Finite Group Databasebeta

← C2×#11754848 #14479925

Subgroups — C2×#11754848 #14479925

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×#91825C211yesmaximal, characteristic, complemented
2C2×C5×#938C211yesmaximal, characteristic
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C2×#91555C212yesmaximal, complemented
5C2×Dic5×#67C212yesmaximal, complemented
6C2×#91531C212yesmaximal, complemented
7C2×#91528C212yesmaximal, complemented
8#11754848C2116yesmaximal, direct product factor
9C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
10C2×#91384C211yesmaximal, characteristic, complemented
11C2×#91365C211yesmaximal, characteristic, complemented
12C2×#91333C211yesmaximal, characteristic, complemented
13C2×#65934—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C22×C5×#67C2212yes—
17C22×C4×C5×D3C2211yescharacteristic
18C23×C3×Dic5C2212yes—
19C22×D3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C2×#6719C2212yes—
22C2×#6719C2212yes—
23#91825C2218yescomplemented
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×#217C2212yes—
26C5×#938C2218yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C3×D4×Dic5C2218yescomplemented
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32#91555C22116yescomplemented
33Dic5×#67C22116yescomplemented
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2212yes—
37C2×#6668C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39#91531C22116yescomplemented
40#91528C22116yescomplemented
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2212yes—
44C4×D3×Dic5C2218yescomplemented
45#91384C2218yescomplemented
46#91365C2218yescomplemented
47#91333C2218yescomplemented
48C2×#5557—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4082—31no—
51C2×#4081—32no—
52C2×D4×Dic5—32no—
53C2×D4×Dic5D311yescharacteristic, complemented
54C2×#4070—31no—
55C22×C4×Dic5—31no—
56#65934—316no—
57C2×#4036—31no—
58C2×#4033—31no—
59C2×#4025—32no—
60C2×#4023—32no—
61C24×C3×C5C2312yes—
62C23×C5×D3C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2312yes—
69C2×Dic30—24no—
70C2×Dic30C2314yes—
71C2×C5×#67—28no—
72C2×C5×#67C2318yes—
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2311yescharacteristic
75C2×C4×C5×D3—24no—
76C2×C4×C5×D3C2314yes—
77C22×C3×Dic5—28no—
78C22×C3×Dic5C2318yes—
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2311yescharacteristic
82C2×D3×Dic5—24no—
83C2×D3×Dic5—24no—
84C2×D3×Dic5C2314yes—
85C2×D3×Dic5C2314yes—
86#6719C2318yes—
87#6719C2318yes—
88C4×Dic15C2314yes—
89C5×#217C2318yes—
90C5×C4⋊Dic3C2314yes—
91C3×C22⋊Dic5C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×C4×Dic5C2314yes—
94Dic3⋊Dic5C2318yes—
95#6669C2318yes—
96#6668C2318yes—
97#6668C2318yes—
98(C2×D3)⋊Dic5C2318yes—
99Dic3×Dic5C2314yes—
100Dic3×Dic5C2314yes—
101Dic3×Dic5C2318yes—
102C2×C3×C4×D4—51no—
103C2×#938D511yescharacteristic
104C2×#936—51no—
105C2×C4×#67—52no—
106C2×#926—52no—
107#5557—516no—
108C2×#897—51no—
109C2×#890—51no—
110C2×#883—52no—
111C2×#879—52no—
112C2×C42×D3—51no—
113C2×C4×Dic6—51no—
114C22×C5×D4—32no—
115C22×C5×D4C2×D311yescharacteristic
116C23×C4×C5—31no—
117C23×Dic5—31no—
118C23×Dic5—31no—
119C23×Dic5C2×D312yes—
120C22×Dic10—31no—
121C5×#121—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C22⋊C4—32no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5C2×D312yes—
128#4082—38no—
129#4081—316no—
