Finite Group Databasebeta

← C2×#11752523 #14479033

Subgroups — C2×#11752523 #14479033

Order 1920.

2976 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
1C22×D3×Dic10C211yesmaximal, characteristic
2C2×C4×Dic30C211yesmaximal, characteristic, complemented
3C2×C5×#872C211yesmaximal, characteristic
4C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
5C2×#91400C212yesmaximal
6C2×#91398C212yesmaximal
7C2×#91340C211yesmaximal, characteristic, complemented
8C2×#91338C211yesmaximal, characteristic
9C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
10C2×#91325C212yesmaximal, complemented
11C2×#91323C212yesmaximal, complemented
12#11752523C2116yesmaximal, direct product factor
13C2×#65850—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C22×#1204C2212yes—
18C22×D3×Dic5C2212yes—
19C2×D3×Dic10C4116yescomplemented
20C2×D3×Dic10C2218yes—
21C2×C3×C42×C5C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C2×C4×Dic15C2212yes—
25C4×Dic30C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C5×Dic3⋊C4C2211yescharacteristic
30C2×C4×C5×Dic3C2211yescharacteristic
31C5×#872C2218yes—
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×#683C2212yes—
34C2×C3×C4×Dic5C2212yes—
35C3×C4×Dic10C2218yescomplemented
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91400C22116yes—
43#91398C22116yes—
44#91340C2218yescomplemented
45#91338C2218yes—
46Dic3×Dic10C2218yescomplemented
47#91325C22116yescomplemented
48#91323C22116yescomplemented
49C2×#5572—51nomaximal, Hall
50C23×Dic10—31no—
51C2×C5×#117—31no—
52C2×#4072—31no—
53#65850—316no—
54C2×#4033—32no—
55C2×#4033—32no—
56C2×#4023—32no—
57C2×#4023—32no—
58C2×C4×Dic10—31no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—31no—
61C2×C4×Dic10D311yescharacteristic, complemented
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2312yes—
68C2×Dic30C2×C418yes—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2311yescharacteristic
73C2×C4×C5×D3C2×C418yes—
74C2×C4×C5×D3C2314yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2312yes—
77C2×C3×Dic10C2×C418yes—
78C2×C3×Dic10C2314yes—
79C2×#1204C2×C4116yes—
80C2×#1204C2318yes—
81C2×D3×Dic5C2×C4116yes—
82C2×D3×Dic5C2318yes—
83D3×Dic10C2×C4164yescomplemented
84C3×C42×C5C2314yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87C4×Dic15C2318yes—
88C5×(C2×D3)⋊C4C2314yes—
89C5×(C2×D3)⋊C4C2314yes—
90C5×Dic3⋊C4C2314yes—
91C5×Dic3⋊C4C2314yes—
92C4×C5×Dic3C2314yes—
93C3×C4⋊Dic5C2314yes—
94C3×#683C2318yes—
95C3×C4×Dic5C2318yes—
96#6669C2318yes—
97#6668C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2318yes—
100Dic3×Dic5C2318yes—
101Dic3×Dic5C2318yes—
102C22×D3×Q8—51no—
103C2×C3×C4×Q8—51no—
104C2×Q8×Dic3—51no—
105#5572—516no—
106C2×#892—51no—
107C2×#892—52no—
108C2×#887—52no—
109C2×#887—51no—
110C2×#872—52no—
111C2×#872D511yescharacteristic
112C2×C4×Dic6—51no—
113C2×C4×Dic6—52no—
114C23×C4×C5—31no—
115C23×Dic5—32no—
116C22×Dic10—31no—
117C22×Dic10—32no—
118C22×Dic10—316no—
119C22×Dic10—38no—
120C22×Dic10C2×D311yescharacteristic
121C5×#117—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C4⋊C4—31no—
124C2×C5×C22⋊C4—31no—
125C2×C5×C22⋊C4—31no—
126C2×C42×C5—31no—
127C2×C42×C5C2×D311yescharacteristic
128C2×C22⋊Dic5—32no—
129#4072—38no—
