Finite Group Databasebeta

← C2×#11753634 #14483899

Subgroups — C2×#11753634 #14483899

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×#91777C211yesmaximal, characteristic, complemented
2C2×C5×#893C211yesmaximal, characteristic
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×C4×#1204C211yesmaximal, characteristic, complemented
5C2×#91436C212yesmaximal, complemented
6C2×#91435C211yesmaximal, characteristic
7C2×#91432C212yesmaximal, complemented
8C2×Dic5×D12C211yesmaximal, characteristic
9C2×D3×#683C212yesmaximal, complemented
10C2×#91381C211yesmaximal, characteristic, complemented
11C2×#91365C212yesmaximal, complemented
12#11753634C2116yesmaximal, direct product factor
13C2×#65873—31nomaximal, Hall
14C22×Dic30C2212yes—
15C22×C5×D12C2211yescharacteristic
16C22×C4×C5×D3C2212yes—
17C22×#1204C2211yescharacteristic
18C22×D3×Dic5C2212yes—
19C22×D3×Dic5C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2212yes—
23C2×C4×Dic15C2211yescharacteristic
24#91777C2218yescomplemented
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C5×#893C2218yes—
28C2×C3×C4⋊Dic5C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4036C2218yescomplemented
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6669C2212yes—
35C2×#6669C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40C4×#1204C2218yescomplemented
41#91436C22116yescomplemented
42#91435C2218yes—
43#91432C22116yescomplemented
44Dic5×D12C2218yes—
45D3×#683C22116yescomplemented
46#91381C2218yescomplemented
47#91365C22116yescomplemented
48C2×#5690—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×D4×Dic5—31no—
51C2×D4×Dic5—31no—
52C2×#4070—32no—
53C22×#683—32no—
54#65873—316no—
55C2×#4036D311yescharacteristic, complemented
56C2×#4034—31no—
57C2×#4024—32no—
58C2×#4024—32no—
59C2×#4016—31no—
60C2×C4×Dic10—31no—
61C23×C5×D3C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C2×Dic30—44no—
68C2×Dic30C2318yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C2×C5×D12Q818yescomplemented
72C2×C5×D12C2314yes—
73C2×C4×C5×D3—44no—
74C2×C4×C5×D3C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C2×#1204—24no—
79C2×#1204C2314yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5—44no—
82C2×D3×Dic5C2318yes—
83C2×D3×Dic5C2318yes—
84C3×C5×C4⋊C4C2314yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87C4×Dic15C2314yes—
88C5×(C2×D3)⋊C4C2318yes—
89C4×C5×Dic3C2314yes—
90C3×C4⋊Dic5C2314yes—
91C3×C4⋊Dic5C2318yes—
92C3×#683C2318yes—
93C3×C4×Dic5C2314yes—
94Dic3⋊Dic5C2314yes—
95#6669C2314yes—
96#6669C2318yes—
97#6668C2318yes—
98#6668C2314yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101C2×C3×#125—51no—
102#5690—516no—
103C2×#897—52no—
104C2×#896—52no—
105C2×#896—52no—
106C2×#893—51no—
107C2×#893D511yescharacteristic
108C2×D3×C4⋊C4—52no—
109C2×#890—51no—
110C2×#888—51no—
111C2×C4×D12—51no—
112C2×C4×Dic6—51no—
113C22×C5×D4—31no—
114C23×C4×C5—32no—
115C23×Dic5—32no—
116C23×Dic5—32no—
117C22×Dic10—31no—
118C22×Dic10—32no—
119C4×C5×D4—38no—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C22⋊C4—32no—
122C2×C42×C5—31no—
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125D4×Dic5—38no—
