Finite Group Databasebeta

← C2×#11753808 #14483701

Subgroups — C2×#11753808 #14483701

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×C4⋊C4×D15C211yesmaximal, characteristic, complemented
2C2×C5×#892C211yesmaximal, characteristic, complemented
3C2×C3×#4039C211yesmaximal, characteristic, complemented
4C2×#91465C211yesmaximal, characteristic, complemented
5C2×#91461C212yesmaximal, complemented
6C2×#91456C211yesmaximal, characteristic, complemented
7C2×#91447C212yesmaximal, complemented
8C2×C4×#1203C211yesmaximal, characteristic, complemented
9C2×C4×#1202C212yesmaximal, complemented
10C2×#91388C211yesmaximal, characteristic, complemented
11C2×#91363C212yesmaximal, complemented
12#11753808C2116yesmaximal, direct product factor
13C2×#65864—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C22×#1203C2211yescharacteristic
20C22×#1202C2212yes—
21C22×#1201C2212yes—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2212yes—
25C4⋊C4×D15C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C4×C5×Dic3C2212yes—
29C5×#892C2218yescomplemented
30C2×C3×#685C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4039C2218yescomplemented
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6668C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91465C2218yescomplemented
41#91461C22116yescomplemented
42#91456C2218yescomplemented
43#91447C22116yescomplemented
44C4×#1203C2218yescomplemented
45C4×#1202C22116yescomplemented
46#91388C2218yescomplemented
47#91363C22116yescomplemented
48C2×#5558—51nomaximal, Hall
49C2×C5×#117—31no—
50C2×#4076—31no—
51C2×C4×C22⋊D5—31no—
52#65864—316no—
53C2×#4041—31no—
54C2×#4039D311yescharacteristic, complemented
55C2×D5×C4⋊C4—31no—
56C2×#4036—31no—
57C2×#4030—32no—
58C2×#4029—32no—
59C2×#4022—32no—
60C2×C4×D20—32no—
61C23×D15C2311yescharacteristic
62C23×C5×D3C2311yescharacteristic
63C23×C3×D5C2312yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C2×C4×D15—24no—
69C2×C4×D15—44no—
70C2×C4×D15C2314yes—
71C2×C4×D15C2318yes—
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2312yes—
74C2×C4×C5×D3—24no—
75C2×C4×C5×D3C2314yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C2×C3×D20—24no—
79C2×C3×D20C2314yes—
80C2×C3×C4×D5—44no—
81C2×C3×C4×D5C2318yes—
82C2×#1203—24no—
83C2×#1203C2314yes—
84C2×#1202—28no—
85C2×#1202C2318yes—
86C2×#1201—44no—
87C2×#1201C2318yes—
88C3×C5×C4⋊C4C2314yes—
89C4⋊Dic15C2314yes—
90#6712C2318yes—
91C5×(C2×D3)⋊C4C2318yes—
92C5×C4⋊Dic3C2314yes—
93C4×C5×Dic3C2318yes—
94C3×#685C2318yes—
95C3×C4×Dic5C2314yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6668C2314yes—
99#6667C2314yes—
100(C2×D3)⋊Dic5C2314yes—
101#6665C2318yes—
102#6665C2318yes—
103C2×C3×C4×D4—51no—
104C2×#938—51no—
105C2×#938—51no—
106C2×#929—52no—
107C2×C4×#67—52no—
108#5558—516no—
109C2×#892D511yescharacteristic, complemented