130C2×C4⋊Dic5—31no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×#683C2×D312yes—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—32no—
140C2×C4×Dic5C2×D312yes—
141#4033—316no—
142#4033—316no—
143#4023—316no—
144#4023—316no—
145C4×Dic10—38no—
146C4×Dic10—38no—
147C4×Dic10—38no—
148C4×Dic10C2×D318yescomplemented
149C2×#519—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3C22×C414yes—
154C22×C5×D3C2412yes—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5C22×C414yes—
158C2×C3×C4×C5C2412yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—24no—
162C2×Dic15C22×C418yes—
163C2×Dic15C2414yes—
164C2×Dic15C2414yes—
165Dic30C22×C4116yes—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C22×C414yes—
169C2×C5×Dic3C2412yes—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2412yes—
172C4×C5×D3C22×C4116yes—
173C2×C3×Dic5—24no—
174C2×C3×Dic5C22×C418yes—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10C22×C4116yes—
178#1204C22×C4132yes—
179D3×Dic5C22×C4132yes—
180C22×C3×Q8—51no—
181C2×D3×Q8—516no—
182C2×D3×Q8—58no—
183C22×C4×D3—52no—
184C22×C4×D3C2×D511yescharacteristic
185C22×Dic6—51no—
186C22×Dic6—52no—
187C3×C4×Q8—58no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C4⋊C4—51no—
190C2×C3×C42—52no—
191C2×C3×C42C2×D511yescharacteristic
192Q8×Dic3—58no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4C2×D511yescharacteristic
195C2×(C2×D3)⋊C4C2×D511yescharacteristic
196C2×C4⋊Dic3—51no—
197C2×C4⋊Dic3—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D511yescharacteristic
201C2×Dic3⋊C4C2×D511yescharacteristic
202C2×C4×Dic3—52no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3C2×D511yescharacteristic
207#892—58no—
208#892—516no—
209#887—516no—
210#887—58no—
211#872—516no—
212#872C2×D518yes—
213C4×Dic6—58no—
214C4×Dic6—516no—
215C24×C5—31no—
216C22×C4×C5—31no—
217C22×C4×C5—38no—
218C22×C4×C5—34no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—32no—
225C22×Dic5—316no—
226C22×Dic5—38no—
227C22×Dic5—32no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C2×Dic10—38no—
231C2×Dic10—34no—
232C2×Dic10—316no—
233C2×Dic10—38no—
234C2×Dic10—364no—
235C2×Dic10C4×D318yes—
236C2×Dic10C22×D314yes—
237C5×C4⋊C4—34no—
238C5×C4⋊C4—34no—
239C5×C22⋊C4—34no—
240C5×C22⋊C4—34no—
241C42×C5—34no—
242C42×C5C22×D314yes—
243C22⋊Dic5—38no—
244C4⋊Dic5—34no—
245C4⋊Dic5C22×D314yes—
246#683—38no—
247#683—38no—
248#683—38no—
249#683C22×D318yes—
250C4×Dic5—38no—
251C4×Dic5—38no—
252C4×Dic5—38no—
253C4×Dic5—38no—
254C4×Dic5C22×D318yes—
255C23×Q8—151no—
256#519—1516no—
257C2×C4×Q8—51no—
258C2×C4×Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×Q8—152no—
262C2×C4×Q8—151no—
263C2×#117—31no—
264C2×#117—152no—
265C2×#117—152no—
266C2×#117—151no—
267C22×C3×C5C23×C412yes—
268C22×C3×C52−1+412yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×C5×D3—28no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3C23×C414yes—
275C3×C4×C5—22no—
276C3×C4×C5—22no—
277C3×C4×C5C23×C414yes—
278Dic15—24no—
279Dic15C23×C418yes—
280C3×Dic5—24no—
281C3×Dic5C23×C418yes—
282C5×Dic3—22no—
283C5×Dic3—22no—
284C5×Dic3C23×C414yes—
285C23×D3C22×D511yescharacteristic
286C2×C3×Q8—58no—
287C2×C3×Q8—54no—
288C22×C3×C4—52no—
289C22×C3×C4—52no—
