Finite Group Databasebeta

← C2×#11752502 #14479875

Subgroups — C2×#11752502 #14479875

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×C42×D15C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×#91466C211yesmaximal, characteristic
5C2×C4×#1203C212yesmaximal, complemented
6C2×#91390C211yesmaximal, characteristic, complemented
7C2×#91384C211yesmaximal, characteristic, complemented
8C2×#91371C212yesmaximal, complemented
9C2×#91370C211yesmaximal, characteristic, complemented
10C2×#91367C212yesmaximal, complemented
11C2×#91355C212yesmaximal, complemented
12#11752502C2116yesmaximal, direct product factor
13C2×#65891—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3C2212yes—
19C22×C3×Dic10C2211yescharacteristic
20C22×#1203C2212yes—
21C2×C3×C42×C5C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C42×D15C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C4×C5×D12C2218yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C3×C4×Dic10C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6668C2212yes—
36C2×#6667C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91466C2218yes—
41C4×#1203C22116yescomplemented
42#91390C2218yescomplemented
43#91384C2218yescomplemented
44#91371C22116yescomplemented
45#91370C2218yescomplemented
46#91367C22116yescomplemented
47#91355C22116yescomplemented
48C2×#5580—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4084—31no—
51C2×#4082—31no—
52C2×C4×C22⋊D5—32no—
53C2×#4072—32no—
54#65891—316no—
55C2×#4043—31no—
56C2×#4036—31no—
57C2×#4029—32no—
58C2×#4025—32no—
59C2×C42×D5—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×D15C2311yescharacteristic
62C23×C5×D3C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C2×C4×D15—24no—
70C2×C4×D15—24no—
71C2×C4×D15—24no—
72C2×C4×D15C2314yes—
73C2×C4×D15C2314yes—
74C2×C4×D15C2314yes—
75C22×C5×Dic3C2312yes—
76C2×C5×D12—24no—
77C2×C5×D12C2314yes—
78C2×C4×C5×D3—28no—
79C2×C4×C5×D3C2318yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C2×C3×Dic10—24no—
83C2×C3×Dic10C2314yes—
84C2×#1203—28no—
85C2×#1203C2318yes—
86C3×C42×C5C2314yes—
87C4×Dic15C2314yes—
88C4×Dic15C2314yes—
89C4×Dic15C2314yes—
90C5×(C2×D3)⋊C4C2318yes—
91C5×C4⋊Dic3C2314yes—
92C3×C4⋊Dic5C2314yes—
93C3×#683C2318yes—
94C3×C4×Dic5C2318yes—
95Dic3⋊Dic5C2318yes—
96Dic3⋊Dic5C2318yes—
97#6668C2318yes—
98#6667C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102C2×C3×C4×Q8—51no—
103C2×#947—51no—
104C2×#946—51no—
105#5580—516no—
106C2×#898—52no—
107C2×#895—51no—
108C2×#894—52no—
109C2×#890—51no—
110C2×C4×D12—52no—
111C2×C4×D12D511yescharacteristic, complemented
112C2×#872—52no—
113C2×C42×D3—51no—
114C22×C5×D4—31no—
115C23×C4×C5—32no—
116C22×C22⋊D5—32no—
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—31no—
120C22×Dic10C2×D311yescharacteristic
121C4×C5×D4—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C22⋊C4—32no—
124C2×C42×C5C2×D311yescharacteristic
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128#4084—38no—
129#4082—38no—
130C4×C22⋊D5—316no—
131C2×#685—32no—
132#4072—316no—
133C2×C4⋊Dic5—32no—
134C2×C4⋊Dic5—32no—
135C2×C4⋊Dic5C2×D311yescharacteristic
136C2×#683—32no—
137C2×#683C2×D312yes—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5C2×D312yes—
