Finite Group Databasebeta

← C2×#11754340 #14480547

Subgroups — C2×#11754340 #14480547

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×Dic6C211yesmaximal, characteristic, complemented
2C22×#6779C211yesmaximal, characteristic
3C2×#91818C211yesmaximal, characteristic, complemented
4C2×C3×#4075C211yesmaximal, characteristic, complemented
5C2×#91542C211yesmaximal, characteristic, complemented
6C2×#91536C211yesmaximal, characteristic, complemented
7C2×#91529C211yesmaximal, characteristic, complemented
8C2×#91455C212yesmaximal, complemented
9C2×#91424C212yesmaximal, complemented
10#11754340C2116yesmaximal, direct product factor
11C2×#91421C212yesmaximal, complemented
12C2×#91329C212yesmaximal, complemented
13C2×#66150—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C23×C5×Dic3C2211yescharacteristic
18C22×C5×Dic6—28no—
19C22×C5×Dic6C2212yes—
20C22×C5×Dic6C2212yes—
21C22×C5×Dic6C2218yescomplemented
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C2×#6779—28no—
27C2×#6779C2218yes—
28C22×D5×Dic3C2211yescharacteristic
29C2×#6719C2211yescharacteristic
30#91818C2218yescomplemented
31C2×#6714C2212yes—
32C2×#6712C2212yes—
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×#4075C2218yescomplemented
35C2×C3×#685C2212yes—
36C2×C3×#683C2212yes—
37C2×Dic3⋊Dic5C2212yes—
38C2×#6669C2212yes—
39#91542C2218yescomplemented
40C2×#6668C2212yes—
41C2×#6667C2212yes—
42#91536C2218yescomplemented
43C2×#6665C2212yes—
44#91529C2218yescomplemented
45C2×Dic3×Dic5C2212yes—
46#91455C22116yescomplemented
47#91424C22116yescomplemented
48#91421C22116yescomplemented
49#91329C22116yescomplemented
50C2×#5648—51nomaximal, Hall
51C23×C5×Q8—31no—
52C22×#709—31no—
53#66150—316no—
54C2×#4093—32no—
55C2×#4092—32no—
56C2×#4092—32no—
57C2×#4090—32no—
58C2×#4075—31no—
59C2×#4075—31no—
60C2×#4075—31no—
61C2×#4075D311yescharacteristic, complemented
62C2×#4072—31no—
63C24×C3×C5C2311yescharacteristic
64C23×D15C2311yescharacteristic
65C23×C3×D5C2311yescharacteristic
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2314yes—
69C2×#1220—24no—
70C2×#1220C2314yes—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2312yes—
73C22×C5×Dic3—24no—
74C22×C5×Dic3D418yes—
75C22×C5×Dic3C2312yes—
76C22×C5×Dic3C2314yes—
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2314yes—
79C22×C5×Dic3C2311yescharacteristic
80C2×C5×Dic6—28no—
81C2×C5×Dic6—28no—
82C2×C5×Dic6—232no—
83C2×C5×Dic6C2318yes—
84C2×C5×Dic6C2318yes—
85C2×C3×C22⋊D5—24no—
86C2×C3×C22⋊D5C2314yes—
87C22×C3×Dic5C2312yes—
88C22×C3×Dic5C2311yescharacteristic
89C2×#1204—24no—
90C2×#1204C2314yes—
91C2×#1202—24no—
92C2×#1202C2314yes—
93C2×#1200—24no—
94C2×#1200C2314yes—
95#6779—232no—
96C2×D5×Dic3—24no—
97C2×D5×Dic3C2314yes—
98#6719C2314yes—
99#6714C2318yes—
100#6712C2318yes—
101C3×C22⋊Dic5C2314yes—
102C3×#685C2318yes—
103C3×#683C2318yes—
104Dic3⋊Dic5C2318yes—
