Finite Group Databasebeta

← C2×#11753578 #14479932

Subgroups — C2×#11753578 #14479932

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#895C211yesmaximal, characteristic
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×#91435C212yesmaximal, complemented
5C2×#91435C211yesmaximal, characteristic, complemented
6C2×#91423C212yesmaximal, complemented
7C2×#91400C212yesmaximal, complemented
8C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
9C2×#91373C211yesmaximal, characteristic, complemented
10C2×#91365C211yesmaximal, characteristic, complemented
11C2×#91341C212yesmaximal, complemented
12#11753578C2116yesmaximal, direct product factor
13C2×#65934—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C5×D12C2212yes—
17C22×C4×C5×D3C2211yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×#6712C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2212yes—
25#91776C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C5×#895C2218yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4036C2218yescomplemented
33C2×#6668C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35C2×(C2×D3)⋊Dic5C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91435C2218yescomplemented
41#91435C22116yescomplemented
42#91423C22116yescomplemented
43#91400C22116yescomplemented
44C4×D3×Dic5C2218yescomplemented
45#91373C2218yescomplemented
46#91365C2218yescomplemented
47#91341C22116yescomplemented
48C2×#5691—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4082—31no—
51C2×#4081—32no—
52C2×D4×Dic5—31no—
53C2×D4×Dic5—32no—
54C2×#4070—31no—
55C22×C4×Dic5—31no—
56#65934—316no—
57C2×#4036D311yescharacteristic, complemented
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4023—32no—
61C23×C5×D3C2312yes—
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C2×C5×D12—28no—
72C2×C5×D12—24no—
73C2×C5×D12C2318yes—
74C2×C5×D12C2314yes—
75C2×C4×C5×D3—24no—
76C2×C4×C5×D3C2314yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2312yes—
80C2×D3×Dic5—24no—
81C2×D3×Dic5—24no—
82C2×D3×Dic5—28no—
83C2×D3×Dic5C2314yes—
84C2×D3×Dic5C2314yes—
85C2×D3×Dic5C2318yes—
86C3×C5×C4⋊C4C2314yes—
87#6712C2318yes—
88C4×Dic15C2314yes—
89C4×Dic15C2318yes—
90C5×(C2×D3)⋊C4C2318yes—
91C3×C4⋊Dic5C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×#683C2318yes—
94C3×C4×Dic5C2314yes—
95#6668C2318yes—
96(C2×D3)⋊Dic5C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100Dic3×Dic5C2314yes—
101Dic3×Dic5C2314yes—
102C2×C3×#125—51no—
103#5691—516no—
104C2×#898—52no—
105C2×#897—51no—
106C2×#895D511yescharacteristic
107C2×#894—52no—
108C2×#893—51no—
109C2×#893—52no—
110C2×#892—52no—
111C2×#887—51no—
112C2×#875—51no—
113C2×C42×D3—51no—
114C22×C5×D4—32no—
115C22×C5×D4—31no—
116C23×C4×C5—31no—
117C23×Dic5—32no—
118C23×Dic5—31no—
119C23×Dic5—31no—
120C22×Dic10—31no—
121C5×#121—38no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C5×C22⋊C4—32no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128#4082—38no—
129#4081—316no—
130D4×Dic5—316no—
131D4×Dic5—38no—
132C2×C4⋊Dic5C2×D312yes—
133C2×C4⋊Dic5C2×D311yescharacteristic
134#4070—38no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683C2×D312yes—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—38no—
143C2×C4×Dic5C2×D311yescharacteristic
