Finite Group Databasebeta

← C2×#11752506 #14480162

Subgroups — C2×#11752506 #14480162

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×#91758C211yesmaximal, characteristic, complemented
2C2×C5×#869C211yesmaximal, characteristic, complemented
3C2×C3×C42×D5C211yesmaximal, characteristic
4C2×#91388C212yesmaximal, complemented
5C2×#91360C212yesmaximal
6C2×#91359C212yesmaximal
7C2×#91358C212yesmaximal
8C2×#91333C212yesmaximal, complemented
9C2×Dic5×Dic6C212yesmaximal, complemented
10#11752506C2116yesmaximal, direct product factor
11C2×#66062—31nomaximal, Hall
12C22×Dic30C2212yes—
13C22×C5×Dic6C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2212yes—
19C2×C4⋊Dic15C2212yes—
20#91758C2218yescomplemented
21C2×C5×C4⋊Dic3C2212yes—
22C2×C5×C4⋊Dic3C2212yes—
23C5×#869C2218yescomplemented
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C3×C42×D5C2218yes—
28C2×Dic3⋊Dic5C2214yes—
29C2×#6669C2214yes—
30C2×#6665C2214yes—
31C2×Dic3×Dic5C2214yes—
32#91388C22116yescomplemented
33#91360C22116yes—
34#91359C22116yes—
35#91358C22116yes—
36#91333C22116yescomplemented
37Dic5×Dic6C22116yescomplemented
38C2×#5470—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×D5D311yescharacteristic
48C2×#4015—31no—
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2314yes—
54C2×Dic30—28no—
55C2×Dic30C2318yes—
56C22×C5×Dic3C2314yes—
57C2×C5×Dic6—28no—
58C2×C5×Dic6C2318yes—
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—24no—
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5Q818yescomplemented
65C2×C3×C4×D5C2314yes—
66C2×C3×C4×D5C2314yes—
67C2×C3×C4×D5C2314yes—
68C3×C42×C5C2314yes—
69C4⋊Dic15C2318yes—
70C4⋊Dic15C2318yes—
71C5×C4⋊Dic3C2318yes—
72C5×C4⋊Dic3C2318yes—
73C3×C4×Dic5C2314yes—
74C3×C4×Dic5C2314yes—
75C3×C4×Dic5C2314yes—
76Dic3⋊Dic5C23116yes—
77#6669C23116yes—
78#6665C23116yes—
79Dic3×Dic5C23116yes—
80C22×C3×C42—51no—
81C2×#926—52no—
82C2×#924—52no—
83C2×#924—52no—
84#5470—516no—
85C2×#870—52no—
86C2×#869—51no—
87C2×#869D511yescharacteristic, complemented
88C2×C4×Dic6—52no—
89C2×C4×Dic6—52no—
90C22×C5×Q8—32no—
91C22×C4×D5C2×D311yescharacteristic
92C22×C4×D5C2×D311yescharacteristic
93C22×C4×D5C2×D311yescharacteristic
94C22×Dic10—32no—
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—32no—
103C2×C4⋊Dic5—32no—
104C2×C4⋊Dic5—34no—
105C2×#683—34no—
106C2×C4×Dic5—34no—
107C2×C4×Dic5C2×D311yescharacteristic
108C2×C4×Dic5C2×D311yescharacteristic
109C2×C4×Dic5C2×D311yescharacteristic
110#4043—316no—
111#4038—316no—
112#4036—316no—
113#4033—316no—
114C42×D5C2×D318yes—
115#4015—38no—
116C2×#533—151noSylow
117C23×C3×C5C2411yescharacteristic
118C22×C3×D5—22no—
