Finite Group Databasebeta

← C2×#11753217 #14480331

Subgroups — C2×#11753217 #14480331

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×#6777C211yesmaximal, characteristic, complemented
3C2×#91772C211yesmaximal, characteristic, complemented
4C2×C5×#882C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91568C211yesmaximal, characteristic, complemented
8C2×#91549C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91457C211yesmaximal, characteristic, complemented
12C2×#91449C211yesmaximal, characteristic, complemented
13C2×#91423C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753217C2116yesmaximal, direct product factor
17C2×#65923—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic
20C23×D3×D5C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic
25C22×C5×D12C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×D20C2211yescharacteristic, complemented
29C22×C3×C4×D5C2211yescharacteristic, complemented
30C2×D3×C22⋊D5—28no—
31C2×D3×C22⋊D5C2218yescomplemented
32C22×#1203C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C22×#1201C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic, complemented
36C22×#1201C2211yescharacteristic, complemented
37C22×D3×Dic5C2211yescharacteristic, complemented
38C22×D5×Dic3C2211yescharacteristic, complemented
39C2×#6777—28no—
40C2×#6777C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
42C2×#6719C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×C4⋊Dic15C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46#91772C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C5×#882C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4030C2218yescomplemented
53#91577C2218yescomplemented
54#91568C2218yescomplemented
55#91549C2218yescomplemented
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
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91457C2218yescomplemented
66#91449C2218yescomplemented
67#91423C2218yescomplemented
68#91408C2218yescomplemented
69#91355C2218yescomplemented
70C2×#5605—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×#4030D311yescharacteristic, complemented
84C2×#4029—31no—
85C2×#4029—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3—24no—
90C23×C5×D3—42no—
91C23×C5×D3—42no—
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2314yescomplemented
96C23×C3×D5C2311yescharacteristic
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×#1220C2314yes—
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2311yescharacteristic
113C2×C4×D15—24no—
114C2×C4×D15C2314yescomplemented
115C2×C5×#67—42no—
116C2×C5×#67C2314yescomplemented
117C22×C5×Dic3C2311yescharacteristic
118C2×C5×D12—24no—
119C2×C5×D12—42no—
120C2×C5×D12C2314yes—
121C2×C5×D12C2314yescomplemented
122C2×C3×C22⋊D5—24no—
123C2×C3×C22⋊D5—42no—
124C2×C3×C22⋊D5C2314yescomplemented
125C2×C3×C22⋊D5C2314yescomplemented
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C2×C3×D20—24no—
129C2×C3×D20C2314yescomplemented
130C2×C3×C4×D5—42no—
131C2×C3×C4×D5C2314yescomplemented
132D3×C22⋊D5—232no—
133C2×#1203—24no—
134C2×#1203C2314yes—
135C2×#1201—24no—
136C2×#1201—24no—
137C2×#1201—24no—
138C2×#1201—42no—
139C2×#1201C2314yes—
140C2×#1201C2314yescomplemented
141C2×#1201C2314yescomplemented
142C2×#1201C2314yescomplemented
143C2×D3×Dic5—24no—
144C2×D3×Dic5C2314yescomplemented
145C2×D5×Dic3—42no—
146C2×D5×Dic3C2314yescomplemented
147#6777—232no—
148C3×C5×C22⋊C4C2314yescomplemented
149#6719C2314yescomplemented
150#6714C2314yescomplemented
151C4⋊Dic15C2314yescomplemented
152#6712C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C3×#685C2314yescomplemented
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—
165C22×D3×D4—51no—
166C2×C3×#121—51no—
167C2×#939—51no—
168C2×#939—51no—
169C2×#937—51no—
170C2×#937—51no—
171C2×#930—51no—
172C22×(C2×D3)⋊C4—51no—
173#5605—516no—
174C2×#894—51no—
