Finite Group Databasebeta

← C2×#11756449 #14483795

Subgroups — C2×#11756449 #14483795

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×C3×C5×#125C211yesmaximal, characteristic, complemented
2#11756449C2116yesmaximal, direct product factor
3C2×#91786C212yesmaximal, complemented
4C2×#91785C212yesmaximal, complemented
5C2×#91785C212yesmaximal, complemented
6C2×#91782C211yesmaximal, characteristic
7C2×#91782C211yesmaximal, characteristic
8C2×C4⋊C4×D15C212yesmaximal, complemented
9C2×#91779C211yesmaximal, characteristic, complemented
10C2×#91777C211yesmaximal, characteristic, complemented
11C2×C4×D60C211yesmaximal, characteristic
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#66024—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×D15C2212yes—
17C22×C4×D15C2212yes—
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C5×#125C2218yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C42×C5C2211yescharacteristic
26C2×#6714C2212yes—
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2211yescharacteristic
31C2×C4⋊Dic15C2212yes—
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×#6712C2212yes—
35C2×#6712C2212yes—
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38#91786C22116yescomplemented
39#91785C22116yescomplemented
40#91785C22116yescomplemented
41#91782C2218yes—
42#91782C2218yes—
43C4⋊C4×D15C22116yescomplemented
44#91779C2218yescomplemented
45#91777C2218yescomplemented
46C4×D60C2218yes—
47C4×Dic30C2218yescomplemented
48C2×#5690—51nomaximal, Hall
49C2×C5×#125D311yescharacteristic, complemented
50#66024—316no—
51C2×#4043—32no—
52C2×#4042—32no—
53C2×#4042—32no—
54C2×#4039—31no—
55C2×#4039—31no—
56C2×D5×C4⋊C4—32no—
57C2×#4036—31no—
58C2×#4034—31no—
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×D15C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C22×Dic15C2311yescharacteristic
72C2×D60Q818yescomplemented
73C2×D60C2314yes—
74C2×C4×D15—28no—
75C2×C4×D15—44no—
76C2×C4×D15—44no—
77C2×C4×D15C2318yes—
78C2×C4×D15C2318yes—
79C2×C4×D15C2318yes—
80C2×Dic30—24no—
81C2×Dic30—44no—
82C2×Dic30C2314yes—
83C2×Dic30C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2314yes—
86C3×C5×C4⋊C4C2318yes—
87C3×C5×C4⋊C4C2318yes—
88C3×C42×C5C2314yes—
89#6714C2318yes—
90#6714C2318yes—
91#6714C2318yes—
92C4⋊Dic15C2314yes—
93C4⋊Dic15C2314yes—
94C4⋊Dic15C2318yes—
95#6712C2314yes—
96#6712C2314yes—
97#6712C2318yes—
98#6712C2318yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C2×C3×#125D511yescharacteristic, complemented
102#5690—516no—
103C2×#897—52no—
104C2×#896—52no—
105C2×#896—52no—
106C2×#893—51no—
107C2×#893—51no—
108C2×D3×C4⋊C4—52no—
109C2×#890—51no—
110C2×#888—51no—
111C2×C4×D12—51no—
112C2×C4×Dic6—51no—
113C22×D20—31no—
114C22×C4×D5—32no—
115C22×C4×D5—32no—
116C22×C4×D5—32no—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C5×#125C2×D318yescomplemented
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D311yescharacteristic
122C2×C5×C4⋊C4C2×D312yes—
123C2×C5×C4⋊C4C2×D312yes—
124C2×C42×C5C2×D311yescharacteristic
125C2×#685—32no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×#683—31no—
