Finite Group Databasebeta

← C2×#11756350 #14482477

Subgroups — C2×#11756350 #14482477

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1220C211yesmaximal, characteristic, complemented
2C22×#6819C211yesmaximal, characteristic, complemented
3C2×C3×C5×#120C211yesmaximal, characteristic, complemented
4C22×#6719C211yesmaximal, characteristic, complemented
5C2×#91828C211yesmaximal, characteristic, complemented
6C2×#91828C211yesmaximal, characteristic, complemented
7C2×#91827C211yesmaximal, characteristic, complemented
8C2×#91826C211yesmaximal, characteristic, complemented
9C2×D4×Dic15C211yesmaximal, characteristic, complemented
10#11756350C2116yesmaximal, direct product factor
11C2×#91775C211yesmaximal, characteristic, complemented
12C2×#91774C211yesmaximal, characteristic, complemented
13C2×#91772C211yesmaximal, characteristic, complemented
14C2×#91770C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
16C2×#91767C211yesmaximal, characteristic, complemented
17C2×#65925—31nomaximal, Hall
18C25×C3×C5C2211yescharacteristic
19C24×D15C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×C3×C5×D4C2211yescharacteristic, complemented
23C22×#1220—28no—
24C22×#1220C2211yescharacteristic
25C22×#1220C2211yescharacteristic
26C22×#1220C2211yescharacteristic
27C22×#1220C2211yescharacteristic
28C22×#1220C2218yescomplemented
29C22×#1220C2211yescharacteristic, complemented
30C22×#1220C2211yescharacteristic, complemented
31C23×Dic15C2211yescharacteristic
32C23×Dic15C2211yescharacteristic, complemented
33C23×Dic15C2211yescharacteristic, complemented
34C23×Dic15C2211yescharacteristic, complemented
35C2×#6819—28no—
36C2×#6819C2218yescomplemented
37C22×C4×D15C2211yescharacteristic, complemented
38C22×C4×D15C2211yescharacteristic, complemented
39C22×Dic30C2211yescharacteristic, complemented
40C3×C5×#120C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic
42C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6719C2211yescharacteristic
45C2×#6719C2211yescharacteristic
46C2×#6719C2218yescomplemented
47C2×#6719C2211yescharacteristic, complemented
48C2×#6719C2211yescharacteristic, complemented
49C2×#6719C2211yescharacteristic, complemented
50#91828C2218yescomplemented
51#91828C2218yescomplemented
52#91827C2218yescomplemented
53#91826C2218yescomplemented
54D4×Dic15C2218yescomplemented
55C2×#6714C2211yescharacteristic, complemented
56C2×#6714C2211yescharacteristic, complemented
57C2×#6714C2211yescharacteristic, complemented
58C2×#6714C2211yescharacteristic, complemented
59C2×C4⋊Dic15C2211yescharacteristic, complemented
60C2×C4⋊Dic15C2211yescharacteristic, complemented
61C2×#6712C2211yescharacteristic, complemented
62C2×#6712C2211yescharacteristic, complemented
63C2×C4×Dic15C2211yescharacteristic, complemented
64#91775C2218yescomplemented
65#91774C2218yescomplemented
66#91772C2218yescomplemented
67#91770C2218yescomplemented
68C22⋊C4×D15C2218yescomplemented
69#91767C2218yescomplemented
70C2×#5591—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#711—31no—
73C2×C5×#120D311yescharacteristic, complemented
74C22×C22⋊Dic5—31no—
75C2×#4085—31no—
76C2×#4085—31no—
77C2×#4084—31no—
78C2×#4083—31no—
79C2×D4×Dic5—31no—
80#65925—316no—
81C2×#4032—31no—
82C2×#4031—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C2×D5×C22⋊C4—31no—
86C2×#4024—31no—
87C24×C3×C5—24no—
88C24×C3×C5—24no—
89C24×C3×C5—42no—
90C24×C3×C5C2311yescharacteristic
