Finite Group Databasebeta

← C2×#11755037 #14482601

Subgroups — C2×#11755037 #14482601

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×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#6780C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C5×#937C211yesmaximal, characteristic, complemented
5C2×C3×#4084C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
8C2×#91558C211yesmaximal, characteristic, complemented
9C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
10C2×#91548C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11755037C2116yesmaximal, direct product factor
13C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#91440C211yesmaximal, characteristic, complemented
15C2×#91436C211yesmaximal, characteristic, complemented
16C2×#91427C211yesmaximal, characteristic, complemented
17C2×#65925—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic, complemented
23C23×Dic15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C2×D3×C22⋊D5—28no—
30C2×D3×C22⋊D5C2218yescomplemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1203C2211yescharacteristic
33C22×#1201C2211yescharacteristic
34C22×D3×Dic5C2211yescharacteristic
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C2×#6780—28no—
38C2×#6780C2218yescomplemented
39C22×D5×Dic3C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41#91828C2218yescomplemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6712C2211yescharacteristic, complemented
44C2×C5×#217C2211yescharacteristic, complemented
45C5×#937C2218yescomplemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C3×#4084C2218yescomplemented
51C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
52#91577C2218yescomplemented
53#67⋊Dic5C2218yescomplemented
54#91558C2218yescomplemented
55D3×C22⋊Dic5C2218yescomplemented
56#91548C2218yescomplemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic
62C2×(C2×D3)⋊Dic5C2211yescharacteristic
63C2×#6665C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91526C2218yescomplemented
66D5×(C2×D3)⋊C4C2218yescomplemented
67#91440C2218yescomplemented
68#91436C2218yescomplemented
69#91427C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×#711—31no—
73C2×C5×#120—31no—
74C22×C22⋊Dic5—31no—
75C2×#4085—31no—
76C2×#4085—31no—
77C2×#4084D311yescharacteristic, complemented
78C2×#4083—31no—
79C2×D4×Dic5—31no—
80#65925—316no—
81C2×#4032—31no—
82C2×#4031—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C2×D5×C22⋊C4—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—24no—
92C23×C5×D3—42no—
93C23×C5×D3C2314yes—
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C2×C3×C5×D4—42no—
102C2×C3×C5×D4C2314yescomplemented
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220—42no—
106C2×#1220C2314yes—
107C2×#1220C2314yescomplemented
108C22×Dic15—24no—
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C22×Dic15C2311yescharacteristic
112C22×Dic15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67—24no—
115C2×C5×#67C2314yes—
116C2×C5×#67C2314yescomplemented
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C2×C3×C22⋊D5—24no—
120C2×C3×C22⋊D5—24no—
121C2×C3×C22⋊D5C2314yes—
122C2×C3×C22⋊D5C2314yescomplemented
123C22×C3×Dic5C2311yescharacteristic
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C2×C3×C4×D5—42no—
127C2×C3×C4×D5C2314yescomplemented
128D3×C22⋊D5—232no—
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1203—24no—
132C2×#1203C2314yes—
133C2×#1201D418yescomplemented
134C2×#1201C2314yes—
135C2×D3×Dic5—24no—
136C2×D3×Dic5—24no—
137C2×D3×Dic5—42no—
138C2×D3×Dic5C2314yes—
139C2×D3×Dic5C2314yescomplemented
140C2×D3×Dic5C2314yescomplemented
141#6780—232no—
142C2×D5×Dic3—24no—
143C2×D5×Dic3C2314yescomplemented
144#6719C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yes—
149C5×(C2×D3)⋊C4C2314yescomplemented
150C3×C22⋊Dic5C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×C4⋊Dic5C2314yescomplemented
153Dic3⋊Dic5C2314yescomplemented
154#6669C2314yescomplemented
155#6667C2314yescomplemented
156#6667C2314yescomplemented
157(C2×D3)⋊Dic5C2314yes—
158(C2×D3)⋊Dic5C2314yes—
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4—51no—
163C2×C3×#121—51no—
164C2×#939—51no—
165C2×#937—51no—
166C2×#937D511yescharacteristic, complemented
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⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C25×C5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4C2×D311yescharacteristic, complemented
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—38no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—68no—
188C22×C22⋊D5C2×D311yescharacteristic
189C22×C22⋊D5C2×D311yescharacteristic, complemented
190C23×Dic5—31no—
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C2×#711—38no—
195C2×#711—68no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×Dic10—31no—
199C5×#120—38no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—38no—
