Finite Group Databasebeta

← C2×#11752617 #14483721

Subgroups — C2×#11752617 #14483721

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D60C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic, complemented
3C2×C3×#4016C211yesmaximal, characteristic, complemented
4C2×#91460C211yesmaximal, characteristic, complemented
5C2×#91460C211yesmaximal, characteristic, complemented
6C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
7C2×#91416C212yesmaximal, complemented
8C2×#91406C212yesmaximal, complemented
9C2×#91355C212yesmaximal, complemented
10C2×#91338C211yesmaximal, characteristic, complemented
11C2×#91337C212yesmaximal, complemented
12#11752617C2116yesmaximal, direct product factor
13C2×#65899—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×#1203C2212yes—
20C22×#1203C2212yes—
21C22×D3×Dic5C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6714C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C4×D60C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C4×C5×D12C2218yescomplemented
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×#683C2212yes—
33C2×C3×#683C2212yes—
34C3×#4016C2218yescomplemented
35C2×Dic3⋊Dic5C2212yes—
36C2×#6667C2212yes—
37C2×#6667C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91460C2218yescomplemented
41#91460C2218yescomplemented
42D3×C4⋊Dic5C2218yescomplemented
43#91416C22116yescomplemented
44#91406C22116yescomplemented
45#91355C22116yescomplemented
46#91338C2218yescomplemented
47#91337C22116yescomplemented
48C2×#5695—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4085—32no—
51C2×#4076—31no—
52C2×#4076—31no—
53C2×#4072—31no—
54C22×C4⋊Dic5—31no—
55#65899—316no—
56C2×#4044—32no—
57C2×#4029—32no—
58C2×#4027—32no—
59C2×C4×D20—31no—
60C2×#4016D311yescharacteristic, complemented
61C23×D15C2312yes—
62C23×C5×D3C2311yescharacteristic
63C23×C5×D3C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C2×D60—24no—
69C2×D60C2314yes—
70C2×C4×D15—44no—
71C2×C4×D15C2318yes—
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2311yescharacteristic
74C2×C5×D12—24no—
75C2×C5×D12C2314yes—
76C2×C4×C5×D3—24no—
77C2×C4×C5×D3—24no—
78C2×C4×C5×D3C2314yes—
79C2×C4×C5×D3C2314yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C2×#1203—28no—
83C2×#1203—44no—
84C2×#1203C2318yes—
85C2×#1203C2318yes—
86C2×D3×Dic5—44no—
87C2×D3×Dic5C2318yes—
88C3×C42×C5C2314yes—
89#6714C2318yes—
90C4⋊Dic15C2314yes—
91C5×(C2×D3)⋊C4C2314yes—
92C5×(C2×D3)⋊C4C2314yes—
93C5×C4⋊Dic3C2314yes—
94C3×C4⋊Dic5C2314yes—
95C3×C4⋊Dic5C2314yes—
96C3×#683C2318yes—
97C3×#683C2318yes—
98Dic3⋊Dic5C2318yes—
99#6667C2318yes—
100#6667C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#125—51no—
104#5695—516no—
105C2×#898—52no—
106C2×#895—52no—
107C2×#895—51no—
108C2×#895—51no—
109C2×#894—52no—
110C2×#893—52no—
111C2×#892—51no—
112C2×D3×C4⋊C4—51no—
113C2×C4×D12—51no—
114C2×C4×D12D511yescharacteristic, complemented
115C22×C5×D4—31no—
116C23×C4×C5—31no—
117C23×C4×C5—31no—
118C22×C22⋊D5—32no—
119C22×C22⋊D5—32no—
120C23×Dic5—32no—
121C22×D20—31no—
122C22×C4×D5—32no—
123C4×C5×D4—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—31no—
126C2×C5×C22⋊C4—31no—
127C2×C42×C5C2×D311yescharacteristic
128C2×C22⋊Dic5—32no—
129#4085—316no—
130#4076—38no—
131#4076—38no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135#4072—38no—
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—32no—
138C2×C4⋊Dic5—38no—
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×C4⋊Dic5C2×D311yescharacteristic
141C2×#683C2×D312yes—
142C2×#683C2×D312yes—
