Finite Group Databasebeta

← C2×#11754185 #14481406

Subgroups — C2×#11754185 #14481406

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91819C211yesmaximal, characteristic
2C2×C5×#926C211yesmaximal, characteristic, complemented
3C2×C3×#4070C211yesmaximal, characteristic, complemented
4C2×#91562C212yesmaximal, complemented
5C2×#91526C212yesmaximal, complemented
6C2×#91469C211yesmaximal, characteristic, complemented
7C2×#91428C211yesmaximal, characteristic, complemented
8C2×#91419C212yesmaximal, complemented
9C2×#91374C211yesmaximal, characteristic, complemented
10C2×#91337C212yesmaximal, complemented
11C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
12#11754185C2116yesmaximal, direct product factor
13C2×#65868—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2212yes—
16C22×D60C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1204C2212yes—
19C22×#1200C2212yes—
20#91819C2218yes—
21C2×#6714C2212yes—
22C2×C4⋊Dic15C2211yescharacteristic
23C2×C5×#217C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C5×#926C2218yescomplemented
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2212yes—
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C3×#4070C2218yescomplemented
33C2×C3×#683C2212yes—
34#91562C22116yescomplemented
35C2×Dic3⋊Dic5C2212yes—
36C2×#6668C2212yes—
37C2×#6667C2212yes—
38C2×#6667C2212yes—
39C2×#6667C2212yes—
40C2×Dic3×Dic5C2212yes—
41#91526C22116yescomplemented
42#91469C2218yescomplemented
43#91428C2218yescomplemented
44#91419C22116yescomplemented
45#91374C2218yescomplemented
46#91337C22116yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5643—51nomaximal, Hall
49C2×C5×#117—31no—
50C2×#4076—31no—
51C2×#4070D311yescharacteristic, complemented
52#65868—316no—
53C2×#4044—32no—
54C2×#4042—32no—
55C2×#4031—32no—
56C2×#4029—32no—
57C2×#4021—31no—
58C2×C4×D20—31no—
59C2×#4015—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2312yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—44no—
68C2×#1220C2318yes—
69C22×Dic15C2312yes—
70C2×D60—24no—
71C2×D60C2314yes—
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2312yes—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1204—44no—
81C2×#1204C2318yes—
82C2×#1200—44no—
83C2×#1200C2318yes—
84#6714C2318yes—
85C4⋊Dic15C2314yes—
86C5×#217C2314yes—
87C5×#217C2314yes—
88C5×C4⋊Dic3C2314yes—
89C5×C4⋊Dic3C2314yes—
90C4×C5×Dic3C2314yes—
91C4×C5×Dic3C2314yes—
92C3×C22⋊Dic5C2318yes—
93C3×C4⋊Dic5C2314yes—
94C3×#683C2318yes—
95Dic3⋊Dic5C2318yes—
96#6668C2318yes—
97#6667C2318yes—
98#6667C2318yes—
99#6667C2318yes—
100Dic3×Dic5C2318yes—
101C2×C3×C22⋊Q8—51no—
102C2×#947—51no—
103C2×Q8×Dic3—51no—
104C2×#930—51no—
105C2×#926D511yescharacteristic, complemented
106#5643—516no—
107C2×#898—52no—
108C2×#897—52no—
109C2×#893—51no—
110C2×#888—51no—
111C2×#885—52no—
112C2×#883—52no—
113C23×C4×C5C2×D311yescharacteristic
114C22×C22⋊D5—32no—
115C22×D20—31no—
116C22×C4×D5—32no—
117C22×Dic10—32no—
118C22×Dic10C2×D311yescharacteristic
119C5×#117—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—31no—
122C2×C5×C22⋊C4—31no—
123C2×C5×C22⋊C4—31no—
124C2×C42×C5—31no—
125C2×C42×C5—31no—
126C2×C22⋊Dic5C2×D312yes—
127#4076—38no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×C4⋊Dic5—31no—
