Finite Group Databasebeta

← C2×#11753659 #14481759

Subgroups — C2×#11753659 #14481759

Order 1920.

2160 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91777C211yesmaximal, characteristic, complemented
2C2×C5×#888C211yesmaximal, characteristic, complemented
3C2×C3×#4038C211yesmaximal, characteristic
4C2×#91431C212yesmaximal
5C2×#91421C212yesmaximal
6C2×D5×C4⋊Dic3C211yesmaximal, characteristic
7C2×#91384C211yesmaximal, characteristic, complemented
8C2×#91381C211yesmaximal, characteristic, complemented
9C2×#91378C212yesmaximal, complemented
10C2×#91376C212yesmaximal, complemented
11C2×#91357C211yesmaximal, characteristic
12#11753659C2116yesmaximal, direct product factor
13C2×#66063—31nomaximal, Hall
14C22×Dic30C2212yes—
15C22×C5×Dic6C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×D5×Dic3C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×#6712C2212yes—
21C2×C4×Dic15C2211yescharacteristic
22#91777C2218yescomplemented
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×Dic3⋊C4C2212yes—
25C2×C4×C5×Dic3C2211yescharacteristic
26C5×#888C2218yescomplemented
27C2×C3×#685C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2212yes—
30C3×#4038C2218yes—
31C2×Dic3⋊Dic5C2212yes—
32C2×#6669C2212yes—
33C2×#6668C2211yescharacteristic
34C2×#6668C2212yes—
35C2×#6668C2212yes—
36C2×#6668C2212yes—
37C2×#6668C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40#91431C22116yes—
41#91421C22116yes—
42D5×C4⋊Dic3C2218yes—
43#91384C2218yescomplemented
44#91381C2218yescomplemented
45#91378C22116yescomplemented
46#91376C22116yescomplemented
47#91357C2218yes—
48C2×#5519—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4092—32no—
51C2×#4090—32no—
52#66063—316no—
53C2×#4042—32no—
54C2×#4038D311yescharacteristic
55C2×D5×C4⋊C4—31no—
56C2×#4036—31no—
57C2×#4035—32no—
58C2×#4034—31no—
59C2×#4018—31no—
60C2×#4016—31no—
61C23×C3×D5C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C2×Dic30—44no—
68C2×Dic30C2318yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2312yes—
72C2×C5×Dic6—44no—
73C2×C5×Dic6C2318yes—
74C22×C3×Dic5C2312yes—
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×C4×D5Q818yescomplemented
77C2×C3×C4×D5C2314yes—
78C2×D5×Dic3—44no—
79C2×D5×Dic3C2318yes—
80C3×C5×C4⋊C4C2314yes—
81C4⋊Dic15C2314yes—
82#6712C2318yes—
83C4×Dic15C2314yes—
84C5×C4⋊Dic3C2314yes—
85C5×Dic3⋊C4C2318yes—
86C4×C5×Dic3C2314yes—
87C3×#685C2318yes—
88C3×C4⋊Dic5C2314yes—
89C3×C4×Dic5C2318yes—
90Dic3⋊Dic5C2318yes—
91#6669C2318yes—
92#6668C2318yes—
93#6668C2318yes—
94#6668C2318yes—
95#6668C2314yes—
96#6668C2314yes—
97#6665C2314yes—
98#6665C2314yes—
99C2×C3×#117—51no—
100C2×#926—51no—
101C22×C4⋊Dic3—51no—
102#5519—516no—
103C2×#890—51no—
104C2×#890—51no—
105C2×#888—51no—
106C2×#888D511yescharacteristic, complemented
107C2×#878—52no—
108C2×#878—52no—
109C2×#870—52no—
110C2×#869—52no—
111C22×C5×Q8—32no—
112C22×C4×D5—32no—
113C22×C4×D5C2×D311yescharacteristic
114C22×Dic10—32no—
115C5×C4⋊Q8—38no—
116C2×C5×C4⋊C4—32no—
117C2×C5×C4⋊C4—31no—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119C2×C42×C5—31no—
120#4092—316no—
121#4090—316no—
122C2×#685—31no—
123C2×#685—31no—
124C2×#685C2×D312yes—
125C2×C4⋊Dic5—31no—
126C2×C4⋊Dic5—32no—
