Finite Group Databasebeta

← C2×#11752503 #14481401

Subgroups — C2×#11752503 #14481401

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×#91761C211yesmaximal, characteristic, complemented
2C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×C4×D20C211yesmaximal, characteristic, complemented
4C2×#91470C211yesmaximal, characteristic, complemented
5C2×#91465C211yesmaximal, characteristic
6C2×#91383C211yesmaximal, characteristic, complemented
7C2×#91368C211yesmaximal, characteristic, complemented
8C2×#91363C212yesmaximal, complemented
9C2×#91353C212yesmaximal, complemented
10C2×#91349C212yesmaximal, complemented
11C2×#91348C212yesmaximal, complemented
12#11752503C2116yesmaximal, direct product factor
13C2×#65916—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×C3×C4×D5C2212yes—
18C22×#1204C2212yes—
19C22×#1202C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26#91761C2218yescomplemented
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×Dic3⋊C4C2212yes—
29C2×C4×C5×Dic3C2212yes—
30C4×C5×Dic6C2218yescomplemented
31C2×C3×#685C2212yes—
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C3×C4×D20C2218yescomplemented
34C2×#6669C2212yes—
35C2×#6668C2212yes—
36C2×#6667C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91470C2218yescomplemented
41#91465C2218yes—
42#91383C2218yescomplemented
43#91368C2218yescomplemented
44#91363C22116yescomplemented
45#91353C22116yescomplemented
46#91349C22116yescomplemented
47#91348C22116yescomplemented
48C2×#5561—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4093—31no—
51C2×#4092—31no—
52#65916—316no—
53C2×#4042—32no—
54C2×#4041—31no—
55C2×#4040—32no—
56C2×#4034—31no—
57C2×#4022—32no—
58C2×#4021—32no—
59C2×C4×D20D311yescharacteristic, complemented
60C2×#4018—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C2×C4×D15—24no—
70C2×C4×D15C2314yes—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2312yes—
76C2×C3×D20—24no—
77C2×C3×D20C2314yes—
78C2×C3×C4×D5—44no—
79C2×C3×C4×D5C2318yes—
80C2×#1204—44no—
81C2×#1204C2318yes—
82C2×#1202—44no—
83C2×#1202C2318yes—
84C3×C42×C5C2314yes—
85#6714C2314yes—
86#6714C2314yes—
87#6712C2314yes—
88#6712C2314yes—
89C4×Dic15C2314yes—
90C5×C4⋊Dic3C2314yes—
91C5×Dic3⋊C4C2318yes—
92C4×C5×Dic3C2318yes—
93C3×#685C2318yes—
94C3×C4⋊Dic5C2314yes—
95#6669C2318yes—
96#6668C2318yes—
97#6667C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100#6665C2318yes—
101C2×C3×C4×D4—51no—
102C2×#938—51no—
103C2×#936—51no—
104C2×#929—52no—
105C2×#924—52no—
106#5561—516no—
107C2×#897—51no—
108C2×#888—51no—
109C2×#885—52no—
110C2×#879—52no—
111C2×#872—51no—
112C2×C4×Dic6D511yescharacteristic, complemented
113C22×C5×Q8—31no—
114C22×D20—32no—
115C22×D20C2×D311yescharacteristic
116C22×C4×D5—31no—
117C22×C4×D5C2×D312yes—
118C22×Dic10—32no—
119C4×C5×Q8—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C42×C5—32no—
123C2×C42×C5C2×D311yescharacteristic
124#4093—38no—
125#4092—38no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×#685—31no—
130C2×#685—31no—
131C2×#685—32no—
132C2×#685C2×D312yes—
133C2×C4⋊Dic5C2×D311yescharacteristic
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—31no—
139#4042—316no—
140#4041—38no—
141#4040—316no—
