Finite Group Databasebeta

← C2×#11754966 #14483979

Subgroups — C2×#11754966 #14483979

Order 1920.

2480 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×#91827C211yesmaximal, characteristic, complemented
2C2×C5×#938C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C2×#91566C212yesmaximal, complemented
5C2×#91528C212yesmaximal, complemented
6C2×#91526C212yesmaximal, complemented
7C2×#91525C212yesmaximal, complemented
8#11754966C2116yesmaximal, direct product factor
9C2×#91468C211yesmaximal, characteristic, complemented
10C2×C4×#1203C211yesmaximal, characteristic, complemented
11C2×#91347C211yesmaximal, characteristic, complemented
12C2×#91338C211yesmaximal, characteristic, complemented
13C2×#65950—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C22×C4×D15C2211yescharacteristic
17C22×C5×#67C2212yes—
18C22×C4×C5×D3C2211yescharacteristic
19C23×C3×Dic5C2212yes—
20C22×#1204C2212yes—
21C22×#1203C2211yescharacteristic
22C2×#6719C2212yes—
23#91827C2218yescomplemented
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×#217C2212yes—
26C5×#938C2218yescomplemented
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C3×D4×Dic5C2218yescomplemented
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32#91566C22116yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6668C2212yes—
35C2×#6667C2211yescharacteristic
36C2×#6667C2212yes—
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2212yes—
39#91528C22116yescomplemented
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91526C22116yescomplemented
43#91525C22116yescomplemented
44#91468C2218yescomplemented
45C4×#1203C2218yescomplemented
46#91347C2218yescomplemented
47#91338C2218yescomplemented
48C2×#5563—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4085—32no—
51C2×#4084—31no—
52C2×#4082—32no—
53C2×D4×Dic5D311yescharacteristic, complemented
54C2×C4×C22⋊D5—31no—
55C2×#4072—31no—
56#65950—316no—
57C2×#4038—31no—
58C2×#4034—31no—
59C2×#4031—32no—
60C2×#4023—32no—
61C24×C3×C5C2312yes—
62C23×D15C2311yescharacteristic
63C23×C5×D3C2311yescharacteristic
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—44no—
68C2×#1220C2318yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C2×C4×D15—24no—
72C2×C4×D15C2314yes—
73C2×C5×#67—44no—
74C2×C5×#67C2318yes—
75C22×C5×Dic3C2312yes—
76C22×C5×Dic3C2311yescharacteristic
77C2×C4×C5×D3—24no—
78C2×C4×C5×D3C2314yes—
79C22×C3×Dic5—28no—
80C22×C3×Dic5C2318yes—
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2312yes—
83C22×C3×Dic5C2311yescharacteristic
84C2×#1204—44no—
85C2×#1204C2318yes—
86C2×#1203—24no—
87C2×#1203C2314yes—
88#6719C2318yes—
89C4⋊Dic15C2314yes—
90C5×#217C2318yes—
91C5×C4⋊Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C4⋊Dic5C2314yes—
94C3×C4×Dic5C2314yes—
95#6668C2314yes—
96#6668C2318yes—
97#6667C2314yes—
98#6667C2318yes—
99(C2×D3)⋊Dic5C2314yes—
100(C2×D3)⋊Dic5C2318yes—