127C2×C4⋊Dic5C2×D311yescharacteristic
128C2×#683—32no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—31no—
132C2×#683—31no—
133C2×#683—32no—
134C2×#683—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5C2×D312yes—
137#4042—316no—
138#4038C2×D318yes—
139D5×C4⋊C4—38no—
140#4036—38no—
141#4035—316no—
142#4034—38no—
143#4018—38no—
144#4016—38no—
145C2×#544—151noSylow
146C23×C3×C5C2411yescharacteristic
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5C2×Q814yes—
150C22×C3×D5C2412yes—
151C2×C3×C4×C5—24no—
152C2×C3×C4×C5C2×Q814yes—
153C2×C3×C4×C5C2414yes—
154C2×C3×C4×C5C2412yes—
155C2×Dic15—24no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15C2412yes—
159C2×Dic15C2412yes—
160C2×Dic15C2414yes—
161Dic30—48no—
162C2×C5×Dic3—24no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C2412yes—
166C2×C5×Dic3C2412yes—
167C2×C5×Dic3C2414yes—
168C5×Dic6—48no—
169C2×C3×Dic5—24no—
170C2×C3×Dic5C2×Q814yes—
171C2×C3×Dic5C2414yes—
172C2×C3×Dic5C2412yes—
173C3×C4×D5C2×Q8116yescomplemented
174D5×Dic3—48no—
175C23×C3×C4—51no—
176C23×Dic3—52no—
177C22×Dic6—52no—
178C22×Dic6C2×D512yes—
179C3×#117—58no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4C2×D511yescharacteristic
182C2×C3×C22⋊C4—52no—
183C2×C3×C42—52no—
184C2×#217—51no—
185C2×#217—51no—
186#926—58no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—51no—
189C2×C4⋊Dic3—52no—
190C2×C4⋊Dic3—52no—
191C2×C4⋊Dic3—52no—
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—58no—
194C2×C4⋊Dic3C2×D511yescharacteristic
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4C2×D512yes—
199C2×C4×Dic3—51no—
200C2×C4×Dic3C2×D511yescharacteristic
201#890—58no—
202#890—58no—
203#888—58no—
204#888C2×D518yescomplemented
205#878—516no—
206#878—516no—
207#870—516no—
208#869—516no—
209C23×D5C22×D311yescharacteristic
210C2×C5×Q8—38no—
211C2×C5×Q8—124no—
212C22×C4×C5—31no—
213C22×C4×C5—31no—
214C22×C4×C5—32no—
215C22×C4×C5C22×D312yes—
216C22×C4×C5C22×D311yescharacteristic
217C22×Dic5—31no—
218C22×Dic5—32no—
219C22×Dic5—31no—
220C22×Dic5C22×D312yes—
221C22×Dic5C22×D311yescharacteristic
222C2×C4×D5—38no—
223C2×C4×D5—124no—
224C2×C4×D5Dic618yescomplemented
225C2×C4×D5C22×D314yes—
226C2×Dic10—38no—
227C2×Dic10—124no—
228C5×C4⋊C4—38no—
229C5×C4⋊C4—34no—
230C5×C4⋊C4C22×D314yes—
231C42×C5—34no—
232#685—34no—
233#685—34no—
234#685C22×D318yes—
235C4⋊Dic5—34no—
236C4⋊Dic5—38no—
237C4⋊Dic5C22×D314yes—
238#683—38no—
239#683—38no—
240#683—34no—
241#683—34no—
242#683—38no—
243#683—38no—
244#683—38no—
245C4×Dic5—34no—
246C4×Dic5C22×D318yes—
247#544—1516no—
248C2×C4⋊Q8—31no—
249C2×C4⋊Q8—152no—
250C2×C4⋊Q8—151no—
251C2×#125—151no—
252C2×#125—152no—
253C2×#125—151no—
254C2×C22⋊Q8—152no—
255C2×C22⋊Q8—152no—
256C2×#117—51no—
257C2×#117—151no—
258C22×C4⋊C4—151no—
259C22×C3×C5C22×Q812yes—
260C22×C3×C5H(5,𝔽2)12yes—
261C22×C3×C52−1+412yes—
262C22×C3×C5C2511yescharacteristic
263C2×C3×D5—28no—
264C2×C3×D5—22no—
265C2×C3×D5—22no—
266C2×C3×D5C22×Q814yes—
267C3×C4×C5—24no—
268C3×C4×C5C22×Q814yes—
269Dic15—24no—
270Dic15—22no—
271Dic15—22no—
272C3×Dic5—24no—
273C3×Dic5C22×Q814yes—
274C5×Dic3—24no—
275C5×Dic3—22no—
276C5×Dic3—22no—
277C24×C3—51no—
278C22×C3×C4—51no—
279C22×C3×C4—58no—
