Finite Group Databasebeta

← C2×#11754878 #14479928

Subgroups — C2×#11754878 #14479928

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4082C211yesmaximal, characteristic, complemented
4C2×#91562C212yesmaximal, complemented
5C2×#91556C212yesmaximal, complemented
6C2×#91531C212yesmaximal, complemented
7C2×#91529C212yesmaximal, complemented
8#11754878C2116yesmaximal, direct product factor
9C2×C4×#1200C211yesmaximal, characteristic, complemented
10C2×#91390C211yesmaximal, characteristic, complemented
11C2×#91388C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
13C2×#65891—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C22×C4×D15C2211yescharacteristic
17C23×C5×Dic3C2212yes—
18C22×C3×Dic10C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C2×#6719C2212yes—
22#91827C2218yes—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C5×#217C2212yes—
25C5×D4×Dic3C2218yescomplemented
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2212yes—
30C3×#4082C2218yescomplemented
31C2×C3×C4×Dic5C2211yescharacteristic
32#91562C22116yescomplemented
33#91556C22116yescomplemented
34C2×Dic3⋊Dic5C2212yes—
35C2×Dic3⋊Dic5C2212yes—
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×#6667C2212yes—
39#91531C22116yescomplemented
40#91529C22116yescomplemented
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2212yes—
44C4×#1200C2218yescomplemented
45#91390C2218yescomplemented
46#91388C2218yescomplemented
47Dic3×Dic10C2218yescomplemented
48C2×#5680—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4084—31no—
51C2×#4082D311yescharacteristic, complemented
52C2×C4×C22⋊D5—32no—
53C2×#4072—32no—
54#65891—316no—
55C2×#4043—31no—
56C2×#4036—31no—
57C2×#4029—32no—
58C2×#4025—32no—
59C2×C42×D5—31no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2312yes—
62C23×D15C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C2×#1220—28no—
67C2×#1220C2318yes—
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2312yes—
70C2×C4×D15—24no—
71C2×C4×D15C2314yes—
72C22×C5×Dic3—28no—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2318yes—
76C22×C5×Dic3C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2312yes—
80C2×C3×Dic10—24no—
81C2×C3×Dic10C2314yes—
82C2×#1200—24no—
83C2×#1200—24no—
84C2×#1200C2314yes—
85C2×#1200C2314yes—
86#6719C2318yes—
87C4⋊Dic15C2314yes—
88C5×#217C2318yes—
89C5×C4⋊Dic3C2314yes—
90C4×C5×Dic3C2314yes—
91C3×C22⋊Dic5C2318yes—
92C3×C22⋊Dic5C2318yes—
93C3×C4×Dic5C2314yes—
94Dic3⋊Dic5C2318yes—
95Dic3⋊Dic5C2318yes—
96#6669C2318yes—
97#6668C2318yes—
98#6667C2318yes—
99Dic3×Dic5C2314yes—
100Dic3×Dic5C2314yes—
101Dic3×Dic5C2318yes—
102C2×C3×#124—51no—
103C2×#946—51no—
104C2×Q8×Dic3—51no—
105C2×#938—51no—
106C2×D4×Dic3D511yescharacteristic, complemented
107#5680—516no—
108C2×#883—52no—
109C2×#67⋊C4—52no—
110C2×#879—52no—
111C2×#877—52no—
112C2×C42×D3—51no—
113C2×#870—51no—
114C22×C5×D4C2×D311yescharacteristic
115C23×C4×C5—32no—
116C22×C22⋊D5—32no—
117C22×C4×D5—31no—
118C22×C4×D5—31no—
119C22×C4×D5—31no—
120C22×Dic10C2×D311yescharacteristic
121C4×C5×D4—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C22⋊C4—32no—
124C2×C42×C5—31no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5C2×D312yes—
127C2×C22⋊Dic5C2×D312yes—
128#4084—38no—
129#4082C2×D318yescomplemented
130C4×C22⋊D5—316no—
131C2×#685—32no—
