Finite Group Databasebeta

← C2×#11753637 #14483725

Subgroups — C2×#11753637 #14483725

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×#895C211yesmaximal, characteristic, complemented
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×#91466C212yesmaximal, complemented
5C2×#91466C211yesmaximal, characteristic, complemented
6C2×C4×#1203C211yesmaximal, characteristic, complemented
7C2×#91423C212yesmaximal, complemented
8C2×Dic5×D12C211yesmaximal, characteristic, complemented
9C2×#91406C212yesmaximal, complemented
10C2×#91341C212yesmaximal, complemented
11C2×#91338C211yesmaximal, characteristic, complemented
12#11753637C2116yesmaximal, direct product factor
13C2×#65948—31nomaximal, Hall
14C22×C4×D15C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×D12C2211yescharacteristic
17C22×C5×D12C2212yes—
18C22×C4×C5×D3C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1203C2212yes—
21C22×D3×Dic5C2212yes—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×#6712C2212yes—
25C4⋊C4×D15C2218yescomplemented
26C2×C5×(C2×D3)⋊C4C2212yes—
27C5×#895C2218yescomplemented
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4036C2218yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2212yes—
37C2×(C2×D3)⋊Dic5C2212yes—
38C2×(C2×D3)⋊Dic5C2212yes—
39C2×Dic3×Dic5C2212yes—
40#91466C22116yescomplemented
41#91466C2218yescomplemented
42C4×#1203C2218yescomplemented
43#91423C22116yescomplemented
44Dic5×D12C2218yescomplemented
45#91406C22116yescomplemented
46#91341C22116yescomplemented
47#91338C2218yescomplemented
48C2×#5695—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4084—32no—
51C2×#4084—31no—
52C2×#4081—32no—
53C2×D4×Dic5—31no—
54C2×C4×C22⋊D5—31no—
55C2×#4072—31no—
56#65948—316no—
57C2×D5×C4⋊C4—31no—
58C2×#4036D311yescharacteristic, complemented
59C2×#4027—32no—
60C2×#4025—32no—
61C23×D15C2311yescharacteristic
62C23×C5×D3C2312yes—
63C23×C5×D3C2311yescharacteristic
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
73C2×C5×D12—24no—
74C2×C5×D12—44no—
75C2×C5×D12C2314yes—
76C2×C5×D12C2318yes—
77C2×C4×C5×D3—24no—
78C2×C4×C5×D3C2314yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C2×#1203—24no—
83C2×#1203—28no—
84C2×#1203C2318yes—
85C2×#1203C2314yes—
86C2×D3×Dic5—44no—
87C2×D3×Dic5C2318yes—
88C3×C5×C4⋊C4C2314yes—
89C4⋊Dic15C2314yes—
90#6712C2318yes—
91C5×(C2×D3)⋊C4C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×C4⋊Dic5C2318yes—
94C3×#683C2318yes—
95C3×C4×Dic5C2314yes—
96#6668C2314yes—
97#6667C2314yes—
98(C2×D3)⋊Dic5C2318yes—
99(C2×D3)⋊Dic5C2314yes—
100(C2×D3)⋊Dic5C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102Dic3×Dic5C2318yes—
103C2×C3×#125—51no—
104#5695—516no—
105C2×#898—52no—
106C2×#895—52no—
107C2×#895—51no—
108C2×#895D511yescharacteristic, complemented
