Finite Group Databasebeta

← C2×#11753464 #14480161

Subgroups — C2×#11753464 #14480161

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×#91786C211yesmaximal, characteristic
2C2×C5×#888C211yesmaximal, characteristic, complemented
3C2×C3×#4033C211yesmaximal, characteristic, complemented
4C2×#91424C212yesmaximal
5C2×#91402C212yesmaximal
6C2×C4×#1200C211yesmaximal, characteristic
7C2×#91390C211yesmaximal, characteristic
8C2×#91389C211yesmaximal, characteristic, complemented
9C2×#91343C212yesmaximal, complemented
10C2×#91333C211yesmaximal, characteristic, complemented
11C2×Dic5×Dic6C212yesmaximal, complemented
12#11753464C2116yesmaximal, direct product factor
13C2×#66062—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×Dic6C2212yes—
17C22×C3×Dic10C2211yescharacteristic
18C22×#1200C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714C2212yes—
22C2×C4⋊Dic15C2212yes—
23#91786C2218yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C5×#888C2218yescomplemented
28C2×C3×#683C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C3×#4033C2218yescomplemented
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×#6667C2212yes—
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2212yes—
40#91424C22116yes—
41#91402C22116yes—
42C4×#1200C2218yes—
43#91390C2218yes—
44#91389C2218yescomplemented
45#91343C22116yescomplemented
46#91333C2218yescomplemented
47Dic5×Dic6C22116yescomplemented
48C2×#5578—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4092—32no—
51C2×Q8×Dic5—32no—
52#66062—316no—
53C2×#4043—31no—
54C2×#4043—31no—
55C2×#4038—32no—
56C2×#4036—32no—
57C2×#4033—31no—
58C2×#4033D311yescharacteristic, complemented
59C2×C42×D5—31no—
60C2×#4015—31no—
61C23×D15C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2312yes—
66C2×C4×D15—24no—
67C2×C4×D15C2314yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2311yescharacteristic
73C2×C5×Dic6—28no—
74C2×C5×Dic6C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2314yes—
80C2×#1200—24no—
81C2×#1200Q818yescomplemented
82C2×#1200C2314yes—
83C2×#1200C2314yes—
84C3×C5×C4⋊C4C2314yes—
85#6714C2318yes—
86C4⋊Dic15C2318yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C4×C5×Dic3C2314yes—
90C3×#683C2318yes—
91C3×C4×Dic5C2314yes—
92C3×C4×Dic5C2318yes—
93Dic3⋊Dic5C2318yes—
94Dic3⋊Dic5C2318yes—
95Dic3⋊Dic5C2318yes—
96#6669C2318yes—
97#6667C2318yes—
98Dic3×Dic5C2314yes—
99Dic3×Dic5C2314yes—
100Dic3×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×#888D511yescharacteristic, complemented
109C2×#872—52no—
110C2×C42×D3—51no—
111C2×C4×Dic6—52no—
112C2×C4×Dic6—51no—
113C22×C5×Q8—32no—
114C22×C4×D5—31no—
115C22×C4×D5—31no—
116C22×C4×D5—31no—
117C22×Dic10—31no—
118C22×Dic10C2×D311yescharacteristic
119C5×C4⋊Q8—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123C2×C42×C5—31no—
124#4092—316no—
125Q8×Dic5—316no—
126C2×#685—32no—
127C2×#685—32no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5—32no—
132C2×#683—32no—
133C2×#683C2×D312yes—
134C2×C4×Dic5—31no—
135C2×C4×Dic5—31no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5C2×D311yescharacteristic
138C2×C4×Dic5C2×D312yes—
139#4043—38no—
140#4043—38no—
141#4038—316no—
142#4036—316no—
143#4033—38no—
144#4033C2×D318yescomplemented
145C42×D5—38no—
146#4015—38no—
147C2×#533—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—22no—
150C22×D15—22no—
151C22×D15C2×Q814yes—
152C22×D15C2412yes—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5#4114yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—24no—
158C2×Dic15—22no—
159C2×Dic15C2412yes—
160C2×Dic15C2414yes—
161C4×D15—28no—
162Dic30—28no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3C2×Q814yes—
165C2×C5×Dic3#4114yes—
166C2×C5×Dic3C2414yes—
167C2×C5×Dic3C2412yes—
168C2×C5×Dic3C2412yes—
169C5×Dic6—216no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—24no—
