Finite Group Databasebeta

← C2×#11754490 #14481407

Subgroups — C2×#11754490 #14481407

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic, complemented
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C2×C3×#4076C211yesmaximal, characteristic
4C2×#91548C212yesmaximal, complemented
5C2×#91534C212yesmaximal, complemented
6C2×#91470C211yesmaximal, characteristic, complemented
7#11754490C2116yesmaximal, direct product factor
8C2×#91434C211yesmaximal, characteristic, complemented
9C2×#91422C212yesmaximal, complemented
10C2×#91368C211yesmaximal, characteristic, complemented
11C2×#91362C212yesmaximal, complemented
12C2×#91344C211yesmaximal, characteristic, complemented
13C2×#65977—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×C22⋊D5C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×#1204C2212yes—
19C22×D5×Dic3C2212yes—
20C2×#6719C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22#91815C2218yescomplemented
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C5×#217C2212yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C5×#924C2218yescomplemented
30C2×C5×Dic3⋊C4C2212yes—
31C3×#4076C2218yes—
32C2×C3×#685C2212yes—
33C2×C3×C4⋊Dic5C2211yescharacteristic
34#91548C22116yescomplemented
35C2×Dic3⋊Dic5C2212yes—
36C2×#6669C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91534C22116yescomplemented
41C2×Dic3×Dic5C2212yes—
42#91470C2218yescomplemented
43#91434C2218yescomplemented
44#91422C22116yescomplemented
45#91368C2218yescomplemented
46#91362C22116yescomplemented
47#91344C2218yescomplemented
48C2×#5603—51nomaximal, Hall
49C2×C5×C22⋊Q8—31no—
50C2×#4093—31no—
51C2×Q8×Dic5—31no—
52C2×#4076D311yescharacteristic
53C2×#4072—31no—
54#65977—316no—
55C2×#4044—32no—
56C2×#4043—32no—
57C2×#4039—31no—
58C2×#4034—31no—
59C2×#4031—32no—
60C2×#4029—32no—
61C24×C3×C5C2311yescharacteristic
62C23×C3×D5C2312yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C2×C3×C22⋊D5—44no—
76C2×C3×C22⋊D5C2318yes—
77C22×C3×Dic5C2312yes—
78C2×C3×D20—24no—
79C2×C3×D20C2314yes—
80C2×#1204—44no—
81C2×#1204C2318yes—
82C2×D5×Dic3—44no—
83C2×D5×Dic3C2318yes—
84#6719C2314yes—
85#6719C2314yes—
86C4⋊Dic15C2314yes—
87C4⋊Dic15C2314yes—
88C4×Dic15C2314yes—
89C4×Dic15C2314yes—
90C5×#217C2318yes—
91C5×C4⋊Dic3C2314yes—
92C5×Dic3⋊C4C2318yes—
93C3×#685C2318yes—
94C3×C4⋊Dic5C2314yes—
95Dic3⋊Dic5C2318yes—
96#6669C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99#6665C2318yes—
100Dic3×Dic5C2318yes—
101C2×C3×#121—51no—
102C2×#936—51no—
103C2×#936—52no—
104C2×#935—52no—
105C2×D4×Dic3—51no—
106C2×#926—51no—
107C2×#924D511yescharacteristic, complemented
108#5603—516no—
109C2×#888—51no—
110C2×#887—51no—
111C2×#879—52no—
112C2×#878—52no—
113C22×C5×Q8—31no—
114C23×C4×C5C2×D311yescharacteristic
115C22×C22⋊D5C2×D312yes—
116C22×D20C2×D311yescharacteristic
117C22×C4×D5—32no—
118C22×Dic10—32no—
119C5×C22⋊Q8—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C5×C22⋊C4—32no—
123C2×C22⋊Dic5—31no—
124C2×C22⋊Dic5—31no—
125#4093—38no—
126Q8×Dic5—38no—
127#4076C2×D318yes—
128C2×#685—32no—
129C2×#685—32no—
130C2×#685—32no—
131C2×#685C2×D312yes—
132#4072—38no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—31no—
135C2×C4⋊Dic5—32no—
136C2×C4⋊Dic5C2×D311yescharacteristic
