Finite Group Databasebeta

← C2×#11755251 #14483023

Subgroups — C2×#11755251 #14483023

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6821C211yesmaximal, characteristic, complemented
2C22×C3×#713C211yesmaximal, characteristic, complemented
3C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
4#11755251C2116yesmaximal, direct product factor
5C2×#91465C213yesmaximal, complemented
6C2×#91458C213yesmaximal, complemented
7C2×#91450C213yesmaximal, complemented
8C2×C4×#1202C213yesmaximal, complemented
9C2×#65911—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—28no—
12C2×#6821C2218yescomplemented
13C22×D60C2213yes—
14C22×C4×D15C2213yes—
15C2×C3×#713—28no—
16C2×C3×#713C2218yescomplemented
17C22×C3×D20C2213yes—
18C22×C3×C4×D5C2213yes—
19C22×#1202C2213yes—
20C22×#1202C2216yes—
21C5×Q8×Dic3C2218yescomplemented
22C2×C5×C4⋊Dic3C2213yes—
23C2×C4×C5×Dic3C2213yes—
24C2×Dic3⋊Dic5C2211yescharacteristic
25C2×#6667C2213yes—
26C2×#6665C2213yes—
27#91465C22124yescomplemented
28#91458C22124yescomplemented
29#91450C22124yescomplemented
30C4×#1202C22124yescomplemented
31C2×#5834—51nomaximal, Hall
32C22×#713—31no—
33C22×#713D311yescharacteristic, complemented
34C2×C4×C5×Q8—31no—
35#65911—316no—
36C2×#4041—33no—
37C2×#4041—33no—
38C2×#4020—33no—
39C2×C4×D20—33no—
40C23×D15C2313yes—
41C23×C3×D5C2313yes—
42C2×C3×C5×Q8D418yescomplemented
43C2×C3×C5×Q8C2314yes—
44C22×C3×C4×C5C2313yes—
45C22×Dic15C2311yescharacteristic
46#6821—232no—
47C2×D60—212no—
48C2×D60C23112yes—
49C2×C4×D15—212no—
50C2×C4×D15C23112yes—
51C22×C5×Dic3C2313yes—
52C22×C5×Dic3C2311yescharacteristic
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×#1202—412no—
61C2×#1202C23112yes—
62C2×#1202C23124yes—
63C5×C4⋊Dic3C23112yes—
64C4×C5×Dic3C23112yes—
65Dic3⋊Dic5C2314yes—
66#6667C23112yes—
67#6665C23112yes—
68C22×C3×#41—51no—
69C22×#239—51no—
70#5834—516no—
71C2×Q8×Dic3D511yescharacteristic, complemented
72C2×#940—53no—
73C2×#938—53no—
74C2×#930—53no—
75C2×C4×#67—53no—
76C22×C5×Q8C2×D311yescharacteristic
77C2×#713—28no—
78C2×#713—38no—
79C2×#713—68no—
80C2×#713C2×D318yescomplemented
81C22×D20—33no—
82C22×D20—33no—
83C22×D20—36no—
84C22×D20C2×D313yes—
85C22×C4×D5—33no—
86C22×C4×D5C2×D313yes—
87C4×C5×Q8—38no—
88C2×C5×C4⋊C4—33no—
89C2×C42×C5—33no—
90C2×#685—33no—
91C2×#685—33no—
92C2×C4⋊Dic5—31no—
93#4041—324no—
94#4041—324no—
95#4020—324no—
96C4×D20—324no—
97C2×#550—151noSylow
98C23×C3×C5C2411yescharacteristic
99C22×D15—26no—
100C22×D15—26no—
101C22×D15—26no—
102C22×D15C2416yes—
103C22×C3×D5—26no—
104C22×C3×D5—26no—
105C22×C3×D5—26no—
106C22×C3×D5C2416yes—
107C3×C5×Q8C2×D4116yescomplemented
