Finite Group Databasebeta

← C2×#11753640 #14481420

Subgroups — C2×#11753640 #14481420

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×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#888C211yesmaximal, characteristic, complemented
3C2×C3×#4041C211yesmaximal, characteristic
4C2×#91434C211yesmaximal, characteristic, complemented
5C2×#91421C212yesmaximal, complemented
6C2×#91407C212yesmaximal, complemented
7C2×#91368C212yesmaximal, complemented
8C2×#91366C212yesmaximal, complemented
9C2×#91364C211yesmaximal, characteristic, complemented
10C2×#91360C211yesmaximal, characteristic, complemented
11C2×#91357C211yesmaximal, characteristic, complemented
12#11753640C2116yesmaximal, direct product factor
13C2×#66067—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2212yes—
16C22×C3×D20C2211yescharacteristic
17C22×C3×D20C2212yes—
18C22×C3×C4×D5C2211yescharacteristic
19C22×D5×Dic3C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6712C2212yes—
22C2×C4×Dic15C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24#91776C2218yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2212yes—
27C2×C4×C5×Dic3C2211yescharacteristic
28C5×#888C2218yescomplemented
29C2×C3×#685C2212yes—
30C3×#4041C2218yes—
31C2×Dic3⋊Dic5C2212yes—
32C2×#6668C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×#6665C2212yes—
35C2×#6665C2212yes—
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40#91434C2218yescomplemented
41#91421C22116yescomplemented
42#91407C22116yescomplemented
43#91368C22116yescomplemented
44#91366C22116yescomplemented
45#91364C2218yescomplemented
46#91360C2218yescomplemented
47#91357C2218yescomplemented
48C2×#5603—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4093—32no—
51C2×#4092—32no—
52#66067—316no—
53C2×#4044—32no—
54C2×#4043—31no—
55C2×#4041D311yescharacteristic
56C2×#4040—32no—
57C2×#4039—31no—
58C2×#4033—31no—
59C2×#4021—31no—
60C2×#4018—31no—
61C23×C3×D5C2312yes—
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2312yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—44no—
74C2×C5×Dic6C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×D20—24no—
77C2×C3×D20—44no—
78C2×C3×D20C2314yes—
79C2×C3×D20C2318yes—
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5C2314yes—
82C2×D5×Dic3—44no—
83C2×D5×Dic3C2318yes—
84C3×C5×C4⋊C4C2314yes—
85#6712C2318yes—
86C4×Dic15C2314yes—
87C4×Dic15C2318yes—
88C5×C4⋊Dic3C2314yes—
89C5×Dic3⋊C4C2318yes—
90C4×C5×Dic3C2314yes—
91C3×#685C2318yes—
92Dic3⋊Dic5C2318yes—
93#6668C2314yes—
94#6668C2314yes—
95#6665C2314yes—
96#6665C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100#6665C2314yes—
101C2×C3×#121—51no—
102C2×#936—52no—
103C2×#936—51no—
104C2×#935—52no—
105C2×D4×Dic3—51no—
106C2×#926—51no—
107C2×#924—51no—
108#5603—516no—
109C2×#888D511yescharacteristic, complemented
110C2×#887—51no—
111C2×#879—52no—
112C2×#878—52no—
113C22×C5×Q8—32no—
114C22×D20C2×D311yescharacteristic
115C22×D20C2×D312yes—
116C22×C4×D5—32no—
117C22×C4×D5C2×D311yescharacteristic
118C22×Dic10—31no—
119C5×C4⋊Q8—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C42×C5—31no—
124#4093—316no—
125#4092—316no—
126C2×#685—31no—
127C2×#685—31no—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685—32no—
132C2×#685C2×D312yes—
133C2×C4⋊Dic5—32no—
