Finite Group Databasebeta

← C2×#11756337 #14480119

Subgroups — C2×#11756337 #14480119

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×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×#91835C211yesmaximal, characteristic
3C2×#91833C211yesmaximal, characteristic, complemented
4#11756337C2116yesmaximal, direct product factor
5C2×#91786C211yesmaximal, characteristic
6C2×#91785C212yesmaximal
7C2×#91778C212yesmaximal, complemented
8C2×#91777C211yesmaximal, characteristic, complemented
9C2×#91761C212yesmaximal
10C2×C42×D15C211yesmaximal, characteristic
11C2×C4×Dic30C212yesmaximal, complemented
12C2×C4×Dic30C211yesmaximal, characteristic, complemented
13C2×#65912—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C4×C5×Q8C2218yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C42×C5C2212yes—
25#91835C2218yes—
26#91833C2218yescomplemented
27C2×#6714C2212yes—
28C2×#6714C2212yes—
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4⋊Dic15C2212yes—
31C2×#6712C2212yes—
32C2×#6712C2212yes—
33C2×#6712C2212yes—
34C2×#6712C2212yes—
35C2×#6712C2212yes—
36C2×C4×Dic15C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2212yes—
39C2×C4×Dic15C2211yescharacteristic
40#91786C2218yes—
41#91785C22116yes—
42#91778C22116yescomplemented
43#91777C2218yescomplemented
44#91761C22116yes—
45C42×D15C2218yes—
46C4×Dic30C22116yescomplemented
47C4×Dic30C2218yescomplemented
48C2×#5578—51nomaximal, Hall
49C2×C4×C5×Q8D311yescharacteristic, complemented
50C2×#4092—31no—
51C2×#4090—31no—
52#65912—316no—
53C2×#4043—31no—
54C2×#4042—32no—
55C2×#4035—32no—
56C2×#4034—31no—
57C2×#4018—32no—
58C2×C42×D5—31no—
59C2×C4×Dic10—31no—
60C2×C4×Dic10—32no—
61C23×D15C2311yescharacteristic
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C22×Dic15C2312yes—
72C22×Dic15C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C2×C4×D15—24no—
75C2×C4×D15—24no—
76C2×C4×D15Q818yescomplemented
77C2×C4×D15C2314yes—
78C2×C4×D15C2314yes—
79C2×C4×D15C2314yes—
80C2×Dic30—24no—
81C2×Dic30—28no—
82C2×Dic30C2318yes—
83C2×Dic30C2314yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2318yes—
86C3×C42×C5C2314yes—
87C3×C42×C5C2318yes—
88#6714C2318yes—
89#6714C2318yes—
90C4⋊Dic15C2314yes—
91C4⋊Dic15C2318yes—
92#6712C2318yes—
93#6712C2318yes—
94#6712C2318yes—
95#6712C2318yes—
96#6712C2318yes—
97C4×Dic15C2314yes—
98C4×Dic15C2318yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C2×C3×C4×Q8D511yescharacteristic, complemented
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×D3—51no—
111C2×C4×Dic6—52no—
112C2×C4×Dic6—51no—
113C22×C5×Q8C2×D311yescharacteristic
114C22×C4×D5—31no—
115C22×C4×D5—31no—
116C22×C4×D5—31no—
117C22×Dic10—32no—
118C22×Dic10—31no—
119C4×C5×Q8C2×D318yescomplemented
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D312yes—
122C2×C42×C5C2×D311yescharacteristic
123C2×C42×C5C2×D312yes—
124#4092—38no—
125#4090—38no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×#683—32no—
131C2×#683—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139#4043—38no—
140#4042—316no—
141#4035—316no—
