Finite Group Databasebeta

← C2×#11753241 #14482658

Subgroups — C2×#11753241 #14482658

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×#6779C211yesmaximal, characteristic, complemented
2C22×D3×D20C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91577C211yesmaximal, characteristic, complemented
8C2×#91569C211yesmaximal, characteristic, complemented
9C2×#91473C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×#1202C211yesmaximal, characteristic, complemented
12C2×#91433C211yesmaximal, characteristic, complemented
13C2×#91407C211yesmaximal, characteristic, complemented
14C2×#91353C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16#11753241C2116yesmaximal, direct product factor
17C2×#65884—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C23×C5×Dic3C2211yescharacteristic, complemented
26C22×C4×C5×D3C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×D20C2211yescharacteristic
30C22×C3×C4×D5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1200C2211yescharacteristic, complemented
35C2×#6779—28no—
36C2×#6779C2218yescomplemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×D3×D20—28no—
39C2×D3×D20C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43#91773C2218yescomplemented
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic
45C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C4×C5×Dic3C2211yescharacteristic, complemented
47C5×#67⋊C4C2218yescomplemented
48C2×C3×#685C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50C3×#4030C2218yescomplemented
51#91577C2218yescomplemented
52#91577C2218yescomplemented
53#91569C2218yescomplemented
54C2×Dic3⋊Dic5C2211yescharacteristic, complemented
55C2×#6667C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×#6665C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91473C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65C4×#1202C2218yescomplemented
66#91433C2218yescomplemented
67#91407C2218yescomplemented
68#91353C2218yescomplemented
69#91352C2218yescomplemented
70C2×#5610—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×#4040—31no—
81C2×#4030—31no—
82C2×#4030D311yescharacteristic, complemented
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4—31no—
85C2×#4021—31no—
86C2×C4×D20—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
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×#1220—42no—
105C2×#1220C2314yescomplemented
106C2×#1220C2314yescomplemented
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×D60—24no—
110C2×D60C2314yes—
111C2×C4×D15—42no—
112C2×C4×D15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67C2314yes—
115C22×C5×Dic3—24no—
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2314yescomplemented
120C2×C4×C5×D3—24no—
121C2×C4×C5×D3C2314yes—
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×#1202—24no—
135C2×#1202D418yescomplemented
136C2×#1202C2314yes—
137C2×#1202C2314yes—
138C2×#1200—24no—
139C2×#1200C2314yescomplemented
140#6779—232no—
141C2×D5×Dic3—24no—
142C2×D5×Dic3C2314yescomplemented
143D3×D20—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×(C2×D3)⋊C4C2314yes—
148C5×Dic3⋊C4C2314yescomplemented
149C4×C5×Dic3C2314yescomplemented
150C3×#685C2314yescomplemented
151C3×#683C2314yescomplemented
152Dic3⋊Dic5C2314yescomplemented
153#6667C2314yescomplemented
154#6667C2314yescomplemented
155#6667C2314yescomplemented
156(C2×D3)⋊Dic5C2314yes—
157(C2×D3)⋊Dic5C2314yes—
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×#884—51no—
175C2×#67⋊C4D511yescharacteristic, complemented
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⋊D5C2×D311yescharacteristic, complemented
185C22×C22⋊D5C2×D311yescharacteristic, complemented
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⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
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×#685—31no—
215C2×#685—31no—
216C2×#685C2×D311yescharacteristic, complemented
217C2×C4⋊Dic5—31no—
218#4070—38no—
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic, complemented
221#4040—38no—
222#4040—38no—
223#4030—38no—
224#4030C2×D318yescomplemented
225D5×C22⋊C4—38no—
226D5×C22⋊C4—38no—
227#4021—38no—
228C4×D20—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—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15C2×D414yes—
241C22×D15C2412yes—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3#4114yescomplemented
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—
268#1220—44no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—44no—
275C5×#67—28no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—28no—
279C2×C5×Dic3C2×D414yes—
280C2×C5×Dic3C2412yes—
281C2×C5×Dic3C2412yes—
282C2×C5×Dic3C2412yes—
283C4×C5×D3—28no—
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#1202—28no—
294#1202C2×D4116yescomplemented
295#1200—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×#67C2×D511yescharacteristic
308C23×Dic3—51no—
309C23×Dic3C2×D511yescharacteristic, complemented
310C2×#237—58no—
311C2×#237—108no—
312C2×D3×D4—58no—
313C2×D3×D4—108no—
