Finite Group Databasebeta

← C2×#11753234 #14482660

Subgroups — C2×#11753234 #14482660

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
1C22×#6780C211yesmaximal, characteristic, complemented
2C22×#6777C211yesmaximal, characteristic, complemented
3C2×#91770C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91577C211yesmaximal, characteristic, complemented
8C2×#91571C211yesmaximal, characteristic, complemented
9C2×D3×#685C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91464C211yesmaximal, characteristic, complemented
12C2×C4×#1201C211yesmaximal, characteristic, complemented
13C2×#91423C211yesmaximal, characteristic, complemented
14C2×#91407C211yesmaximal, characteristic, complemented
15C2×#91377C211yesmaximal, characteristic, complemented
16#11753234C2116yesmaximal, direct product factor
17C2×#65944—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic, complemented
22C22×C4×D15C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×D20C2211yescharacteristic
30C22×C3×C4×D5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C22×D3×Dic5C2211yescharacteristic, complemented
35C2×#6780—28no—
36C2×#6780C2218yescomplemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6777—28no—
39C2×#6777C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic
42C2×#6712C2211yescharacteristic, complemented
43C2×C4×Dic15C2211yescharacteristic, complemented
44#91770C2218yescomplemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C5×#884C2218yescomplemented
48C2×C3×#685C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50C3×#4030C2218yescomplemented
51#91577C2218yescomplemented
52#91577C2218yescomplemented
53#91571C2218yescomplemented
54C2×#6669C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63D3×#685C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91464C2218yescomplemented
66C4×#1201C2218yescomplemented
67#91423C2218yescomplemented
68#91407C2218yescomplemented
69#91377C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030D311yescharacteristic, complemented
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×D3×D5—24no—
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—24no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5C2314yes—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220C2314yes—
105C22×Dic15—24no—
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2314yescomplemented
110C2×C4×D15—24no—
111C2×C4×D15C2314yes—
112C2×C5×#67—24no—
113C2×C5×#67—42no—
114C2×C5×#67C2314yescomplemented
115C2×C5×#67C2314yescomplemented
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C2×C5×D12—24no—
119C2×C5×D12C2314yes—
120C2×C4×C5×D3—42no—
121C2×C4×C5×D3C2314yescomplemented
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×D20C2314yes—
130C2×C3×C4×D5—42no—
131C2×C3×C4×D5C2314yescomplemented
132C2×#1204—24no—
133C2×#1204C2314yescomplemented
134C2×#1201—24no—
135C2×#1201D418yescomplemented
136C2×#1201C2314yes—
137C2×#1201C2314yes—
138C2×D3×Dic5—24no—
139C2×D3×Dic5C2314yescomplemented
140#6780—232no—
141C2×D5×Dic3—24no—
142C2×D5×Dic3C2314yescomplemented
143#6777—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yes—
146#6712C2314yescomplemented
147C4×Dic15C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×Dic3⋊C4C2314yescomplemented
150C3×#685C2314yescomplemented
151C3×#683C2314yescomplemented
152#6669C2314yescomplemented
153#6667C2314yes—
154#6667C2314yes—
155(C2×D3)⋊Dic5C2314yescomplemented
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160#6665C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4—51no—
163C2×C3×#121—51no—
164C2×#939—51no—
165C2×#937—51no—
166C2×#937—51no—
167C2×#935—51no—
168C2×C4×#67—51no—
169C22×(C2×D3)⋊C4—51no—
170#5610—516no—
171C2×#896—51no—
172C2×#894—51no—
173C2×#885—51no—
174C2×#884D511yescharacteristic, complemented
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—31no—
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5C2×D311yescharacteristic, complemented
187C22×C22⋊D5C2×D311yescharacteristic, complemented
188C23×Dic5—31no—
189C23×Dic5—31no—
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20C2×D311yescharacteristic
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—38no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030C2×D318yescomplemented
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15#4114yescomplemented
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3C2×D414yes—
245C22×C5×D3C2412yes—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5C2×D414yes—
253C22×C3×D5C2412yes—
254C22×C3×D5C2412yes—
255C2×D3×D5—28no—
256C2×D3×D5—28no—
257C2×D3×D5—28no—
258C2×D3×D5—28no—
259C2×D3×D5—44no—
260C2×D3×D5—44no—
261C2×D3×D5—416no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—28no—
271C2×Dic15C2×D414yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C4×D15—28no—
276C5×#67—28no—
277C5×#67—44no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3—22no—
280C2×C5×Dic3C2412yes—
281C2×C5×Dic3C2412yes—
282C5×D12—28no—
283C4×C5×D3—44no—
284C3×C22⋊D5—28no—
285C3×C22⋊D5—44no—
286C2×C3×Dic5—22no—
287C2×C3×Dic5—22no—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290C3×D20—28no—
291C3×C4×D5—44no—
292#1204—28no—
293#1201—28no—
294#1201C2×D4116yescomplemented
295D3×Dic5—28no—
296D5×Dic3—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4—51no—
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67C2×D511yescharacteristic, complemented
307C22×#67C2×D511yescharacteristic, complemented
308C23×Dic3—51no—
309C23×Dic3—51no—
310C2×#237—58no—
311C2×#237—108no—
312C2×D3×D4—58no—
313C2×D3×D4—108no—
314C22×D12C2×D511yescharacteristic
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×#121—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326#939—58no—
327#937—58no—
328#937—58no—
329#935—58no—