91C24×C3×C5C2311yescharacteristic
92C24×C3×C5C2314yes—
93C24×C3×C5C2311yescharacteristic
94C24×C3×C5C2311yescharacteristic
95C23×D15—24no—
96C23×D15—24no—
97C23×D15—42no—
98C23×D15C2311yescharacteristic
99C23×D15C2314yes—
100C23×D15C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4—24no—
103C2×C3×C5×D4—42no—
104C2×C3×C5×D4C2314yes—
105C2×C3×C5×D4C2314yescomplemented
106C2×C3×C5×D4C2314yescomplemented
107C22×C3×C4×C5C2311yescharacteristic
108C22×C3×C4×C5C2311yescharacteristic
109C22×C3×C4×C5C2311yescharacteristic
110C2×#1220—24no—
111C2×#1220—24no—
112C2×#1220—24no—
113C2×#1220—232no—
114C2×#1220—24no—
115C2×#1220—42no—
116C2×#1220D418yescomplemented
117C2×#1220C2314yes—
118C2×#1220C2314yes—
119C2×#1220C2314yes—
120C2×#1220C2314yes—
121C2×#1220C2314yescomplemented
122C2×#1220C2314yescomplemented
123C22×Dic15—24no—
124C22×Dic15—24no—
125C22×Dic15—24no—
126C22×Dic15—42no—
127C22×Dic15C2314yes—
128C22×Dic15C2311yescharacteristic
129C22×Dic15C2311yescharacteristic
130C22×Dic15C2311yescharacteristic
131C22×Dic15C2311yescharacteristic
132C22×Dic15C2311yescharacteristic
133C22×Dic15C2311yescharacteristic
134C22×Dic15C2314yescomplemented
135C22×Dic15C2314yescomplemented
136C22×Dic15C2314yescomplemented
137#6819—232no—
138C2×C4×D15—24no—
139C2×C4×D15—42no—
140C2×C4×D15C2314yescomplemented
141C2×C4×D15C2314yescomplemented
142C2×Dic30—24no—
143C2×Dic30C2314yescomplemented
144C3×C5×C22⋊C4C2314yes—
145C3×C5×C22⋊C4C2314yescomplemented
146C3×C5×C22⋊C4C2314yescomplemented
147#6719C2314yes—
148#6719C2314yes—
149#6719C2314yescomplemented
150#6719C2314yescomplemented
151#6719C2314yescomplemented
152#6714C2314yescomplemented
153#6714C2314yescomplemented
154#6714C2314yescomplemented
155#6714C2314yescomplemented
156C4⋊Dic15C2314yescomplemented
157C4⋊Dic15C2314yescomplemented
158#6712C2314yescomplemented
159#6712C2314yescomplemented
160C4×Dic15C2314yescomplemented
161C23×#67—51no—
162C22×#237—51no—
163C2×C3×#120D511yescharacteristic, complemented
164C22×#217—51no—
165C2×#939—51no—
166C2×#939—51no—
167C2×#938—51no—
168C2×#937—51no—
169C2×D4×Dic3—51no—
170#5591—516no—
171C2×#886—51no—
172C2×#885—51no—
173C2×#883—51no—
174C2×#67⋊C4—51no—
175C2×D3×C22⋊C4—51no—
176C2×#878—51no—
177C25×C5C2×D311yescharacteristic
178C24×D5—31no—
179C22×C5×D4C2×D311yescharacteristic
180C22×C5×D4C2×D311yescharacteristic, complemented
181C22×C5×D4C2×D311yescharacteristic, complemented
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—38no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—68no—
190C23×Dic5—31no—
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C2×#711—38no—
195C2×#711—68no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#120C2×D318yescomplemented
200C2×C5×C22⋊C4C2×D311yescharacteristic
201C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5—38no—
209#4085—38no—
210#4085—38no—
211#4084—38no—
212#4083—38no—
213D4×Dic5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×C4⋊Dic5—31no—
219C2×C4⋊Dic5—31no—
220C2×#683—31no—
221C2×#683—31no—
222C2×C4×Dic5—31no—
223#4032—38no—
224#4031—38no—
225#4029—38no—
226#4027—38no—
227D5×C22⋊C4—38no—
228#4024—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—28no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5—22no—
239C23×C3×C5—28no—
240C23×C3×C5—22no—
241C23×C3×C5—22no—
242C23×C3×C5—44no—
243C23×C3×C5—416no—
244C23×C3×C5C2×D414yes—
245C23×C3×C5#4114yescomplemented