108C2×C3×C4×C5C2×D4112yes—
109C2×C3×C4×C5C2416yes—
110C2×Dic15—22no—
111C2×Dic15C2412yes—
112D60—224no—
113C4×D15—224no—
114C2×C5×Dic3—26no—
115C2×C5×Dic3#4114yescomplemented
116C2×C5×Dic3C2416yes—
117C2×C5×Dic3C2412yes—
118C2×C3×Dic5—22no—
119C2×C3×Dic5C2412yes—
120C3×D20—224no—
121C3×C4×D5—224no—
122#1202—224no—
123#1202—424no—
124C2×C3×#41—58no—
125C2×C3×#41—108no—
126C22×C3×Q8C2×D511yescharacteristic
127C22×C3×D4—53no—
128C23×C3×C4—53no—
129C22×#67—53no—
130C22×#67—56no—
131C2×#239—58no—
132C2×#239—108no—
133C22×D12—53no—
134C22×C4×D3—53no—
135C2×#217—53no—
136Q8×Dic3C2×D518yescomplemented
137#940—524no—
138#938—524no—
139#930—524no—
140C4×#67—524no—
141C2×(C2×D3)⋊C4—53no—
142C2×C4⋊Dic3C2×D513yes—
143C2×Dic3⋊C4—51no—
144C2×C4×Dic3C2×D513yes—
145C23×D5—33no—
146C23×D5C22×D313yes—
147C2×C5×Q8#6718yescomplemented
148C2×C5×Q8C22×D314yes—
149C22×C4×C5—31no—
150C22×C4×C5—33no—
151C22×C4×C5C22×D313yes—
152C22×Dic5—31no—
153C22×Dic5C22×D311yescharacteristic
154#713—232no—
155#713—632no—
156C2×D20—212no—
157C2×D20—312no—
158C2×D20—312no—
159C2×D20—324no—
160C2×D20—612no—
161C2×D20—612no—
162C2×D20—1212no—
163C2×D20C22×D3112yes—
164C2×C4×D5—212no—
165C2×C4×D5—312no—
166C2×C4×D5—612no—
167C2×C4×D5C22×D3112yes—
168C5×C4⋊C4—312no—
169C42×C5—312no—
170#685—312no—
171#685—312no—
172C4⋊Dic5—34no—
173C22×#41—51no—
174C22×#41—151no—
175#550—1516no—
176C2×#127—153no—
177C2×#121—153no—
178C2×#121—153no—
179C2×C4×Q8—31no—
180C2×C4×D4—153no—
181C22×C3×C5C22×D412yes—
182C22×C3×C5C2×#4112yes—
183C22×C3×C5H(5,𝔽2)12yes—
184C22×C3×C5C2511yescharacteristic
185C2×D15—26no—
186C2×D15—26no—
187C2×D15—26no—
188C2×D15—412no—
189C2×C3×D5—26no—
190C2×C3×D5—26no—
191C2×C3×D5—26no—
192C2×C3×D5—412no—
193C3×C4×C5C22×D4112yes—
194Dic15—22no—
195C3×Dic5—22no—
196C5×Dic3—26no—
197C5×Dic3C2×#4114yescomplemented
198C24×C3—53no—
199C23×D3—53no—
200C3×#41—1032no—
201C2×C3×Q8D2018yescomplemented
202C2×C3×Q8C22×D514yes—
203C2×C3×D4—512no—
204C2×C3×D4—1012no—
205C22×C3×C4—51no—
206C22×C3×C4—512no—
207C22×C3×C4—1012no—
208C22×C3×C4C22×D513yes—
209C2×#67—512no—
210C2×#67—524no—
211C2×#67—1012no—
212C2×#67—2012no—
213C22×Dic3—51no—
214C22×Dic3C22×D513yes—
215C22×Dic3C22×D511yescharacteristic
216#239—1032no—
217C2×D12—512no—
218C2×D12—1012no—
219C2×C4×D3—512no—
220C2×C4×D3—1012no—
221#217—512no—
222(C2×D3)⋊C4—512no—
223C4⋊Dic3C22×D5112yes—
224Dic3⋊C4—54no—
225C4×Dic3C22×D5112yes—
226C23×C5C23×D311yescharacteristic
227C22×D5—26no—
228C22×D5—26no—
229C22×D5—26no—
230C22×D5—36no—
231C22×D5—66no—
232C22×D5—66no—
233C22×D5—66no—
234C22×D5C23×D316yes—
235C5×Q8C2×#67116yescomplemented
