Finite Group Databasebeta

← C2×#11754467 #14483698

Subgroups — C2×#11754467 #14483698

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×#1220C211yesmaximal, characteristic, complemented
2C2×C5×#930C211yesmaximal, characteristic, complemented
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C2×#91557C212yesmaximal, complemented
5C2×#91555C212yesmaximal, complemented
6C2×#91466C211yesmaximal, characteristic, complemented
7#11754467C2116yesmaximal, direct product factor
8C2×#91437C211yesmaximal, characteristic, complemented
9C2×#91435C211yesmaximal, characteristic, complemented
10C2×#91405C212yesmaximal, complemented
11C2×#91384C211yesmaximal, characteristic, complemented
12C2×#91372C212yesmaximal, complemented
13C2×#65948—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×#1220C2211yescharacteristic
16C22×C4×D15C2211yescharacteristic
17C22×C5×#67C2212yes—
18C22×C5×D12C2211yescharacteristic
19C22×#1203C2212yes—
20C22×#1200C2212yes—
21C22×D3×Dic5C2212yes—
22C2×#6719C2211yescharacteristic
23C4×#1220C2218yescomplemented
24C2×#6714C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C5×#930C2218yescomplemented
28C2×C5×(C2×D3)⋊C4C2212yes—
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C3×C22⋊Dic5C2212yes—
31C3×#4072C2218yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2212yes—
35#91557C22116yescomplemented
36#91555C22116yescomplemented
37C2×Dic3⋊Dic5C2212yes—
38C2×#6669C2212yes—
39C2×#6668C2212yes—
40C2×(C2×D3)⋊Dic5C2212yes—
41C2×(C2×D3)⋊Dic5C2212yes—
42#91466C2218yescomplemented
43#91437C2218yescomplemented
44#91435C2218yescomplemented
45#91405C22116yescomplemented
46#91384C2218yescomplemented
47#91372C22116yescomplemented
48C2×#5530—51nomaximal, Hall
49C2×C5×#121—31no—
50C2×#4084—31no—
51C2×#4084—32no—
52C2×#4081—32no—
53C2×D4×Dic5—31no—
54C2×C4×C22⋊D5—31no—
55C2×#4072D311yescharacteristic, complemented
56#65948—316no—
57C2×D5×C4⋊C4—31no—
58C2×#4036—31no—
59C2×#4027—32no—
60C2×#4025—32no—
61C24×C3×C5C2311yescharacteristic
62C23×D15C2311yescharacteristic
63C23×C5×D3C2312yes—
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2314yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—24no—
69C2×#1220C2314yes—
70C22×Dic15C2311yescharacteristic
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2311yescharacteristic
73C2×C4×D15—24no—
74C2×C4×D15C2314yes—
75C2×C5×#67—44no—
76C2×C5×#67C2318yes—
77C22×C5×Dic3C2312yes—
78C2×C5×D12—24no—
79C2×C5×D12C2314yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C2×#1203—28no—
83C2×#1203C2318yes—
84C2×#1200—44no—
85C2×#1200C2318yes—
86C2×D3×Dic5—44no—
87C2×D3×Dic5C2318yes—
88#6719C2314yes—
89#6714C2314yes—
90#6712C2314yes—
91C4×Dic15C2314yes—
92C5×(C2×D3)⋊C4C2318yes—
93C5×C4⋊Dic3C2314yes—
94C3×C22⋊Dic5C2318yes—
95C3×C4⋊Dic5C2314yes—
96C3×C4⋊Dic5C2314yes—
97C3×C4×Dic5C2318yes—
98Dic3⋊Dic5C2318yes—
99#6669C2318yes—