132C2×#683—31no—
133C2×#683—32no—
134C2×#683—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—31no—
137#4043—316no—
138#4042—316no—
139#4042—316no—
140#4039—38no—
141#4039—38no—
142D5×C4⋊C4—316no—
143#4036—38no—
144#4034—38no—
145C4×D20—38no—
146C4×Dic10—38no—
147C2×#554—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—24no—
150C22×D15—24no—
151C22×D15C2×Q818yes—
152C22×D15C2414yes—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—24no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5C2×Q814yes—
158C2×C3×C4×C5C2412yes—
159C2×C3×C4×C5C2414yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—24no—
166C2×Dic15—22no—
167C2×Dic15#4114yes—
168C2×Dic15C2412yes—
169C2×Dic15C2412yes—
170C2×Dic15C2412yes—
171C2×Dic15C2414yes—
172C2×Dic15C2412yes—
173D60C2×Q8116yescomplemented
174C4×D15—216no—
175C4×D15—48no—
176C4×D15—48no—
177Dic30—28no—
178Dic30—48no—
179C22×D12—51no—
180C22×C4×D3—52no—
181C22×C4×D3—52no—
182C22×C4×D3—52no—
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×#125C2×D518yescomplemented
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C4⋊C4C2×D511yescharacteristic
188C2×C3×C4⋊C4C2×D512yes—
189C2×C3×C4⋊C4C2×D512yes—
190C2×C3×C42C2×D511yescharacteristic
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—51no—
203#897—516no—
204#896—516no—
205#896—516no—
206#893—58no—
207#893—58no—
208D3×C4⋊C4—516no—
209#890—58no—
210#888—58no—
211C4×D12—58no—
212C4×Dic6—58no—
213C23×D5—32no—
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D311yescharacteristic
216C22×C4×C5C22×D312yes—
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—31no—
220C22×Dic5—31no—
221C22×Dic5—32no—
222C22×Dic5—31no—
223C22×Dic5—31no—
224C2×D20—38no—
225C2×D20—34no—
226C2×C4×D5—38no—
227C2×C4×D5—38no—
228C2×C4×D5—38no—
229C2×C4×D5—68no—
230C2×C4×D5—124no—
231C2×C4×D5—124no—
232C2×Dic10—34no—
233C2×Dic10—38no—
234C2×Dic10—64no—
235C2×Dic10—124no—
236C5×C4⋊C4C22×D314yes—
237C5×C4⋊C4C22×D314yes—
238C5×C4⋊C4C22×D318yes—
239C5×C4⋊C4C22×D318yes—
240C42×C5C22×D314yes—
241#685—38no—
242#685—38no—
243#685—38no—
244C4⋊Dic5—34no—
245C4⋊Dic5—34no—
246C4⋊Dic5—38no—
247#683—34no—
248#683—34no—
249#683—38no—
250#683—38no—
251C4×Dic5—34no—
252C4×Dic5—34no—
253#554—1516no—
254C2×C4⋊Q8—151no—
255C2×#125—151no—
256C2×#125D1511yescharacteristic, complemented
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—151no—
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×D15—216no—
270C2×D15—24no—
271C2×D15—24no—
272C2×D15C22×Q818yes—
273C3×C4×C5—22no—
274C3×C4×C5—24no—
275C3×C4×C5—24no—
276C3×C4×C5—22no—
277C3×C4×C5C22×Q814yes—
278Dic15—22no—
279Dic15—22no—
280Dic15—24no—
281Dic15—22no—
282Dic15C2×#4114yes—
283C23×D3—52no—
284C22×C3×C4C22×D511yescharacteristic
285C22×C3×C4C22×D512yes—
286C22×C3×C4C22×D512yes—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3—52no—
294C2×D12—58no—
295C2×D12—54no—
296C2×C4×D3—58no—
297C2×C4×D3—58no—
298C2×C4×D3—58no—
299C2×C4×D3—108no—
300C2×C4×D3—204no—
301C2×C4×D3—204no—
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—204no—
306C3×C4⋊C4C22×D514yes—
307C3×C4⋊C4C22×D514yes—
308C3×C4⋊C4C22×D518yes—
