Finite Group Databasebeta

← C2×#11753769 #14484077

Subgroups — C2×#11753769 #14484077

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×#91781C211yesmaximal, characteristic, complemented
2C2×C5×#888C211yesmaximal, characteristic, complemented
3C2×C3×#4043C211yesmaximal, characteristic, complemented
4C2×#91455C212yesmaximal
5C2×C4×#1202C211yesmaximal, characteristic
6C2×#91390C211yesmaximal, characteristic, complemented
7C2×#91366C212yesmaximal, complemented
8C2×#91358C211yesmaximal, characteristic, complemented
9C2×#91345C212yesmaximal, complemented
10C2×#91344C212yesmaximal, complemented
11C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
12#11753769C2116yesmaximal, direct product factor
13C2×#66066—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C5×Dic6C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1202C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6714C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2212yes—
23#91781C2218yescomplemented
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C5×#888C2218yescomplemented
28C2×C3×#685C2212yes—
29C2×C3×C4⋊Dic5C2212yes—
30C3×#4043C2218yescomplemented
31C2×Dic3⋊Dic5C2212yes—
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×#6668C2212yes—
34C2×#6667C2211yescharacteristic
35C2×#6667C2212yes—
36C2×#6665C2211yescharacteristic
37C2×#6665C2212yes—
38C2×Dic3×Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91455C22116yes—
41C4×#1202C2218yes—
42#91390C2218yescomplemented
43#91366C22116yescomplemented
44#91358C2218yescomplemented
45#91345C22116yescomplemented
46#91344C22116yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5641—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4093—32no—
51C2×Q8×Dic5—32no—
52#66066—316no—
53C2×#4044—32no—
54C2×#4044—32no—
55C2×#4043—31no—
56C2×#4043D311yescharacteristic, complemented
57C2×#4038—31no—
58C2×#4038—31no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C2×C4×D15—24no—
68C2×C4×D15C2314yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2311yescharacteristic
72C2×C5×Dic6—28no—
73C2×C5×Dic6C2318yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2312yes—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5C2314yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1202—24no—
81C2×#1202C2314yes—
82C3×C5×C4⋊C4C2314yes—
83#6714C2318yes—
84C4⋊Dic15C2314yes—
85C4×Dic15C2318yes—
86C5×C4⋊Dic3C2314yes—
87C5×Dic3⋊C4C2318yes—
88C4×C5×Dic3C2314yes—
89C3×#685C2318yes—
90C3×C4⋊Dic5C2318yes—
91Dic3⋊Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93#6668C2318yes—
94#6667C2314yes—
95#6667C2318yes—
96#6665C2314yes—
97#6665C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C22⋊Q8—51no—
101C2×#946—51no—
102C2×Q8×Dic3—51no—
103C2×C4×#67—51no—
104C2×#926—51no—
105#5641—516no—
106C2×#898—52no—
107C2×#892—51no—
108C2×#888D511yescharacteristic, complemented
109C2×#887—52no—
110C2×#885—52no—
111C2×#879—52no—
112C22×C5×Q8—32no—
113C22×D20—31no—
114C22×C4×D5—31no—
115C22×C4×D5C2×D311yescharacteristic
116C22×Dic10C2×D311yescharacteristic
117C5×C4⋊Q8—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4—32no—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C42×C5—31no—
122#4093—316no—
123Q8×Dic5—316no—
124C2×#685—31no—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685—31no—
128C2×#685—32no—
129C2×#685C2×D312yes—
130C2×C4⋊Dic5—31no—
131C2×C4⋊Dic5—31no—
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5C2×D312yes—
134C2×#683—32no—
135C2×C4×Dic5—32no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—32no—
138#4044—316no—
139#4044—316no—
140#4043—38no—
141#4043C2×D318yescomplemented
142#4038—38no—
143#4038—38no—
144C4×D20—38no—
145C4×Dic10—38no—
146C2×#556—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15C2412yes—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5C2412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5#4114yes—
158C2×C3×C4×C5C2414yes—
159C2×C3×C4×C5C2412yes—
160C2×Dic15—22no—
161C2×Dic15—24no—
162C2×Dic15C2414yes—
163C2×Dic15C2412yes—
164C4×D15—28no—
165C2×C5×Dic3—24no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3#4114yes—
168C2×C5×Dic3C2414yes—
169C2×C5×Dic3C2412yes—
170C2×C5×Dic3C2412yes—
171C5×Dic6—216no—
172C2×C3×Dic5—24no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C2412yes—