142#4034—38no—
143#4022—316no—
144#4021—316no—
145C4×D20C2×D318yescomplemented
146#4018—38no—
147C2×#542—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15C2412yes—
153C22×C3×D5—24no—
154C22×C3×D5—24no—
155C22×C3×D5—24no—
156C22×C3×D5C2414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169C4×D15—28no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3—24no—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2414yes—
174C5×Dic6—28no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2414yes—
177C3×D20—28no—
178C3×C4×D5—48no—
179#1204—48no—
180#1202—48no—
181C22×C3×D4—51no—
182C23×C3×C4—52no—
183C22×#67—52no—
184C22×C4×D3—51no—
185C22×Dic6—52no—
186C22×Dic6C2×D511yescharacteristic
187C3×C4×D4—58no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C42C2×D511yescharacteristic
191C2×#217—52no—
192C2×#217—52no—
193C2×#217—52no—
194#938—58no—
195#936—58no—
196#929—516no—
197C2×(C2×D3)⋊C4—51no—
198C2×(C2×D3)⋊C4—51no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—52no—
201C2×C4⋊Dic3C2×D511yescharacteristic
202#924—516no—
203C2×Dic3⋊C4—51no—
204C2×Dic3⋊C4—51no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4C2×D512yes—
207C2×C4×Dic3—51no—
208C2×C4×Dic3C2×D512yes—
209#897—58no—
210#888—58no—
211#885—516no—
212#879—516no—
213#872—58no—
214C4×Dic6C2×D518yescomplemented
215C23×D5—31no—
216C23×D5C22×D312yes—
217C2×C5×Q8—34no—
218C2×C5×Q8—64no—
219C22×C4×C5—32no—
220C22×C4×C5—32no—
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—31no—
225C22×Dic5—31no—
226C22×Dic5—31no—
227C22×Dic5C22×D312yes—
228C2×D20—24no—
229C2×D20—38no—
230C2×D20—124no—
231C2×D20C22×D314yes—
232C2×C4×D5—34no—
233C2×C4×D5—44no—
234C2×C4×D5—64no—
235C2×C4×D5C22×D318yes—
236C2×Dic10—38no—
237C2×Dic10—124no—
238C5×C4⋊C4—38no—
239C5×C4⋊C4—34no—
240C42×C5—38no—
241C42×C5C22×D314yes—
242#685—38no—
243#685—38no—
244#685—38no—
245#685—34no—
246#685—34no—
247#685—38no—
248#685C22×D318yes—
249C4⋊Dic5C22×D314yes—
250#683—34no—
251#683—34no—
252#683—38no—
253#683—38no—
254C4×Dic5—34no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—152no—
259C2×#124—151no—
260C2×#123—152no—
261C2×C22⋊Q8—152no—
262C2×C22⋊Q8—151no—
263C2×#121—151no—
264C2×C4×Q8—31no—
265C2×C4×D4—51no—
266C2×#117—151no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5H(5,𝔽2)12yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×D15—22no—
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—44no—
275C2×C3×D5—24no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—48no—
279C3×C4×C5—22no—
280C3×C4×C5—22no—
281C3×C4×C5C2×#4114yes—
282Dic15—22no—
283Dic15—22no—
284Dic15—22no—
285C3×Dic5—24no—
286C5×Dic3—24no—
287C5×Dic3—24no—
288C24×C3—52no—
289C23×D3—51no—
290C2×C3×D4—54no—
291C2×C3×D4—104no—
292C22×C3×C4—52no—
293C22×C3×C4—58no—
294C22×C3×C4—204no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—58no—
299C2×#67—204no—
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—51no—
303C22×Dic3C22×D512yes—
304C22×Dic3C22×D512yes—
305C2×C4×D3—54no—
306C2×C4×D3—104no—
307C2×Dic6—24no—
308C2×Dic6—58no—
309C2×Dic6—204no—
310C2×Dic6C22×D514yes—
311C3×C4⋊C4—54no—
312C3×C22⋊C4—58no—
313C3×C42C22×D514yes—
314#217—58no—
315#217—58no—
316#217—58no—
317(C2×D3)⋊C4—54no—