246C23×C3×C5C2412yes—
247C23×C3×C5C2412yes—
248C23×C3×C5C2412yes—
249C23×C3×C5C2412yes—
250C23×C3×C5C2411yescharacteristic
251C22×D15—22no—
252C22×D15—22no—
253C22×D15—22no—
254C22×D15—22no—
255C22×D15—28no—
256C22×D15—22no—
257C22×D15—28no—
258C22×D15—44no—
259C22×D15—416no—
260C22×D15C2×D414yes—
261C22×D15C2412yes—
262C22×D15C2412yes—
263C3×C5×D4—28no—
264C3×C5×D4—28no—
265C3×C5×D4—44no—
266C2×C3×C4×C5—22no—
267C2×C3×C4×C5—22no—
268C2×C3×C4×C5—22no—
269C2×C3×C4×C5C2412yes—
270C2×C3×C4×C5C2412yes—
271C2×C3×C4×C5C2412yes—
272#1220—28no—
273#1220—28no—
274#1220—28no—
275#1220—28no—
276#1220—44no—
277#1220C2×D4116yescomplemented
278C2×Dic15—22no—
279C2×Dic15—22no—
280C2×Dic15—28no—
281C2×Dic15—22no—
282C2×Dic15—22no—
283C2×Dic15—22no—
284C2×Dic15—28no—
285C2×Dic15—28no—
286C2×Dic15—44no—
287C2×Dic15C2×D414yes—
288C2×Dic15C2412yes—
289C2×Dic15C2412yes—
290C2×Dic15C2412yes—
291C2×Dic15C2412yes—
292C2×Dic15C2412yes—
293C2×Dic15C2412yes—
294C4×D15—28no—
295C4×D15—44no—
296Dic30—28no—
297C25×C3C2×D511yescharacteristic
298C24×D3—51no—
299C22×C3×D4C2×D511yescharacteristic
300C22×C3×D4C2×D511yescharacteristic, complemented
301C22×C3×D4C2×D511yescharacteristic, complemented
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67—58no—
308C22×#67—51no—
309C22×#67—108no—
310C23×Dic3—51no—
311C23×Dic3—51no—
312C23×Dic3—51no—
313C23×Dic3—51no—
314C2×#237—58no—
315C2×#237—108no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319C3×#120C2×D518yescomplemented
320C2×C3×C22⋊C4C2×D511yescharacteristic
321C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217—51no—
328C2×#217—58no—
329#939—58no—
330#939—58no—
331#938—58no—
332#937—58no—
333D4×Dic3—58no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—51no—
338C2×C4⋊Dic3—51no—
339C2×C4⋊Dic3—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3—51no—
343#886—58no—
344#885—58no—
345#883—58no—
346#67⋊C4—58no—
347D3×C22⋊C4—58no—
348#878—58no—
349C24×C5—24no—
350C24×C5—24no—
351C24×C5—42no—
352C24×C5C22×D311yescharacteristic
353C24×C5C22×D311yescharacteristic
354C24×C5C22×D314yes—
355C24×C5C22×D311yescharacteristic
356C24×C5C22×D311yescharacteristic
357C23×D5—31no—
358C23×D5—31no—
359C23×D5—34no—
360C23×D5—64no—
361C23×D5—64no—
362C23×D5—122no—
363C2×C5×D4—24no—
364C2×C5×D4—24no—
365C2×C5×D4—42no—
366C2×C5×D4C22×D314yes—
367C2×C5×D4C22×D314yescomplemented
368C2×C5×D4C22×D314yescomplemented
369C22×C4×C5C22×D311yescharacteristic
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—38no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—632no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—64no—
384C2×C22⋊D5—122no—
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—31no—
389C22×Dic5—34no—
390C22×Dic5—31no—
391C22×Dic5—31no—
392C22×Dic5—34no—
393C22×Dic5—34no—
394C22×Dic5—34no—
395C22×Dic5—64no—
396C22×Dic5—64no—
397C22×Dic5—64no—
398C22×Dic5—122no—
399#711—632no—
400C2×C4×D5—34no—
401C2×C4×D5—34no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C22⋊C4C22×D314yes—
407C5×C22⋊C4C22×D314yescomplemented
408C5×C22⋊C4C22×D314yescomplemented
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413C22⋊Dic5—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418C4⋊Dic5—34no—
419C4⋊Dic5—34no—
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120D1511yescharacteristic, complemented
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