280C22×C3×C4—54no—
281C22×C3×C4—52no—
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C22×Dic3—51no—
285C22×Dic3—51no—
286C22×Dic3—52no—
287C22×Dic3—58no—
288C22×Dic3—204no—
289C22×Dic3C22×D511yescharacteristic
290C22×Dic3C22×D511yescharacteristic
291C22×Dic3C22×D512yes—
292C2×Dic6—44no—
293C2×Dic6—58no—
294C2×Dic6—204no—
295C2×Dic6C22×D518yes—
296C3×C4⋊C4—54no—
297C3×C4⋊C4C22×D514yes—
298C3×C22⋊C4—58no—
299C3×C42—58no—
300#217—54no—
301#217—54no—
302C4⋊Dic3—54no—
303C4⋊Dic3—54no—
304C4⋊Dic3—58no—
305C4⋊Dic3—58no—
306C4⋊Dic3—58no—
307C4⋊Dic3—54no—
308C4⋊Dic3C22×D514yes—
309Dic3⋊C4—58no—
310Dic3⋊C4—58no—
311Dic3⋊C4—58no—
312Dic3⋊C4C22×D518yes—
313C4×Dic3—54no—
314C4×Dic3C22×D514yes—
315C23×C5C23×D311yescharacteristic
316C22×D5—22no—
317C22×D5—22no—
318C22×D5C2×Dic614yes—
319C22×D5C23×D312yes—
320C5×Q8—128no—
321C2×C4×C5—24no—
322C2×C4×C5—32no—
323C2×C4×C5—32no—
324C2×C4×C5—34no—
325C2×C4×C5—64no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5C2×Dic614yes—
329C2×C4×C5C23×D314yes—
330C2×C4×C5C23×D312yes—
331C2×Dic5—24no—
332C2×Dic5—32no—
333C2×Dic5—32no—
334C2×Dic5—34no—
335C2×Dic5—62no—
336C2×Dic5—64no—
337C2×Dic5—62no—
338C2×Dic5C2×Dic614yes—
339C2×Dic5C23×D314yes—
340C2×Dic5C23×D312yes—
341C4×D5—128no—
342C4×D5C2×Dic6116yescomplemented
343Dic10—128no—
344C22×Q8—32no—
345C22×Q8—152no—
346C23×C4—51no—
347C23×C4—152no—
348C4⋊Q8—38no—
349C4⋊Q8—1516no—
350C4⋊Q8—158no—
351#125—158no—
352#125—1516no—
353#125—158no—
354C22⋊Q8—1516no—
355C22⋊Q8—1516no—
356#117—58no—
357#117—158no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—158no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—151no—
364C2×C4⋊C4—151no—
365C2×C4⋊C4—152no—
366C2×C4⋊C4—152no—
367C2×C4⋊C4—152no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—152no—
371C2×C4⋊C4D3×D511yescharacteristic
372C2×C22⋊C4—52no—
373C2×C22⋊C4—151no—
374C2×C22⋊C4—151no—
375C2×C42—31no—
376C2×C42—52no—
377C2×C42—151no—
378C2×C3×C5#54414yescomplemented
379C2×C3×C5C23×Q811yescharacteristic
380C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
381C2×C3×C5C2×2−1+411yescharacteristic
382C3×D5—24no—
383C23×C3—54no—
384C23×C3—52no—
385C23×C3—102no—
386C23×C3—102no—
387C23×C3C23×D511yescharacteristic
388C2×C3×C4—24no—
389C2×C3×C4—54no—
390C2×C3×C4—52no—
391C2×C3×C4—516no—
392C2×C3×C4—54no—
393C2×C3×C4—104no—
394C2×C3×C4Q8×D514yes—
395C2×C3×C4C23×D514yes—
396C2×C3×C4C23×D512yes—
397C2×Dic3—22no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—52no—
401C2×Dic3—52no—
402C2×Dic3—54no—
403C2×Dic3—102no—
404C2×Dic3—104no—
405C2×Dic3—102no—
406C2×Dic3—208no—
407C2×Dic3C23×D512yes—
408C2×Dic3C23×D512yes—
409C2×Dic3C23×D514yes—
410Dic6—48no—
411Dic6—208no—
412C22×C5C22×Dic612yes—
413C22×C5#100912yes—
414C22×C5#101012yes—
415C22×C5C24×D311yescharacteristic
416C2×D5—22no—
417C2×D5—22no—
418C2×D5—28no—
419C2×D5C22×Dic614yes—
420C4×C5—24no—
421C4×C5—64no—
422C4×C5—62no—
423C4×C5—62no—
424C4×C5C22×Dic614yes—
425Dic5—24no—
426Dic5—62no—
427Dic5—64no—
428Dic5—62no—
429Dic5C22×Dic614yes—
430C24—51no—
431C2×Q8—38no—
432C2×Q8—124no—
433C2×Q8—158no—
434C2×Q8—604no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—51no—
439C22×C4—58no—
440C22×C4—54no—
441C22×C4—52no—