100#6668C2318yes—
101(C2×D3)⋊Dic5C2318yes—
102(C2×D3)⋊Dic5C2318yes—
103C2×C3×#117—51no—
104C2×#930D511yescharacteristic, complemented
105C2×C4×#67—51no—
106#5530—516no—
107C2×#895—51no—
108C2×#893—51no—
109C2×D3×C4⋊C4—51no—
110C2×#890—51no—
111C2×#884—52no—
112C2×#883—52no—
113C2×#876—52no—
114C2×C4×D12—52no—
115C22×C5×D4—32no—
116C22×C5×D4—31no—
117C23×C4×C5C2×D311yescharacteristic
118C22×C22⋊D5—31no—
119C22×C22⋊D5—32no—
120C23×Dic5—32no—
121C22×C4×D5—31no—
122C22×C4×D5—32no—
123C5×#121—38no—
124C2×C5×C4⋊C4—31no—
125C2×C5×C22⋊C4—32no—
126C2×C22⋊Dic5—31no—
127C2×C22⋊Dic5—32no—
128C2×C22⋊Dic5—32no—
129C2×C22⋊Dic5C2×D312yes—
130#4084—316no—
131#4084—38no—
132#4081—316no—
133D4×Dic5—38no—
134C4×C22⋊D5—38no—
135C2×#685—31no—
136#4072C2×D318yescomplemented
137C2×C4⋊Dic5—32no—
138C2×C4⋊Dic5C2×D311yescharacteristic
139C2×C4⋊Dic5C2×D311yescharacteristic
140C2×#683—31no—
141C2×#683—32no—
142C2×#683—32no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5C2×D312yes—
145D5×C4⋊C4—38no—
146#4036—38no—
147#4027—316no—
148#4025—316no—
149C2×#553—151noSylow
150C23×C3×C5—22no—
151C23×C3×C5—22no—
152C23×C3×C5—22no—
153C23×C3×C5C2412yes—
154C23×C3×C5C2411yescharacteristic
155C22×D15—22no—
156C22×D15—22no—
157C22×D15#4114yes—
158C22×D15C2412yes—
159C22×C5×D3—24no—
160C22×C5×D3—24no—
161C22×C5×D3—24no—
162C22×C5×D3C2414yes—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—28no—
165C2×C3×C4×C5#4114yes—
166C2×C3×C4×C5C2412yes—
167C2×C3×C4×C5C2412yes—
168#1220—28no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15C2412yes—
173C2×Dic15C2412yes—
174C2×Dic15C2412yes—
175C4×D15—28no—
176C5×#67—48no—
177C2×C5×Dic3—24no—
178C2×C5×Dic3C2414yes—
179C5×D12—28no—
180C2×C3×Dic5—24no—
181C2×C3×Dic5—24no—
182C2×C3×Dic5C2414yes—
183C2×C3×Dic5C2414yes—
184#1203—216no—
185#1200—48no—
186D3×Dic5—48no—
187C23×C3×C4C2×D511yescharacteristic
188C22×#67—51no—
189C22×#67C2×D512yes—
190C22×D12—52no—
191C22×D12C2×D511yescharacteristic
192C22×C4×D3—51no—
193C22×C4×D3—52no—
194C22×C4×D3—52no—
195C3×#117—58no—
196C2×C3×C4⋊C4—51no—
197C2×C3×C4⋊C4—51no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C42—52no—
200C2×#217—51no—
201#930C2×D518yescomplemented
202C4×#67—58no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×(C2×D3)⋊C4—51no—
206C2×(C2×D3)⋊C4C2×D512yes—
207C2×C4⋊Dic3—52no—
208C2×C4⋊Dic3C2×D511yescharacteristic
209C2×Dic3⋊C4—51no—
210C2×Dic3⋊C4—52no—
211C2×Dic3⋊C4—52no—
212C2×C4×Dic3—51no—
213#895—58no—
214#893—58no—
215D3×C4⋊C4—58no—
216#890—58no—
217#884—516no—
218#883—516no—
219#876—516no—
220C4×D12—516no—
221C24×C5—32no—
222C24×C5C22×D311yescharacteristic
223C23×D5—31no—
224C2×C5×D4—38no—
225C2×C5×D4—34no—
226C2×C5×D4—64no—
227C2×C5×D4—124no—
228C22×C4×C5—24no—
229C22×C4×C5—32no—
230C22×C4×C5C22×D311yescharacteristic
231C22×C4×C5C22×D314yes—
232C22×C4×C5C22×D311yescharacteristic
233C2×C22⋊D5—34no—