133C2×C4⋊Dic5—32no—
134C2×C4⋊Dic5C2×D311yescharacteristic
135#4070C2×D318yescomplemented
136C2×#683—32no—
137C2×#683C2×D312yes—
138C2×C4×Dic5—32no—
139#4044—316no—
140#4042—316no—
141#4031—316no—
142#4029—316no—
143#4021—38no—
144C4×D20—38no—
145#4015—38no—
146C4×Dic10—38no—
147C2×#542—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C2412yes—
152C23×C3×C5C2411yescharacteristic
153C22×D15—24no—
154C22×D15—24no—
155C22×D15—24no—
156C22×D15C2414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162#1220—48no—
163C2×Dic15—24no—
164C2×Dic15C2414yes—
165D60—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2412yes—
173C2×C5×Dic3C2412yes—
174C2×C3×Dic5—24no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2414yes—
177C2×C3×Dic5C2414yes—
178C3×Dic10—28no—
179#1204—48no—
180#1200—48no—
181C22×C3×Q8—51no—
182C23×C3×C4C2×D511yescharacteristic
183C22×#67—52no—
184C22×D12—51no—
185C22×C4×D3—52no—
186C22×Dic6—52no—
187C3×C22⋊Q8—58no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C4⋊C4—52no—
190C2×C3×C22⋊C4—52no—
191C2×#217C2×D511yescharacteristic
192C2×#217C2×D511yescharacteristic
193#947—58no—
194Q8×Dic3—58no—
195#930—58no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200#926C2×D518yescomplemented
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204C2×C4⋊Dic3C2×D511yescharacteristic
205C2×Dic3⋊C4—52no—
206C2×C4×Dic3—52no—
207C2×C4×Dic3C2×D511yescharacteristic
208C2×C4×Dic3C2×D511yescharacteristic
209#898—516no—
210#897—516no—
211#893—58no—
212#888—58no—
213#885—516no—
214#883—516no—
215C24×C5C22×D311yescharacteristic
216C23×D5—32no—
217C22×C4×C5—24no—
218C22×C4×C5—31no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—31no—
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D314yes—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—38no—
226C2×C22⋊D5—124no—
227C22×Dic5—32no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C2×D20—34no—
231C2×D20—64no—
232C2×C4×D5—38no—
233C2×C4×D5—124no—
234C2×Dic10—24no—
235C2×Dic10—38no—
236C2×Dic10—124no—
237C2×Dic10C22×D314yes—
238C5×C4⋊C4—34no—
239C5×C4⋊C4—34no—
240C5×C22⋊C4—34no—
241C5×C22⋊C4—34no—
242C42×C5—34no—
243C42×C5—34no—
244C22⋊Dic5C22×D318yes—
245#685—38no—
246#685—38no—
247#685—38no—
248#685—38no—
249C4⋊Dic5—34no—
250C4⋊Dic5—38no—
251C4⋊Dic5C22×D314yes—
252#683—38no—
253#683C22×D318yes—
254C4×Dic5—38no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—151no—
259C2×#124—152no—
260C2×#123—152no—
261C2×C22⋊Q8—51no—
262C2×C22⋊Q8—152no—
263C2×#121—151no—
264C2×C4×Q8—151no—
265C2×C4×D4—151no—
266C2×#117—31no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5—22no—
270C22×C3×C5—44no—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C22×C3×C52−1+412yes—
274C22×C3×C5C2511yescharacteristic
275C2×D15—24no—
276C2×D15—24no—
277C2×D15—24no—
278C2×D15—48no—
279C3×C4×C5—22no—
280C3×C4×C5C2×#4114yes—
281Dic15—24no—
282C3×Dic5—24no—
283C3×Dic5—24no—
284C5×Dic3—22no—
285C5×Dic3—22no—
286C5×Dic3—22no—
287C5×Dic3—22no—
288C24×C3C22×D511yescharacteristic
289C23×D3—52no—
290C2×C3×Q8—54no—
291C2×C3×Q8—104no—
292C22×C3×C4—24no—
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D514yes—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—58no—
299C2×#67—204no—
300C22×Dic3—52no—