290C22×C3×C4C22×D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×C3×C4C22×D511yescharacteristic
293C22×Dic3—52no—
294C22×Dic3—52no—
295C22×Dic3C22×D511yescharacteristic
296C22×Dic3C22×D511yescharacteristic
297C22×Dic3C22×D511yescharacteristic
298D3×Q8—564no—
299C2×C4×D3—516no—
300C2×C4×D3—58no—
301C2×C4×D3C4×D518yes—
302C2×C4×D3C22×D514yes—
303C2×Dic6—58no—
304C2×Dic6—54no—
305C2×Dic6—516no—
306C2×Dic6—58no—
307C3×C4⋊C4—58no—
308C3×C4⋊C4—54no—
309C3×C42—58no—
310C3×C42C22×D514yes—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4C22×D514yes—
313(C2×D3)⋊C4C22×D514yes—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316Dic3⋊C4—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4C22×D514yes—
319Dic3⋊C4C22×D514yes—
320C4×Dic3—58no—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C4×Dic3C22×D514yes—
325C23×C5—34no—
326C23×C5—32no—
327C23×C5—62no—
328C23×C5—62no—
329C23×C5C23×D311yescharacteristic
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—34no—
333C2×C4×C5—32no—
334C2×C4×C5—316no—
335C2×C4×C5—32no—
336C2×C4×C5—32no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5C2×C4×D314yes—
340C2×C4×C5C23×D312yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—24no—
344C2×Dic5—38no—
345C2×Dic5—34no—
346C2×Dic5—332no—
347C2×Dic5—34no—
348C2×Dic5—64no—
349C2×Dic5C2×C4×D318yes—
350C2×Dic5C23×D314yes—
351C2×Dic5C23×D314yes—
352Dic10—316no—
353Dic10—332no—
354Dic10C2×C4×D3116yes—
355C22×Q8—51no—
356C22×Q8—152no—
357C22×Q8—158no—
358C22×Q8—1516no—
359C22×Q8—151no—
360C23×C4—31no—
361C23×C4—152no—
362C4×Q8—58no—
363C4×Q8—158no—
364C4×Q8—158no—
365C4×Q8—1516no—
366C4×Q8—1516no—
367C4×Q8—158no—
368#117—38no—
369#117—1516no—
370#117—1516no—
371#117—158no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—151no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—152no—
383C2×C42—31no—
384C2×C42—52no—
385C2×C42—152no—
386C2×C42—152no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42D3×D511yescharacteristic
390C2×C3×C5#51914yescomplemented
391C2×C3×C5C24×C411yescharacteristic
392C2×C3×C5C2×2−1+411yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394C5×D3—24no—
395C23×C3C23×D511yescharacteristic
396C22×D3—22no—
397C22×D3—22no—
398C22×D3C2×C4×D514yes—
399C22×D3C23×D512yes—
400C3×Q8—516no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—58no—
404C2×C3×C4—54no—
405C2×C3×C4—54no—
406C2×C3×C4—104no—
407C2×C3×C4C2×C4×D514yes—
408C2×C3×C4C23×D512yes—
409C2×C3×C4C23×D512yes—
410C2×C3×C4C23×D512yes—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—58no—
414C2×Dic3—54no—
415C2×Dic3—54no—
416C2×Dic3—104no—
417C2×Dic3C2×C4×D514yes—
418C2×Dic3C23×D512yes—
419C2×Dic3C23×D512yes—
420C2×Dic3C23×D512yes—
421C4×D3—532no—
422C4×D3C2×C4×D5116yes—
423Dic6—516no—
424Dic6—532no—
425C22×C5—34no—
426C22×C5—62no—
427C22×C5—62no—
428C22×C5—68no—
429C22×C5C22×C4×D312yes—
430C22×C5#100712yes—
431C22×C5#101012yes—
432C22×C5C24×D311yescharacteristic
433C4×C5—22no—
434C4×C5—22no—
435C4×C5—34no—
436C4×C5—62no—
437C4×C5—62no—
438C4×C5C22×C4×D314yes—
439Dic5—24no—
440Dic5—38no—
441Dic5—64no—
442Dic5C22×C4×D318yes—
443C24—31no—
444C2×Q8—58no—
445C2×Q8—54no—
446C2×Q8—158no—
447C2×Q8—1516no—
448C2×Q8—1564no—
449C2×Q8—158no—
450C2×Q8—154no—
451C22×C4—31no—
452C22×C4—38no—
