Finite Group Databasebeta

← C2×#11754510 #14483870

Subgroups — C2×#11754510 #14483870

Order 1920.

2400 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
1C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
2C2×C5×#924C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
4C2×#91576C212yesmaximal, complemented
5C2×#91559C212yesmaximal
6C2×#91468C211yesmaximal, characteristic, complemented
7#11754510C2116yesmaximal, direct product factor
8C2×#91422C212yesmaximal, complemented
9C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#91359C211yesmaximal, characteristic, complemented
11C2×#91334C212yesmaximal, complemented
12C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
13C2×#65969—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C5×Dic6C2211yescharacteristic
17C22×C3×C22⋊D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1204C2212yes—
20C22×D5×Dic3C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4⋊Dic15C2212yes—
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C4⋊Dic15C2218yescomplemented
25C2×C5×#217C2212yes—
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C5×#924C2218yescomplemented
28C2×C5×Dic3⋊C4C2212yes—
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×C4×C22⋊D5C2218yes—
31C2×C3×#685C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34#91576C22116yescomplemented
35#91559C22116yes—
36C2×Dic3⋊Dic5C2212yes—
37C2×#6669C2212yes—
38C2×#6668C2212yes—
39C2×#6668C2212yes—
40C2×#6665C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91468C2218yescomplemented
43#91422C22116yescomplemented
44D5×C4⋊Dic3C2218yescomplemented
45#91359C2218yescomplemented
46#91334C22116yescomplemented
47Dic5×Dic6C2218yescomplemented
48C2×#5543—51nomaximal, Hall
49C2×C5×C22⋊Q8—31no—
50C2×#4092—31no—
51C2×Q8×Dic5—31no—
52C2×C4×C22⋊D5D311yescharacteristic
53C22×C4⋊Dic5—31no—
54#65969—316no—
55C2×#4043—32no—
56C2×D5×C4⋊C4—31no—
57C2×#4035—32no—
58C2×#4034—31no—
59C2×#4027—32no—
60C2×#4024—32no—
61C24×C3×C5C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15—44no—
68C22×Dic15C2312yes—
69C22×Dic15C2312yes—
70C22×Dic15C2318yes—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6—24no—
74C2×C5×Dic6C2314yes—
75C2×C3×C22⋊D5Q818yescomplemented
76C2×C3×C22⋊D5C2314yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5C2314yes—
82C2×#1204—44no—
83C2×#1204C2318yes—
84C2×D5×Dic3—44no—
85C2×D5×Dic3C2318yes—
86C4⋊Dic15C2314yes—
87C4⋊Dic15C2318yes—
88C4⋊Dic15C2314yes—
89C5×#217C2318yes—
90C5×C4⋊Dic3C2314yes—
91C5×Dic3⋊C4C2318yes—
92C3×C22⋊Dic5C2314yes—
93C3×#685C2314yes—
94C3×#683C2314yes—
95C3×C4×Dic5C2314yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6668C2318yes—
99#6668C2318yes—
100#6665C2318yes—
101Dic3×Dic5C2318yes—
102C2×C3×C4×D4—51no—
103C2×D4×Dic3—52no—
104C22×C4⋊Dic3—51no—
105C22×C4⋊Dic3—51no—
106C2×#924—51no—
107C2×#924D511yescharacteristic, complemented
