Finite Group Databasebeta

← C2×#11754942 #14482592

Subgroups — C2×#11754942 #14482592

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×C5×D3×D4C211yesmaximal, characteristic, complemented
2C22×#6780C211yesmaximal, characteristic, complemented
3C2×#91824C211yesmaximal, characteristic, complemented
4C2×C3×#4085C211yesmaximal, characteristic, complemented
5C2×#91568C211yesmaximal, characteristic, complemented
6C2×#91568C211yesmaximal, characteristic, complemented
7C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C2×Dic5×#67C211yesmaximal, characteristic, complemented
9C2×#91549C211yesmaximal, characteristic, complemented
10C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
11C2×#91525C211yesmaximal, characteristic, complemented
12#11754942C2116yesmaximal, direct product factor
13C2×#91453C211yesmaximal, characteristic, complemented
14C2×#91441C211yesmaximal, characteristic, complemented
15C2×#91423C211yesmaximal, characteristic, complemented
16C2×#91352C211yesmaximal, characteristic, complemented
17C2×#66140—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C24×C5×D3C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C23×Dic15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C2×C5×D3×D4—28no—
25C2×C5×D3×D4C2218yescomplemented
26C22×C5×D12C2211yescharacteristic
27C22×C4×C5×D3C2211yescharacteristic
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×C22⋊D5C2211yescharacteristic, complemented
30C23×C3×Dic5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1201C2211yescharacteristic
33C22×#1201C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic, complemented
35C22×D3×Dic5C2211yescharacteristic, complemented
36C22×D3×Dic5C2211yescharacteristic, complemented
37C2×#6780—28no—
38C2×#6780C2218yescomplemented
39C22×D5×Dic3C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6719C2211yescharacteristic, complemented
43#91824C2218yescomplemented
44C2×#6712C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
47C3×#4085C2218yescomplemented
48C2×C3×#685C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50#91568C2218yescomplemented
51#91568C2218yescomplemented
52D3×C22⋊Dic5C2218yescomplemented
53Dic5×#67C2218yescomplemented
54#91549C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2218yescomplemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91525C2218yescomplemented
66#91453C2218yescomplemented
67#91441C2218yescomplemented
68#91423C2218yescomplemented
69#91352C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C23×C5×D4—31no—
72C22×#711—31no—
73C2×#4099—31no—
74C2×#4099—31no—
75C22×C22⋊Dic5—31no—
76C22×C22⋊Dic5—31no—
77#66140—316no—
78C2×#4085—31no—
79C2×#4085D311yescharacteristic, complemented
80C2×#4084—31no—
81C2×#4082—31no—
82C2×#4081—31no—
83C2×#4081—31no—
84C2×D4×Dic5—31no—
85C2×C4×C22⋊D5—31no—
86C2×#4070—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×C5×D3—24no—
90C23×C5×D3—24no—
91C23×C5×D3—24no—
92C23×C5×D3—24no—
93C23×C5×D3—42no—
94C23×C5×D3—42no—
95C23×C5×D3C2311yescharacteristic
96C23×C5×D3C2314yes—
97C23×C5×D3C2314yes—
98C23×C5×D3C2311yescharacteristic
99C23×C5×D3C2311yescharacteristic
100C23×C3×D5C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5C2311yescharacteristic
104C22×Dic15—24no—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2314yescomplemented
110C2×C5×#67—24no—
111C2×C5×#67D418yescomplemented
112C2×C5×#67C2314yes—
113C2×C5×#67C2314yes—
114C22×C5×Dic3C2311yescharacteristic
115C5×D3×D4—232no—
116C2×C5×D12—24no—
117C2×C5×D12C2314yes—
118C2×C4×C5×D3—24no—