236C2×C4×C5—34no—
237C2×C4×C5—32no—
238C2×C4×C5—36no—
239C2×C4×C5—66no—
240C2×C4×C5C2×#67112yes—
241C2×C4×C5C23×D316yes—
242C2×Dic5—22no—
243C2×Dic5—32no—
244C2×Dic5—62no—
245C2×Dic5C23×D312yes—
246D20—224no—
247D20—624no—
248D20—624no—
249D20—1224no—
250C4×D5—224no—
251C4×D5—624no—
252C2×#41—58no—
253C2×#41—108no—
254C2×#41—158no—
255C2×#41—308no—
256C22×Q8D3×D511yescharacteristic
257C22×D4—53no—
258C22×D4—153no—
259C22×D4—156no—
260C22×D4—153no—
261C23×C4—53no—
262C23×C4—153no—
263#127—1524no—
264#121—1524no—
265#121—1524no—
266C4×Q8—38no—
267C4×D4—1524no—
268C2×C4⋊C4—33no—
269C2×C4⋊C4—151no—
270C2×C22⋊C4—153no—
271C2×C22⋊C4—153no—
272C2×C42—33no—
273C2×C3×C5#55014yescomplemented
274C2×C3×C5C23×D411yescharacteristic
275C2×C3×C5C22×#4111yescharacteristic
276C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
277D15—46no—
278C3×D5—46no—
279C23×C3—56no—
280C23×C3—106no—
281C23×C3—106no—
282C23×C3—106no—
283C23×C3C23×D511yescharacteristic
284C22×D3—56no—
285C22×D3—106no—
286C22×D3—106no—
287C22×D3—106no—
288C3×Q8C2×D20116yescomplemented
289C3×D4—1024no—
290C2×C3×C4—52no—
291C2×C3×C4—102no—
292C2×C3×C4—1024no—
293C2×C3×C4C2×D20112yes—
294C2×C3×C4C23×D516yes—
295#67—1024no—
296#67—2024no—
297C2×Dic3—26no—
298C2×Dic3—52no—
299C2×Dic3—102no—
300C2×Dic3#71314yescomplemented
301C2×Dic3C23×D516yes—
302C2×Dic3C23×D512yes—
303D12—1024no—
304C4×D3—1024no—
305C22×C5D3×#4112yes—
306C22×C5#100912yes—
307C22×C5C22×#6712yes—
308C22×C5C24×D311yescharacteristic
309C2×D5—26no—
310C2×D5—26no—
311C2×D5—26no—
312C2×D5—412no—
313C2×D5—66no—
314C2×D5—66no—
315C2×D5—66no—
316C2×D5—1212no—
317C4×C5—34no—
318C4×C5—66no—
319C4×C5C22×#67112yes—
320Dic5—22no—
321Dic5—62no—
322C24—53no—
323C24—153no—
324#41—1032no—
325#41—3032no—
326C2×Q8#120218yescomplemented
327C2×Q8C2×D3×D514yes—
328C2×D4—512no—
329C2×D4—1012no—
330C2×D4—1512no—
331C2×D4—1524no—
332C2×D4—1512no—
333C2×D4—3012no—
334C2×D4—3012no—
335C2×D4—6012no—
336C22×C4—31no—
337C22×C4—33no—
338C22×C4—51no—
339C22×C4—512no—
340C22×C4—1012no—
341C22×C4—151no—
342C22×C4—1512no—
343C22×C4—3012no—
344C22×C4C2×D3×D513yes—
345C4⋊C4—312no—
346C4⋊C4—154no—
347C22⋊C4—1512no—
348C22⋊C4—1512no—
349C42—312no—
350C3×C5C2×#55011yescharacteristic, complemented, Hall
351C22×C3—106no—
352C22×C3—106no—
353C22×C3—106no—
354C22×C3—2012no—
355C22×C3C22×D2012yes—
356C22×C3C2×#71312yes—
357C22×C3#414912yes—
358C22×C3C24×D511yescharacteristic
359C2×D3—106no—
360C2×D3—106no—
361C2×D3—106no—
362C2×D3—2012no—
363C3×C4—102no—
364C3×C4C22×D20112yes—
365Dic3—26no—
366Dic3—102no—
367Dic3C2×#71314yescomplemented
