Finite Group Databasebeta

← #14313696

Subgroups — #14313696

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66150C211yesmaximal, characteristic
2C2×#91120C211yesmaximal, characteristic, complemented
3C2×C5×#836C211yesmaximal, characteristic, complemented
4#11746015C212yesmaximal, complemented
5#11746012C212yesmaximal, complemented
6#10600921—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×#709C411yescharacteristic
9C2×#6710—21no—
10C2×C5×#208—21no—
11C3×#4093C411yescharacteristic
12C3×#4093C2211yescharacteristic
13C3×#4092—21no—
14C3×#4092—21no—
15C3×#4090C411yescharacteristic
16C3×#4090C2211yescharacteristic
17C3×#4075—21no—
18C3×#4075—21no—
19C3×#4072C411yescharacteristic
20#91120—21no—
21#91120C2212yes—
22C5×#836—21no—
23C5×#836C2212yes—
24#71872—51nomaximal, Hall
25#66150D311yescharacteristic
26C2×C5×#101—31no—
27C2×#3968—31no—
28#64698—32no—
29#64697—32no—
30C2×C3×C5×Q8—41no—
31C2×C3×C5×Q8—41no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C2×C3×C5×Q8D411yescharacteristic
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×Q8C2311yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C3×#709—41no—
41C3×#709—41no—
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10C2×C411yescharacteristic
45#6710—22no—
46#6710—41no—
47C2×C3⋊#168—41no—
48C5×#208—22no—
49C5×#208—41no—
50C2×C5×C3⋊C8—41no—
51C3×C22⋊Dic5—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×#683—21no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5C2×C411yescharacteristic
63C3×#536—51no—
64C2×#836—51no—
65C2×#836D511yescharacteristic, complemented
66#4548—52no—
67#4542—52no—
68C22×C5×Q8C2×D311yescharacteristic
69C2×#709Dic311yescharacteristic
70C2×C5×M16—61no—
71#4093Dic311yescharacteristic
72#4093C2×D311yescharacteristic
73#4092—21no—
74#4092—21no—
75#4090Dic311yescharacteristic
76#4090C2×D311yescharacteristic
77#4075—21no—
78#4075—21no—
79#4072Dic311yescharacteristic
80C2×#681—61no—
81C5×#101—32no—
82C5×#101—61no—
83#3968—32no—
84#3968—61no—
85#2133—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C22×C3×D5—21no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×Q8—41no—
91C3×C5×Q8—41no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—41no—
105C3×C22⋊D5—41no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C3×D20—41no—
110C3×C4×D5—42no—
111C3×Dic10—41no—
112C3⋊#168—42no—
113C5×C3⋊C8—42no—
114C2×C3×#41—51no—
115C22×C3×Q8C2×D511yescharacteristic
116C3×C4⋊Q8—51no—
117C3×C4⋊Q8—51no—
118C3×#124—51no—
119C3×#124—51no—
120C3×#123—101no—
121C3×#123—101no—
122C3×C22⋊Q8—101no—
123C3×C22⋊Q8—101no—
124C3×#117—51no—
125C2×#208—21no—
126C2×#208—101no—
127#836—21no—
128#836—52no—
129#836—101no—
130#836C2×D512yes—
131C2×C5×Q8—41no—
132C2×C5×Q8—41no—
133C2×C5×Q8C2×Dic311yescharacteristic
134C2×C5×Q8#6711yescharacteristic
135C2×C5×Q8#6711yescharacteristic
136C2×C5×Q8C22×D311yescharacteristic
137C22×C4×C5C2×Dic311yescharacteristic
138C22×C4×C5#6711yescharacteristic
139C22×C4×C5#6711yescharacteristic
140C2×C22⋊D5—21no—
141#709—41no—
142#709—41no—
143C2×D20C2×Dic311yescharacteristic
144C2×C4×D5—21no—
145C2×Dic10C2×Dic311yescharacteristic
146C5×M16—62no—
147C5×M16—121no—
148C2×C5×C8—121no—
149C22⋊Dic5—21no—
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154C4⋊Dic5—21no—
155#683—21no—
156#683—21no—
157#683—21no—
158#683—21no—
159C4×Dic5C2×Dic311yescharacteristic
160C4×Dic5C2×Dic311yescharacteristic
161#681—62no—
162#681—121no—
163C2×#168—121no—
164#536—51no—
165C2×#101—31no—
166C2×#101—151no—
167#356—152no—
168#355—152no—
169C22×C3×C5—41no—
170C22×C3×C5#9911yescharacteristic
171C22×C3×C5#9911yescharacteristic
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C3×D5—42no—
174C2×C3×D5—41no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×Dic5—41no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×#41—201no—
185C3×#41—201no—
186C2×C3×Q8—41no—
187C2×C3×Q8—41no—
188C2×C3×Q8—51no—
189C2×C3×Q8C4×D511yescharacteristic
190C2×C3×Q8D2011yescharacteristic
191C2×C3×Q8C22⋊D511yescharacteristic
192C2×C3×Q8C22×D511yescharacteristic
193C2×C3×D4—51no—
194C2×C3×D4—101no—
195C22×C3×C4—101no—
196C22×C3×C4C4×D511yescharacteristic
197C22×C3×C4D2011yescharacteristic
198C22×C3×C4C22⋊D511yescharacteristic
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C42—51no—
210C3×C42—51no—
211#208—22no—
