Finite Group Databasebeta

← C2×#11752653 #14495409

Subgroups — C2×#11752653 #14495409

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91759C211yesmaximal, characteristic, complemented
2C2×C5×#875C211yesmaximal, characteristic
3C2×C3×#4016C211yesmaximal, characteristic, complemented
4C2×#91436C212yesmaximal, complemented
5C2×#91423C212yesmaximal
6C2×#91417C212yesmaximal, complemented
7C2×#91342C212yesmaximal, complemented
8C2×#91341C212yesmaximal, complemented
9C2×#91329C212yesmaximal, complemented
10#11752653C2116yesmaximal, direct product factor
11C2×#66006—31nomaximal, Hall
12C22×C5×D12C2211yescharacteristic
13C22×C5×Dic6C2211yescharacteristic
14C22×#1204C2212yes—
15C22×D3×Dic5C2212yes—
16C2×C3×C42×C5C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×#6712C2212yes—
20C2×#6712C2212yes—
21#91759C2218yescomplemented
22C2×C5×(C2×D3)⋊C4C2212yes—
23C2×C5×(C2×D3)⋊C4C2212yes—
24C5×#875C2218yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×#683C2212yes—
28C2×C3×#683C2212yes—
29C3×#4016C2218yescomplemented
30C2×#6669C2212yes—
31C2×#6668C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×Dic3×Dic5C2212yes—
36#91436C22116yescomplemented
37#91423C22116yes—
38#91417C22116yescomplemented
39#91342C22116yescomplemented
40#91341C22116yescomplemented
41#91329C22116yescomplemented
42C2×#5699—51nomaximal, Hall
43C2×C5×#124—31no—
44C2×#4090—32no—
45C2×#4081—32no—
46#66006—316no—
47C2×#4025—32no—
48C2×#4025—32no—
49C2×#4024—32no—
50C2×#4024—32no—
51C2×#4016—31no—
52C2×#4016D311yescharacteristic, complemented
53C23×C5×D3C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3C2312yes—
60C2×C5×D12—42no—
61C2×C5×D12C2314yes—
62C2×C5×Dic6—42no—
63C2×C5×Dic6C2314yes—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2312yes—
66C2×#1204—44no—
67C2×#1204C2318yes—
68C2×D3×Dic5—44no—
69C2×D3×Dic5C2318yes—
70C3×C42×C5C2314yes—
71C4⋊Dic15C2314yes—
72C4⋊Dic15C2314yes—
73#6712C2318yes—
74#6712C2318yes—
75C5×(C2×D3)⋊C4C2318yes—
76C5×(C2×D3)⋊C4C2318yes—
77C3×C4⋊Dic5C2314yes—
78C3×C4⋊Dic5C2314yes—
79C3×#683C2318yes—
80C3×#683C2318yes—
81#6669C2318yes—
82#6668C2318yes—
83(C2×D3)⋊Dic5C2318yes—
84(C2×D3)⋊Dic5C2318yes—
85(C2×D3)⋊Dic5C2318yes—
86Dic3×Dic5C2318yes—
87C2×C3×#125—51no—
88#5699—516no—
89C2×#898—52no—
90C2×#898—52no—
91C2×#897—52no—
92C2×#896—52no—
93C2×#894—52no—
94C2×#888—52no—
95C2×#875D511yescharacteristic
96C2×#870—51no—
97C22×C5×Q8—31no—
98C22×C5×D4—31no—
99C23×Dic5—32no—
100C22×Dic10—32no—
101C5×#124—38no—
102C2×C5×C22⋊C4—32no—
103C2×C5×C22⋊C4—32no—
104C2×C42×C5C2×D311yescharacteristic
105C2×C22⋊Dic5—32no—
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5—32no—
108#4090—316no—
109#4081—316no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5C2×D311yescharacteristic
113C2×C4⋊Dic5C2×D311yescharacteristic
