Finite Group Databasebeta

← C2×#11752630 #14483560

Subgroups — C2×#11752630 #14483560

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D60C211yesmaximal, characteristic
2C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#4016C211yesmaximal, characteristic, complemented
4C2×#91437C211yesmaximal, characteristic, complemented
5C2×#91433C212yesmaximal
6C2×#91403C212yesmaximal, complemented
7C2×#91383C211yesmaximal, characteristic, complemented
8C2×#91383C211yesmaximal, characteristic, complemented
9C2×#91380C212yesmaximal, complemented
10C2×#91347C211yesmaximal, characteristic, complemented
11C2×#91334C212yesmaximal, complemented
12#11752630C2116yesmaximal, direct product factor
13C2×#65915—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C5×Dic6C2211yescharacteristic
18C22×#1200C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C4×D60C2218yes—
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×Dic3⋊C4C2212yes—
26C2×C4×C5×Dic3C2212yes—
27C4×C5×Dic6C2218yescomplemented
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×#683C2212yes—
32C3×#4016C2218yescomplemented
33C2×#6669C2212yes—
34C2×#6668C2212yes—
35C2×#6668C2212yes—
36C2×#6667C2212yes—
37C2×#6667C2212yes—
38C2×#6667C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91437C2218yescomplemented
41#91433C22116yes—
42#91403C22116yescomplemented
43#91383C2218yescomplemented
44#91383C2218yescomplemented
45#91380C22116yescomplemented
46#91347C2218yescomplemented
47#91334C22116yescomplemented
48C2×#5694—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4092—31no—
51C2×#4092—31no—
52#65915—316no—
53C2×#4040—32no—
54C2×#4038—31no—
55C2×D5×C4⋊C4—31no—
56C2×#4035—32no—
57C2×#4022—32no—
58C2×C4×D20—31no—
59C2×#4018—32no—
60C2×#4016D311yescharacteristic, complemented
61C23×D15C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C2×D60—24no—
69C2×D60C2314yes—
70C2×C4×D15—24no—
71C2×C4×D15—24no—
72C2×C4×D15C2314yes—
73C2×C4×D15C2314yes—
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2312yes—
76C2×C5×Dic6—24no—
77C2×C5×Dic6C2314yes—
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2312yes—
80C2×#1200—28no—
81C2×#1200C2318yes—
82C3×C42×C5C2314yes—
83#6714C2314yes—
84#6714C2314yes—
85C4⋊Dic15C2314yes—
86C5×C4⋊Dic3C2314yes—
87C5×Dic3⋊C4C2318yes—
88C4×C5×Dic3C2318yes—
89C3×C4⋊Dic5C2314yes—
90C3×C4⋊Dic5C2314yes—
91C3×#683C2318yes—
92C3×#683C2318yes—
93#6669C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96#6667C2318yes—
97#6667C2318yes—
98#6667C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×#125—51no—
101#5694—516no—
102C2×#898—52no—
103C2×#897—51no—
104C2×#897—51no—
105C2×#894—52no—
106C2×#892—51no—
107C2×#892—52no—
108C2×D3×C4⋊C4—51no—
109C2×#890—52no—
110C2×C4×D12—51no—
111C2×C4×Dic6D511yescharacteristic, complemented
112C22×C5×Q8—31no—
113C22×D20—31no—
114C22×C4×D5—31no—
115C22×C4×D5—31no—
116C22×C4×D5—32no—
117C4×C5×Q8—38no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—31no—
120C2×C42×C5—32no—
121C2×C42×C5C2×D311yescharacteristic
122#4092—38no—
123#4092—38no—
124C2×#685—31no—
125C2×#685—31no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—32no—
135C2×#683C2×D312yes—
136C2×#683C2×D312yes—
137C2×C4×Dic5—32no—
138#4040—316no—
139#4038—38no—
140D5×C4⋊C4—38no—
141#4035—316no—
142#4022—316no—
143C4×D20—38no—
144#4018—316no—
145#4016C2×D318yescomplemented
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—22no—
153C22×D15#4114yes—
154C22×D15C2412yes—
155C22×D15C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15C2412yes—
165C2×Dic15C2412yes—
166D60—28no—
167C4×D15—28no—
168C4×D15—28no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3C2414yes—
172C2×C5×Dic3C2414yes—
173C5×Dic6—28no—
174C2×C3×Dic5—24no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2414yes—
177C2×C3×Dic5C2414yes—
178#1200—216no—
179C22×D12—51no—
180C22×C4×D3—51no—
181C22×C4×D3—51no—
182C22×C4×D3—52no—
183C22×Dic6C2×D511yescharacteristic
184C3×#125—58no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C42C2×D511yescharacteristic
