Finite Group Databasebeta

← C2×#11752583 #14483847

Subgroups — C2×#11752583 #14483847

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×#91759C211yesmaximal, characteristic, complemented
2C2×C4×C5×D12C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×#91468C211yesmaximal, characteristic, complemented
5C2×#91436C212yesmaximal, complemented
6C2×Dic5×D12C211yesmaximal, characteristic
7C2×Dic5×D12C211yesmaximal, characteristic
8C2×#91410C212yesmaximal, complemented
9C2×D3×#683C212yesmaximal, complemented
10C2×#91388C211yesmaximal, characteristic, complemented
11C2×#91352C212yesmaximal, complemented
12#11752583C2116yesmaximal, direct product factor
13C2×#65873—31nomaximal, Hall
14C22×C5×D12C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C3×Dic10C2211yescharacteristic
17C22×#1204C2212yes—
18C22×D3×Dic5C2212yes—
19C22×D3×Dic5C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C2×#6712C2212yes—
25#91759C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C4×C5×D12C2218yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C3×C4×Dic10C2218yescomplemented
35C2×Dic3⋊Dic5C2212yes—
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91468C2218yescomplemented
41#91436C22116yescomplemented
42Dic5×D12C2218yes—
43Dic5×D12C2218yes—
44#91410C22116yescomplemented
45D3×#683C22116yescomplemented
46#91388C2218yescomplemented
47#91352C22116yescomplemented
48C2×#5579—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×#4036—31no—
56C2×#4034—31no—
57C2×#4024—32no—
58C2×#4024—32no—
59C2×#4016—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×C5×D3C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C22×C5×Dic3C2312yes—
68C2×C5×D12Q818yescomplemented
69C2×C5×D12C2314yes—
70C2×C4×C5×D3—44no—
71C2×C4×C5×D3C2318yes—
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×Dic10—24no—
77C2×C3×Dic10C2314yes—
78C2×#1204—44no—
79C2×#1204C2318yes—
80C2×D3×Dic5—28no—
81C2×D3×Dic5—44no—
82C2×D3×Dic5C2318yes—
83C2×D3×Dic5C2318yes—
84C3×C42×C5C2314yes—
85C4⋊Dic15C2314yes—
86C4⋊Dic15C2314yes—
87#6712C2318yes—
88#6712C2318yes—
89C5×(C2×D3)⋊C4C2318yes—
90C5×C4⋊Dic3C2314yes—
91C3×C4⋊Dic5C2314yes—
92C3×#683C2314yes—
93C3×#683C2314yes—
94C3×C4×Dic5C2314yes—
95C3×C4×Dic5C2314yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6668C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101C2×C3×C4×Q8—51no—
102C2×#946—52no—
103#5579—516no—
104C2×#896—52no—
105C2×#896—52no—
106C2×D3×C4⋊C4—52no—
107C2×C4×D12—51no—
108C2×C4×D12—51no—
109C2×C4×D12D511yescharacteristic
110C2×#870—51no—
111C2×#870—51no—
112C2×#869—51no—
113C22×C5×D4—31no—
114C23×C4×C5—32no—
115C23×Dic5—32no—
116C23×Dic5—32no—
117C22×Dic10—32no—
118C22×Dic10C2×D311yescharacteristic
119C4×C5×D4—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C22⋊C4—32no—
122C2×C42×C5C2×D311yescharacteristic
123C2×C22⋊Dic5—32no—
124C2×C22⋊Dic5—32no—
125D4×Dic5—38no—
126D4×Dic5—38no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131#4070—316no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×#683—32no—
136C2×#683—316no—
137C2×#683C2×D311yescharacteristic
138C2×#683C2×D311yescharacteristic
139C2×C4×Dic5C2×D311yescharacteristic
140C2×C4×Dic5C2×D311yescharacteristic
141#4036—38no—
142#4034—38no—
143#4024—316no—
144#4024—316no—
145#4016—38no—
146C4×Dic10C2×D318yescomplemented
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—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5C2×Q814yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×C3×C4×C5C2412yes—
159C2×Dic15—24no—
160C2×Dic15—24no—
161C2×Dic15C2414yes—
162C2×Dic15C2414yes—
163C2×C5×Dic3—24no—
164C2×C5×Dic3C2414yes—
165C5×D12C2×Q8116yescomplemented
166C4×C5×D3—48no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5#4114yes—
171C2×C3×Dic5C2412yes—
172C2×C3×Dic5C2412yes—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2412yes—
175C3×Dic10—28no—
176#1204—48no—
177D3×Dic5—216no—
178D3×Dic5—48no—
179C22×C3×Q8—51no—
