Finite Group Databasebeta

← C2×#11756335 #14482816

Subgroups — C2×#11756335 #14482816

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×#6821C211yesmaximal, characteristic, complemented
2C22×Q8×D15C211yesmaximal, characteristic, complemented
3C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
4#11756335C2116yesmaximal, direct product factor
5C2×#91786C213yesmaximal, complemented
6C2×#91784C213yesmaximal, complemented
7C2×#91764C213yesmaximal, complemented
8C2×C4×D60C213yesmaximal, complemented
9C2×#65910—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—28no—
12C2×#6821C2218yescomplemented
13C2×Q8×D15—28no—
14C2×Q8×D15C2218yescomplemented
15C22×D60C2213yes—
16C22×D60C2213yes—
17C22×C4×D15C2213yes—
18C22×C4×D15C2213yes—
19C22×Dic30C2213yes—
20C3×C4×C5×Q8C2218yescomplemented
21C2×C3×C5×C4⋊C4C2213yes—
22C2×C3×C42×C5C2213yes—
23C2×#6714C2211yescharacteristic
24C2×#6714C2213yes—
25C2×#6714C2216yes—
26C2×C4⋊Dic15C2213yes—
27#91786C22124yescomplemented
28#91784C22124yescomplemented
29#91764C22124yescomplemented
30C4×D60C22124yescomplemented
31C2×#5576—51nomaximal, Hall
32C22×#713—31no—
33C22×Q8×D5—31no—
34C2×C4×C5×Q8D311yescharacteristic, complemented
35#65910—316no—
36C2×#4043—33no—
37C2×#4041—33no—
38C2×#4021—33no—
39C2×C4×D20—33no—
40C23×D15C2313yes—
41C23×D15C2311yescharacteristic
42C2×C3×C5×Q8D418yescomplemented
43C2×C3×C5×Q8C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×C3×C4×C5C2313yes—
47C22×Dic15C2311yescharacteristic
48C22×Dic15C2313yes—
49#6821—232no—
50Q8×D15—232no—
51C2×D60—212no—
52C2×D60—212no—
53C2×D60C23112yes—
54C2×D60C23112yes—
55C2×C4×D15—212no—
56C2×C4×D15—212no—
57C2×C4×D15C23112yes—
58C2×C4×D15C23112yes—
59C2×Dic30—212no—
60C2×Dic30C23112yes—
61C3×C5×C4⋊C4C23112yes—
62C3×C42×C5C23112yes—
63#6714C2314yes—
64#6714C23112yes—
65#6714C23124yes—
66C4⋊Dic15C23112yes—
67C22×#239—51no—
68C22×D3×Q8—51no—
69C2×C3×C4×Q8D511yescharacteristic, complemented
70#5576—516no—
71C2×#897—53no—
72C2×#895—53no—
73C2×#875—53no—
74C2×C4×D12—53no—
75C22×C5×Q8C2×D311yescharacteristic
76C2×#713—38no—
77C2×#713—68no—
78C2×Q8×D5—38no—
79C2×Q8×D5—68no—
80C22×D20—33no—
81C22×D20—33no—
82C22×C4×D5—33no—
83C22×C4×D5—33no—
84C22×Dic10—33no—
85C4×C5×Q8C2×D318yescomplemented
86C2×C5×C4⋊C4C2×D313yes—
87C2×C42×C5C2×D313yes—
88C2×#685—31no—
89C2×#685—33no—
90C2×#685—36no—
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—26no—
101C22×D15—26no—
102C22×D15—26no—
103C22×D15#4114yescomplemented
104C22×D15C2416yes—
105C22×D15C2412yes—
106C3×C5×Q8C2×D4116yescomplemented
