Finite Group Databasebeta

← C2×#11754744 #14483731

Subgroups — C2×#11754744 #14483731

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic, complemented
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic, complemented
4C2×#91556C212yesmaximal, complemented
5C2×#91536C212yesmaximal, complemented
6C2×#91533C212yesmaximal, complemented
7C2×#91530C212yesmaximal, complemented
8#11754744C2116yesmaximal, direct product factor
9C2×C4×#1202C211yesmaximal, characteristic, complemented
10C2×#91437C211yesmaximal, characteristic, complemented
11C2×#91381C211yesmaximal, characteristic, complemented
12C2×#91358C211yesmaximal, characteristic, complemented
13C2×#65892—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C22×C4×D15C2211yescharacteristic
17C23×C5×Dic3C2212yes—
18C22×C3×C22⋊D5C2212yes—
19C22×C3×C4×D5C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1200C2212yes—
22C2×#6719C2212yes—
23#91827C2218yescomplemented
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×#217C2212yes—
26C5×D4×Dic3C2218yescomplemented
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×C22⋊Dic5C2212yes—
30C3×#4084C2218yescomplemented
31C2×C3×C4⋊Dic5C2211yescharacteristic
32#91556C22116yescomplemented
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2212yes—
37C2×#6667C2211yescharacteristic
38#91536C22116yescomplemented
39C2×#6665C2211yescharacteristic
40C2×#6665C2212yes—
41#91533C22116yescomplemented
42#91530C22116yescomplemented
43C2×Dic3×Dic5C2212yes—
44C4×#1202C2218yescomplemented
45#91437C2218yescomplemented
46#91381C2218yescomplemented
47#91358C2218yescomplemented
48C2×#5614—51nomaximal, Hall
49C2×C4×C5×D4—31no—
50C2×#4084—31no—
51C2×#4084D311yescharacteristic, complemented
52C2×#4075—32no—
53C2×C4×C22⋊D5—32no—
54#65892—316no—
55C2×#4038—31no—
56C2×D5×C4⋊C4—31no—
57C2×#4030—32no—
58C2×#4025—32no—
59C2×C4×D20—31no—
60C2×#4016—31no—
61C24×C3×C5C2312yes—
62C23×D15C2311yescharacteristic
63C23×C3×D5C2311yescharacteristic
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2314yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—28no—
68C2×#1220C2318yes—
69C22×Dic15C2312yes—
70C22×Dic15C2311yescharacteristic
71C2×C4×D15—24no—
72C2×C4×D15C2314yes—
73C22×C5×Dic3—44no—
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2312yes—
77C22×C5×Dic3C2318yes—
78C2×C3×C22⋊D5—44no—
79C2×C3×C22⋊D5C2318yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2312yes—
82C2×C3×C4×D5—24no—
83C2×C3×C4×D5C2314yes—
84C2×#1202—24no—
85C2×#1202C2314yes—
86C2×#1200—44no—
87C2×#1200C2318yes—
88#6719C2318yes—
89C4⋊Dic15C2314yes—
90C5×#217C2318yes—
91C5×C4⋊Dic3C2314yes—
92C4×C5×Dic3C2314yes—
93C3×C22⋊Dic5C2318yes—
94C3×C4⋊Dic5C2314yes—
95Dic3⋊Dic5C2314yes—
96#6669C2318yes—
97#6669C2318yes—
98#6668C2318yes—
99#6667C2314yes—
100#6665C2314yes—
101#6665C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#121—51no—
104C2×#938—51no—
