Finite Group Databasebeta

← #14313649

Subgroups — #14313649

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2#11751338C211yesmaximal, characteristic, complemented
3C5×#5237C211yesmaximal, characteristic, complemented
4#11746015C212yesmaximal, complemented
5#11746012C212yesmaximal, complemented
6#10600941—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C3×#709C411yescharacteristic
9C2×#6710—21no—
10C2×C5×#208—21no—
11C3×#4093C2211yescharacteristic
12C3×#4090C2211yescharacteristic
13C3×#4086C411yescharacteristic
14C3×#4085—21no—
15C3×#4085—21no—
16C3×#4082C411yescharacteristic
17C3×C4×C22⋊D5—21no—
18C3×C4×C22⋊D5—21no—
19C2×C3×C4×Dic5C411yescharacteristic
20#91120C2212yes—
21#91117—21no—
22C5×#836C2212yes—
23C5×#833—21no—
24#71820—51nomaximal, Hall
25#66166D311yescharacteristic
26C5×#413—31no—
27#65526—31no—
28#64698—32no—
29#64697—32no—
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2311yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5—21no—
43C3×#709—41no—
44C3×#709—41no—
45C2×C3×D20C2×C411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48#6710—22no—
49#6710—41no—
50C2×C3⋊#168—41no—
51C5×#208—22no—
52C5×#208—41no—
53C2×C5×C3⋊C8—41no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5C2×C411yescharacteristic
63C3×#532—51no—
64#5237—51no—
65#5237D511yescharacteristic, complemented
66#4548—52no—
67#4542—52no—
68C2×C5×#41C2×D311yescharacteristic
69C2×#709Dic311yescharacteristic
70C2×C5×M16—61no—
71#4093C2×D311yescharacteristic
72#4090C2×D311yescharacteristic
73#4086Dic311yescharacteristic
74#4085—21no—
75#4085—21no—
76#4082Dic311yescharacteristic
77C4×C22⋊D5—21no—
78C4×C22⋊D5—21no—
79C2×C4×Dic5Dic311yescharacteristic
80C2×#681—61no—
81C5×#101—32no—
82C5×#100—61no—
83#3968—32no—
84#3965—61no—
85#2132—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C22×C3×D5—21no—
90C3×C5×Q8—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C3×C22⋊D5—42no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—42no—
111C3×D20—41no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×Dic10—41no—
115C3⋊#168—42no—
116C5×C3⋊C8—42no—
117C2×C3×#41—51no—
118C2×C3×#41C2×D511yescharacteristic
119C3×C4⋊Q8—51no—
120C3×#127—51no—
121C3×#124—51no—
122C3×#124—51no—
123C3×#121—101no—
124C3×#121—101no—
125C3×C4×D4—101no—
126C3×C4×D4—101no—
127C2×C3×C42—51no—
128C2×#208—21no—
129C2×#208—101no—
130#836—52no—
131#836C2×D512yes—
132#833—21no—
133#833—101no—
134C5×#41—41no—
135C5×#41—41no—
136C2×C5×Q8C22×D311yescharacteristic
137C2×C5×D4C2×Dic311yescharacteristic
138C2×C5×D4#6711yescharacteristic
139C2×C5×D4#6711yescharacteristic
140C22×C4×C5C2×Dic311yescharacteristic
141C22×C4×C5#6711yescharacteristic
142C22×C4×C5#6711yescharacteristic
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C2×C22⋊D5—21no—
146C22×Dic5—21no—
147#709—41no—
148#709—41no—
149C2×D20C2×Dic311yescharacteristic
150C2×C4×D5—21no—
151C2×Dic10C2×Dic311yescharacteristic
152C5×M16—62no—
153C5×M16—121no—
154C2×C5×C8—121no—
155C22⋊Dic5—21no—
156C22⋊Dic5—21no—
157#685—21no—
158#685—21no—
159#683—21no—
160#683—21no—
161C4×Dic5—21no—
162C4×Dic5C2×Dic311yescharacteristic
163C4×Dic5C2×Dic311yescharacteristic
164#681—62no—
165#681—121no—
166C2×#168—121no—
167#532—51no—
168#413—31no—
169#413—151no—
170#356—152no—
171#355—152no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187C3×Dic5—22no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×#41—41no—
191C3×#41—41no—
192C3×#41—201no—
193C3×#41—201no—
194C2×C3×Q8—51no—
195C2×C3×Q8C22×D511yescharacteristic
196C2×C3×D4—51no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4C4×D511yescharacteristic
201C2×C3×D4D2011yescharacteristic
202C2×C3×D4C22⋊D511yescharacteristic
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C4×D511yescharacteristic
206C22×C3×C4D2011yescharacteristic
207C22×C3×C4C22⋊D511yescharacteristic
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—101no—
217#208—22no—
218#208—41no—
219#208—102no—
220#208—201no—
221C2×C3⋊C8—41no—
222C2×C3⋊C8—201no—
223C23×C5#21711yescharacteristic
224C23×C5#21711yescharacteristic
225C23×C5#21711yescharacteristic
226C22×D5—21no—
227C5×Q8—41no—
228C5×D4—41no—
229C5×D4—41no—
230C5×D4—41no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5#21711yescharacteristic
