Finite Group Databasebeta

← #14472158

Subgroups — #14472158

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#11752483C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3C4×#6706C211yesmaximal, characteristic
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#64970C211yesmaximal, characteristic, complemented
6#11747988C212yesmaximal
7#11747872C212yesmaximal
8#11747864C212yesmaximal, complemented
9#11747831C212yesmaximal, complemented
10#11747104C211yesmaximal, characteristic, complemented
11#11746971C211yesmaximal, characteristic
12#10611665—31nomaximal, Hall
13C2×#6706C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91385—21no—
20#91383—21no—
21#91381C2212yes—
22#91374C2212yes—
23#91347—21no—
24#91345—22no—
25#91340C2212yes—
26#91339—22no—
27#91331—21no—
28Dic3×Dic10C2212yes—
29C2×#6662C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91101C2211yescharacteristic
33#91100C2211yescharacteristic
34C5×Dic3⋊C8C2212yes—
35C5×C8×Dic3C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×#3948C2212yes—
38C3×#3948C2212yes—
39#90990C2212yes—
40#90971C2212yes—
41#90968C2212yes—
42#81625—51nomaximal, Hall
43#65918—31no—
44#65901—31no—
45C5×C8×Q8—31no—
46#65138—31no—
47#65135—31no—
48#65134—32no—
49#65118—32no—
50C4×Dic20—32no—
51#64986—32no—
52C4×#677—31no—
53#64970D311yescharacteristic, complemented
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6D411yescharacteristic
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2312yes—
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63#6714—21no—
64C4⋊Dic15C2311yescharacteristic
65C4⋊Dic15C2311yescharacteristic
66#6712—21no—
67C4×Dic15—21no—
68#6706—22no—
69C5×C4⋊Dic3D411yescharacteristic
70C5×Dic3⋊C4D412yes—
71C4×C5×Dic3C2312yes—
72C2×C5×C3⋊C8C2312yes—
73C3×C4⋊Dic5—21no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2312yes—
77#6669—22no—
78#6669—22no—
79#6668—22no—
80#6668—22no—
81#6667—22no—
82#6667—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6662—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×#204—51no—
96C8×Dic6D511yescharacteristic, complemented
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×D20—31no—
108#4016—32no—
109#4015C2×D311yescharacteristic
110#4015C2×D311yescharacteristic
111C4×Dic10—32no—
112C4×Dic10—31no—
113C4×Dic10—32no—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3953—31no—
119#3953—32no—
120#3950—32no—
121#3949—31no—
122#3948—32no—
123#3948—31no—
124#3948C2×D312yes—
125#3948C2×D312yes—
126#3364—151noSylow
127C22×D15—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134D60—21no—
135D60—21no—
136C4×D15—42no—
137Dic30—21no—
138Dic30#4112yes—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6—22no—
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—
149C5×C3⋊C8—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×#204—51no—
158#898—102no—
159#897—101no—
160#892—101no—
161#890—52no—
162#889—102no—
163#887—52no—
164C4×D12—51no—
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#103—52no—
168C3×#103—52no—
169C3×C4×C8C2×D511yescharacteristic
170#835—52no—
171#821—51no—
172#817—51no—
173#816—51no—
174Dic3⋊C8C2×D512yes—
175C8×Dic3C2×D512yes—
176#809—52no—
177#807—52no—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C2×C5×Q8—31no—
180C2×D20—31no—
181C2×C4×D5—61no—
182C2×Dic10—21no—
183C2×Dic10—31no—
184C2×Dic10C22×D312yes—
185C2×C5×C8—32no—
186C2×C5×C8C22×D311yescharacteristic
187C2×C5×C8C22×D311yescharacteristic
188C5×C4⋊C4—32no—
189C5×C4⋊C4—31no—
190C42×C5—32no—
191C42×C5C22×D311yescharacteristic
192#685—62no—
193#685—62no—
194#685—61no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—31no—
199C4⋊Dic5—31no—
200C4⋊Dic5C22×D312yes—
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—51no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—31no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—41no—
232Dic15—41no—
233C3×Dic5—42no—
234C3×Dic5—42no—
235C5×Dic3—22no—
236C5×Dic3—22no—
237C2×C3×Q8—52no—
238C2×C3×Q8—101no—
239C2×D12—51no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6D2011yescharacteristic