440C22×C3×C5—28no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—22no—
446C22×C3×C5—22no—
447C22×C3×C5—22no—
448C22×C3×C5—22no—
449C22×C3×C5—22no—
450C22×C3×C5—22no—
451C22×C3×C5—416no—
452C22×C3×C5—44no—
453C22×C3×C5—44no—
454C22×C3×C5C22×D414yes—
455C22×C3×C5C22×D412yes—
456C22×C3×C5C2×#4112yes—
457C22×C3×C5C2×#4114yescomplemented
458C22×C3×C5H(5,𝔽2)12yes—
459C22×C3×C5C2511yescharacteristic
460C2×D15—28no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—416no—
467C2×D15—44no—
468C2×D15C22×D414yes—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474Dic15—22no—
475Dic15—22no—
476Dic15—22no—
477Dic15C22×D414yes—
478C24×C3—24no—
479C24×C3—24no—
480C24×C3—42no—
481C24×C3C22×D511yescharacteristic
482C24×C3C22×D511yescharacteristic
483C24×C3C22×D514yes—
484C24×C3C22×D511yescharacteristic
485C24×C3C22×D511yescharacteristic
486C23×D3—51no—
487C23×D3—51no—
488C23×D3—54no—
489C23×D3—104no—
490C23×D3—104no—
491C23×D3—202no—
492C2×C3×D4—24no—
493C2×C3×D4—24no—
494C2×C3×D4—42no—
495C2×C3×D4C22×D514yes—
496C2×C3×D4C22×D514yescomplemented
497C2×C3×D4C22×D514yescomplemented
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—58no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—1032no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—202no—
514C22×Dic3—51no—
515C22×Dic3—54no—
516C22×Dic3—54no—
517C22×Dic3—51no—
518C22×Dic3—51no—
519C22×Dic3—51no—
520C22×Dic3—51no—
521C22×Dic3—51no—
522C22×Dic3—54no—
523C22×Dic3—54no—
524C22×Dic3—104no—
525C22×Dic3—104no—
526C22×Dic3—104no—
527C22×Dic3—202no—
528#237—1032no—
529C2×C4×D3—54no—
530C2×C4×D3—54no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C22⋊C4C22×D514yes—
536C3×C22⋊C4C22×D514yescomplemented
537C3×C22⋊C4C22×D514yescomplemented
538#217—54no—
539#217—54no—
540#217—54no—
541#217—54no—
542#217—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547C4⋊Dic3—54no—
548C4⋊Dic3—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—28no—
558C23×C5—22no—
559C23×C5—22no—
560C23×C5—22no—
561C23×C5—28no—
562C23×C5—22no—
563C23×C5—22no—
564C23×C5—44no—
565C23×C5—416no—
566C23×C5D3×D414yes—
567C23×C5#23714yescomplemented
568C23×C5C23×D312yes—
569C23×C5C23×D312yes—
570C23×C5C23×D312yes—
571C23×C5C23×D312yes—
572C23×C5C23×D311yescharacteristic
573C22×D5—34no—
574C22×D5—32no—
575C22×D5—32no—
576C22×D5—68no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—62no—
581C22×D5—68no—
582C22×D5—62no—
583C22×D5—124no—
584C22×D5—1216no—
585C5×D4—28no—
586C5×D4—28no—
587C5×D4—44no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—22no—
591C2×C4×C5C23×D312yes—
592C2×C4×C5C23×D312yes—
593C2×C4×C5C23×D312yes—
594C22⋊D5—316no—
595C22⋊D5—68no—
596C22⋊D5—68no—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C2×Dic5—34no—
601C2×Dic5—32no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—68no—
609C2×Dic5—62no—
610C2×Dic5—62no—
611C2×Dic5—68no—
612C2×Dic5—62no—
613C2×Dic5—62no—
614C2×Dic5—62no—
615C2×Dic5—124no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25C2×D1511yescharacteristic
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—151no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—308no—
632C22×D4C2×D1511yescharacteristic
633C22×D4C2×D1511yescharacteristic, complemented
634C22×D4C2×D1511yescharacteristic, complemented
635C23×C4—151no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120C2×D1518yescomplemented
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—151no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—151no—
