Finite Group Databasebeta

← C2×#11754455 #14478931

Subgroups — C2×#11754455 #14478931

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#235C211yesmaximal, characteristic
2C22×C4×Dic15C211yesmaximal, characteristic, complemented
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic5C214yesmaximal, complemented
5#11754455C2116yesmaximal, direct product factor
6C2×#91435C212yesmaximal, complemented
7C2×C4×D3×Dic5C212yesmaximal, complemented
8C2×#91371C212yesmaximal, complemented
9C2×#91344C212yesmaximal, complemented
10C2×#41×Dic5—31nomaximal, Hall
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2212yes—
13C22×C5×#67C2212yes—
14C2×C5×#235C4116yescomplemented
15C2×C5×#235C2218yes—
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3C2212yes—
18C22×C5×Dic6C2211yescharacteristic
19C22×D3×Dic5C2214yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C4×Dic15C2212yes—
23C2×C4×Dic15C2218yescomplemented
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4072C2218yescomplemented
26C2×C3×C4⋊Dic5C2212yes—
27C2×C3×C4×Dic5C2212yes—
28#67⋊Dic5C22132yescomplemented
29C2×Dic3⋊Dic5C2214yes—
30C2×(C2×D3)⋊Dic5C2214yes—
31C2×Dic3×Dic5C2214yes—
32#91435C22116yescomplemented
33C4×D3×Dic5C22116yescomplemented
34#91371C22116yescomplemented
35#91344C22116yescomplemented
36C2×#5522—51nomaximal, Hall
37C22×C5×#41—31no—
38#41×Dic5—316no—
39C2×Q8×Dic5—32no—
40C2×D4×Dic5—32no—
41C2×D4×Dic5—34no—
42C2×#4072—32no—
43C2×#4072D311yescharacteristic, complemented
44C22×C4×Dic5—32no—
45C22×C4×Dic5—31no—
46C24×C3×C5C2311yescharacteristic
47C23×C5×D3C2312yes—
48C22×C3×C4×C5C2×C418yescomplemented
49C22×C3×C4×C5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2314yes—
52C22×Dic15—28no—
53C22×Dic15C2312yes—
54C22×Dic15C2318yes—
55C22×Dic15C2312yes—
56C2×C5×#67C2×C4116yescomplemented
57C2×C5×#67C2318yes—
58C22×C5×Dic3C2312yes—
59C5×#235C2×C4164yescomplemented
60C2×C5×D12C2×C418yescomplemented
61C2×C5×D12C2314yes—
62C2×C4×C5×D3C2×C4116yescomplemented
63C2×C4×C5×D3C2318yes—
64C2×C5×Dic6C2×C418yescomplemented
65C2×C5×Dic6C2314yes—
66C22×C3×Dic5C2314yes—
67C2×D3×Dic5—216no—
68C2×D3×Dic5C23116yes—
69C4×Dic15C2314yes—
70C4×Dic15C2318yes—
71C4×Dic15C2314yes—
72C3×C22⋊Dic5C2318yes—
73C3×C4⋊Dic5C2318yes—
74C3×C4×Dic5C2318yes—
75Dic3⋊Dic5C23116yes—
76(C2×D3)⋊Dic5C23116yes—
77Dic3×Dic5C23116yes—
78C22×#235D511yescharacteristic
79C2×C3×#117—51no—
80C22×C4×Dic3—51no—
81#5522—516no—
82C2×#893—52no—
83C2×#887—52no—
84C2×#67⋊C4—54no—