110C2×D3×C4⋊C4—51no—
111C2×#884—52no—
112C2×#879—52no—
113C2×C4×D12—51no—
114C2×#870—51no—
115C23×C4×C5—31no—
116C22×C22⋊D5—32no—
117C22×C22⋊D5—31no—
118C22×D20—32no—
119C22×D20C2×D311yescharacteristic
120C22×C4×D5—31no—
121C22×C4×D5—32no—
122C22×C4×D5C2×D312yes—
123C5×#117—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C4⋊C4C2×D311yescharacteristic
126C2×C5×C22⋊C4—32no—
127C2×C42×C5—32no—
128C2×C22⋊Dic5—31no—
129#4076—38no—
130C4×C22⋊D5—38no—
131C2×#685—32no—
132C2×#685—32no—
133C2×#685—31no—
134C2×#685C2×D312yes—
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5—32no—
137C2×#683—32no—
138C2×#683—31no—
139C2×#683—32no—
140C2×C4×Dic5C2×D311yescharacteristic
141#4041—38no—
142#4039C2×D318yescomplemented
143D5×C4⋊C4—38no—
144#4036—38no—
145#4030—316no—
146#4029—316no—
147#4022—316no—
148C4×D20—316no—
149C2×#553—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×D15—22no—
152C22×D15—22no—
153C22×D15#4114yes—
154C22×D15C2412yes—
155C22×C5×D3—22no—
156C22×C5×D3—22no—
157C22×C5×D3—22no—
158C22×C5×D3C2412yes—
159C22×C3×D5—24no—
160C22×C3×D5—24no—
161C22×C3×D5—24no—
162C22×C3×D5C2414yes—
163C2×C3×C4×C5—24no—
164C2×C3×C4×C5#4114yes—
165C2×C3×C4×C5C2414yes—
166C2×C3×C4×C5C2412yes—
167C2×Dic15—22no—
168C2×Dic15—24no—
169C2×Dic15C2412yes—
170C2×Dic15C2414yes—
171C4×D15—28no—
172C4×D15—48no—
173C2×C5×Dic3—24no—
174C2×C5×Dic3—22no—
175C2×C5×Dic3C2412yes—
176C2×C5×Dic3C2414yes—
177C4×C5×D3—28no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5C2412yes—
181C2×C3×Dic5C2412yes—
182C3×D20—28no—
183C3×C4×D5—48no—
184#1203—28no—
185#1202—216no—
186#1201—48no—
187C22×C3×D4—51no—
188C23×C3×C4—52no—
189C22×#67—52no—
190C22×#67—52no—
191C22×D12—51no—
192C22×C4×D3—51no—
193C22×C4×D3—52no—
194C22×C4×D3C2×D511yescharacteristic
195C3×C4×D4—58no—
196C2×C3×C4⋊C4C2×D511yescharacteristic
197C2×C3×C22⋊C4—52no—
198C2×C3×C42—51no—
199C2×#217—52no—
200C2×#217—52no—
201#938—58no—
202#938—58no—
203#929—516no—
204C4×#67—516no—
205C2×(C2×D3)⋊C4—51no—
206C2×(C2×D3)⋊C4—51no—
207C2×(C2×D3)⋊C4C2×D512yes—
208C2×C4⋊Dic3—51no—
209C2×C4⋊Dic3—51no—
210C2×C4⋊Dic3C2×D511yescharacteristic
211C2×Dic3⋊C4—52no—
212C2×Dic3⋊C4—52no—
213C2×Dic3⋊C4—52no—
214C2×C4×Dic3C2×D512yes—
215#892C2×D518yescomplemented
216D3×C4⋊C4—58no—
217#884—516no—
218#879—516no—
219C4×D12—58no—
220#870—58no—
221C24×C5—31no—
222C23×D5—31no—
223C23×D5C22×D312yes—
224C22×C4×C5—31no—
225C22×C4×C5—32no—
226C22×C4×C5—34no—
227C22×C4×C5—64no—
228C22×C4×C5C22×D312yes—
229C22×C4×C5C22×D311yescharacteristic
230C2×C22⋊D5—38no—
231C2×C22⋊D5—34no—
232C2×C22⋊D5—64no—
233C2×C22⋊D5—124no—
234C22×Dic5—31no—
235C22×Dic5—32no—
236C22×Dic5C22×D311yescharacteristic
237C22×Dic5C22×D311yescharacteristic
238C2×D20—24no—
239C2×D20—38no—
240C2×D20—68no—
241C2×D20C22×D314yes—
242C2×C4×D5—34no—
243C2×C4×D5—38no—