238C2×C4×C5C22×Dic311yescharacteristic
239C2×C4×C5C2×#6711yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C22⋊D5—42no—
242C22⋊D5—42no—
243C22⋊D5—42no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—42no—
248D20—41no—
249C4×D5—41no—
250C4×D5—41no—
251Dic10—41no—
252C5×C8—122no—
253#168—122no—
254C2×#41—51no—
255C2×#41D3×D511yescharacteristic
256C2×M16—61no—
257C2×M16—301no—
258C4⋊Q8—51no—
259#127—51no—
260#124—51no—
261#124—51no—
262#121—101no—
263#121—101no—
264C4×D4—101no—
265C4×D4—101no—
266C2×C42—51no—
267#101—32no—
268#101—152no—
269#100—61no—
270#100—301no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5—41no—
275C2×C3×C5C2×#9911yescharacteristic
276C3×D5—81no—
277C23×C3—101no—
278C23×C3#68511yescharacteristic
279C23×C3#68511yescharacteristic
280C23×C3#68511yescharacteristic
281C3×Q8—41no—
282C3×Q8—201no—
283C3×D4—41no—
284C3×D4—41no—
285C3×D4—41no—
286C3×D4—201no—
287C3×D4—202no—
288C3×D4—202no—
289C3×D4—202no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—202no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4#68511yescharacteristic
303C2×C3×C4C2×C4×D511yescharacteristic
304C2×C3×C4C2×D2011yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C3⋊C8—42no—
307C3⋊C8—202no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C2×#21711yescharacteristic
315C2×D5—41no—
316C2×D5—41no—
317C2×D5—41no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5#83411yescharacteristic
322C4×C5#83411yescharacteristic
323Dic5—22no—
324Dic5—41no—
325Dic5—41no—
326#41—41no—
327#41—41no—
328#41—201no—
329#41—201no—
330C2×Q8—51no—
331C2×Q8C2×D3×D511yescharacteristic
332C2×D4—51no—
333C2×D4—101no—
334C2×D4—101no—
335C2×D4—101no—
336C2×D4D5×Dic311yescharacteristic
337C2×D4#120111yescharacteristic
338C2×D4#120211yescharacteristic
339C22×C4—101no—
340C22×C4—101no—
341C22×C4D5×Dic311yescharacteristic
342C22×C4#120111yescharacteristic
343C22×C4#120211yescharacteristic
344M16—62no—
345M16—121no—
346M16—302no—
347M16—601no—
348C2×C8—121no—
349C2×C8—601no—
350C4⋊C4—101no—
351C4⋊C4—101no—
352C22⋊C4—101no—
353C22⋊C4—101no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C42—51no—
357C42—51no—
358C42—101no—
359C3×C5#213211yescharacteristic, complemented, Hall
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—201no—
367C22×C3—201no—
368C22×C3—201no—
369C22×C3C2×#68511yescharacteristic
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—102no—
374C3×C4—201no—
375C3×C4—201no—
376C3×C4#393811yescharacteristic
377C3×C4#393811yescharacteristic
378C2×C5—21no—
379C2×C5—41no—
380C2×C5—41no—
381C2×C5—41no—
382C2×C5C2×#83411yescharacteristic
383D5—81no—
384C23—101no—
385C23#666511yescharacteristic
386C23#666511yescharacteristic
387C23#666511yescharacteristic
388Q8—41no—
389Q8—201no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—201no—
394D4—202no—
395D4—202no—
396D4—202no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—101no—
406C2×C4—202no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4#666511yescharacteristic
410C2×C4C2×D5×Dic311yescharacteristic
411C2×C4C2×#120111yescharacteristic
412C2×C4C2×#120211yescharacteristic
413C8—122no—
414C8—602no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—401no—
420C2×C3C2×#393811yescharacteristic
421C5#7182011yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—201no—
429C22—201no—
430C22—201no—
431C22C2×#666511yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—102no—
436C4—201no—
437C4—201no—
438C4#9099511yescharacteristic
439C4#9099511yescharacteristic
440C3#1060094111yescharacteristic, complemented, Sylow
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—401no—
446C2C2×#9099511yescharacteristic
subgroupG/H
centerC4#90995
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC3×#66166C2
cosocleC2×C3×C5×Q8C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2132
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751338C2semidirect
3. C5×#5237C2semidirect
4. #11746015C2semidirect
5. #11746012C2semidirect
65. #5237D5semidirect
359. C3×C5#2132semidirect
421. C5#71820semidirect
440. C3#10600941semidirect

Maximal subgroups

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

subgroupindex
C3×#661662
#117513382
C5×#52372
#117460152
#117460122
#106009413
#718205