Finite Group Databasebeta

← C2×#11752484 #14480163

Subgroups — C2×#11752484 #14480163

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D15C211yesmaximal, characteristic
2C2×C5×#869C211yesmaximal, characteristic, complemented
3C2×C3×#4015C211yesmaximal, characteristic, complemented
4C2×#91390C212yesmaximal
5C2×#91384C212yesmaximal, complemented
6C2×#91383C212yesmaximal
7C2×#91347C212yesmaximal
8C2×#91344C212yesmaximal, complemented
9C2×#91331C212yesmaximal, complemented
10#11752484C2116yesmaximal, direct product factor
11C2×#66062—31nomaximal, Hall
12C22×C4×D15C2211yescharacteristic
13C22×C4×D15C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C22×C5×Dic6C2212yes—
16C22×C3×Dic10C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C42×D15C2218yes—
22C2×C5×C4⋊Dic3C2212yes—
23C2×C5×C4⋊Dic3C2212yes—
24C5×#869C2218yescomplemented
25C2×C3×C4⋊Dic5C2212yes—
26C2×C3×C4⋊Dic5C2212yes—
27C3×#4015C2218yescomplemented
28C2×Dic3⋊Dic5C2214yes—
29C2×#6668C2214yes—
30C2×#6667C2214yes—
31C2×Dic3×Dic5C2214yes—
32#91390C22116yes—
33#91384C22116yescomplemented
34#91383C22116yes—
35#91347C22116yes—
36#91344C22116yescomplemented
37#91331C22116yescomplemented
38C2×#5728—51nomaximal, Hall
39C2×C5×C4⋊Q8—31no—
40C2×#4092—32no—
41C2×Q8×Dic5—32no—
42#66062—316no—
43C2×#4043—32no—
44C2×#4038—32no—
45C2×#4036—32no—
46C2×#4033—32no—
47C2×C42×D5—31no—
48C2×#4015D311yescharacteristic, complemented
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C2×C4×D15—24no—
57C2×C4×D15—24no—
58C2×C4×D15Q818yescomplemented
59C2×C4×D15C2314yes—
60C2×C4×D15C2314yes—
61C2×C4×D15C2314yes—
62C22×C5×Dic3C2314yes—
63C2×C5×Dic6—28no—
64C2×C5×Dic6C2318yes—
65C22×C3×Dic5C2314yes—
66C2×C3×Dic10—28no—
67C2×C3×Dic10C2318yes—
68C3×C42×C5C2314yes—
69C4×Dic15C2314yes—
70C4×Dic15C2314yes—
71C4×Dic15C2314yes—
72C5×C4⋊Dic3C2318yes—
73C5×C4⋊Dic3C2318yes—
74C3×C4⋊Dic5C2318yes—
75C3×C4⋊Dic5C2318yes—
76Dic3⋊Dic5C23116yes—
77#6668C23116yes—
78#6667C23116yes—
79Dic3×Dic5C23116yes—
80C2×C3×C4⋊Q8—51no—
81C2×#946—52no—
82C2×Q8×Dic3—52no—
83#5728—516no—
84C2×#897—52no—
85C2×#892—52no—
86C2×#890—52no—
87C2×#887—52no—
88C2×C42×D3—51no—
89C2×#869D511yescharacteristic, complemented
90C22×C5×Q8—32no—
91C22×C4×D5—31no—
92C22×C4×D5—31no—
93C22×C4×D5—31no—
94C22×Dic10C2×D312yes—
95C5×C4⋊Q8—38no—
96C2×C5×C4⋊C4—32no—
97C2×C5×C4⋊C4—32no—
98C2×C42×C5C2×D311yescharacteristic
99#4092—316no—
100Q8×Dic5—316no—
101C2×#685—34no—
102C2×C4⋊Dic5—34no—
103C2×C4⋊Dic5C2×D312yes—
104C2×C4⋊Dic5C2×D312yes—
105C2×#683—34no—
106C2×C4×Dic5—31no—
107C2×C4×Dic5—31no—
108C2×C4×Dic5—31no—
109C2×C4×Dic5—34no—
110#4043—316no—
111#4038—316no—
112#4036—316no—
113#4033—316no—
114C42×D5—38no—
