Finite Group Databasebeta

← C2×#11753527 #14483904

Subgroups — C2×#11753527 #14483904

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91779C211yesmaximal, characteristic, complemented
2C2×C5×#890C211yesmaximal, characteristic, complemented
3C2×C3×#4039C211yesmaximal, characteristic
4C2×#91468C211yesmaximal, characteristic, complemented
5C2×C4×#1204C211yesmaximal, characteristic, complemented
6C2×#91434C211yesmaximal, characteristic
7C2×#91430C212yesmaximal, complemented
8C2×Dic3×D20C211yesmaximal, characteristic
9C2×#91422C212yesmaximal, complemented
10C2×D5×C4⋊Dic3C212yesmaximal, complemented
11C2×#91349C212yesmaximal, complemented
12#11753527C2116yesmaximal, direct product factor
13C2×#66024—31nomaximal, Hall
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C22×#1204C2211yescharacteristic
17C22×#1204C2212yes—
18C22×D5×Dic3C2212yes—
19C22×D5×Dic3C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C4⋊Dic15C2212yes—
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C2×C4×Dic15C2211yescharacteristic
25#91779C2218yescomplemented
26C2×C5×C4⋊Dic3C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×Dic3⋊C4C2212yes—
29C2×C4×C5×Dic3C2211yescharacteristic
30C5×#890C2218yescomplemented
31C2×C3×#685C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×#4039C2218yes—
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2212yes—
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91468C2218yescomplemented
41C4×#1204C2218yescomplemented
42#91434C2218yes—
43#91430C22116yescomplemented
44Dic3×D20C2218yes—
45#91422C22116yescomplemented
46D5×C4⋊Dic3C22116yescomplemented
47#91349C22116yescomplemented
48C2×#5543—51nomaximal, Hall
49C2×C5×#125—31no—
50#66024—316no—
51C2×#4043—32no—
52C2×#4042—32no—
53C2×#4042—32no—
54C2×#4039—31no—
55C2×#4039D311yescharacteristic
56C2×D5×C4⋊C4—32no—
57C2×#4036—31no—
58C2×#4034—31no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×C3×D5C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C22×C5×Dic3C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×D20Q818yescomplemented
73C2×C3×D20C2314yes—
74C2×C3×C4×D5—28no—
75C2×C3×C4×D5C2318yes—
76C2×#1204—24no—
77C2×#1204—44no—
78C2×#1204C2314yes—
79C2×#1204C2318yes—
80C2×D5×Dic3—44no—
81C2×D5×Dic3—44no—
82C2×D5×Dic3C2318yes—
83C2×D5×Dic3C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C4⋊Dic15C2318yes—
86C4⋊Dic15C2314yes—
87#6712C2318yes—
88C4×Dic15C2314yes—
89C5×C4⋊Dic3C2318yes—
90C5×C4⋊Dic3C2314yes—
91C5×Dic3⋊C4C2318yes—
92C4×C5×Dic3C2314yes—
93C3×#685C2318yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2314yes—
96#6669C2314yes—
97#6668C2314yes—
98#6668C2318yes—
99#6665C2318yes—
100#6665C2318yes—
101C2×C3×C4×D4—51no—
102C2×D4×Dic3—51no—
103C2×D4×Dic3—51no—
104C22×C4⋊Dic3—52no—
105C2×#924—52no—
106#5543—516no—
107C2×#890—51no—
108C2×#890D511yescharacteristic, complemented
109C2×#878—52no—
110C2×#878—52no—
111C2×#869—51no—
112C2×C4×Dic6—51no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—32no—
115C22×C4×D5—32no—
116C22×C4×D5C2×D312yes—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C5×#125—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C5×C4⋊C4—32no—
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C42×C5—31no—
125C2×#685—32no—