130D4×Dic5—316no—
131D4×Dic5C2×D318yescomplemented
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5C2×D311yescharacteristic
134#4070—38no—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—32no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—38no—
143C2×C4×Dic5C2×D311yescharacteristic
144#4036—38no—
145#4033—38no—
146#4025—316no—
147#4023—316no—
148C2×#529—151noSylow
149C23×C3×C5—24no—
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5C2414yes—
153C23×C3×C5C2411yescharacteristic
154C22×C5×D3—22no—
155C22×C5×D3—22no—
156C22×C5×D3#4114yes—
157C22×C5×D3C2412yes—
158C3×C5×D4—28no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2412yes—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15C2414yes—
165C2×Dic15C2412yes—
166C2×Dic15C2412yes—
167Dic30—28no—
168C5×#67—216no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2414yes—
173C4×C5×D3—28no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5—216no—
177C2×C3×Dic5#4114yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2412yes—
181D3×Dic5—28no—
182D3×Dic5—28no—
183C22×C3×D4C2×D511yescharacteristic
184C23×C3×C4—52no—
185C22×#67C2×D512yes—
186C22×C4×D3—51no—
187C22×C4×D3—51no—
188C22×C4×D3C2×D511yescharacteristic
189C22×Dic6—51no—
190C3×C4×D4—58no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C42—51no—
194C2×#217—52no—
195C2×#217—52no—
196C2×#217C2×D512yes—
197#938C2×D518yes—
198#936—58no—
199C4×#67—516no—
200C2×(C2×D3)⋊C4—52no—
201#926—516no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3—52no—
204C2×C4⋊Dic3C2×D511yescharacteristic
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4—52no—
207C2×C4×Dic3—51no—
208C2×C4×Dic3—52no—
209C2×C4×Dic3—51no—
210C2×C4×Dic3—51no—
211#897—58no—
212#890—58no—
213#883—516no—
214#879—516no—
215C42×D3—58no—
216C4×Dic6—58no—
217C24×C5—31no—
218C24×C5C22×D312yes—
219C2×C5×D4—24no—
220C2×C5×D4—38no—
221C2×C5×D4—68no—
222C2×C5×D4C22×D314yes—
223C22×C4×C5—31no—
224C22×C4×C5—32no—
225C22×C4×C5—34no—
226C22×C4×C5—64no—
227C22×C4×C5C22×D311yescharacteristic
228C22×Dic5—28no—
229C22×Dic5—32no—
230C22×Dic5—31no—
231C22×Dic5—31no—
232C22×Dic5—34no—
233C22×Dic5—34no—
234C22×Dic5—64no—
235C22×Dic5—64no—
236C22×Dic5C22×D312yes—
237C22×Dic5C22×D311yescharacteristic
238C22×Dic5C22×D318yes—
239C22×Dic5C22×D311yescharacteristic
240C2×Dic10—34no—
241C2×Dic10—64no—
242C5×C4⋊C4—34no—
243C5×C22⋊C4—38no—
244C22⋊Dic5—38no—
245C22⋊Dic5—38no—
246C22⋊Dic5—38no—
247C22⋊Dic5C22×D318yes—
248C4⋊Dic5—38no—
249C4⋊Dic5C22×D314yes—
250#683—38no—
251#683—38no—
252#683—38no—
253C4×Dic5—34no—
254C4×Dic5—34no—
255C4×Dic5—38no—
256C4×Dic5—34no—
257C4×Dic5C22×D314yes—
258#529—1516no—
259C2×#126—152no—
260C2×#125—151no—
261C2×#124—151no—
262C2×#123—152no—
263C2×C22⋊Q8—151no—
264C2×#121—31no—
265C2×C4×Q8—151no—
266C2×C4×D4—51no—
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×C5×D3—28no—
279C2×C5×D3—22no—
280C2×C5×D3—22no—
281C2×C5×D3C2×#4114yes—
282C3×C4×C5C2×#4114yes—
283Dic15—22no—
284Dic15—22no—
285Dic15—24no—
286C3×Dic5—22no—
287C3×Dic5—24no—
288C3×Dic5C2×#4114yes—
289C5×Dic3—22no—
290C5×Dic3—24no—
291C24×C3C22×D512yes—
292C23×D3C22×D511yescharacteristic
293C2×C3×D4—24no—
294C2×C3×D4C22×D514yes—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—52no—
298C22×C3×C4—58no—
299C22×C3×C4—108no—
300C22×C3×C4C22×D511yescharacteristic
301C2×#67—28no—