144#4036C2×D318yescomplemented
145#4033—38no—
146#4025—316no—
147#4023—316no—
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—24no—
153C22×C5×D3—24no—
154C22×C5×D3—24no—
155C22×C5×D3#4114yes—
156C22×C5×D3C2414yes—
157C22×C5×D3C2412yes—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15#4114yes—
165C2×Dic15C2412yes—
166C2×Dic15C2414yes—
167C2×Dic15C2412yes—
168Dic30—28no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2412yes—
171C5×D12—216no—
172C5×D12—28no—
173C4×C5×D3—28no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5C2412yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2414yes—
180D3×Dic5—28no—
181D3×Dic5—28no—
182D3×Dic5—216no—
183C22×D12C2×D511yescharacteristic
184C22×D12C2×D512yes—
185C22×C4×D3—51no—
186C22×C4×D3—51no—
187C22×C4×D3—52no—
188C22×C4×D3C2×D511yescharacteristic
189C22×Dic6—51no—
190C3×#125—58no—
191C2×C3×C4⋊C4—52no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—52no—
194C2×C3×C4⋊C4C2×D511yescharacteristic
195C2×C3×C42—51no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4C2×D512yes—
201C2×C4⋊Dic3—52no—
202C2×Dic3⋊C4—52no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—51no—
206C2×C4×Dic3—51no—
207#898—516no—
208#897—58no—
209#895C2×D518yes—
210#894—516no—
211#893—58no—
212#893—516no—
213#892—516no—
214#887—58no—
215#875—58no—
216C42×D3—58no—
217C24×C5—31no—
218C24×C5—32no—
219C2×C5×D4—38no—
220C2×C5×D4—34no—
221C2×C5×D4—68no—
222C2×C5×D4—64no—
223C22×C4×C5—31no—
224C22×C4×C5—34no—
225C22×C4×C5—64no—
226C22×C4×C5C22×D312yes—
227C22×C4×C5C22×D311yescharacteristic
228C22×Dic5—31no—
229C22×Dic5—32no—
230C22×Dic5—31no—
231C22×Dic5—38no—
232C22×Dic5—34no—
233C22×Dic5—34no—
234C22×Dic5—64no—
235C22×Dic5—68no—
236C22×Dic5—64no—
237C22×Dic5C22×D311yescharacteristic
238C22×Dic5C22×D311yescharacteristic
239C22×Dic5C22×D312yes—
240C2×Dic10—34no—
241C2×Dic10—64no—
242C5×C4⋊C4C22×D314yes—
243C5×C22⋊C4—38no—
244C22⋊Dic5—38no—
245C22⋊Dic5—38no—
246C22⋊Dic5—38no—
247C22⋊Dic5—38no—
248C4⋊Dic5C22×D318yes—
249C4⋊Dic5C22×D314yes—
250#683—38no—
251#683—38no—
252#683C22×D318yes—
253C4×Dic5—38no—
254C4×Dic5—34no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5C22×D314yes—
258#529—1516no—
259C2×#126—152no—
260C2×#125—51no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—31no—
265C2×C4×Q8—151no—
266C2×C4×D4—152no—
267C2×C4×D4—151no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×C5×D3—28no—
275C2×C5×D3—22no—
276C2×C5×D3—22no—
277C2×C5×D3—24no—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—48no—
281C2×C5×D3C2×#4114yes—
282C3×C4×C5—24no—
283C3×C4×C5C2×#4114yes—
284Dic15—22no—
285Dic15—24no—
286Dic15C2×#4114yes—
287C3×Dic5—22no—
288C3×Dic5—22no—
289C3×Dic5—24no—
290C5×Dic3—22no—
291C23×D3C22×D512yes—
292C23×D3C22×D511yescharacteristic
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—52no—
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—52no—
301C22×Dic3C22×D511yescharacteristic
302C2×D12—28no—
303C2×D12—24no—
304C2×D12C22×D514yes—
305C2×D12C22×D518yes—
306C2×C4×D3—24no—
307C2×C4×D3—54no—
308C2×C4×D3—54no—
309C2×C4×D3—58no—
310C2×C4×D3—104no—
311C2×C4×D3—108no—
312C2×C4×D3—104no—
313C2×C4×D3C22×D514yes—
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C4⋊C4—58no—