108#5543—516no—
109C2×#890—52no—
110C2×#878—52no—
111C2×#878—52no—
112C2×#869—51no—
113C2×C4×Dic6—51no—
114C22×C5×Q8—31no—
115C23×C4×C5C2×D311yescharacteristic
116C22×C22⋊D5C2×D311yescharacteristic
117C23×Dic5—32no—
118C22×C4×D5—32no—
119C22×C4×D5C2×D311yescharacteristic
120C22×Dic10—32no—
121C5×C22⋊Q8—38no—
122C2×C5×C4⋊C4—31no—
123C2×C5×C4⋊C4—32no—
124C2×C5×C22⋊C4—32no—
125C2×C22⋊Dic5C2×D311yescharacteristic
126#4092—38no—
127Q8×Dic5—38no—
128C4×C22⋊D5C2×D318yes—
129C2×#685—32no—
130C2×#685C2×D311yescharacteristic
131C2×C4⋊Dic5—31no—
132C2×C4⋊Dic5—32no—
133C2×C4⋊Dic5—31no—
134C2×C4⋊Dic5—38no—
135C2×C4⋊Dic5—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683—32no—
139C2×#683C2×D311yescharacteristic
140C2×C4×Dic5—32no—
141C2×C4×Dic5C2×D311yescharacteristic
142#4043—316no—
143D5×C4⋊C4—38no—
144#4035—316no—
145#4034—38no—
146#4027—316no—
147#4024—316no—
148C2×#554—151noSylow
149C23×C3×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C2×Q814yes—
152C23×C3×C5C2412yes—
153C23×C3×C5C2411yescharacteristic
154C22×C3×D5—22no—
155C22×C3×D5—22no—
156C22×C3×D5C2×Q814yes—
157C22×C3×D5C2412yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5#4114yes—
161C2×C3×C4×C5C2412yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—24no—
164C2×Dic15—24no—
165C2×Dic15—48no—
166C2×Dic15C2414yes—
167C2×Dic15C2414yes—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—24no—
170C2×C5×Dic3C2414yes—
171C2×C5×Dic3C2414yes—
172C5×Dic6—28no—
173C3×C22⋊D5C2×Q8116yescomplemented
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2×Q814yes—
177C2×C3×Dic5C2412yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2412yes—
180C3×C4×D5—28no—
181#1204—48no—
182D5×Dic3—48no—
183C22×C3×D4—51no—
184C23×C3×C4—51no—
185C23×C3×C4C2×D511yescharacteristic
186C23×Dic3—52no—
187C23×Dic3—52no—
188C22×Dic6—52no—
189C22×Dic6C2×D511yescharacteristic
190C3×C4×D4—58no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C22⋊C4—51no—
193C2×C3×C22⋊C4—51no—
194C2×C3×C42—51no—
195C2×#217—52no—
196C2×#217C2×D512yes—
197D4×Dic3—516no—
198C2×C4⋊Dic3—51no—
199C2×C4⋊Dic3—51no—
200C2×C4⋊Dic3—52no—
201C2×C4⋊Dic3—58no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3—52no—
204C2×C4⋊Dic3—58no—
205C2×C4⋊Dic3C2×D511yescharacteristic
206#924—58no—
207#924C2×D518yescomplemented
208C2×Dic3⋊C4—52no—
209C2×Dic3⋊C4—52no—
210C2×Dic3⋊C4C2×D512yes—
211C2×C4×Dic3—52no—
212#890—516no—
213#878—516no—
214#878—516no—
215#869—58no—
216C4×Dic6—58no—
217C24×C5C22×D311yescharacteristic
218C23×D5C22×D311yescharacteristic
219C2×C5×Q8—34no—
220C2×C5×Q8—64no—
221C22×C4×C5—24no—
222C22×C4×C5—32no—
223C22×C4×C5—32no—
224C22×C4×C5C22×D311yescharacteristic
225C22×C4×C5C22×D314yes—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5Dic618yescomplemented
228C2×C22⋊D5C22×D314yes—
229C22×Dic5—32no—
230C22×Dic5—32no—
231C22×Dic5—38no—
232C22×Dic5—124no—