85C2×#872—52no—
86C2×C42×D3—52no—
87C2×C5×#41—316no—
88C2×C5×#41—38no—
89C22×C5×Q8—31no—
90C22×C5×D4—32no—
91C22×C5×D4—31no—
92C23×C4×C5—32no—
93C23×C4×C5C2×D311yescharacteristic
94C23×Dic5—32no—
95C23×Dic5—34no—
96C2×C22⋊Dic5—34no—
97C2×C22⋊Dic5C2×D312yes—
98Q8×Dic5—316no—
99D4×Dic5—332no—
100D4×Dic5—316no—
101#4072—316no—
102#4072C2×D318yescomplemented
103C2×C4⋊Dic5—34no—
104C2×C4⋊Dic5C2×D312yes—
105C2×C4×Dic5—31no—
106C2×C4×Dic5—31no—
107C2×C4×Dic5—32no—
108C2×C4×Dic5—38no—
109C2×C4×Dic5—34no—
110C2×C4×Dic5—316no—
111C2×C4×Dic5C2×D312yes—
112C2×C4×#41—151noSylow
113C23×C3×C5—24no—
114C23×C3×C5C22×C414yes—
115C23×C3×C5C2412yes—
116C23×C3×C5C2411yescharacteristic
117C22×C5×D3—28no—
118C22×C5×D3C22×C418yes—
119C22×C5×D3C2414yes—
120C2×C3×C4×C5C22×C414yes—
121C2×C3×C4×C5C22×C414yes—
122C2×C3×C4×C5C22×C4116yescomplemented
123C2×C3×C4×C5C2412yes—
124C2×C3×C4×C5C2412yes—
125C2×Dic15—24no—
126C2×Dic15—216no—
127C2×Dic15#4118yescomplemented
128C2×Dic15C2414yes—
129C2×Dic15C2414yes—
130C5×#67C22×C4132yescomplemented
131C2×C5×Dic3C22×C418yes—
132C2×C5×Dic3C2414yes—
133C5×D12C22×C4116yescomplemented
134C4×C5×D3C22×C4132yescomplemented
135C5×Dic6C22×C4116yescomplemented
136C2×C3×Dic5—28no—
137C2×C3×Dic5C2418yes—
138D3×Dic5—232no—
139C23×C3×C4C2×D511yescharacteristic
140C22×#67C2×D512yes—
141C23×Dic3—52no—
142C2×#235Dic5116yescomplemented
143C2×#235C2×D518yes—
144C22×D12C2×D511yescharacteristic
145C22×C4×D3—54no—
146C22×C4×D3C2×D512yes—
147C22×Dic6C2×D511yescharacteristic
148C3×#117—58no—
149C2×C3×C4⋊C4—52no—
150C2×C3×C22⋊C4—52no—
151C2×C3×C42—52no—
152C2×(C2×D3)⋊C4—54no—
153C2×Dic3⋊C4—54no—
154C2×C4×Dic3—51no—
155C2×C4×Dic3—51no—
156C2×C4×Dic3—52no—
157C2×C4×Dic3—58no—
158C2×C4×Dic3—54no—
159#893—516no—
160#887—516no—
161#67⋊C4—532no—
162#872—516no—
163C42×D3—516no—
164C24×C5—32no—
165C24×C5C22×D311yescharacteristic
166C5×#41—364no—
167C2×C5×Q8—38no—
168C2×C5×Q8—34no—
169C2×C5×D4—316no—
170C2×C5×D4—38no—
171C2×C5×D4—38no—
172C2×C5×D4—34no—
173C22×C4×C5—32no—
174C22×C4×C5—316no—
175C22×C4×C5—38no—
176C22×C4×C5C4×D318yescomplemented
177C22×C4×C5C22×D311yescharacteristic
178C22×C4×C5C22×D314yes—
179C22×C4×C5C22×D311yescharacteristic
180C22×Dic5—32no—
181C22×Dic5—32no—
182C22×Dic5—38no—
183C22×Dic5—316no—
184C22×Dic5—616no—
185C22×Dic5—68no—
186C22×Dic5C22×D314yes—
187C22⋊Dic5—316no—
188C22⋊Dic5C22×D318yes—
189C4⋊Dic5—316no—
190C4⋊Dic5C22×D318yes—
191C4×Dic5—34no—
192C4×Dic5—34no—
193C4×Dic5—38no—
