Finite Group Databasebeta

← C2×#11756379 #14495183

Subgroups — C2×#11756379 #14495183

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic, complemented
2C2×#91829C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×#91828C211yesmaximal, characteristic, complemented
5C2×#91827C211yesmaximal, characteristic, complemented
6C2×#91826C211yesmaximal, characteristic, complemented
7C2×#91826C211yesmaximal, characteristic, complemented
8C2×#91819C211yesmaximal, characteristic, complemented
9C2×#91818C211yesmaximal, characteristic, complemented
10#11756379C2116yesmaximal, direct product factor
11C2×#91787C211yesmaximal, characteristic, complemented
12C2×#91783C211yesmaximal, characteristic, complemented
13C2×#91775C211yesmaximal, characteristic, complemented
14C2×#91773C211yesmaximal, characteristic, complemented
15C2×#91771C211yesmaximal, characteristic, complemented
16C2×#91768C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C23×C3×C4×C5C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic
24C22×#1220C2211yescharacteristic
25C22×#1220C2211yescharacteristic
26C22×#1220C2211yescharacteristic
27C22×#1220C2211yescharacteristic
28C22×#1220C2211yescharacteristic, complemented
29C22×#1220C2211yescharacteristic, complemented
30C23×Dic15C2211yescharacteristic, complemented
31C22×D60C2211yescharacteristic
32C22×D60C2211yescharacteristic
33C22×C4×D15C2211yescharacteristic, complemented
34C3×C5×#121C2218yescomplemented
35C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
36C2×C3×C5×C22⋊C4C2211yescharacteristic
37C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
38C2×#6719C2211yescharacteristic
39C2×#6719C2211yescharacteristic
40C2×#6719C2211yescharacteristic, complemented
41#91829C2218yescomplemented
42#91828C2218yescomplemented
43#91828C2218yescomplemented
44#91827C2218yescomplemented
45#91826C2218yescomplemented
46#91826C2218yescomplemented
47#91819C2218yescomplemented
48#91818C2218yescomplemented
49C2×#6714C2211yescharacteristic
50C2×#6714C2211yescharacteristic
51C2×#6714C2211yescharacteristic
52C2×#6714C2211yescharacteristic
53C2×#6714C2211yescharacteristic
54C2×#6714C2211yescharacteristic
55C2×#6714C2211yescharacteristic, complemented
56C2×C4⋊Dic15C2211yescharacteristic, complemented
57C2×C4⋊Dic15C2211yescharacteristic, complemented
58C2×#6712C2211yescharacteristic, complemented
59C2×#6712C2211yescharacteristic, complemented
60C2×#6712C2211yescharacteristic, complemented
61C2×C4×Dic15C2211yescharacteristic, complemented
62#91787C2218yescomplemented
63#91783C2218yescomplemented
64#91775C2218yescomplemented
65#91773C2218yescomplemented
66#91771C2218yescomplemented
67#91768C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#121D311yescharacteristic, complemented
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C24×C3×C5C2311yescharacteristic
88C23×D15—42no—
89C23×D15—42no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yes—
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4—42no—
97C2×C3×C5×D4—42no—
98C2×C3×C5×D4C2314yes—
99C2×C3×C5×D4C2314yes—
100C2×C3×C5×D4C2314yescomplemented
101C22×C3×C4×C5—42no—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C22×C3×C4×C5C2311yescharacteristic
105C22×C3×C4×C5C2311yescharacteristic
106C22×C3×C4×C5C2314yescomplemented
107C2×#1220—42no—
108C2×#1220—42no—
109C2×#1220—42no—
110C2×#1220—42no—
111C2×#1220—42no—
112C2×#1220—42no—
113C2×#1220—42no—
114C2×#1220C2314yes—
115C2×#1220C2314yes—
116C2×#1220C2314yes—
117C2×#1220C2314yes—
118C2×#1220C2314yes—
119C2×#1220C2314yescomplemented
120C2×#1220C2314yescomplemented
121C22×Dic15—42no—
122C22×Dic15C2311yescharacteristic
123C22×Dic15C2311yescharacteristic
124C22×Dic15C2311yescharacteristic
125C22×Dic15C2311yescharacteristic