175C2×#894—51no—
176C2×#883—51no—
177C2×#883—51no—
178C2×#882—51no—
179C2×#882D511yescharacteristic, complemented
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—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—38no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5—68no—
194C22×C22⋊D5C2×D311yescharacteristic, complemented
195C22×C22⋊D5C2×D311yescharacteristic, complemented
196C23×Dic5—31no—
197C2×D4×D5—38no—
198C2×D4×D5—68no—
199C22×D20C2×D311yescharacteristic, complemented
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⋊Dic5—31no—
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⋊Dic5—31no—
224C2×#683—31no—
225C2×#683C2×D311yescharacteristic, complemented
226#4032—38no—
227#4030—38no—
228#4030C2×D318yescomplemented
229#4029—38no—
230#4029—38no—
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×D15C2×D414yes—
241C22×D15C2412yes—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—28no—
251C22×C5×D3—44no—
252C22×C5×D3—44no—
253C22×C5×D3—416no—
254C22×C5×D3C2×D414yes—
255C22×C5×D3C2412yes—
256C22×C5×D3C2412yes—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5C2×D414yes—
264C22×C3×D5C2412yes—
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—
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284C2×Dic15C2412yes—
285C4×D15—28no—
286C5×#67—44no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3C2412yes—
289C5×D12—28no—
290C5×D12—44no—
291C3×C22⋊D5—28no—
292C3×C22⋊D5—44no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297C3×D20—28no—
298C3×C4×D5—44no—
299#1203—28no—
300#1201—28no—
301#1201—28no—
302#1201—28no—
303#1201—44no—
304D3×Dic5—28no—
305D5×Dic3—44no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3C2×D511yescharacteristic, complemented
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—51no—
312C23×C3×C4—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67C2×D511yescharacteristic, complemented
319C23×Dic3—51no—
320C2×D3×D4—58no—
321C2×D3×D4—58no—
322C2×D3×D4—108no—
323C2×D3×D4—108no—
324C22×D12—51no—
325C22×D12C2×D511yescharacteristic
326C22×D12C2×D511yescharacteristic, complemented
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C3×#121—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
333C2×#217—51no—
334C2×#217—51no—
335#939—58no—
336#939—58no—
337#937—58no—
338#937—58no—
339#930—58no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4—58no—
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
349C2×C4⋊Dic3—51no—
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4—51no—
352#894—58no—
353#894—58no—
354#883—58no—
355#883—58no—
356#882—58no—
357#882C2×D518yescomplemented
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—34no—
370C23×D5—64no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5C22×D311yescharacteristic
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—42no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—632no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—64no—
399C2×C22⋊D5—64no—
400C2×C22⋊D5—122no—
401C2×C22⋊D5C22×D314yescomplemented
402C2×C22⋊D5C22×D314yescomplemented
403C22×Dic5—31no—
404C22×Dic5—31no—
405C22×Dic5—31no—
406C22×Dic5—34no—
407C22×Dic5—64no—
408C22×Dic5C22×D311yescharacteristic
409C22×Dic5C22×D311yescharacteristic
410D4×D5—632no—
411C2×D20—24no—
412C2×D20C22×D314yescomplemented
413C2×C4×D5—34no—
414C2×C4×D5—34no—
415C2×C4×D5—42no—
416C2×C4×D5—64no—
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⋊Dic5—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4⋊Dic5—34no—
433#683—34no—
434#683C22×D314yescomplemented
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—151no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—51no—
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×D15C22×D414yes—
463C2×C5×D3—28no—
464C2×C5×D3—22no—
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—416no—
