Finite Group Databasebeta

← C2×#11752500 #14480173

Subgroups — C2×#11752500 #14480173

Order 1920.

2336 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×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C42×C5×D3C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C2×#91469C211yesmaximal, characteristic, complemented
5C2×C4×#1204C212yesmaximal, complemented
6C2×#91389C211yesmaximal, characteristic, complemented
7C2×#91379C212yesmaximal, complemented
8C2×#91371C212yesmaximal
9C2×#91369C211yesmaximal, characteristic
10C2×#91365C211yesmaximal, characteristic
11C2×#91352C212yesmaximal
12#11752500C2116yesmaximal, direct product factor
13C2×#65804—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C22×C4×C5×D3C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C22×#1204C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×#6712C2212yes—
23C2×C4×Dic15C2212yes—
24C4×Dic30C2218yescomplemented
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C42×C5×D3C2218yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C3×C4×Dic10C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×Dic3⋊Dic5C2212yes—
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×(C2×D3)⋊Dic5C2212yes—
40#91469C2218yescomplemented
41C4×#1204C22116yescomplemented
42#91389C2218yescomplemented
43#91379C22116yescomplemented
44#91371C22116yes—
45#91369C2218yes—
46#91365C2218yes—
47#91352C22116yes—
48C2×#5578—51nomaximal, Hall
49C22×C42×C5—31no—
50C2×#4072—32no—
51C2×#4070—31no—
52C2×#4070—32no—
53C2×#4070—31no—
54#65804—316no—
55C2×#4016—32no—
56C2×#4015—31no—
57C2×#4015—31no—
58C2×C4×Dic10—32no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10D311yescharacteristic, complemented
61C23×C5×D3C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C2×Dic30—24no—
68C2×Dic30C2314yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C2×C4×C5×D3—24no—
73C2×C4×C5×D3—24no—
74C2×C4×C5×D3Q818yescomplemented
75C2×C4×C5×D3C2314yes—
76C2×C4×C5×D3C2314yes—
77C2×C4×C5×D3C2314yes—
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2312yes—
80C2×C3×Dic10—24no—
81C2×C3×Dic10C2314yes—
82C2×#1204—28no—
83C2×#1204C2318yes—
84C3×C42×C5C2314yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87C4×Dic15C2318yes—
88C4×C5×Dic3C2314yes—
89C4×C5×Dic3C2314yes—
90C4×C5×Dic3C2314yes—
91C3×C4⋊Dic5C2314yes—
92C3×#683C2318yes—
93C3×C4×Dic5C2318yes—
94Dic3⋊Dic5C2318yes—
95Dic3⋊Dic5C2318yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6668C2318yes—
99(C2×D3)⋊Dic5C2318yes—
100(C2×D3)⋊Dic5C2318yes—
101C2×C3×C4×Q8—51no—
102C2×#946—51no—
103C2×#944—51no—
104#5578—516no—
105C2×#897—51no—
106C2×#896—52no—
107C2×#889—52no—
108C2×#888—51no—
109C2×#872—52no—
110C2×C42×D3D511yescharacteristic
111C2×C4×Dic6—51no—
112C2×C4×Dic6—52no—
113C23×C4×C5—31no—
114C23×C4×C5—31no—
115C23×C4×C5—31no—
116C22×Dic10—31no—
117C22×Dic10—32no—
118C22×Dic10C2×D311yescharacteristic
119C2×C42×C5—31no—
120C2×C42×C5—31no—
121C2×C42×C5—31no—
122C2×C42×C5—38no—
123C2×C42×C5C2×D311yescharacteristic
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—32no—
126#4072—316no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132#4070—38no—
133#4070—38no—