172C2×C3×Dic5C2×Q814yes—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2414yes—
175C2×C3×Dic5C2412yes—
176C3×Dic10—28no—
177#1200—28no—
178#1200C2×Q8116yescomplemented
179C22×C3×Q8—51no—
180C22×C4×D3—51no—
181C22×C4×D3—51no—
182C22×C4×D3—51no—
183C22×Dic6—51no—
184C22×Dic6C2×D512yes—
185C3×C4×Q8—58no—
186C2×C3×C4⋊C4—52no—
187C2×C3×C4⋊C4C2×D511yescharacteristic
188C2×C3×C42—51no—
189C2×C3×C42—52no—
190#946—58no—
191#944—58no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×C4⋊Dic3—52no—
195C2×C4⋊Dic3C2×D511yescharacteristic
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—51no—
202C2×C4×Dic3—52no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3C2×D511yescharacteristic
205#897—58no—
206#896—516no—
207#889—516no—
208#888C2×D518yescomplemented
209#872—516no—
210C42×D3—58no—
211C4×Dic6—516no—
212C4×Dic6—58no—
213C23×D5—31no—
214C2×C5×Q8—38no—
215C2×C5×Q8—68no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—32no—
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D311yescharacteristic
221C22×Dic5—32no—
222C22×Dic5—31no—
223C22×Dic5C22×D312yes—
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D311yescharacteristic
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—24no—
233C2×Dic10—34no—
234C2×Dic10—64no—
235C2×Dic10C22×D314yes—
236C5×C4⋊C4—38no—
237C5×C4⋊C4—34no—
238C5×C4⋊C4C22×D314yes—
239C42×C5—34no—
240#685—38no—
241#685—38no—
242C4⋊Dic5—38no—
243C4⋊Dic5—38no—
244C4⋊Dic5—38no—
245C4⋊Dic5—38no—
246#683—38no—
247#683C22×D318yes—
248C4×Dic5—34no—
249C4×Dic5—34no—
250C4×Dic5—38no—
251C4×Dic5C22×D314yes—
252C4×Dic5C22×D318yes—
253#533—1516no—
254C2×C4⋊Q8—31no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—151no—
260C2×C4×Q8—51no—
261C2×C4×Q8—151no—
262C2×C4×Q8—152no—
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×C5C2×#4114yes—
275Dic15—24no—
276Dic15—22no—
277C3×Dic5—22no—
278C3×Dic5—24no—
279C3×Dic5C22×Q814yes—
280C5×Dic3—24no—
281C5×Dic3C22×Q814yes—
282C5×Dic3C2×#4114yes—
283C23×D3—51no—
284C2×C3×Q8—54no—
285C2×C3×Q8—104no—
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—52no—
293C22×Dic3C22×D512yes—
294C22×Dic3C22×D511yescharacteristic
295C22×Dic3C22×D511yescharacteristic
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—28no—
303C2×Dic6—54no—
304C2×Dic6—104no—
305C2×Dic6C22×D518yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4C22×D514yes—
308C3×C42—54no—
309C3×C42—58no—
310(C2×D3)⋊C4—58no—
311(C2×D3)⋊C4—58no—
312C4⋊Dic3—58no—
313C4⋊Dic3C22×D514yes—
314Dic3⋊C4—58no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4C22×D518yes—
319C4×Dic3—54no—
320C4×Dic3—58no—
321C4×Dic3—54no—
322C4×Dic3C22×D514yes—
323C23×C5C23×D311yescharacteristic
324C22×D5—34no—
325C22×D5—32no—
326C22×D5—62no—
327C22×D5—62no—
328C5×Q8—616no—
329C2×C4×C5—24no—
330C2×C4×C5—34no—
331C2×C4×C5—34no—
332C2×C4×C5—32no—
333C2×C4×C5—32no—
334C2×C4×C5—34no—
335C2×C4×C5—64no—
336C2×C4×C5#23514yes—
337C2×C4×C5C23×D314yes—
338C2×C4×C5C23×D312yes—
339C2×Dic5—24no—
340C2×Dic5—22no—
341C2×Dic5—32no—
342C2×Dic5—34no—
343C2×Dic5—64no—
344C2×Dic5—62no—
345C2×Dic5D3×Q814yes—
346C2×Dic5C23×D312yes—
347C2×Dic5C23×D314yes—
348C2×Dic5C23×D312yes—
349C4×D5—316no—
350C4×D5—68no—
351C4×D5—68no—
352Dic10—28no—
353Dic10—68no—
354C22×Q8—32no—
355C22×Q8—51no—
356C22×Q8—151no—
357C23×C4—151no—
358C23×C4—151no—
359C23×C4—151no—
360C4⋊Q8—38no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—158no—
364C22⋊Q8—1516no—
365C22⋊Q8—158no—
366C4×Q8—58no—
367C4×Q8—158no—
368C4×Q8—1516no—
369#117—1516no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—52no—
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—152no—
380C2×C22⋊C4—152no—
381C2×C42—31no—
382C2×C42—52no—
383C2×C42—51no—
384C2×C42—158no—
385C2×C42—152no—
386C2×C42—151no—
387C2×C42—151no—
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—108no—
399C2×C3×C4—24no—
400C2×C3×C4—54no—
401C2×C3×C4—52no—
402C2×C3×C4—52no—