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—58no—
338C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4C2×D511yescharacteristic, complemented
342C2×C4×Dic3—51no—
343#896—58no—
344#894—58no—
345#885—58no—
346#884C2×D518yescomplemented
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5C22×D311yescharacteristic
352C23×D5—31no—
353C23×D5—34no—
354C23×D5—34no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5—122no—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4—122no—
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—34no—
372C22×C4×C5—122no—
373C22×C4×C5C22×D311yescharacteristic
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—24no—
376C2×C22⋊D5—38no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—42no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5C22×D314yescomplemented
384C2×C22⋊D5C22×D314yescomplemented
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—64no—
391C22×Dic5—64no—
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D311yescharacteristic
394#711—632no—
395D4×D5—632no—
396C2×D20—24no—
397C2×D20C22×D314yes—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—42no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4C22×D314yescomplemented
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yescomplemented
419#683—34no—
420#683—34no—
421#683C22×D314yescomplemented
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—31no—
431C2×#121—51no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—28no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15C2×#4114yescomplemented
451C2×C5×D3—28no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—44no—
458C2×C5×D3C22×D414yes—
459C2×C3×D5—28no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—44no—
466C2×C3×D5C22×D414yes—
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15C22×D414yes—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3C22×D511yescharacteristic
481C23×D3—51no—
482C23×D3—54no—
483C23×D3—54no—
484C23×D3—104no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3—202no—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4—202no—
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4—54no—
501C22×C3×C4—202no—
502C22×C3×C4C22×D511yescharacteristic
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—24no—
505C2×#67—42no—
506C2×#67—58no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67C22×D514yescomplemented
513C2×#67C22×D514yescomplemented
514C22×Dic3—51no—
515C22×Dic3—54no—
516C22×Dic3—51no—
517C22×Dic3—51no—
518C22×Dic3—54no—
519C22×Dic3—104no—
520C22×Dic3—104no—
521C22×Dic3C22×D511yescharacteristic
522C22×Dic3C22×D511yescharacteristic
523#237—1032no—
524D3×D4—1032no—
525C2×D12—24no—
526C2×D12C22×D514yes—
527C2×C4×D3—42no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4C22×D514yescomplemented
538#217—54no—
539#217—54no—
540#217—54no—
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4C22×D514yescomplemented
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—32no—
557C23×C5—32no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5—62no—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—22no—
570C22×D5—34no—
571C22×D5—32no—
572C22×D5—68no—
573C22×D5—68no—
574C22×D5—68no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—124no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5—1216no—
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C5×D4—68no—
587C5×D4—124no—
588C2×C4×C5—22no—
589C2×C4×C5—22no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—124no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—316no—
599C22⋊D5—44no—
600C22⋊D5—68no—
601C22⋊D5—68no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—34no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—32no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—28no—
615C4×D5—44no—
616C4×D5—68no—
617C4×D5—68no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—31no—
627C22×D4—51no—
628C22×D4—51no—
629C22×D4—51no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—51no—
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—38no—
646#121—58no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—158no—
659C2×C22⋊C4—158no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677C3×D5—24no—
678C3×D5—42no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—52no—
686C23×C3—52no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—54no—
700C22×D3—52no—
701C22×D3—108no—
702C22×D3—108no—
703C22×D3—108no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—2016no—
711C22×D3D4×D514yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—204no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—44no—
728#67—516no—
729#67—108no—
730#67—108no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—54no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—52no—
737C2×Dic3—108no—
738C2×Dic3—108no—
739C2×Dic3—102no—
740C2×Dic3—102no—
741C2×Dic3C23×D512yes—
742C2×Dic3C23×D512yes—
743D12—28no—
744C4×D3—44no—
745C4×D3—108no—
746C4×D3—108no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—34no—
752C22×C5—44no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—68no—
756C22×C5—62no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—124no—
760C22×C5C2×D3×D412yes—
761C22×C5#100412yes—
762C22×C5D3×#4112yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—28no—
767C2×D5—22no—
768C2×D5—22no—
769C2×D5—22no—
770C2×D5—34no—
771C2×D5—44no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—68no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—51no—
791C24—154no—
792C24—154no—
793C24—151no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—602no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—34no—
807C2×D4—54no—
808C2×D4—54no—
809C2×D4—54no—
810C2×D4—64no—
811C2×D4—64no—