180C22×D12C2×D511yescharacteristic
181C22×C4×D3—52no—
182C22×C4×D3—52no—
183C22×C4×D3C2×D512yes—
184C22×Dic6—52no—
185C3×C4×Q8—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C42—51no—
190C2×C3×C42—51no—
191C2×C3×C42C2×D511yescharacteristic
192#946—516no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×(C2×D3)⋊C4C2×D512yes—
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—51no—
198C2×C4⋊Dic3—52no—
199C2×C4⋊Dic3C2×D511yescharacteristic
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204#896—516no—
205#896—516no—
206D3×C4⋊C4—516no—
207C4×D12—58no—
208C4×D12—58no—
209C4×D12C2×D518yes—
210#870—58no—
211#870—58no—
212#869—58no—
213C24×C5—32no—
214C2×C5×D4—38no—
215C2×C5×D4—34no—
216C22×C4×C5—32no—
217C22×C4×C5—38no—
218C22×C4×C5—124no—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—32no—
223C22×Dic5—32no—
224C22×Dic5—38no—
225C22×Dic5—38no—
226C22×Dic5—68no—
227C22×Dic5—124no—
228C22×Dic5C22×D311yescharacteristic
229C22×Dic5C22×D311yescharacteristic
230C22×Dic5C22×D311yescharacteristic
231C22×Dic5C22×D311yescharacteristic
232C2×Dic10—24no—
233C2×Dic10—38no—
234C2×Dic10—124no—
235C2×Dic10C22×D314yes—
236C5×C4⋊C4—34no—
237C5×C22⋊C4—38no—
238C42×C5C22×D314yes—
239C22⋊Dic5—38no—
240C22⋊Dic5—38no—
241C4⋊Dic5—34no—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244C4⋊Dic5C22×D314yes—
245#683—38no—
246#683—38no—
247#683—38no—
248#683—38no—
249#683C22×D314yes—
250#683C22×D314yes—
251C4×Dic5C22×D314yes—
252C4×Dic5C22×D314yes—
253#554—1516no—
254C2×C4⋊Q8—151no—
255C2×#125—151no—
256C2×#125—151no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—51no—
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—22no—
274C3×C4×C5—22no—
275C3×C4×C5C22×Q814yes—
276Dic15—24no—
277Dic15—24no—
278C3×Dic5—22no—
279C3×Dic5—22no—
280C3×Dic5—22no—
281C3×Dic5C2×#4114yes—
282C5×Dic3—24no—
283C23×D3C22×D512yes—
284C2×C3×Q8—54no—
285C2×C3×Q8—104no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4C22×D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×Dic3—52no—
294C22×Dic3—52no—
295C22×Dic3C22×D512yes—
296C2×D12Dic1018yescomplemented
297C2×D12C22×D514yes—
298C2×C4×D3—44no—
299C2×C4×D3—58no—
300C2×C4×D3—58no—
301C2×C4×D3—108no—
302C2×C4×D3—204no—
303C2×C4×D3C22×D518yes—
304C2×Dic6—58no—
305C2×Dic6—204no—
306C3×C4⋊C4—54no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4—54no—
309C3×C42—54no—
310C3×C42—54no—
311C3×C42C22×D514yes—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—58no—
314(C2×D3)⋊C4C22×D518yes—
315C4⋊Dic3—54no—
316C4⋊Dic3—54no—
317C4⋊Dic3—58no—
318C4⋊Dic3C22×D514yes—
319Dic3⋊C4—58no—
320Dic3⋊C4—58no—
321Dic3⋊C4—58no—
322Dic3⋊C4—58no—
323C23×C5—38no—
324C23×C5—34no—
325C23×C5—64no—
326C23×C5—64no—
327C23×C5C23×D311yescharacteristic
328C5×D4—316no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—34no—
332C2×C4×C5—64no—
333C2×C4×C5—128no—
334C2×C4×C5D3×Q814yes—
335C2×C4×C5C23×D312yes—
336C2×C4×C5C23×D312yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—34no—
342C2×Dic5—34no—
343C2×Dic5—64no—
344C2×Dic5—64no—
345C2×Dic5—616no—
346C2×Dic5—128no—
347C2×Dic5#23514yes—
348C2×Dic5C23×D312yes—
349C2×Dic5C23×D312yes—
350C2×Dic5C23×D312yes—
351C2×Dic5C23×D312yes—
352Dic10—28no—
353Dic10—128no—
354C22×Q8—51no—
355C22×Q8—152no—
356C22×D4—31no—
357C23×C4—32no—
358C23×C4—152no—
359C23×C4—152no—
360C4⋊Q8—158no—
361#125—158no—
362#125—158no—
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—58no—
367C4×D4—38no—
368C4×D4—158no—
369C4×D4—158no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—1516no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—51no—
386C2×C42—51no—
387C2×C42D3×D511yescharacteristic
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—
398C3×Q8—108no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—54no—
402C2×C3×C4—52no—
403C2×C3×C4—52no—
404C2×C3×C4—52no—
405C2×C3×C4—52no—
406C2×C3×C4—102no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4C2×Dic1014yes—
410C2×C3×C4C23×D512yes—
