Finite Group Databasebeta

← C2×#11753856 #14482652

Subgroups — C2×#11753856 #14482652

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×#6777C211yesmaximal, characteristic, complemented
2C22×#6765C211yesmaximal, characteristic, complemented
3C2×#91785C211yesmaximal, characteristic, complemented
4C2×C5×#894C211yesmaximal, characteristic, complemented
5C2×C3×#4041C211yesmaximal, characteristic, complemented
6C2×#91474C211yesmaximal, characteristic, complemented
7C2×#91474C211yesmaximal, characteristic, complemented
8C2×D3×#685C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#91462C211yesmaximal, characteristic, complemented
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×#91440C211yesmaximal, characteristic, complemented
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×#91407C211yesmaximal, characteristic, complemented
15C2×#91396C211yesmaximal, characteristic, complemented
16#11753856C2116yesmaximal, direct product factor
17C2×#65988—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic, complemented
24C22×C3×D20C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C22×#1202C2211yescharacteristic
29C22×#1201C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic, complemented
33C22×D3×Dic5C2211yescharacteristic, complemented
34C22×D5×Dic3C2211yescharacteristic, complemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36C2×#6777—28no—
37C2×#6777C2218yescomplemented
38C2×#6765—28no—
39C2×#6765C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6712C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91785C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
50C5×#894C2218yescomplemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C3×#4041C2218yescomplemented
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56C2×#6665C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91474C2218yescomplemented
61#91474C2218yescomplemented
62D3×#685C2218yescomplemented
63D5×(C2×D3)⋊C4C2218yescomplemented
64#91462C2218yescomplemented
65#91453C2218yescomplemented
66#91440C2218yescomplemented
67#91408C2218yescomplemented
68#91407C2218yescomplemented
69#91396C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
75C22×#685—31no—
76#65988—316no—
77C2×#4042—31no—
78C2×#4041D311yescharacteristic, complemented
79C2×#4040—31no—
80C2×#4039—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
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
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C2×C4×D15—24no—
108C2×C4×D15C2314yes—
109C2×Dic30—24no—
110C2×Dic30C2314yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×D12—24no—
114C2×C5×D12C2314yes—
115C2×C4×C5×D3—24no—
116C2×C4×C5×D3C2314yescomplemented
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—24no—
119C2×C3×D20—24no—
120C2×C3×D20—42no—
121C2×C3×D20C2314yes—
122C2×C3×D20C2314yescomplemented
123C2×C3×D20C2314yescomplemented
124C2×C3×C4×D5—42no—
125C2×C3×C4×D5C2314yescomplemented
126C2×#1202—24no—
127C2×#1202C2314yes—
128C2×#1201—24no—
129C2×#1201—24no—
130C2×#1201—42no—
131C2×#1201D418yescomplemented
132C2×#1201C2314yes—
133C2×#1201C2314yes—
134C2×#1201C2314yescomplemented
135C2×#1201C2314yescomplemented
136C2×D3×Dic5—42no—
137C2×D3×Dic5C2314yescomplemented
138C2×D5×Dic3—24no—
139C2×D5×Dic3—24no—
140C2×D5×Dic3C2314yescomplemented
141C2×D5×Dic3C2314yescomplemented
142#6777—232no—
143#6765—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yes—
146#6714C2314yes—
147#6712C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C5×Dic3⋊C4C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×#685C2314yescomplemented
155#6667C2314yes—
156(C2×D3)⋊Dic5C2314yescomplemented
157#6665C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
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×#894D511yescharacteristic, complemented
173C2×#885—51no—
174C2×#884—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C23×Dic5—31no—
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20C2×D311yescharacteristic
192C22×D20C2×D311yescharacteristic, complemented
193C22×D20C2×D311yescharacteristic, complemented
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#123—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5—31no—
206#4085—38no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—38no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×#685C2×D311yescharacteristic, complemented
216C2×#683—31no—
217C2×#683—31no—
218C2×C4×Dic5—31no—
219#4042—38no—
220#4041C2×D318yescomplemented
221#4040—38no—
222#4039—38no—
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15#4114yescomplemented
234C22×D15C2412yes—
235C22×C5×D3—22no—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3C2×D414yes—
241C22×C5×D3C2412yes—
242C22×C5×D3C2412yes—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5C2×D414yes—
252C22×C3×D5C2412yes—
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×C5—22no—
266C2×C3×C4×C5C2412yes—
267C2×C3×C4×C5C2412yes—
268C2×C3×C4×C5C2412yes—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2×D414yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C4×D15—28no—
276Dic30—28no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C5×D12—28no—
282C4×C5×D3—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2412yes—
285C3×D20—28no—
286C3×D20—28no—
287C3×D20—44no—
288C3×C4×D5—44no—
289#1202—28no—
290#1201—28no—
291#1201—28no—
292#1201—44no—
293#1201C2×D4116yescomplemented
294D3×Dic5—44no—
295D5×Dic3—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×#67—51no—
307C22×#67—51no—
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⋊C4C2×D511yescharacteristic, complemented