812C2×D4—104no—
813C2×D4—104no—
814C2×D4—122no—
815C2×D4—154no—
816C2×D4—158no—
817C2×D4—154no—
818C2×D4—154no—
819C2×D4—202no—
820C2×D4—304no—
821C2×D4—3032no—
822C2×D4—304no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—122no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—154no—
837C22×C4—202no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—54no—
850C22⋊C4—154no—
851C22⋊C4—154no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—204no—
874C22×C3C2×D4×D512yes—
875C22×C3#414412yes—
876C22×C3D5×#4112yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—44no—
885C2×D3—54no—
886C2×D3—108no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5—122no—
904C2×C5#561014yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×#100411yescharacteristic
907C2×C5C2×D3×#4111yescharacteristic
908D5—24no—
909D5—42no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—32no—
916C23—32no—
917C23—54no—
918C23—52no—
919C23—52no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—102no—
929C23—102no—
930C23—154no—
931C23—152no—
932C23—308no—
933C23—308no—
934C23—308no—
935C23—308no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—604no—
940C23—6016no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—68no—
947D4—108no—
948D4—108no—
949D4—124no—
950D4—1516no—
951D4—204no—
952D4—308no—
953D4—308no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—124no—
965C2×C4—154no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—204no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—308no—
974C2×C4—302no—
975C2×C4—302no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—202no—
981C2×C3#6594414yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×#414411yescharacteristic
984C2×C3C2×D5×#4111yescharacteristic
985D3—24no—
986D3—42no—
987D3—104no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—44no—
994C22—54no—
995C22—68no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—108no—
1002C22—102no—
1003C22—102no—
1004C22—102no—
1005C22—102no—
1006C22—102no—
1007C22—124no—
1008C22—154no—
1009C22—204no—
1010C22—308no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22#9201612yes—
1016C22D3×D4×D512yes—
1017C22#9202512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—62no—
1022C4—62no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—104no—
1032C2—122no—
1033C2—202no—
1034C2—304no—
1035C2#1175323414yesdirect product factor
1036C2C2×#9201611yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#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×#546
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×#6780C2semidirect
2. C22×#6777C2semidirect
3. C2×#91770C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91577C2semidirect
7. C2×#91577C2semidirect
8. C2×#91571C2semidirect
9. C2×D3×#685C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91464C2semidirect
12. C2×C4×#1201C2semidirect
13. C2×#91423C2semidirect
14. C2×#91407C2semidirect
15. C2×#91377C2semidirect
16. #11753234C2direct (N × H)
21. C23×Dic15C22semidirect
23. C22×C5×#67C22semidirect
24. C22×C5×#67C22semidirect
26. C22×C4×C5×D3C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C22⋊D5C22semidirect
30. C22×C3×C4×D5C22semidirect
31. C22×#1204C22semidirect
34. C22×D3×Dic5C22semidirect
36. C2×#6780C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6777C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
42. C2×#6712C22semidirect
43. C2×C4×Dic15C22semidirect
44. #91770C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C5×#884C22semidirect
48. C2×C3×#685C22semidirect
49. C2×C3×#683C22semidirect
50. C3×#4030C22semidirect
51. #91577C22semidirect
52. #91577C22semidirect
53. #91571C22semidirect
54. C2×#6669C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×#6665C22semidirect
61. C2×#6665C22semidirect
62. C2×#6665C22semidirect
63. D3×#685C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91464C22semidirect
66. C4×#1201C22semidirect
67. #91423C22semidirect
68. #91407C22semidirect
69. #91377C22semidirect
84. C2×#4030D3semidirect
109. C22×Dic15C23semidirect
114. C2×C5×#67C23semidirect
115. C2×C5×#67C23semidirect
121. C2×C4×C5×D3C23semidirect
124. C2×C3×C22⋊D5C23semidirect
125. C2×C3×C22⋊D5C23semidirect
131. C2×C3×C4×D5C23semidirect
133. C2×#1204C23semidirect
135. C2×#1201D4semidirect
139. C2×D3×Dic5C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
146. #6712C23semidirect
147. C4×Dic15C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×Dic3⋊C4C23semidirect
150. C3×#685C23semidirect
151. C3×#683C23semidirect
152. #6669C23semidirect
155. (C2×D3)⋊Dic5C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. #6665C23semidirect
174. C2×#884D5semidirect
186. C22×C22⋊D5C2×D3semidirect
187. C22×C22⋊D5C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
218. C2×#685C2×D3semidirect
221. C2×#683C2×D3semidirect
226. #4030C2×D3semidirect
237. C22×D15#41semidirect
294. #1201C2×D4semidirect
306. C22×#67C2×D5semidirect
307. C22×#67C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
338. C2×(C2×D3)⋊C4C2×D5semidirect
341. C2×Dic3⋊C4C2×D5semidirect
346. #884C2×D5semidirect
383. C2×C22⋊D5C22×D3semidirect
384. C2×C22⋊D5C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
418. #685C22×D3semidirect
421. #683C22×D3semidirect
450. C2×D15C2×#41semidirect
512. C2×#67C22×D5semidirect
513. C2×#67C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5610semidirect
981. C2×C3#65944semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65944semidirect
1035. C2#11753234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67802
C22×#67772
C2×#917702
C2×C5×#8842
C2×C3×#40302
C2×#915772
C2×#915712
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914642
C2×C4×#12012
C2×#914232
C2×#914072
C2×#913772
#117532342
C2×#659443
C2×#56105