109C2×#894—52no—
110C2×#893—52no—
111C2×#892—51no—
112C2×D3×C4⋊C4—51no—
113C2×C4×D12—51no—
114C2×C4×D12—51no—
115C22×C5×D4—31no—
116C22×C5×D4—32no—
117C23×C4×C5—31no—
118C22×C22⋊D5—32no—
119C22×C22⋊D5—31no—
120C23×Dic5—32no—
121C22×C4×D5—31no—
122C22×C4×D5—32no—
123C5×#121—38no—
124C2×C5×C4⋊C4C2×D311yescharacteristic
125C2×C5×C22⋊C4—32no—
126C2×C22⋊Dic5—32no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—32no—
129C2×C22⋊Dic5—31no—
130#4084—316no—
131#4084—38no—
132#4081—316no—
133D4×Dic5—38no—
134C4×C22⋊D5—38no—
135C2×#685—31no—
136#4072—38no—
137C2×C4⋊Dic5—31no—
138C2×C4⋊Dic5C2×D312yes—
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×#683—32no—
141C2×#683—31no—
142C2×#683C2×D312yes—
143C2×C4×Dic5—32no—
144C2×C4×Dic5C2×D311yescharacteristic
145D5×C4⋊C4—38no—
146#4036C2×D318yescomplemented
147#4027—316no—
148#4025—316no—
149C2×#553—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×D15—22no—
152C22×D15—22no—
153C22×D15#4114yes—
154C22×D15C2412yes—
155C22×C5×D3—24no—
156C22×C5×D3—22no—
157C22×C5×D3—22no—
158C22×C5×D3—24no—
159C22×C5×D3—24no—
160C22×C5×D3—22no—
161C22×C5×D3C2412yes—
162C22×C5×D3C2414yes—
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×Dic15C2414yes—
170C2×Dic15C2412yes—
171C4×D15—28no—
172C4×D15—48no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3C2412yes—
175C5×D12—28no—
176C5×D12—48no—
177C4×C5×D3—28no—
178C2×C3×Dic5—24no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5C2414yes—
182C2×C3×Dic5C2412yes—
183C2×C3×Dic5C2412yes—
184#1203—216no—
185#1203—28no—
186D3×Dic5—48no—
187C22×D12—51no—
188C22×D12—52no—
189C22×D12C2×D511yescharacteristic
190C22×D12C2×D512yes—
191C22×C4×D3—51no—
192C22×C4×D3—52no—
193C22×C4×D3—52no—
194C22×C4×D3C2×D511yescharacteristic
195C3×#125—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C4⋊C4—52no—
198C2×C3×C4⋊C4—52no—
199C2×C3×C4⋊C4C2×D511yescharacteristic
200C2×C3×C42—51no—
201C2×(C2×D3)⋊C4—51no—
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—51no—
206C2×(C2×D3)⋊C4C2×D512yes—
207C2×C4⋊Dic3—51no—
208C2×C4⋊Dic3—51no—
209C2×Dic3⋊C4—52no—
210C2×C4×Dic3—52no—
211#898—516no—
212#895—516no—
213#895—58no—
214#895C2×D518yescomplemented
215#894—516no—
216#893—516no—
217#892—58no—
218D3×C4⋊C4—58no—
219C4×D12—58no—
220C4×D12—58no—
221C24×C5—31no—
222C24×C5—32no—
223C23×D5—31no—
224C2×C5×D4—34no—
225C2×C5×D4—38no—
226C2×C5×D4—64no—
227C2×C5×D4—124no—
228C22×C4×C5—31no—
229C22×C4×C5—34no—
230C22×C4×C5—64no—
231C22×C4×C5C22×D312yes—
232C22×C4×C5C22×D311yescharacteristic
233C2×C22⋊D5—38no—
234C2×C22⋊D5—34no—
235C2×C22⋊D5—68no—
236C2×C22⋊D5—64no—
237C22×Dic5—31no—
238C22×Dic5—32no—
239C22×Dic5—38no—
240C22×Dic5—124no—
241C22×Dic5C22×D312yes—
242C22×Dic5C22×D311yescharacteristic
