Finite Group Databasebeta

← C2×#11754236 #14483708

Subgroups — C2×#11754236 #14483708

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×#91819C211yesmaximal, characteristic, complemented
2C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×#91569C212yesmaximal, complemented
5C2×#91556C212yesmaximal, complemented
6C2×#91450C211yesmaximal, characteristic, complemented
7C2×#91418C211yesmaximal, characteristic, complemented
8C2×#91388C211yesmaximal, characteristic, complemented
9C2×#91358C211yesmaximal, characteristic, complemented
10#11754236C2116yesmaximal, direct product factor
11C2×#91356C212yesmaximal, complemented
12C2×#91337C212yesmaximal, complemented
13C2×#65848—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C23×C5×Dic3C2212yes—
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1202C2212yes—
21C22×#1200C2212yes—
22#91819C2218yescomplemented
23C2×#6714C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×C4⋊Dic3C2212yes—
28C2×C5×C4⋊Dic3C2218yescomplemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×C4×C22⋊D5C2218yescomplemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34#91569C22116yescomplemented
35#91556C22116yescomplemented
36C2×Dic3⋊Dic5C2212yes—
37C2×#6669C2212yes—
38C2×#6667C2212yes—
39C2×#6667C2212yes—
40C2×#6665C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91450C2218yescomplemented
43#91418C2218yescomplemented
44#91388C2218yescomplemented
45#91358C2218yescomplemented
46#91356C22116yescomplemented
47#91337C22116yescomplemented
48C2×#5565—51nomaximal, Hall
49C22×C5×C4⋊C4—31no—
50C2×#4076—31no—
51C2×#4076—32no—
52C2×C4×C22⋊D5—32no—
53C2×C4×C22⋊D5D311yescharacteristic, complemented
54#65848—316no—
55C2×#4044—32no—
56C2×#4041—31no—
57C2×#4040—32no—
58C2×#4039—31no—
59C2×#4038—31no—
60C2×#4036—31no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C23×C3×D5C2311yescharacteristic
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2314yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—28no—
69C2×#1220C2318yes—
70C22×Dic15C2312yes—
71C2×D60—24no—
72C2×D60C2314yes—
73C22×C5×Dic3—44no—
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2312yes—
76C22×C5×Dic3C2318yes—
77C2×C3×C22⋊D5—24no—
78C2×C3×C22⋊D5C2314yes—
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×C3×C4×D5—24no—
83C2×C3×C4×D5C2314yes—
84C2×#1202—44no—
85C2×#1202C2318yes—
86C2×#1200—44no—
87C2×#1200C2318yes—
88#6714C2318yes—
89C4⋊Dic15C2314yes—
90C5×C4⋊Dic3C2314yes—
91C5×C4⋊Dic3C2314yes—
92C5×C4⋊Dic3C2318yes—
93C3×C22⋊Dic5C2314yes—
94C3×#685C2314yes—
95C3×#683C2314yes—
96C3×C4×Dic5C2314yes—
97Dic3⋊Dic5C2318yes—
98#6669C2318yes—
99#6667C2318yes—
100#6667C2318yes—
101#6665C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×C4×D4—51no—
104C2×#939—52no—
105C2×#930—51no—
106C2×#930—51no—
107C2×#926—51no—
108C22×C4⋊Dic3D511yescharacteristic, complemented
109#5565—516no—
110C2×#898—52no—