137C2×#683—32no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—32no—
141#4044—316no—
142#4043—316no—
143#4039—38no—
144#4034—38no—
145#4031—316no—
146#4029—316no—
147C2×#542—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C2412yes—
152C23×C3×C5C2411yescharacteristic
153C22×C3×D5—24no—
154C22×C3×D5—24no—
155C22×C3×D5—24no—
156C22×C3×D5C2414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15C2412yes—
167C2×Dic15C2412yes—
168C2×Dic15C2412yes—
169C2×Dic15C2412yes—
170C2×C5×Dic3—24no—
171C2×C5×Dic3—24no—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2414yes—
174C5×Dic6—28no—
175C3×C22⋊D5—48no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5C2414yes—
178C3×D20—28no—
179#1204—48no—
180D5×Dic3—48no—
181C22×C3×D4—52no—
182C22×C3×D4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C23×Dic3—52no—
185C22×Dic6—52no—
186C22×Dic6C2×D511yescharacteristic
187C3×#121—58no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—52no—
190C2×#217—51no—
191C2×#217—51no—
192C2×#217—52no—
193C2×#217—52no—
194C2×#217—52no—
195C2×#217C2×D512yes—
196#936—58no—
197#936—516no—
198#935—516no—
199D4×Dic3—58no—
200#926—58no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—51no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204#924C2×D518yescomplemented
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×Dic3⋊C4C2×D512yes—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—52no—
211#888—58no—
212#887—58no—
213#879—516no—
214#878—516no—
215C24×C5C22×D311yescharacteristic
216C23×D5C22×D312yes—
217C2×C5×Q8—34no—
218C2×C5×Q8—64no—
219C22×C4×C5—24no—
220C22×C4×C5—32no—
221C22×C4×C5—32no—
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D314yes—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—44no—
226C2×C22⋊D5C22×D318yes—
227C22×Dic5—31no—
228C22×Dic5—31no—
229C22×Dic5—31no—
230C22×Dic5—31no—
231C22×Dic5C22×D312yes—
232C2×D20—24no—
233C2×D20C22×D314yes—
234C2×C4×D5—38no—
235C2×C4×D5—124no—
236C2×Dic10—38no—
237C2×Dic10—124no—
238C5×C4⋊C4—38no—
239C5×C4⋊C4—34no—
240C5×C22⋊C4—38no—
241C22⋊Dic5—34no—
242C22⋊Dic5—34no—
243#685—38no—
244#685—38no—
245#685—38no—
246#685C22×D318yes—
247C4⋊Dic5—34no—
248C4⋊Dic5—34no—
249C4⋊Dic5—38no—
250C4⋊Dic5C22×D314yes—
251#683—38no—
252C4×Dic5—34no—
253C4×Dic5—34no—
254C4×Dic5—38no—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—152no—
259C2×#124—151no—
260C2×#123—152no—
261C2×C22⋊Q8—31no—
262C2×C22⋊Q8—152no—
263C2×#121—51no—
264C2×C4×Q8—151no—
265C2×C4×D4—151no—
266C2×#117—151no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5—22no—
270C22×C3×C5—44no—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C22×C3×C52−1+412yes—
274C22×C3×C5C2511yescharacteristic
275C2×C3×D5—24no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—48no—
279C3×C4×C5—22no—
280C3×C4×C5C2×#4114yes—
281Dic15—22no—
282Dic15—22no—
283Dic15—22no—
284Dic15—22no—
285C3×Dic5—24no—
286C5×Dic3—24no—
287C5×Dic3—24no—
288C24×C3—52no—
289C24×C3C22×D511yescharacteristic
290C2×C3×D4—58no—
291C2×C3×D4—54no—
292C2×C3×D4—104no—
293C2×C3×D4—204no—
294C22×C3×C4—24no—
295C22×C3×C4—52no—
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D514yes—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—51no—