134#4070—316no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683C2×D312yes—
139C2×C4×Dic5—32no—
140C2×C4×Dic5C2×D312yes—
141#4016—316no—
142#4015—38no—
143#4015—38no—
144C4×Dic10—38no—
145C4×Dic10—316no—
146C4×Dic10C2×D318yescomplemented
147C2×#533—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3C2×Q814yes—
152C22×C5×D3C2412yes—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5C2×Q814yes—
155C2×C3×C4×C5#4114yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×C3×C4×C5C2412yes—
159C2×Dic15—24no—
160C2×Dic15—24no—
161C2×Dic15C2414yes—
162C2×Dic15C2414yes—
163Dic30—28no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C2×Q814yes—
166C2×C5×Dic3#4114yes—
167C2×C5×Dic3C2412yes—
168C2×C5×Dic3C2412yes—
169C2×C5×Dic3C2412yes—
170C4×C5×D3—28no—
171C4×C5×D3—28no—
172C4×C5×D3C2×Q8116yescomplemented
173C2×C3×Dic5—24no—
174C2×C3×Dic5—24no—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10—28no—
178#1204—216no—
179C22×C3×Q8—51no—
180C22×C4×D3C2×D511yescharacteristic
181C22×C4×D3C2×D511yescharacteristic
182C22×C4×D3C2×D511yescharacteristic
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×C4×Q8—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C42—52no—
189C2×C3×C42C2×D511yescharacteristic
190#946—58no—
191#944—58no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4—52no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3C2×D511yescharacteristic
203C2×C4×Dic3C2×D511yescharacteristic
204C2×C4×Dic3C2×D511yescharacteristic
205#897—58no—
206#896—516no—
207#889—516no—
208#888—58no—
209#872—516no—
210C42×D3C2×D518yes—
211C4×Dic6—58no—
212C4×Dic6—516no—
213C24×C5—31no—
214C22×C4×C5—31no—
215C22×C4×C5—31no—
216C22×C4×C5—38no—
217C22×C4×C5—34no—
218C22×C4×C5—31no—
219C22×C4×C5—34no—
220C22×C4×C5—34no—
221C22×C4×C5—64no—
222C22×C4×C5—64no—
223C22×C4×C5C22×D311yescharacteristic
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C2×Dic10—24no—
231C2×Dic10—34no—
232C2×Dic10—38no—
233C2×Dic10—68no—
234C2×Dic10—64no—
235C2×Dic10C22×D314yes—
236C42×C5—34no—
237C42×C5—34no—
238C42×C5—34no—
239C42×C5C22×D314yes—
240C22⋊Dic5—38no—
241C22⋊Dic5—38no—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244C4⋊Dic5—38no—
245C4⋊Dic5—38no—
246C4⋊Dic5C22×D314yes—
247#683—38no—
248#683—38no—
249#683—38no—
250#683C22×D318yes—
251C4×Dic5—38no—
252C4×Dic5C22×D318yes—
253#533—1516no—
254C2×C4⋊Q8—151no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—151no—
259C2×C22⋊Q8—151no—
260C2×C4×Q8—51no—
261C2×C4×Q8—152no—
262C2×C4×Q8—151no—
263C2×#117—152no—
264C22×C42—31no—
265C22×C3×C5C22×Q812yes—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5C2511yescharacteristic
269C2×C5×D3—28no—
270C2×C5×D3—22no—
271C2×C5×D3—22no—
272C2×C5×D3C22×Q814yes—
273C3×C4×C5—22no—
274C3×C4×C5C22×Q814yes—
275C3×C4×C5C2×#4114yes—
276Dic15—24no—
277Dic15—24no—
278C3×Dic5—24no—
279C3×Dic5—24no—
280C5×Dic3—22no—
281C5×Dic3C22×Q814yes—
282C5×Dic3C2×#4114yes—
283C23×D3C22×D511yescharacteristic
284C2×C3×Q8—54no—
285C2×C3×Q8—104no—
286C22×C3×C4—52no—
287C22×C3×C4—52no—
288C22×C3×C4C22×D511yescharacteristic
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D511yescharacteristic