309C3×C4⋊C4C22×D518yes—
310C3×C42C22×D514yes—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—58no—
314C4⋊Dic3—54no—
315C4⋊Dic3—54no—
316C4⋊Dic3—58no—
317Dic3⋊C4—54no—
318Dic3⋊C4—54no—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321C4×Dic3—54no—
322C4×Dic3—54no—
323C23×C5C23×D311yescharacteristic
324C22×D5—38no—
325C22×D5—34no—
326C22×D5—64no—
327C22×D5—64no—
328C2×C4×C5—22no—
329C2×C4×C5—24no—
330C2×C4×C5—24no—
331C2×C4×C5—22no—
332C2×C4×C5D3×Q814yes—
333C2×C4×C5C23×D312yes—
334C2×C4×C5C23×D314yes—
335C2×C4×C5C23×D314yes—
336C2×C4×C5C23×D312yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—34no—
339C2×Dic5—32no—
340C2×Dic5—32no—
341C2×Dic5—32no—
342C2×Dic5—32no—
343C2×Dic5—34no—
344C2×Dic5—62no—
345C2×Dic5—62no—
346C2×Dic5—64no—
347C2×Dic5—62no—
348D20—316no—
349C4×D5—616no—
350C4×D5—128no—
351C4×D5—128no—
352Dic10—68no—
353Dic10—128no—
354C22×Q8—151no—
355C22×Q8—152no—
356C22×D4—151no—
357C23×C4—152no—
358C23×C4—152no—
359C23×C4—152no—
360C4⋊Q8—158no—
361#125—158no—
362#125C2×D1518yescomplemented
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—158no—
367C4×D4—158no—
368C4×D4—158no—
369C4×D4—158no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—151no—
374C2×C4⋊C4—151no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—1516no—
378C2×C4⋊C4C2×D1512yes—
379C2×C4⋊C4C2×D1511yescharacteristic
380C2×C4⋊C4C2×D1511yescharacteristic
381C2×C4⋊C4C2×D1512yes—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42C2×D1511yescharacteristic
388C2×C3×C5#55414yescomplemented
389C2×C3×C5C23×Q811yescharacteristic
390C2×C3×C5C22×#4111yescharacteristic
391C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
392D15—28no—
393C23×C3C23×D511yescharacteristic
394C22×D3—58no—
395C22×D3—54no—
396C22×D3—104no—
397C22×D3—104no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4Q8×D514yes—
403C2×C3×C4C23×D512yes—
404C2×C3×C4C23×D514yes—
405C2×C3×C4C23×D514yes—
406C2×C3×C4C23×D512yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—54no—
409C2×Dic3—52no—
410C2×Dic3—52no—
411C2×Dic3—52no—
412C2×Dic3—52no—
413C2×Dic3—54no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416C2×Dic3—104no—
417C2×Dic3—102no—
418D12—516no—
419C4×D3—1016no—
420C4×D3—208no—
421C4×D3—208no—
422Dic6—108no—
423Dic6—208no—
424C22×C5C2×D3×Q812yes—
425C22×C5D3×#4112yes—
426C22×C5#100912yes—
427C22×C5C24×D311yescharacteristic
428C2×D5—38no—
429C2×D5—616no—
430C2×D5—64no—
431C2×D5—64no—
432C4×C5—22no—
433C4×C5—24no—
434C4×C5—24no—
435C4×C5—22no—
436C4×C5C2×D3×Q814yes—
437Dic5—34no—
438Dic5—62no—
439Dic5—62no—
440Dic5—64no—
441Dic5—62no—
442C24—152no—
443C2×Q8—154no—
444C2×Q8—158no—
445C2×Q8—304no—
446C2×Q8—604no—
447C2×D4—158no—
448C2×D4—154no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—152no—
454C22×C4—158no—
455C22×C4—158no—
456C22×C4—158no—
457C22×C4—308no—
458C22×C4—604no—
459C22×C4—604no—
460C22×C4C22×D1511yescharacteristic
461C22×C4C22×D1511yescharacteristic
462C22×C4C22×D1512yes—
463C22×C4C22×D1512yes—
464C22×C4C22×D1511yescharacteristic
465C4⋊C4—154no—
466C4⋊C4—158no—
467C4⋊C4—158no—
468C4⋊C4—154no—
469C4⋊C4—154no—
470C4⋊C4—154no—