302C2×#67C22×D518yes—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—52no—
306C22×Dic3C22×D511yescharacteristic
307C22×Dic3C22×D512yes—
308C2×C4×D3—24no—
309C2×C4×D3—54no—
310C2×C4×D3—54no—
311C2×C4×D3—104no—
312C2×C4×D3—104no—
313C2×C4×D3C22×D514yes—
314C2×Dic6—54no—
315C2×Dic6—104no—
316C3×C4⋊C4—54no—
317C3×C22⋊C4—58no—
318C3×C42—54no—
319#217—58no—
320#217—58no—
321#217C22×D518yes—
322(C2×D3)⋊C4—58no—
323C4⋊Dic3—58no—
324C4⋊Dic3—58no—
325C4⋊Dic3C22×D514yes—
326Dic3⋊C4—58no—
327Dic3⋊C4—58no—
328C4×Dic3—54no—
329C4×Dic3—58no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C23×C5—24no—
333C23×C5—24no—
334C23×C5—24no—
335C23×C5—34no—
336C23×C5—32no—
337C23×C5—62no—
338C23×C5—62no—
339C23×C5C23×D314yes—
340C23×C5C23×D311yescharacteristic
341C5×D4—28no—
342C5×D4—616no—
343C2×C4×C5—32no—
344C2×C4×C5—34no—
345C2×C4×C5—62no—
346C2×C4×C5—64no—
347C2×C4×C5—68no—
348C2×C4×C5#23514yes—
349C2×C4×C5C23×D312yes—
350C2×Dic5—24no—
351C2×Dic5—22no—
352C2×Dic5—216no—
353C2×Dic5—32no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—68no—
357C2×Dic5—64no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5—68no—
361C2×Dic5#23714yes—
362C2×Dic5C23×D312yes—
363C2×Dic5C23×D314yes—
364C2×Dic5C23×D312yes—
365Dic10—68no—
366C22×Q8—151no—
367C22×D4—32no—
368C22×D4D3×D511yescharacteristic
369C23×C4—31no—
370C23×C4—52no—
371C23×C4—151no—
372C23×C4—151no—
373#126—1516no—
374#125—158no—
375#124—158no—
376#123—1516no—
377C22⋊Q8—158no—
378#121—38no—
379C4×Q8—158no—
380C4×D4—58no—
381C4×D4—1516no—
382#117—1516no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—152no—
394C2×C42—51no—
395C2×C42—158no—
396C2×C42—151no—
397C2×C42—152no—
398C2×C42—151no—
399C2×C42—151no—
400C2×C3×C5—44no—
401C2×C3×C5#52914yescomplemented
402C2×C3×C5C22×#4111yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C22×#4111yescharacteristic
405C5×D3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3C23×D514yes—
410C23×C3C23×D511yescharacteristic
411C22×D3—22no—
412C22×D3—22no—
413C22×D3#71114yes—
414C22×D3C23×D512yes—
415C3×D4—28no—
416C2×C3×C4—54no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—54no—
420C2×C3×C4—1016no—
421C2×C3×C4—102no—
422C2×C3×C4—104no—
423C2×C3×C4#71114yes—
424C2×C3×C4C23×D512yes—
425#67—216no—
426C2×Dic3—22no—
427C2×Dic3—24no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—54no—
431C2×Dic3—104no—
432C2×Dic3—102no—
433C2×Dic3—102no—
434C2×Dic3C23×D512yes—
435C2×Dic3C23×D514yes—
436C4×D3—28no—
437C4×D3—108no—
438C4×D3—108no—
439Dic6—108no—
440C22×C5—24no—
441C22×C5—24no—
442C22×C5—24no—
443C22×C5—34no—
444C22×C5—48no—
445C22×C5—62no—
446C22×C5—62no—
447C22×C5—68no—
448C22×C5C2×#23512yes—
449C22×C5C2×#23712yes—
450C22×C5D3×#4112yes—
451C22×C5C24×D311yescharacteristic
452C4×C5—62no—
453C4×C5—64no—
454C4×C5C2×#23514yes—
455Dic5—24no—
456Dic5—22no—
457Dic5—64no—
458Dic5—62no—
459Dic5—62no—
460Dic5C2×#23714yes—
461C24—31no—
462C24C2×D3×D512yes—
463C2×Q8—154no—
464C2×Q8—304no—
465C2×D4—24no—
466C2×D4—38no—
467C2×D4—68no—
468C2×D4C2×D3×D514yes—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—34no—
472C22×C4—51no—
473C22×C4—58no—
474C22×C4—51no—
475C22×C4—52no—
476C22×C4—64no—
477C22×C4—108no—
478C22×C4—154no—
479C22×C4—154no—
480C22×C4—151no—
481C22×C4—151no—
482C22×C4—152no—
483C22×C4—304no—
484C22×C4—304no—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—54no—