126C2×#685—32no—
127C2×#685C2×D312yes—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—31no—
131C2×#683—32no—
132C2×#683—31no—
133C2×#683—31no—
134C2×#683—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5C2×D311yescharacteristic
137#4043—316no—
138#4042—316no—
139#4042—316no—
140#4039—38no—
141#4039C2×D318yes—
142D5×C4⋊C4—316no—
143#4036—38no—
144#4034—38no—
145C4×D20—38no—
146C4×Dic10—38no—
147C2×#554—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×C3×D5—24no—
150C22×C3×D5—24no—
151C22×C3×D5C2×Q818yes—
152C22×C3×D5C2414yes—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5C2×Q814yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—24no—
160C2×Dic15C2412yes—
161C2×Dic15C2414yes—
162C2×Dic15C2412yes—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—24no—
166C2×C5×Dic3C2412yes—
167C2×C5×Dic3C2414yes—
168C2×C5×Dic3C2412yes—
169C2×C3×Dic5—22no—
170C2×C3×Dic5#4114yes—
171C2×C3×Dic5C2412yes—
172C2×C3×Dic5C2412yes—
173C3×D20C2×Q8116yescomplemented
174C3×C4×D5—216no—
175#1204—28no—
176#1204—48no—
177D5×Dic3—48no—
178D5×Dic3—48no—
179C22×C3×D4—51no—
180C23×C3×C4—52no—
181C23×Dic3—52no—
182C23×Dic3—52no—
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×C4×D4—58no—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4—52no—
188C2×C3×C42—51no—
189C2×#217—52no—
190C2×#217—52no—
191D4×Dic3—58no—
192D4×Dic3—58no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—516no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199C2×C4⋊Dic3C2×D512yes—
200#924—516no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4—51no—
204C2×Dic3⋊C4C2×D512yes—
205C2×C4×Dic3—51no—
206C2×C4×Dic3C2×D511yescharacteristic
207#890—58no—
208#890C2×D518yescomplemented
209#878—516no—
210#878—516no—
211#869—58no—
212C4×Dic6—58no—
213C23×D5C22×D312yes—
214C22×C4×C5—31no—
215C22×C4×C5—31no—
216C22×C4×C5—32no—
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—32no—
220C22×Dic5—31no—
221C22×Dic5—31no—
222C22×Dic5C22×D311yescharacteristic
223C22×Dic5C22×D311yescharacteristic
224C2×D20Dic618yescomplemented
225C2×D20C22×D314yes—
226C2×C4×D5—28no—
227C2×C4×D5—38no—
228C2×C4×D5—38no—
229C2×C4×D5—124no—
230C2×C4×D5—124no—
231C2×C4×D5C22×D318yes—
232C2×Dic10—34no—
233C2×Dic10—38no—
234C2×Dic10—64no—
235C2×Dic10—124no—
236C5×C4⋊C4—38no—
237C5×C4⋊C4—34no—
238C5×C4⋊C4—38no—
239C5×C4⋊C4C22×D314yes—
240C42×C5—34no—
241#685—38no—
242#685—38no—
243#685C22×D318yes—
244C4⋊Dic5—34no—
245C4⋊Dic5—38no—
246C4⋊Dic5—34no—
247#683—38no—
248#683—34no—
249#683—38no—
250#683—34no—
251C4×Dic5—34no—
252C4×Dic5C22×D314yes—
253#554—1516no—
254C2×C4⋊Q8—151no—
255C2×#125—31no—
256C2×#125—151no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—51no—
262C2×C4×D4—151no—
263C2×C4×D4—151no—
264C22×C4⋊C4—152no—
265C22×C3×C5C22×Q812yes—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5H(5,𝔽2)12yes—
268C22×C3×C5C2511yescharacteristic
269C2×C3×D5—216no—
270C2×C3×D5—24no—
271C2×C3×D5—24no—
272C2×C3×D5C22×Q818yes—
273C3×C4×C5—24no—
274C3×C4×C5C22×Q814yes—
275Dic15—22no—
276Dic15—22no—
277Dic15—24no—
278C3×Dic5—22no—
279C3×Dic5C2×#4114yes—
280C5×Dic3—22no—
281C5×Dic3—22no—
282C5×Dic3—24no—
283C24×C3—52no—
284C2×C3×D4—58no—
285C2×C3×D4—54no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—58no—