194C4×Dic5—316no—
195C4×Dic5C22×D318yes—
196C22×#41—31no—
197C4×#41—1516no—
198C2×C4×Q8—152no—
199C2×C4×D4—154no—
200C2×C4×D4—152no—
201C2×#117—51no—
202C2×#117—152no—
203C22×C42—152no—
204C22×C42—151no—
205C22×C3×C5—28no—
206C22×C3×C5—24no—
207C22×C3×C5C23×C414yes—
208C22×C3×C5C23×C412yes—
209C22×C3×C5C2×#4114yes—
210C22×C3×C5C2511yescharacteristic
211C2×C5×D3—216no—
212C2×C5×D3—28no—
213C2×C5×D3C23×C418yes—
214C3×C4×C5C23×C414yes—
215C3×C4×C5C23×C414yes—
216Dic15—24no—
217Dic15C2×#4118yescomplemented
218C3×Dic5—28no—
219C5×Dic3C23×C418yes—
220C24×C3C22×D511yescharacteristic
221C23×D3C22×D512yes—
222C22×C3×C4—54no—
223C22×C3×C4C2×Dic518yescomplemented
224C22×C3×C4C22×D511yescharacteristic
225C22×C3×C4C22×D514yes—
226C22×C3×C4C22×D511yescharacteristic
227C2×#67C2×Dic5116yescomplemented
228C2×#67C22×D518yes—
229C22×Dic3—52no—
230C22×Dic3—58no—
231C22×Dic3—52no—
232C22×Dic3—108no—
233C22×Dic3C22×D512yes—
234#235C2×Dic5164yescomplemented
235C2×D12C2×Dic518yescomplemented
236C2×D12C22×D514yes—
237C2×C4×D3—516no—
238C2×C4×D3—1016no—
239C2×C4×D3C2×Dic5116yescomplemented
240C2×C4×D3C22×D518yes—
241C2×Dic6C2×Dic518yescomplemented
242C2×Dic6C22×D514yes—
243C3×C4⋊C4—58no—
244C3×C22⋊C4—58no—
245C3×C42—58no—
246(C2×D3)⋊C4—516no—
247Dic3⋊C4—516no—
248C4×Dic3—54no—
249C4×Dic3—54no—
250C4×Dic3—58no—
251C4×Dic3—516no—
252C23×C5—24no—
253C23×C5—38no—
254C23×C5—34no—
255C23×C5—68no—
256C23×C5C2×C4×D314yes—
257C23×C5C23×D312yes—
258C23×C5C23×D311yescharacteristic
259C5×Q8—316no—
260C5×D4—332no—
261C5×D4—316no—
262C2×C4×C5—38no—
263C2×C4×C5—34no—
264C2×C4×C5—332no—
265C2×C4×C5C2×C4×D314yes—
266C2×C4×C5C2×C4×D314yes—
267C2×C4×C5C2×C4×D3116yescomplemented
268C2×C4×C5C23×D312yes—
269C2×C4×C5C23×D312yes—
270C2×Dic5—28no—
271C2×Dic5—38no—
272C2×Dic5—34no—
273C2×Dic5—34no—
274C2×Dic5—632no—
275C2×Dic5—616no—
276C2×Dic5—64no—
277C2×Dic5C23×D318yes—
278C2×#41—316no—
279C2×#41—38no—
280C22×Q8—31no—
281C22×D4—32no—
282C22×D4—31no—
283C23×C4—32no—
284C23×C4—154no—
285C23×C4—152no—
286C23×C4D3×D511yescharacteristic
287C4×Q8—1516no—
288C4×D4—1532no—
289C4×D4—1516no—
290#117—58no—
291#117—1516no—
292C2×C4⋊C4—52no—
293C2×C4⋊C4—154no—
294C2×C22⋊C4—52no—
295C2×C22⋊C4—154no—
296C2×C42—52no—
297C2×C42—1516no—
298C2×C42—154no—
299C2×C42—152no—
300C2×C42—158no—
301C2×C42—151no—
302C2×C42—151no—
303C2×C3×C5—24no—
304C2×C3×C5C4×#4114yescomplemented
305C2×C3×C5C24×C411yescharacteristic
306C2×C3×C5C22×#4112yes—
307C5×D3—28no—
308C23×C3—24no—
