Finite Group Databasebeta

← C2×#11753601 #14483901

Subgroups — C2×#11753601 #14483901

Order 1920.

2400 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×#91782C211yesmaximal, characteristic
2C2×C5×#888C211yesmaximal, characteristic, complemented
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×C4×#1204C211yesmaximal, characteristic, complemented
5C2×#91429C212yesmaximal, complemented
6C2×#91428C211yesmaximal, characteristic
7C2×#91424C212yesmaximal, complemented
8C2×#91418C211yesmaximal, characteristic
9C2×#91404C212yesmaximal, complemented
10C2×#91384C211yesmaximal, characteristic, complemented
11C2×#91383C212yesmaximal, complemented
12#11753601C2116yesmaximal, direct product factor
13C2×#66064—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×Dic6C2212yes—
17C22×#1204C2211yescharacteristic
18C22×#1200C2212yes—
19C22×#1200C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×#6714C2212yes—
22C2×C4×Dic15C2211yescharacteristic
23#91782C2218yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2211yescharacteristic
27C5×#888C2218yescomplemented
28C2×C3×C4⋊Dic5C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4036C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2212yes—
38C2×#6667C2212yes—
39C2×#6667C2212yes—
40C4×#1204C2218yescomplemented
41#91429C22116yescomplemented
42#91428C2218yes—
43#91424C22116yescomplemented
44#91418C2218yes—
45#91404C22116yescomplemented
46#91384C2218yescomplemented
47#91383C22116yescomplemented
48C2×#5690—51nomaximal, Hall
49C2×C5×C4⋊Q8—31no—
50C2×#4092—32no—
51C2×#4092—32no—
52#66064—316no—
53C2×#4043—32no—
54C2×#4039—31no—
55C2×#4039—31no—
56C2×D5×C4⋊C4—32no—
57C2×#4036—31no—
58C2×#4036D311yescharacteristic, complemented
59C2×C4×D20—31no—
60C2×C4×Dic10—31no—
61C23×D15C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C2×D60Q818yescomplemented
67C2×D60C2314yes—
68C2×C4×D15—44no—
69C2×C4×D15C2318yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2311yescharacteristic
73C2×C5×Dic6—44no—
74C2×C5×Dic6C2318yes—
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C2×#1204—24no—
79C2×#1204C2314yes—
80C2×#1200—28no—
81C2×#1200—44no—
82C2×#1200C2318yes—
83C2×#1200C2318yes—
84C3×C5×C4⋊C4C2314yes—
85#6714C2318yes—
86C4×Dic15C2314yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C4×C5×Dic3C2314yes—
90C3×C4⋊Dic5C2314yes—
91C3×C4⋊Dic5C2318yes—
92C3×#683C2318yes—
93C3×C4×Dic5C2314yes—
94Dic3⋊Dic5C2314yes—
95Dic3⋊Dic5C2318yes—
96#6669C2314yes—
97#6668C2318yes—
98#6668C2314yes—
99#6667C2318yes—
100#6667C2318yes—
101C2×C3×#125—51no—
102#5690—516no—
103C2×#897—52no—
104C2×#896—52no—
105C2×#896—52no—
106C2×#893—51no—
107C2×#893—51no—
108C2×D3×C4⋊C4—52no—
109C2×#890—51no—
110C2×#888D511yescharacteristic, complemented
111C2×C4×D12—51no—
112C2×C4×Dic6—51no—
113C22×C5×Q8—32no—
114C22×D20—31no—
115C22×C4×D5—32no—
116C22×C4×D5—32no—
117C22×C4×D5—32no—
118C22×Dic10—31no—
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—
125#4092—316no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×C4⋊Dic5C2×D312yes—
133C2×#683—31no—
134C2×#683—31no—
135C2×#683—32no—
136C2×#683C2×D312yes—
137C2×C4×Dic5—31no—