142#4043—38no—
143#4036—38no—
144#4029—316no—
145#4025—316no—
146C42×D5—38no—
147C4×Dic10C2×D318yescomplemented
148C2×#529—151noSylow
149C23×C3×C5C2411yescharacteristic
150C22×D15—22no—
151C22×D15—22no—
152C22×D15#4114yes—
153C22×D15C2412yes—
154C22×C5×D3—24no—
155C22×C5×D3—24no—
156C22×C5×D3—24no—
157C22×C5×D3C2414yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15—22no—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169C2×Dic15C2412yes—
170C4×D15—28no—
171C4×D15—28no—
172C4×D15—28no—
173C2×C5×Dic3—24no—
174C2×C5×Dic3C2414yes—
175C5×D12—28no—
176C4×C5×D3—216no—
177C2×C3×Dic5—24no—
178C2×C3×Dic5—24no—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2414yes—
181C3×Dic10—28no—
182#1203—216no—
183C22×C3×Q8—51no—
184C22×D12—52no—
185C22×D12C2×D511yescharacteristic
186C22×C4×D3—51no—
187C22×C4×D3—51no—
188C22×C4×D3—51no—
189C22×C4×D3C2×D512yes—
190C3×C4×Q8—58no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—52no—
193C2×C3×C42—52no—
194C2×C3×C42C2×D511yescharacteristic
195#947—58no—
196#946—58no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×(C2×D3)⋊C4—52no—
201C2×(C2×D3)⋊C4C2×D512yes—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—51no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209#898—516no—
210#895—58no—
211#894—516no—
212#890—58no—
213C4×D12—516no—
214C4×D12C2×D518yescomplemented
215#872—516no—
216C42×D3—58no—
217C24×C5—32no—
218C23×D5—31no—
219C2×C5×D4—34no—
220C2×C5×D4—64no—
221C22×C4×C5—32no—
222C22×C4×C5—38no—
223C22×C4×C5—68no—
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—38no—
228C2×C22⋊D5—68no—
229C22×Dic5—31no—
230C22×Dic5—31no—
231C22×Dic5—31no—
232C22×Dic5C22×D312yes—
233C22×Dic5C22×D312yes—
234C2×C4×D5—34no—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—64no—
238C2×C4×D5—64no—
239C2×C4×D5—64no—
240C2×Dic10—24no—
241C2×Dic10C22×D314yes—
242C5×C4⋊C4—34no—
243C5×C22⋊C4—38no—
244C42×C5C22×D314yes—
245C22⋊Dic5—38no—
246C22⋊Dic5—38no—
247C22⋊Dic5—38no—
248#685—38no—
249C4⋊Dic5—38no—
250C4⋊Dic5—38no—
251C4⋊Dic5C22×D314yes—
252#683—38no—
253#683C22×D318yes—
254C4×Dic5—34no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5C22×D318yes—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—151no—
265C2×C4×Q8—51no—
266C2×C4×D4—31no—
267C2×C4×D4—152no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2×#4112yes—
273C22×C3×C5C2511yescharacteristic
274C2×D15—28no—
275C2×D15—22no—
276C2×D15—22no—
277C2×D15C2×#4114yes—
278C2×C5×D3—24no—
279C2×C5×D3—24no—
280C2×C5×D3—24no—
281C2×C5×D3—48no—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284C3×C4×C5C2×#4114yes—
285Dic15—22no—
286Dic15—22no—
287Dic15—22no—
288C3×Dic5—24no—
289C3×Dic5—24no—
290C5×Dic3—24no—
291C23×D3—51no—
292C23×D3C22×D512yes—
293C2×C3×Q8—54no—
294C2×C3×Q8—104no—
295C22×C3×C4—52no—
296C22×C3×C4—52no—
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D511yescharacteristic
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—51no—
303C22×Dic3C22×D512yes—
304C2×D12—24no—
305C2×D12—58no—
306C2×D12—108no—
307C2×D12C22×D514yes—
308C2×C4×D3—28no—
309C2×C4×D3—54no—
310C2×C4×D3—54no—
311C2×C4×D3—54no—
312C2×C4×D3—104no—
313C2×C4×D3—104no—
314C2×C4×D3—104no—