234C2×C22⋊D5—38no—
235C2×C22⋊D5—68no—
236C2×C22⋊D5—64no—
237C22×Dic5—31no—
238C22×Dic5—31no—
239C22×Dic5—31no—
240C22×Dic5—38no—
241C22×Dic5—124no—
242C22×Dic5C22×D312yes—
243C22×Dic5C22×D312yes—
244C2×C4×D5—34no—
245C2×C4×D5—38no—
246C2×C4×D5—64no—
247C2×C4×D5—124no—
248C5×C4⋊C4—34no—
249C5×C22⋊C4—38no—
250C22⋊Dic5—34no—
251C22⋊Dic5—38no—
252C22⋊Dic5—38no—
253C22⋊Dic5C22×D318yes—
254#685—34no—
255C4⋊Dic5—38no—
256C4⋊Dic5C22×D314yes—
257C4⋊Dic5C22×D314yes—
258#683—34no—
259#683—38no—
260#683—38no—
261C4×Dic5—34no—
262C4×Dic5C22×D318yes—
263#553—1516no—
264C2×#126—152no—
265C2×#125—151no—
266C2×#123—152no—
267C2×#121—31no—
268C2×#121—152no—
269C2×#121—151no—
270C2×C4×D4—152no—
271C2×C4×D4—151no—
272C2×C4×D4—151no—
273C2×#117—51no—
274C22×C4⋊C4—151no—
275C22×C3×C5—22no—
276C22×C3×C5—22no—
277C22×C3×C5—22no—
278C22×C3×C5—44no—
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×C5×D3—24no—
288C2×C5×D3—24no—
289C2×C5×D3—24no—
290C2×C5×D3—48no—
291C3×C4×C5—22no—
292C3×C4×C5C2×#4114yes—
293Dic15—22no—
294Dic15—22no—
295Dic15—22no—
296C3×Dic5—24no—
297C3×Dic5—24no—
298C5×Dic3—24no—
299C24×C3C22×D511yescharacteristic
300C23×D3—51no—
301C23×D3C22×D512yes—
302C22×C3×C4—24no—
303C22×C3×C4—52no—
304C22×C3×C4—52no—
305C22×C3×C4C22×D511yescharacteristic
306C22×C3×C4C22×D514yes—
307C22×C3×C4C22×D511yescharacteristic
308C2×#67—44no—
309C2×#67—54no—
310C2×#67—104no—
311C2×#67C22×D518yes—
312C22×Dic3—51no—
313C22×Dic3—51no—
314C22×Dic3—51no—
315C22×Dic3C22×D512yes—
316C2×D12—24no—
317C2×D12—58no—
318C2×D12—108no—
319C2×D12C22×D514yes—
320C2×C4×D3—54no—
321C2×C4×D3—58no—
322C2×C4×D3—58no—
323C2×C4×D3—104no—
324C2×C4×D3—204no—
325C2×C4×D3—204no—
326C3×C4⋊C4—54no—
327C3×C4⋊C4—54no—
328C3×C22⋊C4—58no—
329C3×C42—58no—
330#217—54no—
331(C2×D3)⋊C4—58no—
332(C2×D3)⋊C4—58no—
333(C2×D3)⋊C4—54no—
334(C2×D3)⋊C4C22×D518yes—
335C4⋊Dic3—58no—
336C4⋊Dic3C22×D514yes—
337Dic3⋊C4—54no—
338Dic3⋊C4—58no—
339Dic3⋊C4—58no—
340C4×Dic3—54no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—34no—
345C23×C5—64no—
346C23×C5—64no—
347C23×C5—64no—
348C23×C5C23×D312yes—
349C23×C5C23×D311yescharacteristic
350C22×D5—34no—
351C22×D5—32no—
352C22×D5—62no—
353C22×D5—62no—
354C5×D4—68no—
355C5×D4—128no—
356C2×C4×C5—22no—
357C2×C4×C5—28no—
358C2×C4×C5—34no—
359C2×C4×C5—64no—
360C2×C4×C5#23514yes—
361C2×C4×C5C23×D312yes—
362C2×C4×C5C23×D312yes—
363C22⋊D5—616no—
364C22⋊D5—68no—
365C2×Dic5—24no—
366C2×Dic5—24no—
367C2×Dic5—32no—
368C2×Dic5—32no—
369C2×Dic5—32no—
370C2×Dic5—62no—
371C2×Dic5—62no—
372C2×Dic5—62no—
373C2×Dic5—128no—
374C2×Dic5C23×D314yes—
375C2×Dic5C23×D314yes—
376C4×D5—68no—
377C4×D5—128no—
378C22×D4—32no—
379C22×D4—31no—
380C22×D4—152no—
381C22×D4—151no—
382C23×C4—152no—
383C23×C4—152no—
384C23×C4—151no—
385C23×C4D3×D511yescharacteristic
386#126—1516no—
387#125—158no—
388#123—1516no—
389#121—38no—
390#121—1516no—
