemented
12#10611665—31nomaximal, Hall
13C2×Dic60C2212yes—
14#91758C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91385—21no—
20#91381C2212yes—
21#91364C2212yes—
22#91362—22no—
23#91359—21no—
24#91358—21no—
25#91340C2212yes—
26#91340C2212yes—
27#91339—22no—
28#91331—21no—
29C2×#6657C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91100C2212yes—
32C5×Dic3⋊C8C2212yes—
33C5×C8×Dic3C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3953C2212yes—
36C3×#3950C2212yes—
37#90987C2211yescharacteristic
38#90974C2211yescharacteristic
39#90974C2212yes—
40#90974C2212yes—
41#90965C2211yescharacteristic
42#80994—51nomaximal, Hall
43#65918—31no—
44#65901—31no—
45C5×C8×Q8—31no—
46#65138—31no—
47#65135D311yescharacteristic
48#65134—32no—
49#65118—32no—
50C4×Dic20—32no—
51#64986—32no—
52C4×#677—31no—
53#64970—31no—
54C2×Dic30C2312yes—
55C2×Dic30C2311yescharacteristic
56C2×C5×Dic6D411yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10—21no—
60C2×C3×C5×C8C2312yes—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15—21no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2311yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67Dic60—24no—
68C5×C4⋊Dic3D411yescharacteristic
69C5×Dic3⋊C4D412yes—
70C4×C5×Dic3C2312yes—
71C2×C5×C3⋊C8C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C3×#685—21no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5C2312yes—
76C3×C4⋊Dic5C2311yescharacteristic
77#6669—22no—
78#6669—22no—
79#6669—22no—
80#6668—22no—
81#6665—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6657—22no—
86#5721—51no—
87#5542—51no—
88C3×#474—51no—
89#5093—51no—
90C4×#214—51no—
91#4877—52no—
92#4873—52no—
93#4849—51no—
94#4830D511yescharacteristic, complemented
95#4768—52no—
96#4767—52no—
97C4×C5×Q8—31no—
98#4092—61no—
99#4090—61no—
100C2×Dic20—32no—
101C2×#677—31no—
102#4044—62no—
103#4038—61no—
104#4035—62no—
105#4033—61no—
106#4021—32no—
107C4×D20C2×D311yescharacteristic
108#4016—32no—
109#4015—31no—
110#4015C2×D311yescharacteristic
111C4×Dic10—31no—
112C4×Dic10—32no—
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C4×C5×C8—32no—
117C4×C5×C8—31no—
118#3953—31no—
119#3953C2×D312yes—
120#3950C2×D312yes—
121#3949—31no—
122#3948—32no—
123#3948—32no—
124#3948—32no—
125#3948—31no—
126#3364—151noSylow
127C22×C3×D5—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134Dic30—21no—
135Dic30—22no—
136Dic30—22no—
137Dic30#4112yes—
138C2×C5×Dic3C2×D412yes—
139C2×C5×Dic3C2×D412yes—
140C5×Dic6—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—22no—
143C3×D20—21no—
144C3×D20—21no—
145C3×C4×D5—42no—
146C3×Dic10—42no—
147C3×C5×C8—22no—
148C5×C3⋊C8—21no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8—51no—
151C3×C4×D4—51no—
152Q8×Dic3—101no—
153#944—101no—
154#936—52no—
155C2×#214—51no—
156#926—101no—
157#924—101no—
158C2×Dic12—52no—
159#890—52no—
160#889—102no—
161#887—52no—
162#887—52no—
163#879—102no—
164#869—51no—
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#107—52no—
168C3×C4⋊C8C2×D511yescharacteristic
169C3×#102—52no—
170#832—51no—
171#816—52no—
172Dic3⋊C8C2×D512yes—
173C8×Dic3C2×D512yes—
174#810—51no—
175#810—52no—
176#810—52no—
177#808—51no—
178C4×C3⋊C8C2×D511yescharacteristic
179C2×C5×Q8—31no—
180C2×D20C22×D311yescharacteristic
181C2×C4×D5—21no—
182C2×Dic10—21no—
183C2×Dic10—31no—
184C2×Dic10—32no—
185C2×C5×C8—31no—
186C2×C5×C8—31no—
187C2×C5×C8C22×D312yes—
188C5×C4⋊C4—32no—
189C5×C4⋊C4—31no—
190C42×C5—32no—
191C42×C5C22×D311yescharacteristic
192#685—21no—
193#685—62no—
194#685—62no—
195C4⋊Dic5—21no—
196C4⋊Dic5—31no—
197C4⋊Dic5—61no—
198C4⋊Dic5—61no—
199C4⋊Dic5C22×D312yes—
200C4⋊Dic5C22×D311yescharacteristic
201#683—62no—
202#683—62no—
203#683—62no—
204#683—62no—
205#683—61no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5—61no—
209Dic20—64no—
210#677—62no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—51no—
217#464—152no—
218#462—151no—
219C8×Q8—31no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C3×D5—41no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—42no—
232Dic15—41no—
233C3×Dic5—42no—
234C3×Dic5—41no—
235C5×Dic3—22no—
236C5×Dic3—22no—
237C2×C3×Q8—101no—
238C2×C3×D4—51no—
239C22×C3×C4—101no—
240C2×Dic6—51no—
241C2×Dic6—52no—
242C2×Dic6D2011yescharacteristic
243C2×C3×C8C22×D512yes—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—52no—
