Finite Group Databasebeta

← C2×#11752593 #14484743

Subgroups — C2×#11752593 #14484743

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91764C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×#91451C211yesmaximal, characteristic
5C2×#91446C212yesmaximal, complemented
6C2×#91438C212yesmaximal, complemented
7C2×#91418C211yesmaximal, characteristic, complemented
8C2×#91373C211yesmaximal, characteristic, complemented
9C2×#91351C212yesmaximal, complemented
10C2×#91333C211yesmaximal, characteristic, complemented
11C2×#91326C212yesmaximal, complemented
12#11752593C2116yesmaximal, direct product factor
13C2×#65893—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3C2212yes—
18C22×C3×Dic10C2211yescharacteristic
19C22×#1203C2212yes—
20C22×#1203C2212yes—
21C22×#1200C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6714C2212yes—
24C2×#6714C2212yes—
25#91764C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C4×C5×D12C2218yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C3×C4×Dic10C2218yescomplemented
35C2×#6669C2212yes—
36C2×#6667C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91451C2218yes—
41#91446C22116yescomplemented
42#91438C22116yescomplemented
43#91418C2218yescomplemented
44#91373C2218yescomplemented
45#91351C22116yescomplemented
46#91333C2218yescomplemented
47#91326C22116yescomplemented
48C2×#5585—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4086—31no—
51C2×#4082—31no—
52C2×#4075—32no—
53C2×C4×C22⋊D5—32no—
54#65893—316no—
55C2×#4039—31no—
56C2×#4033—31no—
57C2×#4031—32no—
58C2×#4029—32no—
59C2×#4021—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×D15C2312yes—
62C23×C5×D3C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C2×D60—24no—
68C2×D60C2314yes—
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C22×C5×Dic3C2312yes—
72C2×C5×D12—24no—
73C2×C5×D12C2314yes—
74C2×C4×C5×D3—44no—
75C2×C4×C5×D3C2318yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C2×C3×Dic10—24no—
81C2×C3×Dic10C2314yes—
82C2×#1203—28no—
83C2×#1203—44no—
84C2×#1203C2318yes—
85C2×#1203C2318yes—
86C2×#1200—44no—
87C2×#1200C2318yes—
88C3×C42×C5C2314yes—
89#6714C2318yes—
90#6714C2318yes—
91C5×(C2×D3)⋊C4C2318yes—
92C5×C4⋊Dic3C2314yes—
93C3×C4⋊Dic5C2314yes—
94C3×#683C2314yes—
95C3×#683C2314yes—
96C3×C4×Dic5C2314yes—
97C3×C4×Dic5C2314yes—
98#6669C2318yes—
99#6667C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×C4×Q8—51no—
104C2×#947—52no—
105#5585—516no—
106C2×#894—52no—
107C2×#894—52no—
108C2×#893—52no—
109C2×#875—51no—
110C2×#875—51no—
111C2×#874—51no—
112C2×C4×D12—51no—
113C2×C4×D12D511yescharacteristic, complemented
114C2×C4×Dic6—51no—
115C22×C5×D4—31no—
116C23×C4×C5—32no—
117C22×C22⋊D5—32no—
118C22×C22⋊D5—32no—
119C22×D20—31no—
120C22×C4×D5—32no—
121C22×Dic10—31no—
122C22×Dic10C2×D311yescharacteristic
123C4×C5×D4—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—32no—
126C2×C42×C5C2×D311yescharacteristic
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—32no—
129#4086—38no—
130#4082—38no—
131#4075—316no—
132C4×C22⋊D5—316no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136C2×C4⋊Dic5C2×D311yescharacteristic
137C2×#683—32no—
138C2×#683C2×D311yescharacteristic
139C2×#683C2×D311yescharacteristic
140C2×C4×Dic5—32no—
141C2×C4×Dic5C2×D311yescharacteristic
142C2×C4×Dic5C2×D311yescharacteristic
143#4039—38no—
144#4033—38no—
145#4031—316no—
146#4029—316no—
147#4021—38no—
