Finite Group Databasebeta

← C2×#11755257 #14482876

Subgroups — C2×#11755257 #14482876

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic, complemented
2C22×C3×#713C211yesmaximal, characteristic, complemented
3C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
4#11755257C2116yesmaximal, direct product factor
5C2×#91465C213yesmaximal, complemented
6C2×C4×#1202C213yesmaximal, complemented
7C2×#91364C213yesmaximal, complemented
8C2×#91360C213yesmaximal, complemented
9C2×#65910—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×Q8×D15—28no—
12C2×Q8×D15C2218yescomplemented
13C22×C4×D15C2213yes—
14C22×Dic30C2213yes—
15C2×C3×#713—28no—
16C2×C3×#713C2218yescomplemented
17C22×C3×D20C2213yes—
18C22×C3×C4×D5C2213yes—
19C22×#1202C2213yes—
20C5×Q8×Dic3C2218yescomplemented
21C2×C5×C4⋊Dic3C2213yes—
22C2×C4×C5×Dic3C2213yes—
23C2×Dic3⋊Dic5C2213yes—
24C2×#6667C2211yescharacteristic
25C2×#6665C2216yes—
26C2×#6665C2213yes—
27#91465C22124yescomplemented
28C4×#1202C22124yescomplemented
29#91364C22124yescomplemented
30#91360C22124yescomplemented
31C2×#5831—51nomaximal, Hall
32C22×#713D311yescharacteristic, complemented
33C22×Q8×D5—31no—
34C2×C4×C5×Q8—31no—
35#65910—316no—
36C2×#4043—33no—
37C2×#4041—33no—
38C2×#4021—33no—
39C2×C4×D20—33no—
40C23×D15C2311yescharacteristic
41C23×C3×D5C2313yes—
42C2×C3×C5×Q8D418yescomplemented
43C2×C3×C5×Q8C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×Dic15C2313yes—
46Q8×D15—232no—
47C2×C4×D15—212no—
48C2×C4×D15C23112yes—
49C2×Dic30—212no—
50C2×Dic30C23112yes—
51C22×C5×Dic3C2311yescharacteristic
52C22×C5×Dic3C2313yes—
53C22×C3×Dic5C2311yescharacteristic
54C3×#713—232no—
55C2×C3×D20—212no—
56C2×C3×D20C23112yes—
57C2×C3×C4×D5—212no—
58C2×C3×C4×D5C23112yes—
59C2×#1202—212no—
60C2×#1202C23112yes—
61C5×C4⋊Dic3C23112yes—
62C4×C5×Dic3C23112yes—
63Dic3⋊Dic5C23112yes—
64#6667C2314yes—
65#6665C23112yes—
66#6665C23124yes—
67C22×C3×#41—51no—
68C22×D3×Q8—51no—
69#5831—516no—
70C2×Q8×Dic3D511yescharacteristic, complemented
71C2×#938—53no—
72C2×#936—53no—
73C2×C4×#67—53no—
74C2×#924—53no—
75C22×C5×Q8C2×D311yescharacteristic
76C2×#713—28no—
77C2×#713C2×D318yescomplemented
78C2×Q8×D5—38no—
79C2×Q8×D5—68no—
80C22×D20—33no—
81C22×D20C2×D313yes—
82C22×C4×D5—33no—
83C22×C4×D5C2×D313yes—
84C22×Dic10—33no—
85C4×C5×Q8—38no—
86C2×C5×C4⋊C4—33no—
87C2×C42×C5—33no—
88C2×#685—33no—
89C2×#685—36no—
90C2×#685—31no—
91C2×C4⋊Dic5—33no—
92#4043—324no—
93#4041—324no—
94#4021—324no—
95C4×D20—324no—
96C2×#548—151noSylow
97C23×C3×C5C2411yescharacteristic
98C22×D15—22no—
99C22×D15—22no—