190C2×(C2×D3)⋊C4—51no—
191C2×(C2×D3)⋊C4—51no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—52no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—52no—
197C2×C4⋊Dic3—52no—
198C2×C4⋊Dic3C2×D511yescharacteristic
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—52no—
202C2×C4×Dic3C2×D512yes—
203#898—516no—
204#897—58no—
205#897—58no—
206#894—516no—
207#892—58no—
208#892—516no—
209D3×C4⋊C4—58no—
210#890—516no—
211C4×D12—58no—
212C4×Dic6C2×D518yescomplemented
213C23×D5—31no—
214C23×D5—31no—
215C2×C5×Q8—34no—
216C2×C5×Q8—64no—
217C22×C4×C5—32no—
218C22×C4×C5—32no—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—31no—
224C22×Dic5C22×D312yes—
225C22×Dic5C22×D312yes—
226C2×D20—34no—
227C2×D20—64no—
228C2×C4×D5—34no—
229C2×C4×D5—34no—
230C2×C4×D5—38no—
231C2×C4×D5—68no—
232C2×C4×D5—64no—
233C2×C4×D5—64no—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—34no—
236C42×C5—38no—
237C42×C5C22×D314yes—
238#685—34no—
239#685—34no—
240#685—38no—
241#685—38no—
242#685—38no—
243C4⋊Dic5—34no—
244C4⋊Dic5C22×D314yes—
245C4⋊Dic5C22×D314yes—
246#683—38no—
247#683—38no—
248#683—38no—
249#683C22×D318yes—
250#683C22×D318yes—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—51no—
255C2×#125—152no—
256C2×#123—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—31no—
260C2×C4×D4—151no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×D15—28no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15—22no—
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—44no—
275C2×D15C2×#4114yes—
276C3×C4×C5—22no—
277C3×C4×C5—22no—
278C3×C4×C5C2×#4114yes—
279Dic15—22no—
280Dic15—22no—
281C3×Dic5—24no—
282C3×Dic5—24no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C23×D3—51no—
286C23×D3—51no—
287C22×C3×C4—52no—
288C22×C3×C4—52no—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—51no—
293C22×Dic3—51no—
294C22×Dic3C22×D512yes—
295C22×Dic3C22×D512yes—
296C2×D12—54no—
297C2×D12—104no—
298C2×C4×D3—54no—
299C2×C4×D3—54no—
300C2×C4×D3—58no—
301C2×C4×D3—108no—
302C2×C4×D3—104no—
303C2×C4×D3—104no—
304C2×Dic6—24no—
305C2×Dic6C22×D514yes—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—58no—
308C3×C4⋊C4—54no—
309C3×C4⋊C4—54no—
310C3×C42C22×D514yes—
311(C2×D3)⋊C4—54no—
312(C2×D3)⋊C4—54no—
313(C2×D3)⋊C4—58no—
314(C2×D3)⋊C4—58no—
315(C2×D3)⋊C4—58no—
316C4⋊Dic3—54no—
317C4⋊Dic3—58no—
318C4⋊Dic3—58no—
319C4⋊Dic3C22×D514yes—
320Dic3⋊C4—58no—
321Dic3⋊C4C22×D518yes—
322C4×Dic3—58no—
323C4×Dic3C22×D518yes—
324C23×C5C23×D311yescharacteristic
325C22×D5—34no—
326C22×D5—32no—
327C22×D5—32no—
328C22×D5—62no—
329C22×D5—62no—
330C22×D5—62no—
331C22×D5—62no—
332C22×D5—62no—
333C5×Q8—68no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—34no—
337C2×C4×C5—34no—
338C2×C4×C5—64no—
339C2×C4×C5—64no—
340C2×C4×C5#23914yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×C4×C5C23×D312yes—
344C2×Dic5—24no—
345C2×Dic5—24no—
346C2×Dic5—32no—
347C2×Dic5—32no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5C23×D314yes—
351C2×Dic5C23×D314yes—
352D20—68no—
353C4×D5—616no—
354C4×D5—68no—
355C4×D5—68no—
356C22×Q8—31no—
357C22×D4—151no—
358C23×C4—152no—
359C23×C4—151no—
360C23×C4—151no—
361#126—1516no—
362#125—58no—
363#125—1516no—
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—38no—
368C4×D4—158no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4—52no—
377C2×C4⋊C4—158no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—151no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C42—32no—
388C2×C42—152no—
389C2×C42D3×D511yescharacteristic
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394D15—24no—
395D15—42no—
396C23×C3C23×D511yescharacteristic
397C22×D3—54no—
398C22×D3—52no—
399C22×D3—52no—
400C22×D3—102no—
401C22×D3—102no—
402C22×D3—102no—
403C22×D3—102no—
404C22×D3—102no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—54no—
408C2×C3×C4—54no—
409C2×C3×C4—104no—
410C2×C3×C4—104no—
411C2×C3×C4#70914yes—
412C2×C3×C4C23×D512yes—
413C2×C3×C4C23×D512yes—
