Finite Group Databasebeta

← C2×#11754210 #14483528

Subgroups — C2×#11754210 #14483528

Order 1920.

2248 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×C4×#1220C211yesmaximal, characteristic
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
4C2×#91546C212yesmaximal
5C2×#91528C212yesmaximal, complemented
6C2×#91384C211yesmaximal, characteristic, complemented
7C2×#91383C211yesmaximal, characteristic, complemented
8#11754210C2116yesmaximal, direct product factor
9C2×#91347C211yesmaximal, characteristic, complemented
10C2×#91346C212yesmaximal, complemented
11C2×#91345C212yesmaximal, complemented
12C2×#91344C211yesmaximal, characteristic, complemented
13C2×#65976—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C5×Dic6C2211yescharacteristic
18C23×C3×Dic5C2212yes—
19C2×#6719C2211yescharacteristic
20C4×#1220C2218yes—
21C2×#6714C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×#217C2212yes—
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C5×#924C2218yescomplemented
27C2×C5×Dic3⋊C4C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2212yes—
31C2×C3×C4⋊Dic5C2218yescomplemented
32#91546C22116yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6668C2212yes—
36C2×#6668C2212yes—
37C2×#6667C2212yes—
38C2×#6667C2212yes—
39#91528C22116yescomplemented
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91384C2218yescomplemented
43#91383C2218yescomplemented
44#91347C2218yescomplemented
45#91346C22116yescomplemented
46#91345C22116yescomplemented
47#91344C2218yescomplemented
48C2×#5513—51nomaximal, Hall
49C2×C5×C22⋊Q8—31no—
50C2×#4092—31no—
51C2×Q8×Dic5—31no—
52C2×C4×C22⋊D5—31no—
53C22×C4⋊Dic5D311yescharacteristic, complemented
54#65976—316no—
55C2×#4044—32no—
56C2×#4038—31no—
57C2×#4036—31no—
58C2×#4036—32no—
59C2×#4032—32no—
60C2×#4023—32no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—24no—
68C2×#1220C2314yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C2×C4×D15—24no—
73C2×C4×D15C2314yes—
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2312yes—
76C2×C5×Dic6—24no—
77C2×C5×Dic6C2314yes—
78C22×C3×Dic5—28no—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2318yes—
81C22×C3×Dic5C2312yes—
82#6719C2314yes—
83#6714C2314yes—
84#6712C2314yes—
85C4×Dic15C2314yes—
86C5×#217C2318yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C3×C4⋊Dic5C2314yes—
90C3×C4⋊Dic5C2318yes—
91C3×C4⋊Dic5C2314yes—
92Dic3⋊Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96#6667C2318yes—
97#6667C2318yes—
98Dic3×Dic5C2318yes—
99Dic3×Dic5C2318yes—
100C22×C3×C4⋊C4—51no—
101C2×#929—52no—
102C2×C4×#67—51no—
103C2×#926—52no—
104C2×#924D511yescharacteristic, complemented
105#5513—516no—
106C2×#898—52no—
107C2×#897—51no—
108C2×#892—51no—
109C2×#890—51no—
110C2×#889—52no—
111C2×#887—51no—
112C22×C5×Q8—31no—
113C23×C4×C5C2×D311yescharacteristic
114C22×C22⋊D5—31no—
115C23×Dic5C2×D312yes—
116C22×C4×D5—31no—
117C5×C22⋊Q8—38no—
118C2×C5×C4⋊C4—31no—
119C2×C5×C4⋊C4—32no—
120C2×C5×C22⋊C4—32no—
121C2×C22⋊Dic5—31no—
122#4092—38no—
123Q8×Dic5—38no—
124C4×C22⋊D5—38no—
125C2×#685—31no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5C2×D312yes—
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×C4⋊Dic5C2×D311yescharacteristic
133C2×C4⋊Dic5C2×D318yescomplemented
134C2×#683—31no—
135C2×#683—32no—
136C2×#683—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—32no—
140#4044—316no—
141#4038—38no—
142#4036—316no—
143#4036—38no—
144#4032—316no—
145#4023—316no—
146C2×#552—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5#4114yes—
150C23×C3×C5C2412yes—
151C23×C3×C5C2411yescharacteristic
152C22×D15—22no—
153C22×D15—22no—
154C22×D15—22no—
155C22×D15C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161#1220—28no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15C2412yes—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168C4×D15—28no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3C2414yes—
172C2×C5×Dic3C2414yes—
173C5×Dic6—28no—
174C2×C3×Dic5—216no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2414yes—
179C23×C3×C4—52no—
180C23×C3×C4C2×D511yescharacteristic
181C22×#67—51no—
182C22×C4×D3—51no—
183C22×Dic6C2×D511yescharacteristic