126D4×Dic5—38no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5C2×D311yescharacteristic
130C2×C4⋊Dic5C2×D312yes—
131#4070—316no—
132C2×#683—32no—
133C2×#683—31no—
134C2×#683—31no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—316no—
138C2×#683C2×D312yes—
139C2×C4×Dic5—31no—
140C2×C4×Dic5C2×D311yescharacteristic
141#4036C2×D318yescomplemented
142#4034—38no—
143#4024—316no—
144#4024—316no—
145#4016—38no—
146C4×Dic10—38no—
147C2×#554—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×C5×D3—24no—
150C22×C5×D3—24no—
151C22×C5×D3C2×Q818yes—
152C22×C5×D3C2414yes—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5C2×Q814yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—24no—
158C2×Dic15—22no—
159C2×Dic15#4114yes—
160C2×Dic15C2412yes—
161C2×Dic15C2414yes—
162C2×Dic15C2412yes—
163Dic30—48no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3C2412yes—
167C2×C5×Dic3C2412yes—
168C5×D12C2×Q8116yescomplemented
169C4×C5×D3—48no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2414yes—
175C2×C3×Dic5C2412yes—
176#1204—28no—
177D3×Dic5—216no—
178D3×Dic5—48no—
179C22×D12C2×D511yescharacteristic
180C22×C4×D3—52no—
181C22×C4×D3—52no—
182C22×C4×D3C2×D512yes—
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×#125—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C4⋊C4C2×D511yescharacteristic
190C2×C3×C42—51no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—51no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—51no—
202C2×C4×Dic3C2×D511yescharacteristic
203#897—516no—
204#896—516no—
205#896—516no—
206#893—58no—
207#893C2×D518yes—
208D3×C4⋊C4—516no—
209#890—58no—
210#888—58no—
211C4×D12—58no—
212C4×Dic6—58no—
213C24×C5—32no—
214C2×C5×D4—38no—
215C2×C5×D4—34no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—38no—
219C22×C4×C5—124no—
220C22×C4×C5C22×D312yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—31no—
224C22×Dic5—32no—
225C22×Dic5—38no—
226C22×Dic5—38no—
227C22×Dic5—68no—
228C22×Dic5—124no—
229C22×Dic5C22×D311yescharacteristic
230C22×Dic5C22×D312yes—
231C22×Dic5C22×D311yescharacteristic
232C2×Dic10—34no—
233C2×Dic10—38no—
234C2×Dic10—64no—
235C2×Dic10—124no—
236C5×C4⋊C4C22×D314yes—
237C5×C22⋊C4—38no—
238C42×C5—34no—
239C22⋊Dic5—38no—
240C22⋊Dic5—38no—
241C4⋊Dic5—34no—
242C4⋊Dic5—34no—
243C4⋊Dic5C22×D314yes—
244C4⋊Dic5C22×D318yes—
245#683—38no—
246#683—34no—
247#683—38no—
248#683—34no—
249#683—38no—
250#683C22×D318yes—
251C4×Dic5—34no—
252C4×Dic5C22×D314yes—
253#554—1516no—
254C2×C4⋊Q8—151no—
255C2×#125—51no—
256C2×#125—151no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—31no—
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×C5×D3—216no—
270C2×C5×D3—24no—
271C2×C5×D3—24no—
272C2×C5×D3C22×Q818yes—
273C3×C4×C5—24no—
274C3×C4×C5C22×Q814yes—
275Dic15—24no—
276Dic15—22no—
277Dic15C2×#4114yes—
278C3×Dic5—24no—
279C3×Dic5—22no—
280C3×Dic5—22no—
281C5×Dic3—22no—
282C5×Dic3—22no—
283C23×D3C22×D512yes—
284C22×C3×C4—51no—
285C22×C3×C4—52no—
286C22×C3×C4—51no—
287C22×C3×C4C22×D512yes—
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3—52no—