132#4072—316no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—32no—
135C2×C4⋊Dic5—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—31no—
141C2×C4×Dic5C2×D311yescharacteristic
142#4043—38no—
143#4036—38no—
144#4029—316no—
145#4025—316no—
146C42×D5—38no—
147C4×Dic10—38no—
148C2×#529—151noSylow
149C23×C3×C5—24no—
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5C2414yes—
153C23×C3×C5C2411yescharacteristic
154C22×D15—22no—
155C22×D15—22no—
156C22×D15#4114yes—
157C22×D15C2412yes—
158C3×C5×D4—28no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2412yes—
161#1220—216no—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15C2412yes—
165C2×Dic15C2414yes—
166C4×D15—28no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—216no—
170C2×C5×Dic3#4114yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2412yes—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—24no—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2412yes—
180C3×Dic10—28no—
181#1200—28no—
182#1200—28no—
183C22×C3×Q8—51no—
184C22×C3×D4C2×D511yescharacteristic
185C22×#67—52no—
186C23×Dic3C2×D512yes—
187C22×C4×D3—51no—
188C22×C4×D3—51no—
189C22×C4×D3—51no—
190C3×#124—58no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C42—51no—
194C2×#217—52no—
195C2×#217C2×D512yes—
196#946—58no—
197Q8×Dic3—58no—
198#938—58no—
199D4×Dic3C2×D518yescomplemented
200C2×(C2×D3)⋊C4—52no—
201C2×C4⋊Dic3—51no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—52no—
210C2×C4×Dic3C2×D511yescharacteristic
211#883—516no—
212#67⋊C4—516no—
213#879—516no—
214#877—516no—
215C42×D3—58no—
216#870—58no—
217C24×C5C22×D312yes—
218C23×D5—31no—
219C2×C5×D4—24no—
220C2×C5×D4C22×D314yes—
221C22×C4×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—32no—
224C22×C4×C5—38no—
225C22×C4×C5—68no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—38no—
228C2×C22⋊D5—68no—
229C22×Dic5—31no—
230C22×Dic5—32no—
231C22×Dic5C22×D312yes—
232C22×Dic5C22×D311yescharacteristic
233C22×Dic5C22×D311yescharacteristic
234C2×C4×D5—34no—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—64no—
238C2×C4×D5—64no—
239C2×C4×D5—64no—
240C2×Dic10—24no—
241C2×Dic10C22×D314yes—
242C5×C4⋊C4—34no—
243C5×C22⋊C4—38no—
244C42×C5—34no—
245C22⋊Dic5—38no—
246C22⋊Dic5C22×D318yes—
247C22⋊Dic5C22×D318yes—
248#685—38no—
249C4⋊Dic5—34no—
250C4⋊Dic5—38no—
251C4⋊Dic5—38no—
252#683—38no—
253#683—38no—
254C4×Dic5—38no—
255C4×Dic5—34no—
256C4×Dic5—34no—
257C4×Dic5C22×D314yes—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—51no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—151no—
265C2×C4×Q8—151no—
266C2×C4×D4—31no—
267C2×C4×D4—152no—
268C2×#117—152no—
269C22×C42—151no—
270C22×C3×C5—24no—
271C22×C3×C5—24no—
272C22×C3×C5—24no—
273C22×C3×C5—48no—
274C22×C3×C5C2×#4112yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5C2511yescharacteristic
278C2×D15—28no—
279C2×D15—22no—
280C2×D15—22no—
281C2×D15C2×#4114yes—
282C3×C4×C5C2×#4114yes—
283Dic15—22no—
284Dic15—24no—
285C3×Dic5—22no—
286C3×Dic5—22no—
287C3×Dic5—24no—
288C5×Dic3—22no—
289C5×Dic3—24no—
290C5×Dic3C2×#4114yes—
291C24×C3C22×D512yes—
292C23×D3—51no—
293C2×C3×Q8—54no—
294C2×C3×Q8—104no—
295C2×C3×D4—24no—
296C2×C3×D4C22×D514yes—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4—52no—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—58no—