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—101no—
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—102no—
254C4⋊Dic3—51no—
255C4⋊Dic3—51no—
256C4⋊Dic3—102no—
257C4⋊Dic3—102no—
258C4⋊Dic3D2011yescharacteristic
259Dic3⋊C4—101no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4D2012yes—
263C4×Dic3—101no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3C22×D512yes—
267C2×C3⋊C8C22×D512yes—
268#204—102no—
269C22×D5—61no—
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—22no—
277C2×Dic5—22no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—61no—
281D20—61no—
282D20—61no—
283C4×D5—122no—
284Dic10—22no—
285Dic10—22no—
286Dic10—32no—
287Dic10—42no—
288Dic10—61no—
289C5×C8—21no—
290C5×C8—21no—
291C5×C8—62no—
292C2×Q16—152no—
293C2×SD16—151no—
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—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—32no—
312C4⋊C8—31no—
313#103—52no—
314#103—52no—
315#103—152no—
316#103—151no—
317#102—152no—
318#102—151no—
319C4×C8—32no—
320C4×C8D3×D511yescharacteristic
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—202no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4C2×D2011yescharacteristic
332C2×C3×C4C2×D2011yescharacteristic
333C2×C3×C4C23×D511yescharacteristic
334C2×Dic3—101no—
335C2×Dic3—101no—
336C2×Dic3—101no—
337C2×Dic3C2×D2012yes—
338C2×Dic3C2×D2012yes—
339D12—101no—
340D12—101no—
341C4×D3—202no—
342Dic6—22no—
343Dic6—52no—
344Dic6—101no—
345C3×C8—21no—
346C3×C8—21no—
347C3⋊C8—22no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—62no—
354C4×C5—62no—
355C4×C5#91612yes—
356C4×C5D3×#4111yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—42no—
359Dic5—42no—
360Dic5—62no—
361Dic5—121no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—52no—
365C2×Q8—101no—
366C2×Q8—151no—
367C2×D4—151no—
368C22×C4—301no—
369Q16—304no—
370SD16—302no—
371C2×C8—32no—
372C2×C8C2×D3×D511yescharacteristic
373C2×C8C2×D3×D511yescharacteristic
374C4⋊C4—31no—
375C4⋊C4—32no—
376C4⋊C4—52no—
377C4⋊C4—101no—
378C4⋊C4—101no—
379C4⋊C4—101no—
380C4⋊C4—151no—
381C4⋊C4—151no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—301no—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—32no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C22×D2011yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—202no—
402C3×C4—202no—
403C3×C4#405012yes—
404C3×C4#414711yescharacteristic
405C3×C4D5×#4111yescharacteristic
406Dic3—22no—
407Dic3—22no—
408Dic3—102no—
409Dic3—201no—
410Dic3—201no—
411C2×C5#567711yescharacteristic
412C2×C5C2×#91611yescharacteristic
413C2×C5#576611yescharacteristic
414D5—241no—
415C23—301no—
416Q8—62no—
417Q8—102no—
418Q8—102no—
419Q8—152no—
420Q8—202no—
421Q8—301no—
422D4—301no—
423D4—301no—
424C2×C4—32no—
425C2×C4—32no—
426C2×C4—102no—
427C2×C4—102no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4D3×D2011yescharacteristic
433C2×C4D3×D2011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—21no—
436C8—21no—
437C8—62no—
438C2×C3#6591011yescharacteristic
439C2×C3C2×#405011yescharacteristic
440C2×C3#6608711yescharacteristic
441D3—401no—
442C5#8162511yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D3×D2011yescharacteristic
447C4—21no—
448C4—62no—
449C4—62no—
450C4—202no—
451C4—202no—
452C4—302no—
453C4—601no—
454C4—601no—
455C4#9127212yes—
456C4#9200011yescharacteristic
457C4#9201611yescharacteristic
458C3#1061166511yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175254611yescharacteristic
461C2#1175399111yescharacteristic
462C2C2×#9127211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
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
4. C5×C8×Dic6C2semidirect
5. C3×#64970C2semidirect
8. #11747864C2semidirect
9. #11747831C2semidirect
10. #11747104C2semidirect
53. #64970D3semidirect
96. C8×Dic6D5semidirect
395. C3×C5#3364semidirect
442. C5#81625semidirect
458. C3#10611665semidirect

Maximal subgroups

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

subgroupindex
#117524832
#117524812
C4×#67062
C5×C8×Dic62
C3×#649702
#117479882
#117478722
#117478642
#117478312
#117471042
#117469712
#106116653
#816255