115#4015C2×D318yescomplemented
116C2×#533—151noSylow
117C23×C3×C5C2411yescharacteristic
118C22×D15—22no—
119C22×D15—22no—
120C22×D15C2×Q814yes—
121C22×D15C2412yes—
122C2×C3×C4×C5C2×Q814yes—
123C2×C3×C4×C5#4114yes—
124C2×C3×C4×C5#4114yes—
125C2×C3×C4×C5C2412yes—
126C2×C3×C4×C5C2412yes—
127C2×C3×C4×C5C2412yes—
128C2×Dic15—22no—
129C2×Dic15—22no—
130C2×Dic15C2×Q814yes—
131C2×Dic15C2412yes—
132C2×Dic15C2412yes—
133C2×Dic15C2412yes—
134C4×D15—28no—
135C4×D15—28no—
136C4×D15C2×Q8116yescomplemented
137C2×C5×Dic3—28no—
138C2×C5×Dic3C2418yes—
139C5×Dic6—216no—
140C2×C3×Dic5—28no—
141C2×C3×Dic5C2418yes—
142C3×Dic10—216no—
143C22×C3×Q8—52no—
144C22×C4×D3—51no—
145C22×C4×D3—51no—
146C22×C4×D3—51no—
147C22×Dic6C2×D512yes—
148C3×C4⋊Q8—58no—
149C2×C3×C4⋊C4—52no—
150C2×C3×C4⋊C4—52no—
151C2×C3×C42C2×D511yescharacteristic
152#946—516no—
153Q8×Dic3—516no—
154C2×(C2×D3)⋊C4—54no—
155C2×C4⋊Dic3—54no—
156C2×C4⋊Dic3C2×D512yes—
157C2×C4⋊Dic3C2×D512yes—
158C2×Dic3⋊C4—54no—
159C2×C4×Dic3—51no—
160C2×C4×Dic3—51no—
161C2×C4×Dic3—51no—
162C2×C4×Dic3—54no—
163#897—516no—
164#892—516no—
165#890—516no—
166#887—516no—
167C42×D3—58no—
168#869C2×D518yescomplemented
169C23×D5—31no—
170C2×C5×Q8—38no—
171C2×C5×Q8—68no—
172C22×C4×C5—34no—
173C22×C4×C5C22×D311yescharacteristic
174C22×C4×C5C22×D311yescharacteristic
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—31no—
177C22×Dic5—31no—
178C22×Dic5—31no—
179C22×Dic5C22×D314yes—
180C2×C4×D5—38no—
181C2×C4×D5—34no—
182C2×C4×D5—34no—
183C2×C4×D5—34no—
184C2×C4×D5—64no—
185C2×C4×D5—64no—
186C2×Dic10—28no—
187C2×Dic10C22×D318yes—
188C5×C4⋊C4—38no—
189C5×C4⋊C4—38no—
190C42×C5C22×D314yes—
191#685—316no—
192C4⋊Dic5—316no—
193C4⋊Dic5C22×D318yes—
194C4⋊Dic5C22×D318yes—
195#683—316no—
196C4×Dic5—34no—
197C4×Dic5—34no—
198C4×Dic5—34no—
199C4×Dic5—316no—
200#533—1516no—
201C2×C4⋊Q8—31no—
202C2×C4⋊Q8—51no—
203C2×#125—152no—
204C2×C22⋊Q8—152no—
205C2×C22⋊Q8—152no—
206C2×C4×Q8—152no—
207C2×C4×Q8—152no—
208C2×#117—152no—
209C22×C42—151no—
210C22×C3×C5C22×Q812yes—
211C22×C3×C5C2×#4112yes—
212C22×C3×C5C2×#4112yes—
213C22×C3×C5C2511yescharacteristic
214C2×D15—28no—
215C2×D15—22no—
216C2×D15—22no—
217C2×D15C22×Q814yes—
218C3×C4×C5C22×Q814yes—
219C3×C4×C5C2×#4114yes—
220C3×C4×C5C2×#4114yes—
221Dic15—22no—
222Dic15—22no—
223Dic15C22×Q814yes—
224C3×Dic5—28no—
225C5×Dic3—28no—
226C23×D3—51no—
227C2×C3×Q8—58no—
228C2×C3×Q8—108no—
229C22×C3×C4—54no—
230C22×C3×C4C22×D511yescharacteristic
231C22×C3×C4C22×D511yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C22×Dic3—51no—
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3C22×D514yes—
237C2×C4×D3—58no—
238C2×C4×D3—54no—
239C2×C4×D3—54no—
240C2×C4×D3—54no—
241C2×C4×D3—104no—