105C2×#938—52no—
106C2×#935—52no—
107C2×D4×Dic3D511yescharacteristic, complemented
108C2×C4×#67—51no—
109C2×#926—51no—
110#5614—516no—
111C2×D3×C4⋊C4—51no—
112C2×#890—51no—
113C2×#67⋊C4—52no—
114C2×#879—52no—
115C22×C5×D4C2×D311yescharacteristic
116C23×C4×C5—32no—
117C22×C22⋊D5—32no—
118C22×C22⋊D5C2×D312yes—
119C22×D20—31no—
120C22×C4×D5—31no—
121C22×C4×D5—32no—
122C22×C4×D5C2×D311yescharacteristic
123C4×C5×D4—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—32no—
126C2×C42×C5—31no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5C2×D312yes—
129#4084—38no—
130#4084C2×D318yescomplemented
131#4075—316no—
132C4×C22⋊D5—316no—
133C2×#685—31no—
134C2×#685—32no—
135C2×#685—31no—
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5C2×D311yescharacteristic
139C2×#683—32no—
140C2×#683—32no—
141C2×#683—32no—
142C2×C4×Dic5—32no—
143#4038—38no—
144D5×C4⋊C4—38no—
145#4030—316no—
146#4025—316no—
147C4×D20—38no—
148#4016—38no—
149C2×#553—151noSylow
150C23×C3×C5—24no—
151C23×C3×C5—24no—
152C23×C3×C5—24no—
153C23×C3×C5C2414yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—22no—
156C22×D15—22no—
157C22×D15#4114yes—
158C22×D15C2412yes—
159C22×C3×D5—22no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5C2412yes—
163C3×C5×D4—28no—
164C2×C3×C4×C5#4114yes—
165C2×C3×C4×C5C2412yes—
166#1220—216no—
167C2×Dic15—22no—
168C2×Dic15—24no—
169C2×Dic15C2414yes—
170C2×Dic15C2412yes—
171C4×D15—28no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—24no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3—48no—
176C2×C5×Dic3C2414yes—
177C2×C5×Dic3C2412yes—
178C2×C5×Dic3C2412yes—
179C3×C22⋊D5—48no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—24no—
182C2×C3×Dic5C2412yes—
183C2×C3×Dic5C2414yes—
184C3×C4×D5—28no—
185#1202—28no—
186#1200—48no—
187C22×C3×D4—52no—
188C22×C3×D4C2×D511yescharacteristic
189C23×C3×C4—51no—
190C22×#67—52no—
191C22×#67—51no—
192C23×Dic3C2×D512yes—
193C22×C4×D3—51no—
194C22×C4×D3—52no—
195C3×#121—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C22⋊C4—52no—
198C2×#217—52no—
199C2×#217—52no—
200C2×#217—51no—
201C2×#217C2×D512yes—
202#938—58no—
203#938—516no—
204#935—516no—
205D4×Dic3C2×D518yescomplemented
206C4×#67—58no—
207C2×(C2×D3)⋊C4—51no—
208#926—58no—
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3—52no—
211C2×C4⋊Dic3C2×D511yescharacteristic
212C2×Dic3⋊C4—51no—
213C2×Dic3⋊C4—52no—
214C2×Dic3⋊C4—52no—
215C2×C4×Dic3—52no—
216C2×C4×Dic3C2×D511yescharacteristic
217D3×C4⋊C4—58no—
218#890—58no—
219#67⋊C4—516no—
220#879—516no—
221C24×C5C22×D312yes—
222C23×D5—31no—
223C23×D5C22×D311yescharacteristic
224C2×C5×D4—24no—
225C2×C5×D4C22×D314yes—
226C22×C4×C5—31no—
227C22×C4×C5—31no—
228C22×C4×C5—32no—
229C22×C4×C5—38no—
230C22×C4×C5—124no—
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—38no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—68no—
235C2×C22⋊D5C22×D318yes—