471C4⋊C4—158no—
472C4⋊C4C22×D1518yes—
473C4⋊C4C22×D1514yes—
474C4⋊C4C22×D1514yes—
475C4⋊C4C22×D1518yes—
476C22⋊C4—158no—
477C22⋊C4—158no—
478C22⋊C4—158no—
479C42—154no—
480C42—154no—
481C42C22×D1514yes—
482C3×C5C2×#55411yescharacteristic, complemented, Hall
483C22×C3C2×Q8×D512yes—
484C22×C3D5×#4112yes—
485C22×C3#414912yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—58no—
488C2×D3—1016no—
489C2×D3—104no—
490C2×D3—104no—
491C3×C4—22no—
492C3×C4—24no—
493C3×C4—24no—
494C3×C4—22no—
495C3×C4C2×Q8×D514yes—
496Dic3—54no—
497Dic3—102no—
498Dic3—102no—
499Dic3—104no—
500Dic3—102no—
501C2×C5#569014yescomplemented
502C2×C5C22×D3×Q811yescharacteristic
503C2×C5C2×D3×#4111yescharacteristic
504C2×C5C2×#100911yescharacteristic
505D5—68no—
506C23—158no—
507C23—154no—
508C23—304no—
509C23—304no—
510C23C23×D1511yescharacteristic
511Q8—308no—
512Q8—608no—
513D4—1516no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—154no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—152no—
522C2×C4—152no—
523C2×C4—154no—
524C2×C4—3016no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—304no—
528C2×C4—302no—
529C2×C4—608no—
530C2×C4—608no—
531C2×C4Q8×D1514yes—
532C2×C4C23×D1512yes—
533C2×C4C23×D1512yes—
534C2×C4C23×D1514yes—
535C2×C4C23×D1514yes—
536C2×C4C23×D1512yes—
537C2×C3#6602414yescomplemented
538C2×C3C22×Q8×D511yescharacteristic
539C2×C3C2×D5×#4111yescharacteristic
540C2×C3C2×#414911yescharacteristic
541D3—108no—
542C5C2×#569011yescharacteristic, complemented, Sylow
543C22—158no—
544C22—304no—
545C22—304no—
546C22—3016no—
547C22C2×Q8×D1512yes—
548C22#41×D1512yes—
549C22#9210012yes—
550C22C24×D1511yescharacteristic
551C4—24no—
552C4—22no—
553C4—22no—
554C4—24no—
555C4—154no—
556C4—302no—
557C4—302no—
558C4—304no—
559C4—302no—
560C4C2×Q8×D1514yes—
561C3C2×#6602411yescharacteristic, complemented, Sylow
562C2—308no—
563C2#1175644914yesdirect product factor
564C2C22×Q8×D1511yescharacteristic
565C2C2×#41×D1511yescharacteristic
566C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×#125D15
hypocenterC3×C5C2×#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. #11756449C2direct (N × H)
3. C2×#91786C2semidirect
4. C2×#91785C2semidirect
5. C2×#91785C2semidirect
8. C2×C4⋊C4×D15C2semidirect
9. C2×#91779C2semidirect
10. C2×#91777C2semidirect
12. C2×C4×Dic30C2semidirect
20. C3×C5×#125C22semidirect
38. #91786C22semidirect
39. #91785C22semidirect
40. #91785C22semidirect
43. C4⋊C4×D15C22semidirect
44. #91779C22semidirect
45. #91777C22semidirect
47. C4×Dic30C22semidirect
49. C2×C5×#125D3semidirect
72. C2×D60Q8semidirect
101. C2×C3×#125D5semidirect
119. C5×#125C2×D3semidirect
173. D60C2×Q8semidirect
185. C3×#125C2×D5semidirect
256. C2×#125D15semidirect
362. #125C2×D15semidirect
388. C2×C3×C5#554semidirect
482. C3×C5C2×#554semidirect
501. C2×C5#5690semidirect
537. C2×C3#66024semidirect
542. C5C2×#5690semidirect
561. C3C2×#66024semidirect
563. C2#11756449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1252
#117564492
C2×#917862
C2×#917852
C2×#917822
C2×C4⋊C4×D152
C2×#917792
C2×#917772
C2×C4×D602
C2×C4×Dic302
C2×#660243
C2×#56905