207C2×C22⋊Dic5C2×D311yescharacteristic, complemented
208C2×C22⋊Dic5C2×D311yescharacteristic, complemented
209#4085—38no—
210#4085—38no—
211#4084C2×D318yescomplemented
212#4083—38no—
213D4×Dic5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×C4⋊Dic5—31no—
219C2×C4⋊Dic5C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683—31no—
222C2×C4×Dic5—31no—
223#4032—38no—
224#4031—38no—
225#4029—38no—
226#4027—38no—
227D5×C22⋊C4—38no—
228#4024—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—28no—
248C22×C5×D3—28no—
249C22×C5×D3—44no—
250C22×C5×D3—416no—
251C22×C5×D3C2×D414yes—
252C22×C5×D3#4114yescomplemented
253C22×C5×D3C2412yes—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5C2×D414yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C3×C5×D4—44no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220—44no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—28no—
271C2×Dic15C2×D414yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C5×#67—28no—
276C5×#67—28no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3—22no—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C3×C22⋊D5—28no—
282C3×C22⋊D5—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5C2412yes—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C3×C4×D5—44no—
290#1204—28no—
291#1203—28no—
292#1201C2×D4116yescomplemented
293D3×Dic5—28no—
294D3×Dic5—28no—
295D3×Dic5—44no—
296D5×Dic3—28no—
297C24×D3—51no—
298C24×D3C2×D511yescharacteristic
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4C2×D511yescharacteristic, complemented
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67C2×D511yescharacteristic
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×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319C3×#121—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217C2×D511yescharacteristic, complemented
326#939—58no—
327#937—58no—
328#937C2×D518yescomplemented
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—58no—
337C2×(C2×D3)⋊C4C2×D511yescharacteristic
338C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3—51no—
343#896—58no—
344#894—58no—
345#885—58no—
346#884—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5—31no—
351C24×C5—34no—
352C24×C5—64no—
353C24×C5—64no—
354C24×C5—122no—
355C24×C5C22×D311yescharacteristic
356C24×C5C22×D311yescharacteristic
357C23×D5—31no—
358C23×D5—34no—
359C23×D5—64no—
360C23×D5—64no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—42no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4C22×D314yescomplemented
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—24no—
373C2×C22⋊D5—24no—
374C2×C22⋊D5—38no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—64no—
381C2×C22⋊D5—632no—
382C2×C22⋊D5—122no—
383C2×C22⋊D5C22×D314yes—
384C2×C22⋊D5C22×D314yescomplemented
385C22×Dic5—31no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—34no—
390C22×Dic5—34no—
391C22×Dic5—34no—
392C22×Dic5—64no—
393C22×Dic5—64no—
394C22×Dic5—64no—
395C22×Dic5—122no—
396C22×Dic5C22×D311yescharacteristic
397C22×Dic5C22×D311yescharacteristic
398C22×Dic5C22×D311yescharacteristic
399#711—632no—
400C2×C4×D5—34no—
401C2×C4×D5—42no—
402C2×C4×D5—64no—
403C2×C4×D5C22×D314yescomplemented
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5C22×D314yescomplemented
413C22⋊Dic5C22×D314yescomplemented
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418C4⋊Dic5—34no—
419C4⋊Dic5C22×D314yescomplemented
420#683—34no—
421#683—34no—
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—51no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—31no—
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—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5—44no—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—22no—
454C2×D15—44no—
455C2×C5×D3—28no—
456C2×C5×D3—28no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—22no—
461C2×C5×D3—416no—
462C2×C5×D3C22×D414yes—
463C2×C5×D3C2×#4114yescomplemented
464C2×C3×D5—28no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5C22×D414yes—
468D3×D5—416no—
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472Dic15C22×D414yes—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C24×C3C22×D511yescharacteristic
481C23×D3—24no—
482C23×D3—24no—
483C23×D3—42no—
484C23×D3—51no—
485C23×D3—54no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—202no—
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—42no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4C22×D514yescomplemented
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4—51no—
501C22×C3×C4—54no—
502C22×C3×C4—202no—
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—24no—
505C2×#67—24no—
506C2×#67—58no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—202no—
512C2×#67C22×D514yes—
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—54no—
526C2×D12—104no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538#217—54no—