657C2×C22⋊C4—151no—
658C2×C22⋊C4—151no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—158no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—158no—
667C2×C22⋊C4C2×D1511yescharacteristic
668C2×C22⋊C4C2×D1511yescharacteristic, complemented
669C2×C22⋊C4C2×D1511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—24no—
672C2×C3×C5—24no—
673C2×C3×C5—42no—
674C2×C3×C5—42no—
675C2×C3×C5#54614yescomplemented
676C2×C3×C5C23×D411yescharacteristic
677C2×C3×C5C22×#4111yescharacteristic
678C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
679D15—24no—
680D15—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—28no—
687C23×C3—22no—
688C23×C3—22no—
689C23×C3—22no—
690C23×C3—28no—
691C23×C3—22no—
692C23×C3—22no—
693C23×C3—44no—
694C23×C3—416no—
695C23×C3D4×D514yes—
696C23×C3#71114yescomplemented
697C23×C3C23×D512yes—
698C23×C3C23×D512yes—
699C23×C3C23×D512yes—
700C23×C3C23×D512yes—
701C23×C3C23×D511yescharacteristic
702C22×D3—54no—
703C22×D3—52no—
704C22×D3—52no—
705C22×D3—108no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—102no—
710C22×D3—108no—
711C22×D3—102no—
712C22×D3—204no—
713C22×D3—2016no—
714C3×D4—28no—
715C3×D4—28no—
716C3×D4—44no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4C23×D512yes—
721C2×C3×C4C23×D512yes—
722C2×C3×C4C23×D512yes—
723#67—516no—
724#67—108no—
725#67—108no—
726#67—108no—
727#67—108no—
728#67—204no—
729C2×Dic3—54no—
730C2×Dic3—52no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—108no—
737C2×Dic3—108no—
738C2×Dic3—102no—
739C2×Dic3—102no—
740C2×Dic3—108no—
741C2×Dic3—102no—
742C2×Dic3—102no—
743C2×Dic3—102no—
744C2×Dic3—204no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—28no—
753C22×C5—28no—
754C22×C5—22no—
755C22×C5—22no—
756C22×C5—22no—
757C22×C5—22no—
758C22×C5—22no—
759C22×C5—22no—
760C22×C5—416no—
761C22×C5—44no—
762C22×C5—44no—
763C22×C5C2×D3×D414yes—
764C22×C5C2×D3×D412yes—
765C22×C5C2×#23712yes—
766C22×C5C2×#23714yescomplemented
767C22×C5#100412yes—
768C22×C5C24×D311yescharacteristic
769C2×D5—34no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—68no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—62no—
776C2×D5—1216no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781Dic5—34no—
782Dic5—62no—
783Dic5—62no—
784Dic5—62no—
785Dic5—62no—
786Dic5—62no—
787C24—24no—
788C24—24no—
789C24—42no—
790C24—151no—
791C24—151no—
792C24—154no—
793C24—304no—
794C24—304no—
795C24—602no—
796C24C22×D1511yescharacteristic
797C24C22×D1511yescharacteristic
798C24C22×D1514yes—
799C24C22×D1511yescharacteristic
800C24C22×D1511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—42no—
807C2×D4—158no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—304no—
815C2×D4—3032no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—602no—
820C2×D4C22×D1514yes—
821C2×D4C22×D1514yescomplemented
822C2×D4C22×D1514yescomplemented
823C22×C4—151no—
824C22×C4—154no—
825C22×C4—154no—
826C22×C4—154no—
827C22×C4—151no—
828C22×C4—151no—
829C22×C4—151no—
830C22×C4—151no—
831C22×C4—151no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—304no—
836C22×C4—304no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—602no—
840C22×C4—602no—
841C22×C4C22×D1511yescharacteristic
842C22×C4C22×D1511yescharacteristic
843C22×C4C22×D1511yescharacteristic
844C4⋊C4—154no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—154no—