143C2×C4×Dic5—32no—
144#4044—316no—
145#4029—316no—
146#4027—316no—
147C4×D20—38no—
148#4016C2×D318yescomplemented
149C2×#553—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×D15—24no—
152C22×D15—24no—
153C22×D15—24no—
154C22×D15C2414yes—
155C22×C5×D3—22no—
156C22×C5×D3—22no—
157C22×C5×D3—22no—
158C22×C5×D3—22no—
159C22×C5×D3—22no—
160C22×C5×D3#4114yes—
161C22×C5×D3C2412yes—
162C22×C5×D3C2412yes—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168C2×C3×C4×C5C2412yes—
169C2×Dic15—24no—
170C2×Dic15C2414yes—
171D60—28no—
172C4×D15—48no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2412yes—
177C5×D12—28no—
178C4×C5×D3—28no—
179C4×C5×D3—28no—
180C2×C3×Dic5—24no—
181C2×C3×Dic5—24no—
182C2×C3×Dic5C2414yes—
183C2×C3×Dic5C2414yes—
184#1203—216no—
185#1203—48no—
186D3×Dic5—48no—
187C22×D12—52no—
188C22×D12—51no—
189C22×D12—52no—
190C22×D12C2×D511yescharacteristic
191C22×C4×D3—52no—
192C22×C4×D3—52no—
193C22×C4×D3C2×D511yescharacteristic
194C22×C4×D3C2×D511yescharacteristic
195C3×#125—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C4⋊C4—51no—
198C2×C3×C4⋊C4—52no—
199C2×C3×C4⋊C4—52no—
200C2×C3×C42C2×D511yescharacteristic
201C2×(C2×D3)⋊C4—52no—
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4C2×D511yescharacteristic
206C2×(C2×D3)⋊C4C2×D511yescharacteristic
207C2×C4⋊Dic3—51no—
208C2×C4⋊Dic3C2×D511yescharacteristic
209C2×Dic3⋊C4—52no—
210C2×C4×Dic3—52no—
211#898—516no—
212#895—516no—
213#895—58no—
214#895—58no—
215#894—516no—
216#893—516no—
217#892—58no—
218D3×C4⋊C4—58no—
219C4×D12—58no—
220C4×D12C2×D518yescomplemented
221C24×C5—31no—
222C24×C5—31no—
223C23×D5—32no—
224C2×C5×D4—34no—
225C2×C5×D4—64no—
226C22×C4×C5—31no—
227C22×C4×C5—31no—
228C22×C4×C5—34no—
229C22×C4×C5—34no—
230C22×C4×C5—64no—
231C22×C4×C5—64no—
232C22×C4×C5C22×D311yescharacteristic
233C22×C4×C5C22×D311yescharacteristic
234C22×C4×C5C22×D311yescharacteristic
235C2×C22⋊D5—38no—
236C2×C22⋊D5—38no—
237C2×C22⋊D5—68no—
238C2×C22⋊D5—124no—
239C22×Dic5—32no—
240C22×Dic5—38no—
241C22×Dic5—124no—
242C22×Dic5C22×D312yes—
243C22×Dic5C22×D312yes—
244C2×D20—34no—
245C2×D20—64no—
246C2×C4×D5—38no—
247C2×C4×D5—124no—
248C5×C4⋊C4—34no—
249C5×C22⋊C4—34no—
250C5×C22⋊C4—34no—
251C42×C5C22×D314yes—
252C22⋊Dic5—38no—
253#685—38no—
254#685—38no—
255#685—38no—
256C4⋊Dic5—34no—
257C4⋊Dic5—38no—
258C4⋊Dic5C22×D314yes—
259C4⋊Dic5C22×D314yes—
260#683C22×D318yes—
261#683C22×D318yes—
262C4×Dic5—38no—
263#553—1516no—
264C2×#126—152no—
265C2×#125—51no—
266C2×#123—152no—
267C2×#121—151no—
268C2×#121—151no—
269C2×#121—152no—
270C2×C4×D4—31no—
271C2×C4×D4—152no—
272C2×C4×D4—151no—
273C2×#117—151no—
274C22×C4⋊C4—151no—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5H(5,𝔽2)12yes—
278C22×C3×C5C2511yescharacteristic
279C2×D15—24no—
280C2×D15—24no—
281C2×D15—24no—
282C2×D15—48no—
283C2×C5×D3—28no—
284C2×C5×D3—22no—
285C2×C5×D3—22no—
286C2×C5×D3—22no—
287C2×C5×D3—22no—
288C2×C5×D3—22no—
289C2×C5×D3—44no—
290C2×C5×D3C2×#4114yes—
291C3×C4×C5—22no—
292C3×C4×C5—22no—
293C3×C4×C5C2×#4114yes—
294Dic15—24no—
295C3×Dic5—24no—
296C3×Dic5—24no—
297C5×Dic3—22no—
298C5×Dic3—22no—
299C23×D3—52no—
300C23×D3C22×D511yescharacteristic
301C23×D3C22×D511yescharacteristic
302C22×C3×C4—52no—
303C22×C3×C4—52no—
304C22×C3×C4C22×D511yescharacteristic
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D511yescharacteristic
307C22×Dic3—52no—
308C22×Dic3C22×D511yescharacteristic
309C22×Dic3C22×D511yescharacteristic
310C2×D12—24no—
311C2×D12—58no—
312C2×D12—54no—
313C2×D12—58no—
314C2×D12—108no—
315C2×D12—104no—