175C2×C3×Dic5C2414yes—
176C3×C4×D5—28no—
177C3×Dic10—28no—
178#1202—28no—
179C22×C3×Q8—51no—
180C23×C3×C4—51no—
181C22×#67—51no—
182C22×C4×D3—51no—
183C22×Dic6C2×D512yes—
184C3×C22⋊Q8—58no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4—52no—
188C2×#217—51no—
189C2×#217—52no—
190#946—58no—
191Q8×Dic3—58no—
192C4×#67—58no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×(C2×D3)⋊C4—51no—
196#926—58no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3—52no—
199C2×C4⋊Dic3C2×D511yescharacteristic
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—51no—
202C2×Dic3⋊C4C2×D512yes—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3C2×D511yescharacteristic
207#898—516no—
208#892—58no—
209#888C2×D518yescomplemented
210#887—516no—
211#885—516no—
212#879—516no—
213C23×D5—31no—
214C23×D5C22×D311yescharacteristic
215C2×C5×Q8—38no—
216C2×C5×Q8—68no—
217C22×C4×C5—31no—
218C22×C4×C5—31no—
219C22×C4×C5—32no—
220C22×C4×C5C22×D312yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—32no—
224C22×Dic5C22×D312yes—
225C22×Dic5C22×D311yescharacteristic
226C2×D20—34no—
227C2×D20—64no—
228C2×C4×D5—24no—
229C2×C4×D5—34no—
230C2×C4×D5—64no—
231C2×C4×D5C22×D314yes—
232C2×Dic10—24no—
233C2×Dic10C22×D314yes—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C5×C4⋊C4C22×D314yes—
237C42×C5—34no—
238#685—34no—
239#685—38no—
240#685—38no—
241#685—34no—
242#685—38no—
243#685C22×D318yes—
244C4⋊Dic5—34no—
245C4⋊Dic5—34no—
246C4⋊Dic5—38no—
247C4⋊Dic5C22×D318yes—
248#683—38no—
249C4×Dic5—38no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#556—1516no—
253C2×C4⋊Q8—31no—
254C2×#126—152no—
255C2×#126—152no—
256C2×#124—152no—
257C2×C22⋊Q8—51no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×D4—151no—
262C2×#117—151no—
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×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—44no—
276C3×C4×C5—24no—
277C3×C4×C5C2×#4114yes—
278Dic15—22no—
279Dic15—24no—
280C3×Dic5—24no—
281C3×Dic5—22no—
282C5×Dic3—24no—
283C5×Dic3—22no—
284C5×Dic3C2×#4114yes—
285C24×C3—51no—
286C23×D3—51no—
287C2×C3×Q8—54no—
288C2×C3×Q8—104no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—54no—
292C22×C3×C4—104no—
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C2×#67—54no—
296C2×#67—104no—
297C22×Dic3—52no—
298C22×Dic3—51no—
299C22×Dic3C22×D512yes—
300C22×Dic3C22×D511yescharacteristic
301C22×Dic3C22×D511yescharacteristic
302C2×C4×D3—54no—
303C2×C4×D3—104no—
304C2×Dic6—28no—
305C2×Dic6C22×D518yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4C22×D514yes—
308C3×C22⋊C4—58no—
309#217—54no—
310#217—58no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—54no—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—54no—
319Dic3⋊C4C22×D518yes—
320C4×Dic3—58no—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3C22×D514yes—
324C23×C5C23×D311yescharacteristic
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—32no—
329C22×D5—62no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5C23×D312yes—
333C5×Q8—616no—
334C2×C4×C5—24no—
335C2×C4×C5—34no—
336C2×C4×C5—32no—
337C2×C4×C5—34no—
338C2×C4×C5—32no—
339C2×C4×C5—62no—
340C2×C4×C5—64no—
341C2×C4×C5#23714yes—
342C2×C4×C5C23×D314yes—
343C2×C4×C5C23×D312yes—
344C2×Dic5—24no—
345C2×Dic5—22no—
346C2×Dic5—34no—
347C2×Dic5—32no—
348C2×Dic5—62no—
349C2×Dic5—64no—
350C2×Dic5C23×D312yes—
351C2×Dic5C23×D314yes—
352D20—68no—
353C4×D5—28no—
354C4×D5—68no—
355Dic10—28no—
356C22×Q8—32no—
357C22×Q8—51no—
358C22×D4—151no—
359C23×C4—51no—
360C23×C4—151no—
361C4⋊Q8—38no—
362#126—1516no—
363#126—1516no—
364#124—1516no—
365C22⋊Q8—58no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×Q8—1516no—
369C4×D4—158no—
370#117—158no—
371#117—158no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4D3×D511yescharacteristic
380C2×C22⋊C4—52no—
381C2×C22⋊C4—151no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—151no—
385C2×C22⋊C4—152no—
386C2×C42—31no—
387C2×C42—152no—
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—
395C3×D5—42no—
396C23×C3—52no—
397C23×C3—102no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3C23×D511yescharacteristic
401C22×D3—52no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C3×Q8—108no—
406C2×C3×C4—24no—
407C2×C3×C4—52no—
408C2×C3×C4—54no—
409C2×C3×C4—102no—
