Finite Group Databasebeta

← C2×#11753214 #14480332

Subgroups — C2×#11753214 #14480332

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×D5×D12C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#882C211yesmaximal, characteristic, complemented
5C2×C3×#4029C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91570C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91466C211yesmaximal, characteristic, complemented
12C2×#91447C211yesmaximal, characteristic, complemented
13C2×#91427C211yesmaximal, characteristic, complemented
14C2×#91423C211yesmaximal, characteristic, complemented
15C2×#91420C211yesmaximal, characteristic, complemented
16#11753214C2116yesmaximal, direct product factor
17C2×#65923—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic
20C23×D3×D5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C22×D60C2211yescharacteristic, complemented
24C22×C4×D15C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C5×D12C2211yescharacteristic
27C22×C5×D12C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic
29C22×C3×C4×D5C2211yescharacteristic, complemented
30C2×D3×C22⋊D5—28no—
31C2×D3×C22⋊D5C2218yescomplemented
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1203C2211yescharacteristic, complemented
36C22×#1201C2211yescharacteristic
37C22×#1200C2211yescharacteristic, complemented
38C22×D3×Dic5C2211yescharacteristic, complemented
39C2×D5×D12—28no—
40C2×D5×D12C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44#91773C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C5×#882C2218yescomplemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C2×C3×#685C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4029C2218yescomplemented
53#91577C2218yescomplemented
54#91570C2218yescomplemented
55#91557C2218yescomplemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64#91473C2218yescomplemented
65#91466C2218yescomplemented
66#91447C2218yescomplemented
67#91427C2218yescomplemented
68#91423C2218yescomplemented
69#91420C2218yescomplemented
70C2×#5653—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×D4×D5—31no—
73C2×C5×#120—31no—
74C2×#4099—31no—
75C2×#4084—31no—
76C2×#4084—31no—
77C2×#4083—31no—
78C2×#4083—31no—
79C2×#4081—31no—
80#65923—316no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4030—31no—
84C2×#4029—31no—
85C2×#4029D311yescharacteristic, complemented
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—42no—
92C23×C5×D3—42no—
93C23×C5×D3C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C5×D3C2314yescomplemented
97C23×C3×D5C2311yescharacteristic
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5—42no—
102C22×D3×D5—42no—
103C22×D3×D5D418yescomplemented
104C22×D3×D5C2314yes—
105C22×D3×D5C2314yescomplemented
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C2×#1220—24no—
109C2×#1220—42no—
110C2×#1220C2314yescomplemented
111C2×#1220C2314yescomplemented
112C22×Dic15C2311yescharacteristic
113C22×Dic15C2311yescharacteristic
114C2×D60—24no—
115C2×D60C2314yescomplemented
116C2×C4×D15—42no—
117C2×C4×D15C2314yescomplemented
118C2×C5×#67—42no—
119C2×C5×#67C2314yescomplemented
120C22×C5×Dic3C2311yescharacteristic
121C2×C5×D12—24no—
122C2×C5×D12—42no—
123C2×C5×D12C2314yes—
124C2×C5×D12C2314yescomplemented
125C2×C3×C22⋊D5—24no—
126C2×C3×C22⋊D5C2314yes—
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2311yescharacteristic
130C2×C3×C4×D5—24no—
131C2×C3×C4×D5C2314yescomplemented
132D3×C22⋊D5—232no—
133C2×#1203—24no—
134C2×#1203—24no—
135C2×#1203—24no—
136C2×#1203—42no—
137C2×#1203C2314yes—
138C2×#1203C2314yescomplemented
139C2×#1203C2314yescomplemented
140C2×#1203C2314yescomplemented
141C2×#1201—24no—
142C2×#1201C2314yes—
143C2×#1200—42no—
144C2×#1200C2314yescomplemented
145C2×D3×Dic5—24no—
146C2×D3×Dic5C2314yescomplemented
147D5×D12—232no—