236C22×Dic5—31no—
237C22×Dic5—32no—
238C22×Dic5C22×D311yescharacteristic
239C22×Dic5C22×D312yes—
240C2×D20—34no—
241C2×D20—64no—
242C2×C4×D5—24no—
243C2×C4×D5—34no—
244C2×C4×D5—38no—
245C2×C4×D5—64no—
246C2×C4×D5—124no—
247C2×C4×D5C22×D314yes—
248C5×C4⋊C4—34no—
249C5×C22⋊C4—38no—
250C42×C5—34no—
251C22⋊Dic5—38no—
252C22⋊Dic5C22×D318yes—
253#685—34no—
254#685—38no—
255#685—34no—
256C4⋊Dic5—34no—
257C4⋊Dic5—34no—
258C4⋊Dic5C22×D314yes—
259#683—38no—
260#683—38no—
261#683—38no—
262C4×Dic5—38no—
263#553—1516no—
264C2×#126—152no—
265C2×#125—151no—
266C2×#123—152no—
267C2×#121—51no—
268C2×#121—152no—
269C2×#121—151no—
270C2×C4×D4—31no—
271C2×C4×D4—151no—
272C2×C4×D4—152no—
273C2×#117—151no—
274C22×C4⋊C4—151no—
275C22×C3×C5—24no—
276C22×C3×C5—24no—
277C22×C3×C5—24no—
278C22×C3×C5—48no—
279C22×C3×C5C2×#4112yes—
280C22×C3×C5C2×#4112yes—
281C22×C3×C5H(5,𝔽2)12yes—
282C22×C3×C5C2511yescharacteristic
283C2×D15—28no—
284C2×D15—22no—
285C2×D15—22no—
286C2×D15C2×#4114yes—
287C2×C3×D5—22no—
288C2×C3×D5—22no—
289C2×C3×D5—22no—
290C2×C3×D5—44no—
291C3×C4×C5C2×#4114yes—
292Dic15—22no—
293Dic15—24no—
294C3×Dic5—22no—
295C3×Dic5—24no—
296C5×Dic3—22no—
297C5×Dic3—24no—
298C5×Dic3—22no—
299C24×C3—51no—
300C24×C3C22×D512yes—
301C23×D3—51no—
302C2×C3×D4—24no—
303C2×C3×D4—58no—
304C2×C3×D4—204no—
305C2×C3×D4C22×D514yes—
306C22×C3×C4—51no—
307C22×C3×C4—52no—
308C22×C3×C4—54no—
309C22×C3×C4—104no—
310C22×C3×C4C22×D511yescharacteristic
311C2×#67—58no—
312C2×#67—54no—
313C2×#67—104no—
314C2×#67—108no—
315C22×Dic3—44no—
316C22×Dic3—52no—
317C22×Dic3—51no—
318C22×Dic3C22×D512yes—
319C22×Dic3C22×D511yescharacteristic
320C22×Dic3C22×D511yescharacteristic
321C22×Dic3C22×D518yes—
322C2×C4×D3—54no—
323C2×C4×D3—58no—
324C2×C4×D3—104no—
325C2×C4×D3—204no—
326C3×C4⋊C4—54no—
327C3×C22⋊C4—58no—
328#217—58no—
329#217—58no—
330#217—54no—
331#217C22×D518yes—
332(C2×D3)⋊C4—54no—
333C4⋊Dic3—54no—
334C4⋊Dic3—58no—
335C4⋊Dic3C22×D514yes—
336Dic3⋊C4—58no—
337Dic3⋊C4—58no—
338Dic3⋊C4—54no—
339C4×Dic3—58no—
340C4×Dic3C22×D514yes—
341C23×C5—24no—
342C23×C5—24no—
343C23×C5—24no—
344C23×C5C23×D314yes—
345C23×C5C23×D311yescharacteristic
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—34no—
350C22×D5—32no—
351C22×D5—62no—
352C22×D5—62no—
353C22×D5C23×D312yes—
354C5×D4—28no—
355C2×C4×C5—34no—
356C2×C4×C5—32no—
357C2×C4×C5—32no—
358C2×C4×C5—64no—
359C2×C4×C5—62no—
360C2×C4×C5—62no—
361C2×C4×C5—128no—
362C2×C4×C5#23714yes—
363C2×C4×C5C23×D312yes—
364C22⋊D5—48no—
365C22⋊D5—616no—
366C2×Dic5—22no—
367C2×Dic5—24no—
368C2×Dic5—34no—
369C2×Dic5—32no—
370C2×Dic5—62no—
371C2×Dic5—64no—
372C2×Dic5C23×D312yes—
373C2×Dic5C23×D314yes—
374D20—68no—
375C4×D5—28no—
376C4×D5—68no—
377C4×D5—128no—
378C22×D4—52no—
379C22×D4—151no—
380C22×D4—152no—
381C22×D4D3×D511yescharacteristic
382C23×C4—32no—
383C23×C4—51no—
384C23×C4—152no—
385C23×C4—151no—
386#126—1516no—
387#125—158no—