391#121—158no—
392C4×D4—1516no—
393C4×D4—158no—
394C4×D4—158no—
395#117—58no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—51no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—158no—
400C2×C4⋊C4—152no—
401C2×C4⋊C4—152no—
402C2×C4⋊C4—152no—
403C2×C4⋊C4—151no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—52no—
406C2×C22⋊C4—152no—
407C2×C22⋊C4—152no—
408C2×C22⋊C4—151no—
409C2×C22⋊C4—151no—
410C2×C42—52no—
411C2×C42—151no—
412C2×C3×C5—42no—
413C2×C3×C5#55314yescomplemented
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C22×#4111yescharacteristic
416C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
417D15—24no—
418C5×D3—44no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3C23×D512yes—
423C23×C3C23×D511yescharacteristic
424C22×D3—24no—
425C22×D3—24no—
426C22×D3—24no—
427C22×D3—54no—
428C22×D3—52no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3C23×D514yes—
432C2×C3×C4—22no—
433C2×C3×C4—28no—
434C2×C3×C4—54no—
435C2×C3×C4—54no—
436C2×C3×C4—104no—
437C2×C3×C4—104no—
438C2×C3×C4#71114yes—
439C2×C3×C4C23×D512yes—
440C2×C3×C4C23×D512yes—
441#67—48no—
442#67—108no—
443C2×Dic3—24no—
444C2×Dic3—52no—
445C2×Dic3—52no—
446C2×Dic3—52no—
447C2×Dic3—102no—
448C2×Dic3—102no—
449C2×Dic3—102no—
450C2×Dic3C23×D514yes—
451D12—28no—
452D12—1016no—
453C4×D3—108no—
454C4×D3—208no—
455C4×D3—208no—
456C22×C5—22no—
457C22×C5—22no—
458C22×C5—22no—
459C22×C5—44no—
460C22×C5—64no—
461C22×C5—64no—
462C22×C5—64no—
463C22×C5—128no—
464C22×C5C2×#23512yes—
465C22×C5D3×#4112yes—
466C22×C5#100912yes—
467C22×C5C24×D311yescharacteristic
468C2×D5—34no—
469C2×D5—62no—
470C2×D5—62no—
471C2×D5—68no—
472C4×C5—22no—
473C4×C5—64no—
474C4×C5C2×#23514yes—
475Dic5—24no—
476Dic5—24no—
477Dic5—62no—
478Dic5—62no—
479Dic5—62no—
480C24—32no—
481C24—151no—
482C24C2×D3×D511yescharacteristic
483C2×D4—38no—
484C2×D4—34no—
485C2×D4—64no—
486C2×D4—124no—
487C2×D4—158no—
488C2×D4—154no—
489C2×D4—308no—
490C2×D4—304no—
491C22×C4—24no—
492C22×C4—32no—
493C22×C4—52no—
494C22×C4—52no—
495C22×C4—158no—
496C22×C4—158no—
497C22×C4—151no—
498C22×C4—151no—
499C22×C4—151no—
500C22×C4—154no—
501C22×C4—304no—
502C22×C4—604no—
503C22×C4—604no—
504C22×C4C2×D3×D514yes—
505C22×C4C2×D3×D511yescharacteristic
506C22×C4C2×D3×D511yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—54no—
509C4⋊C4—54no—
510C4⋊C4—158no—
511C4⋊C4—158no—
512C4⋊C4—158no—
513C4⋊C4—154no—
514C22⋊C4—38no—
515C22⋊C4—58no—
516C22⋊C4—158no—
517C22⋊C4—158no—
518C22⋊C4—154no—
519C22⋊C4—154no—
520C42—58no—
521C42—154no—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—44no—
527C22×C3C2×#71112yes—
528C22×C3#414412yes—
529C22×C3D5×#4112yes—
530C22×C3C24×D511yescharacteristic
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—48no—
535C2×D3—54no—
536C2×D3—108no—
537C2×D3—102no—
538C2×D3—102no—
539C3×C4—22no—
540C3×C4—104no—
541C3×C4—104no—