148C4×Dic10C2×D318yescomplemented
149C2×#559—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×D15—24no—
152C22×D15—24no—
153C22×D15—24no—
154C22×D15C2414yes—
155C22×C5×D3—24no—
156C22×C5×D3—24no—
157C22×C5×D3—24no—
158C22×C5×D3C2414yes—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5#4114yes—
162C2×C3×C4×C5C2412yes—
163C2×C3×C4×C5C2412yes—
164C2×C3×C4×C5C2412yes—
165C2×Dic15—24no—
166C2×Dic15C2414yes—
167D60—28no—
168Dic30—28no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3C2414yes—
171C5×D12—28no—
172C4×C5×D3—48no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5#4114yes—
177C2×C3×Dic5C2412yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2412yes—
180C2×C3×Dic5C2412yes—
181C3×Dic10—28no—
182#1203—216no—
183#1203—48no—
184#1200—48no—
185C22×C3×Q8—51no—
186C22×D12—52no—
187C22×D12—51no—
188C22×D12—52no—
189C22×D12C2×D511yescharacteristic
190C22×C4×D3—52no—
191C22×C4×D3C2×D512yes—
192C22×Dic6—51no—
193C3×C4×Q8—58no—
194C2×C3×C4⋊C4—51no—
195C2×C3×C4⋊C4—51no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C42—51no—
198C2×C3×C42—51no—
199C2×C3×C42C2×D511yescharacteristic
200#947—516no—
201C2×(C2×D3)⋊C4—52no—
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4C2×D512yes—
207C2×C4⋊Dic3C2×D511yescharacteristic
208C2×Dic3⋊C4—52no—
209C2×C4×Dic3—52no—
210#894—516no—
211#894—516no—
212#893—516no—
213#875—58no—
214#875—58no—
215#874—58no—
216C4×D12—58no—
217C4×D12C2×D518yescomplemented
218C4×Dic6—58no—
219C24×C5—32no—
220C23×D5—32no—
221C2×C5×D4—34no—
222C2×C5×D4—64no—
223C22×C4×C5—32no—
224C22×C4×C5—38no—
225C22×C4×C5—124no—
226C22×C4×C5C22×D311yescharacteristic
227C22×C4×C5C22×D311yescharacteristic
228C22×C4×C5C22×D311yescharacteristic
229C2×C22⋊D5—38no—
230C2×C22⋊D5—38no—
231C2×C22⋊D5—68no—
232C2×C22⋊D5—124no—
233C22×Dic5—32no—
234C22×Dic5C22×D311yescharacteristic
235C22×Dic5C22×D311yescharacteristic
236C22×Dic5C22×D311yescharacteristic
237C22×Dic5C22×D311yescharacteristic
238C2×D20—34no—
239C2×D20—64no—
240C2×C4×D5—38no—
241C2×C4×D5—124no—
242C2×Dic10—24no—
243C2×Dic10—34no—
244C2×Dic10—64no—
245C2×Dic10C22×D314yes—
246C5×C4⋊C4—34no—
247C5×C22⋊C4—38no—
248C42×C5C22×D314yes—
249C22⋊Dic5—38no—
250C22⋊Dic5—38no—
251#685—38no—
252#685—38no—
253#685—38no—
254C4⋊Dic5C22×D314yes—
255#683—38no—
256#683C22×D314yes—
257#683C22×D314yes—
258C4×Dic5—38no—
259C4×Dic5C22×D314yes—
260C4×Dic5C22×D314yes—
261#559—1516no—
262C2×#127—151no—
263C2×#124—151no—
264C2×#124—152no—
265C2×#124—151no—
266C2×#123—152no—
267C2×#123—152no—
268C2×C4×Q8—51no—
269C2×C4×Q8—151no—
270C2×C4×D4—31no—
271C2×C4×D4—151no—
272C2×C4×D4—152no—
273C22×C3×C5C2×#4112yes—
274C22×C3×C5C2×#4112yes—
275C22×C3×C5H(5,𝔽2)12yes—
276C22×C3×C5C2511yescharacteristic
277C2×D15—24no—
278C2×D15—24no—
279C2×D15—24no—
280C2×D15—48no—
281C2×C5×D3—24no—
282C2×C5×D3—24no—
283C2×C5×D3—24no—
284C2×C5×D3—48no—
285C3×C4×C5—22no—
286C3×C4×C5—22no—
287C3×C4×C5C2×#4114yes—
288Dic15—24no—
289C3×Dic5—22no—
290C3×Dic5—22no—
291C3×Dic5—22no—
292C3×Dic5C2×#4114yes—
293C5×Dic3—24no—
294C23×D3—52no—
295C23×D3C22×D512yes—
296C2×C3×Q8—54no—
297C2×C3×Q8—104no—
298C22×C3×C4—51no—
299C22×C3×C4—51no—
300C22×C3×C4—51no—
301C22×C3×C4—51no—
302C22×C3×C4C22×D511yescharacteristic
303C22×C3×C4C22×D511yescharacteristic
304C22×C3×C4C22×D511yescharacteristic
305C22×Dic3—52no—
306C22×Dic3C22×D512yes—
307C2×D12—24no—
308C2×D12—58no—
309C2×D12—54no—
310C2×D12—58no—
311C2×D12—108no—