243C22×Dic5C22×D311yescharacteristic
244C2×C4×D5—34no—
245C2×C4×D5—38no—
246C2×C4×D5—64no—
247C2×C4×D5—124no—
248C5×C4⋊C4C22×D314yes—
249C5×C22⋊C4—38no—
250C22⋊Dic5—38no—
251C22⋊Dic5—38no—
252C22⋊Dic5—38no—
253C22⋊Dic5—34no—
254#685—34no—
255C4⋊Dic5—34no—
256C4⋊Dic5C22×D318yes—
257C4⋊Dic5C22×D314yes—
258#683—38no—
259#683—34no—
260#683C22×D318yes—
261C4×Dic5—38no—
262C4×Dic5C22×D314yes—
263#553—1516no—
264C2×#126—152no—
265C2×#125—51no—
266C2×#123—152no—
267C2×#121—31no—
268C2×#121—152no—
269C2×#121—151no—
270C2×C4×D4—151no—
271C2×C4×D4—151no—
272C2×C4×D4—152no—
273C2×#117—151no—
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—24no—
285C2×C5×D3—22no—
286C2×C5×D3—24no—
287C2×C5×D3—24no—
288C2×C5×D3—22no—
289C2×C5×D3—44no—
290C2×C5×D3—48no—
291C3×C4×C5—24no—
292C3×C4×C5C2×#4114yes—
293Dic15—22no—
294Dic15—24no—
295C3×Dic5—24no—
296C3×Dic5—22no—
297C3×Dic5—22no—
298C5×Dic3—22no—
299C23×D3—51no—
300C23×D3C22×D511yescharacteristic
301C23×D3C22×D512yes—
302C22×C3×C4—52no—
303C22×C3×C4—51no—
304C22×C3×C4—51no—
305C22×C3×C4C22×D512yes—
306C22×C3×C4C22×D511yescharacteristic
307C22×Dic3—52no—
308C22×Dic3—51no—
309C22×Dic3C22×D511yescharacteristic
310C2×D12—24no—
311C2×D12—44no—
312C2×D12—54no—
313C2×D12—58no—
314C2×D12—104no—
315C2×D12—108no—
316C2×D12C22×D514yes—
317C2×D12C22×D518yes—
318C2×C4×D3—24no—
319C2×C4×D3—54no—
320C2×C4×D3—58no—
321C2×C4×D3—58no—
322C2×C4×D3—104no—
323C2×C4×D3—204no—
324C2×C4×D3—204no—
325C2×C4×D3C22×D514yes—
326C3×C4⋊C4—58no—
327C3×C4⋊C4—54no—
328C3×C4⋊C4—58no—
329C3×C4⋊C4C22×D514yes—
330C3×C42—54no—
331(C2×D3)⋊C4—54no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—58no—
334(C2×D3)⋊C4—58no—
335(C2×D3)⋊C4—54no—
336(C2×D3)⋊C4C22×D518yes—
337C4⋊Dic3—54no—
338C4⋊Dic3—54no—
339Dic3⋊C4—58no—
340C4×Dic3—58no—
341C23×C5—32no—
342C23×C5—34no—
343C23×C5—62no—
344C23×C5—64no—
345C23×C5—62no—
346C23×C5—64no—
347C23×C5—64no—
348C23×C5—62no—
349C23×C5C23×D311yescharacteristic
350C22×D5—34no—
351C22×D5—32no—
352C22×D5—62no—
353C22×D5—62no—
354C5×D4—68no—
355C5×D4—128no—
356C2×C4×C5—24no—
357C2×C4×C5—32no—
358C2×C4×C5—62no—
359C2×C4×C5—68no—
360C2×C4×C5#23914yes—
361C2×C4×C5C23×D314yes—
362C2×C4×C5C23×D312yes—
363C22⋊D5—616no—
364C22⋊D5—68no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—34no—
369C2×Dic5—32no—
370C2×Dic5—62no—
371C2×Dic5—64no—
372C2×Dic5—128no—
373C2×Dic5C23×D314yes—
374C2×Dic5C23×D312yes—
375C2×Dic5C23×D312yes—
376C4×D5—68no—
377C4×D5—128no—
378C22×D4—31no—
379C22×D4—32no—
380C22×D4—151no—
381C22×D4—152no—
382C23×C4—31no—
383C23×C4—152no—
384C23×C4—151no—
385C23×C4—152no—
386#126—1516no—
387#125—58no—
388#123—1516no—
389#121—38no—
390#121—1516no—
391#121—158no—
392C4×D4—158no—
393C4×D4—158no—
394C4×D4—1516no—
395#117—158no—
