Finite Group Databasebeta

← C2×#11753459 #14480157

Subgroups — C2×#11753459 #14480157

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×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#897C211yesmaximal, characteristic
3C2×C3×#4034C211yesmaximal, characteristic, complemented
4C2×#91410C212yesmaximal
5C2×#91400C212yesmaximal
6C2×C4×D3×Dic5C211yesmaximal, characteristic
7C2×#91376C211yesmaximal, characteristic, complemented
8C2×#91365C211yesmaximal, characteristic
9C2×#91344C211yesmaximal, characteristic, complemented
10C2×#91335C212yesmaximal, complemented
11C2×#91331C212yesmaximal, complemented
12#11753459C2116yesmaximal, direct product factor
13C2×#65956—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×Dic10C2212yes—
18C22×D3×Dic5C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6712C2212yes—
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2212yes—
24#91776C2218yescomplemented
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C5×C4⋊Dic3C2212yes—
27C5×#897C2218yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2212yes—
30C2×C3×C4×Dic5C2211yescharacteristic
31C3×#4034C2218yescomplemented
32C2×Dic3⋊Dic5C2212yes—
33C2×#6668C2212yes—
34C2×#6668C2212yes—
35C2×#6668C2212yes—
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2212yes—
40#91410C22116yes—
41#91400C22116yes—
42C4×D3×Dic5C2218yes—
43#91376C2218yescomplemented
44#91365C2218yes—
45#91344C2218yescomplemented
46#91335C22116yescomplemented
47#91331C22116yescomplemented
48C2×#5728—51nomaximal, Hall
49C2×C5×C22⋊Q8—31no—
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4070—31no—
53C22×C4×Dic5—31no—
54#65956—316no—
55C2×#4035—32no—
56C2×#4034D311yescharacteristic, complemented
57C2×#4033—32no—
58C2×#4033—31no—
59C2×#4024—32no—
60C2×#4023—32no—
61C23×C5×D3C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2311yescharacteristic
67C2×Dic30—24no—
68C2×Dic30C2314yes—
69C22×C5×Dic3C2311yescharacteristic
70C22×C5×Dic3C2312yes—
71C2×C4×C5×D3—24no—
72C2×C4×C5×D3C2314yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×Dic10—28no—
79C2×C3×Dic10C2318yes—
80C2×D3×Dic5—24no—
81C2×D3×Dic5Q818yescomplemented
82C2×D3×Dic5C2314yes—
83C2×D3×Dic5C2314yes—
84C3×C5×C4⋊C4C2314yes—
85#6712C2318yes—
86C4×Dic15C2314yes—
87C4×Dic15C2318yes—
88C5×(C2×D3)⋊C4C2318yes—
89C5×C4⋊Dic3C2318yes—
90C3×C4⋊Dic5C2314yes—
91C3×#683C2318yes—
92C3×C4×Dic5C2314yes—
93Dic3⋊Dic5C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96#6668C2318yes—
97(C2×D3)⋊Dic5C2318yes—
98Dic3×Dic5C2314yes—
99Dic3×Dic5C2314yes—
100Dic3×Dic5C2318yes—
101C2×C3×C4⋊Q8—51no—
102C2×#946—52no—
103C2×Q8×Dic3—52no—
104#5728—516no—
105C2×#897—51no—
106C2×#897D511yescharacteristic
107C2×#892—52no—
108C2×#890—52no—
109C2×#887—51no—
110C2×#887—51no—
111C2×C42×D3—51no—
112C2×#869—51no—
113C22×C5×Q8—31no—
114C23×C4×C5—31no—
115C23×Dic5—31no—
116C23×Dic5—31no—
117C22×Dic10—31no—
118C22×Dic10C2×D312yes—
119C5×C22⋊Q8—38no—
120C2×C5×C4⋊C4—32no—
121C2×C5×C4⋊C4C2×D311yescharacteristic