368C2×C5#583414yescomplemented
369C2×C5C2×D3×#4111yescharacteristic
370C2×C5C2×#100911yescharacteristic
371C2×C5C23×#6711yescharacteristic
372D5—46no—
373D5—126no—
374C23—56no—
375C23—106no—
376C23—106no—
377C23—106no—
378C23—156no—
379C23—306no—
380C23—306no—
381C23—306no—
382C23C22×D3×D511yescharacteristic
383Q8C2×#1202116yescomplemented
384D4—1024no—
385D4—3024no—
386D4—3024no—
387D4—6024no—
388C2×C4—34no—
389C2×C4—32no—
390C2×C4—36no—
391C2×C4—52no—
392C2×C4—66no—
393C2×C4—102no—
394C2×C4—1024no—
395C2×C4—152no—
396C2×C4—302no—
397C2×C4—3024no—
398C2×C4C2×#1202112yes—
399C2×C4C22×D3×D516yes—
400C2×C3—206no—
401C2×C3#6591114yescomplemented
402C2×C3C23×D2011yescharacteristic
403C2×C3C22×#71311yescharacteristic
404C2×C3C2×#414911yescharacteristic
405D3—206no—
406C5C2×#583411yescharacteristic, complemented, Sylow
407C22—106no—
408C22—106no—
409C22—106no—
410C22—2012no—
411C22—306no—
412C22—306no—
413C22—306no—
414C22—6012no—
415C22D3×#71312yes—
416C22#9203512yes—
417C22C22×#120212yes—
418C22C23×D3×D511yescharacteristic
419C4—34no—
420C4—66no—
421C4—102no—
422C4—302no—
423C4C22×#1202112yes—
424C3C2×#6591111yescharacteristic, complemented, Sylow
425C2—206no—
426C2—606no—
427C2#1175525114yesdirect product factor
428C2C2×D3×#71311yescharacteristic
429C2C2×#9203511yescharacteristic
430C2C23×#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×#550
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×#6821C2semidirect
2. C22×C3×#713C2semidirect
3. C2×C5×Q8×Dic3C2semidirect
4. #11755251C2direct (N × H)
5. C2×#91465C2semidirect
6. C2×#91458C2semidirect
7. C2×#91450C2semidirect
8. C2×C4×#1202C2semidirect
12. C2×#6821C22semidirect
16. C2×C3×#713C22semidirect
21. C5×Q8×Dic3C22semidirect
27. #91465C22semidirect
28. #91458C22semidirect
29. #91450C22semidirect
30. C4×#1202C22semidirect
33. C22×#713D3semidirect
42. C2×C3×C5×Q8D4semidirect
71. C2×Q8×Dic3D5semidirect
80. C2×#713C2×D3semidirect
107. C3×C5×Q8C2×D4semidirect
115. C2×C5×Dic3#41semidirect
136. Q8×Dic3C2×D5semidirect
147. C2×C5×Q8#67semidirect
197. C5×Dic3C2×#41semidirect
201. C2×C3×Q8D20semidirect
235. C5×Q8C2×#67semidirect
273. C2×C3×C5#550semidirect
288. C3×Q8C2×D20semidirect
300. C2×Dic3#713semidirect
326. C2×Q8#1202semidirect
350. C3×C5C2×#550semidirect
367. Dic3C2×#713semidirect
368. C2×C5#5834semidirect
383. Q8C2×#1202semidirect
401. C2×C3#65911semidirect
406. C5C2×#5834semidirect
424. C3C2×#65911semidirect
427. C2#11755251direct (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×C3×#7132
C2×C5×Q8×Dic32
#117552512
C2×#914652
C2×#914582
C2×#914502
C2×C4×#12022
C2×#659113
C2×#58345