107C2×C3×C4×C5—26no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5C2×D4112yes—
110C2×C3×C4×C5C2416yes—
111C2×C3×C4×C5C2412yes—
112C2×C3×C4×C5C2416yes—
113C2×Dic15—26no—
114C2×Dic15—22no—
115C2×Dic15C2412yes—
116C2×Dic15C2416yes—
117D60—224no—
118D60—224no—
119C4×D15—224no—
120C4×D15—224no—
121Dic30—224no—
122C22×C3×Q8C2×D511yescharacteristic
123C2×#239—58no—
124C2×#239—108no—
125C2×D3×Q8—58no—
126C2×D3×Q8—108no—
127C22×D12—53no—
128C22×D12—53no—
129C22×C4×D3—53no—
130C22×C4×D3—53no—
131C22×Dic6—53no—
132C3×C4×Q8C2×D518yescomplemented
133C2×C3×C4⋊C4C2×D513yes—
134C2×C3×C42C2×D513yes—
135C2×(C2×D3)⋊C4—51no—
136C2×(C2×D3)⋊C4—53no—
137C2×(C2×D3)⋊C4—56no—
138C2×C4⋊Dic3—53no—
139#897—524no—
140#895—524no—
141#875—524no—
142C4×D12—524no—
143C23×D5—31no—
144C23×D5—33no—
145C2×C5×Q8D1218yescomplemented
146C2×C5×Q8C22×D314yes—
147C22×C4×C5C22×D311yescharacteristic
148C22×C4×C5C22×D313yes—
149C22×C4×C5C22×D313yes—
150C22×Dic5—33no—
151C22×Dic5—31no—
152#713—632no—
153Q8×D5—632no—
154C2×D20—312no—
155C2×D20—312no—
156C2×D20—612no—
157C2×D20—612no—
158C2×C4×D5—312no—
159C2×C4×D5—312no—
160C2×C4×D5—612no—
161C2×C4×D5—612no—
162C2×Dic10—312no—
163C2×Dic10—612no—
164C5×C4⋊C4C22×D3112yes—
165C42×C5C22×D3112yes—
166#685—34no—
167#685—312no—
168#685—324no—
169C4⋊Dic5—312no—
170C22×#41—151no—
171C23×Q8—151no—
172#548—1516no—
173C2×#124—153no—
174C2×C22⋊Q8—153no—
175C2×#121—153no—
176C2×C4×Q8D1511yescharacteristic, complemented
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×D15—26no—
186C2×D15—26no—
187C2×D15—26no—
188C2×D15—412no—
189C2×D15C2×#4114yescomplemented
190C3×C4×C5—26no—
191C3×C4×C5—22no—
192C3×C4×C5C22×D4112yes—
193Dic15—26no—
194Dic15—22no—
195C23×D3—51no—
196C23×D3—53no—
197C2×C3×Q8D2018yescomplemented
198C2×C3×Q8C22×D514yes—
199C22×C3×C4C22×D513yes—
200C22×C3×C4C22×D511yescharacteristic
201C22×C3×C4C22×D513yes—
202C22×Dic3—51no—
203C22×Dic3—53no—
204#239—1032no—
205D3×Q8—1032no—
206C2×D12—512no—
207C2×D12—512no—
208C2×D12—1012no—
209C2×D12—1012no—
210C2×C4×D3—512no—
211C2×C4×D3—512no—
212C2×C4×D3—1012no—
213C2×C4×D3—1012no—
214C2×Dic6—512no—
215C2×Dic6—1012no—
216C3×C4⋊C4C22×D5112yes—
217C3×C42C22×D5112yes—
218(C2×D3)⋊C4—54no—
219(C2×D3)⋊C4—512no—
220(C2×D3)⋊C4—524no—
221C4⋊Dic3—512no—
222C23×C5C23×D311yescharacteristic
223C22×D5—34no—
224C22×D5—32no—
225C22×D5—36no—
226C22×D5—62no—
227C22×D5—62no—
228C22×D5—66no—
229C22×D5—66no—
230C22×D5—66no—
231C5×Q8C2×D12116yescomplemented
232C2×C4×C5—22no—
233C2×C4×C5—26no—
234C2×C4×C5C2×D12112yes—
235C2×C4×C5C23×D316yes—