184C2×C3×C4⋊C4—51no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—58no—
188C2×#217—51no—
189C2×#217C2×D512yes—
190#929—516no—
191C4×#67—58no—
192C2×(C2×D3)⋊C4—51no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195#926—516no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199#924C2×D518yescomplemented
200C2×Dic3⋊C4—51no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4C2×D512yes—
204C2×C4×Dic3—51no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3—52no—
207#898—516no—
208#897—58no—
209#892—58no—
210#890—58no—
211#889—516no—
212#887—58no—
213C24×C5C22×D311yescharacteristic
214C23×D5—31no—
215C2×C5×Q8—34no—
216C2×C5×Q8—64no—
217C22×C4×C5—24no—
218C22×C4×C5—32no—
219C22×C4×C5—32no—
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D314yes—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—34no—
224C2×C22⋊D5—64no—
225C22×Dic5—28no—
226C22×Dic5—31no—
227C22×Dic5—31no—
228C22×Dic5—31no—
229C22×Dic5C22×D318yes—
230C22×Dic5C22×D312yes—
231C22×Dic5C22×D312yes—
232C2×C4×D5—34no—
233C2×C4×D5—64no—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C5×C22⋊C4—38no—
237C22⋊Dic5—34no—
238#685—34no—
239#685—38no—
240#685—38no—
241C4⋊Dic5—38no—
242C4⋊Dic5—38no—
243C4⋊Dic5C22×D318yes—
244C4⋊Dic5C22×D314yes—
245C4⋊Dic5C22×D314yes—
246#683—34no—
247#683—38no—
248#683—38no—
249C4×Dic5—34no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—152no—
255C2×#125—151no—
256C2×#123—152no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—51no—
264C22×C3×C5—28no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5C2×#4114yes—
269C22×C3×C5C2×#4112yes—
270C22×C3×C52−1+412yes—
271C22×C3×C5C2511yescharacteristic
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—22no—
275C2×D15—44no—
276C3×C4×C5—22no—
277C3×C4×C5C2×#4114yes—
278Dic15—22no—
279Dic15—22no—
280Dic15—22no—
281C3×Dic5—24no—
282C3×Dic5—24no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C24×C3C22×D511yescharacteristic
286C23×D3—51no—
287C22×C3×C4—24no—
288C22×C3×C4—52no—
289C22×C3×C4—52no—
290C22×C3×C4—58no—
291C22×C3×C4—108no—
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D514yes—
294C22×C3×C4C22×D511yescharacteristic
295C2×#67—54no—
296C2×#67—104no—
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3C22×D512yes—
301C22×Dic3C22×D512yes—
302C2×C4×D3—54no—
303C2×C4×D3—104no—
304C2×Dic6—24no—
305C2×Dic6C22×D514yes—
306C3×C4⋊C4—54no—
307C3×C4⋊C4—58no—
308C3×C4⋊C4—54no—
309#217—54no—
310#217C22×D518yes—
311(C2×D3)⋊C4—54no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—58no—
314C4⋊Dic3—58no—
315C4⋊Dic3—58no—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—54no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4C22×D518yes—
321C4×Dic3—54no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5#23714yes—
327C23×C5C23×D312yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—32no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C5×Q8—68no—
334C2×C4×C5—22no—
335C2×C4×C5—28no—
336C2×C4×C5—34no—
337C2×C4×C5—34no—
338C2×C4×C5—64no—
339C2×C4×C5—64no—
340C2×C4×C5#23514yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C22⋊D5—68no—
344C2×Dic5—216no—
345C2×Dic5—24no—
346C2×Dic5—24no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—32no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5—62no—
353C2×Dic5C23×D314yes—
354C2×Dic5C23×D314yes—
355C4×D5—68no—
356C22×Q8—31no—
357C22×D4—151no—
358C23×C4—52no—
359C23×C4—151no—
360C23×C4D3×D511yescharacteristic
361#126—1516no—
362#125—1516no—
363#125—158no—
364#123—1516no—
365C22⋊Q8—38no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—158no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4—58no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—151no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42—151no—
390C2×C3×C5—24no—
391C2×C3×C5#55214yescomplemented
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C22×#4111yescharacteristic
394C2×C3×C5C2×2−1+411yescharacteristic
395D15—42no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3#71314yes—
399C23×C3C23×D512yes—
400C23×C3C23×D511yescharacteristic
401C22×D3—52no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C2×C3×C4—22no—
406C2×C3×C4—28no—
407C2×C3×C4—54no—
408C2×C3×C4—54no—
409C2×C3×C4—1016no—