126C22×Dic15C2311yescharacteristic
127C22×Dic15C2314yescomplemented
128C2×D60—42no—
129C2×D60—42no—
130C2×D60C2314yes—
131C2×D60C2314yes—
132C2×C4×D15—42no—
133C2×C4×D15C2314yescomplemented
134C3×C5×C4⋊C4C2314yescomplemented
135C3×C5×C22⋊C4C2314yes—
136C3×C5×C22⋊C4C2314yescomplemented
137#6719C2314yes—
138#6719C2314yes—
139#6719C2314yescomplemented
140#6714C2314yes—
141#6714C2314yes—
142#6714C2314yes—
143#6714C2314yes—
144#6714C2314yes—
145#6714C2314yes—
146#6714C2314yescomplemented
147C4⋊Dic15C2314yescomplemented
148C4⋊Dic15C2314yescomplemented
149#6712C2314yescomplemented
150#6712C2314yescomplemented
151#6712C2314yescomplemented
152C4×Dic15C2314yescomplemented
153C2×C3×#121D511yescharacteristic, complemented
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929—51no—
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4C2×D311yescharacteristic
171C22×C5×D4C2×D311yescharacteristic
172C22×C5×D4C2×D311yescharacteristic, complemented
173C23×C4×C5C2×D311yescharacteristic, complemented
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5—31no—
185C5×#121C2×D318yescomplemented
186C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
187C2×C5×C22⋊C4C2×D311yescharacteristic
188C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083—38no—
198#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685—31no—
206C2×#685—31no—
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5C2412yes—
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—44no—
243C22×D15—44no—
244C22×D15—44no—
245C22×D15—416no—
246C22×D15C2412yes—
247C22×D15C2412yes—
248C22×D15C2412yes—
249C3×C5×D4—44no—
250C3×C5×D4—44no—
251C3×C5×D4—44no—
252C2×C3×C4×C5—22no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5—22no—
255C2×C3×C4×C5—22no—
256C2×C3×C4×C5—44no—
257C2×C3×C4×C5C2412yes—
258C2×C3×C4×C5C2412yes—
259C2×C3×C4×C5C2412yes—
260C2×C3×C4×C5C2412yes—
261#1220—44no—
262#1220—44no—
263#1220—44no—
264#1220—44no—
265#1220—44no—
266#1220—44no—
267#1220—44no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15—22no—
272C2×Dic15—22no—
273C2×Dic15—44no—
274C2×Dic15C2412yes—
275C2×Dic15C2412yes—
276C2×Dic15C2412yes—
277C2×Dic15C2412yes—
278C2×Dic15C2412yes—
279D60—44no—
280D60—44no—
281C4×D15—44no—
282C24×D3—51no—
283C22×C3×D4C2×D511yescharacteristic
284C22×C3×D4C2×D511yescharacteristic
285C22×C3×D4C2×D511yescharacteristic, complemented
286C23×C3×C4C2×D511yescharacteristic, complemented
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121C2×D518yescomplemented
299C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
300C2×C3×C22⋊C4C2×D511yescharacteristic
301C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
302C2×#217—51no—
303C2×#217—51no—
304C2×#217—51no—
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4—51no—
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5C22×D311yescharacteristic
333C24×C5C22×D311yescharacteristic
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—31no—
337C23×D5—31no—
338C23×D5—34no—
339C23×D5—122no—
340C23×D5—122no—
341C23×D5—122no—
342C2×C5×D4—42no—
343C2×C5×D4—42no—
344C2×C5×D4—42no—
345C2×C5×D4C22×D314yes—
346C2×C5×D4C22×D314yes—
347C2×C5×D4C22×D314yescomplemented
348C22×C4×C5—42no—
349C22×C4×C5C22×D311yescharacteristic
350C22×C4×C5C22×D311yescharacteristic
351C22×C4×C5C22×D311yescharacteristic
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D314yescomplemented
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5—122no—
367C2×C22⋊D5—122no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—31no—
372C22×Dic5—31no—
373C22×Dic5—34no—
374C22×Dic5—122no—
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4C22×D314yescomplemented
382C5×C22⋊C4C22×D314yes—
383C5×C22⋊C4C22×D314yescomplemented