100C22×D15#4114yescomplemented
101C22×D15C2412yes—
102C22×C3×D5—26no—
103C22×C3×D5—26no—
104C22×C3×D5—26no—
105C22×C3×D5C2416yes—
106C3×C5×Q8C2×D4116yescomplemented
107C2×C3×C4×C5C2×D4112yes—
108C2×C3×C4×C5C2416yes—
109C2×Dic15—26no—
110C2×Dic15C2416yes—
111C4×D15—224no—
112Dic30—224no—
113C2×C5×Dic3—26no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3C2412yes—
116C2×C5×Dic3C2416yes—
117C2×C3×Dic5—22no—
118C2×C3×Dic5C2412yes—
119C3×D20—224no—
120C3×C4×D5—224no—
121#1202—224no—
122C2×C3×#41—58no—
123C2×C3×#41—108no—
124C22×C3×Q8C2×D511yescharacteristic
125C22×C3×D4—53no—
126C23×C3×C4—53no—
127C22×#67—53no—
128C2×D3×Q8—58no—
129C2×D3×Q8—108no—
130C22×C4×D3—53no—
131C22×Dic6—53no—
132C2×#217—56no—
133C2×#217—53no—
134Q8×Dic3C2×D518yescomplemented
135#938—524no—
136#936—524no—
137C4×#67—524no—
138C2×(C2×D3)⋊C4—51no—
139C2×C4⋊Dic3C2×D513yes—
140#924—524no—
141C2×Dic3⋊C4—53no—
142C2×C4×Dic3C2×D513yes—
143C23×D5—31no—
144C23×D5C22×D313yes—
145C2×C5×Q8#6718yescomplemented
146C2×C5×Q8C22×D314yes—
147C22×C4×C5—31no—
148C22×C4×C5—33no—
149C22×C4×C5C22×D313yes—
150C22×Dic5—33no—
151C22×Dic5C22×D311yescharacteristic
152#713—232no—
153Q8×D5—632no—
154C2×D20—212no—
155C2×D20—312no—
156C2×D20—612no—
157C2×D20C22×D3112yes—
158C2×C4×D5—212no—
159C2×C4×D5—312no—
160C2×C4×D5—612no—
161C2×C4×D5C22×D3112yes—
162C2×Dic10—312no—
163C2×Dic10—612no—
164C5×C4⋊C4—312no—
165C42×C5—312no—
166#685—312no—
167#685—324no—
168#685—34no—
169C4⋊Dic5—312no—
170C22×#41—51no—
171C23×Q8—151no—
172#548—1516no—
173C2×#124—153no—
174C2×C22⋊Q8—153no—
175C2×#121—153no—
176C2×C4×Q8—31no—
177C2×C4×D4—153no—
178C22×C3×C5C22×D412yes—
179C22×C3×C5C2×#4112yes—
180C22×C3×C52−1+412yes—
181C22×C3×C5C2511yescharacteristic
182C2×D15—28no—
183C2×D15—22no—
184C2×D15—22no—
185C2×D15C2×#4114yescomplemented
186C2×C3×D5—26no—
187C2×C3×D5—26no—
188C2×C3×D5—26no—
189C2×C3×D5—412no—
190C3×C4×C5C22×D4112yes—
191Dic15—26no—
192C3×Dic5—22no—
193C5×Dic3—26no—
194C5×Dic3—22no—
195C24×C3—53no—
196C23×D3—51no—
197C3×#41—1032no—
198C2×C3×Q8D2018yescomplemented
199C2×C3×Q8C22×D514yes—
200C2×C3×D4—512no—
201C2×C3×D4—1012no—
202C22×C3×C4—51no—
203C22×C3×C4—512no—
204C22×C3×C4—1012no—
205C22×C3×C4C22×D513yes—
206C2×#67—512no—
207C2×#67—1012no—
208C22×Dic3—53no—
209C22×Dic3C22×D511yescharacteristic
210C22×Dic3C22×D513yes—
211D3×Q8—1032no—
212C2×C4×D3—512no—
213C2×C4×D3—1012no—
214C2×Dic6—512no—
215C2×Dic6—1012no—
216#217—524no—
217#217—512no—
218(C2×D3)⋊C4—54no—
219C4⋊Dic3C22×D5112yes—
220Dic3⋊C4—512no—
221C4×Dic3C22×D5112yes—
222C23×C5C23×D311yescharacteristic
