Finite Group Databasebeta

← #14313672

Subgroups — #14313672

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
1#11756575C211yesmaximal, characteristic
2C2×C3×C5×#101C211yesmaximal, characteristic, complemented
3C2×#91120C211yesmaximal, characteristic, complemented
4#11746299C212yesmaximal, complemented
5#11746298C212yesmaximal, complemented
6#10600921—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×#6817C411yescharacteristic
9C2×C3×C5×M16—21no—
10#91836C411yescharacteristic
11#91836C2211yescharacteristic
12#91835—21no—
13#91835—21no—
14#91833C411yescharacteristic
15#91833C2211yescharacteristic
16#91818—21no—
17#91818—21no—
18#91815C411yescharacteristic
19C2×#6710—21no—
20C3×C5×#101—21no—
21C3×C5×#101C2212yes—
22#91120—21no—
23#91120C2212yes—
24#70128—51nomaximal, Hall
25#66150—31no—
26C2×C5×#101D311yescharacteristic, complemented
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×#1220—21no—
40#6817—41no—
41#6817—41no—
42C2×D60C2×C411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30C2×C411yescharacteristic
45C3×C5×M16—22no—
46C3×C5×M16—41no—
47C2×C3×C5×C8—41no—
48#6719—21no—
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53C4⋊Dic15—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57#6712—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15C2×C411yescharacteristic
60#6710—22no—
61#6710—41no—
62C2×C3⋊#168—41no—
63#5816—51no—
64C2×C3×#101D511yescharacteristic, complemented
65C2×#836—51no—
66#4478—52no—
67#4477—52no—
68C22×C5×Q8C2×D311yescharacteristic
69C2×#709—31no—
70C2×C5×M16—21no—
71#4093—31no—
72#4093—31no—
73#4092—61no—
74#4092—61no—
75#4090—31no—
76#4090—31no—
77#4075—61no—
78#4075—61no—
79#4072—31no—
80C2×#681—61no—
81C5×#101—21no—
82C5×#101C2×D312yes—
83#3968—32no—
84#3968—61no—
85#2133—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C22×D15—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
104#1220—41no—
105#1220—41no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109D60—41no—
110C4×D15—42no—
111Dic30—41no—
112C3×C5×C8—42no—
113C3⋊#168—42no—
114C22×C3×Q8C2×D511yescharacteristic
115C2×#235—51no—
116C2×C3×M16—21no—
117#947—51no—
118#947—51no—
119#946—101no—
120#946—101no—
121#944—51no—
122#944—51no—
123#929—101no—
124#929—101no—
125#926—51no—
126C2×#208—101no—
127C3×#101—21no—
128C3×#101C2×D512yes—
129#836—52no—
130#836—101no—
131C2×C5×Q8—41no—
132C2×C5×Q8—41no—
133C2×C5×Q8C4×D311yescharacteristic
134C2×C5×Q8D1211yescharacteristic
135C2×C5×Q8#6711yescharacteristic
136C2×C5×Q8C22×D311yescharacteristic
137C22×C4×C5C4×D311yescharacteristic
138C22×C4×C5D1211yescharacteristic
139C22×C4×C5#6711yescharacteristic
140C2×C22⋊D5—61no—
141#709—121no—
142#709—121no—
143C2×D20—31no—
144C2×C4×D5—61no—
145C2×Dic10—31no—
146C5×M16—22no—
147C5×M16—41no—
148C2×C5×C8—41no—
149C22⋊Dic5—61no—
150#685—61no—
151#685—61no—
152#685—61no—
153#685—61no—
154C4⋊Dic5—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161#681—62no—
162#681—121no—
163C2×#168—121no—
164#536—151no—
165C2×#101—151no—
166C2×#101D1511yescharacteristic, complemented
167#356—152no—
168#355—152no—
169C22×C3×C5—41no—
170C22×C3×C5#9911yescharacteristic
171C22×C3×C5#9911yescharacteristic
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—42no—
174C2×D15—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—
181Dic15—41no—
182Dic15—41no—
183Dic15—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8—41no—
186C2×C3×Q8C4×D511yescharacteristic
187C2×C3×Q8D2011yescharacteristic
188C2×C3×Q8C22⋊D511yescharacteristic
189C2×C3×Q8C22×D511yescharacteristic
190C22×C3×C4C4×D511yescharacteristic
191C22×C3×C4D2011yescharacteristic
192C22×C3×C4C22⋊D511yescharacteristic
193C2×#67—101no—
194#235—201no—
195#235—201no—
196C2×D12—51no—
197C2×C4×D3—101no—
198C2×Dic6—51no—
199C3×M16—22no—
200C3×M16—41no—
201C2×C3×C8—41no—
202#217—101no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207C4⋊Dic3—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C4×Dic3—51no—
213C4×Dic3—51no—
214#208—102no—
215#208—201no—
216C2×C3⋊C8—201no—
217C23×C5(C2×D3)⋊C411yescharacteristic
218C22×D5—61no—
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(C2×D3)⋊C411yescharacteristic
230C2×C4×C5(C2×D3)⋊C411yescharacteristic
231C2×C4×C5(C2×D3)⋊C411yescharacteristic