148C3×C5×C22⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6712C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C3×C22⋊Dic5C2314yescomplemented
154C3×#685C2314yescomplemented
155C3×C4⋊Dic5C2314yescomplemented
156C3×#683C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6667C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
161(C2×D3)⋊Dic5C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C23×D12—51no—
166C2×C3×#123—51no—
167C2×#937—51no—
168C2×#929—51no—
169#5653—516no—
170C2×#895—51no—
171C2×#895—51no—
172C2×#894—51no—
173C2×#894—51no—
174C2×#884—51no—
175C2×#884—51no—
176C2×#882—51no—
177C2×#882—51no—
178C2×#882D511yescharacteristic, complemented
179C2×D3×C22⋊C4—51no—
180C25×C5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C5×D4—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—38no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—31no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5—31no—
194C22×C22⋊D5—68no—
195C22×C22⋊D5C2×D311yescharacteristic
196C23×Dic5—31no—
197C2×D4×D5—38no—
198C2×D4×D5—68no—
199C22×D20—31no—
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#120—38no—
204C2×C5×C22⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
207#4099—38no—
208C2×C22⋊Dic5—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211C2×C22⋊Dic5—31no—
212C2×C22⋊Dic5C2×D311yescharacteristic, complemented
213#4084—38no—
214#4084—38no—
215#4083—38no—
216#4083—38no—
217#4081—38no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685C2×D311yescharacteristic, complemented
222C2×C4⋊Dic5—31no—
223C2×C4⋊Dic5C2×D311yescharacteristic, complemented
224C2×#683—31no—
225C2×#683C2×D311yescharacteristic, complemented
226#4032—38no—
227#4030—38no—
228#4030—38no—
229#4029—38no—
230#4029C2×D318yescomplemented
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15C2×D414yes—
244C22×D15C2412yes—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—22no—
251C22×C5×D3—22no—
252C22×C5×D3—22no—
253C22×C5×D3—22no—
254C22×C5×D3—28no—
255C22×C5×D3—44no—
256C22×C5×D3—44no—
257C22×C5×D3—416no—
258C22×C5×D3C2×D414yes—
259C22×C5×D3C2412yes—
260C22×C5×D3C2412yes—
261C22×C5×D3C2412yes—
262C22×C3×D5—22no—
263C22×C3×D5—22no—
264C22×C3×D5C2×D414yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—416no—
268C2×D3×D5—44no—
269C2×D3×D5—44no—
270C2×D3×D5—44no—
271C2×D3×D5—44no—
272C2×D3×D5—416no—
273C2×D3×D5C2×D4116yescomplemented
274C2×C3×C4×C5—22no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277C2×C3×C4×C5C2412yes—
278#1220—28no—
279#1220—44no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284D60—28no—
285C4×D15—44no—
286C5×#67—44no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3C2412yes—
289C5×D12—28no—
290C5×D12—44no—
291C3×C22⋊D5—28no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297C2×C3×Dic5C2412yes—
298C3×C4×D5—28no—
299#1203—28no—
300#1203—28no—
301#1203—28no—
302#1203—44no—
303#1201—28no—
304#1200—44no—
305D3×Dic5—28no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3C2×D511yescharacteristic, complemented
309C22×C3×D4—51no—
310C23×C3×C4—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67C2×D511yescharacteristic, complemented
315C2×D3×D4—58no—
316C2×D3×D4—108no—
317C22×D12—51no—
318C22×D12—51no—
319C22×D12—51no—
320C22×D12—51no—
321C22×D12—51no—
322C22×D12—58no—
323C22×D12—108no—
324C22×D12C2×D511yescharacteristic
325C22×D12C2×D511yescharacteristic, complemented
326C22×C4×D3—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C3×#123—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C4⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4—51no—
334C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
335C2×#217—51no—
336#937—58no—
337#929—58no—
338C2×(C2×D3)⋊C4—51no—
339C2×(C2×D3)⋊C4—51no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
345C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