488C4⋊C4—158no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—158no—
492C22⋊C4—38no—
493C22⋊C4—58no—
494C22⋊C4—158no—
495C22⋊C4—158no—
496C22⋊C4—158no—
497C42—54no—
498C42—154no—
499C42—154no—
500C42—158no—
501C42—154no—
502C3×C5C2×#52911yescharacteristic, complemented, Hall
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—48no—
507C22×C3C2×#71112yes—
508C22×C3C2×#71112yes—
509C22×C3D5×#4112yes—
510C22×C3C24×D511yescharacteristic
511C2×D3—28no—
512C2×D3—22no—
513C2×D3—22no—
514C2×D3C2×#71114yes—
515C3×C4—54no—
516C3×C4—102no—
517C3×C4—104no—
518C3×C4C2×#71114yes—
519Dic3—22no—
520Dic3—24no—
521Dic3—104no—
522Dic3—102no—
523Dic3—102no—
524C2×C5—44no—
525C2×C5—64no—
526C2×C5#555714yescomplemented
527C2×C5C22×#23511yescharacteristic
528C2×C5C22×#23711yescharacteristic
529C2×C5C2×D3×#4111yescharacteristic
530C23—24no—
531C23—24no—
532C23—24no—
533C23—34no—
534C23—32no—
535C23—62no—
536C23—62no—
537C23C22×D3×D514yes—
538C23C22×D3×D511yescharacteristic
539Q8—308no—
540D4—28no—
541D4—616no—
542C2×C4—32no—
543C2×C4—34no—
544C2×C4—54no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—54no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—68no—
551C2×C4—1016no—
552C2×C4—104no—
553C2×C4—102no—
554C2×C4—152no—
555C2×C4—152no—
556C2×C4—154no—
557C2×C4—308no—
558C2×C4—308no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4—304no—
562C2×C4#678214yes—
563C2×C4C22×D3×D512yes—
564C2×C3—44no—
565C2×C3#6593414yescomplemented
566C2×C3C22×#71111yescharacteristic
567C2×C3C22×#71111yescharacteristic
568C2×C3C2×D5×#4111yescharacteristic
569D3—24no—
570C5C2×#555711yescharacteristic, complemented, Sylow
571C22—24no—
572C22—24no—
573C22—24no—
574C22—34no—
575C22—48no—
576C22—62no—
577C22—68no—
578C22—62no—
579C22D5×#23712yes—
580C22D3×#71112yes—
581C22C2×#678212yes—
582C22C23×D3×D511yescharacteristic
583C4—54no—
584C4—62no—
585C4—64no—
586C4—104no—
587C4—102no—
588C4—304no—
589C4—302no—
590C4—302no—
591C4C2×#678214yes—
592C3C2×#6593411yescharacteristic, complemented, Sylow
593C2—44no—
594C2—64no—
595C2#1175484814yesdirect product factor
596C2C2×D5×#23711yescharacteristic
597C2C2×D3×#71111yescharacteristic
598C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
prime radicalC2×C5×#938C2
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
1. C2×#91825C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C2×#91555C2semidirect
5. C2×Dic5×#67C2semidirect
6. C2×#91531C2semidirect
7. C2×#91528C2semidirect
8. #11754848C2direct (N × H)
9. C2×C4×D3×Dic5C2semidirect
10. C2×#91384C2semidirect
11. C2×#91365C2semidirect
12. C2×#91333C2semidirect
23. #91825C22semidirect
29. C3×D4×Dic5C22semidirect
32. #91555C22semidirect
33. Dic5×#67C22semidirect
39. #91531C22semidirect
40. #91528C22semidirect
44. C4×D3×Dic5C22semidirect
45. #91384C22semidirect
46. #91365C22semidirect
47. #91333C22semidirect
53. C2×D4×Dic5D3semidirect
131. D4×Dic5C2×D3semidirect
401. C2×C3×C5#529semidirect
502. C3×C5C2×#529semidirect
526. C2×C5#5557semidirect
565. C2×C3#65934semidirect
570. C5C2×#5557semidirect
592. C3C2×#65934semidirect
595. C2#11754848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918252
C2×C5×#9382
C2×C3×D4×Dic52
C2×#915552
C2×Dic5×#672
C2×#915312
C2×#915282
#117548482
C2×C4×D3×Dic52
C2×#913842
C2×#913652
C2×#913332
C2×#659343
C2×#55575