388#123—1516no—
389#121—58no—
390#121—1516no—
391#121—158no—
392C4×D4—38no—
393C4×D4—158no—
394C4×D4—1516no—
395#117—158no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—51no—
398C2×C4⋊C4—158no—
399C2×C4⋊C4—152no—
400C2×C4⋊C4—152no—
401C2×C4⋊C4—151no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—151no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—52no—
406C2×C22⋊C4—151no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—151no—
409C2×C22⋊C4—152no—
410C2×C42—31no—
411C2×C42—152no—
412C2×C3×C5—44no—
413C2×C3×C5#55314yescomplemented
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C22×#4111yescharacteristic
416C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
417D15—24no—
418C3×D5—42no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—52no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—102no—
426C23×C3C23×D514yes—
427C23×C3C23×D511yescharacteristic
428C22×D3—54no—
429C22×D3—52no—
430C22×D3—102no—
431C22×D3—102no—
432C3×D4—28no—
433C3×D4—208no—
434C2×C3×C4—52no—
435C2×C3×C4—54no—
436C2×C3×C4—102no—
437C2×C3×C4—104no—
438C2×C3×C4—108no—
439C2×C3×C4#70914yes—
440C2×C3×C4C23×D512yes—
441#67—108no—
442#67—1016no—
443C2×Dic3—24no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—48no—
447C2×Dic3—54no—
448C2×Dic3—52no—
449C2×Dic3—102no—
450C2×Dic3—104no—
451C2×Dic3C23×D514yes—
452C2×Dic3C23×D512yes—
453C2×Dic3C23×D512yes—
454C4×D3—108no—
455C4×D3—208no—
456C22×C5—24no—
457C22×C5—24no—
458C22×C5—24no—
459C22×C5—48no—
460C22×C5C2×#23712yes—
461C22×C5#100412yes—
462C22×C5D3×#4112yes—
463C22×C5C24×D311yescharacteristic
464C2×D5—22no—
465C2×D5—22no—
466C2×D5—22no—
467C2×D5—34no—
468C2×D5—44no—
469C2×D5—62no—
470C2×D5—62no—
471C2×D5—68no—
472C4×C5—64no—
473C4×C5—62no—
474C4×C5—62no—
475C4×C5C2×#23714yes—
476Dic5—22no—
477Dic5—24no—
478Dic5—62no—
479Dic5—64no—
480C24—51no—
481C24—151no—
482C24C2×D3×D512yes—
483C2×D4—24no—
484C2×D4—58no—
485C2×D4—154no—
486C2×D4—158no—
487C2×D4—204no—
488C2×D4—304no—
489C2×D4—308no—
490C2×D4C2×D3×D514yes—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—32no—
494C22×C4—38no—
495C22×C4—51no—
496C22×C4—52no—
497C22×C4—54no—
498C22×C4—104no—
499C22×C4—124no—
500C22×C4—158no—
501C22×C4—152no—
502C22×C4—151no—
503C22×C4—154no—
504C22×C4—304no—
505C22×C4—604no—
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—54no—
509C4⋊C4—158no—
510C4⋊C4—158no—
511C4⋊C4—154no—
512C4⋊C4—158no—
513C4⋊C4—154no—
514C22⋊C4—38no—
515C22⋊C4—58no—
516C22⋊C4—154no—
517C22⋊C4—158no—
518C22⋊C4—154no—
519C22⋊C4—158no—
520C42—34no—
521C42—158no—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—48no—
527C22×C3—102no—
528C22×C3—102no—
529C22×C3—102no—
530C22×C3—204no—
531C22×C3C2×#70912yes—
532C22×C3#414412yes—
533C22×C3D5×#4112yes—
534C22×C3C24×D511yescharacteristic
535C2×D3—54no—
536C2×D3—108no—
537C2×D3—102no—
538C2×D3—102no—
539C3×C4—102no—
540C3×C4—104no—