111C2×#883—52no—
112C2×#67⋊C4—52no—
113C2×C4×D12—51no—
114C2×#870—51no—
115C23×C4×C5—32no—
116C23×C4×C5C2×D311yescharacteristic
117C22×C22⋊D5—32no—
118C22×C22⋊D5C2×D311yescharacteristic
119C22×D20—31no—
120C22×D20—32no—
121C22×C4×D5—32no—
122C22×C4×D5C2×D311yescharacteristic
123C2×C5×C4⋊C4—31no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C4⋊C4—32no—
126C2×C5×C4⋊C4—38no—
127C2×C22⋊Dic5C2×D311yescharacteristic
128#4076—38no—
129#4076—316no—
130C4×C22⋊D5—316no—
131C4×C22⋊D5C2×D318yescomplemented
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136C2×#685C2×D311yescharacteristic
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5—32no—
139C2×#683—32no—
140C2×#683C2×D311yescharacteristic
141C2×C4×Dic5—32no—
142C2×C4×Dic5C2×D311yescharacteristic
143#4044—316no—
144#4041—38no—
145#4040—316no—
146#4039—38no—
147#4038—38no—
148#4036—38no—
149C2×#553—151noSylow
150C23×C3×C5—22no—
151C23×C3×C5—22no—
152C23×C3×C5#4114yes—
153C23×C3×C5C2412yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—24no—
156C22×D15—24no—
157C22×D15—24no—
158C22×D15C2414yes—
159C22×C3×D5—22no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5C2412yes—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—28no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168#1220—216no—
169C2×Dic15—24no—
170C2×Dic15C2414yes—
171D60—28no—
172C2×C5×Dic3—24no—
173C2×C5×Dic3—24no—
174C2×C5×Dic3—48no—
175C2×C5×Dic3C2414yes—
176C2×C5×Dic3C2414yes—
177C3×C22⋊D5—28no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C2412yes—
182C2×C3×Dic5C2412yes—
183C2×C3×Dic5C2412yes—
184C3×C4×D5—28no—
185#1202—48no—
186#1200—48no—
187C22×C3×D4—51no—
188C23×C3×C4—51no—
189C23×C3×C4C2×D511yescharacteristic
190C22×#67—52no—
191C22×#67—52no—
192C23×Dic3C2×D512yes—
193C22×D12—51no—
194C22×C4×D3—52no—
195C3×C4×D4—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C22⋊C4—51no—
198C2×C3×C22⋊C4—51no—
199C2×C3×C42—51no—
200C2×#217—52no—
201#939—516no—
202#930—58no—
203#930—58no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4—52no—
207#926—58no—
208C2×C4⋊Dic3—51no—
209C2×C4⋊Dic3C2×D511yescharacteristic
210C2×C4⋊Dic3C2×D511yescharacteristic
211C2×C4⋊Dic3C2×D512yes—
212C2×C4⋊Dic3C2×D518yescomplemented
213C2×Dic3⋊C4—52no—
214C2×Dic3⋊C4—52no—
215C2×C4×Dic3—52no—
216#898—516no—
217#883—516no—
218#67⋊C4—516no—
219C4×D12—58no—
220#870—58no—
221C24×C5C22×D311yescharacteristic
222C23×D5—32no—
223C23×D5C22×D311yescharacteristic
224C22×C4×C5—24no—
225C22×C4×C5—32no—
226C22×C4×C5—32no—
227C22×C4×C5—38no—
228C22×C4×C5—124no—
229C22×C4×C5C22×D311yescharacteristic
230C22×C4×C5C22×D314yes—
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—24no—
233C2×C22⋊D5—38no—
234C2×C22⋊D5—68no—
235C2×C22⋊D5C22×D314yes—
236C22×Dic5—32no—
237C22×Dic5C22×D311yescharacteristic
238C22×Dic5C22×D311yescharacteristic
239C22×Dic5C22×D311yescharacteristic
240C2×D20—34no—
241C2×D20—38no—
242C2×D20—64no—