410C2×C3×C4—104no—
411C2×C3×C4—108no—
412C2×C3×C4#71314yes—
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415#67—108no—
416C2×Dic3—24no—
417C2×Dic3—22no—
418C2×Dic3—54no—
419C2×Dic3—52no—
420C2×Dic3—102no—
421C2×Dic3—104no—
422C2×Dic3#71114yes—
423C2×Dic3C23×D514yes—
424C2×Dic3C23×D512yes—
425C2×Dic3C23×D512yes—
426C4×D3—108no—
427Dic6—216no—
428C22×C5C2×#23712yes—
429C22×C5#100712yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—44no—
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—24no—
441C4×C5—34no—
442C4×C5—62no—
443C4×C5—64no—
444C4×C5C2×#23714yes—
445Dic5—24no—
446Dic5—22no—
447Dic5—62no—
448Dic5—64no—
449C24—51no—
450C24—151no—
451C2×Q8—38no—
452C2×Q8—54no—
453C2×Q8—68no—
454C2×Q8—104no—
455C2×D4—154no—
456C2×D4—304no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—51no—
461C22×C4—52no—
462C22×C4—54no—
463C22×C4—104no—
464C22×C4—152no—
465C22×C4—151no—
466C22×C4—154no—
467C22×C4—304no—
468C22×C4C2×D3×D512yes—
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—58no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4—158no—
476C4⋊C4—154no—
477C4⋊C4C2×D3×D514yes—
478C22⋊C4—58no—
479C22⋊C4—154no—
480C22⋊C4—158no—
481C22⋊C4—158no—
482C22⋊C4—154no—
483C22⋊C4—158no—
484C42—34no—
485C42—158no—
486C42—158no—
487C42—158no—
488C3×C5C2×#55611yescharacteristic, complemented, Hall
489C22×C3—102no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—204no—
493C22×C3C2×#71112yes—
494C22×C3C2×#71312yes—
495C22×C3#414712yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—24no—
502C3×C4—102no—
503C3×C4—104no—
504C3×C4C2×#71314yes—
505Dic3—24no—
506Dic3—22no—
507Dic3—102no—
508Dic3—104no—
509Dic3C2×#71114yes—
510C2×C5#564114yescomplemented
511C2×C5C22×#23711yescharacteristic
512C2×C5C2×#100711yescharacteristic
513C2×C5C2×D3×#4111yescharacteristic
514D5—42no—
515D5—122no—
516C23—52no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—152no—
521C23—302no—
522C23—302no—
523C23—302no—
524C23C22×D3×D511yescharacteristic
525Q8—616no—
526Q8—108no—
527D4—308no—
528C2×C4—24no—
529C2×C4—34no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—34no—
533C2×C4—52no—
534C2×C4—54no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—102no—
538C2×C4—104no—
539C2×C4—108no—
540C2×C4—154no—
541C2×C4—152no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—308no—
545C2×C4#676614yes—
546C2×C4C22×D3×D514yes—
547C2×C4C22×D3×D512yes—
548C2×C3—202no—
549C2×C3#6606614yescomplemented
550C2×C3C22×#71111yescharacteristic
551C2×C3C22×#71311yescharacteristic
552C2×C3C2×#414711yescharacteristic
553D3—202no—
554C5C2×#564111yescharacteristic, complemented, Sylow
555C22—102no—
556C22—102no—
557C22—102no—
558C22—204no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22—604no—
563C22C2×#676612yes—
564C22D3×#71112yes—
565C22#9202912yes—
566C22C23×D3×D511yescharacteristic
567C4—24no—
568C4—34no—
569C4—64no—
570C4—62no—
571C4—102no—
572C4—104no—
573C4—302no—
574C4—304no—
575C4C2×#676614yes—
576C3C2×#6606611yescharacteristic, complemented, Sylow
577C2—202no—
578C2—602no—
579C2#1175376914yesdirect product factor
580C2C22×#676611yescharacteristic
581C2C2×D3×#71111yescharacteristic
582C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1202C22
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×#91781C2semidirect
2. C2×C5×#888C2semidirect
3. C2×C3×#4043C2semidirect
6. C2×#91390C2semidirect
7. C2×#91366C2semidirect
8. C2×#91358C2semidirect
9. C2×#91345C2semidirect
10. C2×#91344C2semidirect
11. C2×Dic3×Dic10C2semidirect
12. #11753769C2direct (N × H)
23. #91781C22semidirect
27. C5×#888C22semidirect
30. C3×#4043C22semidirect
42. #91390C22semidirect
43. #91366C22semidirect
44. #91358C22semidirect
45. #91345C22semidirect
46. #91344C22semidirect
47. Dic3×Dic10C22semidirect
56. C2×#4043D3semidirect
108. C2×#888D5semidirect
141. #4043C2×D3semidirect
209. #888C2×D5semidirect
390. C2×C3×C5#556semidirect
488. C3×C5C2×#556semidirect
510. C2×C5#5641semidirect
549. C2×C3#66066semidirect
554. C5C2×#5641semidirect
576. C3C2×#66066semidirect
579. C2#11753769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917812
C2×C5×#8882
C2×C3×#40432
C2×#914552
C2×C4×#12022
C2×#913902
C2×#913662
C2×#913582
C2×#913452
C2×#913442
C2×Dic3×Dic102
#117537692
C2×#660663
C2×#56415