301C22×Dic3C22×D511yescharacteristic
302C22×Dic3C22×D511yescharacteristic
303C22×Dic3C22×D511yescharacteristic
304C22×Dic3C22×D511yescharacteristic
305C2×D12—54no—
306C2×D12—104no—
307C2×C4×D3—58no—
308C2×C4×D3—204no—
309C2×Dic6—58no—
310C2×Dic6—204no—
311C3×C4⋊C4—58no—
312C3×C4⋊C4—54no—
313C3×C22⋊C4—58no—
314#217C22×D514yes—
315#217C22×D514yes—
316(C2×D3)⋊C4—58no—
317(C2×D3)⋊C4—58no—
318(C2×D3)⋊C4—58no—
319(C2×D3)⋊C4—58no—
320C4⋊Dic3—54no—
321C4⋊Dic3—58no—
322C4⋊Dic3C22×D514yes—
323C4⋊Dic3C22×D514yes—
324Dic3⋊C4—58no—
325C4×Dic3—58no—
326C4×Dic3C22×D514yes—
327C4×Dic3C22×D514yes—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5C23×D312yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—34no—
334C22×D5—64no—
335C22×D5—64no—
336C22×D5—64no—
337C2×C4×C5—22no—
338C2×C4×C5—28no—
339C2×C4×C5—32no—
340C2×C4×C5—32no—
341C2×C4×C5—32no—
342C2×C4×C5—32no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5—62no—
346C2×C4×C5—62no—
347C2×C4×C5#23714yes—
348C2×C4×C5C23×D312yes—
349C2×C4×C5C23×D312yes—
350C22⋊D5—128no—
351C2×Dic5—24no—
352C2×Dic5—24no—
353C2×Dic5—34no—
354C2×Dic5—64no—
355C2×Dic5C23×D314yes—
356C2×Dic5C23×D314yes—
357D20—68no—
358C4×D5—128no—
359Dic10—28no—
360Dic10—128no—
361C22×Q8—51no—
362C22×Q8—152no—
363C22×D4—152no—
364C22×D4—151no—
365C23×C4—152no—
366C23×C4D3×D511yescharacteristic
367C4⋊Q8—158no—
368#126—1516no—
369#124—158no—
370#124—1516no—
371#123—1516no—
372C22⋊Q8—58no—
373C22⋊Q8—1516no—
374#121—158no—
375C4×Q8—158no—
376C4×D4—158no—
377#117—38no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—51no—
381C2×C4⋊C4—52no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4—151no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—52no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—152no—
395C2×C3×C5—42no—
396C2×C3×C5#54214yescomplemented
397C2×C3×C5C22×#4111yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400D15—44no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3C23×D512yes—
405C23×C3C23×D511yescharacteristic
406C22×D3—54no—
407C22×D3—104no—
408C22×D3—104no—
409C22×D3—104no—
410C3×Q8—108no—
411C2×C3×C4—22no—
412C2×C3×C4—28no—
413C2×C3×C4—54no—
414C2×C3×C4—54no—
415C2×C3×C4—104no—
416C2×C3×C4—104no—
417C2×C3×C4#70914yes—
418C2×C3×C4C23×D512yes—
419C2×C3×C4C23×D512yes—
420#67—208no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—54no—
426C2×Dic3—104no—
427C2×Dic3C23×D512yes—
428C2×Dic3C23×D512yes—
429C2×Dic3C23×D512yes—
430C2×Dic3C23×D512yes—
431D12—108no—
432C4×D3—208no—
433Dic6—208no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—44no—
438C22×C5C2×#23712yes—
439C22×C5#100712yes—
440C22×C5#100912yes—
441C22×C5C24×D311yescharacteristic
442C2×D5—64no—
443C2×D5—64no—
444C2×D5—64no—
445C2×D5—128no—
446C4×C5—22no—
447C4×C5—62no—
448C4×C5—62no—
449C4×C5—62no—
450C4×C5—62no—
451C4×C5C2×#23714yes—
452Dic5—24no—
453Dic5—24no—
454Dic5—64no—
455C24—152no—
456C24C2×D3×D511yescharacteristic
457C2×Q8—54no—
458C2×Q8—104no—
459C2×Q8—158no—
460C2×Q8—604no—
461C2×D4—158no—
462C2×D4—154no—
463C2×D4—304no—
464C2×D4—604no—
465C22×C4—24no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—158no—
473C22×C4—152no—
474C22×C4—604no—
475C22×C4C2×D3×D514yes—
476C22×C4C2×D3×D511yescharacteristic