289C22×C3×C4—108no—
290C22×C3×C4C22×D512yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—51no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—58no—
296C22×Dic3—58no—
297C22×Dic3—204no—
298C22×Dic3—204no—
299C22×Dic3C22×D511yescharacteristic
300C22×Dic3C22×D511yescharacteristic
301C22×Dic3C22×D512yes—
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—204no—
306C3×C4⋊C4C22×D514yes—
307C3×C22⋊C4—58no—
308C3×C42—54no—
309#217—58no—
310#217—58no—
311C4⋊Dic3—54no—
312C4⋊Dic3—58no—
313C4⋊Dic3—54no—
314C4⋊Dic3—58no—
315C4⋊Dic3C22×D514yes—
316C4⋊Dic3C22×D518yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—54no—
319Dic3⋊C4—54no—
320Dic3⋊C4C22×D518yes—
321C4×Dic3—54no—
322C4×Dic3C22×D514yes—
323C23×C5C23×D311yescharacteristic
324C22×D5—24no—
325C22×D5—24no—
326C22×D5C2×Dic618yes—
327C22×D5C23×D314yes—
328C2×C4×C5—24no—
329C2×C4×C5—32no—
330C2×C4×C5—34no—
331C2×C4×C5—32no—
332C2×C4×C5—62no—
333C2×C4×C5—64no—
334C2×C4×C5—62no—
335C2×C4×C5C2×Dic614yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—22no—
339C2×Dic5—32no—
340C2×Dic5—32no—
341C2×Dic5—34no—
342C2×Dic5—62no—
343C2×Dic5—64no—
344C2×Dic5—62no—
345C2×Dic5#23714yes—
346C2×Dic5C23×D312yes—
347C2×Dic5C23×D312yes—
348D20C2×Dic6116yescomplemented
349C4×D5—216no—
350C4×D5—128no—
351C4×D5—128no—
352Dic10—68no—
353Dic10—128no—
354C22×Q8—151no—
355C22×Q8—152no—
356C22×D4—51no—
357C23×C4—52no—
358C23×C4—152no—
359C23×C4—152no—
360C4⋊Q8—158no—
361#125—38no—
362#125—158no—
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—158no—
367C4×D4—58no—
368C4×D4—158no—
369C4×D4—158no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—1516no—
374C2×C4⋊C4—151no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—151no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C22⋊C4—52no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—31no—
386C2×C42—51no—
387C2×C42—151no—
388C2×C3×C5#55414yescomplemented
389C2×C3×C5C23×Q811yescharacteristic
390C2×C3×C5C22×#4111yescharacteristic
391C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
392C3×D5—28no—
393C23×C3—58no—
394C23×C3—54no—
395C23×C3—104no—
396C23×C3—104no—
397C23×C3C23×D511yescharacteristic
398C3×D4—516no—
399C2×C3×C4—24no—
400C2×C3×C4—54no—
401C2×C3×C4—52no—
402C2×C3×C4—52no—
403C2×C3×C4—1016no—
404C2×C3×C4—102no—
405C2×C3×C4Q8×D514yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—22no—
409C2×Dic3—24no—
410C2×Dic3—22no—
411C2×Dic3—52no—
412C2×Dic3—52no—
413C2×Dic3—54no—
414C2×Dic3—102no—
415C2×Dic3—104no—
416C2×Dic3—102no—
417C2×Dic3—208no—
418C2×Dic3—208no—
419C2×Dic3C23×D512yes—
420C2×Dic3C23×D512yes—
421C2×Dic3C23×D514yes—
422Dic6—108no—
423Dic6—208no—
424C22×C5C22×Dic612yes—
425C22×C5C2×#23712yes—
426C22×C5#100912yes—
427C22×C5C24×D311yescharacteristic
428C2×D5—24no—
429C2×D5—24no—
430C2×D5—216no—
431C2×D5C22×Dic618yes—
432C4×C5—24no—
433C4×C5—62no—
434C4×C5—64no—
435C4×C5—62no—
436C4×C5C22×Dic614yes—
437Dic5—22no—
438Dic5—62no—
439Dic5—64no—
440Dic5—62no—
441Dic5C2×#23714yes—
442C24—52no—
443C2×Q8—154no—
444C2×Q8—158no—
445C2×Q8—304no—
446C2×Q8—604no—
447C2×D4—58no—
448C2×D4—54no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—58no—
455C22×C4—108no—
456C22×C4—158no—
457C22×C4—158no—
458C22×C4—151no—