473C2×C5×D3—44no—
474C2×C5×D3—44no—
475C2×C5×D3C22×D414yes—
476C2×C3×D5—28no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—22no—
482C2×C3×D5—44no—
483C2×C3×D5C22×D414yes—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488Dic15—22no—
489Dic15—22no—
490Dic15—22no—
491C3×Dic5—22no—
492C3×Dic5—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3C22×D511yescharacteristic
497C23×D3—24no—
498C23×D3—42no—
499C23×D3—42no—
500C23×D3—51no—
501C23×D3—58no—
502C23×D3—54no—
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—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—104no—
518C2×C3×D4—202no—
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4—54no—
522C22×C3×C4—202no—
523C22×C3×C4C22×D511yescharacteristic
524C22×C3×C4C22×D511yescharacteristic
525C2×#67—42no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—104no—
535C2×#67—202no—
536C2×#67C22×D514yescomplemented
537C22×Dic3—51no—
538C22×Dic3—51no—
539C22×Dic3—51no—
540C22×Dic3—54no—
541C22×Dic3—202no—
542C22×Dic3C22×D511yescharacteristic
543D3×D4—1032no—
544D3×D4—1032no—
545C2×D12—24no—
546C2×D12—42no—
547C2×D12—54no—
548C2×D12—104no—
549C2×D12C22×D514yes—
550C2×D12C22×D514yescomplemented
551C2×C4×D3—54no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3—104no—
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217—54no—
560(C2×D3)⋊C4—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)⋊C4C22×D514yescomplemented
567(C2×D3)⋊C4C22×D514yescomplemented
568C4⋊Dic3—54no—
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—22no—
595C22×D5—22no—
596C22×D5—22no—
597C22×D5—34no—
598C22×D5—32no—
599C22×D5—316no—
600C22×D5—68no—
601C22×D5—62no—
602C22×D5—62no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—1216no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—1216no—
609C22×D5D3×D414yes—
610C22×D5C23×D312yes—
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—44no—
623C22⋊D5—68no—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—124no—
629C2×Dic5—22no—
630C2×Dic5—22no—
631C2×Dic5—32no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—68no—
635C2×Dic5—62no—
636C2×Dic5—62no—
637C2×Dic5—62no—
638C2×Dic5C23×D312yes—
639C2×Dic5C23×D312yes—
640D20—28no—
641C4×D5—44no—
642C4×D5—68no—
643C4×D5—124no—
644C25—31no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—31no—
650C22×D4—51no—
651C22×D4—51no—
652C22×D4—51no—
653C22×D4—151no—
654C22×D4—158no—
655C22×D4—158no—
656C22×D4—151no—
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—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—58no—
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—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—158no—
687C2×C22⋊C4—151no—
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—
702C3×D5—24no—
703C3×D5—42no—
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—52no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3C23×D512yes—
719C23×C3C23×D511yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—22no—
726C22×D3—22no—
727C22×D3—22no—
728C22×D3—28no—
729C22×D3—44no—
730C22×D3—44no—
731C22×D3—416no—
732C22×D3—54no—
733C22×D3—52no—
734C22×D3—516no—
735C22×D3—108no—
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—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—52no—
754C2×C3×C4—52no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—204no—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—44no—
761#67—108no—
762#67—108no—
763#67—108no—
764#67—108no—
765#67—204no—
766C2×Dic3—22no—
767C2×Dic3—52no—
768C2×Dic3—52no—
769C2×Dic3—52no—
770C2×Dic3—102no—
771C2×Dic3—102no—
772C2×Dic3—102no—
773C2×Dic3—204no—
774C2×Dic3C23×D512yes—
775D12—28no—
776D12—44no—
777D12—108no—
778C4×D3—108no—
779C4×D3—108no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—34no—
784C22×C5—44no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—68no—