101Dic3×Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×C4×D4—51no—
104C2×#938—51no—
105C2×#938D511yescharacteristic, complemented
106C2×#930—52no—
107C2×#926—52no—
108#5563—516no—
109C2×#892—51no—
110C2×#892—51no—
111C2×#885—52no—
112C2×#885—52no—
113C2×C4×D12—51no—
114C2×#869—51no—
115C22×C5×D4—32no—
116C22×C5×D4C2×D311yescharacteristic
117C23×C4×C5—31no—
118C22×C22⋊D5—32no—
119C22×C22⋊D5—31no—
120C23×Dic5C2×D312yes—
121C22×C4×D5—31no—
122C22×Dic10—32no—
123C5×#121—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—31no—
129C2×C22⋊Dic5C2×D312yes—
130#4085—316no—
131#4084—38no—
132#4082—316no—
133D4×Dic5C2×D318yescomplemented
134C4×C22⋊D5—38no—
135C2×#685—31no—
136C2×#685—32no—
137#4072—38no—
138C2×C4⋊Dic5—31no—
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×#683—31no—
141C2×#683—32no—
142C2×C4×Dic5—32no—
143C2×C4×Dic5—32no—
144C2×C4×Dic5C2×D311yescharacteristic
145#4038—38no—
146#4034—38no—
147#4031—316no—
148#4023—316no—
149C2×#555—151noSylow
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5—24no—
153C23×C3×C5C2414yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—22no—
156C22×D15—22no—
157C22×D15—22no—
158C22×D15C2412yes—
159C22×C5×D3—22no—
160C22×C5×D3—22no—
161C22×C5×D3—22no—
162C22×C5×D3C2412yes—
163C3×C5×D4—28no—
164C2×C3×C4×C5#4114yes—
165C2×C3×C4×C5C2412yes—
166#1220—48no—
167C2×Dic15—22no—
168C2×Dic15—24no—
169C2×Dic15C2412yes—
170C2×Dic15C2414yes—
171C4×D15—28no—
172C5×#67—48no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—24no—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2414yes—
177C4×C5×D3—28no—
178C2×C3×Dic5—24no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—216no—
181C2×C3×Dic5#4114yes—
182C2×C3×Dic5C2414yes—
183C2×C3×Dic5C2412yes—
184C2×C3×Dic5C2412yes—
185#1204—48no—
186#1203—28no—
187C22×C3×D4C2×D511yescharacteristic
188C23×C3×C4—52no—
189C22×#67—52no—
190C22×#67C2×D512yes—
191C22×D12—51no—
192C22×C4×D3—51no—
193C22×C4×D3C2×D511yescharacteristic
194C22×Dic6—52no—
195C3×C4×D4—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C42—51no—
199C2×#217—52no—
200C2×#217C2×D512yes—
201#938—58no—
202#938C2×D518yescomplemented
203#930—516no—
204C2×(C2×D3)⋊C4—51no—
205C2×(C2×D3)⋊C4—52no—
206C2×(C2×D3)⋊C4—51no—
207C2×(C2×D3)⋊C4—52no—
208#926—516no—
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3—52no—
211C2×C4⋊Dic3—51no—
212C2×C4⋊Dic3C2×D511yescharacteristic
213C2×C4×Dic3—52no—
214C2×C4×Dic3—52no—
215#892—58no—
216#892—58no—
217#885—516no—
218#885—516no—
219C4×D12—58no—
220#869—58no—
221C24×C5—31no—
222C24×C5C22×D312yes—
223C23×D5—31no—
224C2×C5×D4—24no—
225C2×C5×D4—38no—
226C2×C5×D4—124no—
227C2×C5×D4C22×D314yes—
228C22×C4×C5—31no—
229C22×C4×C5—32no—
230C22×C4×C5—34no—
231C22×C4×C5—64no—
232C22×C4×C5C22×D311yescharacteristic
233C2×C22⋊D5—38no—
234C2×C22⋊D5—34no—
235C2×C22⋊D5—64no—
236C2×C22⋊D5—124no—
237C22×Dic5—28no—