459C22×C4—151no—
460C22×C4—152no—
461C22×C4—604no—
462C22×C4—604no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—34no—
467C4⋊C4—38no—
468C4⋊C4—154no—
469C4⋊C4—158no—
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—158no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4C2×D3×D514yes—
476C22⋊C4—58no—
477C22⋊C4—158no—
478C22⋊C4—158no—
479C42—34no—
480C42—54no—
481C42—154no—
482C3×C5C2×#55411yescharacteristic, complemented, Hall
483C22×C3—58no—
484C22×C3—1016no—
485C22×C3—104no—
486C22×C3—104no—
487C22×C3C2×Q8×D512yes—
488C22×C3D5×#4112yes—
489C22×C3#414912yes—
490C22×C3C24×D511yescharacteristic
491C3×C4—24no—
492C3×C4—54no—
493C3×C4—102no—
494C3×C4C2×Q8×D514yes—
495Dic3—22no—
496Dic3—24no—
497Dic3—22no—
498Dic3—102no—
499Dic3—104no—
500Dic3—102no—
501C2×C5#554314yescomplemented
502C2×C5C23×Dic611yescharacteristic
503C2×C5C22×#23711yescharacteristic
504C2×C5C2×#100911yescharacteristic
505D5—28no—
506C23—58no—
507C23—54no—
508C23—104no—
509C23—104no—
510C23C22×D3×D511yescharacteristic
511Q8—308no—
512Q8—608no—
513D4—516no—
514C2×C4—24no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—34no—
518C2×C4—54no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—64no—
524C2×C4—1016no—
525C2×C4—102no—
526C2×C4—152no—
527C2×C4—152no—
528C2×C4—154no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4—304no—
532C2×C4—608no—
533C2×C4—608no—
534C2×C4D5×Dic614yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3—108no—
538C2×C3#6602414yescomplemented
539C2×C3C22×Q8×D511yescharacteristic
540C2×C3C2×D5×#4111yescharacteristic
541C2×C3C2×#414911yescharacteristic
542C5C2×#554311yescharacteristic, complemented, Sylow
543C22—58no—
544C22—1016no—
545C22—104no—
546C22—104no—
547C22C2×D5×Dic612yes—
548C22D5×#23712yes—
549C22#9203512yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—54no—
553C4—62no—
554C4—62no—
555C4—64no—
556C4—102no—
557C4—302no—
558C4—302no—
559C4—304no—
560C4C2×D5×Dic614yes—
561C3C2×#6602411yescharacteristic, complemented, Sylow
562C2—108no—
563C2#1175352714yesdirect product factor
564C2C22×D5×Dic611yescharacteristic
565C2C2×D5×#23711yescharacteristic
566C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#554
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×#91779C2semidirect
2. C2×C5×#890C2semidirect
4. C2×#91468C2semidirect
5. C2×C4×#1204C2semidirect
7. C2×#91430C2semidirect
9. C2×#91422C2semidirect
10. C2×D5×C4⋊Dic3C2semidirect
11. C2×#91349C2semidirect
12. #11753527C2direct (N × H)
25. #91779C22semidirect
30. C5×#890C22semidirect
40. #91468C22semidirect
41. C4×#1204C22semidirect
43. #91430C22semidirect
45. #91422C22semidirect
46. D5×C4⋊Dic3C22semidirect
47. #91349C22semidirect
72. C2×C3×D20Q8semidirect
108. C2×#890D5semidirect
173. C3×D20C2×Q8semidirect
208. #890C2×D5semidirect
224. C2×D20Dic6semidirect
348. D20C2×Dic6semidirect
388. C2×C3×C5#554semidirect
482. C3×C5C2×#554semidirect
501. C2×C5#5543semidirect
538. C2×C3#66024semidirect
542. C5C2×#5543semidirect
561. C3C2×#66024semidirect
563. C2#11753527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917792
C2×C5×#8902
C2×C3×#40392
C2×#914682
C2×C4×#12042
C2×#914342
C2×#914302
C2×Dic3×D202
C2×#914222
C2×D5×C4⋊Dic32
C2×#913492
#117535272
C2×#660243
C2×#55435