302C2×#67—108no—
303C22×Dic3—28no—
304C22×Dic3—51no—
305C22×Dic3—52no—
306C22×Dic3C22×D518yes—
307C22×Dic3C22×D511yescharacteristic
308C22×Dic3C22×D512yes—
309C22×Dic3C22×D511yescharacteristic
310C2×C4×D3—54no—
311C2×C4×D3—54no—
312C2×C4×D3—54no—
313C2×C4×D3—104no—
314C2×C4×D3—104no—
315C2×C4×D3—104no—
316C3×C22⋊C4—58no—
317C3×C22⋊C4—58no—
318C3×C42—54no—
319#217—58no—
320#217C22×D518yes—
321(C2×D3)⋊C4—58no—
322C4⋊Dic3—54no—
323C4⋊Dic3—58no—
324C4⋊Dic3C22×D514yes—
325Dic3⋊C4—58no—
326Dic3⋊C4—58no—
327Dic3⋊C4—58no—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3—58no—
331C4×Dic3C22×D514yes—
332C23×C5—24no—
333C23×C5—24no—
334C23×C5—24no—
335C23×C5C23×D314yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—34no—
338C22×D5—32no—
339C22×D5—62no—
340C22×D5—62no—
341C5×D4—28no—
342C2×C4×C5—34no—
343C2×C4×C5—32no—
344C2×C4×C5—32no—
345C2×C4×C5—34no—
346C2×C4×C5—616no—
347C2×C4×C5—62no—
348C2×C4×C5—64no—
349C2×C4×C5#23714yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5—616no—
352C2×Dic5—24no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—32no—
356C2×Dic5—34no—
357C2×Dic5—62no—
358C2×Dic5—64no—
359C2×Dic5C23×D312yes—
360C2×Dic5C23×D312yes—
361C2×Dic5C23×D314yes—
362C4×D5—68no—
363C4×D5—68no—
364C4×D5—68no—
365Dic10—28no—
366C22×Q8—51no—
367C22×D4—152no—
368C22×D4D3×D511yescharacteristic
369C23×C4—32no—
370C23×C4—151no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125—158no—
375#124—58no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—158no—
379C4×Q8—158no—
380C4×D4—38no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—151no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—52no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—31no—
395C2×C42—51no—
396C2×C42—158no—
397C2×C42—151no—
398C2×C42—152no—
399C2×C42—151no—
400C2×C3×C5—44no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405D15—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3C23×D514yes—
410C23×C3C23×D511yescharacteristic
411C22×D3—54no—
412C22×D3—52no—
413C22×D3—102no—
414C22×D3—102no—
415C3×Q8—108no—
416C3×D4—28no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—54no—
420C2×C3×C4—104no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4#70914yes—
424C2×C3×C4C23×D512yes—
425#67—1016no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—216no—
429C2×Dic3—52no—
430C2×Dic3—54no—
431C2×Dic3—102no—
432C2×Dic3—104no—
433C2×Dic3#71114yes—
434C2×Dic3C23×D512yes—
435C2×Dic3C23×D514yes—
436C2×Dic3C23×D512yes—
437C4×D3—108no—
438C4×D3—108no—
439C4×D3—108no—
440C22×C5—24no—
441C22×C5—24no—
442C22×C5—24no—
443C22×C5—48no—
444C22×C5C2×#23712yes—
445C22×C5D3×#4112yes—
446C22×C5D3×#4112yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—34no—
449C2×D5—68no—
450C2×D5—62no—
451C2×D5—62no—
452C4×C5—34no—
453C4×C5—62no—
454C4×C5—64no—
455C4×C5C2×#23714yes—
456Dic5—24no—
457Dic5—22no—
458Dic5—22no—
459Dic5—62no—
460Dic5—64no—
461C24—151no—
462C24C2×D3×D512yes—
463C2×Q8—54no—
464C2×Q8—104no—
465C2×D4—24no—
466C2×D4—158no—
467C2×D4—308no—
468C2×D4C2×D3×D514yes—
469C22×C4—31no—
470C22×C4—38no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—52no—
476C22×C4—68no—
477C22×C4—154no—
478C22×C4—154no—
479C22×C4—151no—
480C22×C4—152no—
481C22×C4—154no—
482C22×C4—304no—
483C22×C4—304no—