122C2×C5×C22⋊C4—32no—
123C2×C22⋊Dic5—32no—
124Q8×Dic5—38no—
125#4090—38no—
126C2×C4⋊Dic5—32no—
127C2×C4⋊Dic5C2×D311yescharacteristic
128#4070—38no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—32no—
132C2×#683—32no—
133C2×#683C2×D312yes—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—38no—
140C2×C4×Dic5C2×D311yescharacteristic
141#4035—316no—
142#4034C2×D318yescomplemented
143#4033—316no—
144#4033—38no—
145#4024—316no—
146#4023—316no—
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—24no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—22no—
158C2×Dic15—24no—
159C2×Dic15C2×Q814yes—
160C2×Dic15C2412yes—
161C2×Dic15C2414yes—
162C2×Dic15C2412yes—
163Dic30—28no—
164C2×C5×Dic3—24no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3C2412yes—
167C2×C5×Dic3C2414yes—
168C4×C5×D3—28no—
169C5×Dic6—28no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5C2×Q814yes—
172C2×C3×Dic5#4114yes—
173C2×C3×Dic5C2414yes—
174C2×C3×Dic5C2412yes—
175C2×C3×Dic5C2412yes—
176C3×Dic10—216no—
177D3×Dic5—28no—
178D3×Dic5C2×Q8116yescomplemented
179C22×C3×Q8—52no—
180C22×C4×D3—51no—
181C22×C4×D3—51no—
182C22×C4×D3C2×D511yescharacteristic
183C22×Dic6—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×C4⋊Q8—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C42—51no—
190#946—516no—
191Q8×Dic3—516no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3C2×D512yes—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—51no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—52no—
205#897—58no—
206#897C2×D518yes—
207#892—516no—
208#890—516no—
209#887—58no—
210#887—58no—
211C42×D3—58no—
212#869—58no—
213C24×C5—31no—
214C2×C5×Q8—34no—
215C2×C5×Q8—64no—
216C22×C4×C5—32no—
217C22×C4×C5—31no—
218C22×C4×C5—34no—
219C22×C4×C5—64no—
220C22×C4×C5C22×D312yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—38no—
224C22×Dic5—34no—
225C22×Dic5—32no—
226C22×Dic5—31no—
227C22×Dic5—34no—
228C22×Dic5—64no—
229C22×Dic5C22×D312yes—
230C22×Dic5C22×D311yescharacteristic
231C22×Dic5C22×D311yescharacteristic
232C2×Dic10—28no—
233C2×Dic10—34no—
234C2×Dic10—64no—
235C2×Dic10C22×D318yes—
236C5×C4⋊C4—38no—
237C5×C4⋊C4C22×D314yes—
238C5×C22⋊C4—38no—
239C22⋊Dic5—38no—
240C4⋊Dic5—38no—
241C4⋊Dic5C22×D314yes—
242#683—38no—
243#683—38no—
244#683—38no—
245#683—38no—
246#683C22×D318yes—
247C4×Dic5—38no—
248C4×Dic5—34no—
249C4×Dic5—38no—
250C4×Dic5—34no—
251C4×Dic5—34no—
252C4×Dic5C22×D314yes—
253#533—1516no—
254C2×C4⋊Q8—51no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×Q8—151no—
262C2×C4×Q8—151no—
263C2×#117—152no—
264C22×C42—151no—
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—24no—
274C3×C4×C5C2×#4114yes—
275Dic15—22no—
276Dic15—24no—
277Dic15C22×Q814yes—
278C3×Dic5—24no—
279C3×Dic5C22×Q814yes—
280C3×Dic5C2×#4114yes—
281C5×Dic3—24no—
282C5×Dic3—22no—
283C23×D3C22×D511yescharacteristic
284C2×C3×Q8—58no—
285C2×C3×Q8—108no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—52no—
289C22×C3×C4C22×D512yes—
290C22×C3×C4C22×D511yescharacteristic