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
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—58no—
336C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
337C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
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#894C2×D518yescomplemented
345#885—58no—
346#884—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C23×D5—31no—
352C23×D5—34no—
353C23×D5—34no—
354C23×D5—64no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—122no—
359C23×D5—122no—
360C23×D5C22×D311yescharacteristic
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—34no—
368C22×C4×C5—64no—
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—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—31no—
383C22×Dic5—34no—
384C22×Dic5—122no—
385C22×Dic5C22×D311yescharacteristic
386D4×D5—632no—
387#709—632no—
388C2×D20—24no—
389C2×D20—24no—
390C2×D20—34no—
391C2×D20—42no—
392C2×D20—64no—
393C2×D20C22×D314yes—
394C2×D20C22×D314yescomplemented
395C2×D20C22×D314yescomplemented
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—42no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C4⋊C4C22×D314yescomplemented
408C5×C22⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4—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#685C22×D314yescomplemented
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—31no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—51no—
431C2×#121—151no—
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×C5C22×D412yes—
440C22×C3×C5C2×#4112yes—
441C22×C3×C5H(5,𝔽2)12yes—
442C22×C3×C5C2511yescharacteristic
443C2×D15—28no—
444C2×D15—22no—
445C2×D15—22no—
446C2×D15C2×#4114yescomplemented
447C2×C5×D3—28no—
448C2×C5×D3—22no—
449C2×C5×D3—22no—
450C2×C5×D3—22no—
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—44no—
454C2×C5×D3C22×D414yes—
455C2×C3×D5—28no—
456C2×C3×D5—22no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—44no—
465C2×C3×D5—44no—
466C2×C3×D5C22×D414yes—
467D3×D5—416no—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474Dic15C22×D414yes—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—51no—
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—54no—
500C22×C3×C4—202no—
501C22×C3×C4C22×D511yescharacteristic
502C22×C3×C4C22×D511yescharacteristic
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—58no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—202no—
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
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—24no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4C22×D514yescomplemented
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
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)⋊C4C22×D514yescomplemented
546(C2×D3)⋊C4C22×D514yescomplemented
547(C2×D3)⋊C4C22×D514yescomplemented
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—34no—
553C23×C5—32no—
554C23×C5—32no—
555C23×C5—62no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5—62no—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—22no—
569C22×D5—34no—
570C22×D5—32no—
571C22×D5—68no—
572C22×D5—68no—
573C22×D5—68no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—68no—
577C22×D5—124no—
578C22×D5—124no—
579C22×D5—1216no—
580C22×D5—1216no—
581C22×D5D3×D414yes—
582C22×D5C23×D312yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×D4—68no—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—68no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5C23×D312yes—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—316no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—34no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5—124no—
609C2×Dic5C23×D312yes—
610D20—28no—
611D20—28no—
612D20—44no—
613D20—68no—
614C4×D5—44no—
615C4×D5—68no—
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—51no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
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—38no—
643#123—158no—
644C22⋊Q8—158no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—158no—
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⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5#54614yescomplemented
672C2×C3×C5C23×D411yescharacteristic
673C2×C3×C5C22×#4111yescharacteristic
674C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
675D15—24no—
676C3×D5—24no—
677C3×D5—42no—
678C3×D5—42no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—52no—
684C23×C3—52no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3—102no—
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—22no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—204no—
723C2×C3×C4C23×D512yes—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—204no—
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—28no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—34no—
749C22×C5—62no—
750C22×C5—62no—
751C22×C5—68no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×D3×D412yes—
757C22×C5#100412yes—
758C22×C5D3×#4112yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—28no—
763C2×D5—22no—
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—22no—
768C2×D5—22no—
769C2×D5—34no—
770C2×D5—44no—
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—22no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—51no—
791C24—51no—
792C24—154no—
793C24—154no—
794C24—151no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24—602no—
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—54no—
806C2×D4—54no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—104no—