292C22×Dic3C22×D511yescharacteristic
293C22×Dic3C22×D511yescharacteristic
294C2×D12Dic1018yescomplemented
295C2×D12C22×D514yes—
296C2×C4×D3—44no—
297C2×C4×D3—58no—
298C2×C4×D3—58no—
299C2×C4×D3—108no—
300C2×C4×D3—204no—
301C2×C4×D3C22×D518yes—
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—204no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4—58no—
309C3×C4⋊C4C22×D514yes—
310C3×C42—54no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4C22×D518yes—
314C4⋊Dic3—54no—
315C4⋊Dic3—54no—
316C4⋊Dic3—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4—54no—
319Dic3⋊C4—58no—
320Dic3⋊C4—54no—
321C4×Dic3—54no—
322C4×Dic3C22×D514yes—
323C23×C5—38no—
324C23×C5—34no—
325C23×C5—64no—
326C23×C5—64no—
327C23×C5C23×D311yescharacteristic
328C5×D4—316no—
329C2×C4×C5—24no—
330C2×C4×C5—32no—
331C2×C4×C5—32no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5—128no—
335C2×C4×C5D3×Q814yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—22no—
339C2×Dic5—24no—
340C2×Dic5—22no—
341C2×Dic5—34no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—34no—
345C2×Dic5—616no—
346C2×Dic5—62no—
347C2×Dic5—64no—
348C2×Dic5—128no—
349C2×Dic5C23×D312yes—
350C2×Dic5C23×D312yes—
351C2×Dic5C23×D314yes—
352Dic10—68no—
353Dic10—128no—
354C22×Q8—151no—
355C22×Q8—152no—
356C22×D4—31no—
357C23×C4—32no—
358C23×C4—152no—
359C23×C4—152no—
360C4⋊Q8—158no—
361#125—58no—
362#125—158no—
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—158no—
367C4×D4—38no—
368C4×D4—158no—
369C4×D4—158no—
370C2×C4⋊C4—52no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—52no—
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—152no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C22⋊C4—32no—
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
392C5×D3—28no—
393C23×C3C23×D511yescharacteristic
394C22×D3—24no—
395C22×D3—24no—
396C22×D3C2×Dic1018yes—
397C22×D3C23×D514yes—
398C2×C3×C4—24no—
399C2×C3×C4—52no—
400C2×C3×C4—54no—
401C2×C3×C4—52no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—104no—
405C2×C3×C4C2×Dic1014yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—54no—
411C2×Dic3—52no—
412C2×Dic3—52no—
413C2×Dic3—54no—
414C2×Dic3—102no—
415C2×Dic3—104no—
416C2×Dic3C23×D512yes—
417C2×Dic3C23×D512yes—
418D12C2×Dic10116yescomplemented
419C4×D3—48no—
420C4×D3—1016no—
421C4×D3—208no—
422Dic6—108no—
423Dic6—208no—
424C22×C5—38no—
425C22×C5—616no—
426C22×C5—64no—
427C22×C5—64no—
428C22×C5C2×D3×Q812yes—
429C22×C5D3×#4112yes—
430C22×C5#100912yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—24no—
433C4×C5—62no—
434C4×C5—62no—
435C4×C5C2×D3×Q814yes—
436Dic5—22no—
437Dic5—24no—
438Dic5—22no—
439Dic5—34no—
440Dic5—62no—
441Dic5—64no—
442C24—32no—
443C2×Q8—154no—
444C2×Q8—158no—
445C2×Q8—304no—
446C2×Q8—604no—
447C2×D4—38no—
448C2×D4—34no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—38no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—52no—
455C22×C4—124no—
456C22×C4—158no—
457C22×C4—158no—
458C22×C4—151no—
459C22×C4—151no—
460C22×C4—152no—
461C22×C4—308no—
462C22×C4—604no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—58no—