105#6669C2318yes—
106#6668C2318yes—
107#6667C2318yes—
108#6665C2318yes—
109Dic3×Dic5C2318yes—
110C22×#237—51no—
111C23×Dic6D511yescharacteristic, complemented
112C2×C3×#123—51no—
113C2×#935—51no—
114C2×#929—51no—
115#5648—516no—
116C2×#896—52no—
117C2×#888—52no—
118C2×#886—51no—
119C2×#885—52no—
120C2×#878—52no—
121C2×#877—51no—
122C22×C5×Q8—32no—
123C22×C5×Q8—32no—
124C22×C5×Q8—38no—
125C22×C5×Q8—68no—
126C23×C4×C5—31no—
127C23×C4×C5—31no—
128C23×C4×C5C2×D311yescharacteristic
129C22×C22⋊D5—31no—
130C22×C22⋊D5C2×D311yescharacteristic
131C2×#709—38no—
132C2×#709—68no—
133C22×D20—31no—
134C22×C4×D5—31no—
135C22×C4×D5—31no—
136C22×Dic10—31no—
137C2×C22⋊Dic5—31no—
138C2×C22⋊Dic5C2×D311yescharacteristic
139#4093—316no—
140#4092—316no—
141#4092—316no—
142#4090—316no—
143#4075—38no—
144#4075—38no—
145#4075—38no—
146#4075C2×D318yescomplemented
147C2×#685—32no—
148C2×#685—32no—
149C2×#685—32no—
150C2×#685C2×D312yes—
151#4072—38no—
152C2×C4⋊Dic5—32no—
153C2×#683—32no—
154C2×#683—32no—
155C2×#683—32no—
156C2×#683C2×D312yes—
157C2×C4×Dic5—32no—
158C2×#536—151noSylow
159C23×C3×C5—24no—
160C23×C3×C5C2×D414yes—
161C23×C3×C5C2412yes—
162C23×C3×C5C2411yescharacteristic
163C22×D15—22no—
164C22×D15—24no—
165C22×D15C2412yes—
166C22×C3×D5—22no—
167C22×C3×D5—24no—
168C22×C3×D5C2412yes—
169C2×C3×C4×C5—28no—
170C2×C3×C4×C5—24no—
171C2×C3×C4×C5C2414yes—
172#1220—28no—
173C2×Dic15—22no—
174C2×Dic15—24no—
175C2×Dic15C2414yes—
176C2×Dic15C2412yes—
177C2×C5×Dic3—28no—
178C2×C5×Dic3—24no—
179C2×C5×Dic3C2×D414yes—
180C2×C5×Dic3C2×D4116yes—
181C2×C5×Dic3C2×D414yes—
182C2×C5×Dic3C2414yes—
183C2×C5×Dic3C2412yes—
184C2×C5×Dic3C2412yes—
185C5×Dic6—216no—
186C5×Dic6—216no—
187C3×C22⋊D5—28no—
188C2×C3×Dic5—22no—
189C2×C3×Dic5—24no—
190C2×C3×Dic5C2414yes—
191C2×C3×Dic5C2412yes—
192#1204—28no—
193#1202—28no—
194#1200—28no—
195D5×Dic3—28no—
196C22×C3×D4—51no—
197C23×C3×C4C2×D511yescharacteristic
198C22×#67—51no—
199C22×#67—51no—
200C23×Dic3—51no—
201C23×Dic3C2×D511yescharacteristic
202C23×Dic3C2×D511yescharacteristic
203C2×#237—58no—
204C2×#237—108no—
205C22×C4×D3—51no—
206C22×Dic6—28no—
207C22×Dic6—51no—
208C22×Dic6C2×D512yes—
209C22×Dic6C2×D512yes—
210C22×Dic6C2×D518yescomplemented
211C3×#123—58no—
212C2×C3×C4⋊C4—52no—
213C2×C3×C22⋊C4—51no—
214C2×C3×C22⋊C4—52no—
215C2×#217—51no—
216C2×#217—52no—
217#935—58no—
218#929—58no—
219C2×(C2×D3)⋊C4—52no—
220C2×(C2×D3)⋊C4—52no—
221C2×C4⋊Dic3—52no—
222C2×Dic3⋊C4—52no—
223C2×Dic3⋊C4—52no—
224C2×Dic3⋊C4—52no—
225C2×C4×Dic3—52no—
226#896—516no—
227#888—516no—
228#886—58no—
229#885—516no—
230#878—516no—
231#877—58no—
232C24×C5C22×D311yescharacteristic
233C23×D5—31no—
234C23×D5C22×D311yescharacteristic
235C2×C5×Q8—38no—
236C2×C5×Q8—38no—
237C2×C5×Q8—68no—
238C2×C5×Q8—68no—
239C2×C5×Q8—632no—
240C22×C4×C5—24no—
241C22×C4×C5—38no—
242C22×C4×C5—31no—
243C22×C4×C5—31no—