309C23×C3C22×Dic514yes—
310C23×C3C23×D512yes—
311C23×C3C23×D511yescharacteristic
312C22×D3—28no—
313C22×D3C22×Dic518yes—
314C22×D3C23×D514yes—
315C2×C3×C4—58no—
316C2×C3×C4—108no—
317C2×C3×C4C22×Dic514yes—
318C2×C3×C4C22×Dic514yes—
319C2×C3×C4C22×Dic5116yescomplemented
320C2×C3×C4C23×D512yes—
321C2×C3×C4C23×D512yes—
322#67C22×Dic5132yescomplemented
323C2×Dic3—58no—
324C2×Dic3—54no—
325C2×Dic3—54no—
326C2×Dic3—1016no—
327C2×Dic3—104no—
328C2×Dic3C22×Dic518yes—
329C2×Dic3C23×D514yes—
330D12C22×Dic5116yescomplemented
331C4×D3—1032no—
332C4×D3C22×Dic5132yescomplemented
333Dic6C22×Dic5116yescomplemented
334C22×C5—24no—
335C22×C5—28no—
336C22×C5—38no—
337C22×C5—68no—
338C22×C5—616no—
339C22×C5C22×C4×D314yes—
340C22×C5C22×C4×D312yes—
341C22×C5D3×#4114yes—
342C22×C5C24×D311yescharacteristic
343C4×C5—38no—
344C4×C5C22×C4×D314yes—
345C4×C5C22×C4×D314yes—
346Dic5—28no—
347Dic5—38no—
348Dic5—64no—
349C24—32no—
350C24C2×D3×D511yescharacteristic
351#41—364no—
352C2×Q8—38no—
353C2×Q8—34no—
354C2×D4—316no—
355C2×D4—38no—
356C2×D4—38no—
357C2×D4—34no—
358C22×C4—32no—
359C22×C4—316no—
360C22×C4—38no—
361C22×C4—54no—
362C22×C4—1516no—
363C22×C4—152no—
364C22×C4—152no—
365C22×C4—158no—
366C22×C4—3016no—
367C22×C4—308no—
368C22×C4D3×Dic518yescomplemented
369C22×C4C2×D3×D511yescharacteristic
370C22×C4C2×D3×D514yes—
371C22×C4C2×D3×D511yescharacteristic
372C4⋊C4—58no—
373C4⋊C4—1516no—
374C22⋊C4—58no—
375C22⋊C4—1516no—
376C42—58no—
377C42—1516no—
378C42—154no—
379C42—154no—
380C42—158no—
381C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
382C22×C3—28no—
383C22×C3—24no—
384C22×C3D5×#4114yes—
385C22×C3C23×Dic514yes—
386C22×C3C23×Dic512yes—
387C22×C3C24×D511yescharacteristic
388C2×D3—216no—
389C2×D3—28no—
390C2×D3C23×Dic518yes—
391C3×C4—108no—
392C3×C4C23×Dic514yes—
393C3×C4C23×Dic514yes—
394Dic3—58no—
395Dic3—104no—
396Dic3C23×Dic518yes—
397C2×C5—24no—
398C2×C5—68no—
399C2×C5#552214yescomplemented
400C2×C5C23×C4×D311yescharacteristic
401C2×C5C2×D3×#4112yes—
402C23—24no—
403C23—38no—
404C23—34no—
405C23—68no—
406C23C2×D3×Dic514yes—
407C23C22×D3×D512yes—
408C23C22×D3×D511yescharacteristic
409Q8—316no—
410D4—332no—
411D4—316no—
412C2×C4—38no—
413C2×C4—34no—
414C2×C4—332no—
415C2×C4—58no—
416C2×C4—108no—
417C2×C4—158no—
418C2×C4—154no—
419C2×C4—154no—
420C2×C4—3032no—
421C2×C4—3016no—
422C2×C4—304no—
423C2×C4C2×D3×Dic514yes—
424C2×C4C2×D3×Dic514yes—
425C2×C4C2×D3×Dic5116yescomplemented
426C2×C4C22×D3×D512yes—