233C22×Dic5C22×D311yescharacteristic
234C22×Dic5C22×D311yescharacteristic
235C22×Dic5C22×D311yescharacteristic
236C2×C4×D5—24no—
237C2×C4×D5—38no—
238C2×C4×D5—124no—
239C2×C4×D5C22×D314yes—
240C2×Dic10—38no—
241C2×Dic10—124no—
242C5×C4⋊C4—38no—
243C5×C4⋊C4—34no—
244C5×C22⋊C4—38no—
245C22⋊Dic5C22×D314yes—
246#685—38no—
247#685C22×D314yes—
248C4⋊Dic5—34no—
249C4⋊Dic5—38no—
250C4⋊Dic5—34no—
251C4⋊Dic5—38no—
252#683—38no—
253#683—38no—
254#683—38no—
255#683C22×D314yes—
256C4×Dic5—38no—
257C4×Dic5C22×D314yes—
258#554—1516no—
259C2×C4⋊Q8—151no—
260C2×#125—152no—
261C2×C22⋊Q8—31no—
262C2×C22⋊Q8—152no—
263C2×C22⋊Q8—152no—
264C2×C22⋊Q8—151no—
265C2×C4×Q8—151no—
266C2×C4×D4—51no—
267C2×C4×D4—152no—
268C22×C4⋊C4—151no—
269C22×C4⋊C4—151no—
270C22×C3×C5—28no—
271C22×C3×C5—22no—
272C22×C3×C5—22no—
273C22×C3×C5C22×Q814yes—
274C22×C3×C5C22×Q812yes—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5H(5,𝔽2)12yes—
277C22×C3×C5C2511yescharacteristic
278C2×C3×D5—28no—
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5C22×Q814yes—
282C3×C4×C5—22no—
283C3×C4×C5C2×#4114yes—
284Dic15—24no—
285Dic15—24no—
286C3×Dic5—22no—
287C3×Dic5—22no—
288C3×Dic5C22×Q814yes—
289C5×Dic3—24no—
290C5×Dic3—24no—
291C24×C3—51no—
292C24×C3C22×D511yescharacteristic
293C2×C3×D4—58no—
294C2×C3×D4—54no—
295C22×C3×C4—24no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4—54no—
300C22×C3×C4—104no—
301C22×C3×C4C22×D511yescharacteristic
302C22×C3×C4C22×D514yes—
303C22×C3×C4C22×D511yescharacteristic
304C22×Dic3—52no—
305C22×Dic3—52no—
306C22×Dic3—58no—
307C22×Dic3—58no—
308C22×Dic3—204no—
309C22×Dic3—204no—
310C22×Dic3C22×D512yes—
311C22×Dic3C22×D512yes—
312C2×Dic6—24no—
313C2×Dic6—58no—
314C2×Dic6—204no—
315C2×Dic6C22×D514yes—
316C3×C4⋊C4—54no—
317C3×C22⋊C4—54no—
318C3×C22⋊C4—54no—
319C3×C42—54no—
320#217—58no—
321#217C22×D518yes—
322C4⋊Dic3—54no—
323C4⋊Dic3—54no—
324C4⋊Dic3—58no—
325C4⋊Dic3—58no—
326C4⋊Dic3—58no—
327C4⋊Dic3C22×D514yes—
328Dic3⋊C4—58no—
329Dic3⋊C4—58no—
330Dic3⋊C4C22×D518yes—
331C4×Dic3—58no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5C2×Dic614yes—
335C23×C5C23×D312yes—
336C23×C5C23×D311yescharacteristic
337C22×D5—22no—
338C22×D5—22no—
339C22×D5C2×Dic614yes—
340C22×D5C23×D312yes—
341C5×Q8—68no—
342C2×C4×C5—22no—
343C2×C4×C5—28no—
344C2×C4×C5—34no—
345C2×C4×C5—34no—
346C2×C4×C5—64no—
347C2×C4×C5—64no—
348C2×C4×C5#23714yes—
349C2×C4×C5C23×D312yes—
350C2×C4×C5C23×D312yes—
351C22⋊D5C2×Dic6116yescomplemented
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—34no—
355C2×Dic5—34no—
356C2×Dic5—64no—
357C2×Dic5—64no—
358C2×Dic5—128no—
359C2×Dic5C2×Dic614yes—
360C2×Dic5C23×D312yes—
361C2×Dic5C23×D312yes—
362C2×Dic5C23×D312yes—
363C4×D5—28no—
364C4×D5—128no—
365Dic10—128no—
366C22×Q8—31no—
367C22×Q8—152no—
368C22×D4—51no—
369C23×C4—51no—
370C23×C4—152no—
371C23×C4—152no—
372C23×C4D3×D511yescharacteristic