539#217—54no—
540#217C22×D514yescomplemented
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)⋊C4C22×D514yes—
547(C2×D3)⋊C4C22×D514yescomplemented
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—22no—
558C23×C5—34no—
559C23×C5—34no—
560C23×C5—32no—
561C23×C5—32no—
562C23×C5—68no—
563C23×C5—68no—
564C23×C5—62no—
565C23×C5—62no—
566C23×C5—62no—
567C23×C5—62no—
568C23×C5—124no—
569C23×C5—1216no—
570C23×C5C23×D312yes—
571C23×C5C23×D312yes—
572C23×C5C23×D311yescharacteristic
573C22×D5—22no—
574C22×D5—22no—
575C22×D5—32no—
576C22×D5—68no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—68no—
581C22×D5—124no—
582C22×D5—1216no—
583C22×D5D3×D414yes—
584C22×D5C23×D312yes—
585C5×D4—44no—
586C5×D4—68no—
587C5×D4—68no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—62no—
592C2×C4×C5—62no—
593C2×C4×C5C23×D312yes—
594C22⋊D5—28no—
595C22⋊D5—28no—
596C22⋊D5—316no—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C2×Dic5—22no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—34no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—68no—
609C2×Dic5—68no—
610C2×Dic5—62no—
611C2×Dic5—62no—
612C2×Dic5—124no—
613C2×Dic5C23×D312yes—
614C2×Dic5C23×D312yes—
615C2×Dic5C23×D312yes—
616C4×D5—44no—
617C4×D5—68no—
618Dic10—68no—
619C25—31no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4D3×D511yescharacteristic, complemented
635C23×C4—51no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—38no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—51no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
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—42no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—42no—
678C3×D5—24no—
679C5×D3—24no—
680C5×D3—24no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—54no—
688C23×C3—52no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3C23×D512yes—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—28no—
699C22×D3—28no—
700C22×D3—44no—
701C22×D3—416no—
702C22×D3—52no—
703C22×D3—108no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—108no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3D4×D514yes—
711C22×D3#71114yescomplemented
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—44no—
715C3×D4—108no—
716C3×D4—108no—
717C2×C3×C4—22no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4—204no—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—28no—
728#67—516no—
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—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—34no—
755C22×C5—34no—
756C22×C5—44no—
757C22×C5—44no—
758C22×C5—62no—
759C22×C5—62no—
760C22×C5—62no—
761C22×C5—62no—
762C22×C5—68no—
763C22×C5—68no—
764C22×C5—1216no—
765C22×C5C2×D3×D412yes—
766C22×C5#100412yes—
767C22×C5D3×#4112yes—
768C22×C5C24×D311yescharacteristic
769C2×D5—22no—
770C2×D5—22no—
771C2×D5—28no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—124no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781Dic5—22no—
782Dic5—22no—
783Dic5—22no—
784Dic5—34no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—34no—
790C24—51no—
791C24—64no—
792C24—64no—
793C24—122no—
794C24—154no—
795C24—151no—
796C24—304no—
797C24—304no—
798C24—602no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—42no—
807C2×D4—54no—
808C2×D4—54no—
809C2×D4—64no—
810C2×D4—64no—
811C2×D4—104no—
812C2×D4—104no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—158no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—602no—
822C2×D4C2×D3×D514yescomplemented
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—151no—
834C22×C4—154no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—202no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
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—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—44no—
870C22×C3—54no—
871C22×C3—108no—
872C22×C3—102no—
873C22×C3—102no—
874C22×C3C2×D4×D512yes—
875C22×C3C2×#71112yes—
876C22×C3#414412yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—28no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—416no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—2016no—
889C2×D3—204no—
890C2×D3C2×D4×D514yes—
891C2×D3C2×#71114yescomplemented
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—54no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—42no—
903C2×C5—64no—
904C2×C5—64no—
905C2×C5#561014yescomplemented
906C2×C5C22×D3×D411yescharacteristic
907C2×C5C2×#100411yescharacteristic
908C2×C5C2×D3×#4111yescharacteristic
909D5—24no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—34no—
918C23—34no—
919C23—32no—
920C23—32no—
921C23—54no—
922C23—52no—
923C23—68no—
924C23—68no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—102no—
930C23—102no—
931C23—124no—
932C23—1216no—
933C23—152no—
934C23—308no—
935C23—308no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—604no—
