Finite Group Databasebeta

← #14302963

Subgroups — #14302963

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
1C3×#66159C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic
4C5×#5236C211yesmaximal, characteristic
5C2×#90961C211yesmaximal, characteristic, complemented
6#11745970C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10601204—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4090C412yescomplemented
16C3×#4082C412yescomplemented
17C3×#4081—22no—
18C3×#4072C2211yescharacteristic
19C3×#4070—22no—
20#91528—22no—
21#91331—22no—
22Dic3×Dic10—22no—
23#91121—22no—
24C5×#837—22no—
25#90961—22no—
26#71864—51nomaximal, Hall
27#66159D311yescharacteristic
28#65850—31no—
29C5×#421—31no—
30#65525—31no—
31C2×#3956—31no—
32#64777—31no—
33#64751—31no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C2×C3×C5×Q8C2×C411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×C3×Dic5D412yes—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10—21no—
48C2×C3×Dic10C2×C412yes—
49C2×C3×Dic10D412yes—
50#6719—21no—
51C4⋊Dic15—21no—
52C4×Dic15D412yes—
53#6710—21no—
54#6710—21no—
55C2×C3⋊#168—21no—
56C5×#217—21no—
57C5×C4⋊Dic3—21no—
58C4×C5×Dic3D412yes—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C22⋊Dic5—21no—
63C3×C22⋊Dic5—24no—
64C3×C4⋊Dic5—21no—
65C3×#683—24no—
66C3×C4×Dic5C2×C412yes—
67#6668—24no—
68Dic3×Dic5—24no—
69C3×#536—51no—
70#5812—51no—
71#5236—51no—
72#5236D511yescharacteristic
73C2×#836—51no—
74#4531—51no—
75#4531—51no—
76C2×C5×#41C2×D311yescharacteristic
77C22×Dic10C2×D311yescharacteristic
78C2×C5×M16—31no—
79C5×#117—31no—
80#4090Dic312yescomplemented
81#4082Dic312yescomplemented
82#4081—22no—
83#4072—31no—
84#4072C2×D311yescharacteristic
85#4070—22no—
86C2×#681—31no—
87#4033—62no—
88#4023—62no—
89C4×Dic10—62no—
90C5×#104—62no—
91#3969—62no—
92#3956—62no—
93#1912—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—21no—
97C3×C5×Q8—21no—
98C3×C5×D4—21no—
99C3×C5×D4—21no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—22no—
112C2×C5×Dic3—22no—
113C2×C3×Dic5—22no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5C22⋊C414yes—
117C3×Dic10—22no—
118C3×Dic10—22no—
119C3×Dic10—22no—
120C3×Dic10—22no—
121C3⋊#168—41no—
122C5×C3⋊C8—41no—
123C2×C3×#41C2×D511yescharacteristic
124C22×C3×Q8—51no—
125C3×C4⋊Q8—52no—
126C3×#124—52no—
127C3×#123—102no—
128C3×C22⋊Q8—102no—
129C3×#117—51no—
130Q8×Dic3—102no—
131Q8×Dic3—102no—
132#926—51no—
133#926—102no—
134#926C2×D511yescharacteristic
135C2×#208—51no—
136C2×#208C2×D511yescharacteristic
137#837—22no—
138#837—102no—
139#836—102no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41—21no—
143C5×#41—21no—
144C2×C5×Q8C2×Dic311yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4C2×Dic311yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5#6712yes—
150C2×Dic10—21no—
151C2×Dic10—21no—
152C2×Dic10—21no—
153C2×Dic10—21no—
154C2×Dic10C2×Dic312yes—
155C2×Dic10#6712yes—
156C5×M16—61no—
157C5×M16—61no—
158C2×C5×C8—61no—
159C5×C4⋊C4—61no—
160C5×C22⋊C4—61no—
161C42×C5—32no—
162C22⋊Dic5—21no—
163C22⋊Dic5—24no—
164C22⋊Dic5—61no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167#683—24no—
168#683—64no—
169C4×Dic5—32no—
170C4×Dic5—64no—
171C4×Dic5C2×Dic312yes—
172#681—61no—
173#681—61no—
174C2×#168—61no—
175#536—51no—
176#519—151no—
177#421—31no—
178#421—151no—
179C2×#101—151no—
180H(3,ℤ/4)—151no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5—42no—
184C22×C3×C5—41no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12311yescharacteristic
188C3×C4×C5—41no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5#12111yescharacteristic
193Dic15—42no—
194C3×Dic5—24no—
195C3×Dic5—42no—
196C5×Dic3—42no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C2×C3×Q8—52no—
202C2×C3×Q8—52no—
203C2×C3×Q8—101no—
204C2×C3×Q8—101no—
205C2×C3×Q8—101no—
206C2×C3×Q8—101no—
207C2×C3×Q8C4×D511yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4C4×D511yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—52no—
212C22×C3×C4C22×D511yescharacteristic
213C3×C4⋊C4—104no—
214C3×C4⋊C4—101no—
215C3×C22⋊C4—104no—
216C3×C22⋊C4—101no—
217C3×C42—52no—
218#217—21no—
219#217—101no—
220C4⋊Dic3—21no—
221C4⋊Dic3—104no—
222C4⋊Dic3—101no—
223C4×Dic3—52no—
224C4×Dic3—104no—
225C4×Dic3C22⋊D512yes—
226#208—21no—
227#208—21no—
228#208—101no—
229#208—101no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—101no—
232C23×C5—21no—
233C23×C5C2×#6711yescharacteristic
234C5×Q8—21no—
235C5×Q8—21no—