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—32no—
117C2×#683—32no—
118C2×#683C2×D312yes—
119C2×#683C2×D312yes—
120C2×C4×Dic5—32no—
121#4025—316no—
122#4025—316no—
123#4024—316no—
124#4024—316no—
125#4016—38no—
126#4016C2×D318yescomplemented
127C2×#563—151noSylow
128C23×C3×C5C2411yescharacteristic
129C22×C5×D3—24no—
130C22×C5×D3—24no—
131C22×C5×D3—24no—
132C22×C5×D3C2414yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C2412yes—
137C2×C3×C4×C5C2412yes—
138C2×C3×C4×C5C2412yes—
139C2×Dic15—24no—
140C2×Dic15—24no—
141C2×Dic15C2414yes—
142C2×Dic15C2414yes—
143C2×C5×Dic3—24no—
144C2×C5×Dic3C2414yes—
145C5×D12—44no—
146C5×Dic6—44no—
147C2×C3×Dic5—24no—
148C2×C3×Dic5—24no—
149C2×C3×Dic5C2414yes—
150C2×C3×Dic5C2414yes—
151#1204—48no—
152D3×Dic5—48no—
153C22×D12C2×D511yescharacteristic
154C22×C4×D3—52no—
155C22×Dic6—52no—
156C22×Dic6C2×D511yescharacteristic
157C3×#125—58no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C42C2×D511yescharacteristic
163C2×(C2×D3)⋊C4—52no—
164C2×(C2×D3)⋊C4—52no—
165C2×(C2×D3)⋊C4—52no—
166C2×(C2×D3)⋊C4C2×D512yes—
167C2×(C2×D3)⋊C4C2×D512yes—
168C2×C4⋊Dic3—51no—
169C2×C4⋊Dic3—51no—
170C2×C4⋊Dic3—52no—
171C2×Dic3⋊C4—52no—
172C2×Dic3⋊C4—52no—
173C2×Dic3⋊C4—52no—
174C2×C4×Dic3—52no—
175#898—516no—
176#898—516no—
177#897—516no—
178#896—516no—
179#894—516no—
180#888—516no—
181#875C2×D518yes—
182#870—58no—
183C24×C5—32no—
184C2×C5×Q8—34no—
185C2×C5×Q8—122no—
186C2×C5×D4—34no—
187C2×C5×D4—122no—
188C22×C4×C5—32no—
189C22×C4×C5C22×D311yescharacteristic
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—32no—
193C22×Dic5—32no—
194C22×Dic5—38no—
195C22×Dic5—124no—
196C22×Dic5C22×D312yes—
197C22×Dic5C22×D312yes—
198C2×Dic10—38no—
199C2×Dic10—124no—
200C5×C22⋊C4—38no—
201C5×C22⋊C4—38no—
202C42×C5C22×D314yes—
203C22⋊Dic5—38no—
204C22⋊Dic5—38no—
205C22⋊Dic5—38no—
206C4⋊Dic5—34no—
207C4⋊Dic5—34no—
208C4⋊Dic5C22×D314yes—
209C4⋊Dic5C22×D314yes—
210#683—38no—
211#683—38no—
212#683—38no—
213#683—38no—
214#683C22×D318yes—
215#683C22×D318yes—
216C4×Dic5—38no—
217#563—1516no—
218C2×C4⋊Q8—152no—
219C2×#126—152no—
220C2×#126—152no—
221C2×#125—51no—
222C2×#125—151no—
223C2×#124—31no—
224C2×#123—152no—
225C2×C22⋊Q8—152no—
226C2×C22⋊Q8—152no—
227C22×C3×C5H(5,𝔽2)12yes—
228C22×C3×C52−1+412yes—
229C22×C3×C52−1+412yes—
230C22×C3×C5C2511yescharacteristic
231C2×C5×D3—24no—
232C2×C5×D3—24no—
233C2×C5×D3—24no—
234C2×C5×D3—48no—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237C3×C4×C5—22no—
238Dic15—24no—
239Dic15—24no—
240C3×Dic5—24no—
241C3×Dic5—24no—
242C5×Dic3—24no—
243C23×D3C22×D512yes—
244C22×C3×C4—52no—
245C22×C3×C4—52no—
246C22×C3×C4C22×D511yescharacteristic
247C22×C3×C4C22×D511yescharacteristic
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—52no—
250C22×Dic3—52no—
251C22×Dic3C22×D512yes—
252C2×D12—42no—