303C22×Dic3—58no—
304C22×Dic3—204no—
305C22×Dic3C22×D512yes—
306C22×Dic3C22×D512yes—
307C2×Dic6—24no—
308C2×Dic6—58no—
309C2×Dic6—204no—
310C2×Dic6C22×D514yes—
311C3×C4⋊C4—54no—
312C3×C22⋊C4—58no—
313#217—54no—
314#217—54no—
315#217—58no—
316#217—58no—
317#217—58no—
318#217C22×D518yes—
319C4⋊Dic3—54no—
320C4⋊Dic3—54no—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4C22×D518yes—
325C4×Dic3—54no—
326C4×Dic3—54no—
327C4×Dic3—58no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5C23×D312yes—
332C23×C5C23×D311yescharacteristic
333C22×D5—24no—
334C22×D5—24no—
335C22×D5—24no—
336C22×D5C23×D314yes—
337C5×Q8—68no—
338C2×C4×C5—22no—
339C2×C4×C5—28no—
340C2×C4×C5—34no—
341C2×C4×C5—34no—
342C2×C4×C5—64no—
343C2×C4×C5—64no—
344C2×C4×C5#23714yes—
345C2×C4×C5C23×D312yes—
346C2×C4×C5C23×D312yes—
347C22⋊D5—48no—
348C2×Dic5—24no—
349C2×Dic5—32no—
350C2×Dic5—32no—
351C2×Dic5—32no—
352C2×Dic5—32no—
353C2×Dic5—62no—
354C2×Dic5—62no—
355C2×Dic5—62no—
356C2×Dic5—62no—
357C2×Dic5C23×D314yes—
358D20—28no—
359C4×D5—128no—
360Dic10—128no—
361C22×Q8—31no—
362C22×Q8—152no—
363C22×D4—52no—
364C22×D4—51no—
365C23×C4—152no—
366C23×C4D3×D511yescharacteristic
367C4⋊Q8—158no—
368#126—1516no—
369#124—1516no—
370#124—158no—
371#123—1516no—
372C22⋊Q8—38no—
373C22⋊Q8—1516no—
374#121—58no—
375C4×Q8—158no—
376C4×D4—158no—
377#117—158no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—51no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—151no—
384C2×C4⋊C4—151no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—52no—
387C2×C22⋊C4—152no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—151no—
391C2×C22⋊C4—151no—
392C2×C42—152no—
393C2×C42—151no—
394C2×C42—151no—
395C2×C3×C5—42no—
396C2×C3×C5#54214yescomplemented
397C2×C3×C5C22×#4111yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400C3×D5—44no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—54no—
405C23×C3—104no—
406C23×C3—104no—
407C23×C3—104no—
408C23×C3C23×D512yes—
409C23×C3C23×D511yescharacteristic
410C3×D4—108no—
411C3×D4—208no—
412C2×C3×C4—22no—
413C2×C3×C4—28no—
414C2×C3×C4—54no—
415C2×C3×C4—104no—
416C2×C3×C4#71114yes—
417C2×C3×C4C23×D512yes—
418C2×C3×C4C23×D512yes—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—52no—
422C2×Dic3—52no—
423C2×Dic3—52no—
424C2×Dic3—52no—
425C2×Dic3—102no—
426C2×Dic3—102no—
427C2×Dic3—102no—
428C2×Dic3—102no—
429C2×Dic3—208no—
430C2×Dic3C23×D514yes—
431C2×Dic3C23×D514yes—
432Dic6—28no—
433Dic6—208no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—44no—
438C22×C5C2×#23712yes—
439C22×C5#100412yes—
440C22×C5#101012yes—
441C22×C5C24×D311yescharacteristic
442C2×D5—24no—
443C2×D5—24no—
444C2×D5—24no—
445C2×D5—48no—
446C4×C5—22no—
447C4×C5—64no—
448C4×C5—64no—
449C4×C5C2×#23714yes—
450Dic5—24no—
451Dic5—62no—
452Dic5—62no—
453Dic5—62no—
454Dic5—62no—
455C24—52no—
456C24C2×D3×D511yescharacteristic
457C2×Q8—34no—
458C2×Q8—64no—
459C2×Q8—158no—
460C2×Q8—604no—
461C2×D4—58no—
462C2×D4—54no—
463C2×D4—104no—
464C2×D4—204no—
465C22×C4—24no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—52no—
469C22×C4—158no—
470C22×C4—151no—
471C22×C4—151no—
472C22×C4—151no—
473C22×C4—151no—
474C22×C4—604no—
475C22×C4C2×D3×D514yes—