317C3×C4⋊C4—54no—
318C3×C4⋊C4—58no—
319C3×C4⋊C4C22×D514yes—
320C3×C42—54no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323(C2×D3)⋊C4—58no—
324(C2×D3)⋊C4—58no—
325(C2×D3)⋊C4C22×D518yes—
326C4⋊Dic3—58no—
327Dic3⋊C4—58no—
328C4×Dic3—54no—
329C4×Dic3—58no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C23×C5—34no—
333C23×C5—32no—
334C23×C5—34no—
335C23×C5—62no—
336C23×C5—62no—
337C23×C5—64no—
338C23×C5—64no—
339C23×C5—64no—
340C23×C5C23×D311yescharacteristic
341C5×D4—616no—
342C5×D4—68no—
343C2×C4×C5—24no—
344C2×C4×C5—32no—
345C2×C4×C5—62no—
346C2×C4×C5—68no—
347C2×C4×C5#23914yes—
348C2×C4×C5C23×D314yes—
349C2×C4×C5C23×D312yes—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—24no—
353C2×Dic5—34no—
354C2×Dic5—32no—
355C2×Dic5—32no—
356C2×Dic5—34no—
357C2×Dic5—68no—
358C2×Dic5—616no—
359C2×Dic5—68no—
360C2×Dic5—64no—
361C2×Dic5—62no—
362C2×Dic5C23×D312yes—
363C2×Dic5C23×D312yes—
364C2×Dic5C23×D314yes—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—32no—
368C22×D4—31no—
369C23×C4—31no—
370C23×C4—152no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125—58no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—38no—
379C4×Q8—158no—
380C4×D4—158no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—52no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—52no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4D3×D511yescharacteristic
389C2×C22⋊C4—32no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—51no—
395C2×C42—158no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—152no—
399C2×C42—151no—
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C5×D3—24no—
405C5×D3—44no—
406C23×C3C23×D511yescharacteristic
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—24no—
410C22×D3—24no—
411C22×D3—24no—
412C22×D3#71114yes—
413C22×D3C23×D514yes—
414C22×D3C23×D512yes—
415C2×C3×C4—24no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—54no—
419C2×C3×C4—102no—
420C2×C3×C4—102no—
421C2×C3×C4—104no—
422C2×C3×C4#71114yes—
423C2×C3×C4C23×D514yes—
424C2×C3×C4C23×D512yes—
425C2×Dic3—22no—
426C2×Dic3—54no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—54no—
430C2×Dic3—104no—
431C2×Dic3—102no—
432C2×Dic3C23×D512yes—
433D12—216no—
434D12—28no—
435C4×D3—28no—
436C4×D3—108no—
437C4×D3—1016no—
438C4×D3—108no—
439Dic6—108no—
440C22×C5—34no—
441C22×C5—68no—
442C22×C5—62no—
443C22×C5—62no—
444C22×C5—64no—
445C22×C5—64no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5C2×#23912yes—
449C22×C5D3×#4112yes—
450C22×C5D3×#4112yes—
451C22×C5C24×D311yescharacteristic
452C4×C5—24no—
453C4×C5—62no—
454C4×C5C2×#23914yes—
455Dic5—22no—
456Dic5—22no—
457Dic5—24no—
458Dic5—34no—
459Dic5—64no—
460Dic5—62no—
461C24—31no—
462C24—32no—
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—38no—
466C2×D4—34no—
467C2×D4—68no—
468C2×D4—64no—
469C22×C4—31no—
470C22×C4—34no—
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—52no—
474C22×C4—64no—
475C22×C4—154no—
476C22×C4—154no—
477C22×C4—158no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—152no—
481C22×C4—304no—
482C22×C4—308no—
483C22×C4—304no—
484C22×C4C2×D3×D512yes—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—58no—
487C4⋊C4—54no—