244C2×C4×D5—44no—
245C2×C4×D5—64no—
246C2×C4×D5—124no—
247C2×C4×D5C22×D318yes—
248C5×C4⋊C4—34no—
249C5×C4⋊C4C22×D314yes—
250C5×C22⋊C4—38no—
251C42×C5—38no—
252C22⋊Dic5—34no—
253#685—38no—
254#685—38no—
255#685—34no—
256#685C22×D318yes—
257C4⋊Dic5—34no—
258C4⋊Dic5—38no—
259#683—38no—
260#683—34no—
261#683—38no—
262C4×Dic5C22×D314yes—
263#553—1516no—
264C2×#126—152no—
265C2×#125—151no—
266C2×#123—152no—
267C2×#121—152no—
268C2×#121—151no—
269C2×#121—151no—
270C2×C4×D4—51no—
271C2×C4×D4—152no—
272C2×C4×D4—151no—
273C2×#117—31no—
274C22×C4⋊C4—151no—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5H(5,𝔽2)12yes—
278C22×C3×C5C2511yescharacteristic
279C2×D15—28no—
280C2×D15—22no—
281C2×D15—22no—
282C2×D15C2×#4114yes—
283C2×C5×D3—22no—
284C2×C5×D3—22no—
285C2×C5×D3—22no—
286C2×C5×D3—44no—
287C2×C3×D5—24no—
288C2×C3×D5—24no—
289C2×C3×D5—24no—
290C2×C3×D5—48no—
291C3×C4×C5—24no—
292C3×C4×C5C2×#4114yes—
293Dic15—22no—
294Dic15—24no—
295C3×Dic5—22no—
296C3×Dic5—22no—
297C5×Dic3—24no—
298C5×Dic3—22no—
299C24×C3—52no—
300C23×D3—51no—
301C23×D3C22×D511yescharacteristic
302C2×C3×D4—54no—
303C2×C3×D4—104no—
304C22×C3×C4—51no—
305C22×C3×C4—51no—
306C22×C3×C4—58no—
307C22×C3×C4—204no—
308C22×C3×C4C22×D512yes—
309C22×C3×C4C22×D511yescharacteristic
310C2×#67—58no—
311C2×#67—58no—
312C2×#67—108no—
313C2×#67—204no—
314C22×Dic3—52no—
315C22×Dic3—51no—
316C22×Dic3C22×D511yescharacteristic
317C22×Dic3C22×D512yes—
318C2×D12—54no—
319C2×D12—104no—
320C2×C4×D3—24no—
321C2×C4×D3—54no—
322C2×C4×D3—58no—
323C2×C4×D3—104no—
324C2×C4×D3—204no—
325C2×C4×D3C22×D514yes—
326C3×C4⋊C4C22×D514yes—
327C3×C22⋊C4—58no—
328C3×C42—54no—
329#217—58no—
330#217—58no—
331(C2×D3)⋊C4—54no—
332(C2×D3)⋊C4—54no—
333(C2×D3)⋊C4C22×D518yes—
334C4⋊Dic3—54no—
335C4⋊Dic3—54no—
336C4⋊Dic3C22×D514yes—
337Dic3⋊C4—58no—
338Dic3⋊C4—58no—
339Dic3⋊C4—58no—
340C4×Dic3C22×D518yes—
341C23×C5—32no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5C23×D311yescharacteristic
346C22×D5—24no—
347C22×D5—24no—
348C22×D5—24no—
349C22×D5—34no—
350C22×D5—32no—
351C22×D5—62no—
352C22×D5—62no—
353C22×D5C23×D314yes—
354C2×C4×C5—24no—
355C2×C4×C5—34no—
356C2×C4×C5—32no—
357C2×C4×C5—62no—
358C2×C4×C5—64no—
359C2×C4×C5—68no—
360C2×C4×C5#23514yes—
361C2×C4×C5C23×D314yes—
362C2×C4×C5C23×D312yes—
363C22⋊D5—68no—
364C22⋊D5—128no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—32no—
368C2×Dic5—34no—
369C2×Dic5—62no—
370C2×Dic5—64no—
371C2×Dic5C23×D312yes—
372C2×Dic5C23×D312yes—
373D20—28no—
374D20—616no—
375C4×D5—48no—
376C4×D5—68no—
377C4×D5—128no—
378C22×D4—51no—
379C22×D4—152no—
380C22×D4—151no—
381C22×D4—152no—
382C23×C4—31no—
383C23×C4—52no—
384C23×C4—151no—
385C23×C4—152no—
386#126—1516no—
387#125—158no—
388#123—1516no—
389#121—1516no—
390#121—158no—
391#121—158no—
392C4×D4—58no—
393C4×D4—1516no—
