Finite Group Databasebeta

← #14302947

Subgroups — #14302947

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#11754251C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3C2×C5×#824C211yesmaximal, characteristic, complemented
4C3×#65428C211yesmaximal, characteristic
5#11748420C211yesmaximal, characteristic
6#11746378C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10600898—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13#91815C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16#91536—22no—
17#91529—22no—
18#91385C412yescomplemented
19#91368C412yescomplemented
20#91359—22no—
21#91344—22no—
22Dic5×Dic6—22no—
23C5×#824—22no—
24C3×#3957—22no—
25#90976—22no—
26#70411—51nomaximal, Hall
27#66150—31no—
28#66146—31no—
29C2×C5×#101—31no—
30#65428—31no—
31#65428D311yescharacteristic
32#64777—31no—
33#64777—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3D412yes—
36C2×C5×Dic6—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6C2×C412yes—
41C2×C5×Dic6D412yes—
42C2×C3×C22⋊D5—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53#6719—21no—
54#6719—21no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4×Dic15C2×C412yes—
58C4×Dic15D412yes—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C22⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×C4×Dic5D412yes—
65Dic3⋊Dic5—24no—
66#6669—24no—
67#6665—24no—
68Dic3×Dic5—24no—
69#5825—51no—
70#5516—51no—
71C3×#421—51no—
72#5236—51no—
73C2×#824D511yescharacteristic, complemented
74#4557—51no—
75#4531—51no—
76C22×C5×Q8—31no—
77C2×#709C2×D311yescharacteristic
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—31no—
88#4072—62no—
89#4072C2×D311yescharacteristic
90C5×#101—62no—
91#3957—22no—
92#3957—62no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—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
102C2×Dic15—22no—
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3C22⋊C414yes—
107C5×Dic6—22no—
108C5×Dic6—22no—
109C5×Dic6—22no—
110C5×Dic6—22no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—22no—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—41no—
118C3×C4×D5—41no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×C5×C8—41no—
122C5×C3⋊C8—41no—
123C2×C3×#41—51no—
124C22×Dic6C2×D511yescharacteristic
125C2×C3×M16C2×D511yescharacteristic
126C3×#117—51no—
127#944—52no—
128#936—52no—
129#935—102no—
130#926—51no—
131#926—51no—
132#924—102no—
133C2×#208C2×D511yescharacteristic
134#887—102no—
135#877—102no—
136C4×Dic6—102no—
137C3×#104—102no—
138#837—102no—
139#824—22no—
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—21no—
149#709—21no—
150#709—21no—
151#709—21no—
152#709—21no—
153C2×D20C4×D311yescharacteristic
154C2×C4×D5—21no—
155C2×Dic10C4×D311yescharacteristic
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—61no—
164C22⋊Dic5—61no—
165#685—64no—
166C4⋊Dic5—21no—
167C4⋊Dic5—64no—
168C4⋊Dic5—61no—
169C4⋊Dic5—61no—
170#683—64no—
171C4×Dic5—32no—
172C4×Dic5—32no—
173C4×Dic5—64no—
174C4×Dic5#6712yes—
175#536—151no—
176#519—151no—
177#421—51no—
178#421—151no—
179C2×#101—31no—
180H(3,ℤ/4)—151no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—42no—
187C2×C3×D5—41no—
188C3×C4×C5C4×D411yescharacteristic
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5#12111yescharacteristic
191C3×C4×C5#12111yescharacteristic
192Dic15—42no—
193Dic15—42no—
194C3×Dic5—42no—
195C3×Dic5—41no—
196C5×Dic3—24no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3D2012yes—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6C4×D512yes—
212C2×Dic6C22⋊D512yes—
213C3×M16—21no—
214C3×M16—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C42—52no—
219#217—101no—
220#217—101no—
221#217—104no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224Dic3⋊C4—104no—
225Dic3⋊C4—104no—
226C4×Dic3—52no—
227C4×Dic3—52no—
228C4×Dic3—104no—
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—21no—