314C22×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic
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
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4C2×D511yescharacteristic, complemented
342C2×C4×Dic3C2×D511yescharacteristic, complemented
343#896—58no—
344#894—58no—
345#885—58no—
346#884—58no—
347#67⋊C4C2×D518yescomplemented
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
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—31no—
368C22×C4×C5—34no—
369C22×C4×C5—34no—
370C22×C4×C5—64no—
371C22×C4×C5—64no—
372C22×C4×C5C22×D311yescharacteristic
373C22×C4×C5C22×D311yescharacteristic
374C2×C22⋊D5—24no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—42no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—122no—
380C2×C22⋊D5C22×D314yescomplemented
381C2×C22⋊D5C22×D314yescomplemented
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—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—42no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—122no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4C22×D314yescomplemented
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#685—34no—
418#685—34no—
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—151no—
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—31no—
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×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—44no—
454C2×D15C22×D414yes—
455C2×C5×D3—28no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
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—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3C22×D511yescharacteristic
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
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—54no—
506C2×#67—54no—
507C2×#67—58no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—202no—
513C2×#67C22×D514yes—
514C22×Dic3—24no—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
518C22×Dic3—104no—
519C22×Dic3C22×D511yescharacteristic
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522C22×Dic3C22×D514yescomplemented
523#237—1032no—
524D3×D4—1032no—
525C2×D12—54no—
526C2×D12—104no—
527C2×C4×D3—24no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yes—
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×D514yes—
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3C22×D514yescomplemented
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—34no—
556C23×C5—32no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
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—34no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—68no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5—62no—
596C2×C4×C5C23×D312yes—
597C2×C4×C5C23×D312yes—
598C22⋊D5—28no—
599C22⋊D5—44no—
600C22⋊D5—68no—
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—44no—
615C4×D5—68no—
616C4×D5—68no—
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—51no—
627C22×D4—51no—
628C22×D4—158no—
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—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—38no—
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—31no—
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—
677D15—42no—
678C3×D5—24no—
679C3×D5—42no—
680C5×D3—24no—
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—54no—
697C22×D3—52no—
698C22×D3—52no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—102no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—108no—
707C22×D3—108no—
708C22×D3—204no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3—2016no—
712C22×D3#70914yescomplemented
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—516no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—28no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—108no—
737C2×Dic3—102no—
738C2×Dic3—102no—
739C2×Dic3D4×D514yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742C2×Dic3C23×D512yes—
743D12—108no—
744C4×D3—28no—
745C4×D3—108no—
746C4×D3—204no—
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×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—34no—
767C2×D5—44no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—68no—
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—34no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—154no—
791C24—154no—
792C24—151no—
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—54no—
806C2×D4—54no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—104no—
810C2×D4—104no—
811C2×D4—154no—
812C2×D4—158no—
813C2×D4—154no—
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—34no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—34no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—54no—
831C22×C4—64no—
832C22×C4—64no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—202no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
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—34no—
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×#70912yes—
875C22×C3C2×D4×D512yes—
876C22×C3#414912yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—22no—
880C2×D3—22no—