253C2×D12C22×D514yes—
254C2×C4×D3—58no—
255C2×C4×D3—204no—
256C2×Dic6—42no—
257C2×Dic6—58no—
258C2×Dic6—204no—
259C2×Dic6C22×D514yes—
260C3×C4⋊C4—58no—
261C3×C4⋊C4—58no—
262C3×C4⋊C4—54no—
263C3×C4⋊C4—54no—
264C3×C42C22×D514yes—
265(C2×D3)⋊C4—58no—
266(C2×D3)⋊C4—58no—
267(C2×D3)⋊C4—58no—
268(C2×D3)⋊C4C22×D518yes—
269(C2×D3)⋊C4C22×D518yes—
270C4⋊Dic3—54no—
271C4⋊Dic3—54no—
272C4⋊Dic3—58no—
273Dic3⋊C4—58no—
274Dic3⋊C4—58no—
275Dic3⋊C4—58no—
276C4×Dic3—58no—
277C23×C5—34no—
278C23×C5—64no—
279C23×C5—64no—
280C23×C5—64no—
281C23×C5C23×D311yescharacteristic
282C5×Q8—124no—
283C5×D4—124no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—34no—
288C2×C4×C5—64no—
289C2×C4×C5C23×D312yes—
290C2×C4×C5C23×D312yes—
291C2×C4×C5C23×D312yes—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5—34no—
295C2×Dic5—34no—
296C2×Dic5—64no—
297C2×Dic5—64no—
298C2×Dic5—128no—
299C2×Dic5C23×D314yes—
300C2×Dic5C23×D314yes—
301Dic10—128no—
302C22×Q8—31no—
303C22×Q8—152no—
304C22×D4—31no—
305C23×C4—152no—
306C4⋊Q8—1516no—
307#126—1516no—
308#126—1516no—
309#125—58no—
310#125—158no—
311#124—38no—
312#123—1516no—
313C22⋊Q8—1516no—
314C22⋊Q8—1516no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—52no—
317C2×C4⋊C4—52no—
318C2×C4⋊C4—51no—
319C2×C4⋊C4—152no—
320C2×C4⋊C4—152no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4—152no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—151no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—152no—
328C2×C22⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C42—152no—
331C2×C42D3×D511yescharacteristic
332C2×C3×C5#56314yescomplemented
333C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
334C2×C3×C5C2×2−1+411yescharacteristic
335C2×C3×C5C2×2−1+411yescharacteristic
336C5×D3—44no—
337C23×C3C23×D511yescharacteristic
338C22×D3—24no—
339C22×D3—24no—
340C22×D3—24no—
341C22×D3C23×D514yes—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—54no—
346C2×C3×C4—54no—
347C2×C3×C4—104no—
348C2×C3×C4—104no—
349C2×C3×C4C23×D512yes—
350C2×C3×C4C23×D512yes—
351C2×C3×C4C23×D512yes—
352C2×Dic3—24no—
353C2×Dic3—54no—
354C2×Dic3—54no—
355C2×Dic3—104no—
356C2×Dic3—104no—
357C2×Dic3C23×D514yes—
358D12—44no—
359C4×D3—208no—
360Dic6—44no—
361Dic6—208no—
362C22×C5—64no—
363C22×C5—64no—
364C22×C5—64no—
365C22×C5—128no—
366C22×C5#100712yes—
367C22×C5#100912yes—
368C22×C5#101012yes—
369C22×C5C24×D311yescharacteristic
370C4×C5—22no—
371C4×C5—22no—
372C4×C5—22no—
373C4×C5—64no—
374Dic5—24no—
375Dic5—24no—
376Dic5—64no—
377Dic5—64no—
378C24—32no—
379C2×Q8—34no—
380C2×Q8—122no—
381C2×Q8—158no—
382C2×Q8—604no—
383C2×D4—34no—
384C2×D4—122no—
385C22×C4—32no—
386C22×C4—52no—
387C22×C4—52no—
388C22×C4—158no—
389C22×C4—152no—
390C22×C4—152no—
391C22×C4—604no—
392C22×C4C2×D3×D511yescharacteristic
393C22×C4C2×D3×D511yescharacteristic
