Finite Group Databasebeta

← C2×#11753858 #14482655

Subgroups — C2×#11753858 #14482655

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×D3×D20C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#893C211yesmaximal, characteristic, complemented
5C2×C3×#4040C211yesmaximal, characteristic, complemented
6C2×#91475C211yesmaximal, characteristic, complemented
7C2×#91475C211yesmaximal, characteristic, complemented
8C2×#91473C211yesmaximal, characteristic, complemented
9C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#91454C211yesmaximal, characteristic, complemented
11C2×#91420C211yesmaximal, characteristic, complemented
12C2×#91408C211yesmaximal, characteristic, complemented
13C2×#91395C211yesmaximal, characteristic, complemented
14C2×#91353C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16#11753858C2116yesmaximal, direct product factor
17C2×#65884—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×D12C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×C3×D20C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic, complemented
27C22×#1204C2211yescharacteristic, complemented
28C22×#1203C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×#1201C2211yescharacteristic, complemented
34C22×#1200C2211yescharacteristic, complemented
35C22×D5×Dic3C2211yescharacteristic, complemented
36C2×D3×D20—28no—
37C2×D3×D20C2218yescomplemented
38C2×#6771—28no—
39C2×#6771C2218yescomplemented
40C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91783C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C4×C5×Dic3C2211yescharacteristic, complemented
49C5×#893C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C3×#4040C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×#6665C2211yescharacteristic, complemented
60#91475C2218yescomplemented
61#91475C2218yescomplemented
62#91473C2218yescomplemented
63D5×(C2×D3)⋊C4C2218yescomplemented
64#91454C2218yescomplemented
65#91420C2218yescomplemented
66#91408C2218yescomplemented
67#91395C2218yescomplemented
68#91353C2218yescomplemented
69#91352C2218yescomplemented
70C2×#5654—51nomaximal, Hall
71C22×#709—31no—
72C23×D20—31no—
73C2×C4×C5×D4—31no—
74C2×#4083—31no—
75C2×#4083—31no—
76C2×#4076—31no—
77C2×#4070—31no—
78#65884—316no—
79C2×#4040—31no—
80C2×#4040D311yescharacteristic, complemented
81C2×#4030—31no—
82C2×#4030—31no—
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4—31no—
85C2×#4021—31no—
86C2×C4×D20—31no—
87C23×D15C2311yescharacteristic
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
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×D60—24no—
107C2×D60C2314yes—
108C2×C4×D15—24no—
109C2×C4×D15C2314yescomplemented
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C2×C5×D12—24no—
113C2×C5×D12C2314yes—
114C2×C4×C5×D3—24no—
115C2×C4×C5×D3—24no—
116C2×C4×C5×D3C2314yes—
117C2×C4×C5×D3C2314yescomplemented
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×D20—24no—
121C2×C3×D20C2314yes—
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yescomplemented
124C2×#1204—24no—
125C2×#1204C2314yescomplemented
126C2×#1203—24no—
127C2×#1203—42no—
128C2×#1203C2314yescomplemented
129C2×#1203C2314yescomplemented
130C2×#1202—24no—
131C2×#1202D418yescomplemented
132C2×#1202C2314yes—
133C2×#1202C2314yes—
134C2×#1201—24no—
135C2×#1201—42no—
136C2×#1201C2314yescomplemented
137C2×#1201C2314yescomplemented
138C2×#1200—42no—
139C2×#1200C2314yescomplemented
140C2×D5×Dic3—42no—
141C2×D5×Dic3C2314yescomplemented
142D3×D20—232no—
143#6771—232no—
144C3×C5×C4⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6714C2314yescomplemented
147#6714C2314yescomplemented
148#6712C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yes—
150C5×(C2×D3)⋊C4C2314yescomplemented
151C4×C5×Dic3C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#685C2314yescomplemented
154C3×#685C2314yescomplemented
155C3×#683C2314yescomplemented
156Dic3⋊Dic5C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yes—
159(C2×D3)⋊Dic5C2314yes—
160#6665C2314yescomplemented
161C22×D3×D4—51no—
162C22×#235—51no—
163C2×C3×#123—51no—
164C2×#939—51no—
165C22×(C2×D3)⋊C4—51no—
166#5654—516no—
167C2×#896—51no—
168C2×#895—51no—
169C2×#894—51no—
170C2×#893D511yescharacteristic, complemented
171C2×#885—51no—
172C2×#884—51no—
173C2×#882—51no—
174C2×#882—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C23×C4×C5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C2×#709—38no—
187C2×#709—68no—
188C22×D20—31no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20—38no—
192C22×D20—68no—
193C22×D20C2×D311yescharacteristic
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C4×C5×D4—38no—
200C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C42×C5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206#4083—38no—