243C2×D20—124no—
244C2×C4×D5—24no—
245C2×C4×D5—38no—
246C2×C4×D5—124no—
247C2×C4×D5C22×D314yes—
248C5×C4⋊C4—34no—
249C5×C4⋊C4—34no—
250C5×C4⋊C4—38no—
251C22⋊Dic5C22×D314yes—
252#685—38no—
253#685—38no—
254#685—38no—
255#685—38no—
256#685C22×D314yes—
257C4⋊Dic5—34no—
258C4⋊Dic5—38no—
259#683—38no—
260#683C22×D314yes—
261C4×Dic5—38no—
262C4×Dic5C22×D314yes—
263#553—1516no—
264C2×#126—152no—
265C2×#125—151no—
266C2×#123—152no—
267C2×#121—151no—
268C2×#121—152no—
269C2×#121—151no—
270C2×C4×D4—51no—
271C2×C4×D4—151no—
272C2×C4×D4—152no—
273C2×#117—151no—
274C22×C4⋊C4—31no—
275C22×C3×C5—28no—
276C22×C3×C5—22no—
277C22×C3×C5—22no—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5C2×#4114yes—
280C22×C3×C5C2×#4112yes—
281C22×C3×C5H(5,𝔽2)12yes—
282C22×C3×C5C2511yescharacteristic
283C2×D15—24no—
284C2×D15—24no—
285C2×D15—24no—
286C2×D15—48no—
287C2×C3×D5—22no—
288C2×C3×D5—22no—
289C2×C3×D5—22no—
290C2×C3×D5—44no—
291C3×C4×C5—22no—
292C3×C4×C5C2×#4114yes—
293Dic15—24no—
294C3×Dic5—22no—
295C3×Dic5—22no—
296C3×Dic5—22no—
297C5×Dic3—24no—
298C5×Dic3—24no—
299C24×C3—51no—
300C24×C3C22×D511yescharacteristic
301C23×D3—52no—
302C2×C3×D4—54no—
303C2×C3×D4—104no—
304C22×C3×C4—24no—
305C22×C3×C4—51no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—54no—
309C22×C3×C4—104no—
310C22×C3×C4C22×D511yescharacteristic
311C22×C3×C4C22×D514yes—
312C22×C3×C4C22×D511yescharacteristic
313C2×#67—58no—
314C2×#67—58no—
315C2×#67—108no—
316C2×#67—204no—
317C22×Dic3—44no—
318C22×Dic3—52no—
319C22×Dic3C22×D512yes—
320C22×Dic3C22×D512yes—
321C22×Dic3C22×D518yes—
322C2×D12—54no—
323C2×D12—104no—
324C2×C4×D3—58no—
325C2×C4×D3—204no—
326C3×C4⋊C4—54no—
327C3×C22⋊C4—54no—
328C3×C22⋊C4—54no—
329C3×C42—54no—
330#217—58no—
331(C2×D3)⋊C4—58no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—58no—
334C4⋊Dic3—54no—
335C4⋊Dic3C22×D514yes—
336C4⋊Dic3C22×D514yes—
337C4⋊Dic3C22×D518yes—
338Dic3⋊C4—58no—
339Dic3⋊C4—58no—
340C4×Dic3—58no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5#23514yes—
344C23×C5C23×D312yes—
345C23×C5C23×D311yescharacteristic
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—34no—
350C22×D5—64no—
351C22×D5—64no—
352C22×D5—64no—
353C22×D5C23×D312yes—
354C2×C4×C5—22no—
355C2×C4×C5—28no—
356C2×C4×C5—34no—
357C2×C4×C5—34no—
358C2×C4×C5—64no—
359C2×C4×C5—64no—
360C2×C4×C5—128no—
361C2×C4×C5#23714yes—
362C2×C4×C5C23×D312yes—
363C2×C4×C5C23×D312yes—
364C22⋊D5—28no—
365C22⋊D5—616no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—34no—
370C2×Dic5—64no—
371C2×Dic5C23×D312yes—
372C2×Dic5C23×D312yes—
373C2×Dic5C23×D312yes—
374D20—68no—
375D20—128no—
376C4×D5—28no—
377C4×D5—128no—
378C22×D4—51no—
379C22×D4—152no—
380C22×D4—152no—
381C22×D4—151no—
382C23×C4—32no—
383C23×C4—51no—
384C23×C4—152no—
385C23×C4D3×D511yescharacteristic
386#126—1516no—
387#125—158no—
388#123—1516no—
389#121—158no—
390#121—1516no—
391#121—158no—