373C4⋊Q8—158no—
374#125—1516no—
375C22⋊Q8—38no—
376C22⋊Q8—1516no—
377C22⋊Q8—1516no—
378C22⋊Q8—158no—
379C4×Q8—158no—
380C4×D4—58no—
381C4×D4—1516no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—158no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—152no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—151no—
391C2×C4⋊C4—152no—
392C2×C4⋊C4—151no—
393C2×C4⋊C4—158no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—51no—
396C2×C22⋊C4—51no—
397C2×C22⋊C4—152no—
398C2×C42—51no—
399C2×C42—152no—
400C2×C3×C5—24no—
401C2×C3×C5#55414yescomplemented
402C2×C3×C5C23×Q811yescharacteristic
403C2×C3×C5C22×#4111yescharacteristic
404C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
405C3×D5—24no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—54no—
409C23×C3—52no—
410C23×C3—102no—
411C23×C3—102no—
412C23×C3Q8×D514yes—
413C23×C3C23×D512yes—
414C23×C3C23×D511yescharacteristic
415C3×D4—516no—
416C2×C3×C4—22no—
417C2×C3×C4—28no—
418C2×C3×C4—54no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—52no—
422C2×C3×C4—102no—
423C2×C3×C4—102no—
424C2×C3×C4—108no—
425C2×C3×C4#71114yes—
426C2×C3×C4C23×D512yes—
427C2×C3×C4C23×D512yes—
428C2×Dic3—24no—
429C2×Dic3—24no—
430C2×Dic3—54no—
431C2×Dic3—54no—
432C2×Dic3—104no—
433C2×Dic3—104no—
434C2×Dic3—208no—
435C2×Dic3—208no—
436C2×Dic3C23×D514yes—
437C2×Dic3C23×D514yes—
438Dic6—28no—
439Dic6—208no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—28no—
443C22×C5C22×Dic614yes—
444C22×C5C22×Dic612yes—
445C22×C5C2×#23712yes—
446C22×C5#100912yes—
447C22×C5C24×D311yescharacteristic
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—28no—
451C2×D5C22×Dic614yes—
452C4×C5—22no—
453C4×C5—64no—
454C4×C5—64no—
455C4×C5C2×#23714yes—
456Dic5—22no—
457Dic5—22no—
458Dic5—64no—
459Dic5—64no—
460Dic5C22×Dic614yes—
461C24—51no—
462C24C2×D3×D511yescharacteristic
463C2×Q8—34no—
464C2×Q8—64no—
465C2×Q8—158no—
466C2×Q8—604no—
467C2×D4—58no—
468C2×D4—54no—
469C22×C4—24no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—51no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—54no—
476C22×C4—104no—
477C22×C4—158no—
478C22×C4—152no—
479C22×C4—152no—
480C22×C4—158no—
481C22×C4—604no—
482C22×C4—604no—
483C22×C4C2×D3×D514yes—
484C22×C4C2×D3×D511yescharacteristic
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—34no—
487C4⋊C4—38no—
488C4⋊C4—54no—
489C4⋊C4—158no—
490C4⋊C4—158no—
491C4⋊C4—158no—
492C4⋊C4—158no—
493C4⋊C4—154no—
494C4⋊C4—158no—
495C4⋊C4—154no—
496C22⋊C4—38no—
497C22⋊C4—54no—
498C22⋊C4—54no—
499C22⋊C4—158no—
500C42—54no—
501C42—158no—
502C3×C5C2×#55411yescharacteristic, complemented, Hall
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—54no—
507C22×C3—108no—
508C22×C3—102no—
509C22×C3—102no—
510C22×C3C2×#71112yes—
511C22×C3C2×Q8×D514yes—
512C22×C3C2×Q8×D512yes—
513C22×C3#414912yes—
514C22×C3C24×D511yescharacteristic
515C3×C4—22no—