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394C4⋊Dic5—34no—
395C4⋊Dic5—34no—
396#683—34no—
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—151no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121D1511yescharacteristic, complemented
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—22no—
422C22×C3×C5—22no—
423C22×C3×C5—22no—
424C22×C3×C5—22no—
425C22×C3×C5—44no—
426C22×C3×C5—44no—
427C22×C3×C5—44no—
428C22×C3×C5H(5,𝔽2)12yes—
429C22×C3×C5H(5,𝔽2)12yes—
430C22×C3×C5H(5,𝔽2)12yes—
431C22×C3×C5C2511yescharacteristic
432C2×D15—22no—
433C2×D15—22no—
434C2×D15—22no—
435C2×D15—22no—
436C2×D15—22no—
437C2×D15—22no—
438C2×D15—22no—
439C2×D15—22no—
440C2×D15—22no—
441C2×D15—416no—
442C2×D15—44no—
443C2×D15—44no—
444C2×D15—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447C3×C4×C5—22no—
448C3×C4×C5—22no—
449Dic15—22no—
450Dic15—22no—
451Dic15—22no—
452Dic15—22no—
453Dic15—22no—
454C24×C3C22×D511yescharacteristic
455C24×C3C22×D511yescharacteristic
456C24×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—51no—
460C23×D3—54no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3—202no—
464C2×C3×D4—42no—
465C2×C3×D4—42no—
466C2×C3×D4—42no—
467C2×C3×D4C22×D514yes—
468C2×C3×D4C22×D514yes—
469C2×C3×D4C22×D514yescomplemented
470C22×C3×C4—42no—
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D514yescomplemented
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67—202no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—51no—
494C22×Dic3—51no—
495C22×Dic3—54no—
496C22×Dic3—202no—
497C2×D12—54no—
498C2×D12—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4C22×D514yescomplemented
504C3×C22⋊C4C22×D514yes—
505C3×C22⋊C4C22×D514yescomplemented
506#217—54no—
507#217—54no—
508#217—54no—
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515(C2×D3)⋊C4—54no—
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—22no—
528C23×C5—22no—
529C23×C5—22no—
530C23×C5—22no—
531C23×C5C23×D312yes—
532C23×C5C23×D312yes—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—32no—
536C22×D5—32no—
537C22×D5—32no—
538C22×D5—62no—
539C22×D5—62no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—62no—
547C22×D5—124no—
548C22×D5—124no—
549C22×D5—124no—
550C22×D5—1216no—
551C5×D4—44no—
552C5×D4—44no—
553C5×D4—44no—
554C2×C4×C5—22no—
555C2×C4×C5—22no—
556C2×C4×C5—22no—
557C2×C4×C5—22no—
558C2×C4×C5—44no—
559C2×C4×C5C23×D312yes—
560C2×C4×C5C23×D312yes—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—124no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—62no—
579C2×Dic5—62no—
580C2×Dic5—124no—
581D20—124no—
582D20—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—151no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4C2×D1511yescharacteristic
595C22×D4C2×D1511yescharacteristic
596C22×D4C2×D1511yescharacteristic, complemented
597C23×C4—151no—
598C23×C4—151no—
599C23×C4C2×D1511yescharacteristic, complemented
600#127—158no—
601#126—158no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—158no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121C2×D1518yescomplemented
612#120—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—151no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4C2×D1511yescharacteristic, complemented
621C2×C22⋊C4—151no—
622C2×C22⋊C4—151no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4—151no—
625C2×C22⋊C4—151no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4C2×D1511yescharacteristic
632C2×C22⋊C4C2×D1511yescharacteristic, complemented
633C2×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5—42no—
636C2×C3×C5—42no—
637C2×C3×C5#56014yescomplemented
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
641D15—42no—
642D15—42no—