346C2×Dic3⋊C4—51no—
347C2×Dic3⋊C4—51no—
348#895—58no—
349#895—58no—
350#894—58no—
351#894—58no—
352#884—58no—
353#884—58no—
354#882—58no—
355#882—58no—
356#882C2×D518yescomplemented
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5—31no—
360C24×C5—31no—
361C24×C5—34no—
362C24×C5—64no—
363C24×C5—122no—
364C24×C5—122no—
365C24×C5C22×D311yescharacteristic
366C23×D5—31no—
367C23×D5—38no—
368C23×D5—34no—
369C23×D5—31no—
370C23×D5—34no—
371C23×D5—64no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5—122no—
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—34no—
378C2×C5×D4—34no—
379C2×C5×D4—34no—
380C2×C5×D4—64no—
381C2×C5×D4—122no—
382C2×C5×D4—122no—
383C22×C4×C5—31no—
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—24no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—34no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—632no—
398C2×C22⋊D5—64no—
399C2×C22⋊D5—64no—
400C2×C22⋊D5—122no—
401C2×C22⋊D5—122no—
402C2×C22⋊D5C22×D314yes—
403C22×Dic5—31no—
404C22×Dic5—31no—
405C22×Dic5—34no—
406C22×Dic5—64no—
407C22×Dic5C22×D311yescharacteristic
408C22×Dic5C22×D311yescharacteristic
409C22×Dic5C22×D311yescharacteristic
410D4×D5—632no—
411C2×D20—34no—
412C2×D20—64no—
413C2×C4×D5—24no—
414C2×C4×D5—34no—
415C2×C4×D5—34no—
416C2×C4×D5—122no—
417C2×C4×D5—122no—
418C2×C4×D5C22×D314yescomplemented
419C5×C22⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4C22×D314yescomplemented
422C22⋊Dic5—34no—
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425C22⋊Dic5—34no—
426C22⋊Dic5C22×D314yescomplemented
427#685—34no—
428#685—34no—
429#685—34no—
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4⋊Dic5C22×D314yescomplemented
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—51no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—31no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—44no—
455C22×C3×C5C22×D412yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5H(5,𝔽2)12yes—
458C22×C3×C5C2511yescharacteristic
459C2×D15—28no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—44no—
466C2×D15C22×D414yes—
467C2×C5×D3—28no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3—22no—
476C2×C5×D3—416no—
477C2×C5×D3—44no—
478C2×C5×D3—44no—
479C2×C5×D3C22×D414yes—
480C2×C3×D5—28no—
481C2×C3×D5—22no—
482C2×C3×D5—22no—
483C2×C3×D5C22×D414yes—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488Dic15—22no—
489Dic15—22no—
490C3×Dic5—22no—
491C3×Dic5—22no—
492C3×Dic5—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3C22×D511yescharacteristic
496C23×D3—24no—
497C23×D3—42no—
498C23×D3—42no—
499C23×D3—51no—
500C23×D3—58no—
501C23×D3—54no—
502C23×D3—51no—
503C23×D3—54no—
504C23×D3—104no—
505C23×D3—202no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3C22×D511yescharacteristic
510C23×D3C22×D511yescharacteristic
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D514yescomplemented
513C2×C3×D4—54no—
514C2×C3×D4—104no—
515C22×C3×C4—51no—
516C22×C3×C4—51no—
517C22×C3×C4—51no—
518C22×C3×C4—54no—
519C22×C3×C4—104no—
520C22×C3×C4C22×D511yescharacteristic
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—42no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—104no—
527C2×#67—104no—
528C2×#67—202no—
529C2×#67C22×D514yescomplemented
530C22×Dic3—51no—
531C22×Dic3—51no—
532C22×Dic3C22×D511yescharacteristic
533D3×D4—1032no—
534C2×D12—24no—
535C2×D12—42no—
536C2×D12—54no—
537C2×D12—54no—
538C2×D12—54no—
539C2×D12—54no—
540C2×D12—54no—
541C2×D12—1032no—
542C2×D12—104no—
543C2×D12—104no—
544C2×D12—104no—
545C2×D12—104no—
546C2×D12—202no—
547C2×D12C22×D514yes—
548C2×D12C22×D514yescomplemented
549C2×C4×D3—54no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×C4×D3—202no—
554C2×C4×D3—202no—
555C3×C4⋊C4—54no—
556C3×C4⋊C4—54no—
557C3×C22⋊C4—54no—
558C3×C22⋊C4—54no—
559C3×C22⋊C4C22×D514yescomplemented