411C2×C3×C4C23×D512yes—
412C2×C3×C4C23×D512yes—
413C2×Dic3—24no—
414C2×Dic3—54no—
415C2×Dic3—54no—
416C2×Dic3—104no—
417C2×Dic3—104no—
418C2×Dic3C23×D514yes—
419D12C2×Dic10116yescomplemented
420C4×D3—48no—
421C4×D3—1016no—
422C4×D3—208no—
423Dic6—208no—
424C22×C5—38no—
425C22×C5—64no—
426C22×C5—64no—
427C22×C5—616no—
428C22×C5C2×#23512yes—
429C22×C5C2×D3×Q812yes—
430C22×C5#100912yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—22no—
433C4×C5—22no—
434C4×C5—64no—
435C4×C5C2×D3×Q814yes—
436Dic5—22no—
437Dic5—22no—
438Dic5—22no—
439Dic5—64no—
440Dic5—64no—
441Dic5C2×#23514yes—
442C24—32no—
443C2×Q8—54no—
444C2×Q8—104no—
445C2×Q8—158no—
446C2×Q8—604no—
447C2×D4—38no—
448C2×D4—34no—
449C22×C4—32no—
450C22×C4—38no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—124no—
456C22×C4—158no—
457C22×C4—158no—
458C22×C4—152no—
459C22×C4—152no—
460C22×C4—308no—
461C22×C4—604no—
462C22×C4C2×D3×D511yescharacteristic
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—34no—
466C4⋊C4—54no—
467C4⋊C4—54no—
468C4⋊C4—54no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4—154no—
474C4⋊C4—154no—
475C4⋊C4—158no—
476C22⋊C4—38no—
477C22⋊C4—158no—
478C22⋊C4—158no—
479C42—54no—
480C42—54no—
481C42C2×D3×D514yes—
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—22no—
492C3×C4—22no—
493C3×C4—54no—
494C3×C4—102no—
495C3×C4—102no—
496C3×C4—102no—
497C3×C4C22×Dic1014yes—
498Dic3—24no—
499Dic3—104no—
500Dic3—104no—
501C2×C5—68no—
502C2×C5#557914yescomplemented
503C2×C5C22×#23511yescharacteristic
504C2×C5C22×D3×Q811yescharacteristic
505C2×C5C2×#100911yescharacteristic
506C23—38no—
507C23—34no—
508C23—64no—
509C23—64no—
510C23C22×D3×D511yescharacteristic
511Q8—108no—
512Q8—608no—
513D4—316no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—34no—
517C2×C4—54no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—64no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—128no—
527C2×C4—154no—
528C2×C4—154no—
529C2×C4—3016no—
530C2×C4—304no—
531C2×C4—304no—
532C2×C4—608no—
533C2×C4D3×Dic1014yes—
534C2×C4C22×D3×D512yes—
535C2×C4C22×D3×D512yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6587314yescomplemented
538C2×C3C23×Dic1011yescharacteristic
539C2×C3C2×#414411yescharacteristic
540C2×C3C2×D5×#4111yescharacteristic
541D3—28no—
542C5C2×#557911yescharacteristic, complemented, Sylow
543C22—38no—
544C22—616no—
545C22—64no—
546C22—64no—
547C22C2×D3×Dic1012yes—
548C22D5×#23512yes—
549C22#9201812yes—
550C22C23×D3×D511yescharacteristic
551C4—22no—
552C4—22no—
553C4—54no—
554C4—64no—
555C4—102no—
556C4—102no—
557C4—102no—
558C4—304no—
559C4—304no—
560C4C2×D3×Dic1014yes—
561C3C2×#6587311yescharacteristic, complemented, Sylow
562C2—68no—
563C2#1175258314yesdirect product factor
564C2C22×D3×Dic1011yescharacteristic
565C2C2×D5×#23511yescharacteristic
566C2C2×#9201811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#554
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×#91759C2semidirect
3. C2×C3×C4×Dic10C2semidirect
4. C2×#91468C2semidirect
5. C2×#91436C2semidirect
8. C2×#91410C2semidirect
9. C2×D3×#683C2semidirect
10. C2×#91388C2semidirect
11. C2×#91352C2semidirect
12. #11752583C2direct (N × H)
25. #91759C22semidirect
34. C3×C4×Dic10C22semidirect
40. #91468C22semidirect
41. #91436C22semidirect
44. #91410C22semidirect
45. D3×#683C22semidirect
46. #91388C22semidirect
47. #91352C22semidirect
60. C2×C4×Dic10D3semidirect
68. C2×C5×D12Q8semidirect
146. C4×Dic10C2×D3semidirect
165. C5×D12C2×Q8semidirect
296. C2×D12Dic10semidirect
388. C2×C3×C5#554semidirect
419. D12C2×Dic10semidirect
482. C3×C5C2×#554semidirect
502. C2×C5#5579semidirect
537. C2×C3#65873semidirect
542. C5C2×#5579semidirect
561. C3C2×#65873semidirect
563. C2#11752583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917592
C2×C4×C5×D122
C2×C3×C4×Dic102
C2×#914682
C2×#914362
C2×Dic5×D122
C2×#914102
C2×D3×#6832
C2×#913882
C2×#913522
#117525832
C2×#658733
C2×#55795