238C22×Dic5—31no—
239C22×Dic5—32no—
240C22×Dic5C22×D311yescharacteristic
241C22×Dic5C22×D312yes—
242C22×Dic5C22×D318yes—
243C22×Dic5C22×D311yescharacteristic
244C2×C4×D5—34no—
245C2×C4×D5—64no—
246C2×Dic10—38no—
247C2×Dic10—124no—
248C5×C4⋊C4—34no—
249C5×C22⋊C4—38no—
250C22⋊Dic5—38no—
251C22⋊Dic5—38no—
252C22⋊Dic5—34no—
253C22⋊Dic5C22×D318yes—
254#685—34no—
255#685—38no—
256C4⋊Dic5—34no—
257C4⋊Dic5C22×D314yes—
258#683—34no—
259#683—38no—
260C4×Dic5—38no—
261C4×Dic5—38no—
262C4×Dic5C22×D314yes—
263#555—1516no—
264C2×C4⋊Q8—151no—
265C2×#124—152no—
266C2×#124—152no—
267C2×#121—31no—
268C2×#121—152no—
269C2×#121—151no—
270C2×C4×D4—51no—
271C2×C4×D4—151no—
272C2×#117—152no—
273C2×#117—151no—
274C2×#117—151no—
275C22×C3×C5—24no—
276C22×C3×C5—24no—
277C22×C3×C5—24no—
278C22×C3×C5—48no—
279C22×C3×C5C2×#4112yes—
280C22×C3×C5C2×#4112yes—
281C22×C3×C5H(5,𝔽2)12yes—
282C22×C3×C5C2511yescharacteristic
283C2×D15—22no—
284C2×D15—22no—
285C2×D15—22no—
286C2×D15—44no—
287C2×C5×D3—22no—
288C2×C5×D3—22no—
289C2×C5×D3—22no—
290C2×C5×D3—44no—
291C3×C4×C5C2×#4114yes—
292Dic15—22no—
293Dic15—24no—
294C3×Dic5—24no—
295C3×Dic5—22no—
296C3×Dic5C2×#4114yes—
297C5×Dic3—22no—
298C5×Dic3—24no—
299C24×C3C22×D512yes—
300C23×D3—51no—
301C23×D3C22×D511yescharacteristic
302C2×C3×D4—24no—
303C2×C3×D4C22×D514yes—
304C22×C3×C4—51no—
305C22×C3×C4—52no—
306C22×C3×C4—58no—
307C22×C3×C4—51no—
308C22×C3×C4—108no—
309C22×C3×C4C22×D511yescharacteristic
310C2×#67—44no—
311C2×#67—58no—
312C2×#67—204no—
313C2×#67C22×D518yes—
314C22×Dic3—51no—
315C22×Dic3—52no—
316C22×Dic3C22×D511yescharacteristic
317C22×Dic3C22×D512yes—
318C2×D12—54no—
319C2×D12—104no—
320C2×C4×D3—24no—
321C2×C4×D3—54no—
322C2×C4×D3—104no—
323C2×C4×D3C22×D514yes—
324C2×Dic6—58no—
325C2×Dic6—204no—
326C3×C4⋊C4—54no—
327C3×C22⋊C4—58no—
328C3×C42—54no—
329#217—58no—
330#217C22×D518yes—
331(C2×D3)⋊C4—54no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—54no—
334(C2×D3)⋊C4—58no—
335C4⋊Dic3—54no—
336C4⋊Dic3—58no—
337C4⋊Dic3—54no—
338C4⋊Dic3C22×D514yes—
339C4×Dic3—58no—
340C4×Dic3—58no—
341C23×C5—24no—
342C23×C5—24no—
343C23×C5—24no—
344C23×C5—32no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5C23×D314yes—
349C23×C5C23×D311yescharacteristic
350C22×D5—32no—
351C22×D5—62no—
352C22×D5—62no—
353C22×D5—62no—
354C5×D4—28no—
355C5×D4—128no—
356C2×C4×C5—32no—
357C2×C4×C5—34no—
358C2×C4×C5—62no—
359C2×C4×C5—64no—
360C2×C4×C5—68no—
361C2×C4×C5#23514yes—
362C2×C4×C5C23×D312yes—
363C22⋊D5—68no—
364C22⋊D5—128no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—216no—
368C2×Dic5—32no—
369C2×Dic5—34no—
370C2×Dic5—62no—
371C2×Dic5—64no—
372C2×Dic5#23714yes—
373C2×Dic5C23×D314yes—
374C2×Dic5C23×D312yes—
375C2×Dic5C23×D312yes—
376C4×D5—68no—
377Dic10—128no—
378C22×Q8—152no—
379C22×D4—32no—
380C22×D4—151no—
381C22×D4—152no—
382C22×D4D3×D511yescharacteristic
383C23×C4—31no—