142#4034—38no—
143#4018—316no—
144C42×D5—38no—
145C4×Dic10—316no—
146C4×Dic10—38no—
147C2×#533—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—22no—
150C22×D15—22no—
151C22×D15C2×Q814yes—
152C22×D15C2412yes—
153C3×C5×Q8—28no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5C2×Q814yes—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2412yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15—24no—
165C2×Dic15—24no—
166C2×Dic15—22no—
167C2×Dic15C2×Q814yes—
168C2×Dic15#4114yes—
169C2×Dic15C2412yes—
170C2×Dic15C2414yes—
171C2×Dic15C2414yes—
172C2×Dic15C2412yes—
173C2×Dic15C2412yes—
174C4×D15—28no—
175C4×D15—28no—
176C4×D15C2×Q8116yescomplemented
177Dic30—28no—
178Dic30—216no—
179C22×C3×Q8C2×D511yescharacteristic
180C22×C4×D3—51no—
181C22×C4×D3—51no—
182C22×C4×D3—51no—
183C22×Dic6—52no—
184C22×Dic6—51no—
185C3×C4×Q8C2×D518yescomplemented
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C4⋊C4C2×D512yes—
188C2×C3×C42C2×D511yescharacteristic
189C2×C3×C42C2×D512yes—
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—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—51no—
205#897—58no—
206#896—516no—
207#889—516no—
208#888—58no—
209#872—516no—
210C42×D3—58no—
211C4×Dic6—516no—
212C4×Dic6—58no—
213C23×D5—31no—
214C2×C5×Q8—24no—
215C2×C5×Q8C22×D314yes—
216C22×C4×C5C22×D312yes—
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×Dic5—31no—
222C22×Dic5—31no—
223C22×Dic5—32no—
224C22×Dic5—32no—
225C22×Dic5—31no—
226C2×C4×D5—38no—
227C2×C4×D5—34no—
228C2×C4×D5—34no—
229C2×C4×D5—34no—
230C2×C4×D5—64no—
231C2×C4×D5—64no—
232C2×Dic10—38no—
233C2×Dic10—34no—
234C2×Dic10—68no—
235C2×Dic10—64no—
236C5×C4⋊C4C22×D314yes—
237C5×C4⋊C4C22×D318yes—
238C42×C5C22×D314yes—
239C42×C5C22×D318yes—
240#685—38no—
241#685—38no—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244#683—38no—
245#683—38no—
246#683—38no—
247#683—38no—
248#683—38no—
249C4×Dic5—34no—
250C4×Dic5—38no—
251C4×Dic5—34no—
252C4×Dic5—34no—
253#533—1516no—
254C2×C4⋊Q8—151no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—151no—
260C2×C4×Q8—151no—
261C2×C4×Q8—152no—
262C2×C4×Q8D1511yescharacteristic, complemented
263C2×#117—152no—
264C22×C42—151no—
265C22×C3×C5C22×Q812yes—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5C2511yescharacteristic
269C2×D15—28no—
270C2×D15—22no—
271C2×D15—22no—
272C2×D15C22×Q814yes—
273C3×C4×C5—24no—
274C3×C4×C5—22no—
275C3×C4×C5—24no—
276C3×C4×C5C22×Q814yes—
277C3×C4×C5C2×#4114yes—
278Dic15—24no—
279Dic15—24no—
280Dic15—22no—
281Dic15C22×Q814yes—
282Dic15C2×#4114yes—
283C23×D3—51no—
284C2×C3×Q8—24no—
285C2×C3×Q8C22×D514yes—
286C22×C3×C4C22×D511yescharacteristic
287C22×C3×C4C22×D512yes—
288C22×C3×C4C22×D512yes—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D511yescharacteristic
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—52no—
296C2×C4×D3—58no—
297C2×C4×D3—54no—
298C2×C4×D3—54no—
299C2×C4×D3—54no—
300C2×C4×D3—104no—
301C2×C4×D3—104no—
302C2×Dic6—58no—
303C2×Dic6—54no—
304C2×Dic6—108no—
305C2×Dic6—104no—
306C3×C4⋊C4C22×D514yes—