242C2×C4×D3—104no—
243C2×Dic6—28no—
244C2×Dic6C22×D518yes—
245C3×C4⋊C4—58no—
246C3×C4⋊C4—58no—
247C3×C42C22×D514yes—
248(C2×D3)⋊C4—516no—
249C4⋊Dic3—516no—
250C4⋊Dic3C22×D518yes—
251C4⋊Dic3C22×D518yes—
252Dic3⋊C4—516no—
253C4×Dic3—54no—
254C4×Dic3—54no—
255C4×Dic3—54no—
256C4×Dic3—516no—
257C23×C5C23×D311yescharacteristic
258C22×D5—34no—
259C22×D5—32no—
260C22×D5—62no—
261C22×D5—62no—
262C5×Q8—616no—
263C2×C4×C5—38no—
264C2×C4×C5—68no—
265C2×C4×C5#23714yes—
266C2×C4×C5D3×Q814yes—
267C2×C4×C5#23914yes—
268C2×C4×C5C23×D312yes—
269C2×C4×C5C23×D312yes—
270C2×C4×C5C23×D312yes—
271C2×Dic5—28no—
272C2×Dic5—34no—
273C2×Dic5—32no—
274C2×Dic5—32no—
275C2×Dic5—32no—
276C2×Dic5—62no—
277C2×Dic5—62no—
278C2×Dic5C23×D318yes—
279C4×D5—316no—
280C4×D5—68no—
281C4×D5—68no—
282Dic10—216no—
283C22×Q8—32no—
284C22×Q8—52no—
285C23×C4—151no—
286C23×C4—151no—
287C23×C4—151no—
288C4⋊Q8—38no—
289C4⋊Q8—58no—
290#125—1516no—
291C22⋊Q8—1516no—
292C22⋊Q8—1516no—
293C4×Q8—1516no—
294C4×Q8—1516no—
295#117—1516no—
296C2×C4⋊C4—32no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—52no—
299C2×C4⋊C4—52no—
300C2×C4⋊C4—154no—
301C2×C4⋊C4—154no—
302C2×C22⋊C4—154no—
303C2×C42—154no—
304C2×C42—151no—
305C2×C42—151no—
306C2×C42—151no—
307C2×C42—158no—
308C2×C42D3×D511yescharacteristic
309C2×C3×C5#53314yescomplemented
310C2×C3×C5C23×Q811yescharacteristic
311C2×C3×C5C22×#4111yescharacteristic
312C2×C3×C5C22×#4111yescharacteristic
313D15—24no—
314C23×C3C23×D511yescharacteristic
315C22×D3—54no—
316C22×D3—52no—
317C22×D3—102no—
318C22×D3—102no—
319C3×Q8—1016no—
320C2×C3×C4—58no—
321C2×C3×C4—108no—
322C2×C3×C4#71114yes—
323C2×C3×C4Q8×D514yes—
324C2×C3×C4#71314yes—
325C2×C3×C4C23×D512yes—
326C2×C3×C4C23×D512yes—
327C2×C3×C4C23×D512yes—
328C2×Dic3—28no—
329C2×Dic3—54no—
330C2×Dic3—52no—
331C2×Dic3—52no—
332C2×Dic3—52no—
333C2×Dic3—102no—
334C2×Dic3—102no—
335C2×Dic3C23×D518yes—
336C4×D3—516no—
337C4×D3—108no—
338C4×D3—108no—
339Dic6—216no—
340C22×C5C2×#23712yes—
341C22×C5C2×D3×Q812yes—
342C22×C5C2×#23912yes—
343C22×C5C24×D311yescharacteristic
344C2×D5—34no—
345C2×D5—62no—
346C2×D5—62no—
347C2×D5—68no—
348C4×C5—68no—
349C4×C5C2×#23714yes—
350C4×C5C2×D3×Q814yes—
351C4×C5C2×#23914yes—
352Dic5—28no—
353Dic5—34no—
354Dic5—62no—
355Dic5—62no—
356C24—151no—
357C2×Q8—38no—
358C2×Q8—58no—
359C2×Q8—68no—
360C2×Q8—108no—
361C22×C4—34no—
362C22×C4—54no—
363C22×C4—151no—
364C22×C4—158no—
365C22×C4—154no—
366C22×C4—151no—
367C22×C4—151no—
368C22×C4—154no—
369C22×C4—154no—
370C22×C4—304no—
371C22×C4—304no—
372C22×C4C2×D3×D511yescharacteristic
373C22×C4C2×D3×D511yescharacteristic
374C22×C4C2×D3×D511yescharacteristic
375C4⋊C4—38no—
376C4⋊C4—38no—