291C22×Dic3—52no—
292C22×Dic3—52no—
293C22×Dic3C22×D511yescharacteristic
294C22×Dic3C22×D511yescharacteristic
295C22×Dic3C22×D511yescharacteristic
296C2×C4×D3—24no—
297C2×C4×D3—24no—
298C2×C4×D3Dic1018yescomplemented
299C2×C4×D3C22×D514yes—
300C2×C4×D3C22×D514yes—
301C2×C4×D3C22×D514yes—
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—108no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C42—58no—
309C3×C42C22×D514yes—
310(C2×D3)⋊C4—58no—
311(C2×D3)⋊C4—58no—
312C4⋊Dic3—54no—
313C4⋊Dic3—58no—
314Dic3⋊C4—58no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319C4×Dic3—58no—
320C4×Dic3C22×D514yes—
321C4×Dic3C22×D514yes—
322C4×Dic3C22×D514yes—
323C23×C5—34no—
324C23×C5—32no—
325C23×C5—62no—
326C23×C5—62no—
327C23×C5C23×D311yescharacteristic
328C2×C4×C5—22no—
329C2×C4×C5—34no—
330C2×C4×C5—34no—
331C2×C4×C5—32no—
332C2×C4×C5—32no—
333C2×C4×C5—316no—
334C2×C4×C5—32no—
335C2×C4×C5—68no—
336C2×C4×C5—62no—
337C2×C4×C5—68no—
338C2×C4×C5#23514yes—
339C2×C4×C5D3×Q814yes—
340C2×C4×C5C23×D312yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—24no—
344C2×Dic5—24no—
345C2×Dic5—34no—
346C2×Dic5—34no—
347C2×Dic5—64no—
348C2×Dic5—64no—
349C2×Dic5C23×D314yes—
350C2×Dic5C23×D314yes—
351Dic10—28no—
352Dic10—616no—
353Dic10—68no—
354C22×Q8—51no—
355C22×Q8—152no—
356C22×Q8—151no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C4⋊Q8—158no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—1516no—
364C22⋊Q8—158no—
365C22⋊Q8—158no—
366C4×Q8—58no—
367C4×Q8—1516no—
368C4×Q8—158no—
369#117—1516no—
370C2×C4⋊C4—52no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C22⋊C4—152no—
380C2×C22⋊C4—152no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—38no—
385C2×C42—52no—
386C2×C42—152no—
387C2×C42D3×D511yescharacteristic
388C2×C3×C5#53314yescomplemented
389C2×C3×C5C23×Q811yescharacteristic
390C2×C3×C5C22×#4111yescharacteristic
391C2×C3×C5C22×#4111yescharacteristic
392C5×D3—24no—
393C23×C3C23×D511yescharacteristic
394C22×D3—22no—
395C22×D3—22no—
396C22×D3C2×Dic1014yes—
397C22×D3C23×D512yes—
398C3×Q8—108no—
399C2×C3×C4—22no—
400C2×C3×C4—54no—
401C2×C3×C4—54no—
402C2×C3×C4—104no—
403C2×C3×C4—104no—
404C2×C3×C4C2×Dic1014yes—
405C2×C3×C4#70914yes—
406C2×C3×C4C23×D512yes—
407C2×C3×C4C23×D512yes—
408C2×C3×C4C23×D512yes—
409C2×Dic3—22no—
410C2×Dic3—54no—
411C2×Dic3—54no—
412C2×Dic3—104no—
413C2×Dic3—104no—
414C2×Dic3C2×Dic1014yes—
415C2×Dic3#70914yes—
416C2×Dic3C23×D512yes—
417C2×Dic3C23×D512yes—
418C2×Dic3C23×D512yes—
419C4×D3—28no—
420C4×D3—28no—
421C4×D3C2×Dic10116yescomplemented
422Dic6—108no—
423Dic6—1016no—
424C22×C5—34no—
425C22×C5—62no—
426C22×C5—62no—
427C22×C5—68no—
428C22×C5C2×#23512yes—
429C22×C5C2×D3×Q812yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—22no—
433C4×C5—34no—
434C4×C5—34no—
435C4×C5—62no—
436C4×C5C2×#23514yes—
437C4×C5C2×D3×Q814yes—
438Dic5—24no—
439Dic5—24no—
440Dic5—64no—
441Dic5—64no—
442C24—31no—
443C2×Q8—54no—
444C2×Q8—104no—
445C2×Q8—158no—
446C2×Q8—154no—
447C2×Q8—308no—
448C2×Q8—304no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—38no—
452C22×C4—34no—
453C22×C4—31no—
454C22×C4—34no—
455C22×C4—34no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—64no—