244C22×C4×C5—34no—
245C22×C4×C5—32no—
246C22×C4×C5—34no—
247C22×C4×C5—64no—
248C22×C4×C5C22×D312yes—
249C22×C4×C5C22×D314yes—
250C2×C22⋊D5—24no—
251C2×C22⋊D5—34no—
252C2×C22⋊D5—64no—
253C2×C22⋊D5C22×D314yes—
254C22×Dic5—32no—
255C22×Dic5—31no—
256C22×Dic5C22×D312yes—
257C22×Dic5C22×D311yescharacteristic
258#709—632no—
259C2×D20—34no—
260C2×D20—64no—
261C2×C4×D5—34no—
262C2×C4×D5—34no—
263C2×C4×D5—64no—
264C2×C4×D5—64no—
265C2×Dic10—34no—
266C2×Dic10—64no—
267C22⋊Dic5—34no—
268C22⋊Dic5C22×D314yes—
269#685—38no—
270#685—38no—
271#685—38no—
272#685C22×D318yes—
273C4⋊Dic5—38no—
274#683—38no—
275#683—38no—
276#683—38no—
277#683C22×D318yes—
278C4×Dic5—38no—
279C22×#41—151no—
280C23×Q8—31no—
281#536—1516no—
282C2×C4⋊Q8—152no—
283C2×#124—152no—
284C2×#123—51no—
285C2×#123—151no—
286C2×#123—151no—
287C2×#123—151no—
288C2×C22⋊Q8—152no—
289C2×C22⋊Q8—152no—
290C2×#117—151no—
291C22×C3×C5—28no—
292C22×C3×C5—24no—
293C22×C3×C5C22×D414yes—
294C22×C3×C5C22×D412yes—
295C22×C3×C52−1+414yes—
296C22×C3×C5C2511yescharacteristic
297C2×D15—22no—
298C2×D15—24no—
299C2×D15—44no—
300C2×C3×D5—22no—
301C2×C3×D5—24no—
302C2×C3×D5—44no—
303C3×C4×C5—24no—
304Dic15—22no—
305Dic15—24no—
306C3×Dic5—22no—
307C3×Dic5—24no—
308C5×Dic3—24no—
309C5×Dic3C22×D414yes—
310C5×Dic3C22×D414yes—
311C24×C3—51no—
312C24×C3C22×D511yescharacteristic
313C23×D3—51no—
314C2×C3×D4—54no—
315C2×C3×D4—104no—
316C22×C3×C4—24no—
317C22×C3×C4—52no—
318C22×C3×C4—51no—
319C22×C3×C4C22×D512yes—
320C22×C3×C4C22×D514yes—
321C2×#67—54no—
322C2×#67—54no—
323C2×#67—104no—
324C2×#67—104no—
325C22×Dic3—24no—
326C22×Dic3—52no—
327C22×Dic3—51no—
328C22×Dic3—54no—
329C22×Dic3—104no—
330C22×Dic3C22⋊D518yes—
331C22×Dic3C22×D514yes—
332C22×Dic3C22×D512yes—
333C22×Dic3C22×D514yes—
334C22×Dic3C22×D511yescharacteristic
335C22×Dic3C22×D511yescharacteristic
336#237—1032no—
337C2×C4×D3—54no—
338C2×C4×D3—104no—
339C2×Dic6—28no—
340C2×Dic6—28no—
341C2×Dic6—232no—
342C2×Dic6—54no—
343C2×Dic6—104no—
344C2×Dic6C22×D518yes—
345C2×Dic6C22×D518yes—
346C3×C4⋊C4—58no—
347C3×C22⋊C4—54no—
348C3×C22⋊C4—58no—
349#217—54no—
350#217—58no—
351(C2×D3)⋊C4—58no—
352(C2×D3)⋊C4—58no—
353C4⋊Dic3—58no—
354Dic3⋊C4—58no—
355Dic3⋊C4—58no—
356Dic3⋊C4—58no—
357C4×Dic3—58no—
358C23×C5—24no—
359C23×C5D3×D414yes—
360C23×C5C23×D312yes—
361C23×C5C23×D311yescharacteristic
362C22×D5—22no—
363C22×D5—24no—
364C22×D5—32no—
365C22×D5—62no—
366C22×D5—64no—
367C22×D5C23×D312yes—
368C5×Q8—616no—
369C5×Q8—616no—
370C2×C4×C5—28no—
371C2×C4×C5—24no—
372C2×C4×C5—34no—
373C2×C4×C5—34no—
374C2×C4×C5—316no—
375C2×C4×C5—32no—
376C2×C4×C5—32no—
377C2×C4×C5—34no—
378C2×C4×C5—68no—
379C2×C4×C5—64no—
380C2×C4×C5C23×D314yes—
381C22⋊D5—28no—
382C22⋊D5—68no—
383C2×Dic5—22no—
384C2×Dic5—24no—
385C2×Dic5—34no—
386C2×Dic5—32no—
387C2×Dic5—62no—
388C2×Dic5—64no—
389C2×Dic5C23×D314yes—
390C2×Dic5C23×D312yes—
391D20—68no—