119C22×C3×D5—22no—
120C22×C3×D5C2×Q814yes—
121C22×C3×D5C2412yes—
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—28no—
129C2×Dic15C2418yes—
130Dic30—216no—
131C2×C5×Dic3—28no—
132C2×C5×Dic3C2418yes—
133C5×Dic6—216no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5C2×Q814yes—
137C2×C3×Dic5C2412yes—
138C2×C3×Dic5C2412yes—
139C2×C3×Dic5C2412yes—
140C3×C4×D5—28no—
141C3×C4×D5—28no—
142C3×C4×D5C2×Q8116yescomplemented
143C23×C3×C4—51no—
144C23×C3×C4—51no—
145C23×C3×C4—51no—
146C22×Dic6—52no—
147C22×Dic6C2×D512yes—
148C2×C3×C42—51no—
149C2×C3×C42—51no—
150C2×C3×C42—51no—
151C2×C3×C42—58no—
152C2×C3×C42C2×D511yescharacteristic
153C2×#217—54no—
154#926—516no—
155C2×C4⋊Dic3—52no—
156C2×C4⋊Dic3—52no—
157C2×C4⋊Dic3C2×D512yes—
158C2×C4⋊Dic3C2×D512yes—
159#924—516no—
160#924—516no—
161C2×Dic3⋊C4—54no—
162C2×Dic3⋊C4—54no—
163C2×C4×Dic3—54no—
164#870—516no—
165#869—58no—
166#869C2×D518yescomplemented
167C4×Dic6—516no—
168C4×Dic6—516no—
169C23×D5C22×D311yescharacteristic
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—34no—
177C22×Dic5C22×D311yescharacteristic
178C22×Dic5C22×D311yescharacteristic
179C22×Dic5C22×D311yescharacteristic
180C2×C4×D5—24no—
181C2×C4×D5—24no—
182C2×C4×D5Dic618yescomplemented
183C2×C4×D5C22×D314yes—
184C2×C4×D5C22×D314yes—
185C2×C4×D5C22×D314yes—
186C2×Dic10—38no—
187C2×Dic10—68no—
188C5×C4⋊C4—38no—
189C5×C4⋊C4—38no—
190C42×C5C22×D314yes—
191#685—316no—
192C4⋊Dic5—38no—
193C4⋊Dic5—38no—
194C4⋊Dic5—316no—
195#683—316no—
196C4×Dic5—316no—
197C4×Dic5C22×D314yes—
198C4×Dic5C22×D314yes—
199C4×Dic5C22×D314yes—
200#533—1516no—
201C2×C4⋊Q8—31no—
202C2×C4⋊Q8—151no—
203C2×#125—152no—
204C2×C22⋊Q8—152no—
205C2×C22⋊Q8—152no—
206C2×C4×Q8—152no—
207C2×C4×Q8—152no—
208C2×#117—152no—
209C22×C42—51no—
210C22×C3×C5C22×Q812yes—
211C22×C3×C5C2×#4112yes—
212C22×C3×C5C2×#4112yes—
213C22×C3×C5C2511yescharacteristic
214C2×C3×D5—28no—
215C2×C3×D5—22no—
216C2×C3×D5—22no—
217C2×C3×D5C22×Q814yes—
218C3×C4×C5C22×Q814yes—
219C3×C4×C5C2×#4114yes—
220C3×C4×C5C2×#4114yes—
221Dic15—28no—
222C3×Dic5—22no—
223C3×Dic5—22no—
224C3×Dic5C22×Q814yes—
225C5×Dic3—28no—
226C24×C3—51no—
227C22×C3×C4—51no—
228C22×C3×C4—58no—
229C22×C3×C4—54no—
230C22×C3×C4—51no—
231C22×C3×C4—51no—
232C22×C3×C4—54no—
233C22×C3×C4—54no—
234C22×C3×C4—104no—
235C22×C3×C4—104no—
236C22×C3×C4C22×D511yescharacteristic
237C22×C3×C4C22×D511yescharacteristic
238C22×C3×C4C22×D511yescharacteristic
239C22×Dic3—54no—
240C22×Dic3C22×D514yes—
241C2×Dic6—28no—
242C2×Dic6—58no—
243C2×Dic6—108no—
244C2×Dic6C22×D518yes—
245C3×C42—54no—
246C3×C42—54no—
247C3×C42—54no—
248C3×C42C22×D514yes—
249#217—516no—