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#100412yes—
799C22×C5#100912yes—
800C22×C5C24×D311yescharacteristic
801C2×D5—22no—
802C2×D5—22no—
803C2×D5—28no—
804C2×D5—22no—
805C2×D5—22no—
806C2×D5—22no—
807C2×D5—34no—
808C2×D5—44no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—68no—
812C2×D5—1216no—
813C2×D5—1216no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—62no—
818Dic5—22no—
819Dic5—22no—
820Dic5—62no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—31no—
826C24—34no—
827C24—51no—
828C24—51no—
829C24—64no—
830C24—122no—
831C24—122no—
832C24—154no—
833C24—158no—
834C24—154no—
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—54no—
847C2×D4—54no—
848C2×D4—64no—
849C2×D4—104no—
850C2×D4—104no—
851C2×D4—122no—
852C2×D4—122no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—154no—
858C2×D4—154no—
859C2×D4—202no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—3032no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—304no—
866C2×D4—304no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—51no—
870C22×C4—51no—
871C22×C4—54no—
872C22×C4—154no—
873C22×C4—154no—
874C22×C4—151no—
875C22×C4—151no—
876C22×C4—151no—
877C22×C4—154no—
878C22×C4—202no—
879C22×C4—304no—
880C22×C4—304no—
881C22×C4—602no—
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—54no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—54no—
891C22⋊C4—154no—
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×C3—102no—
910C22×C3—102no—
911C22×C3—102no—
912C22×C3—204no—
913C22×C3C2×D4×D512yes—
914C22×C3#414412yes—
915C22×C3#414412yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—416no—
927C2×D3—44no—
928C2×D3—44no—
929C2×D3—54no—
930C2×D3—108no—
931C2×D3—102no—
932C2×D3—102no—
933C2×D3—2016no—
934C2×D3—2016no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—102no—
939C3×C4—102no—
940Dic3—22no—
941Dic3—102no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—64no—
946C2×C5—122no—
947C2×C5—122no—
948C2×C5#560514yescomplemented
949C2×C5C22×D3×D411yescharacteristic
950C2×C5C2×#100411yescharacteristic
951C2×C5C2×#100911yescharacteristic
952D5—24no—
953D5—42no—
954D5—64no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—34no—
959C23—32no—
960C23—32no—
961C23—32no—
962C23—54no—
963C23—52no—
964C23—52no—
965C23—68no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—102no—
975C23—102no—
976C23—102no—
977C23—102no—
978C23—102no—
979C23—124no—
980C23—124no—
981C23—1216no—
982C23—1516no—
983C23—154no—
984C23—152no—
985C23—308no—
986C23—302no—
987C23—302no—
988C23—6016no—
989C23—604no—
990C23—604no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—108no—
999D4—124no—
1000D4—124no—
1001D4—204no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—308no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—32no—
1011C2×C4—52no—
1012C2×C4—52no—
1013C2×C4—62no—
1014C2×C4—102no—
1015C2×C4—102no—
1016C2×C4—152no—
1017C2×C4—152no—
1018C2×C4—152no—
1019C2×C4—204no—
1020C2×C4—308no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—302no—
1025C2×C4—604no—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—104no—
1030C2×C3—202no—
1031C2×C3#6592314yescomplemented
1032C2×C3C22×D4×D511yescharacteristic
1033C2×C3C2×#414411yescharacteristic
1034C2×C3C2×#414411yescharacteristic
1035D3—24no—
1036D3—42no—
1037D3—42no—
1038D3—104no—
1039C5C2×#560511yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—44no—
1045C22—54no—
1046C22—68no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—108no—
1056C22—102no—
1057C22—102no—
1058C22—102no—
1059C22—102no—
1060C22—102no—
1061C22—1216no—
1062C22—124no—
1063C22—124no—
1064C22—154no—
1065C22—204no—
1066C22—308no—
1067C22—302no—
1068C22—302no—
1069C22—6016no—
1070C22—6016no—
1071C22#9201812yes—
1072C22D3×D4×D512yes—
1073C22#9202512yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—62no—