212#208—41no—
213#208—102no—
214#208—201no—
215C2×C3⋊C8—41no—
216C2×C3⋊C8—201no—
217C23×C5#21711yescharacteristic
218C22×D5—21no—
219C5×Q8—41no—
220C5×Q8—41no—
221C5×Q8—41no—
222C5×Q8—41no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5#21711yescharacteristic
230C2×C4×C5#21711yescharacteristic
231C2×C4×C5#21711yescharacteristic
232C2×C4×C5C22×Dic311yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C22⋊D5—41no—
236C22⋊D5—41no—
237C2×Dic5—21no—
238C2×Dic5—21no—
239C2×Dic5—21no—
240D20—41no—
241C4×D5—42no—
242Dic10—41no—
243C5×C8—122no—
244#168—122no—
245C2×#41—51no—
246C22×Q8D3×D511yescharacteristic
247C2×M16—61no—
248C2×M16—301no—
249C4⋊Q8—51no—
250C4⋊Q8—51no—
251#124—51no—
252#124—51no—
253#123—101no—
254#123—101no—
255C22⋊Q8—101no—
256C22⋊Q8—101no—
257#117—51no—
258#101—32no—
259#101—61no—
260#101—152no—
261#101—301no—
262C2×C3×C5—21no—
263C2×C3×C5—21no—
264C2×C3×C5—21no—
265C2×C3×C5C2×#9911yescharacteristic
266C3×D5—81no—
267C23×C3—101no—
268C23×C3#68511yescharacteristic
269C3×Q8—41no—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—41no—
273C3×Q8—201no—
274C3×D4—201no—
275C3×D4—201no—
276C3×D4—201no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—101no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4—202no—
287C2×C3×C4#68511yescharacteristic
288C2×C3×C4#68511yescharacteristic
289C2×C3×C4#68511yescharacteristic
290C2×C3×C4C2×C4×D511yescharacteristic
291C2×C3×C4C2×D2011yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C3⋊C8—42no—
294C3⋊C8—202no—
295C22×C5—41no—
296C22×C5#83411yescharacteristic
297C22×C5#83411yescharacteristic
298C22×C5C2×#21711yescharacteristic
299C2×D5—42no—
300C2×D5—41no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—21no—
304C4×C5—21no—
305C4×C5—21no—
306C4×C5—21no—
307Dic5—41no—
308Dic5—41no—
309Dic5—41no—
310#41—201no—
311#41—201no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—51no—
315C2×Q8D5×Dic311yescharacteristic
316C2×Q8#120111yescharacteristic
317C2×Q8#120211yescharacteristic
318C2×Q8C2×D3×D511yescharacteristic
319C2×D4—51no—
320C2×D4—101no—
321C22×C4—101no—
322C22×C4D5×Dic311yescharacteristic
323C22×C4#120111yescharacteristic
324C22×C4#120211yescharacteristic
325M16—62no—
326M16—121no—
327M16—302no—
328M16—601no—
329C2×C8—121no—
330C2×C8—601no—
331C4⋊C4—101no—
332C4⋊C4—101no—
333C4⋊C4—101no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C22⋊C4—101no—
337C22⋊C4—101no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C42—51no—
342C42—51no—
343C3×C5#213311yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3—202no—
346C22×C3—201no—
347C22×C3#393811yescharacteristic
348C22×C3#393811yescharacteristic
349C22×C3C2×#68511yescharacteristic
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—201no—
357C3×C4—201no—
358C3×C4—201no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5—21no—
362C2×C5C2×#83411yescharacteristic
363D5—81no—
364C23—101no—
365C23#666511yescharacteristic
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—201no—
371D4—201no—
372D4—201no—
373D4—201no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—202no—
384C2×C4#666511yescharacteristic
385C2×C4#666511yescharacteristic
386C2×C4#666511yescharacteristic
387C2×C4C2×D5×Dic311yescharacteristic
388C2×C4C2×#120111yescharacteristic
389C2×C4C2×#120211yescharacteristic
390C8—122no—
391C8—602no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—401no—
396C2×C3C2×#393811yescharacteristic
397C5#7187211yescharacteristic, complemented, Sylow
398C22—41no—
399C22—202no—
400C22—201no—
401C22#9099511yescharacteristic
402C22#9099511yescharacteristic
403C22C2×#666511yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—201no—
411C4—201no—
412C4—201no—
413C3#1060092111yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2—21no—
417C2—401no—
418C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5C2×#99
prime radicalC2×C3×#709C4
cosocleC2×C3×C5×Q8C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91120C2semidirect
3. C2×C5×#836C2semidirect
4. #11746015C2semidirect
5. #11746012C2semidirect
65. C2×#836D5semidirect
343. C3×C5#2133semidirect
397. C5#71872semidirect
413. C3#10600921semidirect

Maximal subgroups

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

subgroupindex
C3×#661502
C2×#911202
C2×C5×#8362
#117460152
#117460122
#106009213
#718725