466C4⋊C4—54no—
467C4⋊C4—58no—
468C4⋊C4—154no—
469C4⋊C4—158no—
470C4⋊C4—154no—
471C4⋊C4—154no—
472C4⋊C4—158no—
473C4⋊C4—158no—
474C4⋊C4—154no—
475C4⋊C4C2×D3×D514yes—
476C22⋊C4—38no—
477C22⋊C4—158no—
478C22⋊C4—158no—
479C42—34no—
480C42—54no—
481C42—154no—
482C3×C5C2×#55411yescharacteristic, complemented, Hall
483C22×C3C22×Dic1012yes—
484C22×C3#414412yes—
485C22×C3D5×#4112yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—216no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3C22×Dic1018yes—
491C3×C4—24no—
492C3×C4—102no—
493C3×C4—102no—
494C3×C4—104no—
495C3×C4C22×Dic1014yes—
496Dic3—22no—
497Dic3—22no—
498Dic3—54no—
499Dic3—102no—
500Dic3—104no—
501C2×C5—68no—
502C2×C5#569014yescomplemented
503C2×C5C22×D3×Q811yescharacteristic
504C2×C5C2×D3×#4111yescharacteristic
505C2×C5C2×#100911yescharacteristic
506C23—38no—
507C23—34no—
508C23—64no—
509C23—64no—
510C23C22×D3×D511yescharacteristic
511Q8—308no—
512Q8—608no—
513D4—316no—
514C2×C4—24no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—54no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—102no—
523C2×C4—104no—
524C2×C4—102no—
525C2×C4—128no—
526C2×C4—154no—
527C2×C4—152no—
528C2×C4—152no—
529C2×C4—154no—
530C2×C4—3016no—
531C2×C4—304no—
532C2×C4—302no—
533C2×C4—608no—
534C2×C4D3×Dic1014yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6587314yescomplemented
538C2×C3C23×Dic1011yescharacteristic
539C2×C3C2×#414411yescharacteristic
540C2×C3C2×D5×#4111yescharacteristic
541D3—28no—
542C5C2×#569011yescharacteristic, complemented, Sylow
543C22—38no—
544C22—616no—
545C22—64no—
546C22—64no—
547C22C2×D3×Dic1012yes—
548C22#9202712yes—
549C22#9203412yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—62no—
553C4—62no—
554C4—102no—
555C4—104no—
556C4—102no—
557C4—154no—
558C4—304no—
559C4—302no—
560C4C2×D3×Dic1014yes—
561C3C2×#6587311yescharacteristic, complemented, Sylow
562C2—68no—
563C2#1175363414yesdirect product factor
564C2C22×D3×Dic1011yescharacteristic
565C2C2×#9202711yescharacteristic
566C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
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×#91777C2semidirect
3. C2×C3×#4036C2semidirect
4. C2×C4×#1204C2semidirect
5. C2×#91436C2semidirect
7. C2×#91432C2semidirect
9. C2×D3×#683C2semidirect
10. C2×#91381C2semidirect
11. C2×#91365C2semidirect
12. #11753634C2direct (N × H)
24. #91777C22semidirect
32. C3×#4036C22semidirect
40. C4×#1204C22semidirect
41. #91436C22semidirect
43. #91432C22semidirect
45. D3×#683C22semidirect
46. #91381C22semidirect
47. #91365C22semidirect
55. C2×#4036D3semidirect
71. C2×C5×D12Q8semidirect
141. #4036C2×D3semidirect
168. C5×D12C2×Q8semidirect
294. C2×D12Dic10semidirect
388. C2×C3×C5#554semidirect
418. D12C2×Dic10semidirect
482. C3×C5C2×#554semidirect
502. C2×C5#5690semidirect
537. C2×C3#65873semidirect
542. C5C2×#5690semidirect
561. C3C2×#65873semidirect
563. C2#11753634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917772
C2×C5×#8932
C2×C3×#40362
C2×C4×#12042
C2×#914362
C2×#914352
C2×#914322
C2×Dic5×D122
C2×D3×#6832
C2×#913812
C2×#913652
#117536342
C2×#658733
C2×#56905