316C2×D12—204no—
317C2×D12C22×D514yes—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—58no—
321C2×C4×D3—58no—
322C2×C4×D3—204no—
323C2×C4×D3—204no—
324C2×C4×D3C22×D514yes—
325C2×C4×D3C22×D514yes—
326C3×C4⋊C4—58no—
327C3×C4⋊C4—58no—
328C3×C4⋊C4—54no—
329C3×C4⋊C4—54no—
330C3×C42C22×D514yes—
331(C2×D3)⋊C4—58no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—58no—
334(C2×D3)⋊C4—58no—
335(C2×D3)⋊C4C22×D514yes—
336(C2×D3)⋊C4C22×D514yes—
337C4⋊Dic3—54no—
338C4⋊Dic3C22×D514yes—
339Dic3⋊C4—58no—
340C4×Dic3—58no—
341C23×C5—34no—
342C23×C5—32no—
343C23×C5—32no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—62no—
349C23×C5C23×D311yescharacteristic
350C22×D5—34no—
351C22×D5—64no—
352C22×D5—64no—
353C22×D5—64no—
354C5×D4—68no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—32no—
358C2×C4×C5—32no—
359C2×C4×C5—62no—
360C2×C4×C5—62no—
361C2×C4×C5—68no—
362C2×C4×C5—68no—
363C2×C4×C5#23914yes—
364C2×C4×C5C23×D312yes—
365C2×C4×C5C23×D312yes—
366C2×C4×C5C23×D312yes—
367C22⋊D5—616no—
368C22⋊D5—128no—
369C2×Dic5—24no—
370C2×Dic5—24no—
371C2×Dic5—34no—
372C2×Dic5—64no—
373C2×Dic5—128no—
374C2×Dic5C23×D314yes—
375C2×Dic5C23×D314yes—
376D20—68no—
377C4×D5—128no—
378C22×D4—31no—
379C22×D4—152no—
380C22×D4—152no—
381C22×D4—151no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—152no—
385C23×C4—152no—
386#126—1516no—
387#125—58no—
388#123—1516no—
389#121—158no—
390#121—158no—
391#121—1516no—
392C4×D4—38no—
393C4×D4—1516no—
394C4×D4—158no—
395#117—158no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—51no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—52no—
400C2×C4⋊C4—52no—
401C2×C4⋊C4—158no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—151no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—152no—
409C2×C22⋊C4—152no—
410C2×C42—152no—
411C2×C42D3×D511yescharacteristic
412C2×C3×C5#55314yescomplemented
413C2×C3×C5C22×#4111yescharacteristic
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
416D15—44no—
417C5×D3—24no—
418C5×D3—42no—
419C23×C3C23×D511yescharacteristic
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—54no—
426C22×D3—104no—
427C22×D3—104no—
428C22×D3—104no—
429C22×D3#70914yes—
430C22×D3C23×D512yes—
431C22×D3C23×D512yes—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—54no—
435C2×C3×C4—54no—
436C2×C3×C4—104no—
437C2×C3×C4—104no—
438C2×C3×C4#71114yes—
439C2×C3×C4C23×D512yes—
440C2×C3×C4C23×D512yes—
441C2×C3×C4C23×D512yes—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—54no—
445C2×Dic3—104no—
446C2×Dic3C23×D512yes—
447C2×Dic3C23×D512yes—
448D12—28no—
449D12—1016no—
450D12—108no—
451D12—208no—
452C4×D3—28no—
453C4×D3—28no—
454C4×D3—208no—
455C4×D3—208no—
456C22×C5—34no—
457C22×C5—68no—
458C22×C5—62no—
459C22×C5—62no—
460C22×C5—62no—
461C22×C5—62no—
462C22×C5—62no—
463C22×C5—124no—
464C22×C5C2×#23912yes—
465C22×C5D3×#4112yes—
466C22×C5#100912yes—
467C22×C5C24×D311yescharacteristic
468C2×D5—64no—
469C2×D5—64no—
470C2×D5—64no—
471C2×D5—128no—
472C4×C5—22no—
473C4×C5—22no—
474C4×C5—62no—
475C4×C5—62no—
476C4×C5C2×#23914yes—
477Dic5—24no—
478Dic5—24no—
479Dic5—64no—
480C24—31no—
481C24—31no—
482C24—152no—
483C2×D4—34no—
484C2×D4—64no—
485C2×D4—158no—
486C2×D4—158no—
487C2×D4—154no—
488C2×D4—308no—
489C2×D4—304no—
490C2×D4—604no—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—34no—
494C22×C4—34no—
495C22×C4—52no—
496C22×C4—52no—
497C22×C4—64no—
498C22×C4—64no—
499C22×C4—158no—
500C22×C4—152no—
501C22×C4—158no—
502C22×C4—604no—
503C22×C4—604no—
504C22×C4C2×D3×D511yescharacteristic