392C4×D5—68no—
393C4×D5—68no—
394Dic10—68no—
395C2×#41—158no—
396C2×#41—308no—
397C22×Q8—32no—
398C22×Q8—32no—
399C22×Q8—38no—
400C22×Q8—68no—
401C22×Q8—151no—
402C22×D4—51no—
403C22×D4—151no—
404C22×D4—151no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—151no—
408C23×C4—151no—
409C23×C4D3×D511yescharacteristic
410C4⋊Q8—1516no—
411#124—1516no—
412#123—58no—
413#123—158no—
414#123—158no—
415#123—158no—
416C22⋊Q8—1516no—
417C22⋊Q8—1516no—
418#117—158no—
419C2×C4⋊C4—52no—
420C2×C4⋊C4—152no—
421C2×C4⋊C4—152no—
422C2×C4⋊C4—152no—
423C2×C4⋊C4—152no—
424C2×C22⋊C4—51no—
425C2×C22⋊C4—52no—
426C2×C22⋊C4—152no—
427C2×C22⋊C4—152no—
428C2×C22⋊C4—151no—
429C2×C22⋊C4—152no—
430C2×C42—152no—
431C2×C3×C5—24no—
432C2×C3×C5#53614yescomplemented
433C2×C3×C5C23×D411yescharacteristic
434C2×C3×C5C2×2−1+412yes—
435D15—42no—
436C3×D5—42no—
437C23×C3—24no—
438C23×C3—52no—
439C23×C3—104no—
440C23×C3—102no—
441C23×C3C2×C22⋊D514yes—
442C23×C3C23×D512yes—
443C23×C3C23×D511yescharacteristic
444C22×D3—52no—
445C22×D3—104no—
446C22×D3—102no—
447C3×D4—108no—
448C2×C3×C4—28no—
449C2×C3×C4—24no—
450C2×C3×C4—54no—
451C2×C3×C4—52no—
452C2×C3×C4—104no—
453C2×C3×C4—102no—
454C2×C3×C4C23×D514yes—
455#67—108no—
456#67—108no—
457C2×Dic3—28no—
458C2×Dic3—24no—
459C2×Dic3—54no—
460C2×Dic3—52no—
461C2×Dic3—104no—
462C2×Dic3—102no—
463C2×Dic3—108no—
464C2×Dic3C2×C22⋊D514yes—
465C2×Dic3C2×C22⋊D514yes—
466C2×Dic3C2×C22⋊D5116yes—
467C2×Dic3C23×D514yes—
468C2×Dic3C23×D512yes—
469C2×Dic3C23×D512yes—
470C4×D3—108no—
471Dic6—216no—
472Dic6—216no—
473Dic6—108no—
474C22×C5—28no—
475C22×C5—24no—
476C22×C5C2×D3×D414yes—
477C22×C5C2×D3×D412yes—
478C22×C5#101014yes—
479C22×C5C24×D311yescharacteristic
480C2×D5—22no—
481C2×D5—24no—
482C2×D5—44no—
483C2×D5—62no—
484C2×D5—64no—
485C2×D5—124no—
486C4×C5—24no—
487C4×C5—34no—
488C4×C5—34no—
489C4×C5—64no—
490Dic5—22no—
491Dic5—24no—
492Dic5—62no—
493Dic5—64no—
494C24—51no—
495C24—151no—
496C24C2×D3×D511yescharacteristic
497#41—3032no—
498C2×Q8—38no—
499C2×Q8—38no—
500C2×Q8—68no—
501C2×Q8—68no—
502C2×Q8—632no—
503C2×Q8—154no—
504C2×Q8—304no—
505C2×D4—54no—
506C2×D4—104no—
507C2×D4—154no—
508C2×D4—154no—
509C2×D4—304no—
510C2×D4—304no—
511C22×C4—24no—
512C22×C4—38no—
513C22×C4—34no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—34no—
517C22×C4—32no—
518C22×C4—52no—
519C22×C4—51no—
520C22×C4—64no—
521C22×C4—154no—
522C22×C4—154no—
523C22×C4—152no—
524C22×C4—151no—
525C22×C4—304no—
526C22×C4—304no—
527C22×C4C2×D3×D514yes—
528C22×C4C2×D3×D512yes—
529C4⋊C4—58no—
530C4⋊C4—158no—
531C4⋊C4—158no—
532C4⋊C4—158no—
533C4⋊C4—158no—
534C22⋊C4—54no—
535C22⋊C4—58no—
536C22⋊C4—158no—
537C22⋊C4—158no—
538C22⋊C4—154no—
539C22⋊C4—158no—
540C42—158no—
541C3×C5C2×#53611yescharacteristic, complemented, Hall
542C22×C3—28no—
543C22×C3—24no—
544C22×C3—104no—
545C22×C3—102no—
546C22×C3—204no—