453C22×C4—34no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—158no—
459C22×C4—1516no—
460C22×C4—152no—
461C22×C4—152no—
462C22×C4C2×D3×D511yescharacteristic
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—34no—
466C4⋊C4—34no—
467C4⋊C4—58no—
468C4⋊C4—54no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—154no—
473C22⋊C4—34no—
474C22⋊C4—34no—
475C22⋊C4—158no—
476C42—34no—
477C42—58no—
478C42—158no—
479C42—158no—
480C42—158no—
481C42—158no—
482C42C2×D3×D514yes—
483C3×C5C2×#51911yescharacteristic, complemented, Hall
484C22×C3C22×C4×D512yes—
485C22×C3#415012yes—
486C22×C3#415012yes—
487C22×C3C24×D511yescharacteristic
488C2×D3—28no—
489C2×D3—22no—
490C2×D3—22no—
491C2×D3C22×C4×D514yes—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—58no—
495C3×C4—104no—
496C3×C4C22×C4×D514yes—
497Dic3—22no—
498Dic3—22no—
499Dic3—58no—
500Dic3—104no—
501Dic3C22×C4×D514yes—
502C2×C5—64no—
503C2×C5#557214yescomplemented
504C2×C5C23×C4×D311yescharacteristic
505C2×C5C2×#100711yescharacteristic
506C2×C5C2×#101011yescharacteristic
507C23—34no—
508C23—32no—
509C23—62no—
510C23—62no—
511C23C22×D3×D511yescharacteristic
512Q8—516no—
513Q8—1532no—
514Q8—1516no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—316no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—58no—
523C2×C4—54no—
524C2×C4—54no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—104no—
528C2×C4—1532no—
529C2×C4—158no—
530C2×C4—154no—
531C2×C4—154no—
532C2×C4—304no—
533C2×C4C4×D3×D514yes—
534C2×C4C22×D3×D512yes—
535C2×C4C22×D3×D512yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6585014yescomplemented
538C2×C3C23×C4×D511yescharacteristic
539C2×C3C2×#415011yescharacteristic
540C2×C3C2×#415011yescharacteristic
541D3—24no—
542C5C2×#557211yescharacteristic, complemented, Sylow
543C22—34no—
544C22—68no—
545C22—62no—
546C22—62no—
547C22#9200112yes—
548C22#9200412yes—
549C22C2×C4×D3×D512yes—
550C22C23×D3×D511yescharacteristic
551C4—22no—
552C4—22no—
553C4—34no—
554C4—58no—
555C4—62no—
556C4—62no—
557C4—104no—
558C4—158no—
559C4—304no—
560C4C2×C4×D3×D514yes—
561C3C2×#6585011yescharacteristic, complemented, Sylow
562C2—64no—
563C2#1175252314yesdirect product factor
564C2C2×#9200111yescharacteristic
565C2C2×#9200411yescharacteristic
566C2C22×C4×D3×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
cosocleC22×C3×C5C25
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic30C2semidirect
4. C2×C3×C4×Dic10C2semidirect
7. C2×#91340C2semidirect
9. C2×Dic3×Dic10C2semidirect
10. C2×#91325C2semidirect
11. C2×#91323C2semidirect
12. #11752523C2direct (N × H)
19. C2×D3×Dic10C4semidirect
25. C4×Dic30C22semidirect
35. C3×C4×Dic10C22semidirect
44. #91340C22semidirect
46. Dic3×Dic10C22semidirect
47. #91325C22semidirect
48. #91323C22semidirect
61. C2×C4×Dic10D3semidirect
83. D3×Dic10C2×C4semidirect
148. C4×Dic10C2×D3semidirect
390. C2×C3×C5#519semidirect
483. C3×C5C2×#519semidirect
503. C2×C5#5572semidirect
537. C2×C3#65850semidirect
542. C5C2×#5572semidirect
561. C3C2×#65850semidirect
563. C2#11752523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C2×C4×Dic302
C2×C5×#8722
C2×C3×C4×Dic102
C2×#914002
C2×#913982
C2×#913402
C2×#913382
C2×Dic3×Dic102
C2×#913252
C2×#913232
#117525232
C2×#658503
C2×#55725