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—34no—
480C4⋊C4—54no—
481C4⋊C4—58no—
482C4⋊C4—158no—
483C4⋊C4—158no—
484C4⋊C4—154no—
485C22⋊C4—34no—
486C22⋊C4—34no—
487C22⋊C4—58no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4—158no—
492C42—34no—
493C42—34no—
494C42—158no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—44no—
500C22×C3C2×#70912yes—
501C22×C3#414912yes—
502C22×C3#415012yes—
503C22×C3C24×D511yescharacteristic
504C2×D3—104no—
505C2×D3—104no—
506C2×D3—104no—
507C2×D3—208no—
508C3×C4—22no—
509C3×C4—104no—
510C3×C4—104no—
511C3×C4C2×#70914yes—
512Dic3—22no—
513Dic3—22no—
514Dic3—22no—
515Dic3—22no—
516Dic3—104no—
517C2×C5—42no—
518C2×C5#564314yescomplemented
519C2×C5C22×#23711yescharacteristic
520C2×C5C2×#100711yescharacteristic
521C2×C5C2×#100911yescharacteristic
522D5—124no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—154no—
527C23—304no—
528C23—304no—
529C23—304no—
530C23C22×D3×D512yes—
531C23C22×D3×D511yescharacteristic
532Q8—108no—
533Q8—608no—
534D4—308no—
535D4—608no—
536C2×C4—22no—
537C2×C4—28no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—32no—
541C2×C4—32no—
542C2×C4—54no—
543C2×C4—54no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—104no—
549C2×C4—104no—
550C2×C4—154no—
551C2×C4—304no—
552C2×C4—608no—
553C2×C4#677914yes—
554C2×C4C22×D3×D512yes—
555C2×C4C22×D3×D512yes—
556C2×C3—42no—
557C2×C3#6586814yescomplemented
558C2×C3C22×#70911yescharacteristic
559C2×C3C2×#414911yescharacteristic
560C2×C3C2×#415011yescharacteristic
561D3—204no—
562C5C2×#564311yescharacteristic, complemented, Sylow
563C22—22no—
564C22—22no—
565C22—22no—
566C22—44no—
567C22—304no—
568C22—304no—
569C22—304no—
570C22—608no—
571C22#9200412yes—
572C22#9201912yes—
573C22C2×#677912yes—
574C22C23×D3×D511yescharacteristic
575C4—22no—
576C4—62no—
577C4—62no—
578C4—62no—
579C4—62no—
580C4—104no—
581C4—104no—
582C4—304no—
583C4C2×#677914yes—
584C3C2×#6586811yescharacteristic, complemented, Sylow
585C2—42no—
586C2—604no—
587C2#1175418514yesdirect product factor
588C2C2×#9200411yescharacteristic
589C2C2×#9201911yescharacteristic
590C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC2×#91819C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#926C2semidirect
3. C2×C3×#4070C2semidirect
4. C2×#91562C2semidirect
5. C2×#91526C2semidirect
6. C2×#91469C2semidirect
7. C2×#91428C2semidirect
8. C2×#91419C2semidirect
9. C2×#91374C2semidirect
10. C2×#91337C2semidirect
11. C2×Dic3×Dic10C2semidirect
12. #11754185C2direct (N × H)
25. C5×#926C22semidirect
32. C3×#4070C22semidirect
34. #91562C22semidirect
41. #91526C22semidirect
42. #91469C22semidirect
43. #91428C22semidirect
44. #91419C22semidirect
45. #91374C22semidirect
46. #91337C22semidirect
47. Dic3×Dic10C22semidirect
51. C2×#4070D3semidirect
105. C2×#926D5semidirect
135. #4070C2×D3semidirect
200. #926C2×D5semidirect
396. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
518. C2×C5#5643semidirect
557. C2×C3#65868semidirect
562. C5C2×#5643semidirect
584. C3C2×#65868semidirect
587. C2#11754185direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C2×C5×#9262
C2×C3×#40702
C2×#915622
C2×#915262
C2×#914692
C2×#914282
C2×#914192
C2×#913742
C2×#913372
C2×Dic3×Dic102
#117541852
C2×#658683
C2×#56435