442C22×C4—158no—
443C22×C4—151no—
444C22×C4—151no—
445C22×C4—152no—
446C22×C4—604no—
447C22×C4C2×D3×D512yes—
448C22×C4C2×D3×D511yescharacteristic
449C4⋊C4—34no—
450C4⋊C4—38no—
451C4⋊C4—54no—
452C4⋊C4—158no—
453C4⋊C4—154no—
454C4⋊C4—154no—
455C4⋊C4—158no—
456C4⋊C4—158no—
457C4⋊C4—158no—
458C4⋊C4—158no—
459C4⋊C4—154no—
460C4⋊C4—158no—
461C4⋊C4C2×D3×D514yes—
462C22⋊C4—58no—
463C22⋊C4—154no—
464C22⋊C4—154no—
465C42—34no—
466C42—58no—
467C42—154no—
468C3×C5C2×#54411yescharacteristic, complemented, Hall
469C22×C3—54no—
470C22×C3—108no—
471C22×C3—102no—
472C22×C3—102no—
473C22×C3#414412yes—
474C22×C3C2×Q8×D512yes—
475C22×C3#414712yes—
476C22×C3C24×D511yescharacteristic
477C3×C4—24no—
478C3×C4—54no—
479C3×C4—104no—
480C3×C4C2×Q8×D514yes—
481Dic3—22no—
482Dic3—24no—
483Dic3—22no—
484Dic3—102no—
485Dic3—104no—
486Dic3—102no—
487C2×C5#551914yescomplemented
488C2×C5C23×Dic611yescharacteristic
489C2×C5C2×#100911yescharacteristic
490C2×C5C2×#101011yescharacteristic
491D5—24no—
492C23—54no—
493C23—52no—
494C23—102no—
495C23—102no—
496C23C22×D3×D511yescharacteristic
497Q8—128no—
498Q8—608no—
499C2×C4—24no—
500C2×C4—32no—
501C2×C4—32no—
502C2×C4—34no—
503C2×C4—54no—
504C2×C4—52no—
505C2×C4—516no—
506C2×C4—54no—
507C2×C4—64no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—104no—
511C2×C4—152no—
512C2×C4—152no—
513C2×C4—154no—
514C2×C4—304no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4—608no—
518C2×C4D5×Dic614yes—
519C2×C4C22×D3×D514yes—
520C2×C4C22×D3×D512yes—
521C2×C3—104no—
522C2×C3#6606314yescomplemented
523C2×C3C2×#414411yescharacteristic
524C2×C3C22×Q8×D511yescharacteristic
525C2×C3C2×#414711yescharacteristic
526C5C2×#551911yescharacteristic, complemented, Sylow
527C22—54no—
528C22—108no—
529C22—102no—
530C22—102no—
531C22C2×D5×Dic612yes—
532C22#9202712yes—
533C22#9202812yes—
534C22C23×D3×D511yescharacteristic
535C4—24no—
536C4—54no—
537C4—64no—
538C4—62no—
539C4—62no—
540C4—104no—
541C4—304no—
542C4—302no—
543C4—302no—
544C4C2×D5×Dic614yes—
545C3C2×#6606311yescharacteristic, complemented, Sylow
546C2—104no—
547C2#1175365914yesdirect product factor
548C2C22×D5×Dic611yescharacteristic
549C2C2×#9202711yescharacteristic
550C2C2×#9202811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#544
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91777C2semidirect
2. C2×C5×#888C2semidirect
7. C2×#91384C2semidirect
8. C2×#91381C2semidirect
9. C2×#91378C2semidirect
10. C2×#91376C2semidirect
12. #11753659C2direct (N × H)
22. #91777C22semidirect
26. C5×#888C22semidirect
43. #91384C22semidirect
44. #91381C22semidirect
45. #91378C22semidirect
46. #91376C22semidirect
76. C2×C3×C4×D5Q8semidirect
106. C2×#888D5semidirect
173. C3×C4×D5C2×Q8semidirect
204. #888C2×D5semidirect
224. C2×C4×D5Dic6semidirect
342. C4×D5C2×Dic6semidirect
378. C2×C3×C5#544semidirect
468. C3×C5C2×#544semidirect
487. C2×C5#5519semidirect
522. C2×C3#66063semidirect
526. C5C2×#5519semidirect
545. C3C2×#66063semidirect
547. C2#11753659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917772
C2×C5×#8882
C2×C3×#40382
C2×#914312
C2×#914212
C2×D5×C4⋊Dic32
C2×#913842
C2×#913812
C2×#913782
C2×#913762
C2×#913572
#117536592
C2×#660633
C2×#55195