223C22×D5—26no—
224C22×D5—26no—
225C22×D5—26no—
226C22×D5—34no—
227C22×D5—32no—
228C22×D5—62no—
229C22×D5—62no—
230C22×D5C23×D316yes—
231C5×Q8C2×#67116yescomplemented
232C2×C4×C5—36no—
233C2×C4×C5—32no—
234C2×C4×C5—66no—
235C2×C4×C5—62no—
236C2×C4×C5C2×#67112yes—
237C2×C4×C5C23×D316yes—
238C2×Dic5—22no—
239C2×Dic5—36no—
240C2×Dic5—66no—
241C2×Dic5C23×D312yes—
242D20—224no—
243D20—624no—
244C4×D5—224no—
245C4×D5—624no—
246Dic10—624no—
247C2×#41—58no—
248C2×#41—108no—
249C22×Q8—158no—
250C22×Q8—153no—
251C22×Q8—308no—
252C22×Q8D3×D511yescharacteristic
253C22×D4—53no—
254C22×D4—153no—
255C23×C4—53no—
256C23×C4—153no—
257#124—1524no—
258C22⋊Q8—1524no—
259#121—1524no—
260C4×Q8—38no—
261C4×D4—1524no—
262C2×C4⋊C4—33no—
263C2×C4⋊C4—153no—
264C2×C22⋊C4—151no—
265C2×C22⋊C4—153no—
266C2×C22⋊C4—156no—
267C2×C42—33no—
268C2×C3×C5#54814yescomplemented
269C2×C3×C5C23×D411yescharacteristic
270C2×C3×C5C22×#4111yescharacteristic
271C2×C3×C5C2×2−1+411yescharacteristic
272D15—24no—
273C3×D5—46no—
274C23×C3—56no—
275C23×C3—106no—
276C23×C3—106no—
277C23×C3—106no—
278C23×C3C23×D511yescharacteristic
279C22×D3—54no—
280C22×D3—52no—
281C22×D3—102no—
282C22×D3—102no—
283C3×Q8C2×D20116yescomplemented
284C3×D4—1024no—
285C2×C3×C4—52no—
286C2×C3×C4—102no—
287C2×C3×C4—1024no—
288C2×C3×C4C2×D20112yes—
289C2×C3×C4C23×D516yes—
290#67—1024no—
291C2×Dic3—22no—
292C2×Dic3—26no—
293C2×Dic3—56no—
294C2×Dic3—106no—
295C2×Dic3C23×D512yes—
296C2×Dic3C23×D516yes—
297C4×D3—1024no—
298Dic6—1024no—
299C22×C5D3×#4112yes—
300C22×C5#101012yes—
301C22×C5C22×#6712yes—
302C22×C5C24×D311yescharacteristic
303C2×D5—26no—
304C2×D5—26no—
305C2×D5—26no—
306C2×D5—34no—
307C2×D5—412no—
308C2×D5—62no—
309C2×D5—62no—
310C2×D5—68no—
311C4×C5—66no—
312C4×C5—62no—
313C4×C5C22×#67112yes—
314Dic5—22no—
315Dic5—66no—
316C24—53no—
317C24—151no—
318#41—1032no—
319C2×Q8—1512no—
320C2×Q8—3032no—
321C2×Q8—3012no—
322C2×Q8#120218yescomplemented
323C2×Q8C2×D3×D514yes—
324C2×D4—512no—
325C2×D4—1012no—
326C2×D4—1512no—
327C2×D4—3012no—
328C22×C4—31no—
329C22×C4—33no—
330C22×C4—51no—
331C22×C4—512no—
332C22×C4—1012no—
333C22×C4—153no—
334C22×C4—1512no—
335C22×C4—3012no—
336C22×C4C2×D3×D513yes—
337C4⋊C4—312no—
338C4⋊C4—1512no—
339C22⋊C4—154no—
340C22⋊C4—1512no—
341C22⋊C4—1524no—
342C42—312no—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3—106no—
345C22×C3—106no—
346C22×C3—106no—
347C22×C3—2012no—
348C22×C3C22×D2012yes—
349C22×C3#414712yes—
350C22×C3D5×#4112yes—
351C22×C3C24×D511yescharacteristic
352C2×D3—54no—
353C2×D3—108no—
354C2×D3—102no—
355C2×D3—102no—