318(C2×D3)⋊C4—54no—
319(C2×D3)⋊C4—58no—
320C4⋊Dic3—58no—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—54no—
323Dic3⋊C4—54no—
324Dic3⋊C4—58no—
325Dic3⋊C4C22×D518yes—
326C4×Dic3—54no—
327C4×Dic3C22×D518yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—24no—
330C22×D5—24no—
331C22×D5—24no—
332C22×D5—32no—
333C22×D5—62no—
334C22×D5—62no—
335C22×D5—62no—
336C22×D5C23×D314yes—
337C5×Q8—68no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—34no—
341C2×C4×C5—34no—
342C2×C4×C5—64no—
343C2×C4×C5—64no—
344C2×C4×C5#23514yes—
345C2×C4×C5C23×D312yes—
346C2×C4×C5C23×D312yes—
347C2×C4×C5C23×D312yes—
348C2×Dic5—24no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—32no—
352C2×Dic5—62no—
353C2×Dic5—62no—
354C2×Dic5—62no—
355C2×Dic5C23×D314yes—
356D20—28no—
357D20—128no—
358C4×D5—48no—
359C4×D5—68no—
360Dic10—128no—
361C22×Q8—31no—
362C22×Q8—152no—
363C22×D4—51no—
364C22×D4—152no—
365C23×C4—52no—
366C23×C4—151no—
367C4⋊Q8—158no—
368#126—1516no—
369#124—1516no—
370#124—158no—
371#123—1516no—
372C22⋊Q8—1516no—
373C22⋊Q8—158no—
374#121—158no—
375C4×Q8—38no—
376C4×D4—58no—
377#117—158no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—51no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—151no—
384C2×C4⋊C4—151no—
385C2×C22⋊C4—52no—
386C2×C22⋊C4—152no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—151no—
391C2×C22⋊C4—151no—
392C2×C42—32no—
393C2×C42—151no—
394C2×C42D3×D511yescharacteristic
395C2×C3×C5#54214yescomplemented
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
398C2×C3×C5C2×2−1+411yescharacteristic
399D15—42no—
400C3×D5—44no—
401C23×C3—54no—
402C23×C3—104no—
403C23×C3—104no—
404C23×C3—104no—
405C23×C3C23×D511yescharacteristic
406C22×D3—52no—
407C22×D3—102no—
408C22×D3—102no—
409C22×D3—102no—
410C3×D4—108no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—54no—
414C2×C3×C4—104no—
415C2×C3×C4—208no—
416C2×C3×C4#70914yes—
417C2×C3×C4C23×D512yes—
418C2×C3×C4C23×D512yes—
419C2×C3×C4C23×D512yes—
420#67—208no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—52no—
424C2×Dic3—52no—
425C2×Dic3—52no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3C23×D514yes—
430C2×Dic3C23×D514yes—
431C4×D3—108no—
432Dic6—28no—
433Dic6—208no—
434C22×C5C2×#23512yes—
435C22×C5#100412yes—
436C22×C5#101012yes—
437C22×C5C24×D311yescharacteristic
438C2×D5—24no—
439C2×D5—24no—
440C2×D5—24no—
441C2×D5—48no—
442C2×D5—62no—
443C2×D5—62no—
444C2×D5—62no—
445C2×D5—124no—
446C4×C5—22no—
447C4×C5—22no—
448C4×C5—64no—
449C4×C5—64no—
450C4×C5C2×#23514yes—
451Dic5—24no—
452Dic5—62no—
453Dic5—62no—
454Dic5—62no—
455C24—52no—
456C24—151no—
457C2×Q8—34no—
458C2×Q8—64no—
459C2×Q8—158no—
460C2×Q8—604no—
461C2×D4—54no—
462C2×D4—104no—
463C2×D4—158no—
464C2×D4—604no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—52no—
468C22×C4—58no—
469C22×C4—151no—
470C22×C4—151no—
471C22×C4—151no—
472C22×C4—154no—
473C22×C4—204no—
474C22×C4—304no—
475C22×C4C2×D3×D511yescharacteristic
476C22×C4C2×D3×D511yescharacteristic
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—54no—
481C4⋊C4—158no—
482C4⋊C4—158no—
483C4⋊C4—154no—
484C4⋊C4—154no—
485C22⋊C4—58no—
486C22⋊C4—158no—
487C22⋊C4—158no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—154no—
