Finite Group Databasebeta

← C2×#11753311 #14484073

Subgroups — C2×#11753311 #14484073

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91786C211yesmaximal, characteristic, complemented
2C2×C5×#892C211yesmaximal, characteristic, complemented
3C2×C3×#4034C211yesmaximal, characteristic, complemented
4C2×C4×#1203C211yesmaximal, characteristic
5C2×#91380C212yesmaximal, complemented
6C2×#91365C211yesmaximal, characteristic, complemented
7C2×#91347C211yesmaximal, characteristic, complemented
8C2×#91342C212yesmaximal, complemented
9C2×#91333C211yesmaximal, characteristic, complemented
10C2×Dic3×Dic10C212yesmaximal, complemented
11C2×#91326C212yesmaximal
12#11753311C2116yesmaximal, direct product factor
13C2×#65867—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×Dic10C2212yes—
18C22×#1203C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6714C2212yes—
21C2×C4⋊Dic15C2212yes—
22#91786C2218yescomplemented
23C2×C5×(C2×D3)⋊C4C2212yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2212yes—
26C5×#892C2218yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#683C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×#4034C2218yescomplemented
31C2×#6669C2212yes—
32C2×#6668C2212yes—
33C2×#6668C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40C4×#1203C2218yes—
41#91380C22116yescomplemented
42#91365C2218yescomplemented
43#91347C2218yescomplemented
44#91342C22116yescomplemented
45#91333C2218yescomplemented
46Dic3×Dic10C22116yescomplemented
47#91326C22116yes—
48C2×#5732—51nomaximal, Hall
49C2×C5×#117—31no—
50C2×C4×C22⋊D5—31no—
51C2×#4070—31no—
52#65867—316no—
53C2×#4043—31no—
54C2×#4038—31no—
55C2×#4034D311yescharacteristic, complemented
56C2×#4033—31no—
57C2×#4031—32no—
58C2×#4025—32no—
59C2×#4022—32no—
60C2×C4×Dic10—32no—
61C23×D15C2311yescharacteristic
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C2×C4×D15—24no—
68C2×C4×D15C2314yes—
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C4×C5×D3—24no—
74C2×C4×C5×D3C2314yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×Dic10—28no—
79C2×C3×Dic10C2318yes—
80C2×#1203—24no—
81C2×#1203C2314yes—
82C3×C5×C4⋊C4C2314yes—
83#6714C2318yes—
84C4⋊Dic15C2318yes—
85C5×(C2×D3)⋊C4C2318yes—
86C5×C4⋊Dic3C2314yes—
87C4×C5×Dic3C2318yes—
88C3×C4⋊Dic5C2314yes—
89C3×#683C2318yes—
90C3×C4×Dic5C2314yes—
91#6669C2318yes—
92#6668C2314yes—
93#6668C2318yes—
94#6667C2314yes—
95#6667C2318yes—
96(C2×D3)⋊Dic5C2314yes—
97(C2×D3)⋊Dic5C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4⋊Q8—51no—
101C2×#947—52no—
102C2×Q8×Dic3—52no—
103#5732—516no—
104C2×#898—52no—
105C2×#898—52no—
106C2×#897—51no—
107C2×#897—51no—
108C2×#892—51no—
109C2×#892D511yescharacteristic, complemented
110C2×C4×D12—51no—
111C2×C4×Dic6—51no—
112C23×C4×C5—31no—
113C22×C22⋊D5—31no—
114C22×C4×D5—31no—
115C22×Dic10—31no—
116C22×Dic10C2×D312yes—
117C5×#117—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4—32no—
121C2×C42×C5—32no—
122C2×C22⋊Dic5—31no—
123C2×C22⋊Dic5—32no—
124C4×C22⋊D5—38no—
125C2×#685—32no—
126C2×#685—31no—
127C2×#685—32no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5C2×D311yescharacteristic
130#4070—38no—
131C2×#683—31no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683C2×D312yes—