484C22×C4—304no—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—158no—
488C4⋊C4—158no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—154no—
492C22⋊C4—38no—
493C22⋊C4—58no—
494C22⋊C4—58no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—34no—
498C42—54no—
499C42—154no—
500C42—154no—
501C42—158no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—48no—
507C22×C3C2×#70912yes—
508C22×C3C2×#71112yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—54no—
512C2×D3—108no—
513C2×D3—102no—
514C2×D3—102no—
515C3×C4—104no—
516C3×C4—102no—
517C3×C4—102no—
518C3×C4C2×#70914yes—
519Dic3—24no—
520Dic3—22no—
521Dic3—102no—
522Dic3—104no—
523Dic3C2×#71114yes—
524C2×C5—44no—
525C2×C5#568014yescomplemented
526C2×C5C22×#23711yescharacteristic
527C2×C5C2×D3×#4111yescharacteristic
528C2×C5C2×D3×#4111yescharacteristic
529D5—64no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—154no—
534C23—152no—
535C23—302no—
536C23—302no—
537C23C22×D3×D514yes—
538C23C22×D3×D511yescharacteristic
539Q8—108no—
540D4—28no—
541D4—3016no—
542C2×C4—34no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—34no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—54no—
549C2×C4—616no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—104no—
555C2×C4—152no—
556C2×C4—154no—
557C2×C4—308no—
558C2×C4—308no—
559C2×C4—304no—
560C2×C4—302no—
561C2×C4—308no—
562C2×C4#677914yes—
563C2×C4C22×D3×D512yes—
564C2×C3—44no—
565C2×C3#6589114yescomplemented
566C2×C3C22×#70911yescharacteristic
567C2×C3C22×#71111yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—104no—
570C5C2×#568011yescharacteristic, complemented, Sylow
571C22—24no—
572C22—24no—
573C22—24no—
574C22—48no—
575C22—154no—
576C22—302no—
577C22—308no—
578C22—302no—
579C22D3×#71112yes—
580C22#9202412yes—
581C22C2×#677912yes—
582C22C23×D3×D511yescharacteristic
583C4—34no—
584C4—64no—
585C4—62no—
586C4—104no—
587C4—102no—
588C4—102no—
589C4—302no—
590C4—304no—
591C4C2×#677914yes—
592C3C2×#6589111yescharacteristic, complemented, Sylow
593C2—44no—
594C2—304no—
595C2#1175487814yesdirect product factor
596C2C2×D3×#71111yescharacteristic
597C2C2×#9202411yescharacteristic
598C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×#91827C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×D4×Dic3C2semidirect
3. C2×C3×#4082C2semidirect
4. C2×#91562C2semidirect
5. C2×#91556C2semidirect
6. C2×#91531C2semidirect
7. C2×#91529C2semidirect
8. #11754878C2direct (N × H)
9. C2×C4×#1200C2semidirect
10. C2×#91390C2semidirect
11. C2×#91388C2semidirect
12. C2×Dic3×Dic10C2semidirect
25. C5×D4×Dic3C22semidirect
30. C3×#4082C22semidirect
32. #91562C22semidirect
33. #91556C22semidirect
39. #91531C22semidirect
40. #91529C22semidirect
44. C4×#1200C22semidirect
45. #91390C22semidirect
46. #91388C22semidirect
47. Dic3×Dic10C22semidirect
51. C2×#4082D3semidirect
106. C2×D4×Dic3D5semidirect
129. #4082C2×D3semidirect
199. D4×Dic3C2×D5semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
525. C2×C5#5680semidirect
565. C2×C3#65891semidirect
570. C5C2×#5680semidirect
592. C3C2×#65891semidirect
595. C2#11754878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918272
C2×C5×D4×Dic32
C2×C3×#40822
C2×#915622
C2×#915562
C2×#915312
C2×#915292
#117548782
C2×C4×#12002
C2×#913902
C2×#913882
C2×Dic3×Dic102
C2×#658913
C2×#56805