396C2×C4⋊C4—51no—
397C2×C4⋊C4—52no—
398C2×C4⋊C4—52no—
399C2×C4⋊C4—151no—
400C2×C4⋊C4—151no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—158no—
403C2×C4⋊C4D3×D511yescharacteristic
404C2×C22⋊C4—32no—
405C2×C22⋊C4—151no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—151no—
409C2×C22⋊C4—152no—
410C2×C42—51no—
411C2×C42—152no—
412C2×C3×C5#55314yescomplemented
413C2×C3×C5C22×#4111yescharacteristic
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
416D15—24no—
417C5×D3—42no—
418C5×D3—44no—
419C23×C3C23×D511yescharacteristic
420C22×D3—22no—
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—24no—
426C22×D3—54no—
427C22×D3—52no—
428C22×D3—102no—
429C22×D3—102no—
430C22×D3C23×D512yes—
431C22×D3C23×D514yes—
432C2×C3×C4—24no—
433C2×C3×C4—54no—
434C2×C3×C4—52no—
435C2×C3×C4—52no—
436C2×C3×C4—102no—
437C2×C3×C4—104no—
438C2×C3×C4—102no—
439C2×C3×C4#71114yes—
440C2×C3×C4C23×D514yes—
441C2×C3×C4C23×D512yes—
442C2×Dic3—22no—
443C2×Dic3—54no—
444C2×Dic3—52no—
445C2×Dic3—102no—
446C2×Dic3—104no—
447C2×Dic3C23×D512yes—
448D12—28no—
449D12—48no—
450D12—108no—
451D12—1016no—
452C4×D3—28no—
453C4×D3—108no—
454C4×D3—208no—
455C4×D3—208no—
456C22×C5—62no—
457C22×C5—64no—
458C22×C5—62no—
459C22×C5—64no—
460C22×C5—64no—
461C22×C5—62no—
462C22×C5—124no—
463C22×C5—128no—
464C22×C5C2×#23912yes—
465C22×C5D3×#4112yes—
466C22×C5#100912yes—
467C22×C5C24×D311yescharacteristic
468C2×D5—34no—
469C2×D5—68no—
470C2×D5—62no—
471C2×D5—62no—
472C4×C5—24no—
473C4×C5—62no—
474C4×C5C2×#23914yes—
475Dic5—24no—
476Dic5—22no—
477Dic5—22no—
478Dic5—62no—
479Dic5—64no—
480C24—32no—
481C24—31no—
482C24—151no—
483C2×D4—34no—
484C2×D4—38no—
485C2×D4—64no—
486C2×D4—124no—
487C2×D4—154no—
488C2×D4—158no—
489C2×D4—304no—
490C2×D4—308no—
491C22×C4—31no—
492C22×C4—34no—
493C22×C4—51no—
494C22×C4—51no—
495C22×C4—52no—
496C22×C4—64no—
497C22×C4—158no—
498C22×C4—152no—
499C22×C4—151no—
500C22×C4—154no—
501C22×C4—158no—
502C22×C4—304no—
503C22×C4—604no—
504C22×C4—604no—
505C22×C4C2×D3×D512yes—
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—54no—
508C4⋊C4—58no—
509C4⋊C4—58no—
510C4⋊C4—154no—
511C4⋊C4—154no—
512C4⋊C4—158no—
513C4⋊C4C2×D3×D514yes—
514C22⋊C4—38no—
515C22⋊C4—154no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—154no—
519C22⋊C4—158no—
520C42—54no—
521C42—158no—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3C2×#71112yes—
524C22×C3#414412yes—
525C22×C3D5×#4112yes—
526C22×C3C24×D511yescharacteristic
527C2×D3—22no—
528C2×D3—24no—
529C2×D3—24no—
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—24no—
533C2×D3—44no—
534C2×D3—48no—
535C2×D3—54no—
536C2×D3—108no—
537C2×D3—102no—
538C2×D3—102no—
539C3×C4—24no—
540C3×C4—102no—
541C3×C4—104no—
542C3×C4—102no—
543C3×C4C2×#71114yes—