246C3×C4⋊C4—101no—
247C3×C22⋊C4—101no—
248C3×C42C22×D511yescharacteristic
249#217—102no—
250#217—102no—
251#214—102no—
252C4⋊Dic3—51no—
253C4⋊Dic3—101no—
254C4⋊Dic3—101no—
255C4⋊Dic3—102no—
256C4⋊Dic3D2011yescharacteristic
257Dic3⋊C4—101no—
258Dic3⋊C4—102no—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4D2012yes—
262C4×Dic3—101no—
263C4×Dic3—102no—
264C4×Dic3—102no—
265C4×Dic3C22×D512yes—
266C2×C3⋊C8C22×D511yescharacteristic
267C2×C3⋊C8C22×D511yescharacteristic
268Dic12—104no—
269C22×D5—21no—
270C5×Q8—62no—
271C2×C4×C5—32no—
272C2×C4×C5—32no—
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5C23×D311yescharacteristic
276C2×Dic5—21no—
277C2×Dic5—22no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281D20—21no—
282D20—21no—
283C4×D5—42no—
284Dic10—32no—
285Dic10—42no—
286Dic10—61no—
287Dic10—62no—
288Dic10—62no—
289C5×C8—22no—
290C5×C8—61no—
291C5×C8—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—51no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—51no—
308#117—301no—
309#107—52no—
310#106—151no—
311C4⋊C8—32no—
312C4⋊C8D3×D511yescharacteristic
313#103—151no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—52no—
318#102—151no—
319C4×C8—32no—
320C4×C8—31no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—202no—
327C3×D4—101no—
328C3×D4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—102no—
331C2×C3×C4—202no—
332C2×C3×C4C2×D2011yescharacteristic
333C2×C3×C4C2×D2011yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—101no—
336C2×Dic3—101no—
337C2×Dic3—102no—
338C2×Dic3C2×D2012yes—
339C2×Dic3C2×D2012yes—
340Dic6—22no—
341Dic6—52no—
342Dic6—101no—
343Dic6—102no—
344Dic6—102no—
345C3×C8—22no—
346C3⋊C8—21no—
347C3⋊C8—21no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—62no—
354C4×C5—62no—
355C4×C5#91212yes—
356C4×C5#100711yescharacteristic
357C4×C5D3×#4111yescharacteristic
358Dic5—42no—
359Dic5—41no—
360Dic5—62no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—101no—
365C2×Q8—151no—
366C2×Q8—152no—
367C2×D4—51no—
368C22×C4—101no—
369Q16—304no—
370SD16—302no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—31no—
375C4⋊C4—32no—
376C4⋊C4—52no—
377C4⋊C4—51no—
378C4⋊C4—101no—
379C4⋊C4—151no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4—301no—
387C22⋊C4—101no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—32no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—201no—
397C22×C3—201no—
398C22×C3—201no—
399C22×C3C22×D2011yescharacteristic
400C3×C4—21no—
401C3×C4—201no—
402C3×C4—202no—
403C3×C4#405012yes—
404C3×C4#414711yescharacteristic
405C3×C4D5×#4111yescharacteristic
406Dic3—22no—
407Dic3—22no—
408Dic3—102no—
409Dic3—201no—
410Dic3—202no—
411C2×C5#563311yescharacteristic
412C2×C5C2×#91211yescharacteristic
413C2×C5#577911yescharacteristic
414D5—81no—
415C23—101no—
416Q8—62no—
417Q8—152no—
418Q8—202no—
419Q8—301no—
420Q8—302no—
421Q8—302no—
422D4—101no—
423D4—101no—
424C2×C4—32no—
425C2×C4—32no—
426C2×C4—101no—
427C2×C4—102no—
428C2×C4—202no—
429C2×C4—301no—
430C2×C4—302no—
431C2×C4—301no—
432C2×C4D3×D2011yescharacteristic
433C2×C4D3×D2011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—22no—
436C8—61no—
437C8—61no—
438C2×C3—401no—
439C2×C3#6591011yescharacteristic
440C2×C3C2×#405011yescharacteristic
441C2×C3#6608711yescharacteristic
442C5#8099411yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×D3×D2011yescharacteristic
447C4—21no—
448C4—62no—
449C4—62no—
450C4—201no—
451C4—202no—
452C4—302no—
453C4—601no—
454C4—602no—
455C4#9127312yes—
456C4#9202411yescharacteristic
457C4#9202911yescharacteristic
458C3#1061166511yescharacteristic, complemented, Sylow
459C2—401no—
460C2#1175334211yescharacteristic
461C2C2×#9127311yescharacteristic
462C2#1175404211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
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. #11752481C2semidirect
3. #11750950C2semidirect
4. C5×#4830C2semidirect
8. #11747874C2semidirect
9. #11747873C2semidirect
11. #11746921C2semidirect
94. #4830D5semidirect
395. C3×C5#3364semidirect
442. C5#80994semidirect
458. C3#10611665semidirect

Maximal subgroups

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

subgroupindex
#117525072
#117524812
#117509502
C5×#48302
C3×#651352
#117479722
#117479702
#117478742
#117478732
C4×#66572
#117469212
#106116653
#809945