384C23×C4—52no—
385C23×C4—151no—
386C4⋊Q8—158no—
387#124—1516no—
388#124—1516no—
389#121—38no—
390#121—1516no—
391#121—158no—
392C4×D4—58no—
393C4×D4—158no—
394#117—1516no—
395#117—158no—
396#117—158no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—151no—
400C2×C4⋊C4—152no—
401C2×C4⋊C4—151no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—52no—
404C2×C22⋊C4—152no—
405C2×C22⋊C4—151no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—151no—
408C2×C22⋊C4—152no—
409C2×C42—51no—
410C2×C42—152no—
411C2×C42—152no—
412C2×C3×C5—44no—
413C2×C3×C5#55514yescomplemented
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C22×#4111yescharacteristic
416C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
417D15—42no—
418C5×D3—42no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3C23×D514yes—
423C23×C3C23×D511yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—52no—
428C22×D3—102no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3C23×D512yes—
432C3×D4—28no—
433C2×C3×C4—54no—
434C2×C3×C4—52no—
435C2×C3×C4—54no—
436C2×C3×C4—52no—
437C2×C3×C4—1016no—
438C2×C3×C4—102no—
439C2×C3×C4—104no—
440C2×C3×C4#71114yes—
441C2×C3×C4C23×D512yes—
442#67—48no—
443#67—208no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—52no—
447C2×Dic3—54no—
448C2×Dic3—102no—
449C2×Dic3—104no—
450C2×Dic3C23×D512yes—
451C2×Dic3C23×D514yes—
452D12—108no—
453C4×D3—28no—
454C4×D3—108no—
455Dic6—208no—
456C22×C5—24no—
457C22×C5—24no—
458C22×C5—24no—
459C22×C5—48no—
460C22×C5—62no—
461C22×C5—62no—
462C22×C5—62no—
463C22×C5—124no—
464C22×C5C2×#23512yes—
465C22×C5C2×#23712yes—
466C22×C5#100912yes—
467C22×C5C24×D311yescharacteristic
468C2×D5—62no—
469C2×D5—62no—
470C2×D5—62no—
471C2×D5—124no—
472C4×C5—62no—
473C4×C5—64no—
474C4×C5C2×#23514yes—
475Dic5—24no—
476Dic5—22no—
477Dic5—62no—
478Dic5—64no—
479Dic5C2×#23714yes—
480C24—31no—
481C24—151no—
482C24C2×D3×D512yes—
483C2×Q8—158no—
484C2×Q8—604no—
485C2×D4—24no—
486C2×D4—38no—
487C2×D4—124no—
488C2×D4—154no—
489C2×D4—158no—
490C2×D4—304no—
491C2×D4—604no—
492C2×D4C2×D3×D514yes—
493C22×C4—31no—
494C22×C4—32no—
495C22×C4—34no—
496C22×C4—51no—
497C22×C4—58no—
498C22×C4—51no—
499C22×C4—52no—
500C22×C4—64no—
501C22×C4—108no—
502C22×C4—151no—
503C22×C4—152no—
504C22×C4—154no—
505C22×C4—304no—
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—54no—
509C4⋊C4—154no—
510C4⋊C4—158no—
511C4⋊C4—154no—
512C22⋊C4—38no—
513C22⋊C4—58no—
514C22⋊C4—158no—
515C22⋊C4—154no—
516C22⋊C4—158no—
517C22⋊C4—154no—
518C22⋊C4—158no—
519C42—54no—
520C42—158no—
521C42—158no—
522C3×C5C2×#55511yescharacteristic, complemented, Hall
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—48no—
527C22×C3C2×#71112yes—
528C22×C3#414412yes—
529C22×C3D5×#4112yes—
530C22×C3C24×D511yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—44no—
535C2×D3—102no—
536C2×D3—102no—
537C2×D3—102no—
538C2×D3—204no—