394C4×D4—158no—
395#117—38no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—152no—
398C2×C4⋊C4—151no—
399C2×C4⋊C4—152no—
400C2×C4⋊C4—151no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—158no—
403C2×C4⋊C4D3×D511yescharacteristic
404C2×C22⋊C4—32no—
405C2×C22⋊C4—52no—
406C2×C22⋊C4—151no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—152no—
409C2×C22⋊C4—151no—
410C2×C42—32no—
411C2×C42—51no—
412C2×C3×C5#55314yescomplemented
413C2×C3×C5C22×#4111yescharacteristic
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
416D15—24no—
417C3×D5—44no—
418C5×D3—42no—
419C23×C3—54no—
420C23×C3—104no—
421C23×C3—104no—
422C23×C3—104no—
423C23×C3C23×D511yescharacteristic
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—54no—
428C22×D3—52no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3C23×D512yes—
432C3×D4—108no—
433C2×C3×C4—24no—
434C2×C3×C4—52no—
435C2×C3×C4—52no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×C3×C4—208no—
439C2×C3×C4#70914yes—
440C2×C3×C4C23×D514yes—
441C2×C3×C4C23×D512yes—
442#67—1016no—
443#67—208no—
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—54no—
447C2×Dic3—52no—
448C2×Dic3—102no—
449C2×Dic3—104no—
450C2×Dic3C23×D512yes—
451C2×Dic3C23×D514yes—
452D12—108no—
453C4×D3—28no—
454C4×D3—108no—
455C4×D3—208no—
456C22×C5—62no—
457C22×C5—62no—
458C22×C5—62no—
459C22×C5—124no—
460C22×C5C2×#23512yes—
461C22×C5#100412yes—
462C22×C5D3×#4112yes—
463C22×C5C24×D311yescharacteristic
464C2×D5—24no—
465C2×D5—24no—
466C2×D5—24no—
467C2×D5—34no—
468C2×D5—48no—
469C2×D5—62no—
470C2×D5—62no—
471C2×D5—68no—
472C4×C5—24no—
473C4×C5—62no—
474C4×C5—64no—
475C4×C5C2×#23514yes—
476Dic5—22no—
477Dic5—22no—
478Dic5—62no—
479Dic5—64no—
480C24—31no—
481C24—52no—
482C24—151no—
483C2×D4—54no—
484C2×D4—104no—
485C2×D4—158no—
486C2×D4—154no—
487C2×D4—158no—
488C2×D4—308no—
489C2×D4—304no—
490C2×D4—604no—
491C22×C4—31no—
492C22×C4—32no—
493C22×C4—34no—
494C22×C4—51no—
495C22×C4—51no—
496C22×C4—58no—
497C22×C4—64no—
498C22×C4—151no—
499C22×C4—152no—
500C22×C4—154no—
501C22×C4—158no—
502C22×C4—204no—
503C22×C4—304no—
504C22×C4—604no—
505C22×C4C2×D3×D512yes—
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—158no—
509C4⋊C4—154no—
510C4⋊C4—158no—
511C4⋊C4—154no—
512C4⋊C4—158no—
513C4⋊C4C2×D3×D514yes—
514C22⋊C4—38no—
515C22⋊C4—58no—
516C22⋊C4—154no—
517C22⋊C4—158no—
518C22⋊C4—158no—
519C22⋊C4—154no—
520C42—38no—
521C42—54no—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3—104no—
524C22×C3—104no—
525C22×C3—104no—
526C22×C3—208no—
527C22×C3C2×#70912yes—
528C22×C3D5×#4112yes—
529C22×C3#414912yes—
530C22×C3C24×D511yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—44no—
535C2×D3—54no—
536C2×D3—108no—
537C2×D3—102no—
538C2×D3—102no—
539C3×C4—24no—
540C3×C4—102no—
541C3×C4—102no—
542C3×C4C2×#70914yes—