135C2×C4×Dic5—32no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5C2×D311yescharacteristic
138#4043—38no—
139#4038—38no—
140#4034C2×D318yescomplemented
141#4033—38no—
142#4031—316no—
143#4025—316no—
144#4022—316no—
145C4×Dic10—316no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15C2412yes—
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3—22no—
155C22×C5×D3C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5#4114yes—
158C2×C3×C4×C5C2414yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—24no—
161C2×Dic15—22no—
162C2×Dic15C2412yes—
163C2×Dic15C2414yes—
164C4×D15—28no—
165Dic30—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—24no—
168C2×C5×Dic3C2414yes—
169C2×C5×Dic3C2412yes—
170C4×C5×D3—28no—
171C2×C3×Dic5—24no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5#4114yes—
174C2×C3×Dic5C2414yes—
175C2×C3×Dic5C2412yes—
176C2×C3×Dic5C2412yes—
177C3×Dic10—216no—
178#1203—28no—
179C22×C3×Q8—52no—
180C22×D12—51no—
181C22×C4×D3—51no—
182C22×C4×D3C2×D511yescharacteristic
183C22×Dic6—51no—
184C3×C4⋊Q8—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C4⋊C4—52no—
187C2×C3×C4⋊C4C2×D511yescharacteristic
188C2×C3×C42—51no—
189#947—516no—
190Q8×Dic3—516no—
191C2×(C2×D3)⋊C4—51no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—51no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4C2×D512yes—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3—51no—
199C2×C4⋊Dic3—52no—
200C2×C4⋊Dic3C2×D511yescharacteristic
201C2×Dic3⋊C4—52no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3C2×D512yes—
205#898—516no—
206#898—516no—
207#897—58no—
208#897—58no—
209#892—58no—
210#892C2×D518yescomplemented
211C4×D12—58no—
212C4×Dic6—58no—
213C24×C5—31no—
214C23×D5—31no—
215C22×C4×C5—31no—
216C22×C4×C5—32no—
217C22×C4×C5—34no—
218C22×C4×C5—64no—
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D311yescharacteristic
221C2×C22⋊D5—34no—
222C2×C22⋊D5—64no—
223C22×Dic5—32no—
224C22×Dic5—31no—
225C22×Dic5C22×D312yes—
226C22×Dic5C22×D311yescharacteristic
227C22×Dic5C22×D311yescharacteristic
228C2×C4×D5—34no—
229C2×C4×D5—64no—
230C2×Dic10—28no—
231C2×Dic10—34no—
232C2×Dic10—64no—
233C2×Dic10C22×D318yes—
234C5×C4⋊C4—34no—
235C5×C4⋊C4C22×D314yes—
236C5×C22⋊C4—38no—
237C42×C5—38no—
238C22⋊Dic5—34no—
239C22⋊Dic5—38no—
240#685—38no—
241#685—34no—
242#685—38no—
243C4⋊Dic5—38no—
244C4⋊Dic5C22×D314yes—
245#683—34no—
246#683—38no—
247#683—38no—
248#683C22×D318yes—
249C4×Dic5—38no—
250C4×Dic5—38no—
251C4×Dic5C22×D314yes—
252#556—1516no—
253C2×C4⋊Q8—51no—
254C2×#126—152no—
255C2×#126—152no—
256C2×#124—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—151no—
262C2×#117—31no—
263C2×#117—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×D15—22no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15—44no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3—44no—
276C3×C4×C5—24no—
277C3×C4×C5C2×#4114yes—
278Dic15—24no—
279Dic15—22no—
280C3×Dic5—24no—
281C3×Dic5—22no—
282C3×Dic5C2×#4114yes—
283C5×Dic3—22no—
284C5×Dic3—24no—
285C23×D3—51no—
286C23×D3C22×D511yescharacteristic
287C2×C3×Q8—58no—
288C2×C3×Q8—108no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—51no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—51no—