491C22⋊C4—154no—
492C42—38no—
493C42—154no—
494C42C2×D3×D514yes—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—104no—
497C22×C3—104no—
498C22×C3—104no—
499C22×C3—208no—
500C22×C3C2×#70912yes—
501C22×C3#414712yes—
502C22×C3#414912yes—
503C22×C3C24×D511yescharacteristic
504C2×D3—102no—
505C2×D3—102no—
506C2×D3—102no—
507C2×D3—204no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—104no—
511C3×C4C2×#70914yes—
512Dic3—24no—
513Dic3—24no—
514Dic3—102no—
515Dic3—102no—
516Dic3—102no—
517C2×C5#556114yescomplemented
518C2×C5C22×#23511yescharacteristic
519C2×C5C2×#100411yescharacteristic
520C2×C5C2×#101011yescharacteristic
521D5—44no—
522D5—122no—
523C23—54no—
524C23—104no—
525C23—104no—
526C23—104no—
527C23—152no—
528C23—302no—
529C23—302no—
530C23—302no—
531C23C22×D3×D511yescharacteristic
532Q8—68no—
533Q8—608no—
534D4—108no—
535D4—608no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—54no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—104no—
544C2×C4—152no—
545C2×C4—152no—
546C2×C4—152no—
547C2×C4—208no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—302no—
551C2×C4—308no—
552C2×C4#677114yes—
553C2×C4C22×D3×D512yes—
554C2×C4C22×D3×D512yes—
555C2×C4C22×D3×D512yes—
556C2×C3—204no—
557C2×C3#6591614yescomplemented
558C2×C3C22×#70911yescharacteristic
559C2×C3C2×#414711yescharacteristic
560C2×C3C2×#414911yescharacteristic
561D3—202no—
562C5C2×#556111yescharacteristic, complemented, Sylow
563C22—104no—
564C22—104no—
565C22—104no—
566C22—208no—
567C22—302no—
568C22—302no—
569C22—302no—
570C22—604no—
571C22#9200012yes—
572C22C2×#677112yes—
573C22#9201712yes—
574C22C23×D3×D511yescharacteristic
575C4—22no—
576C4—22no—
577C4—64no—
578C4—64no—
579C4—104no—
580C4—302no—
581C4—302no—
582C4—302no—
583C4C2×#677114yes—
584C3C2×#6591611yescharacteristic, complemented, Sylow
585C2—204no—
586C2—602no—
587C2#1175250314yesdirect product factor
588C2C2×#9200011yescharacteristic
589C2C22×#677111yescharacteristic
590C2C2×#9201711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91465C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#542
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×#91761C2semidirect
2. C2×C4×C5×Dic6C2semidirect
3. C2×C3×C4×D20C2semidirect
4. C2×#91470C2semidirect
6. C2×#91383C2semidirect
7. C2×#91368C2semidirect
8. C2×#91363C2semidirect
9. C2×#91353C2semidirect
10. C2×#91349C2semidirect
11. C2×#91348C2semidirect
12. #11752503C2direct (N × H)
26. #91761C22semidirect
30. C4×C5×Dic6C22semidirect
33. C3×C4×D20C22semidirect
40. #91470C22semidirect
42. #91383C22semidirect
43. #91368C22semidirect
44. #91363C22semidirect
45. #91353C22semidirect
46. #91349C22semidirect
47. #91348C22semidirect
59. C2×C4×D20D3semidirect
112. C2×C4×Dic6D5semidirect
145. C4×D20C2×D3semidirect
214. C4×Dic6C2×D5semidirect
395. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
517. C2×C5#5561semidirect
557. C2×C3#65916semidirect
562. C5C2×#5561semidirect
584. C3C2×#65916semidirect
587. C2#11752503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C4×C5×Dic62
C2×C3×C4×D202
C2×#914702
C2×#914652
C2×#913832
C2×#913682
C2×#913632
C2×#913532
C2×#913492
C2×#913482
#117525032
C2×#659163
C2×#55615