Finite Group Databasebeta

← C2×#11747452 #14413374

Subgroups — C2×#11747452 #14413374

Order 1920.

1072 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
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C22×#6649C211yesmaximal, characteristic
4C2×#91092C211yesmaximal, characteristic, complemented
5C2×C5×#807C211yesmaximal, characteristic, complemented
6C2×#90989C211yesmaximal, characteristic, complemented
7C2×#90987C211yesmaximal, characteristic, complemented
8#11747452C218yesmaximal, direct product factor
9C2×#65170—31nomaximal, Hall
10C22×C3×C4×D5—21no—
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×#683—21no—
19C3×D5×C4⋊C4—22no—
20C3×D5×C4⋊C4C2214yes—
21C2×#6665—21no—
22C2×Dic3×Dic5—21no—
23#91358—22no—
24#91358C2214yes—
25C2×#6649C418yescomplemented
26C2×#6649C2214yes—
27#91092C2214yescomplemented
28C5×#807C2214yescomplemented
29#90989C2214yescomplemented
30#90987C2214yescomplemented
31C2×#4964—51nomaximal, Hall
32C22×#676—31no—
33C2×#4038—31no—
34C2×D5×C4⋊C4D311yescharacteristic
35C2×C5×#107—31no—
36C2×#3949—31no—
37C2×#3940—31no—
38C2×#3939—31no—
39#65170—38no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×C5×Dic3—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5D411yescharacteristic
47C2×C3×C4×D5—24no—
48C2×C3×C4×D5—44no—
49C2×C3×C4×D5C2×C414yes—
50C2×C3×C4×D5D412yes—
51C2×C3×C4×D5Q814yes—
52C2×C3×C4×D5C2312yes—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2312yes—
55C4⋊Dic15—21no—
56C4⋊Dic15C2312yes—
57C2×C3⋊#168C2×C414yescomplemented
58C2×C3⋊#168C2312yes—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3C2312yes—
61C2×C5×C3⋊C8C2×C414yescomplemented
62C2×C5×C3⋊C8C2312yes—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5C2312yes—
65C3×#683—24no—
66#6665—24no—
67Dic3×Dic5—24no—
68#6649C2×C4116yescomplemented
69C22×C3×C4⋊C4—51no—
70C2×#926—51no—
71C22×#208—51no—
72#4964—58no—
73C2×#808—51no—
74C2×#808—51no—
75C2×#807—51no—
76C2×#807D511yescharacteristic, complemented
77C22×C4×D5—21no—
78C22×C4×D5C2×D311yescharacteristic
79C22×C5×C8—31no—
80C2×C5×C4⋊C4—31no—
81C2×C5×C4⋊C4C2×D311yescharacteristic
82C2×#685—61no—
83C2×C4⋊Dic5—31no—
84C2×C4⋊Dic5C2×D311yescharacteristic
85C2×#683—21no—
86C2×C4×Dic5—61no—
87C22×#168—31no—
88C2×#676—38no—
89C2×#676—34no—
90#4038—34no—
91#4038—62no—
92D5×C4⋊C4—22no—
93D5×C4⋊C4C2×D314yes—
94C5×#107—34no—
95#3949—34no—
96#3940—34no—
97#3939—34no—
98C2×#428—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5C4⋊C414yes—
103C22×C3×D5C2×D412yes—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—42no—
106C2×C3×C4×C5C22×C412yes—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×Q812yes—
109C2×C3×C4×C5C2411yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—42no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—42no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—42no—
116C2×C3×Dic5C4⋊C414yes—
117C2×C3×Dic5C2×D412yes—
118C3×C4×D5—48no—
119C3×C4×D5C4⋊C418yes—
120C3×C4×D5C22×C414yes—
121C3×C4×D5C2×Q814yes—
122C3⋊#168C22×C414yescomplemented
123C5×C3⋊C8C22×C414yescomplemented
124C23×C3×C4—51no—
125C23×C3×C4—101no—
126C2×C3×C4⋊C4—51no—
127C2×C3×C4⋊C4—54no—
128C2×C3×C4⋊C4—102no—
129C2×C3×C4⋊C4—101no—
130C2×C3×C4⋊C4C2×D511yescharacteristic
131C2×#217—101no—
132#926—54no—
133#926—102no—
134C2×C4⋊Dic3—51no—
135C2×C4⋊Dic3C2×D511yescharacteristic
136C2×C4×Dic3—101no—
137C2×#208—58no—
138C2×#208—54no—
139C22×C3⋊C8—51no—
140C22×C3⋊C8C2×D511yescharacteristic
141#808—54no—
142#808—54no—
143#807—54no—
144#807C2×D514yescomplemented