414C2×C3×C4C23×D512yes—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—52no—
418C2×Dic3—52no—
419C2×Dic3—102no—
420C2×Dic3—102no—
421C2×Dic3C23×D514yes—
422C2×Dic3C23×D514yes—
423D12—108no—
424C4×D3—1016no—
425C4×D3—108no—
426C4×D3—108no—
427Dic6—28no—
428C22×C5C2×#23912yes—
429C22×C5D3×#4112yes—
430C22×C5#101012yes—
431C22×C5C24×D311yescharacteristic
432C2×D5—34no—
433C2×D5—68no—
434C2×D5—62no—
435C2×D5—62no—
436C2×D5—62no—
437C2×D5—62no—
438C2×D5—62no—
439C2×D5—124no—
440C4×C5—22no—
441C4×C5—22no—
442C4×C5—64no—
443C4×C5—64no—
444C4×C5C2×#23914yes—
445Dic5—24no—
446Dic5—24no—
447Dic5—62no—
448Dic5—62no—
449C24—151no—
450C24—151no—
451C2×Q8—34no—
452C2×Q8—64no—
453C2×D4—154no—
454C2×D4—304no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—158no—
460C22×C4—151no—
461C22×C4—151no—
462C22×C4—154no—
463C22×C4—154no—
464C22×C4—308no—
465C22×C4—304no—
466C22×C4—304no—
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—38no—
472C4⋊C4—54no—
473C4⋊C4—54no—
474C4⋊C4—58no—
475C4⋊C4—58no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4—154no—
480C22⋊C4—158no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—38no—
486C42—158no—
487C42C2×D3×D514yes—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3C2×#70912yes—
490C22×C3#414712yes—
491C22×C3D5×#4112yes—
492C22×C3C24×D511yescharacteristic
493C2×D3—54no—
494C2×D3—108no—
495C2×D3—102no—
496C2×D3—102no—
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—102no—
500C2×D3—204no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—104no—
504C3×C4—104no—
505C3×C4C2×#70914yes—
506Dic3—24no—
507Dic3—24no—
508Dic3—102no—
509Dic3—102no—
510C2×C5#569414yescomplemented
511C2×C5C22×#23911yescharacteristic
512C2×C5C2×D3×#4111yescharacteristic
513C2×C5C2×#101011yescharacteristic
514D5—64no—
515D5—122no—
516C23—154no—
517C23—152no—
518C23—152no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23—302no—
523C23—302no—
524C23C22×D3×D511yescharacteristic
525Q8—68no—
526D4—308no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—64no—
534C2×C4—64no—
535C2×C4—104no—
536C2×C4—104no—
537C2×C4—152no—
538C2×C4—152no—
539C2×C4—3016no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4#676914yes—
545C2×C4C22×D3×D512yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3#6591514yescomplemented
549C2×C3C22×#70911yescharacteristic
550C2×C3C2×#414711yescharacteristic
551C2×C3C2×D5×#4111yescharacteristic
552D3—104no—
553D3—202no—
554C5C2×#569411yescharacteristic, complemented, Sylow
555C22—154no—
556C22—308no—
557C22—302no—
558C22—302no—
559C22—302no—
560C22—302no—
561C22—302no—
562C22—604no—
563C22#9200012yes—
564C22C2×#676912yes—
565C22#9201612yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—22no—
569C4—64no—
570C4—64no—
571C4—104no—
572C4—104no—
573C4—302no—
574C4—302no—
575C4C2×#676914yes—
576C3C2×#6591511yescharacteristic, complemented, Sylow
577C2—304no—
578C2—602no—
579C2#1175263014yesdirect product factor
580C2C2×#9200011yescharacteristic
581C2C22×#676911yescharacteristic
582C2C2×#9201611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×Dic6C2semidirect
3. C2×C3×#4016C2semidirect
4. C2×#91437C2semidirect
6. C2×#91403C2semidirect
7. C2×#91383C2semidirect
8. C2×#91383C2semidirect
9. C2×#91380C2semidirect
10. C2×#91347C2semidirect
11. C2×#91334C2semidirect
12. #11752630C2direct (N × H)
27. C4×C5×Dic6C22semidirect
32. C3×#4016C22semidirect
40. #91437C22semidirect
42. #91403C22semidirect
43. #91383C22semidirect
44. #91383C22semidirect
45. #91380C22semidirect
46. #91347C22semidirect
47. #91334C22semidirect
60. C2×#4016D3semidirect
111. C2×C4×Dic6D5semidirect
145. #4016C2×D3semidirect
212. C4×Dic6C2×D5semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
510. C2×C5#5694semidirect
548. C2×C3#65915semidirect
554. C5C2×#5694semidirect
576. C3C2×#65915semidirect
579. C2#11752630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D602
C2×C4×C5×Dic62
C2×C3×#40162
C2×#914372
C2×#914332
C2×#914032
C2×#913832
C2×#913802
C2×#913472
C2×#913342
#117526302
C2×#659153
C2×#56945