427C2×C4C22×D3×D512yes—
428C2×C3—24no—
429C2×C3#41×Dic514yescomplemented
430C2×C3C2×D5×#4112yes—
431C2×C3C24×Dic511yescharacteristic
432D3—28no—
433C5C2×#552211yescharacteristic, complemented, Sylow
434C22—28no—
435C22—24no—
436C22—38no—
437C22—616no—
438C22—68no—
439C22#9201614yes—
440C22C22×D3×Dic514yes—
441C22C22×D3×Dic512yes—
442C22C23×D3×D511yescharacteristic
443C4—38no—
444C4—108no—
445C4—158no—
446C4—304no—
447C4C22×D3×Dic514yes—
448C4C22×D3×Dic514yes—
449C3C2×#41×Dic511yescharacteristic, complemented, Sylow
450C2—24no—
451C2—68no—
452C2#1175445514yesdirect product factor
453C2C2×#9201612yes—
454C2C23×D3×Dic511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×#235C2
cosocleC22×C3×C5C25
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic15C2semidirect
3. C2×C3×#4072C2semidirect
4. C2×#67⋊Dic5C2semidirect
5. #11754455C2direct (N × H)
6. C2×#91435C2semidirect
7. C2×C4×D3×Dic5C2semidirect
8. C2×#91371C2semidirect
9. C2×#91344C2semidirect
14. C2×C5×#235C4semidirect
23. C2×C4×Dic15C22semidirect
25. C3×#4072C22semidirect
28. #67⋊Dic5C22semidirect
32. #91435C22semidirect
33. C4×D3×Dic5C22semidirect
34. #91371C22semidirect
35. #91344C22semidirect
43. C2×#4072D3semidirect
48. C22×C3×C4×C5C2×C4semidirect
56. C2×C5×#67C2×C4semidirect
59. C5×#235C2×C4semidirect
60. C2×C5×D12C2×C4semidirect
62. C2×C4×C5×D3C2×C4semidirect
64. C2×C5×Dic6C2×C4semidirect
102. #4072C2×D3semidirect
122. C2×C3×C4×C5C22×C4semidirect
127. C2×Dic15#41semidirect
130. C5×#67C22×C4semidirect
133. C5×D12C22×C4semidirect
134. C4×C5×D3C22×C4semidirect
135. C5×Dic6C22×C4semidirect
142. C2×#235Dic5semidirect
176. C22×C4×C5C4×D3semidirect
217. Dic15C2×#41semidirect
223. C22×C3×C4C2×Dic5semidirect
227. C2×#67C2×Dic5semidirect
234. #235C2×Dic5semidirect
235. C2×D12C2×Dic5semidirect
239. C2×C4×D3C2×Dic5semidirect
241. C2×Dic6C2×Dic5semidirect
267. C2×C4×C5C2×C4×D3semidirect
304. C2×C3×C5C4×#41semidirect
319. C2×C3×C4C22×Dic5semidirect
322. #67C22×Dic5semidirect
330. D12C22×Dic5semidirect
332. C4×D3C22×Dic5semidirect
333. Dic6C22×Dic5semidirect
368. C22×C4D3×Dic5semidirect
381. C3×C5C2×C4×#41semidirect
399. C2×C5#5522semidirect
425. C2×C4C2×D3×Dic5semidirect
429. C2×C3#41×Dic5semidirect
433. C5C2×#5522semidirect
449. C3C2×#41×Dic5semidirect
452. C2#11754455direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C22×C4×Dic152
C2×C3×#40722
C2×#67⋊Dic52
#117544552
C2×#914352
C2×C4×D3×Dic52
C2×#913712
C2×#913442
C2×#41×Dic53
C2×#55225