Finite Group Databasebeta

← #14302948

Subgroups — #14302948

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754270C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3#11751240C211yesmaximal, characteristic
4C2×C5×#824C211yesmaximal, characteristic, complemented
5#11748429C211yesmaximal, characteristic
6C3×#64777C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10600898—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16#91542—22no—
17#91529—22no—
18#91383—22no—
19#91376C412yescomplemented
20#91375C412yescomplemented
21#91344—22no—
22Dic5×Dic6—22no—
23#91109—22no—
24C5×#824—22no—
25#90981—22no—
26#68708—51nomaximal, Hall
27#66150—31no—
28#66146—31no—
29C2×C5×#101—31no—
30#65428—31no—
31#65428—31no—
32#64777—31no—
33#64777D311yescharacteristic, complemented
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—21no—
36#6817—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40C2×D60C2×C411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30C2×C411yescharacteristic
43C22×C5×Dic3D412yes—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6C2×C412yes—
49C2×C5×Dic6D412yes—
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15D412yes—
56C5×#208—21no—
57C5×#208—21no—
58C2×C5×C3⋊C8—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5—21no—
63C3×C4×Dic5C2×C412yes—
64C3×C4×Dic5D412yes—
65Dic3⋊Dic5—24no—
66#6668—24no—
67#6667—24no—
68Dic3×Dic5—24no—
69#5526—51no—
70#5516—51no—
71#5139—51no—
72C2×#824D511yescharacteristic, complemented
73#5005—51no—
74C3×H(3,ℤ/4)—51no—
75#4531—51no—
76C22×C5×Q8—31no—
77C2×#709—31no—
78C2×C5×M16—31no—
79C2×C5×M16C2×D311yescharacteristic
80#4093—32no—
81#4092—62no—
82Q8×Dic5—62no—
83Q8×Dic5—62no—
84#4090—32no—
85#4075—62no—
86#4072—31no—
87#4072—62no—
88#4072C2×D311yescharacteristic
89#4072C2×D311yescharacteristic
90C5×#101—62no—
91#3957—62no—
92#3957—62no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102#1220—41no—
103#1220—41no—
104C2×Dic15—21no—
105C2×Dic15—22no—
106D60—21no—
107D60—21no—
108C4×D15—41no—
109C4×D15—41no—
110Dic30—21no—
111Dic30—21no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3C22⋊C414yes—
115C5×Dic6—22no—
116C5×Dic6—22no—
117C5×Dic6—22no—
118C5×Dic6—22no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5—22no—
121C3×C5×C8—41no—
122C5×C3⋊C8—41no—
123C2×#235—51no—
124C22×Dic6C2×D511yescharacteristic
125C2×C3×M16C2×D511yescharacteristic
126C3×#117—51no—
127C3×#117—51no—
128#926—51no—
129C2×#208C2×D511yescharacteristic
130#897—102no—
131#887—102no—
132#886—102no—
133#877—102no—
134#875—52no—
135#869—52no—
136C4×Dic6—102no—
137#825—102no—
138#824—22no—
139#805—102no—
140C2×C5×Q8—32no—
141C2×C5×Q8—32no—
142C2×C5×Q8—61no—
143C2×C5×Q8—61no—
144C2×C5×Q8—61no—
145C2×C5×Q8—61no—
146C22×C4×C5—32no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—61no—
149#709—61no—
150#709—61no—
151#709—61no—
152#709—61no—
153C2×D20—31no—
154C2×C4×D5—61no—
155C2×Dic10—31no—
156C5×M16—21no—
157C5×M16—21no—
158C5×M16—61no—
159C5×M16—61no—
160C2×C5×C8—21no—
161C2×C5×C8—61no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164C22⋊Dic5—61no—
165#685—64no—
166C4⋊Dic5—21no—
167C4⋊Dic5—21no—
168C4⋊Dic5—64no—
169C4⋊Dic5—61no—
170#683—64no—
171C4×Dic5—32no—
172C4×Dic5—64no—
173C4×Dic5C4×D312yes—
174C4×Dic5D1212yes—
175#536—151no—
176#519—151no—
177#421—151no—
178#421—151no—
179C2×#101—31no—
180H(3,ℤ/4)—51no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×D15—42no—
187C2×D15—41no—
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5#12111yescharacteristic
191C3×C4×C5#12111yescharacteristic
192Dic15—42no—
193Dic15—41no—
194C3×Dic5—42no—
195C3×Dic5—42no—
196C5×Dic3—24no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—101no—
199C22×Dic3D2012yes—
200#235—101no—
201#235—101no—
202#235—101no—
203#235—101no—
204C2×D12—51no—
205C2×C4×D3—101no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—51no—
211C2×Dic6C4×D512yes—
212C2×Dic6C22⋊D512yes—
213C3×M16—21no—
214C3×M16—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C42—52no—
221C3×C42—52no—
222#217—101no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—101no—
225C4⋊Dic3—104no—
226Dic3⋊C4—104no—
227C4×Dic3—52no—
228C4×Dic3—104no—
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—61no—
234C5×Q8—62no—
235C5×Q8—62no—
236C5×Q8—62no—
237C5×Q8—62no—
238C2×C4×C5—34no—