356C3×C4—102no—
357C3×C4C22×D20112yes—
358Dic3—22no—
359Dic3—26no—
360Dic3—106no—
361C2×C5#583114yescomplemented
362C2×C5C2×D3×#4111yescharacteristic
363C2×C5C2×#101011yescharacteristic
364C2×C5C23×#6711yescharacteristic
365D5—46no—
366D5—64no—
367C23—56no—
368C23—106no—
369C23—106no—
370C23—106no—
371C23—154no—
372C23—152no—
373C23—302no—
374C23—302no—
375C23C22×D3×D511yescharacteristic
376Q8—3024no—
377Q8C2×#1202116yescomplemented
378D4—1024no—
379D4—3024no—
380C2×C4—32no—
381C2×C4—36no—
382C2×C4—52no—
383C2×C4—62no—
384C2×C4—66no—
385C2×C4—102no—
386C2×C4—1024no—
387C2×C4—156no—
388C2×C4—306no—
389C2×C4—3024no—
390C2×C4C2×#1202112yes—
391C2×C4C22×D3×D516yes—
392C2×C3—206no—
393C2×C3#6591014yescomplemented
394C2×C3C23×D2011yescharacteristic
395C2×C3C2×#414711yescharacteristic
396C2×C3C2×D5×#4111yescharacteristic
397D3—104no—
398C5C2×#583111yescharacteristic, complemented, Sylow
399C22—106no—
400C22—106no—
401C22—106no—
402C22—154no—
403C22—2012no—
404C22—302no—
405C22—302no—
406C22—308no—
407C22#9202812yes—
408C22#9203412yes—
409C22C22×#120212yes—
410C22C23×D3×D511yescharacteristic
411C4—62no—
412C4—66no—
413C4—102no—
414C4—306no—
415C4C22×#1202112yes—
416C3C2×#6591011yescharacteristic, complemented, Sylow
417C2—206no—
418C2—304no—
419C2#1175525714yesdirect product factor
420C2C2×#9202811yescharacteristic
421C2C2×#9203411yescharacteristic
422C2C23×#120211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D15C2semidirect
2. C22×C3×#713C2semidirect
3. C2×C5×Q8×Dic3C2semidirect
4. #11755257C2direct (N × H)
5. C2×#91465C2semidirect
6. C2×C4×#1202C2semidirect
7. C2×#91364C2semidirect
8. C2×#91360C2semidirect
12. C2×Q8×D15C22semidirect
16. C2×C3×#713C22semidirect
20. C5×Q8×Dic3C22semidirect
27. #91465C22semidirect
28. C4×#1202C22semidirect
29. #91364C22semidirect
30. #91360C22semidirect
32. C22×#713D3semidirect
42. C2×C3×C5×Q8D4semidirect
70. C2×Q8×Dic3D5semidirect
77. C2×#713C2×D3semidirect
100. C22×D15#41semidirect
106. C3×C5×Q8C2×D4semidirect
134. Q8×Dic3C2×D5semidirect
145. C2×C5×Q8#67semidirect
185. C2×D15C2×#41semidirect
198. C2×C3×Q8D20semidirect
231. C5×Q8C2×#67semidirect
268. C2×C3×C5#548semidirect
283. C3×Q8C2×D20semidirect
322. C2×Q8#1202semidirect
343. C3×C5C2×#548semidirect
361. C2×C5#5831semidirect
377. Q8C2×#1202semidirect
393. C2×C3#65910semidirect
398. C5C2×#5831semidirect
416. C3C2×#65910semidirect
419. C2#11755257direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C22×C3×#7132
C2×C5×Q8×Dic32
#117552572
C2×#914652
C2×C4×#12022
C2×#913642
C2×#913602
C2×#659103
C2×#58315