295C22×Dic3—52no—
296C22×Dic3C22×D512yes—
297C22×Dic3C22×D511yescharacteristic
298C2×D12—54no—
299C2×D12—104no—
300C2×C4×D3—24no—
301C2×C4×D3—54no—
302C2×C4×D3—104no—
303C2×C4×D3C22×D514yes—
304C2×Dic6—54no—
305C2×Dic6—104no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4C22×D514yes—
309C3×C42—54no—
310(C2×D3)⋊C4—54no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—54no—
314(C2×D3)⋊C4—58no—
315(C2×D3)⋊C4C22×D518yes—
316C4⋊Dic3—58no—
317C4⋊Dic3—54no—
318C4⋊Dic3—58no—
319C4⋊Dic3C22×D514yes—
320Dic3⋊C4—58no—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3C22×D518yes—
324C23×C5—32no—
325C23×C5—62no—
326C23×C5—62no—
327C23×C5—62no—
328C23×C5C23×D311yescharacteristic
329C22×D5—32no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C2×C4×C5—24no—
334C2×C4×C5—34no—
335C2×C4×C5—32no—
336C2×C4×C5—62no—
337C2×C4×C5—64no—
338C2×C4×C5—68no—
339C2×C4×C5#23914yes—
340C2×C4×C5C23×D314yes—
341C2×C4×C5C23×D312yes—
342C22⋊D5—68no—
343C2×Dic5—24no—
344C2×Dic5—22no—
345C2×Dic5—32no—
346C2×Dic5—34no—
347C2×Dic5—64no—
348C2×Dic5—62no—
349C2×Dic5#23714yes—
350C2×Dic5C23×D314yes—
351C2×Dic5C23×D312yes—
352C2×Dic5C23×D312yes—
353C4×D5—68no—
354Dic10—216no—
355Dic10—68no—
356C22×Q8—52no—
357C22×Q8—151no—
358C22×D4—151no—
359C23×C4—31no—
360C23×C4—151no—
361C4⋊Q8—58no—
362#126—1516no—
363#126—1516no—
364#124—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—1516no—
368C4×Q8—158no—
369C4×D4—158no—
370#117—38no—
371#117—158no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4D3×D511yescharacteristic
380C2×C22⋊C4—32no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—151no—
383C2×C22⋊C4—151no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—152no—
386C2×C42—32no—
387C2×C42—51no—
388C2×C42—152no—
389C2×C42—152no—
390C2×C3×C5#55614yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394D15—42no—
395C5×D3—42no—
396C23×C3C23×D511yescharacteristic
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—52no—
401C22×D3—102no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3C23×D512yes—
405C3×Q8—1016no—
406C2×C3×C4—24no—
407C2×C3×C4—54no—
408C2×C3×C4—52no—
409C2×C3×C4—54no—
410C2×C3×C4—52no—
411C2×C3×C4—104no—
412C2×C3×C4—102no—
413C2×C3×C4#70914yes—
414C2×C3×C4C23×D514yes—
415C2×C3×C4C23×D512yes—
416C2×Dic3—22no—
417C2×Dic3—24no—
418C2×Dic3—52no—
419C2×Dic3—54no—
420C2×Dic3—104no—
421C2×Dic3—102no—
422C2×Dic3C23×D514yes—
423C2×Dic3C23×D512yes—
424D12—108no—
425C4×D3—28no—
426C4×D3—108no—
427Dic6—108no—
428C22×C5—62no—
429C22×C5—62no—
430C22×C5—62no—
431C22×C5—124no—
432C22×C5C2×#23712yes—
433C22×C5C2×#23912yes—
434C22×C5#100712yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—24no—
441C4×C5—62no—
442C4×C5—64no—
443C4×C5C2×#23914yes—
444Dic5—24no—
445Dic5—22no—
446Dic5—64no—
447Dic5—62no—
448Dic5C2×#23714yes—
449C24—31no—
450C24—151no—
451C2×Q8—58no—
452C2×Q8—108no—
453C2×Q8—154no—
454C2×Q8—304no—
455C2×D4—154no—
456C2×D4—304no—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—34no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—52no—
463C22×C4—64no—
464C22×C4—151no—
465C22×C4—152no—
466C22×C4—154no—
467C22×C4—304no—
468C22×C4C2×D3×D512yes—
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—54no—