134C2×#683—32no—
135C2×#683—31no—
136C2×#683—31no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139#4044—316no—
140#4043—38no—
141#4041C2×D318yes—
142#4040—316no—
143#4039—38no—
144#4033—38no—
145#4021—38no—
146#4018—38no—
147C2×#542—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×C3×D5—22no—
150C22×C3×D5—24no—
151C22×C3×D5—24no—
152C22×C3×D5—22no—
153C22×C3×D5—24no—
154C22×C3×D5—22no—
155C22×C3×D5C2412yes—
156C22×C3×D5C2414yes—
157C2×C3×C4×C5—24no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2414yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—24no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15C2412yes—
165C2×Dic15C2414yes—
166C2×Dic15C2412yes—
167Dic30—28no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2412yes—
173C2×C5×Dic3C2414yes—
174C5×Dic6—48no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2412yes—
177C3×D20—28no—
178C3×D20—48no—
179C3×C4×D5—28no—
180D5×Dic3—48no—
181C22×C3×D4—51no—
182C22×C3×D4—52no—
183C23×C3×C4—51no—
184C23×Dic3—52no—
185C22×Dic6—51no—
186C22×Dic6C2×D512yes—
187C3×#121—58no—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C22⋊C4—52no—
190C2×#217—52no—
191C2×#217—52no—
192C2×#217—52no—
193C2×#217—52no—
194C2×#217—51no—
195C2×#217—51no—
196#936—516no—
197#936—58no—
198#935—516no—
199D4×Dic3—58no—
200#926—58no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—51no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204#924—58no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4C2×D512yes—
208C2×C4×Dic3—52no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3C2×D511yescharacteristic
211#888C2×D518yescomplemented
212#887—58no—
213#879—516no—
214#878—516no—
215C23×D5C22×D312yes—
216C23×D5C22×D311yescharacteristic
217C2×C5×Q8—38no—
218C2×C5×Q8—124no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—32no—
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—32no—
225C22×Dic5—31no—
226C22×Dic5—31no—
227C22×Dic5C22×D311yescharacteristic
228C2×D20—24no—
229C2×D20—44no—
230C2×D20C22×D314yes—
231C2×D20C22×D318yes—
232C2×C4×D5—24no—
233C2×C4×D5—38no—
234C2×C4×D5—124no—
235C2×C4×D5C22×D314yes—
236C2×Dic10—34no—
237C2×Dic10—64no—
238C5×C4⋊C4—38no—
239C5×C4⋊C4—34no—
240C5×C4⋊C4C22×D314yes—
241C42×C5—34no—
242#685—34no—
243#685—34no—
244#685—38no—
245#685—38no—
246#685—38no—
247#685—38no—
248#685C22×D318yes—
249C4⋊Dic5—38no—
250#683—38no—
251#683—34no—
252#683—34no—
253C4×Dic5—34no—
254C4×Dic5—38no—
255#542—1516no—
256C2×C4⋊Q8—31no—
257C2×#126—152no—
258C2×#124—151no—
259C2×#124—152no—
260C2×#123—152no—
261C2×C22⋊Q8—152no—
262C2×C22⋊Q8—151no—
263C2×#121—51no—
264C2×C4×Q8—151no—
265C2×C4×D4—151no—
266C2×#117—151no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5H(5,𝔽2)12yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×C3×D5—22no—
272C2×C3×D5—24no—
273C2×C3×D5—24no—
274C2×C3×D5—22no—
275C2×C3×D5—22no—
276C2×C3×D5—24no—
277C2×C3×D5—44no—
278C2×C3×D5—48no—
279C3×C4×C5—24no—
280C3×C4×C5C2×#4114yes—
281Dic15—24no—
282Dic15—22no—
283Dic15—22no—
284C3×Dic5—22no—
285C5×Dic3—24no—
286C5×Dic3—22no—
287C5×Dic3—22no—
288C24×C3—51no—
289C24×C3—52no—
290C2×C3×D4—54no—
291C2×C3×D4—58no—
292C2×C3×D4—104no—
293C2×C3×D4—204no—
294C22×C3×C4—51no—
295C22×C3×C4—54no—
296C22×C3×C4—104no—