810C2×D4—104no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—158no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—202no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—51no—
827C22×C4—54no—
828C22×C4—64no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—151no—
834C22×C4—151no—
835C22×C4—154no—
836C22×C4—202no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—54no—
863C22×C3—108no—
864C22×C3—102no—
865C22×C3—102no—
866C22×C3—102no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—204no—
873C22×C3—204no—
874C22×C3C2×D4×D512yes—
875C22×C3D5×#4112yes—
876C22×C3#414912yes—
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—22no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5#561014yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×#100411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907D5—24no—
908D5—42no—
909D5—42no—
910D5—64no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—54no—
915C23—52no—
916C23—52no—
917C23—52no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—154no—
932C23—152no—
933C23—308no—
934C23—308no—
935C23—308no—
936C23—308no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—108no—
947D4—108no—
948D4—1516no—
949D4—204no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—52no—
960C2×C4—68no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—102no—
964C2×C4—154no—
965C2×C4—152no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—204no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—604no—
975C2×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3—202no—
980C2×C3—202no—
981C2×C3#6598814yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—24no—
986D3—42no—
987D3—104no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—34no—
990C22—54no—
991C22—68no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—108no—
998C22—102no—
999C22—102no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—102no—
1005C22—102no—
1006C22—124no—
1007C22—154no—
1008C22—204no—
1009C22—204no—
1010C22—308no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22#9201712yes—
1016C22D3×D4×D512yes—
1017C22#9203412yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—202no—
1033C2—202no—
1034C2—304no—
1035C2#1175385614yesdirect product factor
1036C2C2×#9201711yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9203411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6777C2semidirect
2. C22×#6765C2semidirect
3. C2×#91785C2semidirect
4. C2×C5×#894C2semidirect
5. C2×C3×#4041C2semidirect
6. C2×#91474C2semidirect
7. C2×#91474C2semidirect
8. C2×D3×#685C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×#91462C2semidirect
11. C2×#91453C2semidirect
12. C2×#91440C2semidirect
13. C2×#91408C2semidirect
14. C2×#91407C2semidirect
15. C2×#91396C2semidirect
16. #11753856C2direct (N × H)
21. C22×Dic30C22semidirect
23. C22×C4×C5×D3C22semidirect
25. C22×C3×D20C22semidirect
26. C22×C3×D20C22semidirect
27. C22×C3×C4×D5C22semidirect
31. C22×#1201C22semidirect
32. C22×#1201C22semidirect
33. C22×D3×Dic5C22semidirect
34. C22×D5×Dic3C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×#6777C22semidirect
39. C2×#6765C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
43. C2×#6712C22semidirect
44. C2×#6712C22semidirect
45. #91785C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×Dic3⋊C4C22semidirect
50. C5×#894C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C3×#4041C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. C2×#6665C22semidirect
57. C2×#6665C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91474C22semidirect
61. #91474C22semidirect
62. D3×#685C22semidirect
63. D5×(C2×D3)⋊C4C22semidirect
64. #91462C22semidirect
65. #91453C22semidirect
66. #91440C22semidirect
67. #91408C22semidirect
68. #91407C22semidirect
69. #91396C22semidirect
78. C2×#4041D3semidirect
110. C2×Dic30C23semidirect
116. C2×C4×C5×D3C23semidirect
122. C2×C3×D20C23semidirect
123. C2×C3×D20C23semidirect
125. C2×C3×C4×D5C23semidirect
131. C2×#1201D4semidirect
134. C2×#1201C23semidirect
135. C2×#1201C23semidirect
137. C2×D3×Dic5C23semidirect
140. C2×D5×Dic3C23semidirect
141. C2×D5×Dic3C23semidirect
144. C3×C5×C4⋊C4C23semidirect
147. #6712C23semidirect
148. #6712C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C5×Dic3⋊C4C23semidirect
153. C3×#685C23semidirect
154. C3×#685C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. #6665C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
172. C2×#894D5semidirect
192. C22×D20C2×D3semidirect
193. C22×D20C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
201. C2×C5×C4⋊C4C2×D3semidirect
214. C2×#685C2×D3semidirect
215. C2×#685C2×D3semidirect
220. #4041C2×D3semidirect
233. C22×D15#41semidirect
293. #1201C2×D4semidirect
317. C22×C4×D3C2×D5semidirect
320. C2×C3×C4⋊C4C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
337. C2×(C2×D3)⋊C4C2×D5semidirect
338. C2×(C2×D3)⋊C4C2×D5semidirect
341. C2×Dic3⋊C4C2×D5semidirect
344. #894C2×D5semidirect
394. C2×D20C22×D3semidirect
395. C2×D20C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
407. C5×C4⋊C4C22×D3semidirect
418. #685C22×D3semidirect
419. #685C22×D3semidirect
446. C2×D15C2×#41semidirect
532. C2×C4×D3C22×D5semidirect
535. C3×C4⋊C4C22×D5semidirect
545. (C2×D3)⋊C4C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5610semidirect
981. C2×C3#65988semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65988semidirect
1035. C2#11753856direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67772
C22×#67652
C2×#917852
C2×C5×#8942
C2×C3×#40412
C2×#914742
C2×D3×#6852
C2×D5×(C2×D3)⋊C42
C2×#914622
C2×#914532
C2×#914402
C2×#914082
C2×#914072
C2×#913962
#117538562
C2×#659883
C2×#56105