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3—52no—
294C22×Dic3C22×D511yescharacteristic
295C22×Dic3C22×D512yes—
296C2×C4×D3—24no—
297C2×C4×D3—58no—
298C2×C4×D3—54no—
299C2×C4×D3—54no—
300C2×C4×D3—104no—
301C2×C4×D3C22×D514yes—
302C2×Dic6—24no—
303C2×Dic6—54no—
304C2×Dic6—104no—
305C2×Dic6C22×D514yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4C22×D514yes—
309C3×C42—54no—
310(C2×D3)⋊C4—58no—
311(C2×D3)⋊C4C22×D518yes—
312C4⋊Dic3—58no—
313C4⋊Dic3—58no—
314C4⋊Dic3—58no—
315C4⋊Dic3C22×D518yes—
316Dic3⋊C4—58no—
317Dic3⋊C4—58no—
318C4×Dic3—54no—
319C4×Dic3—58no—
320C4×Dic3—54no—
321C4×Dic3—54no—
322C4×Dic3—58no—
323C23×C5—34no—
324C23×C5—32no—
325C23×C5—62no—
326C23×C5—62no—
327C23×C5C23×D311yescharacteristic
328C5×Q8—68no—
329C2×C4×C5—24no—
330C2×C4×C5—32no—
331C2×C4×C5—34no—
332C2×C4×C5—62no—
333C2×C4×C5—64no—
334C2×C4×C5—68no—
335C2×C4×C5#23914yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—24no—
339C2×Dic5—34no—
340C2×Dic5—32no—
341C2×Dic5—316no—
342C2×Dic5—32no—
343C2×Dic5—34no—
344C2×Dic5—62no—
345C2×Dic5—64no—
346C2×Dic5—68no—
347C2×Dic5#23714yes—
348C2×Dic5D3×Q814yes—
349C2×Dic5C23×D314yes—
350C2×Dic5C23×D312yes—
351C2×Dic5C23×D312yes—
352Dic10—216no—
353Dic10—68no—
354C22×Q8—31no—
355C22×Q8—52no—
356C22×Q8—151no—
357C23×C4—31no—
358C23×C4—151no—
359C23×C4—151no—
360C4⋊Q8—58no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—38no—
364C22⋊Q8—1516no—
365C22⋊Q8—158no—
366C4×Q8—1516no—
367C4×Q8—158no—
368C4×Q8—158no—
369#117—1516no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—52no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4D3×D511yescharacteristic
379C2×C22⋊C4—32no—
380C2×C22⋊C4—152no—
381C2×C42—51no—
382C2×C42—158no—
383C2×C42—152no—
384C2×C42—151no—
385C2×C42—151no—
386C2×C42—152no—
387C2×C42—151no—
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×D3Q8×D514yes—
397C22×D3C23×D512yes—
398C3×Q8—1016no—
399C2×C3×C4—24no—
400C2×C3×C4—54no—
401C2×C3×C4—54no—
402C2×C3×C4—52no—
403C2×C3×C4—52no—
404C2×C3×C4—54no—
405C2×C3×C4—104no—
406C2×C3×C4#71114yes—
407C2×C3×C4C23×D514yes—
408C2×C3×C4C23×D512yes—
409C2×Dic3—24no—
410C2×Dic3—22no—
411C2×Dic3—54no—
412C2×Dic3—52no—
413C2×Dic3—52no—
414C2×Dic3—54no—
415C2×Dic3—104no—
416C2×Dic3—102no—
417C2×Dic3C23×D512yes—
418C2×Dic3C23×D514yes—
419C4×D3—28no—
420C4×D3—516no—
421C4×D3—108no—
422Dic6—28no—
423Dic6—108no—
424C22×C5—34no—
425C22×C5—62no—
426C22×C5—62no—
427C22×C5—68no—
428C22×C5C2×#23712yes—
429C22×C5C2×D3×Q812yes—
430C22×C5C2×#23912yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—24no—
433C4×C5—62no—
434C4×C5—64no—
435C4×C5C2×#23914yes—
436Dic5—24no—
437Dic5—34no—
438Dic5—62no—
439Dic5—64no—
440Dic5C2×#23714yes—
441Dic5C2×D3×Q814yes—
442C24—31no—
443C2×Q8—34no—
444C2×Q8—58no—
445C2×Q8—64no—
446C2×Q8—108no—
447C2×Q8—154no—
448C2×Q8—304no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—34no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—52no—
455C22×C4—64no—
456C22×C4—154no—
457C22×C4—158no—