307C3×C4⋊C4C22×D518yes—
308C3×C42C22×D514yes—
309C3×C42C22×D518yes—
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—54no—
320C4×Dic3—58no—
321C4×Dic3—54no—
322C4×Dic3—54no—
323C23×C5C23×D311yescharacteristic
324C22×D5—34no—
325C22×D5—32no—
326C22×D5—62no—
327C22×D5—62no—
328C5×Q8—28no—
329C2×C4×C5—24no—
330C2×C4×C5—24no—
331C2×C4×C5—22no—
332C2×C4×C5#23514yes—
333C2×C4×C5D3×Q814yes—
334C2×C4×C5C23×D312yes—
335C2×C4×C5C23×D314yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×C4×C5C23×D312yes—
339C2×Dic5—34no—
340C2×Dic5—34no—
341C2×Dic5—32no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—34no—
345C2×Dic5—34no—
346C2×Dic5—64no—
347C2×Dic5—62no—
348C2×Dic5—64no—
349C4×D5—316no—
350C4×D5—68no—
351C4×D5—68no—
352Dic10—616no—
353Dic10—68no—
354C22×Q8—152no—
355C22×Q8—151no—
356C22×Q8C2×D1511yescharacteristic
357C23×C4—151no—
358C23×C4—151no—
359C23×C4—151no—
360C4⋊Q8—158no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—158no—
364C22⋊Q8—1516no—
365C22⋊Q8—158no—
366C4×Q8—1516no—
367C4×Q8—158no—
368C4×Q8C2×D1518yescomplemented
369#117—1516no—
370C2×C4⋊C4—152no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4C2×D1512yes—
378C2×C4⋊C4C2×D1511yescharacteristic
379C2×C22⋊C4—152no—
380C2×C22⋊C4—152no—
381C2×C42—151no—
382C2×C42—151no—
383C2×C42—152no—
384C2×C42—151no—
385C2×C42—158no—
386C2×C42C2×D1512yes—
387C2×C42C2×D1511yescharacteristic
388C2×C3×C5#53314yescomplemented
389C2×C3×C5C23×Q811yescharacteristic
390C2×C3×C5C22×#4111yescharacteristic
391C2×C3×C5C22×#4111yescharacteristic
392D15—24no—
393C23×C3C23×D511yescharacteristic
394C22×D3—54no—
395C22×D3—52no—
396C22×D3—102no—
397C22×D3—102no—
398C3×Q8—28no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4#70914yes—
403C2×C3×C4Q8×D514yes—
404C2×C3×C4C23×D512yes—
405C2×C3×C4C23×D514yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×C3×C4C23×D512yes—
409C2×Dic3—54no—
410C2×Dic3—54no—
411C2×Dic3—52no—
412C2×Dic3—52no—
413C2×Dic3—52no—
414C2×Dic3—54no—
415C2×Dic3—54no—
416C2×Dic3—104no—
417C2×Dic3—102no—
418C2×Dic3—104no—
419C4×D3—516no—
420C4×D3—108no—
421C4×D3—108no—
422Dic6—1016no—
423Dic6—108no—
424C22×C5C2×#23512yes—
425C22×C5C2×D3×Q812yes—
426C22×C5D3×#4112yes—
427C22×C5C24×D311yescharacteristic
428C2×D5—34no—
429C2×D5—62no—
430C2×D5—62no—
431C2×D5—68no—
432C4×C5—24no—
433C4×C5—24no—
434C4×C5—22no—
435C4×C5C2×#23514yes—
436C4×C5C2×D3×Q814yes—
437Dic5—34no—
438Dic5—34no—
439Dic5—64no—
440Dic5—62no—
441Dic5—64no—
442C24—151no—
443C2×Q8—24no—
444C2×Q8—158no—
445C2×Q8—154no—
446C2×Q8—308no—
447C2×Q8—304no—
448C2×Q8C22×D1514yes—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—158no—
452C22×C4—154no—
453C22×C4—151no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4—154no—
457C22×C4—154no—
458C22×C4—304no—
459C22×C4—304no—
460C22×C4C22×D1511yescharacteristic
461C22×C4C22×D1512yes—
462C22×C4C22×D1512yes—
463C22×C4C22×D1511yescharacteristic
464C22×C4C22×D1511yescharacteristic
465C4⋊C4—158no—
466C4⋊C4—158no—
467C4⋊C4—158no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—154no—