849C22⋊C4—154no—
850C22⋊C4—154no—
851C22⋊C4—154no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4C22×D1514yes—
858C22⋊C4C22×D1514yescomplemented
859C22⋊C4C22×D1514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—28no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—416no—
875C22×C3—44no—
876C22×C3—44no—
877C22×C3C2×D4×D514yes—
878C22×C3C2×D4×D512yes—
879C22×C3C2×#71112yes—
880C22×C3C2×#71114yescomplemented
881C22×C3#414412yes—
882C22×C3C24×D511yescharacteristic
883C2×D3—54no—
884C2×D3—108no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—2016no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895Dic3—54no—
896Dic3—102no—
897Dic3—102no—
898Dic3—102no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—24no—
902C2×C5—24no—
903C2×C5—42no—
904C2×C5—42no—
905C2×C5#559114yescomplemented
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C22×#23711yescharacteristic
908C2×C5C2×#100411yescharacteristic
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—22no—
922C23—22no—
923C23—44no—
924C23—416no—
925C23—154no—
926C23—152no—
927C23—152no—
928C23—308no—
929C23—302no—
930C23—302no—
931C23—302no—
932C23—302no—
933C23—308no—
934C23—302no—
935C23—604no—
936C23—6016no—
937C23D4×D1514yes—
938C23#681914yescomplemented
939C23C23×D1512yes—
940C23C23×D1512yes—
941C23C23×D1512yes—
942C23C23×D1512yes—
943C23C23×D1511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—28no—
947D4—44no—
948D4—1516no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—154no—
958C2×C4—152no—
959C2×C4—152no—
960C2×C4—152no—
961C2×C4—152no—
962C2×C4—152no—
963C2×C4—152no—
964C2×C4—308no—
965C2×C4—308no—
966C2×C4—308no—
967C2×C4—302no—
968C2×C4—302no—
969C2×C4—302no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—604no—
974C2×C4—604no—
975C2×C4C23×D1512yes—
976C2×C4C23×D1512yes—
977C2×C4C23×D1512yes—
978C2×C3—24no—
979C2×C3—24no—
980C2×C3—42no—
981C2×C3—42no—
982C2×C3#6592514yescomplemented
983C2×C3C22×D4×D511yescharacteristic
984C2×C3C22×#71111yescharacteristic
985C2×C3C2×#414411yescharacteristic
986D3—104no—
987D3—202no—
988C5C2×#559111yescharacteristic, complemented, Sylow
989C22—28no—
990C22—28no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—416no—
1002C22—44no—
1003C22—44no—
1004C22—154no—
1005C22—308no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—6016no—
1012C22—604no—
1013C22C2×D4×D1514yes—
1014C22C2×D4×D1512yes—
1015C22C2×#681912yes—
1016C22C2×#681914yescomplemented
1017C22#9209512yes—
1018C22C24×D1511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—154no—
1023C4—302no—
1024C4—302no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6592511yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—24no—
1031C2—42no—
1032C2—42no—
1033C2—304no—
1034C2—602no—
1035C2#1175635014yesdirect product factor
1036C2C22×D4×D1511yescharacteristic
1037C2C22×#681911yescharacteristic
1038C2C2×#9209511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×#120C2
socleC23×C3×C5C24
hypercenterC2×#120D15
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C23×#1220C2semidirect
2. C22×#6819C2semidirect
3. C2×C3×C5×#120C2semidirect
4. C22×#6719C2semidirect
5. C2×#91828C2semidirect
6. C2×#91828C2semidirect
7. C2×#91827C2semidirect
8. C2×#91826C2semidirect
9. C2×D4×Dic15C2semidirect
10. #11756350C2direct (N × H)
11. C2×#91775C2semidirect
12. C2×#91774C2semidirect
13. C2×#91772C2semidirect
14. C2×#91770C2semidirect