560#217—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4—54no—
567(C2×D3)⋊C4C22×D514yescomplemented
568(C2×D3)⋊C4C22×D514yescomplemented
569Dic3⋊C4—54no—
570Dic3⋊C4—54no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—34no—
575C23×C5—32no—
576C23×C5—32no—
577C23×C5—32no—
578C23×C5—68no—
579C23×C5—62no—
580C23×C5—62no—
581C23×C5—62no—
582C23×C5—62no—
583C23×C5—62no—
584C23×C5—62no—
585C23×C5—62no—
586C23×C5—62no—
587C23×C5—124no—
588C23×C5—124no—
589C23×C5—1216no—
590C23×C5C23×D312yes—
591C23×C5C23×D311yescharacteristic
592C22×D5—22no—
593C22×D5—22no—
594C22×D5—34no—
595C22×D5—32no—
596C22×D5—316no—
597C22×D5—32no—
598C22×D5—62no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—62no—
602C22×D5—62no—
603C22×D5—68no—
604C22×D5—1216no—
605C22×D5—124no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—1216no—
610C22×D5D3×D414yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C5×D4—124no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—22no—
617C2×C4×C5—32no—
618C2×C4×C5—62no—
619C2×C4×C5C23×D312yes—
620C2×C4×C5C23×D312yes—
621C22⋊D5—28no—
622C22⋊D5—68no—
623C22⋊D5—68no—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—124no—
628C22⋊D5—124no—
629C2×Dic5—22no—
630C2×Dic5—22no—
631C2×Dic5—22no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—68no—
635C2×Dic5—62no—
636C2×Dic5—62no—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639C2×Dic5C23×D312yes—
640D20—68no—
641C4×D5—28no—
642C4×D5—124no—
643C4×D5—124no—
644C25—31no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—31no—
650C22×D4—51no—
651C22×D4—158no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4—308no—
663C23×C4—51no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667#123—58no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—158no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—38no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—51no—
680C2×C4⋊C4—51no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—158no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4D3×D511yescharacteristic, complemented
696C2×C3×C5—42no—
697C2×C3×C5#53414yescomplemented
698C2×C3×C5C23×D411yescharacteristic
699C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701D15—24no—
702D15—42no—
703C3×D5—24no—
704C5×D3—24no—
705C5×D3—42no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—54no—
711C23×C3—52no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3C23×D512yes—
715C23×C3C23×D511yescharacteristic
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—28no—
725C22×D3—44no—
726C22×D3—44no—
727C22×D3—416no—
728C22×D3—54no—
729C22×D3—52no—
730C22×D3—516no—
731C22×D3—52no—
732C22×D3—108no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—102no—
738C22×D3—2016no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—204no—
743C22×D3—2016no—
744C22×D3D4×D514yes—
745C22×D3C23×D512yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—52no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—108no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—102no—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—44no—
761#67—108no—
762#67—108no—
763#67—204no—
764C2×Dic3—22no—
765C2×Dic3—52no—
766C2×Dic3—52no—
767C2×Dic3—102no—
768C2×Dic3—102no—
769C2×Dic3C23×D512yes—
770D12—28no—
771D12—44no—
772D12—108no—
773D12—108no—
774D12—108no—
775D12—108no—
776D12—204no—
777C4×D3—108no—
778C4×D3—204no—
779C4×D3—204no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—34no—
784C22×C5—44no—
785C22×C5—68no—
786C22×C5—62no—
787C22×C5—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—62no—
791C22×C5—62no—
792C22×C5—62no—
793C22×C5—62no—
794C22×C5—1216no—
795C22×C5—124no—
796C22×C5—124no—
797C22×C5C2×D3×D412yes—
798C22×C5#100912yes—
799C22×C5#100912yes—
800C22×C5C24×D311yescharacteristic
801C2×D5—28no—
802C2×D5—22no—
803C2×D5—22no—
804C2×D5—34no—