250C4⋊Dic3—58no—
251C4⋊Dic3—58no—
252C4⋊Dic3C22×D518yes—
253C4⋊Dic3C22×D518yes—
254Dic3⋊C4—516no—
255Dic3⋊C4—516no—
256C4×Dic3—516no—
257C23×C5C23×D311yescharacteristic
258C22×D5—22no—
259C22×D5—22no—
260C22×D5C2×Dic614yes—
261C22×D5C23×D312yes—
262C5×Q8—616no—
263C2×C4×C5—38no—
264C2×C4×C5—68no—
265C2×C4×C5C2×Dic614yes—
266C2×C4×C5#23514yes—
267C2×C4×C5#23514yes—
268C2×C4×C5C23×D312yes—
269C2×C4×C5C23×D312yes—
270C2×C4×C5C23×D312yes—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—38no—
274C2×Dic5—68no—
275C2×Dic5C2×Dic614yes—
276C2×Dic5C23×D312yes—
277C2×Dic5C23×D312yes—
278C2×Dic5C23×D312yes—
279C4×D5—28no—
280C4×D5—28no—
281C4×D5C2×Dic6116yescomplemented
282Dic10—616no—
283C22×Q8—32no—
284C22×Q8—152no—
285C23×C4—51no—
286C23×C4—51no—
287C23×C4—51no—
288C4⋊Q8—38no—
289C4⋊Q8—158no—
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—154no—
299C2×C4⋊C4—154no—
300C2×C4⋊C4—152no—
301C2×C4⋊C4—152no—
302C2×C22⋊C4—154no—
303C2×C42—51no—
304C2×C42—51no—
305C2×C42—51no—
306C2×C42—58no—
307C2×C42—154no—
308C2×C42D3×D511yescharacteristic
309C2×C3×C5#53314yescomplemented
310C2×C3×C5C23×Q811yescharacteristic
311C2×C3×C5C22×#4111yescharacteristic
312C2×C3×C5C22×#4111yescharacteristic
313C3×D5—24no—
314C23×C3—54no—
315C23×C3—52no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3C23×D511yescharacteristic
319C2×C3×C4—54no—
320C2×C3×C4—52no—
321C2×C3×C4—516no—
322C2×C3×C4—52no—
323C2×C3×C4—52no—
324C2×C3×C4—102no—
325C2×C3×C4—102no—
326C2×C3×C4—108no—
327C2×C3×C4—108no—
328C2×C3×C4#71114yes—
329C2×C3×C4Q8×D514yes—
330C2×C3×C4#71314yes—
331C2×C3×C4C23×D512yes—
332C2×C3×C4C23×D512yes—
333C2×C3×C4C23×D512yes—
334C2×Dic3—28no—
335C2×Dic3—58no—
336C2×Dic3—108no—
337C2×Dic3C23×D518yes—
338Dic6—216no—
339Dic6—1016no—
340C22×C5C22×Dic612yes—
341C22×C5C2×#23512yes—
342C22×C5C2×#23512yes—
343C22×C5C24×D311yescharacteristic
344C2×D5—22no—
345C2×D5—22no—
346C2×D5—28no—
347C2×D5C22×Dic614yes—
348C4×C5—68no—
349C4×C5C22×Dic614yes—
350C4×C5C2×#23514yes—
351C4×C5C2×#23514yes—
352Dic5—22no—
353Dic5—22no—
354Dic5—68no—
355Dic5C22×Dic614yes—
356C24—51no—
357C2×Q8—38no—
358C2×Q8—68no—
359C2×Q8—158no—
360C2×Q8—308no—
361C22×C4—34no—
362C22×C4—51no—
363C22×C4—58no—
364C22×C4—54no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—54no—
368C22×C4—54no—
369C22×C4—104no—
370C22×C4—104no—
371C22×C4—154no—
372C22×C4C2×D3×D511yescharacteristic
373C22×C4C2×D3×D511yescharacteristic
374C22×C4C2×D3×D511yescharacteristic
375C4⋊C4—38no—
376C4⋊C4—38no—
377C4⋊C4—1516no—
378C4⋊C4—1516no—
379C4⋊C4—158no—
380C4⋊C4—158no—
381C22⋊C4—1516no—
382C42—54no—
383C42—54no—
384C42—54no—
385C42—1516no—