410C2×C3×C4—104no—
411C2×C3×C4—104no—
412C2×C3×C4#71114yes—
413C2×C3×C4C23×D512yes—
414C2×C3×C4C23×D512yes—
415#67—108no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—52no—
419C2×Dic3—52no—
420C2×Dic3—52no—
421C2×Dic3—102no—
422C2×Dic3—102no—
423C2×Dic3—102no—
424C2×Dic3C23×D514yes—
425C2×Dic3C23×D514yes—
426C4×D3—108no—
427Dic6—28no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—28no—
431C22×C5C2×#23512yes—
432C22×C5C2×#23714yes—
433C22×C5C2×#23712yes—
434C22×C5#100712yes—
435C22×C5C24×D311yescharacteristic
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—22no—
441C4×C5—64no—
442C4×C5—64no—
443C4×C5C2×#23514yes—
444Dic5—24no—
445Dic5—24no—
446Dic5—62no—
447Dic5—62no—
448Dic5—62no—
449C24—151no—
450C24C2×D3×D511yescharacteristic
451C2×Q8—34no—
452C2×Q8—64no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—24no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—58no—
459C22×C4—52no—
460C22×C4—52no—
461C22×C4—108no—
462C22×C4—151no—
463C22×C4—151no—
464C22×C4—151no—
465C22×C4—154no—
466C22×C4—304no—
467C22×C4C2×D3×D514yes—
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—54no—
473C4⋊C4—54no—
474C4⋊C4—58no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4—154no—
480C22⋊C4—38no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—158no—
486C42—158no—
487C42—154no—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—28no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3C2×#71112yes—
493C22×C3C2×#71314yes—
494C22×C3C2×#71312yes—
495C22×C3#415012yes—
496C22×C3C24×D511yescharacteristic
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—22no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C2×#71114yes—
505Dic3—24no—
506Dic3—24no—
507Dic3—102no—
508Dic3—102no—
509Dic3—102no—
510C2×C5—24no—
511C2×C5#551314yescomplemented
512C2×C5C22×#23511yescharacteristic
513C2×C5C22×#23711yescharacteristic
514C2×C5C2×#100711yescharacteristic
515D5—122no—
516C23—22no—
517C23—22no—
518C23—152no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23#676614yes—
523C23C22×D3×D512yes—
524C23C22×D3×D511yescharacteristic
525Q8—68no—
526D4—308no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—64no—
534C2×C4—64no—
535C2×C4—1016no—
536C2×C4—104no—
537C2×C4—104no—
538C2×C4—152no—
539C2×C4—152no—
540C2×C4—152no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—308no—
545C2×C4#678214yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3—24no—
549C2×C3#6597614yescomplemented
550C2×C3C22×#71111yescharacteristic
551C2×C3C22×#71311yescharacteristic
552C2×C3C2×#415011yescharacteristic
553D3—202no—
554C5C2×#551311yescharacteristic, complemented, Sylow
555C22—22no—
556C22—22no—
557C22—28no—
558C22—302no—
559C22—302no—
560C22—302no—
561C22—604no—
562C22C2×#676614yes—
563C22C2×#676612yes—
564C22#9200412yes—
565C22C2×#678212yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—64no—
569C4—64no—
570C4—104no—
571C4—104no—
572C4—302no—
573C4—302no—
574C4—302no—
575C4C2×#678214yes—
576C3C2×#6597611yescharacteristic, complemented, Sylow
577C2—24no—
578C2—602no—
579C2#1175421014yesdirect product factor
580C2C22×#676611yescharacteristic
581C2C2×#9200411yescharacteristic
582C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#924C2semidirect
3. C22×C3×C4⋊Dic5C2semidirect
5. C2×#91528C2semidirect
6. C2×#91384C2semidirect
7. C2×#91383C2semidirect
8. #11754210C2direct (N × H)
9. C2×#91347C2semidirect
10. C2×#91346C2semidirect
11. C2×#91345C2semidirect
12. C2×#91344C2semidirect
26. C5×#924C22semidirect
31. C2×C3×C4⋊Dic5C22semidirect
39. #91528C22semidirect
42. #91384C22semidirect
43. #91383C22semidirect
44. #91347C22semidirect
45. #91346C22semidirect
46. #91345C22semidirect
47. #91344C22semidirect
53. C22×C4⋊Dic5D3semidirect
104. C2×#924D5semidirect
133. C2×C4⋊Dic5C2×D3semidirect
199. #924C2×D5semidirect
391. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
511. C2×C5#5513semidirect
549. C2×C3#65976semidirect
554. C5C2×#5513semidirect
576. C3C2×#65976semidirect
579. C2#11754210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C5×#9242
C22×C3×C4⋊Dic52
C2×#915462
C2×#915282
C2×#913842
C2×#913832
#117542102
C2×#913472
C2×#913462
C2×#913452
C2×#913442
C2×#659763
C2×#55135