15. C2×C22⋊C4×D15C2semidirect
16. C2×#91767C2semidirect
21. C22×C3×C5×D4C22semidirect
22. C22×C3×C5×D4C22semidirect
28. C22×#1220C22semidirect
29. C22×#1220C22semidirect
30. C22×#1220C22semidirect
32. C23×Dic15C22semidirect
33. C23×Dic15C22semidirect
34. C23×Dic15C22semidirect
36. C2×#6819C22semidirect
37. C22×C4×D15C22semidirect
38. C22×C4×D15C22semidirect
39. C22×Dic30C22semidirect
40. C3×C5×#120C22semidirect
42. C2×C3×C5×C22⋊C4C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
46. C2×#6719C22semidirect
47. C2×#6719C22semidirect
48. C2×#6719C22semidirect
49. C2×#6719C22semidirect
50. #91828C22semidirect
51. #91828C22semidirect
52. #91827C22semidirect
53. #91826C22semidirect
54. D4×Dic15C22semidirect
55. C2×#6714C22semidirect
56. C2×#6714C22semidirect
57. C2×#6714C22semidirect
58. C2×#6714C22semidirect
59. C2×C4⋊Dic15C22semidirect
60. C2×C4⋊Dic15C22semidirect
61. C2×#6712C22semidirect
62. C2×#6712C22semidirect
63. C2×C4×Dic15C22semidirect
64. #91775C22semidirect
65. #91774C22semidirect
66. #91772C22semidirect
67. #91770C22semidirect
68. C22⋊C4×D15C22semidirect
69. #91767C22semidirect
73. C2×C5×#120D3semidirect
105. C2×C3×C5×D4C23semidirect
106. C2×C3×C5×D4C23semidirect
116. C2×#1220D4semidirect
121. C2×#1220C23semidirect
122. C2×#1220C23semidirect
134. C22×Dic15C23semidirect
135. C22×Dic15C23semidirect
136. C22×Dic15C23semidirect
140. C2×C4×D15C23semidirect
141. C2×C4×D15C23semidirect
143. C2×Dic30C23semidirect
145. C3×C5×C22⋊C4C23semidirect
146. C3×C5×C22⋊C4C23semidirect
149. #6719C23semidirect
150. #6719C23semidirect
151. #6719C23semidirect
152. #6714C23semidirect
153. #6714C23semidirect
154. #6714C23semidirect
155. #6714C23semidirect
156. C4⋊Dic15C23semidirect
157. C4⋊Dic15C23semidirect
158. #6712C23semidirect
159. #6712C23semidirect
160. C4×Dic15C23semidirect
163. C2×C3×#120D5semidirect
180. C22×C5×D4C2×D3semidirect
181. C22×C5×D4C2×D3semidirect
199. C5×#120C2×D3semidirect
201. C2×C5×C22⋊C4C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
245. C23×C3×C5#41semidirect
277. #1220C2×D4semidirect
300. C22×C3×D4C2×D5semidirect
301. C22×C3×D4C2×D5semidirect
319. C3×#120C2×D5semidirect
321. C2×C3×C22⋊C4C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
367. C2×C5×D4C22×D3semidirect
368. C2×C5×D4C22×D3semidirect
407. C5×C22⋊C4C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
434. C2×#120D15semidirect
457. C22×C3×C5C2×#41semidirect
496. C2×C3×D4C22×D5semidirect
497. C2×C3×D4C22×D5semidirect
536. C3×C22⋊C4C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
567. C23×C5#237semidirect
633. C22×D4C2×D15semidirect
634. C22×D4C2×D15semidirect
649. #120C2×D15semidirect
668. C2×C22⋊C4C2×D15semidirect
669. C2×C22⋊C4C2×D15semidirect
675. C2×C3×C5#546semidirect
696. C23×C3#711semidirect
766. C22×C5C2×#237semidirect
821. C2×D4C22×D15semidirect
822. C2×D4C22×D15semidirect
858. C22⋊C4C22×D15semidirect
859. C22⋊C4C22×D15semidirect
861. C3×C5C2×#546semidirect
880. C22×C3C2×#711semidirect
905. C2×C5#5591semidirect
938. C23#6819semidirect
982. C2×C3#65925semidirect
988. C5C2×#5591semidirect
1016. C22C2×#6819semidirect
1028. C3C2×#65925semidirect
1035. C2#11756350direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12202
C22×#68192
C2×C3×C5×#1202
C22×#67192
C2×#918282
C2×#918272
C2×#918262
C2×D4×Dic152
#117563502
C2×#917752
C2×#917742
C2×#917722
C2×#917702
C2×C22⋊C4×D152
C2×#917672
C2×#659253
C2×#55915