236C2×C4×C5C23×D312yes—
237C2×C4×C5C23×D316yes—
238C2×Dic5—32no—
239C2×Dic5—36no—
240C2×Dic5—66no—
241C2×Dic5—62no—
242D20—624no—
243D20—624no—
244C4×D5—624no—
245C4×D5—624no—
246Dic10—624no—
247C2×#41—158no—
248C2×#41—308no—
249C22×Q8—158no—
250C22×Q8—153no—
251C22×Q8—308no—
252C22×Q8C2×D1511yescharacteristic
253C22×D4—153no—
254C22×D4—153no—
255C23×C4—153no—
256C23×C4—153no—
257#124—1524no—
258C22⋊Q8—1524no—
259#121—1524no—
260C4×Q8C2×D1518yescomplemented
261C4×D4—1524no—
262C2×C4⋊C4—153no—
263C2×C4⋊C4C2×D1513yes—
264C2×C22⋊C4—151no—
265C2×C22⋊C4—153no—
266C2×C22⋊C4—156no—
267C2×C42C2×D1513yes—
268C2×C3×C5#54814yescomplemented
269C2×C3×C5C23×D411yescharacteristic
270C2×C3×C5C22×#4111yescharacteristic
271C2×C3×C5C2×2−1+411yescharacteristic
272D15—24no—
273D15—46no—
274C23×C3C23×D511yescharacteristic
275C22×D3—54no—
276C22×D3—52no—
277C22×D3—56no—
278C22×D3—102no—
279C22×D3—102no—
280C22×D3—106no—
281C22×D3—106no—
282C22×D3—106no—
283C3×Q8C2×D20116yescomplemented
284C2×C3×C4—22no—
285C2×C3×C4—26no—
286C2×C3×C4C2×D20112yes—
287C2×C3×C4C23×D516yes—
288C2×C3×C4C23×D512yes—
289C2×C3×C4C23×D516yes—
290C2×Dic3—52no—
291C2×Dic3—56no—
292C2×Dic3—106no—
293C2×Dic3—102no—
294D12—1024no—
295D12—1024no—
296C4×D3—1024no—
297C4×D3—1024no—
298Dic6—1024no—
299C22×C5C22×D1212yes—
300C22×C5#100712yes—
301C22×C5D3×#4112yes—
302C22×C5C24×D311yescharacteristic
303C2×D5—34no—
304C2×D5—62no—
305C2×D5—62no—
306C2×D5—68no—
307C2×D5—66no—
308C2×D5—66no—
309C2×D5—66no—
310C2×D5—1212no—
311C4×C5—22no—
312C4×C5—26no—
313C4×C5C22×D12112yes—
314Dic5—66no—
315Dic5—62no—
316C24—151no—
317C24—153no—
318#41—3032no—
319C2×Q8—1512no—
320C2×Q8—3032no—
321C2×Q8—3012no—
322C2×Q8D6018yescomplemented
323C2×Q8C22×D1514yes—
324C2×D4—1512no—
325C2×D4—1512no—
326C2×D4—3012no—
327C2×D4—3012no—
328C22×C4—153no—
329C22×C4—151no—
330C22×C4—1512no—
331C22×C4—1512no—
332C22×C4—3012no—
333C22×C4—3012no—
334C22×C4C22×D1511yescharacteristic
335C22×C4C22×D1513yes—
336C22×C4C22×D1513yes—
337C4⋊C4—1512no—
338C4⋊C4C22×D15112yes—
339C22⋊C4—154no—
340C22⋊C4—1512no—
341C22⋊C4—1524no—
342C42C22×D15112yes—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3C22×D2012yes—
345C22×C3#414712yes—
346C22×C3D5×#4112yes—
347C22×C3C24×D511yescharacteristic
348C2×D3—54no—
349C2×D3—108no—
350C2×D3—102no—
351C2×D3—102no—
352C2×D3—106no—
353C2×D3—106no—
354C2×D3—106no—
355C2×D3—2012no—
356C3×C4—22no—
357C3×C4—26no—
358C3×C4C22×D20112yes—
359Dic3—106no—
360Dic3—102no—
361C2×C5#557614yescomplemented
362C2×C5C23×D1211yescharacteristic