805C2×D5—68no—
806C2×D5—62no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—62no—
818Dic5—22no—
819Dic5—22no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—31no—
826C24—34no—
827C24—51no—
828C24—64no—
829C24—122no—
830C24—122no—
831C24—154no—
832C24—158no—
833C24—154no—
834C24—151no—
835C24—151no—
836C24—304no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—34no—
844C2×D4—34no—
845C2×D4—54no—
846C2×D4—64no—
847C2×D4—104no—
848C2×D4—122no—
849C2×D4—122no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—154no—
858C2×D4—304no—
859C2×D4—3032no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—3032no—
864C2×D4—304no—
865C2×D4—304no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—51no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—54no—
873C22×C4—104no—
874C22×C4—154no—
875C22×C4—154no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—154no—
879C22×C4—304no—
880C22×C4—602no—
881C22×C4—602no—
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—54no—
885C4⋊C4—54no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—54no—
891C22⋊C4—54no—
892C22⋊C4—154no—
893C22⋊C4—154no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4C2×D3×D514yescomplemented
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—44no—
905C22×C3—54no—
906C22×C3—108no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3C2×D4×D512yes—
910C22×C3#414412yes—
911C22×C3#414412yes—
912C22×C3C24×D511yescharacteristic
913C2×D3—28no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—416no—
923C2×D3—44no—
924C2×D3—44no—
925C2×D3—54no—
926C2×D3—108no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—102no—
932C2×D3—2016no—
933C2×D3—2016no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—102no—
939C3×C4—102no—
940C3×C4—102no—
941Dic3—22no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—64no—
946C2×C5—122no—
947C2×C5—122no—
948C2×C5#565314yescomplemented
949C2×C5C22×D3×D411yescharacteristic
950C2×C5C2×#100911yescharacteristic
951C2×C5C2×#100911yescharacteristic
952D5—24no—
953D5—64no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—34no—
959C23—32no—
960C23—32no—
961C23—32no—
962C23—54no—
963C23—52no—
964C23—68no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—102no—
974C23—102no—
975C23—124no—
976C23—124no—
977C23—1216no—
978C23—1516no—
979C23—154no—
980C23—152no—
981C23—152no—
982C23—308no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—302no—
987C23—302no—
988C23—604no—
989C23—604no—
990C23—6016no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—124no—
999D4—124no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—32no—
1011C2×C4—52no—
1012C2×C4—52no—
1013C2×C4—52no—
1014C2×C4—62no—
1015C2×C4—108no—
1016C2×C4—102no—
1017C2×C4—102no—
1018C2×C4—102no—
1019C2×C4—152no—
1020C2×C4—152no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—604no—
1025C2×C4—604no—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—104no—
1030C2×C3#6592314yescomplemented
1031C2×C3C22×D4×D511yescharacteristic
1032C2×C3C2×#414411yescharacteristic
1033C2×C3C2×#414411yescharacteristic
1034D3—24no—
1035D3—42no—
1036D3—42no—
1037D3—104no—
1038D3—202no—
1039C5C2×#565311yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—44no—
1045C22—54no—
1046C22—62no—
1047C22—62no—
1048C22—68no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—102no—
1056C22—102no—
1057C22—108no—
1058C22—1216no—
1059C22—124no—
1060C22—124no—
1061C22—154no—
1062C22—302no—
1063C22—302no—
1064C22—308no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22#9201812yes—
1072C22D3×D4×D512yes—
1073C22#9202712yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—62no—
1078C4—102no—
1079C4—102no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6592311yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—64no—
1086C2—104no—
1087C2—122no—
1088C2—122no—