541C3×C4C2×#70914yes—
542Dic3—24no—
543Dic3—22no—
544Dic3—22no—
545Dic3—102no—
546Dic3—104no—
547C2×C5—44no—
548C2×C5#561414yescomplemented
549C2×C5C22×#23711yescharacteristic
550C2×C5C2×#100411yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552D5—42no—
553D5—64no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—52no—
558C23—102no—
559C23—102no—
560C23—102no—
561C23—154no—
562C23—152no—
563C23—302no—
564C23—302no—
565C23C22×D3×D514yes—
566C23C22×D3×D511yescharacteristic
567D4—28no—
568D4—208no—
569D4—308no—
570D4—3016no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—52no—
575C2×C4—54no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—64no—
579C2×C4—104no—
580C2×C4—102no—
581C2×C4—108no—
582C2×C4—128no—
583C2×C4—154no—
584C2×C4—152no—
585C2×C4—304no—
586C2×C4—302no—
587C2×C4—308no—
588C2×C4—608no—
589C2×C4#677914yes—
590C2×C4C22×D3×D512yes—
591C2×C3—44no—
592C2×C3—202no—
593C2×C3#6589214yescomplemented
594C2×C3C22×#70911yescharacteristic
595C2×C3C2×#414411yescharacteristic
596C2×C3C2×D5×#4111yescharacteristic
597D3—104no—
598C5C2×#561411yescharacteristic, complemented, Sylow
599C22—24no—
600C22—24no—
601C22—24no—
602C22—48no—
603C22—102no—
604C22—102no—
605C22—102no—
606C22—154no—
607C22—204no—
608C22—302no—
609C22—302no—
610C22—308no—
611C22#9202412yes—
612C22#9202512yes—
613C22C2×#677912yes—
614C22C23×D3×D511yescharacteristic
615C4—62no—
616C4—62no—
617C4—64no—
618C4—102no—
619C4—104no—
620C4—302no—
621C4—304no—
622C4C2×#677914yes—
623C3C2×#6589211yescharacteristic, complemented, Sylow
624C2—44no—
625C2—202no—
626C2—304no—
627C2#1175474414yesdirect product factor
628C2C2×#9202411yescharacteristic
629C2C2×#9202511yescharacteristic
630C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#553
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×#91827C2semidirect
2. C2×C5×D4×Dic3C2semidirect
3. C2×C3×#4084C2semidirect
4. C2×#91556C2semidirect
5. C2×#91536C2semidirect
6. C2×#91533C2semidirect
7. C2×#91530C2semidirect
8. #11754744C2direct (N × H)
9. C2×C4×#1202C2semidirect
10. C2×#91437C2semidirect
11. C2×#91381C2semidirect
12. C2×#91358C2semidirect
23. #91827C22semidirect
26. C5×D4×Dic3C22semidirect
30. C3×#4084C22semidirect
32. #91556C22semidirect
38. #91536C22semidirect
41. #91533C22semidirect
42. #91530C22semidirect
44. C4×#1202C22semidirect
45. #91437C22semidirect
46. #91381C22semidirect
47. #91358C22semidirect
51. C2×#4084D3semidirect
107. C2×D4×Dic3D5semidirect
130. #4084C2×D3semidirect
205. D4×Dic3C2×D5semidirect
413. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
548. C2×C5#5614semidirect
593. C2×C3#65892semidirect
598. C5C2×#5614semidirect
623. C3C2×#65892semidirect
627. C2#11754744direct (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×#40842
C2×#915562
C2×#915362
C2×#915332
C2×#915302
#117547442
C2×C4×#12022
C2×#914372
C2×#913812
C2×#913582
C2×#658923
C2×#56145