386C42C2×D3×D514yes—
387C3×C5C2×#53311yescharacteristic, complemented, Hall
388C22×C3—54no—
389C22×C3—108no—
390C22×C3—102no—
391C22×C3—102no—
392C22×C3C2×#71112yes—
393C22×C3C2×Q8×D512yes—
394C22×C3C2×#71312yes—
395C22×C3C24×D511yescharacteristic
396C3×C4—54no—
397C3×C4—102no—
398C3×C4—102no—
399C3×C4C2×#71114yes—
400C3×C4C2×Q8×D514yes—
401C3×C4C2×#71314yes—
402Dic3—28no—
403Dic3—108no—
404C2×C5#547014yescomplemented
405C2×C5C23×Dic611yescharacteristic
406C2×C5C22×#23511yescharacteristic
407C2×C5C22×#23511yescharacteristic
408D5—24no—
409C23—54no—
410C23—52no—
411C23—102no—
412C23—102no—
413C23C22×D3×D511yescharacteristic
414Q8—616no—
415Q8—3016no—
416C2×C4—38no—
417C2×C4—54no—
418C2×C4—52no—
419C2×C4—516no—
420C2×C4—52no—
421C2×C4—52no—
422C2×C4—68no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—108no—
426C2×C4—108no—
427C2×C4—158no—
428C2×C4—308no—
429C2×C4D5×Dic614yes—
430C2×C4#677214yes—
431C2×C4#677314yes—
432C2×C4C22×D3×D512yes—
433C2×C4C22×D3×D512yes—
434C2×C4C22×D3×D512yes—
435C2×C3—104no—
436C2×C3#6606214yescomplemented
437C2×C3C22×#71111yescharacteristic
438C2×C3C22×Q8×D511yescharacteristic
439C2×C3C22×#71311yescharacteristic
440C5C2×#547011yescharacteristic, complemented, Sylow
441C22—54no—
442C22—108no—
443C22—102no—
444C22—102no—
445C22C2×D5×Dic612yes—
446C22C2×#677212yes—
447C22C2×#677312yes—
448C22C23×D3×D511yescharacteristic
449C4—54no—
450C4—68no—
451C4—102no—
452C4—102no—
453C4—308no—
454C4C2×D5×Dic614yes—
455C4C2×#677214yes—
456C4C2×#677314yes—
457C3C2×#6606211yescharacteristic, complemented, Sylow
458C2—104no—
459C2#1175250614yesdirect product factor
460C2C22×D5×Dic611yescharacteristic
461C2C22×#677211yescharacteristic
462C2C22×#677311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
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
1. C2×#91758C2semidirect
2. C2×C5×#869C2semidirect
4. C2×#91388C2semidirect
8. C2×#91333C2semidirect
9. C2×Dic5×Dic6C2semidirect
10. #11752506C2direct (N × H)
20. #91758C22semidirect
23. C5×#869C22semidirect
32. #91388C22semidirect
36. #91333C22semidirect
37. Dic5×Dic6C22semidirect
64. C2×C3×C4×D5Q8semidirect
87. C2×#869D5semidirect
142. C3×C4×D5C2×Q8semidirect
166. #869C2×D5semidirect
182. C2×C4×D5Dic6semidirect
281. C4×D5C2×Dic6semidirect
309. C2×C3×C5#533semidirect
387. C3×C5C2×#533semidirect
404. C2×C5#5470semidirect
436. C2×C3#66062semidirect
440. C5C2×#5470semidirect
457. C3C2×#66062semidirect
459. C2#11752506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917582
C2×C5×#8692
C2×C3×C42×D52
C2×#913882
C2×#913602
C2×#913592
C2×#913582
C2×#913332
C2×Dic5×Dic62
#117525062
C2×#660623
C2×#54705