516C3×C4—54no—
517C3×C4—102no—
518C3×C4—102no—
519C3×C4C2×#71114yes—
520Dic3—24no—
521Dic3—24no—
522Dic3—104no—
523Dic3—104no—
524C2×C5—24no—
525C2×C5#554314yescomplemented
526C2×C5C23×Dic611yescharacteristic
527C2×C5C22×#23711yescharacteristic
528C2×C5C2×#100911yescharacteristic
529D5—24no—
530C23—22no—
531C23—22no—
532C23—54no—
533C23—52no—
534C23—102no—
535C23—102no—
536C23D5×Dic614yes—
537C23C22×D3×D512yes—
538C23C22×D3×D511yescharacteristic
539Q8—68no—
540Q8—608no—
541D4—516no—
542C2×C4—22no—
543C2×C4—28no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—54no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—52no—
550C2×C4—64no—
551C2×C4—64no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—108no—
555C2×C4—154no—
556C2×C4—154no—
557C2×C4—304no—
558C2×C4—304no—
559C2×C4—608no—
560C2×C4—608no—
561C2×C4#678014yes—
562C2×C4C22×D3×D512yes—
563C2×C4C22×D3×D512yes—
564C2×C3—24no—
565C2×C3—104no—
566C2×C3#6596914yescomplemented
567C2×C3C22×#71111yescharacteristic
568C2×C3C22×Q8×D511yescharacteristic
569C2×C3C2×#414911yescharacteristic
570C5C2×#554311yescharacteristic, complemented, Sylow
571C22—22no—
572C22—28no—
573C22—22no—
574C22—54no—
575C22—102no—
576C22—108no—
577C22—102no—
578C22C2×D5×Dic614yes—
579C22C2×D5×Dic612yes—
580C22#9201912yes—
581C22C2×#678012yes—
582C22C23×D3×D511yescharacteristic
583C4—22no—
584C4—54no—
585C4—64no—
586C4—64no—
587C4—102no—
588C4—102no—
589C4—304no—
590C4—304no—
591C4C2×#678014yes—
592C3C2×#6596911yescharacteristic, complemented, Sylow
593C2—24no—
594C2—104no—
595C2#1175451014yesdirect product factor
596C2C22×D5×Dic611yescharacteristic
597C2C2×#9201911yescharacteristic
598C2C22×#678011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#554
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. C22×C4⋊Dic15C2semidirect
2. C2×C5×#924C2semidirect
4. C2×#91576C2semidirect
6. C2×#91468C2semidirect
7. #11754510C2direct (N × H)
8. C2×#91422C2semidirect
9. C2×D5×C4⋊Dic3C2semidirect
10. C2×#91359C2semidirect
11. C2×#91334C2semidirect
12. C2×Dic5×Dic6C2semidirect
24. C2×C4⋊Dic15C22semidirect
27. C5×#924C22semidirect
34. #91576C22semidirect
42. #91468C22semidirect
43. #91422C22semidirect
44. D5×C4⋊Dic3C22semidirect
45. #91359C22semidirect
46. #91334C22semidirect
47. Dic5×Dic6C22semidirect
75. C2×C3×C22⋊D5Q8semidirect
107. C2×#924D5semidirect
173. C3×C22⋊D5C2×Q8semidirect
207. #924C2×D5semidirect
227. C2×C22⋊D5Dic6semidirect
351. C22⋊D5C2×Dic6semidirect
401. C2×C3×C5#554semidirect
502. C3×C5C2×#554semidirect
525. C2×C5#5543semidirect
566. C2×C3#65969semidirect
570. C5C2×#5543semidirect
592. C3C2×#65969semidirect
595. C2#11754510direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic152
C2×C5×#9242
C2×C3×C4×C22⋊D52
C2×#915762
C2×#915592
C2×#914682
#117545102
C2×#914222
C2×D5×C4⋊Dic32
C2×#913592
C2×#913342
C2×Dic5×Dic62
C2×#659693
C2×#55435