488C4⋊C4—58no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4C2×D3×D514yes—
492C22⋊C4—38no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—54no—
498C42—154no—
499C42—154no—
500C42—154no—
501C42—158no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3C2×#71112yes—
504C22×C3C2×#71112yes—
505C22×C3D5×#4112yes—
506C22×C3C24×D511yescharacteristic
507C2×D3—28no—
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—24no—
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—48no—
514C2×D3C2×#71114yes—
515C3×C4—24no—
516C3×C4—102no—
517C3×C4—102no—
518C3×C4—104no—
519C3×C4C2×#71114yes—
520Dic3—22no—
521Dic3—54no—
522Dic3—104no—
523Dic3—102no—
524C2×C5—64no—
525C2×C5—124no—
526C2×C5#569114yescomplemented
527C2×C5C22×#23911yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529C2×C5C2×D3×#4111yescharacteristic
530C23—34no—
531C23—32no—
532C23—34no—
533C23—62no—
534C23—62no—
535C23—64no—
536C23—64no—
537C23—64no—
538C23C22×D3×D511yescharacteristic
539Q8—308no—
540D4—616no—
541D4—68no—
542C2×C4—24no—
543C2×C4—32no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—54no—
547C2×C4—62no—
548C2×C4—68no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—104no—
552C2×C4—154no—
553C2×C4—152no—
554C2×C4—152no—
555C2×C4—154no—
556C2×C4—308no—
557C2×C4—3016no—
558C2×C4—308no—
559C2×C4—304no—
560C2×C4—302no—
561C2×C4#676814yes—
562C2×C4C22×D3×D514yes—
563C2×C4C22×D3×D512yes—
564C2×C3#6593414yescomplemented
565C2×C3C22×#71111yescharacteristic
566C2×C3C22×#71111yescharacteristic
567C2×C3C2×D5×#4111yescharacteristic
568D3—24no—
569D3—44no—
570C5C2×#569111yescharacteristic, complemented, Sylow
571C22—34no—
572C22—68no—
573C22—62no—
574C22—62no—
575C22—64no—
576C22—64no—
577C22—64no—
578C22—128no—
579C22C2×#676812yes—
580C22D3×#71112yes—
581C22#9203412yes—
582C22C23×D3×D511yescharacteristic
583C4—24no—
584C4—62no—
585C4—102no—
586C4—102no—
587C4—104no—
588C4—154no—
589C4—304no—
590C4—302no—
591C4C2×#676814yes—
592C3C2×#6593411yescharacteristic, complemented, Sylow
593C2—64no—
594C2—124no—
595C2#1175357814yesdirect product factor
596C2C22×#676811yescharacteristic
597C2C2×D3×#71111yescharacteristic
598C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×C5×#895C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#529
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×#91776C2semidirect
3. C2×C3×#4036C2semidirect
4. C2×#91435C2semidirect
5. C2×#91435C2semidirect
6. C2×#91423C2semidirect
7. C2×#91400C2semidirect
8. C2×C4×D3×Dic5C2semidirect
9. C2×#91373C2semidirect
10. C2×#91365C2semidirect
11. C2×#91341C2semidirect
12. #11753578C2direct (N × H)
25. #91776C22semidirect
32. C3×#4036C22semidirect
40. #91435C22semidirect
41. #91435C22semidirect
42. #91423C22semidirect
43. #91400C22semidirect
44. C4×D3×Dic5C22semidirect
45. #91373C22semidirect
46. #91365C22semidirect
47. #91341C22semidirect
57. C2×#4036D3semidirect
144. #4036C2×D3semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
526. C2×C5#5691semidirect
564. C2×C3#65934semidirect
570. C5C2×#5691semidirect
592. C3C2×#65934semidirect
595. C2#11753578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8952
C2×C3×#40362
C2×#914352
C2×#914232
C2×#914002
C2×C4×D3×Dic52
C2×#913732
C2×#913652
C2×#913412
#117535782
C2×#659343
C2×#56915