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—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—64no—
903C2×C5#561014yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×#100411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907D5—24no—
908D5—42no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—34no—
915C23—32no—
916C23—54no—
917C23—52no—
918C23—52no—
919C23—62no—
920C23—62no—
921C23—102no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—154no—
927C23—152no—
928C23—152no—
929C23—308no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—604no—
940C23—6016no—
941C23—6016no—
942C23C22×D3×D512yes—
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—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—68no—
963C2×C4—68no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—152no—
969C2×C4—152no—
970C2×C4—204no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—202no—
981C2×C3#6588414yescomplemented
982C2×C3C22×#70911yescharacteristic
983C2×C3C22×D4×D511yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—24no—
986D3—104no—
987D3—202no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—34no—
993C22—44no—
994C22—54no—
995C22—68no—
996C22—62no—
997C22—62no—
998C22—108no—
999C22—102no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
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#9202612yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6588411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—64no—
1031C2—104no—
1032C2—202no—
1033C2—304no—
1034C2—602no—
1035C2#1175324114yesdirect product factor
1036C2C2×D3×#70911yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202611yescharacteristic
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×#6779C2semidirect
2. C22×D3×D20C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#67⋊C4C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91577C2semidirect
7. C2×#91577C2semidirect
8. C2×#91569C2semidirect
9. C2×#91473C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×C4×#1202C2semidirect
12. C2×#91433C2semidirect
13. C2×#91407C2semidirect
14. C2×#91353C2semidirect
15. C2×#91352C2semidirect
16. #11753241C2direct (N × H)
20. C22×#1220C22semidirect
21. C22×#1220C22semidirect
23. C22×C4×D15C22semidirect
25. C23×C5×Dic3C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C22⋊D5C22semidirect
30. C22×C3×C4×D5C22semidirect
31. C22×#1204C22semidirect
34. C22×#1200C22semidirect
36. C2×#6779C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×D3×D20C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
43. #91773C22semidirect
45. C2×C5×Dic3⋊C4C22semidirect
46. C2×C4×C5×Dic3C22semidirect
47. C5×#67⋊C4C22semidirect
48. C2×C3×#685C22semidirect
49. C2×C3×#683C22semidirect
50. C3×#4030C22semidirect
51. #91577C22semidirect
52. #91577C22semidirect
53. #91569C22semidirect
54. C2×Dic3⋊Dic5C22semidirect
55. C2×#6667C22semidirect
56. C2×#6667C22semidirect
57. C2×#6667C22semidirect
60. C2×#6665C22semidirect
61. C2×#6665C22semidirect
62. C2×#6665C22semidirect
63. #91473C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. C4×#1202C22semidirect
66. #91433C22semidirect
67. #91407C22semidirect
68. #91353C22semidirect
69. #91352C22semidirect
82. C2×#4030D3semidirect
105. C2×#1220C23semidirect
106. C2×#1220C23semidirect
112. C2×C4×D15C23semidirect
119. C22×C5×Dic3C23semidirect
124. C2×C3×C22⋊D5C23semidirect
125. C2×C3×C22⋊D5C23semidirect
131. C2×C3×C4×D5C23semidirect
133. C2×#1204C23semidirect
135. C2×#1202D4semidirect
139. C2×#1200C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
148. C5×Dic3⋊C4C23semidirect
149. C4×C5×Dic3C23semidirect
150. C3×#685C23semidirect
151. C3×#683C23semidirect
152. Dic3⋊Dic5C23semidirect
153. #6667C23semidirect
154. #6667C23semidirect
155. #6667C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. #6665C23semidirect
175. C2×#67⋊C4D5semidirect
184. C22×C22⋊D5C2×D3semidirect
185. C22×C22⋊D5C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
202. C2×C5×C22⋊C4C2×D3semidirect
216. C2×#685C2×D3semidirect
220. C2×#683C2×D3semidirect
224. #4030C2×D3semidirect
245. C22×C5×D3#41semidirect
294. #1202C2×D4semidirect
309. C23×Dic3C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
341. C2×Dic3⋊C4C2×D5semidirect
342. C2×C4×Dic3C2×D5semidirect
347. #67⋊C4C2×D5semidirect
380. C2×C22⋊D5C22×D3semidirect
381. C2×C22⋊D5C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
408. C5×C22⋊C4C22×D3semidirect
419. #685C22×D3semidirect
422. #683C22×D3semidirect
458. C2×C5×D3C2×#41semidirect
522. C22×Dic3C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
712. C22×D3#709semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#709semidirect
903. C2×C5#5610semidirect
981. C2×C3#65884semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65884semidirect
1035. C2#11753241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67792
C22×D3×D202
C2×#917732
C2×C5×#67⋊C42
C2×C3×#40302
C2×#915772
C2×#915692
C2×#914732
C2×D5×(C2×D3)⋊C42
C2×C4×#12022
C2×#914332
C2×#914072
C2×#913532
C2×#913522
#117532412
C2×#658843
C2×#56105