138C2×C4×Dic5C2×D311yescharacteristic
139#4043—316no—
140#4039—38no—
141#4039—38no—
142D5×C4⋊C4—316no—
143#4036—38no—
144#4036C2×D318yescomplemented
145C4×D20—38no—
146C4×Dic10—38no—
147C2×#554—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—24no—
150C22×D15—24no—
151C22×D15C2×Q818yes—
152C22×D15C2414yes—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5C2×Q814yes—
155C2×C3×C4×C5C2414yes—
156C2×C3×C4×C5C2412yes—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15C2412yes—
160C2×Dic15C2412yes—
161D60C2×Q8116yescomplemented
162C4×D15—48no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3#4114yes—
166C2×C5×Dic3C2412yes—
167C2×C5×Dic3C2414yes—
168C2×C5×Dic3C2412yes—
169C5×Dic6—48no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2414yes—
175C2×C3×Dic5C2412yes—
176#1204—28no—
177#1200—216no—
178#1200—48no—
179C22×D12—51no—
180C22×C4×D3—52no—
181C22×C4×D3—52no—
182C22×C4×D3—52no—
183C22×Dic6—51no—
184C22×Dic6C2×D512yes—
185C3×#125—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C4⋊C4C2×D511yescharacteristic
190C2×C3×C42—51no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3C2×D511yescharacteristic
197C2×Dic3⋊C4—51no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—51no—
202C2×C4×Dic3C2×D511yescharacteristic
203#897—516no—
204#896—516no—
205#896—516no—
206#893—58no—
207#893—58no—
208D3×C4⋊C4—516no—
209#890—58no—
210#888C2×D518yescomplemented
211C4×D12—58no—
212C4×Dic6—58no—
213C23×D5—32no—
214C2×C5×Q8—38no—
215C2×C5×Q8—124no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—32no—
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D311yescharacteristic
221C22×Dic5—31no—
222C22×Dic5—31no—
223C22×Dic5C22×D311yescharacteristic
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D312yes—
226C2×D20—38no—
227C2×D20—34no—
228C2×C4×D5—38no—
229C2×C4×D5—38no—
230C2×C4×D5—38no—
231C2×C4×D5—68no—
232C2×C4×D5—124no—
233C2×C4×D5—124no—
234C2×Dic10—34no—
235C2×Dic10—64no—
236C5×C4⋊C4—38no—
237C5×C4⋊C4—34no—
238C5×C4⋊C4C22×D314yes—
239C42×C5—34no—
240#685—38no—
241#685—38no—
242#685—38no—
243C4⋊Dic5—34no—
244C4⋊Dic5—38no—
245C4⋊Dic5C22×D314yes—
246C4⋊Dic5C22×D318yes—
247#683—34no—
248#683—38no—
249#683—34no—
250#683C22×D318yes—
251C4×Dic5—34no—
252C4×Dic5C22×D314yes—
253#554—1516no—
254C2×C4⋊Q8—31no—
255C2×#125—51no—
256C2×#125—151no—
257C2×C22⋊Q8—152no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—152no—
260C2×C4×Q8—151no—
261C2×C4×D4—151no—
262C2×C4×D4—151no—
263C2×C4×D4—151no—
264C22×C4⋊C4—152no—
265C22×C3×C5C22×Q812yes—
266C22×C3×C5C2×#4112yes—
267C22×C3×C5H(5,𝔽2)12yes—
268C22×C3×C5C2511yescharacteristic
269C2×D15—216no—
270C2×D15—24no—
271C2×D15—24no—
272C2×D15C22×Q818yes—
273C3×C4×C5—24no—
274C3×C4×C5C22×Q814yes—
275Dic15—22no—
276Dic15—22no—
277C3×Dic5—24no—
278C3×Dic5—22no—
279C3×Dic5—22no—
280C5×Dic3—24no—
281C5×Dic3—22no—
282C5×Dic3C2×#4114yes—
283C23×D3—52no—
284C22×C3×C4—51no—
285C22×C3×C4—52no—
286C22×C3×C4—51no—
287C22×C3×C4C22×D512yes—
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3C22×D511yescharacteristic
292C22×Dic3C22×D512yes—
293C22×Dic3C22×D511yescharacteristic
294C2×D12—58no—
295C2×D12—54no—
296C2×C4×D3—58no—