403C2×C3×C4—54no—
404C2×C3×C4—102no—
405C2×C3×C4—104no—
406C2×C3×C4#71314yes—
407C2×C3×C4C23×D514yes—
408C2×C3×C4C23×D512yes—
409C2×Dic3—24no—
410C2×Dic3—52no—
411C2×Dic3—54no—
412C2×Dic3—104no—
413C2×Dic3—102no—
414C2×Dic3#71114yes—
415C2×Dic3Q8×D514yes—
416C2×Dic3C23×D514yes—
417C2×Dic3C23×D512yes—
418C2×Dic3C23×D512yes—
419C4×D3—516no—
420C4×D3—108no—
421C4×D3—108no—
422Dic6—216no—
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—34no—
434C4×C5—34no—
435C4×C5—64no—
436C4×C5C2×#23514yes—
437Dic5—24no—
438Dic5—22no—
439Dic5—64no—
440Dic5—62no—
441Dic5C2×D3×Q814yes—
442C24—151no—
443C2×Q8—38no—
444C2×Q8—54no—
445C2×Q8—68no—
446C2×Q8—104no—
447C2×Q8—154no—
448C2×Q8—304no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—52no—
455C22×C4—154no—
456C22×C4—158no—
457C22×C4—154no—
458C22×C4—151no—
459C22×C4—152no—
460C22×C4—154no—
461C22×C4—304no—
462C22×C4—304no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—34no—
467C4⋊C4—58no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4C2×D3×D514yes—
474C22⋊C4—158no—
475C22⋊C4—158no—
476C42—34no—
477C42—54no—
478C42—58no—
479C42—154no—
480C42—154no—
481C42—158no—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3C2×#71112yes—
484C22×C3C2×Q8×D512yes—
485C22×C3C2×#71312yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—54no—
488C2×D3—108no—
489C2×D3—102no—
490C2×D3—102no—
491C3×C4—24no—
492C3×C4—54no—
493C3×C4—102no—
494C3×C4—104no—
495C3×C4C2×#71314yes—
496Dic3—24no—
497Dic3—104no—
498Dic3—102no—
499Dic3C2×#71114yes—
500Dic3C2×Q8×D514yes—
501C2×C5#557814yescomplemented
502C2×C5C22×#23511yescharacteristic
503C2×C5C22×D3×Q811yescharacteristic
504C2×C5C2×D3×#4111yescharacteristic
505D5—64no—
506C23—154no—
507C23—152no—
508C23—302no—
509C23—302no—
510C23C22×D3×D511yescharacteristic
511Q8—616no—
512Q8—108no—
513Q8—308no—
514C2×C4—24no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—34no—
520C2×C4—54no—
521C2×C4—52no—
522C2×C4—52no—
523C2×C4—54no—
524C2×C4—64no—
525C2×C4—104no—
526C2×C4—102no—
527C2×C4—1516no—
528C2×C4—152no—
529C2×C4—154no—
530C2×C4—308no—
531C2×C4—302no—
532C2×C4—304no—
533C2×C4—308no—
534C2×C4#677314yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6606214yescomplemented
538C2×C3C22×#71111yescharacteristic
539C2×C3C22×Q8×D511yescharacteristic
540C2×C3C22×#71311yescharacteristic
541D3—104no—
542C5C2×#557811yescharacteristic, complemented, Sylow
543C22—154no—
544C22—302no—
545C22—302no—
546C22—308no—
547C22C2×#677312yes—
548C22D3×#71112yes—
549C22D3×Q8×D512yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—34no—
553C4—34no—
554C4—54no—
555C4—64no—
556C4—104no—
557C4—102no—
558C4—302no—
559C4—304no—
560C4C2×#677314yes—
561C3C2×#6606211yescharacteristic, complemented, Sylow
562C2—304no—
563C2#1175346414yesdirect product factor
564C2C22×#677311yescharacteristic
565C2C2×D3×#71111yescharacteristic
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×D15C23
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
2. C2×C5×#888C2semidirect
3. C2×C3×#4033C2semidirect
8. C2×#91389C2semidirect
9. C2×#91343C2semidirect
10. C2×#91333C2semidirect
11. C2×Dic5×Dic6C2semidirect
12. #11753464C2direct (N × H)
27. C5×#888C22semidirect
31. C3×#4033C22semidirect
44. #91389C22semidirect
45. #91343C22semidirect
46. #91333C22semidirect
47. Dic5×Dic6C22semidirect
58. C2×#4033D3semidirect
81. C2×#1200Q8semidirect
108. C2×#888D5semidirect
144. #4033C2×D3semidirect
178. #1200C2×Q8semidirect
208. #888C2×D5semidirect
388. C2×C3×C5#533semidirect
482. C3×C5C2×#533semidirect
501. C2×C5#5578semidirect
537. C2×C3#66062semidirect
542. C5C2×#5578semidirect
561. C3C2×#66062semidirect
563. C2#11753464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917862
C2×C5×#8882
C2×C3×#40332
C2×#914242
C2×#914022
C2×C4×#12002
C2×#913902
C2×#913892
C2×#913432
C2×#913332
C2×Dic5×Dic62
#117534642
C2×#660623
C2×#55785