239C2×C4×C5—62no—
240C2×C4×C5—62no—
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5C2×D1211yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23911yescharacteristic
247C22⋊D5—121no—
248C22⋊D5—121no—
249C2×Dic5—22no—
250C2×Dic5—22no—
251C2×Dic5—61no—
252C2×Dic5—62no—
253D20—61no—
254D20—61no—
255C4×D5—121no—
256C4×D5—121no—
257Dic10—61no—
258Dic10—61no—
259C5×C8—41no—
260C5×C8—121no—
261C2×#41—151no—
262C22×Q8—31no—
263C2×M16—31no—
264C2×M16D3×D511yescharacteristic
265C4⋊Q8—152no—
266#124—152no—
267#123—302no—
268C22⋊Q8—302no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—51no—
272#117—51no—
273#117—151no—
274#117—302no—
275#104—302no—
276#104—302no—
277#101—62no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282D15—81no—
283C23×C3C2×D2011yescharacteristic
284C22×D3—101no—
285C2×C3×C4—102no—
286C2×C3×C4—102no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4#71111yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293#67—201no—
294#67—201no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—102no—
298C2×Dic3—101no—
299C2×Dic3#68514yes—
300D12—101no—
301D12—101no—
302C4×D3—201no—
303C4×D3—201no—
304Dic6—22no—
305Dic6—22no—
306Dic6—22no—
307Dic6—22no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—41no—
311C3⋊C8—41no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88211yescharacteristic
315C22×C5#89411yescharacteristic
316C2×D5—122no—
317C2×D5—121no—
318C4×C5—64no—
319C4×C5C4×D1211yescharacteristic
320C4×C5#88411yescharacteristic
321C4×C5#89311yescharacteristic
322C4×C5#89511yescharacteristic
323Dic5—42no—
324Dic5—42no—
325Dic5—122no—
326Dic5—121no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—32no—
332C2×Q8—32no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—151no—
338C2×D4—151no—
339C2×D4—301no—
340C22×C4—32no—
341C22×C4—301no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—61no—
346M16—61no—
347C2×C8—21no—
348C2×C8—61no—
349C4⋊C4—101no—
350C4⋊C4—101no—
351C4⋊C4—304no—
352C4⋊C4—304no—
353C4⋊C4—301no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C22⋊C4—304no—
357C22⋊C4—301no—
358C42—52no—
359C42—52no—
360C42—152no—
361C42—304no—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3#402811yescharacteristic
365C22×C3#403211yescharacteristic
366C22×C3C2×#68511yescharacteristic
367C2×D3—202no—
368C2×D3—201no—
369C3×C4—202no—
370C3×C4—202no—
371C3×C4#402711yescharacteristic
372C3×C4#402711yescharacteristic
373C3×C4#408511yescharacteristic
374C3×C4#408511yescharacteristic
375Dic3—24no—
376Dic3—202no—
377Dic3—201no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#466511yescharacteristic
382D5—241no—
383C23—301no—
384C23D3×D2011yescharacteristic
385Q8—62no—
386Q8—62no—
387Q8—62no—
388Q8—62no—
389Q8—301no—
390Q8—301no—
391D4—301no—
392D4—301no—
393D4—601no—
394D4—601no—
395C2×C4—34no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—301no—
401C2×C4—302no—
402C2×C4—601no—
403C2×C4—601no—
404C2×C4#676811yescharacteristic
405C2×C4C4×D3×D511yescharacteristic
406C2×C4D5×D1211yescharacteristic
407C2×C4#678211yescharacteristic
408C2×C4D3×C22⋊D511yescharacteristic
409C2×C4#679011yescharacteristic
410C8—41no—
411C8—121no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3#6524711yescharacteristic
416D3—401no—
417C5#6870811yescharacteristic, complemented, Sylow
418C22—41no—
419C22—602no—
420C22—601no—
421C22#9142711yescharacteristic
422C22D3×#68511yescharacteristic
423C22#9147611yescharacteristic
424C4—64no—
425C4—202no—
426C4—202no—
427C4—602no—
428C4—601no—
429C4#9140511yescharacteristic
430C4#9140611yescharacteristic
431C4#9141611yescharacteristic
432C4#9155811yescharacteristic
433C3#1060089811yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—1201no—
438C2#1174888311yescharacteristic
subgroupG/H
centerC2#11748883
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754211C2semidirect
4. C2×C5×#824C2semidirect
6. C3×#64777C2semidirect
7. #11745970C2semidirect
19. #91376C4semidirect
20. #91375C4semidirect
33. #64777D3semidirect
72. C2×#824D5semidirect
362. C3×C5#1912semidirect
417. C5#68708semidirect
433. C3#10600898semidirect

Maximal subgroups

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

subgroupindex
#117542702
#117542112
#117512402
C2×C5×#8242
#117484292
C3×#647772
#117459702
#106008983
#687085