236C5×D4—21no—
237C5×D4—21no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—21no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—62no—
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5C22×Dic311yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×Dic5—22no—
251C2×Dic5—22no—
252C2×Dic5—22no—
253C2×Dic5—62no—
254C2×Dic5#21714yes—
255Dic10—22no—
256Dic10—22no—
257Dic10—22no—
258Dic10—22no—
259C5×C8—121no—
260#168—121no—
261C2×#41D3×D511yescharacteristic
262C22×Q8—51no—
263C2×M16—31no—
264C2×M16—151no—
265C4⋊Q8—52no—
266#124—52no—
267#123—102no—
268C22⋊Q8—102no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—31no—
272#117—51no—
273#117—151no—
274#117—302no—
275#104—62no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5—81no—
282C2×C3×C5#38611yescharacteristic
283C23×C3—21no—
284C23×C3D4×D511yescharacteristic
285C3×Q8—21no—
286C3×Q8—21no—
287C3×Q8—102no—
288C3×Q8—102no—
289C3×Q8—102no—
290C3×Q8—102no—
291C3×D4—21no—
292C3×D4—21no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—54no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4C2×C4×D511yescharacteristic
303C2×C3×C4#70911yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4#71111yescharacteristic
307C2×C3×C4C2×C22⋊D511yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—102no—
310C3⋊C8—41no—
311C3⋊C8—201no—
312C22×C5—41no—
313C22×C5—42no—
314C22×C5—41no—
315C22×C5#93511yescharacteristic
316C22×C5#93711yescharacteristic
317C22×C5C2×#21711yescharacteristic
318C4×C5—41no—
319C4×C5—122no—
320C4×C5D4×Dic311yescharacteristic
321C4×C5D4×Dic311yescharacteristic
322C4×C5#93911yescharacteristic
323C4×C5#93911yescharacteristic
324Dic5—24no—
325Dic5—42no—
326Dic5—122no—
327#41—21no—
328#41—21no—
329#41—21no—
330#41—21no—
331C2×Q8—52no—
332C2×Q8—52no—
333C2×Q8—101no—
334C2×Q8—101no—
335C2×Q8—101no—
336C2×Q8—101no—
337C2×Q8D5×Dic311yescharacteristic
338C2×D4—21no—
339C2×D4D5×Dic311yescharacteristic
340C22×C4—21no—
341C22×C4—52no—
342C22×C4C2×D3×D511yescharacteristic
343M16—61no—
344M16—61no—
345M16—301no—
346M16—301no—
347C2×C8—61no—
348C2×C8—301no—
349C4⋊C4—61no—
350C4⋊C4—104no—
351C4⋊C4—101no—
352C4⋊C4—304no—
353C4⋊C4—301no—
354C22⋊C4—61no—
355C22⋊C4—104no—
356C22⋊C4—101no—
357C22⋊C4—301no—
358C42—32no—
359C42—52no—
360C42—152no—
361C42—304no—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—42no—
365C22×C3—41no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#402911yescharacteristic
368C22×C3#408311yescharacteristic
369C3×C4—41no—
370C3×C4—104no—
371C3×C4—202no—
372C3×C4#402711yescharacteristic
373C3×C4#403011yescharacteristic
374C3×C4C4×C22⋊D511yescharacteristic
375C3×C4#408411yescharacteristic
376Dic3—42no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5—81no—
382C2×C5#522011yescharacteristic
383C23—21no—
384C23D5×#6711yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—102no—
388Q8—102no—
389Q8—102no—
390Q8—102no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—54no—
399C2×C4—62no—
400C2×C4—102no—
401C2×C4—102no—
402C2×C4—102no—
403C2×C4—302no—
404C2×C4C2×D5×Dic311yescharacteristic
405C2×C4#677911yescharacteristic
406C2×C4#678011yescharacteristic
407C2×C4D5×#6711yescharacteristic
408C2×C4D3×C22⋊D511yescharacteristic
409C2×C4#679011yescharacteristic
410C8—121no—
411C8—601no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—81no—
416C2×C3#6524511yescharacteristic
417C5#7186411yescharacteristic, complemented, Sylow
418C22—41no—
419C22—42no—
420C22—41no—
421C22D5×#21711yescharacteristic
422C22#9154811yescharacteristic
423C22#9157711yescharacteristic
424C4—41no—
425C4—104no—
426C4—122no—
427C4—202no—
428C4—602no—
429C4#9154911yescharacteristic
430C4#9155011yescharacteristic
431C4Dic3×C22⋊D511yescharacteristic
432C4#9155911yescharacteristic
433C3#1060120411yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—81no—
438C2#1174951811yescharacteristic
subgroupG/H
centerC2#11749518
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5#386
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
5. C2×#90961C2semidirect
6. #11745970C2semidirect
7. #11745969C2semidirect
15. C3×#4090C4semidirect
16. C3×#4082C4semidirect
80. #4090Dic3semidirect
81. #4082Dic3semidirect
362. C3×C5#1912semidirect
417. C5#71864semidirect
433. C3#10601204semidirect

Maximal subgroups

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

subgroupindex
C3×#661592
#117541882
#117513372
C5×#52362
C2×#909612
#117459702
#117459692
#106012043
#718645