505C22×C4C2×D3×D511yescharacteristic
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—54no—
509C4⋊C4—54no—
510C4⋊C4—58no—
511C4⋊C4—58no—
512C4⋊C4—158no—
513C4⋊C4—154no—
514C22⋊C4—34no—
515C22⋊C4—34no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—158no—
519C22⋊C4—158no—
520C42—158no—
521C42C2×D3×D514yes—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3C2×#70912yes—
524C22×C3C2×#71112yes—
525C22×C3#414912yes—
526C22×C3C24×D511yescharacteristic
527C2×D3—28no—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—44no—
534C2×D3—104no—
535C2×D3—104no—
536C2×D3—104no—
537C2×D3—208no—
538C2×D3C2×#70914yes—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—104no—
542C3×C4—104no—
543C3×C4C2×#71114yes—
544Dic3—22no—
545Dic3—22no—
546Dic3—104no—
547C2×C5—64no—
548C2×C5—122no—
549C2×C5#569514yescomplemented
550C2×C5C22×#23911yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552C2×C5C2×#100911yescharacteristic
553D5—124no—
554C23—34no—
555C23—32no—
556C23—32no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23—154no—
563C23—304no—
564C23—304no—
565C23—304no—
566C23C22×D3×D511yescharacteristic
567D4—68no—
568D4—3016no—
569D4—308no—
570D4—608no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—54no—
576C2×C4—54no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—68no—
580C2×C4—68no—
581C2×C4—104no—
582C2×C4—104no—
583C2×C4—154no—
584C2×C4—304no—
585C2×C4—608no—
586C2×C4—608no—
587C2×C4#676814yes—
588C2×C4C22×D3×D512yes—
589C2×C4C22×D3×D512yes—
590C2×C4C22×D3×D512yes—
591C2×C3#6589914yescomplemented
592C2×C3C22×#70911yescharacteristic
593C2×C3C22×#71111yescharacteristic
594C2×C3C2×#414911yescharacteristic
595D3—24no—
596D3—42no—
597D3—204no—
598C5C2×#569511yescharacteristic, complemented, Sylow
599C22—34no—
600C22—68no—
601C22—62no—
602C22—62no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—304no—
608C22—304no—
609C22—304no—
610C22—608no—
611C22C2×#676812yes—
612C22D3×#70912yes—
613C22#9201912yes—
614C22C23×D3×D511yescharacteristic
615C4—22no—
616C4—22no—
617C4—62no—
618C4—62no—
619C4—104no—
620C4—104no—
621C4—304no—
622C4C2×#676814yes—
623C3C2×#6589911yescharacteristic, complemented, Sylow
624C2—64no—
625C2—122no—
626C2—604no—
627C2#1175261714yesdirect product factor
628C2C22×#676811yescharacteristic
629C2C2×D3×#70911yescharacteristic
630C2C2×#9201911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#553
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×C4×D60C2semidirect
2. C2×C4×C5×D12C2semidirect
3. C2×C3×#4016C2semidirect
4. C2×#91460C2semidirect
5. C2×#91460C2semidirect
6. C2×D3×C4⋊Dic5C2semidirect
7. C2×#91416C2semidirect
8. C2×#91406C2semidirect
9. C2×#91355C2semidirect
10. C2×#91338C2semidirect
11. C2×#91337C2semidirect
12. #11752617C2direct (N × H)
25. C4×D60C22semidirect
29. C4×C5×D12C22semidirect
34. C3×#4016C22semidirect
40. #91460C22semidirect
41. #91460C22semidirect
42. D3×C4⋊Dic5C22semidirect
43. #91416C22semidirect
44. #91406C22semidirect
45. #91355C22semidirect
46. #91338C22semidirect
47. #91337C22semidirect
60. C2×#4016D3semidirect
114. C2×C4×D12D5semidirect
148. #4016C2×D3semidirect
220. C4×D12C2×D5semidirect
412. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
549. C2×C5#5695semidirect
591. C2×C3#65899semidirect
598. C5C2×#5695semidirect
623. C3C2×#65899semidirect
627. C2#11752617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D602
C2×C4×C5×D122
C2×C3×#40162
C2×#914602
C2×D3×C4⋊Dic52
C2×#914162
C2×#914062
C2×#913552
C2×#913382
C2×#913372
#117526172
C2×#658993
C2×#56955