392C4×D4—58no—
393C4×D4—158no—
394C4×D4—1516no—
395#117—158no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—38no—
400C2×C4⋊C4—51no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—151no—
404C2×C22⋊C4—51no—
405C2×C22⋊C4—51no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—152no—
409C2×C22⋊C4—152no—
410C2×C42—51no—
411C2×C42—152no—
412C2×C3×C5—24no—
413C2×C3×C5#55314yescomplemented
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C22×#4111yescharacteristic
416C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
417D15—44no—
418C3×D5—42no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—52no—
422C23×C3—102no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3#71314yes—
426C23×C3C23×D512yes—
427C23×C3C23×D511yescharacteristic
428C22×D3—54no—
429C22×D3—104no—
430C22×D3—104no—
431C22×D3—104no—
432C3×D4—108no—
433C2×C3×C4—22no—
434C2×C3×C4—28no—
435C2×C3×C4—52no—
436C2×C3×C4—52no—
437C2×C3×C4—52no—
438C2×C3×C4—102no—
439C2×C3×C4—102no—
440C2×C3×C4—102no—
441C2×C3×C4—108no—
442C2×C3×C4#70914yes—
443C2×C3×C4C23×D512yes—
444C2×C3×C4C23×D512yes—
445#67—1016no—
446#67—208no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—48no—
450C2×Dic3—54no—
451C2×Dic3—104no—
452C2×Dic3C23×D514yes—
453C2×Dic3C23×D514yes—
454D12—108no—
455C4×D3—208no—
456C22×C5—22no—
457C22×C5—22no—
458C22×C5—28no—
459C22×C5C2×#23514yes—
460C22×C5C2×#23512yes—
461C22×C5C2×#23712yes—
462C22×C5#100912yes—
463C22×C5C24×D311yescharacteristic
464C2×D5—22no—
465C2×D5—22no—
466C2×D5—22no—
467C2×D5—44no—
468C2×D5—64no—
469C2×D5—64no—
470C2×D5—64no—
471C2×D5—128no—
472C4×C5—22no—
473C4×C5—64no—
474C4×C5—64no—
475C4×C5C2×#23714yes—
476Dic5—22no—
477Dic5—22no—
478Dic5—22no—
479Dic5—64no—
480C24—51no—
481C24—152no—
482C24C2×D3×D511yescharacteristic
483C2×D4—54no—
484C2×D4—104no—
485C2×D4—158no—
486C2×D4—158no—
487C2×D4—154no—
488C2×D4—308no—
489C2×D4—304no—
490C2×D4—604no—
491C22×C4—24no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—38no—
495C22×C4—51no—
496C22×C4—51no—
497C22×C4—51no—
498C22×C4—54no—
499C22×C4—104no—
500C22×C4—124no—
501C22×C4—158no—
502C22×C4—152no—
503C22×C4—604no—
504C22×C4C2×D3×D514yes—
505C22×C4C2×D3×D511yescharacteristic
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—34no—
509C4⋊C4—38no—
510C4⋊C4—54no—
511C4⋊C4—158no—
512C4⋊C4—158no—
513C4⋊C4—154no—
514C22⋊C4—54no—
515C22⋊C4—54no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—158no—
519C22⋊C4—158no—
520C42—54no—
521C42—158no—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3—28no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—102no—
527C22×C3—102no—
528C22×C3—102no—
529C22×C3—204no—
530C22×C3C2×#70912yes—
531C22×C3#414412yes—
532C22×C3C2×#71314yes—
533C22×C3C2×#71312yes—
534C22×C3C24×D511yescharacteristic
535C2×D3—104no—
536C2×D3—104no—
537C2×D3—104no—
538C2×D3—208no—
539C3×C4—22no—
540C3×C4—102no—
541C3×C4—102no—
542C3×C4—102no—