232C2×C4×C5C2×C4×D311yescharacteristic
233C2×C4×C5C2×D1211yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C22⋊D5—121no—
236C22⋊D5—121no—
237C2×Dic5—61no—
238C2×Dic5—61no—
239C2×Dic5—61no—
240D20—121no—
241C4×D5—122no—
242Dic10—121no—
243C5×C8—42no—
244#168—122no—
245C2×#41—151no—
246C22×Q8C2×D1511yescharacteristic
247C2×M16—21no—
248C2×M16—301no—
249C4⋊Q8—151no—
250C4⋊Q8—151no—
251#124—151no—
252#124—151no—
253#123—301no—
254#123—301no—
255C22⋊Q8—301no—
256C22⋊Q8—301no—
257#117—151no—
258#101—21no—
259#101—152no—
260#101—301no—
261#101C2×D1512yes—
262C2×C3×C5—21no—
263C2×C3×C5—21no—
264C2×C3×C5—21no—
265C2×C3×C5C2×#9911yescharacteristic
266D15—81no—
267C23×C3#68511yescharacteristic
268C22×D3—101no—
269C3×Q8—41no—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—41no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4#68511yescharacteristic
280C2×C3×C4#68511yescharacteristic
281C2×C3×C4#68511yescharacteristic
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4C2×D2011yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285#67—201no—
286#67—201no—
287C2×Dic3—101no—
288C2×Dic3—101no—
289C2×Dic3—101no—
290D12—201no—
291C4×D3—202no—
292Dic6—201no—
293C3×C8—42no—
294C3⋊C8—202no—
295C22×C5—41no—
296C22×C5#80611yescharacteristic
297C22×C5#80611yescharacteristic
298C22×C5C2×(C2×D3)⋊C411yescharacteristic
299C2×D5—122no—
300C2×D5—121no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—21no—
304C4×C5—21no—
305C4×C5—21no—
306C4×C5—21no—
307Dic5—121no—
308Dic5—121no—
309Dic5—121no—
310#41—601no—
311#41—601no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—151no—
315C2×Q8C4×D1511yescharacteristic
316C2×Q8D6011yescharacteristic
317C2×Q8#122011yescharacteristic
318C2×Q8C22×D1511yescharacteristic
319C2×D4—151no—
320C2×D4—301no—
321C22×C4—301no—
322C22×C4C4×D1511yescharacteristic
323C22×C4D6011yescharacteristic
324C22×C4#122011yescharacteristic
325M16—22no—
326M16—41no—
327M16—302no—
328M16—601no—
329C2×C8—41no—
330C2×C8—601no—
331C4⋊C4—301no—
332C4⋊C4—301no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C22⋊C4—301no—
337C22⋊C4—301no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C42—151no—
342C42—151no—
343C3×C5#213311yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3#393811yescharacteristic
346C22×C3#393811yescharacteristic
347C22×C3C2×#68511yescharacteristic
348C2×D3—202no—
349C2×D3—201no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356Dic3—201no—
357Dic3—201no—
358Dic3—201no—
359C2×C5—21no—
360C2×C5—21no—
361C2×C5—21no—
362C2×C5C2×#80611yescharacteristic
363D5—241no—
364C23—301no—
365C23#671411yescharacteristic
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—601no—
371D4—601no—
372D4—601no—
373D4—601no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—301no—
381C2×C4—301no—
382C2×C4—301no—
383C2×C4—602no—
384C2×C4#671411yescharacteristic
385C2×C4#671411yescharacteristic
386C2×C4#671411yescharacteristic
387C2×C4C2×C4×D1511yescharacteristic
388C2×C4C2×D6011yescharacteristic
389C2×C4C2×#122011yescharacteristic
390C8—42no—
391C8—602no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3C2×#393811yescharacteristic
396D3—401no—
397C5#7012811yescharacteristic, complemented, Sylow
398C22—41no—
399C22—602no—
400C22—601no—
401C22#9109011yescharacteristic
402C22#9109011yescharacteristic
403C22C2×#671411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—601no—
411C4—601no—
412C4—601no—
413C3#1060092111yescharacteristic, complemented, Sylow
414C2—21no—
415C2—21no—
416C2—21no—
417C2—1201no—
418C2C2×#9109011yescharacteristic
subgroupG/H
centerC2C2×#91090
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C22×D15
FittingC2×C3×C5×#101C2
socleC2×C3×C5C2×#99
prime radicalC2×#6817C4
cosocleC2×C3×C5×Q8C23
hypercenterC2×#101D15
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#101C2semidirect
3. C2×#91120C2semidirect
4. #11746299C2semidirect
5. #11746298C2semidirect
26. C2×C5×#101D3semidirect
64. C2×C3×#101D5semidirect
166. C2×#101D15semidirect
343. C3×C5#2133semidirect
397. C5#70128semidirect
413. C3#10600921semidirect

Maximal subgroups

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

subgroupindex
#117565752
C2×C3×C5×#1012
C2×#911202
#117462992
#117462982
#106009213
#701285