472C4⋊C4—58no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4C2×D3×D514yes—
478C22⋊C4—38no—
479C22⋊C4—158no—
480C22⋊C4—154no—
481C22⋊C4—154no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C42—38no—
485C42—54no—
486C42—158no—
487C42—158no—
488C3×C5C2×#55611yescharacteristic, complemented, Hall
489C22×C3C2×#70912yes—
490C22×C3D5×#4112yes—
491C22×C3#415012yes—
492C22×C3C24×D511yescharacteristic
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—44no—
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—24no—
502C3×C4—54no—
503C3×C4—104no—
504C3×C4—102no—
505C3×C4C2×#70914yes—
506Dic3—22no—
507Dic3—24no—
508Dic3—104no—
509Dic3—102no—
510C2×C5—122no—
511C2×C5#573214yescomplemented
512C2×C5C22×#23711yescharacteristic
513C2×C5C22×#23911yescharacteristic
514C2×C5C2×#100711yescharacteristic
515D5—122no—
516C23—32no—
517C23—62no—
518C23—62no—
519C23—62no—
520C23—152no—
521C23—302no—
522C23—302no—
523C23—302no—
524C23C22×D3×D511yescharacteristic
525Q8—1016no—
526Q8—308no—
527D4—308no—
528C2×C4—24no—
529C2×C4—32no—
530C2×C4—34no—
531C2×C4—54no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—54no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—68no—
538C2×C4—104no—
539C2×C4—102no—
540C2×C4—152no—
541C2×C4—154no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—308no—
545C2×C4#676914yes—
546C2×C4C22×D3×D514yes—
547C2×C4C22×D3×D512yes—
548C2×C3#6586714yescomplemented
549C2×C3C22×#70911yescharacteristic
550C2×C3C2×D5×#4111yescharacteristic
551C2×C3C2×#415011yescharacteristic
552D3—42no—
553D3—202no—
554C5C2×#573211yescharacteristic, complemented, Sylow
555C22—62no—
556C22—62no—
557C22—62no—
558C22—124no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22—604no—
563C22C2×#676912yes—
564C22D5×#23712yes—
565C22#9203012yes—
566C22C23×D3×D511yescharacteristic
567C4—24no—
568C4—54no—
569C4—62no—
570C4—64no—
571C4—104no—
572C4—102no—
573C4—302no—
574C4—304no—
575C4C2×#676914yes—
576C3C2×#6586711yescharacteristic, complemented, Sylow
577C2—122no—
578C2—602no—
579C2#1175331114yesdirect product factor
580C2C22×#676911yescharacteristic
581C2C2×D5×#23711yescharacteristic
582C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#556
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×#91786C2semidirect
2. C2×C5×#892C2semidirect
3. C2×C3×#4034C2semidirect
5. C2×#91380C2semidirect
6. C2×#91365C2semidirect
7. C2×#91347C2semidirect
8. C2×#91342C2semidirect
9. C2×#91333C2semidirect
10. C2×Dic3×Dic10C2semidirect
12. #11753311C2direct (N × H)
22. #91786C22semidirect
26. C5×#892C22semidirect
30. C3×#4034C22semidirect
41. #91380C22semidirect
42. #91365C22semidirect
43. #91347C22semidirect
44. #91342C22semidirect
45. #91333C22semidirect
46. Dic3×Dic10C22semidirect
55. C2×#4034D3semidirect
109. C2×#892D5semidirect
140. #4034C2×D3semidirect
210. #892C2×D5semidirect
390. C2×C3×C5#556semidirect
488. C3×C5C2×#556semidirect
511. C2×C5#5732semidirect
548. C2×C3#65867semidirect
554. C5C2×#5732semidirect
576. C3C2×#65867semidirect
579. C2#11753311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917862
C2×C5×#8922
C2×C3×#40342
C2×C4×#12032
C2×#913802
C2×#913652
C2×#913472
C2×#913422
C2×#913332
C2×Dic3×Dic102
C2×#913262
#117533112
C2×#658673
C2×#57325