472C4⋊C4C22×D1518yes—
473C4⋊C4C22×D1514yes—
474C22⋊C4—158no—
475C22⋊C4—158no—
476C42—154no—
477C42—154no—
478C42—154no—
479C42—158no—
480C42C22×D1514yes—
481C42C22×D1518yes—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3C2×#70912yes—
484C22×C3C2×Q8×D512yes—
485C22×C3D5×#4112yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—54no—
488C2×D3—108no—
489C2×D3—102no—
490C2×D3—102no—
491C3×C4—24no—
492C3×C4—24no—
493C3×C4—22no—
494C3×C4C2×#70914yes—
495C3×C4C2×Q8×D514yes—
496Dic3—54no—
497Dic3—54no—
498Dic3—104no—
499Dic3—102no—
500Dic3—104no—
501C2×C5#557814yescomplemented
502C2×C5C22×#23511yescharacteristic
503C2×C5C22×D3×Q811yescharacteristic
504C2×C5C2×D3×#4111yescharacteristic
505D5—64no—
506C23—154no—
507C23—152no—
508C23—302no—
509C23—302no—
510C23C23×D1511yescharacteristic
511Q8—28no—
512Q8—3016no—
513Q8—308no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—154no—
518C2×C4—154no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—1516no—
522C2×C4—152no—
523C2×C4—154no—
524C2×C4—154no—
525C2×C4—308no—
526C2×C4—302no—
527C2×C4—304no—
528C2×C4—304no—
529C2×C4—308no—
530C2×C4#681714yes—
531C2×C4Q8×D1514yes—
532C2×C4C23×D1512yes—
533C2×C4C23×D1514yes—
534C2×C4C23×D1514yes—
535C2×C4C23×D1512yes—
536C2×C4C23×D1512yes—
537C2×C3#6591214yescomplemented
538C2×C3C22×#70911yescharacteristic
539C2×C3C22×Q8×D511yescharacteristic
540C2×C3C2×D5×#4111yescharacteristic
541D3—104no—
542C5C2×#557811yescharacteristic, complemented, Sylow
543C22—154no—
544C22—308no—
545C22—302no—
546C22—302no—
547C22C2×#681712yes—
548C22C2×Q8×D1512yes—
549C22#41×D1512yes—
550C22C24×D1511yescharacteristic
551C4—24no—
552C4—22no—
553C4—24no—
554C4—154no—
555C4—154no—
556C4—302no—
557C4—304no—
558C4—304no—
559C4C2×#681714yes—
560C4C2×Q8×D1514yes—
561C3C2×#6591211yescharacteristic, complemented, Sylow
562C2—304no—
563C2#1175633714yesdirect product factor
564C2C22×#681711yescharacteristic
565C2C22×Q8×D1511yescharacteristic
566C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC22×C4C22×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4×Q8D15
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
3. C2×#91833C2semidirect
4. #11756337C2direct (N × H)
7. C2×#91778C2semidirect
8. C2×#91777C2semidirect
11. C2×C4×Dic30C2semidirect
12. C2×C4×Dic30C2semidirect
20. C3×C4×C5×Q8C22semidirect
26. #91833C22semidirect
42. #91778C22semidirect
43. #91777C22semidirect
46. C4×Dic30C22semidirect
47. C4×Dic30C22semidirect
49. C2×C4×C5×Q8D3semidirect
76. C2×C4×D15Q8semidirect
101. C2×C3×C4×Q8D5semidirect
119. C4×C5×Q8C2×D3semidirect
176. C4×D15C2×Q8semidirect
185. C3×C4×Q8C2×D5semidirect
262. C2×C4×Q8D15semidirect
368. C4×Q8C2×D15semidirect
388. C2×C3×C5#533semidirect
482. C3×C5C2×#533semidirect
501. C2×C5#5578semidirect
537. C2×C3#65912semidirect
542. C5C2×#5578semidirect
561. C3C2×#65912semidirect
563. C2#11756337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
C2×#918352
C2×#918332
#117563372
C2×#917862
C2×#917852
C2×#917782
C2×#917772
C2×#917612
C2×C42×D152
C2×C4×Dic302
C2×#659123
C2×#55785