297C22×C3×C4C22×D512yes—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—52no—
302C22×Dic3—58no—
303C22×Dic3—204no—
304C22×Dic3C22×D511yescharacteristic
305C22×Dic3C22×D511yescharacteristic
306C22×Dic3C22×D512yes—
307C2×Dic6—44no—
308C2×Dic6—54no—
309C2×Dic6—104no—
310C2×Dic6C22×D518yes—
311C3×C4⋊C4C22×D514yes—
312C3×C22⋊C4—58no—
313#217—58no—
314#217—58no—
315#217—58no—
316#217—58no—
317#217—54no—
318#217—54no—
319C4⋊Dic3—54no—
320C4⋊Dic3—54no—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4C22×D518yes—
325C4×Dic3—58no—
326C4×Dic3—54no—
327C4×Dic3C22×D514yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—22no—
330C22×D5—24no—
331C22×D5—24no—
332C22×D5—22no—
333C22×D5—24no—
334C22×D5—22no—
335C22×D5C23×D312yes—
336C22×D5C23×D314yes—
337C5×Q8—128no—
338C2×C4×C5—24no—
339C2×C4×C5—32no—
340C2×C4×C5—32no—
341C2×C4×C5—34no—
342C2×C4×C5—64no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5#23714yes—
346C2×C4×C5C23×D314yes—
347C2×C4×C5C23×D312yes—
348C2×Dic5—22no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—34no—
352C2×Dic5—64no—
353C2×Dic5—62no—
354C2×Dic5—62no—
355C2×Dic5C23×D312yes—
356D20—28no—
357D20—48no—
358C4×D5—28no—
359C4×D5—128no—
360Dic10—68no—
361C22×Q8—32no—
362C22×Q8—151no—
363C22×D4—51no—
364C22×D4—52no—
365C23×C4—51no—
366C23×C4—152no—
367C4⋊Q8—38no—
368#126—1516no—
369#124—158no—
370#124—1516no—
371#123—1516no—
372C22⋊Q8—1516no—
373C22⋊Q8—158no—
374#121—58no—
375C4×Q8—158no—
376C4×D4—158no—
377#117—158no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—151no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—152no—
384C2×C4⋊C4D3×D511yescharacteristic
385C2×C22⋊C4—52no—
386C2×C22⋊C4—151no—
387C2×C22⋊C4—151no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C42—31no—
393C2×C42—151no—
394C2×C42—152no—
395C2×C3×C5#54214yescomplemented
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
398C2×C3×C5C2×2−1+411yescharacteristic
399C3×D5—42no—
400C3×D5—44no—
401C23×C3—52no—
402C23×C3—54no—
403C23×C3—104no—
404C23×C3—102no—
405C23×C3—102no—
406C23×C3—104no—
407C23×C3—102no—
408C23×C3—104no—
409C23×C3C23×D511yescharacteristic
410C3×D4—108no—
411C3×D4—208no—
412C2×C3×C4—24no—
413C2×C3×C4—52no—
414C2×C3×C4—102no—
415C2×C3×C4—108no—
416C2×C3×C4#71314yes—
417C2×C3×C4C23×D514yes—
418C2×C3×C4C23×D512yes—
419C2×Dic3—22no—
420C2×Dic3—24no—
421C2×Dic3—22no—
422C2×Dic3—52no—
423C2×Dic3—52no—
424C2×Dic3—54no—
425C2×Dic3—102no—
426C2×Dic3—104no—
427C2×Dic3—102no—
428C2×Dic3—208no—
429C2×Dic3C23×D512yes—
430C2×Dic3C23×D512yes—
431C2×Dic3C23×D514yes—
432Dic6—48no—
433Dic6—108no—
434C22×C5C2×#23712yes—
435C22×C5#100412yes—
436C22×C5#101012yes—
437C22×C5C24×D311yescharacteristic
438C2×D5—22no—
439C2×D5—24no—
440C2×D5—24no—
441C2×D5—22no—
442C2×D5—22no—
443C2×D5—24no—
444C2×D5—44no—
445C2×D5—48no—
446C4×C5—24no—
447C4×C5—64no—
448C4×C5—62no—
449C4×C5—62no—
450C4×C5C2×#23714yes—
451Dic5—22no—
452Dic5—64no—
453Dic5—62no—
454Dic5—62no—
455C24—52no—
456C24—51no—
457C2×Q8—38no—
458C2×Q8—124no—
459C2×Q8—154no—
460C2×Q8—304no—
461C2×D4—54no—
462C2×D4—58no—
463C2×D4—104no—
464C2×D4—204no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—51no—
469C22×C4—54no—
470C22×C4—104no—
471C22×C4—158no—
472C22×C4—151no—
473C22×C4—152no—
474C22×C4—151no—
475C22×C4—604no—
476C22×C4C2×D3×D512yes—