543Dic3—22no—
544Dic3—24no—
545Dic3—102no—
546Dic3—104no—
547C2×C5—122no—
548C2×C5#555814yescomplemented
549C2×C5C22×#23511yescharacteristic
550C2×C5C2×#100411yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552D5—44no—
553D5—64no—
554C23—32no—
555C23—54no—
556C23—62no—
557C23—62no—
558C23—62no—
559C23—104no—
560C23—104no—
561C23—104no—
562C23—154no—
563C23—152no—
564C23—302no—
565C23—302no—
566C23C22×D3×D511yescharacteristic
567D4—108no—
568D4—3016no—
569D4—308no—
570D4—608no—
571C2×C4—24no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—52no—
575C2×C4—52no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—68no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—152no—
582C2×C4—154no—
583C2×C4—208no—
584C2×C4—302no—
585C2×C4—304no—
586C2×C4—308no—
587C2×C4—608no—
588C2×C4#677114yes—
589C2×C4C22×D3×D514yes—
590C2×C4C22×D3×D512yes—
591C2×C3—204no—
592C2×C3#6586414yescomplemented
593C2×C3C22×#70911yescharacteristic
594C2×C3C2×D5×#4111yescharacteristic
595C2×C3C2×#414911yescharacteristic
596D3—42no—
597D3—104no—
598C5C2×#555811yescharacteristic, complemented, Sylow
599C22—62no—
600C22—62no—
601C22—62no—
602C22—104no—
603C22—104no—
604C22—104no—
605C22—124no—
606C22—154no—
607C22—208no—
608C22—308no—
609C22—302no—
610C22—302no—
611C22C2×#677112yes—
612C22#9202612yes—
613C22#9203412yes—
614C22C23×D3×D511yescharacteristic
615C4—24no—
616C4—62no—
617C4—64no—
618C4—102no—
619C4—102no—
620C4—302no—
621C4—304no—
622C4C2×#677114yes—
623C3C2×#6586411yescharacteristic, complemented, Sylow
624C2—122no—
625C2—204no—
626C2—304no—
627C2#1175380814yesdirect product factor
628C2C22×#677111yescharacteristic
629C2C2×#9202611yescharacteristic
630C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D15C2semidirect
2. C2×C5×#892C2semidirect
3. C2×C3×#4039C2semidirect
4. C2×#91465C2semidirect
5. C2×#91461C2semidirect
6. C2×#91456C2semidirect
7. C2×#91447C2semidirect
8. C2×C4×#1203C2semidirect
9. C2×C4×#1202C2semidirect
10. C2×#91388C2semidirect
11. C2×#91363C2semidirect
12. #11753808C2direct (N × H)
25. C4⋊C4×D15C22semidirect
29. C5×#892C22semidirect
32. C3×#4039C22semidirect
40. #91465C22semidirect
41. #91461C22semidirect
42. #91456C22semidirect
43. #91447C22semidirect
44. C4×#1203C22semidirect
45. C4×#1202C22semidirect
46. #91388C22semidirect
47. #91363C22semidirect
54. C2×#4039D3semidirect
109. C2×#892D5semidirect
142. #4039C2×D3semidirect
215. #892C2×D5semidirect
412. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
548. C2×C5#5558semidirect
592. C2×C3#65864semidirect
598. C5C2×#5558semidirect
623. C3C2×#65864semidirect
627. C2#11753808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×C5×#8922
C2×C3×#40392
C2×#914652
C2×#914612
C2×#914562
C2×#914472
C2×C4×#12032
C2×C4×#12022
C2×#913882
C2×#913632
#117538082
C2×#658643
C2×#55585