1089C2—304no—
1090C2—602no—
1091C2#1175321414yesdirect product factor
1092C2C2×#9201811yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9202711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×C22⋊D5C2semidirect
2. C22×D5×D12C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#882C2semidirect
5. C2×C3×#4029C2semidirect
6. C2×#91577C2semidirect
7. C2×#91570C2semidirect
8. C2×#91557C2semidirect
9. C2×#91475C2semidirect
10. C2×#91473C2semidirect
11. C2×#91466C2semidirect
12. C2×#91447C2semidirect
13. C2×#91427C2semidirect
14. C2×#91423C2semidirect
15. C2×#91420C2semidirect
16. #11753214C2direct (N × H)
18. C24×C5×D3C22semidirect
20. C23×D3×D5C22semidirect
21. C22×#1220C22semidirect
22. C22×#1220C22semidirect
23. C22×D60C22semidirect
24. C22×C4×D15C22semidirect
25. C22×C5×#67C22semidirect
27. C22×C5×D12C22semidirect
29. C22×C3×C4×D5C22semidirect
31. C2×D3×C22⋊D5C22semidirect
33. C22×#1203C22semidirect
34. C22×#1203C22semidirect
35. C22×#1203C22semidirect
37. C22×#1200C22semidirect
38. C22×D3×Dic5C22semidirect
40. C2×D5×D12C22semidirect
41. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6712C22semidirect
44. #91773C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C5×#882C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4029C22semidirect
53. #91577C22semidirect
54. #91570C22semidirect
55. #91557C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×#6667C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91475C22semidirect
64. #91473C22semidirect
65. #91466C22semidirect
66. #91447C22semidirect
67. #91427C22semidirect
68. #91423C22semidirect
69. #91420C22semidirect
85. C2×#4029D3semidirect
96. C23×C5×D3C23semidirect
103. C22×D3×D5D4semidirect
105. C22×D3×D5C23semidirect
110. C2×#1220C23semidirect
111. C2×#1220C23semidirect
115. C2×D60C23semidirect
117. C2×C4×D15C23semidirect
119. C2×C5×#67C23semidirect
124. C2×C5×D12C23semidirect
131. C2×C3×C4×D5C23semidirect
138. C2×#1203C23semidirect
139. C2×#1203C23semidirect
140. C2×#1203C23semidirect
144. C2×#1200C23semidirect
146. C2×D3×Dic5C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6714C23semidirect
150. #6712C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C3×C22⋊Dic5C23semidirect
154. C3×#685C23semidirect
155. C3×C4⋊Dic5C23semidirect
156. C3×#683C23semidirect
157. Dic3⋊Dic5C23semidirect
158. #6667C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
161. (C2×D3)⋊Dic5C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. #6665C23semidirect
178. C2×#882D5semidirect
202. C22×C4×D5C2×D3semidirect
206. C2×C5×C22⋊C4C2×D3semidirect
212. C2×C22⋊Dic5C2×D3semidirect
221. C2×#685C2×D3semidirect
223. C2×C4⋊Dic5C2×D3semidirect
225. C2×#683C2×D3semidirect
230. #4029C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
308. C24×D3C2×D5semidirect
314. C22×#67C2×D5semidirect
325. C22×D12C2×D5semidirect
334. C2×C3×C22⋊C4C2×D5semidirect
344. C2×(C2×D3)⋊C4C2×D5semidirect
345. C2×(C2×D3)⋊C4C2×D5semidirect
356. #882C2×D5semidirect
418. C2×C4×D5C22×D3semidirect
421. C5×C22⋊C4C22×D3semidirect
426. C22⋊Dic5C22×D3semidirect
430. #685C22×D3semidirect
432. C4⋊Dic5C22×D3semidirect
434. #683C22×D3semidirect
512. C23×D3C22×D5semidirect
529. C2×#67C22×D5semidirect
548. C2×D12C22×D5semidirect
559. C3×C22⋊C4C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
568. (C2×D3)⋊C4C22×D5semidirect
695. C2×C22⋊C4D3×D5semidirect
697. C2×C3×C5#534semidirect
899. C22⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
948. C2×C5#5653semidirect
1030. C2×C3#65923semidirect
1039. C5C2×#5653semidirect
1083. C3C2×#65923semidirect
1091. C2#11753214direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×D5×D122
C2×#917732
C2×C5×#8822
C2×C3×#40292
C2×#915772
C2×#915702
C2×#915572
C2×#914752
C2×#914732
C2×#914662
C2×#914472
C2×#914272
C2×#914232
C2×#914202
#117532142
C2×#659233
C2×#56535