207#4083—38no—
208#4076—38no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×#685C2×D311yescharacteristic, complemented
216C2×#685C2×D311yescharacteristic, complemented
217C2×C4⋊Dic5—31no—
218#4070—38no—
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic, complemented
221#4040—38no—
222#4040C2×D318yescomplemented
223#4030—38no—
224#4030—38no—
225D5×C22⋊C4—38no—
226D5×C22⋊C4—38no—
227#4021—38no—
228C4×D20—38no—
229C2×#546—151noSylow
230C23×C3×C5C2411yescharacteristic
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15C2×D414yes—
237C22×D15C2412yes—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3#4114yescomplemented
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×C5—22no—
266C2×C3×C4×C5C2412yes—
267C2×C3×C4×C5C2412yes—
268C2×C3×C4×C5C2412yes—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—28no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3C2×D414yes—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C4×C5×D3—28no—
281C4×C5×D3—28no—
282C2×C3×Dic5—22no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5C2412yes—
285C2×C3×Dic5C2412yes—
286C3×D20—28no—
287C3×C4×D5—28no—
288#1204—28no—
289#1203—28no—
290#1203—44no—
291#1202—28no—
292#1202C2×D4116yescomplemented
293#1201—28no—
294#1201—44no—
295#1200—44no—
296D5×Dic3—44no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C23×Dic3—51no—
306C2×D3×D4—58no—
307C2×D3×D4—108no—
308C2×#235—58no—
309C2×#235—108no—
310C22×D12—51no—
311C22×D12—51no—
312C22×D12—51no—
313C22×D12C2×D511yescharacteristic
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3C2×D511yescharacteristic
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×#123—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×#217—51no—
326#939—58no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4—51no—
330C2×(C2×D3)⋊C4—51no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—58no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4—51no—
338C2×C4×Dic3C2×D511yescharacteristic, complemented
339#896—58no—
340#895—58no—
341#894—58no—
342#893C2×D518yescomplemented
343#885—58no—
344#884—58no—
345#882—58no—
346#882—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C23×D5—31no—
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—64no—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—34no—
368C22×C4×C5—34no—
369C22×C4×C5—64no—
370C22×C4×C5—64no—
371C22×C4×C5C22×D311yescharacteristic
372C22×C4×C5C22×D311yescharacteristic
373C22×C4×C5C22×D311yescharacteristic
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—122no—
381C2×C22⋊D5—122no—
382C22×Dic5—31no—
383C22×Dic5—31no—
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D311yescharacteristic
386#709—632no—
387C2×D20—24no—
388C2×D20—38no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—632no—
393C2×D20—64no—
394C2×D20—64no—
395C2×D20C22×D314yes—
396C2×C4×D5—24no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—122no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4C22×D314yescomplemented
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C42×C5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yescomplemented
418#685C22×D314yescomplemented
419#685C22×D314yescomplemented
420C4⋊Dic5—34no—
421#683—34no—
422#683C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—51no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—31no—
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×D15—22no—
447C2×D15—22no—
448C2×D15—22no—
449C2×D15—44no—
450C2×D15C22×D414yes—
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×D3C2×#4114yescomplemented
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—
471C3×C4×C5—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C23×D3—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—104no—
494C22×C3×C4—51no—
495C22×C3×C4—51no—
496C22×C3×C4—54no—
497C22×C3×C4—104no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—54no—
502C2×#67—54no—
503C2×#67—58no—
504C2×#67—54no—
505C2×#67—54no—
506C2×#67—104no—
507C2×#67—104no—
508C2×#67—202no—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—54no—
512C22×Dic3—202no—
513C22×Dic3C22×D511yescharacteristic
514C22×Dic3C22×D511yescharacteristic
515D3×D4—1032no—
516#235—1032no—
517C2×D12—24no—
518C2×D12—54no—
519C2×D12—54no—
520C2×D12—54no—
521C2×D12—104no—
522C2×D12—104no—
523C2×D12—202no—
524C2×D12C22×D514yes—
525C2×C4×D3—24no—
526C2×C4×D3—24no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—104no—
530C2×C4×D3—202no—
531C2×C4×D3C22×D514yes—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C4⋊C4C22×D514yescomplemented
537C3×C22⋊C4—54no—
538C3×C22⋊C4—54no—
539C3×C22⋊C4—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×D514yes—
548(C2×D3)⋊C4C22×D514yescomplemented