940C23—6016no—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—44no—
946D4—68no—
947D4—68no—
948D4—108no—
949D4—108no—
950D4—1516no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—52no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—102no—
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×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—104no—
981C2×C3#6592514yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C22×#71111yescharacteristic
984C2×C3C2×#414411yescharacteristic
985D3—24no—
986D3—24no—
987D3—202no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—34no—
996C22—34no—
997C22—44no—
998C22—44no—
999C22—54no—
1000C22—62no—
1001C22—62no—
1002C22—68no—
1003C22—68no—
1004C22—62no—
1005C22—62no—
1006C22—102no—
1007C22—108no—
1008C22—102no—
1009C22—1216no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22D3×D4×D512yes—
1016C22D3×#71112yes—
1017C22#9204912yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—62no—
1021C4—62no—
1022C4—102no—
1023C4—102no—
1024C4—102no—
1025C4—154no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6592511yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—42no—
1031C2—64no—
1032C2—64no—
1033C2—104no—
1034C2—602no—
1035C2#1175503714yesdirect product factor
1036C2C2×D3×D4×D511yescharacteristic
1037C2C2×D3×#71111yescharacteristic
1038C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D3×C22⋊D5C2semidirect
2. C22×#6780C2semidirect
3. C2×#91828C2semidirect
4. C2×C5×#937C2semidirect
5. C2×C3×#4084C2semidirect
6. C2×#91577C2semidirect
7. C2×#67⋊Dic5C2semidirect
8. C2×#91558C2semidirect
9. C2×D3×C22⋊Dic5C2semidirect
10. C2×#91548C2semidirect
11. C2×#91526C2semidirect
12. #11755037C2direct (N × H)
13. C2×D5×(C2×D3)⋊C4C2semidirect
14. C2×#91440C2semidirect
15. C2×#91436C2semidirect
16. C2×#91427C2semidirect
20. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
23. C23×Dic15C22semidirect
25. C22×C5×#67C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C2×D3×C22⋊D5C22semidirect
31. C22×#1204C22semidirect
35. C22×D3×Dic5C22semidirect
36. C22×D3×Dic5C22semidirect
38. C2×#6780C22semidirect
39. C22×D5×Dic3C22semidirect
40. C2×#6719C22semidirect
41. #91828C22semidirect
42. C2×#6714C22semidirect
43. C2×#6712C22semidirect
44. C2×C5×#217C22semidirect
45. C5×#937C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C3×#4084C22semidirect
51. C2×C3×C4⋊Dic5C22semidirect
52. #91577C22semidirect
53. #67⋊Dic5C22semidirect
54. #91558C22semidirect
55. D3×C22⋊Dic5C22semidirect
56. #91548C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6669C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
63. C2×#6665C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91526C22semidirect
66. D5×(C2×D3)⋊C4C22semidirect
67. #91440C22semidirect
68. #91436C22semidirect
69. #91427C22semidirect
77. C2×#4084D3semidirect
102. C2×C3×C5×D4C23semidirect
107. C2×#1220C23semidirect
112. C22×Dic15C23semidirect
116. C2×C5×#67C23semidirect
122. C2×C3×C22⋊D5C23semidirect
127. C2×C3×C4×D5C23semidirect
130. C2×#1204C23semidirect
133. C2×#1201D4semidirect
139. C2×D3×Dic5C23semidirect
140. C2×D3×Dic5C23semidirect
143. C2×D5×Dic3C23semidirect
144. #6719C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×#217C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C3×C22⋊Dic5C23semidirect
151. C3×C22⋊Dic5C23semidirect
152. C3×C4⋊Dic5C23semidirect
153. Dic3⋊Dic5C23semidirect
154. #6669C23semidirect
155. #6667C23semidirect
156. #6667C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
166. C2×#937D5semidirect
181. C22×C5×D4C2×D3semidirect
189. C22×C22⋊D5C2×D3semidirect
197. C22×C4×D5C2×D3semidirect
207. C2×C22⋊Dic5C2×D3semidirect
208. C2×C22⋊Dic5C2×D3semidirect
211. #4084C2×D3semidirect
219. C2×C4⋊Dic5C2×D3semidirect
252. C22×C5×D3#41semidirect
292. #1201C2×D4semidirect
301. C22×C3×D4C2×D5semidirect
307. C22×#67C2×D5semidirect
325. C2×#217C2×D5semidirect
328. #937C2×D5semidirect
338. C2×(C2×D3)⋊C4C2×D5semidirect
368. C2×C5×D4C22×D3semidirect
384. C2×C22⋊D5C22×D3semidirect
403. C2×C4×D5C22×D3semidirect
412. C22⋊Dic5C22×D3semidirect
413. C22⋊Dic5C22×D3semidirect
419. C4⋊Dic5C22×D3semidirect
463. C2×C5×D3C2×#41semidirect
497. C2×C3×D4C22×D5semidirect
513. C2×#67C22×D5semidirect
540. #217C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
634. C22×D4D3×D5semidirect
673. C2×C3×C5#546semidirect
711. C22×D3#711semidirect
822. C2×D4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
891. C2×D3C2×#711semidirect
905. C2×C5#5610semidirect
981. C2×C3#65925semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65925semidirect
1035. C2#11755037direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊D52
C22×#67802
C2×#918282
C2×C5×#9372
C2×C3×#40842
C2×#915772
C2×#67⋊Dic52
C2×#915582
C2×D3×C22⋊Dic52
C2×#915482
C2×#915262
#117550372
C2×D5×(C2×D3)⋊C42
C2×#914402
C2×#914362
C2×#914272
C2×#659253
C2×#56105