297C2×C4×D3—58no—
298C2×C4×D3—58no—
299C2×C4×D3—108no—
300C2×C4×D3—204no—
301C2×C4×D3—204no—
302C2×Dic6—44no—
303C2×Dic6—54no—
304C2×Dic6—104no—
305C2×Dic6C22×D518yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C4⋊C4—58no—
309C3×C4⋊C4C22×D514yes—
310C3×C42—54no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—58no—
313(C2×D3)⋊C4—58no—
314C4⋊Dic3—54no—
315C4⋊Dic3—58no—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—54no—
318Dic3⋊C4—54no—
319Dic3⋊C4—58no—
320Dic3⋊C4C22×D518yes—
321C4×Dic3—54no—
322C4×Dic3C22×D514yes—
323C23×C5C23×D311yescharacteristic
324C22×D5—38no—
325C22×D5—34no—
326C22×D5—64no—
327C22×D5—64no—
328C5×Q8—128no—
329C2×C4×C5—24no—
330C2×C4×C5—34no—
331C2×C4×C5—32no—
332C2×C4×C5—32no—
333C2×C4×C5—34no—
334C2×C4×C5—64no—
335C2×C4×C5—62no—
336C2×C4×C5D3×Q814yes—
337C2×C4×C5C23×D314yes—
338C2×C4×C5C23×D312yes—
339C2×Dic5—22no—
340C2×Dic5—24no—
341C2×Dic5—22no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—62no—
345C2×Dic5—62no—
346C2×Dic5C23×D312yes—
347C2×Dic5C23×D312yes—
348C2×Dic5C23×D314yes—
349D20—316no—
350C4×D5—616no—
351C4×D5—128no—
352C4×D5—128no—
353Dic10—68no—
354C22×Q8—32no—
355C22×Q8—151no—
356C22×D4—151no—
357C23×C4—152no—
358C23×C4—152no—
359C23×C4—152no—
360C4⋊Q8—38no—
361#125—58no—
362#125—158no—
363C22⋊Q8—1516no—
364C22⋊Q8—1516no—
365C22⋊Q8—1516no—
366C4×Q8—158no—
367C4×D4—158no—
368C4×D4—158no—
369C4×D4—158no—
370C2×C4⋊C4—32no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—52no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—1516no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—151no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4D3×D511yescharacteristic
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—31no—
386C2×C42—51no—
387C2×C42—151no—
388C2×C3×C5#55414yescomplemented
389C2×C3×C5C23×Q811yescharacteristic
390C2×C3×C5C22×#4111yescharacteristic
391C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
392D15—28no—
393C23×C3C23×D511yescharacteristic
394C22×D3—58no—
395C22×D3—54no—
396C22×D3—104no—
397C22×D3—104no—
398C2×C3×C4—24no—
399C2×C3×C4—52no—
400C2×C3×C4—54no—
401C2×C3×C4—52no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—104no—
405C2×C3×C4Q8×D514yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—22no—
409C2×Dic3—24no—
410C2×Dic3—52no—
411C2×Dic3—52no—
412C2×Dic3—102no—
413C2×Dic3—102no—
414C2×Dic3#71314yes—
415C2×Dic3C23×D512yes—
416C2×Dic3C23×D514yes—
417C2×Dic3C23×D512yes—
418D12—516no—
419C4×D3—1016no—
420C4×D3—208no—
421C4×D3—208no—
422Dic6—48no—
423Dic6—108no—
424C22×C5C2×D3×Q812yes—
425C22×C5D3×#4112yes—
426C22×C5#100912yes—
427C22×C5C24×D311yescharacteristic
428C2×D5—38no—
429C2×D5—616no—
430C2×D5—64no—
431C2×D5—64no—
432C4×C5—24no—
433C4×C5—34no—
434C4×C5—64no—
435C4×C5—62no—
436C4×C5C2×D3×Q814yes—
437Dic5—22no—
438Dic5—24no—
439Dic5—22no—
440Dic5—62no—
441Dic5—62no—
442C24—152no—
443C2×Q8—38no—
444C2×Q8—124no—
445C2×Q8—154no—
446C2×Q8—304no—
447C2×D4—158no—
448C2×D4—154no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—52no—
455C22×C4—158no—
456C22×C4—158no—
457C22×C4—151no—
458C22×C4—151no—
459C22×C4—158no—
460C22×C4—308no—
461C22×C4—604no—