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3C22×D514yescomplemented
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—34no—
567C22×D5—32no—
568C22×D5—32no—
569C22×D5—68no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
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—
586C2×C4×C5—22no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—68no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C2×C4×C5C23×D312yes—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C22⋊D5—124no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5C23×D312yes—
609C2×Dic5C23×D312yes—
610D20—28no—
611D20—316no—
612D20—68no—
613D20—68no—
614C4×D5—28no—
615C4×D5—68no—
616C4×D5—124no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—51no—
626C22×D4—158no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—31no—
636C23×C4—31no—
637C23×C4—51no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—58no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—38no—
651C4×D4—158no—
652C2×C4⋊C4—51no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4D3×D511yescharacteristic, complemented
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
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—31no—
671C2×C3×C5#54614yescomplemented
672C2×C3×C5C23×D411yescharacteristic
673C2×C3×C5C22×#4111yescharacteristic
674C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
675D15—24no—
676D15—42no—
677C3×D5—24no—
678C3×D5—42no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—54no—
682C23×C3—52no—
683C23×C3—52no—
684C23×C3—102no—
685C23×C3—102no—
686C23×C3—102no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3C23×D511yescharacteristic
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—54no—
696C22×D3—52no—
697C22×D3—52no—
698C22×D3—108no—
699C22×D3—108no—
700C22×D3—102no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—108no—
706C22×D3—108no—
707C22×D3—204no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—2016no—
711C22×D3#70914yescomplemented
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—108no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4C23×D512yes—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—204no—
730C2×Dic3—22no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—102no—
734C2×Dic3—102no—
735C2×Dic3—204no—
736C2×Dic3D4×D514yes—
737C2×Dic3C23×D512yes—
738C2×Dic3C23×D512yes—
739D12—28no—
740D12—108no—
741D12—108no—
742D12—204no—
743C4×D3—28no—
744C4×D3—28no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—34no—
749C22×C5—68no—
750C22×C5—62no—
751C22×C5—62no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×D3×D412yes—
757C22×C5D3×#4112yes—
758C22×C5#100912yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—28no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—22no—
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—34no—
767C2×D5—44no—
768C2×D5—68no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—22no—
781C4×C5—34no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—51no—
790C24—51no—
791C24—154no—
792C24—154no—
793C24—151no—
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—64no—
807C2×D4—104no—
808C2×D4—154no—
809C2×D4—158no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—3032no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—34no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—51no—
829C22×C4—54no—
830C22×C4—64no—
831C22×C4—64no—
832C22×C4—104no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—304no—
839C22×C4—602no—
840C22×C4—602no—
841C22×C4C2×D3×D511yescharacteristic
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4C2×D3×D514yescomplemented
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
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—34no—
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—204no—
870C22×C3C2×#70912yes—
871C22×C3C2×D4×D512yes—
872C22×C3#414912yes—
873C22×C3C24×D511yescharacteristic
874C2×D3—28no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—44no—
881C2×D3—54no—
882C2×D3—108no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—2016no—
890C2×D3—204no—
891C2×D3C2×#70914yescomplemented
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—102no—
896C3×C4—102no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—64no—
902C2×C5—122no—
903C2×C5#565414yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×D3×#4111yescharacteristic
906C2×C5C2×#100911yescharacteristic
907D5—24no—
908D5—42no—
909D5—64no—
910D5—122no—
911C23—34no—
912C23—32no—
913C23—32no—
914C23—54no—
915C23—52no—
916C23—52no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—154no—
928C23—152no—
929C23—152no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—604no—
941C23—6016no—