145C23×D5#6711yescharacteristic
146C22×C4×C5—21no—
147C22×C4×C5—61no—
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—21no—
150C22×Dic5—61no—
151C22×Dic5#6711yescharacteristic
152C2×C4×D5—24no—
153C2×C4×D5—44no—
154C2×C4×D5Dic614yes—
155C2×C4×D5C4×D314yes—
156C2×C4×D5#6712yes—
157C2×C4×D5C22×D312yes—
158C2×C5×C8—34no—
159C2×C5×C8—32no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—32no—
162C5×C4⋊C4—61no—
163C5×C4⋊C4C22×D312yes—
164#685—64no—
165C4⋊Dic5—21no—
166C4⋊Dic5—32no—
167C4⋊Dic5—61no—
168C4⋊Dic5C22×D312yes—
169#683—24no—
170C4×Dic5—64no—
171C2×#168—34no—
172C2×#168—32no—
173#676—316no—
174C22×M16—151no—
175C2×#117—151no—
176C22×C4⋊C4—51no—
177#428—158no—
178C2×#107—31no—
179C2×#107—151no—
180C2×#106—151no—
181C2×#106—151no—
182C22×C3×C5C2×C4⋊C412yes—
183C22×C3×C5AGL(1,ℤ/8)12yes—
184C22×C3×C5#13712yes—
185C22×C3×C5C22×D411yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—22no—
188C2×C3×D5—28no—
189C2×C3×D5C2×C4⋊C414yes—
190C3×C4×C5—42no—
191C3×C4×C5C2×C4⋊C412yes—
192C3×C4×C5C23×C411yescharacteristic
193C3×C4×C5C22×Q811yescharacteristic
194Dic15—42no—
195C3×Dic5—42no—
196C3×Dic5C2×C4⋊C414yes—
197C5×Dic3—42no—
198C24×C3—51no—
199C22×C3×C4—21no—
200C22×C3×C4—51no—
201C22×C3×C4—54no—
202C22×C3×C4—52no—
203C22×C3×C4—54no—
204C22×C3×C4—52no—
205C22×C3×C4—104no—
206C22×C3×C4—101no—
207C22×C3×C4—204no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—21no—
210C22×Dic3—101no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—52no—
213C3×C4⋊C4—104no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4C22×D512yes—
216#217—104no—
217C4⋊Dic3—21no—
218C4⋊Dic3—52no—
219C4⋊Dic3—101no—
220C4⋊Dic3C22×D512yes—
221C4×Dic3—104no—
222#208—516no—
223C2×C3⋊C8—54no—
224C2×C3⋊C8—52no—
225C2×C3⋊C8C4×D514yescomplemented
226C2×C3⋊C8C22×D512yes—
227C23×C5C2×#6711yescharacteristic
228C22×D5—22no—
229C22×D5—22no—
230C22×D5Dic3⋊C414yes—
231C22×D5C2×#6712yes—
232C2×C4×C5—22no—
233C2×C4×C5—42no—
234C2×C4×C5—62no—
235C2×C4×C5—122no—
236C2×C4×C5C2×Dic612yes—
237C2×C4×C5C2×C4×D312yes—
238C2×C4×C5C2×#6711yescharacteristic
239C2×C4×C5C23×D311yescharacteristic
240C2×Dic5—22no—
241C2×Dic5—42no—
242C2×Dic5—62no—
243C2×Dic5—122no—
244C2×Dic5Dic3⋊C414yes—
245C2×Dic5C2×#6712yes—
246C4×D5—48no—
247C4×D5Dic3⋊C418yes—
248C4×D5C2×Dic614yes—
249C4×D5C2×C4×D314yes—
250C5×C8—34no—
251#168—34no—
252C23×C4—51no—
253C23×C4—101no—
254C2×M16—154no—
255C2×M16—158no—
256C22×C8—31no—
257C22×C8—151no—
258#117—154no—
259#117—302no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—54no—
263C2×C4⋊C4—102no—
264C2×C4⋊C4—101no—
265C2×C4⋊C4—151no—
266C2×C4⋊C4D3×D511yescharacteristic
267C2×C22⋊C4—301no—
268C2×C42—301no—
269#107—34no—
270#107—154no—
271#106—154no—
272#106—154no—
273C2×C3×C5#42814yescomplemented
274C2×C3×C5C22×C4⋊C411yescharacteristic
275C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
276C2×C3×C5C2×#13711yescharacteristic
277C3×D5—24no—
278C23×C3—52no—
279C23×C3—54no—
280C23×C3—102no—
281C23×C3—102no—
282C23×C3D4×D511yescharacteristic
283C2×C3×C4—22no—
284C2×C3×C4—42no—
285C2×C3×C4—52no—
286C2×C3×C4—54no—
287C2×C3×C4—54no—
288C2×C3×C4—54no—
289C2×C3×C4—58no—
290C2×C3×C4—102no—
291C2×C3×C4—208no—
292C2×C3×C4—202no—
293C2×C3×C4C2×C4×D512yes—
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4Q8×D512yes—
296C2×C3×C4C23×D511yescharacteristic
297C2×Dic3—22no—
298C2×Dic3—42no—
299C2×Dic3—102no—
300C2×Dic3—202no—
301C3⋊C8—54no—
302C3⋊C8C2×C4×D514yescomplemented
303C22×C5C2×Dic3⋊C412yes—