394C22×C4C2×D3×D511yescharacteristic
395C4⋊C4—54no—
396C4⋊C4—58no—
397C4⋊C4—58no—
398C4⋊C4—54no—
399C4⋊C4—158no—
400C4⋊C4—158no—
401C4⋊C4—154no—
402C4⋊C4—158no—
403C4⋊C4—158no—
404C4⋊C4—154no—
405C22⋊C4—38no—
406C22⋊C4—38no—
407C22⋊C4—158no—
408C22⋊C4—158no—
409C22⋊C4—158no—
410C42—158no—
411C42C2×D3×D514yes—
412C3×C5C2×#56311yescharacteristic, complemented, Hall
413C22×C3#414412yes—
414C22×C3#415012yes—
415C22×C3#415012yes—
416C22×C3C24×D511yescharacteristic
417C2×D3—24no—
418C2×D3—24no—
419C2×D3—24no—
420C2×D3—48no—
421C3×C4—22no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—104no—
425C3×C4—104no—
426Dic3—24no—
427Dic3—104no—
428Dic3—104no—
429C2×C5—124no—
430C2×C5#569914yescomplemented
431C2×C5C2×#100711yescharacteristic
432C2×C5C2×#100911yescharacteristic
433C2×C5C2×#101011yescharacteristic
434C23—34no—
435C23—64no—
436C23—64no—
437C23—64no—
438C23C22×D3×D511yescharacteristic
439Q8—124no—
440Q8—608no—
441D4—124no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—34no—
446C2×C4—54no—
447C2×C4—54no—
448C2×C4—64no—
449C2×C4—104no—
450C2×C4—104no—
451C2×C4—154no—
452C2×C4—154no—
453C2×C4—304no—
454C2×C4—304no—
455C2×C4—608no—
456C2×C4C22×D3×D512yes—
457C2×C4C22×D3×D512yes—
458C2×C4C22×D3×D512yes—
459C2×C3#6600614yescomplemented
460C2×C3C2×#414411yescharacteristic
461C2×C3C2×#415011yescharacteristic
462C2×C3C2×#415011yescharacteristic
463D3—44no—
464C5C2×#569911yescharacteristic, complemented, Sylow
465C22—64no—
466C22—64no—
467C22—64no—
468C22—128no—
469C22#9200112yes—
470C22#9200412yes—
471C22#9201812yes—
472C22C23×D3×D511yescharacteristic
473C4—22no—
474C4—22no—
475C4—22no—
476C4—64no—
477C4—104no—
478C4—104no—
479C4—304no—
480C4—304no—
481C3C2×#6600611yescharacteristic, complemented, Sylow
482C2—124no—
483C2#1175265314yesdirect product factor
484C2C2×#9200111yescharacteristic
485C2C2×#9200411yescharacteristic
486C2C2×#9201811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#563
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×#91759C2semidirect
3. C2×C3×#4016C2semidirect
4. C2×#91436C2semidirect
6. C2×#91417C2semidirect
7. C2×#91342C2semidirect
8. C2×#91341C2semidirect
9. C2×#91329C2semidirect
10. #11752653C2direct (N × H)
21. #91759C22semidirect
29. C3×#4016C22semidirect
36. #91436C22semidirect
38. #91417C22semidirect
39. #91342C22semidirect
40. #91341C22semidirect
41. #91329C22semidirect
52. C2×#4016D3semidirect
126. #4016C2×D3semidirect
332. C2×C3×C5#563semidirect
412. C3×C5C2×#563semidirect
430. C2×C5#5699semidirect
459. C2×C3#66006semidirect
464. C5C2×#5699semidirect
481. C3C2×#66006semidirect
483. C2#11752653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917592
C2×C5×#8752
C2×C3×#40162
C2×#914362
C2×#914232
C2×#914172
C2×#913422
C2×#913412
C2×#913292
#117526532
C2×#660063
C2×#56995