643D15—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3C23×D512yes—
654C23×C3C23×D512yes—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—52no—
658C22×D3—52no—
659C22×D3—52no—
660C22×D3—102no—
661C22×D3—102no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—204no—
672C22×D3—2016no—
673C3×D4—44no—
674C3×D4—44no—
675C3×D4—44no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—44no—
681C2×C3×C4C23×D512yes—
682C2×C3×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—52no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—102no—
700C2×Dic3—102no—
701C2×Dic3—102no—
702C2×Dic3—204no—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—22no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—44no—
716C22×C5—44no—
717C22×C5—44no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100912yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—62no—
723C2×D5—62no—
724C2×D5—62no—
725C2×D5—62no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—1216no—
732C2×D5—124no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—22no—
738C4×C5—22no—
739Dic5—62no—
740Dic5—62no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—151no—
745C24—151no—
746C24—151no—
747C24—154no—
748C24—602no—
749C24—602no—
750C24—602no—
751C24C22×D1511yescharacteristic
752C24C22×D1511yescharacteristic
753C24C22×D1511yescharacteristic
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—154no—
758C2×D4—154no—
759C2×D4—154no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—602no—
767C2×D4—602no—
768C2×D4—602no—
769C2×D4—602no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4C22×D1514yes—
776C2×D4C22×D1514yes—
777C2×D4C22×D1514yescomplemented
778C22×C4—42no—
779C22×C4—151no—
780C22×C4—151no—
781C22×C4—151no—
782C22×C4—151no—
783C22×C4—151no—
784C22×C4—154no—
785C22×C4—154no—
786C22×C4—602no—
787C22×C4—602no—
788C22×C4C22×D1511yescharacteristic
789C22×C4C22×D1511yescharacteristic
790C22×C4C22×D1511yescharacteristic
791C22×C4C22×D1511yescharacteristic
792C22×C4C22×D1514yescomplemented
793C4⋊C4—154no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4C22×D1514yescomplemented
799C22⋊C4—154no—
800C22⋊C4—154no—
801C22⋊C4—154no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4C22×D1514yes—
810C22⋊C4C22×D1514yescomplemented
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—44no—
823C22×C3—44no—
824C22×C3—44no—
825C22×C3#414412yes—
826C22×C3#414412yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—102no—
830C2×D3—102no—
831C2×D3—102no—
832C2×D3—102no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—2016no—
839C2×D3—204no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—22no—
846Dic3—102no—
847Dic3—102no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—42no—
853C2×C5—42no—
854C2×C5#562014yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100911yescharacteristic
858D5—122no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—152no—
871C23—152no—
872C23—152no—
873C23—302no—
874C23—302no—
875C23—302no—
876C23—302no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—604no—
883C23—604no—
884C23—604no—
885C23—6016no—
886C23C23×D1512yes—
887C23C23×D1512yes—
888C23C23×D1512yes—
889C23C23×D1511yescharacteristic
890D4—44no—
891D4—44no—
892D4—44no—
893D4—604no—
894D4—604no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—44no—
907C2×C4—152no—
908C2×C4—152no—
909C2×C4—152no—
910C2×C4—152no—
911C2×C4—152no—
912C2×C4—302no—
913C2×C4—302no—
914C2×C4—302no—
915C2×C4—302no—
916C2×C4—302no—
917C2×C4—604no—
918C2×C4—604no—
919C2×C4C23×D1512yes—
920C2×C4C23×D1512yes—
921C2×C4C23×D1512yes—
922C2×C4C23×D1512yes—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—42no—
926C2×C3#6595414yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—202no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—302no—