1078C4—102no—
1079C4—102no—
1080C4—302no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6592311yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—64no—
1086C2—104no—
1087C2—122no—
1088C2—122no—
1089C2—202no—
1090C2—304no—
1091C2#1175321714yesdirect product factor
1092C2C2×#9201811yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9202511yescharacteristic
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×#6777C2semidirect
3. C2×#91772C2semidirect
4. C2×C5×#882C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91577C2semidirect
7. C2×#91568C2semidirect
8. C2×#91549C2semidirect
9. C2×#91475C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91457C2semidirect
12. C2×#91449C2semidirect
13. C2×#91423C2semidirect
14. C2×#91408C2semidirect
15. C2×#91355C2semidirect
16. #11753217C2direct (N × H)
18. C24×C5×D3C22semidirect
20. C23×D3×D5C22semidirect
22. C22×C4×D15C22semidirect
23. C22×C5×#67C22semidirect
25. C22×C5×D12C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×D20C22semidirect
29. C22×C3×C4×D5C22semidirect
31. C2×D3×C22⋊D5C22semidirect
34. C22×#1201C22semidirect
35. C22×#1201C22semidirect
36. C22×#1201C22semidirect
37. C22×D3×Dic5C22semidirect
38. C22×D5×Dic3C22semidirect
40. C2×#6777C22semidirect
41. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6719C22semidirect
43. C2×#6714C22semidirect
44. C2×C4⋊Dic15C22semidirect
45. C2×#6712C22semidirect
46. #91772C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C5×#882C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4030C22semidirect
53. #91577C22semidirect
54. #91568C22semidirect
55. #91549C22semidirect
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. D5×(C2×D3)⋊C4C22semidirect
65. #91457C22semidirect
66. #91449C22semidirect
67. #91423C22semidirect
68. #91408C22semidirect
69. #91355C22semidirect
83. C2×#4030D3semidirect
95. C23×C5×D3C23semidirect
103. C22×D3×D5D4semidirect
105. C22×D3×D5C23semidirect
114. C2×C4×D15C23semidirect
116. C2×C5×#67C23semidirect
121. C2×C5×D12C23semidirect
124. C2×C3×C22⋊D5C23semidirect
125. C2×C3×C22⋊D5C23semidirect
129. C2×C3×D20C23semidirect
131. C2×C3×C4×D5C23semidirect
140. C2×#1201C23semidirect
141. C2×#1201C23semidirect
142. C2×#1201C23semidirect
144. C2×D3×Dic5C23semidirect
146. C2×D5×Dic3C23semidirect
148. C3×C5×C22⋊C4C23semidirect
149. #6719C23semidirect
150. #6714C23semidirect
151. C4⋊Dic15C23semidirect
152. #6712C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C3×#685C23semidirect
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
179. C2×#882D5semidirect
194. C22×C22⋊D5C2×D3semidirect
195. C22×C22⋊D5C2×D3semidirect
199. C22×D20C2×D3semidirect
202. C22×C4×D5C2×D3semidirect
206. C2×C5×C22⋊C4C2×D3semidirect
221. C2×#685C2×D3semidirect
225. C2×#683C2×D3semidirect
228. #4030C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
308. C24×D3C2×D5semidirect
318. C22×#67C2×D5semidirect
326. C22×D12C2×D5semidirect
332. C2×C3×C22⋊C4C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
348. C2×(C2×D3)⋊C4C2×D5semidirect
357. #882C2×D5semidirect
401. C2×C22⋊D5C22×D3semidirect
402. C2×C22⋊D5C22×D3semidirect
412. C2×D20C22×D3semidirect
418. C2×C4×D5C22×D3semidirect
421. C5×C22⋊C4C22×D3semidirect
430. #685C22×D3semidirect
434. #683C22×D3semidirect
512. C23×D3C22×D5semidirect
536. C2×#67C22×D5semidirect
550. C2×D12C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
567. (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#5605semidirect
1031. C2×C3#65923semidirect
1039. C5C2×#5605semidirect
1083. C3C2×#65923semidirect
1091. C2#11753217direct (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×#67772
C2×#917722
C2×C5×#8822
C2×C3×#40302
C2×#915772
C2×#915682
C2×#915492
C2×#914752
C2×D5×(C2×D3)⋊C42
C2×#914572
C2×#914492
C2×#914232
C2×#914082
C2×#913552
#117532172
C2×#659233
C2×#56055