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×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5C2×#6711yescharacteristic
247C22⋊D5—41no—
248C22⋊D5—41no—
249C2×Dic5—21no—
250C2×Dic5—22no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253D20—21no—
254D20—21no—
255C4×D5—41no—
256C4×D5—41no—
257Dic10—21no—
258Dic10—21no—
259C5×C8—41no—
260C5×C8—121no—
261C2×#41—51no—
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—151no—
273#117—151no—
274#117—302no—
275#104—102no—
276#104—302no—
277#101—62no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282C3×D5—81no—
283C23×C3—101no—
284C23×C3C2×D2011yescharacteristic
285C3×Q8—101no—
286C3×Q8—101no—
287C3×D4—101no—
288C3×D4—101no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—102no—
292C2×C3×C4—101no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3#68514yes—
306Dic6—22no—
307Dic6—22no—
308Dic6—22no—
309Dic6—22no—
310C3×C8—41no—
311C3⋊C8—41no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88311yescharacteristic
315C22×C5#93711yescharacteristic
316C2×D5—42no—
317C2×D5—41no—
318C4×C5—64no—
319C4×C5#67⋊C411yescharacteristic
320C4×C5#88411yescharacteristic
321C4×C5C4×#6711yescharacteristic
322C4×C5#93811yescharacteristic
323Dic5—42no—
324Dic5—41no—
325Dic5—122no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—32no—
332C2×Q8—32no—
333C2×Q8—51no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—61no—
338C2×D4—51no—
339C2×D4—101no—
340C22×C4—32no—
341C22×C4—101no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—61no—
346M16—61no—
347C2×C8—21no—
348C2×C8—61no—
349C4⋊C4—101no—
350C4⋊C4—304no—
351C4⋊C4—304no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C22⋊C4—101no—
355C22⋊C4—304no—
356C22⋊C4—301no—
357C22⋊C4—301no—
358C42—52no—
359C42—152no—
360C42—152no—
361C42—304no—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—202no—
365C22×C3—201no—
366C22×C3#402811yescharacteristic
367C22×C3#403211yescharacteristic
368C22×C3C2×#68511yescharacteristic
369C3×C4—202no—
370C3×C4—201no—
371C3×C4#402711yescharacteristic
372C3×C4#402711yescharacteristic
373C3×C4#408511yescharacteristic
374C3×C4#408511yescharacteristic
375Dic3—24no—
376Dic3—202no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#495611yescharacteristic
382D5—81no—
383C23—101no—
384C23D3×D2011yescharacteristic
385Q8—62no—
386Q8—62no—
387Q8—62no—
388Q8—62no—
389Q8—101no—
390Q8—101no—
391D4—101no—
392D4—101no—
393D4—201no—
394D4—201no—
395C2×C4—34no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—101no—
399C2×C4—102no—
400C2×C4—201no—
401C2×C4—201no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4#677211yescharacteristic
405C2×C4C4×D3×D511yescharacteristic
406C2×C4#677711yescharacteristic
407C2×C4#678011yescharacteristic
408C2×C4D5×#6711yescharacteristic
409C2×C4D3×C22⋊D511yescharacteristic
410C8—41no—
411C8—121no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—401no—
416C2×C3#6524711yescharacteristic
417C5#7041111yescharacteristic, complemented, Sylow
418C22—41no—
419C22—202no—
420C22—201no—
421C22#9145711yescharacteristic
422C22D3×#68511yescharacteristic
423C22#9147411yescharacteristic
424C4—64no—
425C4—202no—
426C4—201no—
427C4—602no—
428C4—602no—
429C4#9144011yescharacteristic
430C4#9144211yescharacteristic
431C4#9145311yescharacteristic
432C4#9156511yescharacteristic
433C3#1060089811yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—401no—
438C2#1174891111yescharacteristic
subgroupG/H
centerC2#11748911
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
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
3. C2×C5×#824C2semidirect
6. #11746378C2semidirect
7. #11745970C2semidirect
18. #91385C4semidirect
19. #91368C4semidirect
73. C2×#824D5semidirect
362. C3×C5#1912semidirect
417. C5#70411semidirect
433. C3#10600898semidirect

Maximal subgroups

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

subgroupindex
#117542512
#117542112
C2×C5×#8242
C3×#654282
#117484202
#117463782
#117459702
#106008983
#704115