312C2×D12—104no—
313C2×D12—204no—
314C2×D12C22×D514yes—
315C2×C4×D3—44no—
316C2×C4×D3—58no—
317C2×C4×D3—204no—
318C2×C4×D3C22×D518yes—
319C2×Dic6—54no—
320C2×Dic6—104no—
321C3×C4⋊C4—54no—
322C3×C4⋊C4—54no—
323C3×C4⋊C4—54no—
324C3×C42—54no—
325C3×C42—54no—
326C3×C42C22×D514yes—
327(C2×D3)⋊C4—58no—
328(C2×D3)⋊C4—58no—
329(C2×D3)⋊C4—58no—
330(C2×D3)⋊C4—58no—
331(C2×D3)⋊C4—58no—
332(C2×D3)⋊C4C22×D518yes—
333C4⋊Dic3C22×D514yes—
334Dic3⋊C4—58no—
335C4×Dic3—58no—
336C23×C5—34no—
337C23×C5—64no—
338C23×C5—64no—
339C23×C5—64no—
340C23×C5C23×D311yescharacteristic
341C22×D5—34no—
342C22×D5—64no—
343C22×D5—64no—
344C22×D5—64no—
345C5×D4—68no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—34no—
349C2×C4×C5—64no—
350C2×C4×C5—128no—
351C2×C4×C5#23914yes—
352C2×C4×C5C23×D312yes—
353C2×C4×C5C23×D312yes—
354C2×C4×C5C23×D312yes—
355C22⋊D5—616no—
356C22⋊D5—128no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—34no—
361C2×Dic5—64no—
362C2×Dic5#23514yes—
363C2×Dic5C23×D312yes—
364C2×Dic5C23×D312yes—
365C2×Dic5C23×D312yes—
366C2×Dic5C23×D312yes—
367D20—68no—
368C4×D5—128no—
369Dic10—28no—
370Dic10—68no—
371C22×Q8—51no—
372C22×Q8—151no—
373C22×D4—31no—
374C22×D4—152no—
375C22×D4—152no—
376C22×D4—151no—
377C23×C4—32no—
378C23×C4—152no—
379#127—158no—
380#124—158no—
381#124—1516no—
382#124—158no—
383#123—1516no—
384#123—1516no—
385C4×Q8—58no—
386C4×Q8—158no—
387C4×D4—38no—
388C4×D4—158no—
389C4×D4—1516no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—51no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—152no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—152no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C42—51no—
402C2×C42—51no—
403C2×C42—152no—
404C2×C42D3×D511yescharacteristic
405C2×C3×C5#55914yescomplemented
406C2×C3×C5C22×#4111yescharacteristic
407C2×C3×C5C22×#4111yescharacteristic
408C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
409D15—44no—
410C5×D3—44no—
411C23×C3C23×D511yescharacteristic
412C22×D3—24no—
413C22×D3—24no—
414C22×D3—24no—
415C22×D3—54no—
416C22×D3—104no—
417C22×D3—104no—
418C22×D3—104no—
419C22×D3C23×D514yes—
420C3×Q8—108no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—54no—
424C2×C3×C4—52no—
425C2×C3×C4—52no—
426C2×C3×C4—52no—
427C2×C3×C4—52no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4#70914yes—
432C2×C3×C4C23×D512yes—
433C2×C3×C4C23×D512yes—
434C2×C3×C4C23×D512yes—
435C2×Dic3—24no—
436C2×Dic3—54no—
437C2×Dic3—104no—
438C2×Dic3C23×D514yes—
439D12—28no—
440D12—1016no—
441D12—108no—
442D12—208no—
443C4×D3—48no—
444C4×D3—208no—
445Dic6—108no—
446C22×C5—64no—
447C22×C5—64no—
448C22×C5—64no—
449C22×C5—128no—
450C22×C5C2×#23512yes—
451C22×C5C2×#23912yes—
452C22×C5#100912yes—
453C22×C5C24×D311yescharacteristic
454C2×D5—64no—
455C2×D5—64no—
456C2×D5—64no—
457C2×D5—128no—
458C4×C5—22no—
459C4×C5—22no—
460C4×C5—64no—
461C4×C5C2×#23914yes—
462Dic5—22no—
463Dic5—22no—
464Dic5—22no—
465Dic5—64no—
466Dic5C2×#23514yes—
467C24—32no—
468C24—152no—
469C2×Q8—54no—
470C2×Q8—104no—
471C2×Q8—154no—
472C2×Q8—304no—
473C2×D4—34no—
474C2×D4—64no—
475C2×D4—158no—
476C2×D4—158no—
477C2×D4—154no—
478C2×D4—308no—
479C2×D4—304no—
480C2×D4—604no—
481C22×C4—32no—
482C22×C4—38no—
483C22×C4—51no—
484C22×C4—51no—
485C22×C4—51no—
486C22×C4—51no—
487C22×C4—124no—
488C22×C4—158no—
489C22×C4—152no—
490C22×C4—604no—
491C22×C4C2×D3×D511yescharacteristic
492C22×C4C2×D3×D511yescharacteristic