942C23—6016no—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—68no—
946D4—108no—
947D4—1516no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—34no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—68no—
964C2×C4—62no—
965C2×C4—108no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—604no—
974C2×C4—604no—
975C2×C4C22×D3×D512yes—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—104no—
979C2×C3—202no—
980C2×C3#6588414yescomplemented
981C2×C3C22×#70911yescharacteristic
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×#414911yescharacteristic
984D3—24no—
985D3—42no—
986D3—104no—
987D3—202no—
988C5C2×#565411yescharacteristic, 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—124no—
1004C22—154no—
1005C22—204no—
1006C22—308no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—6016no—
1013C22—6016no—
1014C22—604no—
1015C22D3×#70912yes—
1016C22D3×D4×D512yes—
1017C22#9203512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—22no—
1022C4—34no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6588411yescharacteristic, complemented, Sylow
1029C2—64no—
1030C2—104no—
1031C2—122no—
1032C2—202no—
1033C2—304no—
1034C2—602no—
1035C2#1175385814yesdirect product factor
1036C2C2×D3×#70911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9203511yescharacteristic
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×D3×D20C2semidirect
2. C22×#6771C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#893C2semidirect
5. C2×C3×#4040C2semidirect
6. C2×#91475C2semidirect
7. C2×#91475C2semidirect
8. C2×#91473C2semidirect
9. C2×D5×(C2×D3)⋊C4C2semidirect
10. C2×#91454C2semidirect
11. C2×#91420C2semidirect
12. C2×#91408C2semidirect
13. C2×#91395C2semidirect
14. C2×#91353C2semidirect
15. C2×#91352C2semidirect
16. #11753858C2direct (N × H)
21. C22×C4×D15C22semidirect
24. C22×C4×C5×D3C22semidirect
26. C22×C3×C4×D5C22semidirect
27. C22×#1204C22semidirect
28. C22×#1203C22semidirect
29. C22×#1203C22semidirect
32. C22×#1201C22semidirect
33. C22×#1201C22semidirect
34. C22×#1200C22semidirect
35. C22×D5×Dic3C22semidirect
37. C2×D3×D20C22semidirect
39. C2×#6771C22semidirect
40. C2×C3×C5×C4⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. #91783C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C4×C5×Dic3C22semidirect
49. C5×#893C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#683C22semidirect
54. C3×#4040C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×#6667C22semidirect
59. C2×#6665C22semidirect
60. #91475C22semidirect
61. #91475C22semidirect
62. #91473C22semidirect
63. D5×(C2×D3)⋊C4C22semidirect
64. #91454C22semidirect
65. #91420C22semidirect
66. #91408C22semidirect
67. #91395C22semidirect
68. #91353C22semidirect
69. #91352C22semidirect
80. C2×#4040D3semidirect
109. C2×C4×D15C23semidirect
117. C2×C4×C5×D3C23semidirect
123. C2×C3×C4×D5C23semidirect
125. C2×#1204C23semidirect
128. C2×#1203C23semidirect
129. C2×#1203C23semidirect
131. C2×#1202D4semidirect
136. C2×#1201C23semidirect
137. C2×#1201C23semidirect
139. C2×#1200C23semidirect
141. C2×D5×Dic3C23semidirect
144. C3×C5×C4⋊C4C23semidirect
145. #6714C23semidirect
146. #6714C23semidirect
147. #6714C23semidirect
148. #6712C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C4×C5×Dic3C23semidirect
152. C3×#685C23semidirect
153. C3×#685C23semidirect
154. C3×#685C23semidirect
155. C3×#683C23semidirect
156. Dic3⋊Dic5C23semidirect
157. #6667C23semidirect
160. #6665C23semidirect
170. C2×#893D5semidirect
197. C22×C4×D5C2×D3semidirect
200. C2×C5×C4⋊C4C2×D3semidirect
214. C2×#685C2×D3semidirect
215. C2×#685C2×D3semidirect
216. C2×#685C2×D3semidirect
220. C2×#683C2×D3semidirect
222. #4040C2×D3semidirect
244. C22×C5×D3#41semidirect
292. #1202C2×D4semidirect
317. C22×C4×D3C2×D5semidirect
321. C2×C3×C4⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
338. C2×C4×Dic3C2×D5semidirect
342. #893C2×D5semidirect
403. C2×C4×D5C22×D3semidirect
406. C5×C4⋊C4C22×D3semidirect
417. #685C22×D3semidirect
418. #685C22×D3semidirect
419. #685C22×D3semidirect
422. #683C22×D3semidirect
458. C2×C5×D3C2×#41semidirect
532. C2×C4×D3C22×D5semidirect
536. C3×C4⋊C4C22×D5semidirect
548. (C2×D3)⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
655. C2×C4⋊C4D3×D5semidirect
671. C2×C3×C5#546semidirect
711. C22×D3#709semidirect
847. C4⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#709semidirect
903. C2×C5#5654semidirect
980. C2×C3#65884semidirect
988. C5C2×#5654semidirect
1028. C3C2×#65884semidirect
1035. C2#11753858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D202
C22×#67712
C2×#917832
C2×C5×#8932
C2×C3×#40402
C2×#914752
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×#914542
C2×#914202
C2×#914082
C2×#913952
C2×#913532
C2×#913522
#117538582
C2×#658843
C2×#56545