377C4⋊C4—58no—
378C4⋊C4—58no—
379C4⋊C4—1516no—
380C4⋊C4—1516no—
381C22⋊C4—1516no—
382C42—1516no—
383C42—154no—
384C42—154no—
385C42—154no—
386C42C2×D3×D514yes—
387C3×C5C2×#53311yescharacteristic, complemented, Hall
388C22×C3C2×#71112yes—
389C22×C3C2×Q8×D512yes—
390C22×C3C2×#71312yes—
391C22×C3C24×D511yescharacteristic
392C2×D3—54no—
393C2×D3—108no—
394C2×D3—102no—
395C2×D3—102no—
396C3×C4—108no—
397C3×C4C2×#71114yes—
398C3×C4C2×Q8×D514yes—
399C3×C4C2×#71314yes—
400Dic3—28no—
401Dic3—54no—
402Dic3—102no—
403Dic3—102no—
404C2×C5#572814yescomplemented
405C2×C5C22×#23711yescharacteristic
406C2×C5C22×D3×Q811yescharacteristic
407C2×C5C22×#23911yescharacteristic
408D5—64no—
409C23—154no—
410C23—152no—
411C23—302no—
412C23—302no—
413C23C22×D3×D511yescharacteristic
414Q8—616no—
415Q8—1016no—
416C2×C4—38no—
417C2×C4—58no—
418C2×C4—68no—
419C2×C4—108no—
420C2×C4—154no—
421C2×C4—152no—
422C2×C4—1516no—
423C2×C4—152no—
424C2×C4—152no—
425C2×C4—302no—
426C2×C4—302no—
427C2×C4—308no—
428C2×C4—308no—
429C2×C4#676614yes—
430C2×C4#676814yes—
431C2×C4D15⋊Q814yes—
432C2×C4C22×D3×D512yes—
433C2×C4C22×D3×D512yes—
434C2×C4C22×D3×D512yes—
435C2×C3#6606214yescomplemented
436C2×C3C22×#71111yescharacteristic
437C2×C3C22×Q8×D511yescharacteristic
438C2×C3C22×#71311yescharacteristic
439D3—104no—
440C5C2×#572811yescharacteristic, complemented, Sylow
441C22—154no—
442C22—308no—
443C22—302no—
444C22—302no—
445C22C2×#676612yes—
446C22C2×#676812yes—
447C22C2×D15⋊Q812yes—
448C22C23×D3×D511yescharacteristic
449C4—68no—
450C4—108no—
451C4—154no—
452C4—302no—
453C4—302no—
454C4C2×#676614yes—
455C4C2×#676814yes—
456C4C2×D15⋊Q814yes—
457C3C2×#6606211yescharacteristic, complemented, Sylow
458C2—304no—
459C2#1175248414yesdirect product factor
460C2C22×#676611yescharacteristic
461C2C22×#676811yescharacteristic
462C2C22×D15⋊Q811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C5×#869C2semidirect
3. C2×C3×#4015C2semidirect
5. C2×#91384C2semidirect
8. C2×#91344C2semidirect
9. C2×#91331C2semidirect
10. #11752484C2direct (N × H)
24. C5×#869C22semidirect
27. C3×#4015C22semidirect
33. #91384C22semidirect
36. #91344C22semidirect
37. #91331C22semidirect
48. C2×#4015D3semidirect
58. C2×C4×D15Q8semidirect
89. C2×#869D5semidirect
115. #4015C2×D3semidirect
136. C4×D15C2×Q8semidirect
168. #869C2×D5semidirect
309. C2×C3×C5#533semidirect
387. C3×C5C2×#533semidirect
404. C2×C5#5728semidirect
435. C2×C3#66062semidirect
440. C5C2×#5728semidirect
457. C3C2×#66062semidirect
459. C2#11752484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×D152
C2×C5×#8692
C2×C3×#40152
C2×#913902
C2×#913842
C2×#913832
C2×#913472
C2×#913442
C2×#913312
#117524842
C2×#660623
C2×#57285