363C2×C5C2×#100711yescharacteristic
364C2×C5C2×D3×#4111yescharacteristic
365D5—64no—
366D5—126no—
367C23—154no—
368C23—152no—
369C23—156no—
370C23—302no—
371C23—302no—
372C23—306no—
373C23—306no—
374C23—306no—
375C23C23×D1511yescharacteristic
376Q8—3024no—
377Q8C2×D60116yescomplemented
378D4—3024no—
379D4—3024no—
380C2×C4—22no—
381C2×C4—26no—
382C2×C4—156no—
383C2×C4—152no—
384C2×C4—302no—
385C2×C4—306no—
386C2×C4—3024no—
387C2×C4—3024no—
388C2×C4C2×D60112yes—
389C2×C4C23×D1512yes—
390C2×C4C23×D1516yes—
391C2×C4C23×D1516yes—
392C2×C3#6591014yescomplemented
393C2×C3C23×D2011yescharacteristic
394C2×C3C2×#414711yescharacteristic
395C2×C3C2×D5×#4111yescharacteristic
396D3—104no—
397D3—206no—
398C5C2×#557611yescharacteristic, complemented, Sylow
399C22—154no—
400C22—308no—
401C22—302no—
402C22—302no—
403C22—306no—
404C22—306no—
405C22—306no—
406C22—6012no—
407C22C22×D6012yes—
408C22#9209812yes—
409C22#41×D1512yes—
410C22C24×D1511yescharacteristic
411C4—22no—
412C4—26no—
413C4—302no—
414C4—306no—
415C4C22×D60112yes—
416C3C2×#6591011yescharacteristic, complemented, Sylow
417C2—304no—
418C2—606no—
419C2#1175633514yesdirect product factor
420C2C23×D6011yescharacteristic
421C2C2×#9209811yescharacteristic
422C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
hypercenterC2×C4×Q8D15
hypocenterC3×C5C2×#548
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6821C2semidirect
2. C22×Q8×D15C2semidirect
3. C2×C3×C4×C5×Q8C2semidirect
4. #11756335C2direct (N × H)
5. C2×#91786C2semidirect
6. C2×#91784C2semidirect
7. C2×#91764C2semidirect
8. C2×C4×D60C2semidirect
12. C2×#6821C22semidirect
14. C2×Q8×D15C22semidirect
20. C3×C4×C5×Q8C22semidirect
27. #91786C22semidirect
28. #91784C22semidirect
29. #91764C22semidirect
30. C4×D60C22semidirect
34. C2×C4×C5×Q8D3semidirect
42. C2×C3×C5×Q8D4semidirect
69. C2×C3×C4×Q8D5semidirect
85. C4×C5×Q8C2×D3semidirect
103. C22×D15#41semidirect
106. C3×C5×Q8C2×D4semidirect
132. C3×C4×Q8C2×D5semidirect
145. C2×C5×Q8D12semidirect
176. C2×C4×Q8D15semidirect
189. C2×D15C2×#41semidirect
197. C2×C3×Q8D20semidirect
231. C5×Q8C2×D12semidirect
260. C4×Q8C2×D15semidirect
268. C2×C3×C5#548semidirect
283. C3×Q8C2×D20semidirect
322. C2×Q8D60semidirect
343. C3×C5C2×#548semidirect
361. C2×C5#5576semidirect
377. Q8C2×D60semidirect
392. C2×C3#65910semidirect
398. C5C2×#5576semidirect
416. C3C2×#65910semidirect
419. C2#11756335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×Q8×D152
C2×C3×C4×C5×Q82
#117563352
C2×#917862
C2×#917842
C2×#917642
C2×C4×D602
C2×#659103
C2×#55765