315C2×C4×D3C22×D518yes—
316C3×C4⋊C4—58no—
317C3×C4⋊C4—54no—
318C3×C42—58no—
319C3×C42C22×D514yes—
320(C2×D3)⋊C4—58no—
321(C2×D3)⋊C4—58no—
322(C2×D3)⋊C4—58no—
323(C2×D3)⋊C4—58no—
324(C2×D3)⋊C4C22×D518yes—
325C4⋊Dic3—58no—
326C4⋊Dic3C22×D514yes—
327Dic3⋊C4—58no—
328Dic3⋊C4—58no—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C23×C5—34no—
333C23×C5—64no—
334C23×C5—64no—
335C23×C5—64no—
336C23×C5C23×D311yescharacteristic
337C22×D5—34no—
338C22×D5—32no—
339C22×D5—62no—
340C22×D5—62no—
341C5×D4—68no—
342C2×C4×C5—22no—
343C2×C4×C5—34no—
344C2×C4×C5—64no—
345C2×C4×C5—616no—
346C2×C4×C5#23514yes—
347C2×C4×C5#23914yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D312yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5—616no—
352C2×Dic5—24no—
353C2×Dic5—24no—
354C2×Dic5—32no—
355C2×Dic5—32no—
356C2×Dic5—32no—
357C2×Dic5—62no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5C23×D314yes—
361C2×Dic5C23×D314yes—
362C4×D5—68no—
363C4×D5—68no—
364C4×D5—68no—
365Dic10—28no—
366C22×Q8—51no—
367C22×D4—31no—
368C22×D4—152no—
369C23×C4—32no—
370C23×C4—151no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—58no—
380C4×D4—38no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—52no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—52no—
395C2×C42—151no—
396C2×C42—151no—
397C2×C42—151no—
398C2×C42—158no—
399C2×C42D3×D511yescharacteristic
400C2×C3×C5#52914yescomplemented
401C2×C3×C5C22×#4111yescharacteristic
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404D15—24no—
405C5×D3—44no—
406C23×C3C23×D511yescharacteristic
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—54no—
411C22×D3—52no—
412C22×D3—102no—
413C22×D3—102no—
414C22×D3C23×D514yes—
415C3×Q8—108no—
416C2×C3×C4—22no—
417C2×C3×C4—54no—
418C2×C3×C4—54no—
419C2×C3×C4—104no—
420C2×C3×C4—104no—
421C2×C3×C4#70914yes—
422C2×C3×C4#71114yes—
423C2×C3×C4C23×D512yes—
424C2×C3×C4C23×D512yes—
425C2×C3×C4C23×D512yes—
426C2×Dic3—24no—
427C2×Dic3—52no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—102no—
431C2×Dic3—102no—
432C2×Dic3—102no—
433C2×Dic3C23×D514yes—
434D12—28no—
435D12—1016no—
436C4×D3—216no—
437C4×D3—108no—
438C4×D3—108no—
439C4×D3—108no—
440C22×C5—64no—
441C22×C5—64no—
442C22×C5—64no—
443C22×C5—128no—
444C22×C5C2×#23512yes—
445C22×C5C2×#23912yes—
446C22×C5D3×#4112yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—34no—
449C2×D5—62no—
450C2×D5—62no—
451C2×D5—68no—
452C4×C5—22no—
453C4×C5—64no—
454C4×C5C2×#23514yes—
455C4×C5C2×#23914yes—
456Dic5—24no—
457Dic5—24no—
458Dic5—62no—
459Dic5—62no—
460Dic5—62no—
461C24—32no—
462C24—151no—
463C2×Q8—54no—
464C2×Q8—104no—
465C2×D4—34no—
466C2×D4—64no—
467C2×D4—158no—
468C2×D4—308no—
469C22×C4—32no—
470C22×C4—38no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—68no—
474C22×C4—151no—
475C22×C4—151no—
476C22×C4—151no—
477C22×C4—154no—
478C22×C4—154no—
479C22×C4—154no—
480C22×C4—304no—
481C22×C4—304no—
482C22×C4—304no—
483C22×C4C2×D3×D511yescharacteristic
484C22×C4C2×D3×D511yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—54no—
488C4⋊C4—58no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—158no—
492C22⋊C4—38no—
493C22⋊C4—158no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—58no—