543C3×C4C2×#70914yes—
544Dic3—24no—
545Dic3—24no—
546Dic3—104no—
547C2×C5—24no—
548C2×C5#556514yescomplemented
549C2×C5C22×#23511yescharacteristic
550C2×C5C22×#23711yescharacteristic
551C2×C5C2×#100911yescharacteristic
552D5—42no—
553D5—124no—
554C23—22no—
555C23—22no—
556C23—52no—
557C23—102no—
558C23—102no—
559C23—102no—
560C23—154no—
561C23—304no—
562C23—304no—
563C23—304no—
564C23#677314yes—
565C23C22×D3×D512yes—
566C23C22×D3×D511yescharacteristic
567D4—108no—
568D4—3016no—
569D4—308no—
570D4—608no—
571C2×C4—22no—
572C2×C4—28no—
573C2×C4—34no—
574C2×C4—34no—
575C2×C4—52no—
576C2×C4—52no—
577C2×C4—52no—
578C2×C4—64no—
579C2×C4—64no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—108no—
584C2×C4—128no—
585C2×C4—154no—
586C2×C4—304no—
587C2×C4—608no—
588C2×C4#677914yes—
589C2×C4C22×D3×D512yes—
590C2×C4C22×D3×D512yes—
591C2×C3—24no—
592C2×C3—202no—
593C2×C3#6584814yescomplemented
594C2×C3C22×#70911yescharacteristic
595C2×C3C2×#414411yescharacteristic
596C2×C3C22×#71311yescharacteristic
597D3—204no—
598C5C2×#556511yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—28no—
602C22—102no—
603C22—102no—
604C22—102no—
605C22—204no—
606C22—304no—
607C22—304no—
608C22—304no—
609C22—608no—
610C22C2×#677314yes—
611C22C2×#677312yes—
612C22#9201812yes—
613C22C2×#677912yes—
614C22C23×D3×D511yescharacteristic
615C4—22no—
616C4—64no—
617C4—64no—
618C4—102no—
619C4—102no—
620C4—102no—
621C4—304no—
622C4C2×#677914yes—
623C3C2×#6584811yescharacteristic, complemented, Sylow
624C2—24no—
625C2—202no—
626C2—604no—
627C2#1175423614yesdirect product factor
628C2C22×#677311yescharacteristic
629C2C2×#9201811yescharacteristic
630C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#553
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. C2×#91819C2semidirect
2. C22×C5×C4⋊Dic3C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C2×#91569C2semidirect
5. C2×#91556C2semidirect
6. C2×#91450C2semidirect
7. C2×#91418C2semidirect
8. C2×#91388C2semidirect
9. C2×#91358C2semidirect
10. #11754236C2direct (N × H)
11. C2×#91356C2semidirect
12. C2×#91337C2semidirect
22. #91819C22semidirect
28. C2×C5×C4⋊Dic3C22semidirect
30. C3×C4×C22⋊D5C22semidirect
34. #91569C22semidirect
35. #91556C22semidirect
42. #91450C22semidirect
43. #91418C22semidirect
44. #91388C22semidirect
45. #91358C22semidirect
46. #91356C22semidirect
47. #91337C22semidirect
53. C2×C4×C22⋊D5D3semidirect
108. C22×C4⋊Dic3D5semidirect
131. C4×C22⋊D5C2×D3semidirect
212. C2×C4⋊Dic3C2×D5semidirect
413. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
548. C2×C5#5565semidirect
593. C2×C3#65848semidirect
598. C5C2×#5565semidirect
623. C3C2×#65848semidirect
627. C2#11754236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C22×C5×C4⋊Dic32
C2×C3×C4×C22⋊D52
C2×#915692
C2×#915562
C2×#914502
C2×#914182
C2×#913882
C2×#913582
#117542362
C2×#913562
C2×#913372
C2×#658483
C2×#55655