493C22×C4C2×D3×D511yescharacteristic
494C4⋊C4—34no—
495C4⋊C4—54no—
496C4⋊C4—54no—
497C4⋊C4—54no—
498C4⋊C4—158no—
499C22⋊C4—38no—
500C22⋊C4—158no—
501C22⋊C4—158no—
502C22⋊C4—158no—
503C22⋊C4—158no—
504C22⋊C4—158no—
505C42—54no—
506C42—54no—
507C42—158no—
508C42C2×D3×D514yes—
509C3×C5C2×#55911yescharacteristic, complemented, Hall
510C22×C3C2×#70912yes—
511C22×C3#414412yes—
512C22×C3D5×#4112yes—
513C22×C3C24×D511yescharacteristic
514C2×D3—24no—
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—48no—
518C2×D3—104no—
519C2×D3—104no—
520C2×D3—104no—
521C2×D3—208no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—54no—
525C3×C4—102no—
526C3×C4—102no—
527C3×C4—102no—
528C3×C4C2×#70914yes—
529Dic3—24no—
530Dic3—104no—
531C2×C5—124no—
532C2×C5#558514yescomplemented
533C2×C5C22×#23511yescharacteristic
534C2×C5C22×#23911yescharacteristic
535C2×C5C2×#100911yescharacteristic
536D5—124no—
537C23—34no—
538C23—64no—
539C23—64no—
540C23—64no—
541C23—154no—
542C23—304no—
543C23—304no—
544C23—304no—
545C23C22×D3×D511yescharacteristic
546Q8—108no—
547Q8—308no—
548D4—68no—
549D4—3016no—
550D4—308no—
551D4—608no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—34no—
555C2×C4—54no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—64no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—128no—
565C2×C4—154no—
566C2×C4—304no—
567C2×C4—608no—
568C2×C4#676914yes—
569C2×C4C22×D3×D512yes—
570C2×C4C22×D3×D512yes—
571C2×C4C22×D3×D512yes—
572C2×C3#6589314yescomplemented
573C2×C3C22×#70911yescharacteristic
574C2×C3C2×#414411yescharacteristic
575C2×C3C2×D5×#4111yescharacteristic
576D3—44no—
577D3—204no—
578C5C2×#558511yescharacteristic, complemented, Sylow
579C22—64no—
580C22—64no—
581C22—64no—
582C22—128no—
583C22—304no—
584C22—304no—
585C22—304no—
586C22—608no—
587C22C2×#676912yes—
588C22D5×#23512yes—
589C22#9201812yes—
590C22C23×D3×D511yescharacteristic
591C4—22no—
592C4—22no—
593C4—54no—
594C4—64no—
595C4—102no—
596C4—102no—
597C4—102no—
598C4—304no—
599C4C2×#676914yes—
600C3C2×#6589311yescharacteristic, complemented, Sylow
601C2—124no—
602C2—604no—
603C2#1175259314yesdirect product factor
604C2C22×#676911yescharacteristic
605C2C2×D5×#23511yescharacteristic
606C2C2×#9201811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91451C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91764C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×C4×Dic10C2semidirect
5. C2×#91446C2semidirect
6. C2×#91438C2semidirect
7. C2×#91418C2semidirect
8. C2×#91373C2semidirect
9. C2×#91351C2semidirect
10. C2×#91333C2semidirect
11. C2×#91326C2semidirect
12. #11752593C2direct (N × H)
25. #91764C22semidirect
28. C4×C5×D12C22semidirect
34. C3×C4×Dic10C22semidirect
41. #91446C22semidirect
42. #91438C22semidirect
43. #91418C22semidirect
44. #91373C22semidirect
45. #91351C22semidirect
46. #91333C22semidirect
47. #91326C22semidirect
60. C2×C4×Dic10D3semidirect
113. C2×C4×D12D5semidirect
148. C4×Dic10C2×D3semidirect
217. C4×D12C2×D5semidirect
405. C2×C3×C5#559semidirect
509. C3×C5C2×#559semidirect
532. C2×C5#5585semidirect
572. C2×C3#65893semidirect
578. C5C2×#5585semidirect
600. C3C2×#65893semidirect
603. C2#11752593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917642
C2×C4×C5×D122
C2×C3×C4×Dic102
C2×#914512
C2×#914462
C2×#914382
C2×#914182
C2×#913732
C2×#913512
C2×#913332
C2×#913262
#117525932
C2×#658933
C2×#55855