498C42—154no—
499C42—154no—
500C42—154no—
501C42C2×D3×D514yes—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3C2×#70912yes—
504C22×C3C2×#71112yes—
505C22×C3D5×#4112yes—
506C22×C3C24×D511yescharacteristic
507C2×D3—24no—
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—48no—
511C2×D3—54no—
512C2×D3—108no—
513C2×D3—102no—
514C2×D3—102no—
515C3×C4—22no—
516C3×C4—104no—
517C3×C4—104no—
518C3×C4C2×#70914yes—
519C3×C4C2×#71114yes—
520Dic3—24no—
521Dic3—102no—
522Dic3—102no—
523Dic3—102no—
524C2×C5—124no—
525C2×C5#558014yescomplemented
526C2×C5C22×#23511yescharacteristic
527C2×C5C22×#23911yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529D5—64no—
530C23—34no—
531C23—64no—
532C23—64no—
533C23—64no—
534C23—154no—
535C23—152no—
536C23—302no—
537C23—302no—
538C23C22×D3×D511yescharacteristic
539Q8—108no—
540D4—68no—
541D4—3016no—
542C2×C4—22no—
543C2×C4—34no—
544C2×C4—54no—
545C2×C4—54no—
546C2×C4—64no—
547C2×C4—616no—
548C2×C4—104no—
549C2×C4—104no—
550C2×C4—152no—
551C2×C4—152no—
552C2×C4—152no—
553C2×C4—308no—
554C2×C4—302no—
555C2×C4—302no—
556C2×C4—302no—
557C2×C4—308no—
558C2×C4—308no—
559C2×C4#676814yes—
560C2×C4#677114yes—
561C2×C4C22×D3×D512yes—
562C2×C4C22×D3×D512yes—
563C2×C4C22×D3×D512yes—
564C2×C3#6589114yescomplemented
565C2×C3C22×#70911yescharacteristic
566C2×C3C22×#71111yescharacteristic
567C2×C3C2×D5×#4111yescharacteristic
568D3—44no—
569D3—104no—
570C5C2×#558011yescharacteristic, complemented, Sylow
571C22—64no—
572C22—64no—
573C22—64no—
574C22—128no—
575C22—154no—
576C22—308no—
577C22—302no—
578C22—302no—
579C22C2×#676812yes—
580C22C2×#677112yes—
581C22#9201612yes—
582C22C23×D3×D511yescharacteristic
583C4—22no—
584C4—64no—
585C4—104no—
586C4—104no—
587C4—302no—
588C4—302no—
589C4—302no—
590C4C2×#676814yes—
591C4C2×#677114yes—
592C3C2×#6589111yescharacteristic, complemented, Sylow
593C2—124no—
594C2—304no—
595C2#1175250214yesdirect product factor
596C2C22×#676811yescharacteristic
597C2C22×#677111yescharacteristic
598C2C2×#9201611yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91466C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×D15C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×C4×Dic10C2semidirect
5. C2×C4×#1203C2semidirect
6. C2×#91390C2semidirect
7. C2×#91384C2semidirect
8. C2×#91371C2semidirect
9. C2×#91370C2semidirect
10. C2×#91367C2semidirect
11. C2×#91355C2semidirect
12. #11752502C2direct (N × H)
25. C42×D15C22semidirect
28. C4×C5×D12C22semidirect
32. C3×C4×Dic10C22semidirect
41. C4×#1203C22semidirect
42. #91390C22semidirect
43. #91384C22semidirect
44. #91371C22semidirect
45. #91370C22semidirect
46. #91367C22semidirect
47. #91355C22semidirect
60. C2×C4×Dic10D3semidirect
111. C2×C4×D12D5semidirect
147. C4×Dic10C2×D3semidirect
214. C4×D12C2×D5semidirect
400. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5580semidirect
564. C2×C3#65891semidirect
570. C5C2×#5580semidirect
592. C3C2×#65891semidirect
595. C2#11752502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×D152
C2×C4×C5×D122
C2×C3×C4×Dic102
C2×#914662
C2×C4×#12032
C2×#913902
C2×#913842
C2×#913712
C2×#913702
C2×#913672
C2×#913552
#117525022
C2×#658913
C2×#55805