459C22×C4—64no—
460C22×C4—152no—
461C22×C4—152no—
462C22×C4C2×D3×D511yescharacteristic
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—58no—
466C4⋊C4—54no—
467C4⋊C4—158no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4—154no—
474C22⋊C4—158no—
475C22⋊C4—158no—
476C42—34no—
477C42—34no—
478C42—34no—
479C42—58no—
480C42—158no—
481C42C2×D3×D514yes—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3C22×Dic1012yes—
484C22×C3C2×#70912yes—
485C22×C3C2×#70912yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—28no—
488C2×D3—22no—
489C2×D3—22no—
490C2×D3C22×Dic1014yes—
491C3×C4—22no—
492C3×C4—104no—
493C3×C4—104no—
494C3×C4C22×Dic1014yes—
495C3×C4C2×#70914yes—
496Dic3—22no—
497Dic3—104no—
498Dic3—104no—
499Dic3C22×Dic1014yes—
500Dic3C2×#70914yes—
501C2×C5—64no—
502C2×C5#557814yescomplemented
503C2×C5C22×#23511yescharacteristic
504C2×C5C22×D3×Q811yescharacteristic
505C2×C5C2×D3×#4111yescharacteristic
506C23—34no—
507C23—32no—
508C23—62no—
509C23—62no—
510C23C22×D3×D511yescharacteristic
511Q8—108no—
512Q8—3016no—
513Q8—308no—
514C2×C4—22no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—316no—
520C2×C4—32no—
521C2×C4—54no—
522C2×C4—54no—
523C2×C4—68no—
524C2×C4—62no—
525C2×C4—68no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—154no—
529C2×C4—154no—
530C2×C4—304no—
531C2×C4—304no—
532C2×C4D3×Dic1014yes—
533C2×C4#677114yes—
534C2×C4C22×D3×D512yes—
535C2×C4C22×D3×D512yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6580414yescomplemented
538C2×C3C23×Dic1011yescharacteristic
539C2×C3C22×#70911yescharacteristic
540C2×C3C22×#70911yescharacteristic
541D3—24no—
542C5C2×#557811yescharacteristic, complemented, Sylow
543C22—34no—
544C22—68no—
545C22—62no—
546C22—62no—
547C22C2×D3×Dic1012yes—
548C22C2×#677112yes—
549C22D3×#70912yes—
550C22C23×D3×D511yescharacteristic
551C4—22no—
552C4—34no—
553C4—34no—
554C4—62no—
555C4—104no—
556C4—104no—
557C4—304no—
558C4—304no—
559C4C2×D3×Dic1014yes—
560C4C2×#677114yes—
561C3C2×#6580411yescharacteristic, complemented, Sylow
562C2—64no—
563C2#1175250014yesdirect product factor
564C2C22×D3×Dic1011yescharacteristic
565C2C22×#677111yescharacteristic
566C2C2×D3×#70911yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic30C2semidirect
3. C2×C3×C4×Dic10C2semidirect
4. C2×#91469C2semidirect
5. C2×C4×#1204C2semidirect
6. C2×#91389C2semidirect
7. C2×#91379C2semidirect
12. #11752500C2direct (N × H)
24. C4×Dic30C22semidirect
32. C3×C4×Dic10C22semidirect
40. #91469C22semidirect
41. C4×#1204C22semidirect
42. #91389C22semidirect
43. #91379C22semidirect
60. C2×C4×Dic10D3semidirect
74. C2×C4×C5×D3Q8semidirect
146. C4×Dic10C2×D3semidirect
172. C4×C5×D3C2×Q8semidirect
298. C2×C4×D3Dic10semidirect
388. C2×C3×C5#533semidirect
421. C4×D3C2×Dic10semidirect
482. C3×C5C2×#533semidirect
502. C2×C5#5578semidirect
537. C2×C3#65804semidirect
542. C5C2×#5578semidirect
561. C3C2×#65804semidirect
563. C2#11752500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C42×C5×D32
C2×C3×C4×Dic102
C2×#914692
C2×C4×#12042
C2×#913892
C2×#913792
C2×#913712
C2×#913692
C2×#913652
C2×#913522
#117525002
C2×#658043
C2×#55785