539C3×C4—54no—
540C3×C4—102no—
541C3×C4—104no—
542C3×C4C2×#71114yes—
543Dic3—22no—
544Dic3—24no—
545Dic3—102no—
546Dic3—104no—
547C2×C5—44no—
548C2×C5—122no—
549C2×C5#556314yescomplemented
550C2×C5C22×#23511yescharacteristic
551C2×C5C22×#23711yescharacteristic
552C2×C5C2×#100911yescharacteristic
553D5—122no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—32no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—152no—
562C23—302no—
563C23—302no—
564C23—302no—
565C23C22×D3×D514yes—
566C23C22×D3×D511yescharacteristic
567Q8—608no—
568D4—28no—
569D4—128no—
570D4—308no—
571D4—608no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—54no—
575C2×C4—52no—
576C2×C4—52no—
577C2×C4—54no—
578C2×C4—64no—
579C2×C4—62no—
580C2×C4—68no—
581C2×C4—1016no—
582C2×C4—104no—
583C2×C4—102no—
584C2×C4—152no—
585C2×C4—154no—
586C2×C4—304no—
587C2×C4—302no—
588C2×C4—308no—
589C2×C4#678214yes—
590C2×C4C22×D3×D512yes—
591C2×C3—44no—
592C2×C3#6595014yescomplemented
593C2×C3C22×#71111yescharacteristic
594C2×C3C2×#414411yescharacteristic
595C2×C3C2×D5×#4111yescharacteristic
596D3—42no—
597D3—202no—
598C5C2×#556311yescharacteristic, complemented, Sylow
599C22—24no—
600C22—24no—
601C22—24no—
602C22—48no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—302no—
608C22—302no—
609C22—302no—
610C22—604no—
611C22D5×#23712yes—
612C22#9202712yes—
613C22C2×#678212yes—
614C22C23×D3×D511yescharacteristic
615C4—54no—
616C4—62no—
617C4—64no—
618C4—104no—
619C4—102no—
620C4—302no—
621C4—304no—
622C4C2×#678214yes—
623C3C2×#6595011yescharacteristic, complemented, Sylow
624C2—44no—
625C2—122no—
626C2—602no—
627C2#1175496614yesdirect product factor
628C2C2×D5×#23711yescharacteristic
629C2C2×#9202711yescharacteristic
630C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91827C2semidirect
2. C2×C5×#938C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C2×#91566C2semidirect
5. C2×#91528C2semidirect
6. C2×#91526C2semidirect
7. C2×#91525C2semidirect
8. #11754966C2direct (N × H)
9. C2×#91468C2semidirect
10. C2×C4×#1203C2semidirect
11. C2×#91347C2semidirect
12. C2×#91338C2semidirect
23. #91827C22semidirect
26. C5×#938C22semidirect
29. C3×D4×Dic5C22semidirect
32. #91566C22semidirect
39. #91528C22semidirect
42. #91526C22semidirect
43. #91525C22semidirect
44. #91468C22semidirect
45. C4×#1203C22semidirect
46. #91347C22semidirect
47. #91338C22semidirect
53. C2×D4×Dic5D3semidirect
105. C2×#938D5semidirect
133. D4×Dic5C2×D3semidirect
202. #938C2×D5semidirect
413. C2×C3×C5#555semidirect
522. C3×C5C2×#555semidirect
549. C2×C5#5563semidirect
592. C2×C3#65950semidirect
598. C5C2×#5563semidirect
623. C3C2×#65950semidirect
627. C2#11754966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918272
C2×C5×#9382
C2×C3×D4×Dic52
C2×#915662
C2×#915282
C2×#915262
C2×#915252
#117549662
C2×#914682
C2×C4×#12032
C2×#913472
C2×#913382
C2×#659503
C2×#55635