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—154no—
481C4⋊C4—154no—
482C4⋊C4—158no—
483C4⋊C4—158no—
484C4⋊C4C2×D3×D514yes—
485C22⋊C4—58no—
486C22⋊C4—154no—
487C22⋊C4—154no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4—158no—
492C42—34no—
493C42—154no—
494C42—158no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—104no—
497C22×C3—102no—
498C22×C3—102no—
499C22×C3—104no—
500C22×C3—102no—
501C22×C3—104no—
502C22×C3—208no—
503C22×C3—204no—
504C22×C3#414412yes—
505C22×C3C2×#71312yes—
506C22×C3#414712yes—
507C22×C3C24×D511yescharacteristic
508C3×C4—24no—
509C3×C4—102no—
510C3×C4C2×#71314yes—
511Dic3—22no—
512Dic3—24no—
513Dic3—22no—
514Dic3—102no—
515Dic3—104no—
516Dic3—102no—
517C2×C5#560314yescomplemented
518C2×C5C22×#23711yescharacteristic
519C2×C5C2×#100411yescharacteristic
520C2×C5C2×#101011yescharacteristic
521D5—42no—
522D5—44no—
523C23—54no—
524C23—52no—
525C23—102no—
526C23—104no—
527C23—104no—
528C23—102no—
529C23—104no—
530C23—102no—
531C23C22×D3×D511yescharacteristic
532Q8—128no—
533Q8—308no—
534D4—108no—
535D4—208no—
536C2×C4—24no—
537C2×C4—32no—
538C2×C4—32no—
539C2×C4—34no—
540C2×C4—52no—
541C2×C4—64no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—102no—
545C2×C4—108no—
546C2×C4—152no—
547C2×C4—154no—
548C2×C4—152no—
549C2×C4—304no—
550C2×C4—302no—
551C2×C4—302no—
552C2×C4—608no—
553C2×C4#676614yes—
554C2×C4C22×D3×D514yes—
555C2×C4C22×D3×D512yes—
556C2×C3—204no—
557C2×C3—202no—
558C2×C3#6606714yescomplemented
559C2×C3C2×#414411yescharacteristic
560C2×C3C22×#71311yescharacteristic
561C2×C3C2×#414711yescharacteristic
562C5C2×#560311yescharacteristic, complemented, Sylow
563C22—102no—
564C22—104no—
565C22—104no—
566C22—102no—
567C22—104no—
568C22—102no—
569C22—204no—
570C22—208no—
571C22C2×#676612yes—
572C22#9202512yes—
573C22#9202812yes—
574C22C23×D3×D511yescharacteristic
575C4—24no—
576C4—64no—
577C4—62no—
578C4—62no—
579C4—102no—
580C4—304no—
581C4—302no—
582C4—302no—
583C4C2×#676614yes—
584C3C2×#6606711yescharacteristic, complemented, Sylow
585C2—202no—
586C2—204no—
587C2#1175364014yesdirect product factor
588C2C22×#676611yescharacteristic
589C2C2×#9202511yescharacteristic
590C2C2×#9202811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×C3×#4041C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91776C2semidirect
2. C2×C5×#888C2semidirect
4. C2×#91434C2semidirect
5. C2×#91421C2semidirect
6. C2×#91407C2semidirect
7. C2×#91368C2semidirect
8. C2×#91366C2semidirect
9. C2×#91364C2semidirect
10. C2×#91360C2semidirect
11. C2×#91357C2semidirect
12. #11753640C2direct (N × H)
24. #91776C22semidirect
28. C5×#888C22semidirect
40. #91434C22semidirect
41. #91421C22semidirect
42. #91407C22semidirect
43. #91368C22semidirect
44. #91366C22semidirect
45. #91364C22semidirect
46. #91360C22semidirect
47. #91357C22semidirect
109. C2×#888D5semidirect
211. #888C2×D5semidirect
395. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
517. C2×C5#5603semidirect
558. C2×C3#66067semidirect
562. C5C2×#5603semidirect
584. C3C2×#66067semidirect
587. C2#11753640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8882
C2×C3×#40412
C2×#914342
C2×#914212
C2×#914072
C2×#913682
C2×#913662
C2×#913642
C2×#913602
C2×#913572
#117536402
C2×#660673
C2×#56035