547C22×C3#414714yes—
548C22×C3C22×C22⋊D514yes—
549C22×C3C22×C22⋊D512yes—
550C22×C3C24×D511yescharacteristic
551C2×D3—104no—
552C2×D3—102no—
553C2×D3—204no—
554C3×C4—24no—
555C3×C4—104no—
556C3×C4—102no—
557Dic3—24no—
558Dic3—104no—
559Dic3—102no—
560Dic3C22×C22⋊D514yes—
561Dic3C22×C22⋊D514yes—
562C2×C5—24no—
563C2×C5#564814yescomplemented
564C2×C5C22×D3×D411yescharacteristic
565C2×C5C2×#101012yes—
566D5—42no—
567D5—122no—
568C23—24no—
569C23—52no—
570C23—104no—
571C23—102no—
572C23—152no—
573C23—304no—
574C23—302no—
575C23D3×C22⋊D514yes—
576C23C22×D3×D512yes—
577C23C22×D3×D511yescharacteristic
578Q8—616no—
579Q8—616no—
580Q8—308no—
581D4—108no—
582D4—308no—
583D4—308no—
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—34no—
587C2×C4—34no—
588C2×C4—316no—
589C2×C4—32no—
590C2×C4—32no—
591C2×C4—34no—
592C2×C4—54no—
593C2×C4—52no—
594C2×C4—68no—
595C2×C4—64no—
596C2×C4—104no—
597C2×C4—102no—
598C2×C4—154no—
599C2×C4—152no—
600C2×C4—308no—
601C2×C4—308no—
602C2×C4—304no—
603C2×C4—302no—
604C2×C4C22×D3×D514yes—
605C2×C3—24no—
606C2×C3—202no—
607C2×C3#6615014yescomplemented
608C2×C3C2×#414712yes—
609C2×C3C23×C22⋊D511yescharacteristic
610D3—202no—
611C5C2×#564811yescharacteristic, complemented, Sylow
612C22—28no—
613C22—24no—
614C22—102no—
615C22—104no—
616C22—204no—
617C22—302no—
618C22—304no—
619C22—604no—
620C22#9200014yes—
621C22C2×D3×C22⋊D514yes—
622C22C2×D3×C22⋊D512yes—
623C22C23×D3×D511yescharacteristic
624C4—24no—
625C4—34no—
626C4—34no—
627C4—64no—
628C4—102no—
629C4—104no—
630C4—302no—
631C4—304no—
632C3C2×#6615011yescharacteristic, complemented, Sylow
633C2—24no—
634C2—202no—
635C2—602no—
636C2#1175434014yesdirect product factor
637C2C2×#9200012yes—
638C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×#6779C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C5×Dic6C2semidirect
3. C2×#91818C2semidirect
4. C2×C3×#4075C2semidirect
5. C2×#91542C2semidirect
6. C2×#91536C2semidirect
7. C2×#91529C2semidirect
8. C2×#91455C2semidirect
9. C2×#91424C2semidirect
10. #11754340C2direct (N × H)
11. C2×#91421C2semidirect
12. C2×#91329C2semidirect
21. C22×C5×Dic6C22semidirect
30. #91818C22semidirect
34. C3×#4075C22semidirect
39. #91542C22semidirect
42. #91536C22semidirect
44. #91529C22semidirect
46. #91455C22semidirect
47. #91424C22semidirect
48. #91421C22semidirect
49. #91329C22semidirect
61. C2×#4075D3semidirect
111. C23×Dic6D5semidirect
146. #4075C2×D3semidirect
210. C22×Dic6C2×D5semidirect
432. C2×C3×C5#536semidirect
541. C3×C5C2×#536semidirect
563. C2×C5#5648semidirect
607. C2×C3#66150semidirect
611. C5C2×#5648semidirect
632. C3C2×#66150semidirect
636. C2#11754340direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×Dic62
C22×#67792
C2×#918182
C2×C3×#40752
C2×#915422
C2×#915362
C2×#915292
C2×#914552
C2×#914242
#117543402
C2×#914212
C2×#913292
C2×#661503
C2×#56485