542C3×C4C2×#71114yes—
543Dic3—24no—
544Dic3—102no—
545Dic3—102no—
546Dic3—102no—
547C2×C5—42no—
548C2×C5—124no—
549C2×C5#553014yescomplemented
550C2×C5C22×#23511yescharacteristic
551C2×C5C2×D3×#4111yescharacteristic
552C2×C5C2×#100911yescharacteristic
553D5—64no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—34no—
558C23—64no—
559C23—64no—
560C23—64no—
561C23—154no—
562C23—152no—
563C23—302no—
564C23—302no—
565C23C22×D3×D512yes—
566C23C22×D3×D511yescharacteristic
567D4—68no—
568D4—128no—
569D4—3016no—
570D4—308no—
571C2×C4—22no—
572C2×C4—28no—
573C2×C4—34no—
574C2×C4—54no—
575C2×C4—54no—
576C2×C4—64no—
577C2×C4—104no—
578C2×C4—104no—
579C2×C4—152no—
580C2×C4—152no—
581C2×C4—152no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4—302no—
585C2×C4—308no—
586C2×C4—608no—
587C2×C4—608no—
588C2×C4#678214yes—
589C2×C4C22×D3×D512yes—
590C2×C4C22×D3×D512yes—
591C2×C3—42no—
592C2×C3#6594814yescomplemented
593C2×C3C22×#71111yescharacteristic
594C2×C3C2×#414411yescharacteristic
595C2×C3C2×D5×#4111yescharacteristic
596D3—44no—
597D3—104no—
598C5C2×#553011yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—44no—
603C22—64no—
604C22—64no—
605C22—64no—
606C22—128no—
607C22—154no—
608C22—302no—
609C22—302no—
610C22—308no—
611C22#9201612yes—
612C22#9201812yes—
613C22C2×#678212yes—
614C22C23×D3×D511yescharacteristic
615C4—22no—
616C4—64no—
617C4—104no—
618C4—104no—
619C4—302no—
620C4—302no—
621C4—302no—
622C4C2×#678214yes—
623C3C2×#6594811yescharacteristic, complemented, Sylow
624C2—42no—
625C2—124no—
626C2—304no—
627C2#1175446714yesdirect product factor
628C2C2×#9201611yescharacteristic
629C2C2×#9201811yescharacteristic
630C2C22×#678211yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#553
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. C2×C4×#1220C2semidirect
2. C2×C5×#930C2semidirect
3. C2×C3×#4072C2semidirect
4. C2×#91557C2semidirect
5. C2×#91555C2semidirect
6. C2×#91466C2semidirect
7. #11754467C2direct (N × H)
8. C2×#91437C2semidirect
9. C2×#91435C2semidirect
10. C2×#91405C2semidirect
11. C2×#91384C2semidirect
12. C2×#91372C2semidirect
23. C4×#1220C22semidirect
27. C5×#930C22semidirect
31. C3×#4072C22semidirect
35. #91557C22semidirect
36. #91555C22semidirect
42. #91466C22semidirect
43. #91437C22semidirect
44. #91435C22semidirect
45. #91405C22semidirect
46. #91384C22semidirect
47. #91372C22semidirect
55. C2×#4072D3semidirect
104. C2×#930D5semidirect
136. #4072C2×D3semidirect
201. #930C2×D5semidirect
413. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
549. C2×C5#5530semidirect
592. C2×C3#65948semidirect
598. C5C2×#5530semidirect
623. C3C2×#65948semidirect
627. C2#11754467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×C5×#9302
C2×C3×#40722
C2×#915572
C2×#915552
C2×#914662
#117544672
C2×#914372
C2×#914352
C2×#914052
C2×#913842
C2×#913722
C2×#659483
C2×#55305