304C22×C5#93212yes—
305C22×C5#94212yes—
306C22×C5C22×#6711yescharacteristic
307C2×D5—28no—
308C2×D5—22no—
309C2×D5—22no—
310C2×D5C2×Dic3⋊C414yes—
311C4×C5—42no—
312C4×C5—122no—
313C4×C5C2×Dic3⋊C412yes—
314C4×C5C22×Dic611yescharacteristic
315C4×C5C22×C4×D311yescharacteristic
316Dic5—42no—
317Dic5—122no—
318Dic5C2×Dic3⋊C414yes—
319C24—51no—
320C22×C4—21no—
321C22×C4—51no—
322C22×C4—54no—
323C22×C4—54no—
324C22×C4—52no—
325C22×C4—52no—
326C22×C4—61no—
327C22×C4—104no—
328C22×C4—101no—
329C22×C4—204no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332M16—1516no—
333C2×C8—34no—
334C2×C8—32no—
335C2×C8—154no—
336C2×C8—152no—
337C4⋊C4—21no—
338C4⋊C4—32no—
339C4⋊C4—52no—
340C4⋊C4—61no—
341C4⋊C4—104no—
342C4⋊C4—101no—
343C4⋊C4—152no—
344C4⋊C4—301no—
345C4⋊C4C2×D3×D512yes—
346C22⋊C4—304no—
347C42—304no—
348C3×C5C2×#42811yescharacteristic, complemented, Hall
349C22×C3—54no—
350C22×C3—102no—
351C22×C3—102no—
352C22×C3—108no—
353C22×C3D5×C4⋊C412yes—
354C22×C3#405712yes—
355C22×C3#406412yes—
356C22×C3C2×D4×D511yescharacteristic
357C3×C4—42no—
358C3×C4—54no—
359C3×C4—202no—
360C3×C4D5×C4⋊C412yes—
361C3×C4C22×C4×D511yescharacteristic
362C3×C4C2×Q8×D511yescharacteristic
363Dic3—42no—
364Dic3—202no—
365C2×C5#496414yescomplemented
366C2×C5C22×Dic3⋊C411yescharacteristic
367C2×C5C2×#93211yescharacteristic
368C2×C5C2×#94211yescharacteristic
369D5—24no—
370C23—54no—
371C23—52no—
372C23—102no—
373C23—102no—
374C23D5×#6711yescharacteristic
375C2×C4—22no—
376C2×C4—42no—
377C2×C4—54no—
378C2×C4—52no—
379C2×C4—58no—
380C2×C4—54no—
381C2×C4—54no—
382C2×C4—62no—
383C2×C4—102no—
384C2×C4—122no—
385C2×C4—208no—
386C2×C4—202no—
387C2×C4—302no—
388C2×C4—602no—
389C2×C4D5×Dic612yes—
390C2×C4C4×D3×D512yes—
391C2×C4D5×#6711yescharacteristic
392C2×C4C22×D3×D511yescharacteristic
393C8—34no—
394C8—154no—
395C2×C3—104no—
396C2×C3#6517014yescomplemented
397C2×C3C2×D5×C4⋊C411yescharacteristic
398C2×C3C2×#405711yescharacteristic
399C2×C3C2×#406411yescharacteristic
400C5C2×#496411yescharacteristic, complemented, Sylow
401C22—54no—
402C22—102no—
403C22—108no—
404C22—102no—
405C22D5×Dic3⋊C412yes—
406C22#9148912yes—
407C22#9151512yes—
408C22C2×D5×#6711yescharacteristic
409C4—42no—
410C4—54no—
411C4—122no—
412C4—202no—
413C4—602no—
414C4D5×Dic3⋊C412yes—
415C4C2×D5×Dic611yescharacteristic
416C4C2×C4×D3×D511yescharacteristic
417C3C2×#6517011yescharacteristic, complemented, Sylow
418C2—104no—
419C2#1174745214yesdirect product factor
420C2C2×D5×Dic3⋊C411yescharacteristic
421C2C2×#9148911yescharacteristic
422C2C2×#9151511yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#428
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#91092C2semidirect
5. C2×C5×#807C2semidirect
6. C2×#90989C2semidirect
7. C2×#90987C2semidirect
8. #11747452C2direct (N × H)
25. C2×#6649C4semidirect
27. #91092C22semidirect
28. C5×#807C22semidirect
29. #90989C22semidirect
30. #90987C22semidirect
57. C2×C3⋊#168C2×C4semidirect
61. C2×C5×C3⋊C8C2×C4semidirect
68. #6649C2×C4semidirect
76. C2×#807D5semidirect
122. C3⋊#168C22×C4semidirect
123. C5×C3⋊C8C22×C4semidirect
144. #807C2×D5semidirect
225. C2×C3⋊C8C4×D5semidirect
273. C2×C3×C5#428semidirect
302. C3⋊C8C2×C4×D5semidirect
348. C3×C5C2×#428semidirect
365. C2×C5#4964semidirect
396. C2×C3#65170semidirect
400. C5C2×#4964semidirect
417. C3C2×#65170semidirect
419. C2#11747452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×#913582
C22×#66492
C2×#910922
C2×C5×#8072
C2×#909892
C2×#909872
#117474522
C2×#651703
C2×#49645