476C22×C4C2×D3×D511yescharacteristic
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—54no—
481C4⋊C4—158no—
482C4⋊C4—158no—
483C4⋊C4—154no—
484C4⋊C4—154no—
485C22⋊C4—38no—
486C22⋊C4—58no—
487C22⋊C4—158no—
488C22⋊C4—158no—
489C22⋊C4—158no—
490C22⋊C4—154no—
491C22⋊C4—154no—
492C42—158no—
493C42—154no—
494C42—154no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—44no—
500C22×C3—104no—
501C22×C3—104no—
502C22×C3—104no—
503C22×C3—208no—
504C22×C3C2×#71112yes—
505C22×C3#414712yes—
506C22×C3#414912yes—
507C22×C3C24×D511yescharacteristic
508C3×C4—22no—
509C3×C4—104no—
510C3×C4C2×#71114yes—
511Dic3—24no—
512Dic3—24no—
513Dic3—102no—
514Dic3—102no—
515Dic3—102no—
516Dic3—102no—
517C2×C5—42no—
518C2×C5#560314yescomplemented
519C2×C5C22×#23711yescharacteristic
520C2×C5C2×#100411yescharacteristic
521C2×C5C2×#101011yescharacteristic
522D5—44no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—54no—
527C23—104no—
528C23—104no—
529C23—104no—
530C23C22×D3×D512yes—
531C23C22×D3×D511yescharacteristic
532Q8—68no—
533Q8—608no—
534D4—108no—
535D4—208no—
536C2×C4—22no—
537C2×C4—28no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—54no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—104no—
544C2×C4—152no—
545C2×C4—152no—
546C2×C4—152no—
547C2×C4—152no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—302no—
551C2×C4—302no—
552C2×C4—608no—
553C2×C4#678014yes—
554C2×C4C22×D3×D512yes—
555C2×C4C22×D3×D512yes—
556C2×C3—42no—
557C2×C3—204no—
558C2×C3#6597714yescomplemented
559C2×C3C22×#71111yescharacteristic
560C2×C3C2×#414711yescharacteristic
561C2×C3C2×#414911yescharacteristic
562C5C2×#560311yescharacteristic, complemented, Sylow
563C22—22no—
564C22—22no—
565C22—22no—
566C22—44no—
567C22—104no—
568C22—104no—
569C22—104no—
570C22—208no—
571C22#9200012yes—
572C22#9201712yes—
573C22C2×#678012yes—
574C22C23×D3×D511yescharacteristic
575C4—22no—
576C4—64no—
577C4—64no—
578C4—104no—
579C4—302no—
580C4—302no—
581C4—302no—
582C4—302no—
583C4C2×#678014yes—
584C3C2×#6597711yescharacteristic, complemented, Sylow
585C2—42no—
586C2—204no—
587C2#1175449014yesdirect product factor
588C2C2×#9200011yescharacteristic
589C2C2×#9201711yescharacteristic
590C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91815C2semidirect
2. C2×C5×#924C2semidirect
4. C2×#91548C2semidirect
5. C2×#91534C2semidirect
6. C2×#91470C2semidirect
7. #11754490C2direct (N × H)
8. C2×#91434C2semidirect
9. C2×#91422C2semidirect
10. C2×#91368C2semidirect
11. C2×#91362C2semidirect
12. C2×#91344C2semidirect
22. #91815C22semidirect
29. C5×#924C22semidirect
34. #91548C22semidirect
40. #91534C22semidirect
42. #91470C22semidirect
43. #91434C22semidirect
44. #91422C22semidirect
45. #91368C22semidirect
46. #91362C22semidirect
47. #91344C22semidirect
107. C2×#924D5semidirect
204. #924C2×D5semidirect
396. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
518. C2×C5#5603semidirect
558. C2×C3#65977semidirect
562. C5C2×#5603semidirect
584. C3C2×#65977semidirect
587. C2#11754490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C5×#9242
C2×C3×#40762
C2×#915482
C2×#915342
C2×#914702
#117544902
C2×#914342
C2×#914222
C2×#913682
C2×#913622
C2×#913442
C2×#659773
C2×#56035