947C22—302no—
948C22—302no—
949C22—302no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—6016no—
956C22—604no—
957C22—604no—
958C22—604no—
959C22#9209512yes—
960C22#9209512yes—
961C22#9210012yes—
962C22C24×D1511yescharacteristic
963C4—22no—
964C4—22no—
965C4—22no—
966C4—22no—
967C4—302no—
968C4—302no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—42no—
975C2—42no—
976C2—602no—
977C2—602no—
978C2—602no—
979C2#1175637914yesdirect product factor
980C2C2×#9209511yescharacteristic
981C2C2×#9209511yescharacteristic
982C2C2×#9210011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×#121D15
hypocenterC3×C5C2×#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#121C2semidirect
2. C2×#91829C2semidirect
3. C2×#91828C2semidirect
4. C2×#91828C2semidirect
5. C2×#91827C2semidirect
6. C2×#91826C2semidirect
7. C2×#91826C2semidirect
8. C2×#91819C2semidirect
9. C2×#91818C2semidirect
10. #11756379C2direct (N × H)
11. C2×#91787C2semidirect
12. C2×#91783C2semidirect
13. C2×#91775C2semidirect
14. C2×#91773C2semidirect
15. C2×#91771C2semidirect
16. C2×#91768C2semidirect
21. C22×C3×C5×D4C22semidirect
22. C23×C3×C4×C5C22semidirect
28. C22×#1220C22semidirect
29. C22×#1220C22semidirect
30. C23×Dic15C22semidirect
33. C22×C4×D15C22semidirect
34. C3×C5×#121C22semidirect
35. C2×C3×C5×C4⋊C4C22semidirect
37. C2×C3×C5×C22⋊C4C22semidirect
40. C2×#6719C22semidirect
41. #91829C22semidirect
42. #91828C22semidirect
43. #91828C22semidirect
44. #91827C22semidirect
45. #91826C22semidirect
46. #91826C22semidirect
47. #91819C22semidirect
48. #91818C22semidirect
55. C2×#6714C22semidirect
56. C2×C4⋊Dic15C22semidirect
57. C2×C4⋊Dic15C22semidirect
58. C2×#6712C22semidirect
59. C2×#6712C22semidirect
60. C2×#6712C22semidirect
61. C2×C4×Dic15C22semidirect
62. #91787C22semidirect
63. #91783C22semidirect
64. #91775C22semidirect
65. #91773C22semidirect
66. #91771C22semidirect
67. #91768C22semidirect
69. C2×C5×#121D3semidirect
100. C2×C3×C5×D4C23semidirect
106. C22×C3×C4×C5C23semidirect
119. C2×#1220C23semidirect
120. C2×#1220C23semidirect
127. C22×Dic15C23semidirect
133. C2×C4×D15C23semidirect
134. C3×C5×C4⋊C4C23semidirect
136. C3×C5×C22⋊C4C23semidirect
139. #6719C23semidirect
146. #6714C23semidirect
147. C4⋊Dic15C23semidirect
148. C4⋊Dic15C23semidirect
149. #6712C23semidirect
150. #6712C23semidirect
151. #6712C23semidirect
152. C4×Dic15C23semidirect
153. C2×C3×#121D5semidirect
172. C22×C5×D4C2×D3semidirect
173. C23×C4×C5C2×D3semidirect
185. C5×#121C2×D3semidirect
186. C2×C5×C4⋊C4C2×D3semidirect
188. C2×C5×C22⋊C4C2×D3semidirect
285. C22×C3×D4C2×D5semidirect
286. C23×C3×C4C2×D5semidirect
298. C3×#121C2×D5semidirect
299. C2×C3×C4⋊C4C2×D5semidirect
301. C2×C3×C22⋊C4C2×D5semidirect
347. C2×C5×D4C22×D3semidirect
353. C22×C4×C5C22×D3semidirect
381. C5×C4⋊C4C22×D3semidirect
383. C5×C22⋊C4C22×D3semidirect
412. C2×#121D15semidirect
469. C2×C3×D4C22×D5semidirect
475. C22×C3×C4C22×D5semidirect
503. C3×C4⋊C4C22×D5semidirect
505. C3×C22⋊C4C22×D5semidirect
596. C22×D4C2×D15semidirect
599. C23×C4C2×D15semidirect
611. #121C2×D15semidirect
620. C2×C4⋊C4C2×D15semidirect
632. C2×C22⋊C4C2×D15semidirect
637. C2×C3×C5#560semidirect
777. C2×D4C22×D15semidirect
792. C22×C4C22×D15semidirect
798. C4⋊C4C22×D15semidirect
810. C22⋊C4C22×D15semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5620semidirect
926. C2×C3#65954semidirect
933. C5C2×#5620semidirect
972. C3C2×#65954semidirect
979. C2#11756379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1212
C2×#918292
C2×#918282
C2×#918272
C2×#918262
C2×#918192
C2×#918182
#117563792
C2×#917872
C2×#917832
C2×#917752
C2×#917732
C2×#917712
C2×#917682
C2×#659543
C2×#56205