458C22×C4—154no—
459C22×C4—151no—
460C22×C4—151no—
461C22×C4—152no—
462C22×C4—304no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—58no—
467C4⋊C4—54no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4C2×D3×D514yes—
474C22⋊C4—38no—
475C22⋊C4—158no—
476C42—54no—
477C42—154no—
478C42—154no—
479C42—158no—
480C42—154no—
481C42—158no—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3C2×#71112yes—
484C22×C3C2×Q8×D512yes—
485C22×C3D5×#4112yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—28no—
488C2×D3—22no—
489C2×D3—22no—
490C2×D3C2×Q8×D514yes—
491C3×C4—24no—
492C3×C4—54no—
493C3×C4—54no—
494C3×C4—104no—
495C3×C4C2×#71114yes—
496Dic3—24no—
497Dic3—22no—
498Dic3—54no—
499Dic3—104no—
500Dic3—102no—
501C2×C5—64no—
502C2×C5#572814yescomplemented
503C2×C5C22×#23711yescharacteristic
504C2×C5C22×D3×Q811yescharacteristic
505C2×C5C22×#23911yescharacteristic
506C23—34no—
507C23—32no—
508C23—62no—
509C23—62no—
510C23C22×D3×D511yescharacteristic
511Q8—68no—
512Q8—1016no—
513Q8—308no—
514C2×C4—24no—
515C2×C4—32no—
516C2×C4—34no—
517C2×C4—54no—
518C2×C4—54no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—54no—
522C2×C4—62no—
523C2×C4—64no—
524C2×C4—68no—
525C2×C4—104no—
526C2×C4—1516no—
527C2×C4—154no—
528C2×C4—152no—
529C2×C4—152no—
530C2×C4—154no—
531C2×C4—308no—
532C2×C4—304no—
533C2×C4—302no—
534C2×C4#676814yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6595614yescomplemented
538C2×C3C22×#71111yescharacteristic
539C2×C3C22×Q8×D511yescharacteristic
540C2×C3C2×D5×#4111yescharacteristic
541D3—24no—
542C5C2×#572811yescharacteristic, complemented, Sylow
543C22—34no—
544C22—62no—
545C22—62no—
546C22—68no—
547C22C2×#676812yes—
548C22D5×#23712yes—
549C22D3×Q8×D512yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—54no—
553C4—54no—
554C4—62no—
555C4—64no—
556C4—104no—
557C4—154no—
558C4—304no—
559C4—302no—
560C4C2×#676814yes—
561C3C2×#6595611yescharacteristic, complemented, Sylow
562C2—64no—
563C2#1175345914yesdirect product factor
564C2C22×#676811yescharacteristic
565C2C2×D5×#23711yescharacteristic
566C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#533
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×#91776C2semidirect
3. C2×C3×#4034C2semidirect
7. C2×#91376C2semidirect
9. C2×#91344C2semidirect
10. C2×#91335C2semidirect
11. C2×#91331C2semidirect
12. #11753459C2direct (N × H)
24. #91776C22semidirect
31. C3×#4034C22semidirect
43. #91376C22semidirect
45. #91344C22semidirect
46. #91335C22semidirect
47. #91331C22semidirect
56. C2×#4034D3semidirect
81. C2×D3×Dic5Q8semidirect
142. #4034C2×D3semidirect
178. D3×Dic5C2×Q8semidirect
388. C2×C3×C5#533semidirect
482. C3×C5C2×#533semidirect
502. C2×C5#5728semidirect
537. C2×C3#65956semidirect
542. C5C2×#5728semidirect
561. C3C2×#65956semidirect
563. C2#11753459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8972
C2×C3×#40342
C2×#914102
C2×#914002
C2×C4×D3×Dic52
C2×#913762
C2×#913652
C2×#913442
C2×#913352
C2×#913312
#117534592
C2×#659563
C2×#57285