544Dic3—22no—
545Dic3—102no—
546Dic3—104no—
547C2×C5—122no—
548C2×C5—124no—
549C2×C5#569514yescomplemented
550C2×C5C22×#23911yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552C2×C5C2×#100911yescharacteristic
553D5—64no—
554C23—34no—
555C23—32no—
556C23—62no—
557C23—64no—
558C23—64no—
559C23—62no—
560C23—64no—
561C23—62no—
562C23—154no—
563C23—152no—
564C23—302no—
565C23—302no—
566C23C22×D3×D511yescharacteristic
567D4—68no—
568D4—128no—
569D4—308no—
570D4—3016no—
571C2×C4—24no—
572C2×C4—32no—
573C2×C4—52no—
574C2×C4—52no—
575C2×C4—54no—
576C2×C4—62no—
577C2×C4—68no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—104no—
581C2×C4—154no—
582C2×C4—152no—
583C2×C4—302no—
584C2×C4—304no—
585C2×C4—308no—
586C2×C4—608no—
587C2×C4—608no—
588C2×C4#676814yes—
589C2×C4C22×D3×D514yes—
590C2×C4C22×D3×D512yes—
591C2×C3#6594814yescomplemented
592C2×C3C22×#71111yescharacteristic
593C2×C3C2×#414411yescharacteristic
594C2×C3C2×D5×#4111yescharacteristic
595D3—42no—
596D3—44no—
597D3—104no—
598C5C2×#569511yescharacteristic, complemented, Sylow
599C22—62no—
600C22—64no—
601C22—64no—
602C22—62no—
603C22—64no—
604C22—62no—
605C22—124no—
606C22—128no—
607C22—154no—
608C22—308no—
609C22—302no—
610C22—302no—
611C22C2×#676812yes—
612C22#9202712yes—
613C22#9203412yes—
614C22C23×D3×D511yescharacteristic
615C4—24no—
616C4—62no—
617C4—102no—
618C4—102no—
619C4—104no—
620C4—302no—
621C4—304no—
622C4C2×#676814yes—
623C3C2×#6594811yescharacteristic, complemented, Sylow
624C2—122no—
625C2—124no—
626C2—304no—
627C2#1175363714yesdirect product factor
628C2C22×#676811yescharacteristic
629C2C2×#9202711yescharacteristic
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×#895C2semidirect
3. C2×C3×#4036C2semidirect
4. C2×#91466C2semidirect
5. C2×#91466C2semidirect
6. C2×C4×#1203C2semidirect
7. C2×#91423C2semidirect
8. C2×Dic5×D12C2semidirect
9. C2×#91406C2semidirect
10. C2×#91341C2semidirect
11. C2×#91338C2semidirect
12. #11753637C2direct (N × H)
25. C4⋊C4×D15C22semidirect
27. C5×#895C22semidirect
32. C3×#4036C22semidirect
40. #91466C22semidirect
41. #91466C22semidirect
42. C4×#1203C22semidirect
43. #91423C22semidirect
44. Dic5×D12C22semidirect
45. #91406C22semidirect
46. #91341C22semidirect
47. #91338C22semidirect
58. C2×#4036D3semidirect
108. C2×#895D5semidirect
146. #4036C2×D3semidirect
214. #895C2×D5semidirect
412. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
549. C2×C5#5695semidirect
591. C2×C3#65948semidirect
598. C5C2×#5695semidirect
623. C3C2×#65948semidirect
627. C2#11753637direct (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×#8952
C2×C3×#40362
C2×#914662
C2×C4×#12032
C2×#914232
C2×Dic5×D122
C2×#914062
C2×#913412
C2×#913382
#117536372
C2×#659483
C2×#56955