462C22×C4—604no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—34no—
467C4⋊C4—58no—
468C4⋊C4—54no—
469C4⋊C4—58no—
470C4⋊C4—154no—
471C4⋊C4—158no—
472C4⋊C4—154no—
473C4⋊C4—154no—
474C4⋊C4—158no—
475C4⋊C4C2×D3×D514yes—
476C22⋊C4—158no—
477C22⋊C4—158no—
478C22⋊C4—158no—
479C42—34no—
480C42—54no—
481C42—154no—
482C3×C5C2×#55411yescharacteristic, complemented, Hall
483C22×C3#414412yes—
484C22×C3C2×Q8×D512yes—
485C22×C3C2×#71312yes—
486C22×C3C24×D511yescharacteristic
487C2×D3—58no—
488C2×D3—1016no—
489C2×D3—104no—
490C2×D3—104no—
491C3×C4—24no—
492C3×C4—102no—
493C3×C4—102no—
494C3×C4—104no—
495C3×C4C2×Q8×D514yes—
496Dic3—22no—
497Dic3—24no—
498Dic3—102no—
499Dic3—102no—
500Dic3C2×#71314yes—
501C2×C5#569014yescomplemented
502C2×C5C22×D3×Q811yescharacteristic
503C2×C5C2×D3×#4111yescharacteristic
504C2×C5C2×#100911yescharacteristic
505D5—68no—
506C23—158no—
507C23—154no—
508C23—304no—
509C23—304no—
510C23C22×D3×D511yescharacteristic
511Q8—128no—
512Q8—308no—
513D4—1516no—
514C2×C4—24no—
515C2×C4—34no—
516C2×C4—32no—
517C2×C4—32no—
518C2×C4—34no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—54no—
522C2×C4—64no—
523C2×C4—62no—
524C2×C4—102no—
525C2×C4—104no—
526C2×C4—102no—
527C2×C4—152no—
528C2×C4—152no—
529C2×C4—3016no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—608no—
533C2×C4—608no—
534C2×C4D15⋊Q814yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3#6606414yescomplemented
538C2×C3C2×#414411yescharacteristic
539C2×C3C22×Q8×D511yescharacteristic
540C2×C3C22×#71311yescharacteristic
541D3—108no—
542C5C2×#569011yescharacteristic, complemented, Sylow
543C22—158no—
544C22—3016no—
545C22—304no—
546C22—304no—
547C22C2×D15⋊Q812yes—
548C22#9202712yes—
549C22D3×#71312yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—34no—
553C4—64no—
554C4—62no—
555C4—102no—
556C4—104no—
557C4—102no—
558C4—302no—
559C4—302no—
560C4C2×D15⋊Q814yes—
561C3C2×#6606411yescharacteristic, complemented, Sylow
562C2—308no—
563C2#1175360114yesdirect product factor
564C2C22×D15⋊Q811yescharacteristic
565C2C2×#9202711yescharacteristic
566C2C2×D3×#71311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#554
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×#4036C2semidirect
4. C2×C4×#1204C2semidirect
5. C2×#91429C2semidirect
7. C2×#91424C2semidirect
9. C2×#91404C2semidirect
10. C2×#91384C2semidirect
11. C2×#91383C2semidirect
12. #11753601C2direct (N × H)
27. C5×#888C22semidirect
32. C3×#4036C22semidirect
40. C4×#1204C22semidirect
41. #91429C22semidirect
43. #91424C22semidirect
45. #91404C22semidirect
46. #91384C22semidirect
47. #91383C22semidirect
58. C2×#4036D3semidirect
66. C2×D60Q8semidirect
110. C2×#888D5semidirect
144. #4036C2×D3semidirect
161. D60C2×Q8semidirect
210. #888C2×D5semidirect
388. C2×C3×C5#554semidirect
482. C3×C5C2×#554semidirect
501. C2×C5#5690semidirect
537. C2×C3#66064semidirect
542. C5C2×#5690semidirect
561. C3C2×#66064semidirect
563. C2#11753601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917822
C2×C5×#8882
C2×C3×#40362
C2×C4×#12042
C2×#914292
C2×#914282
C2×#914242
C2×#914182
C2×#914042
C2×#913842
C2×#913832
#117536012
C2×#660643
C2×#56905