119C2×C4×C5×D3C2314yes—
120C2×C3×C22⋊D5—24no—
121C2×C3×C22⋊D5—42no—
122C2×C3×C22⋊D5C2314yescomplemented
123C2×C3×C22⋊D5C2314yescomplemented
124C22×C3×Dic5—42no—
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2314yescomplemented
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1201—24no—
132C2×#1201—24no—
133C2×#1201—42no—
134C2×#1201C2314yes—
135C2×#1201C2314yescomplemented
136C2×#1201C2314yescomplemented
137C2×D3×Dic5—24no—
138C2×D3×Dic5—42no—
139C2×D3×Dic5C2314yescomplemented
140C2×D3×Dic5C2314yescomplemented
141#6780—232no—
142C2×D5×Dic3—24no—
143C2×D5×Dic3C2314yescomplemented
144#6719C2314yescomplemented
145#6719C2314yescomplemented
146#6719C2314yescomplemented
147#6712C2314yescomplemented
148#6712C2314yescomplemented
149C3×C22⋊Dic5C2314yescomplemented
150C3×#685C2314yescomplemented
151C3×#683C2314yescomplemented
152Dic3⋊Dic5C2314yescomplemented
153(C2×D3)⋊Dic5C2314yes—
154(C2×D3)⋊Dic5C2314yes—
155(C2×D3)⋊Dic5C2314yes—
156(C2×D3)⋊Dic5C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4D511yescharacteristic, complemented
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⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C25×C5—31no—
178C25×C5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4—38no—
182C22×C5×D4—31no—
183C22×C5×D4—68no—
184C22×C5×D4C2×D311yescharacteristic
185C23×C4×C5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5C2×D311yescharacteristic, complemented
190C22×C22⋊D5C2×D311yescharacteristic, complemented
191C23×Dic5—31no—
192C23×Dic5—31no—
193C23×Dic5—31no—
194C23×Dic5C2×D311yescharacteristic, complemented
195C2×#711—38no—
196C2×#711—68no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199#4099—38no—
200#4099—38no—
201C2×C22⋊Dic5—31no—
202C2×C22⋊Dic5—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211C2×C22⋊Dic5—38no—
212C2×C22⋊Dic5—38no—
213C2×C22⋊Dic5C2×D311yescharacteristic, complemented
214#4085—38no—
215#4085C2×D318yescomplemented
216#4084—38no—
217#4082—38no—
218#4081—38no—
219#4081—38no—
220D4×Dic5—38no—
221C4×C22⋊D5—38no—
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224#4070—38no—
225C2×#683—31no—
226C2×#683—31no—
227C2×#683C2×D311yescharacteristic, complemented
228C2×C4×Dic5—31no—
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×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—28no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—28no—
248C22×C5×D3—28no—
249C22×C5×D3—28no—
250C22×C5×D3—44no—
251C22×C5×D3—44no—
252C22×C5×D3—416no—
253C22×C5×D3—416no—
254C22×C5×D3C2×D414yes—
255C22×C5×D3#4114yescomplemented
256C22×C5×D3C2412yes—
257C22×C5×D3C2412yes—
258C22×C5×D3C2412yes—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×Dic15—22no—
267C2×Dic15—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C2×Dic15C2412yes—
275C5×#67—28no—
276C5×#67C2×D4116yescomplemented
277C2×C5×Dic3C2×D414yes—
278C2×C5×Dic3C2412yes—
279C5×D12—28no—
280C4×C5×D3—28no—
281C3×C22⋊D5—28no—
282C3×C22⋊D5—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5—44no—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1201—28no—
292#1201—28no—
293#1201—44no—
294D3×Dic5—28no—
295D3×Dic5—44no—
296D5×Dic3—28no—
297C24×D3C2×D511yescharacteristic
298C24×D3C2×D511yescharacteristic
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4C2×D511yescharacteristic
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67C2×D511yescharacteristic
307C22×#67C2×D511yescharacteristic
308C23×Dic3—51no—
309C23×Dic3—51no—
310C2×#237—58no—
311C2×#237—108no—
312C2×D3×D4—28no—
313C2×D3×D4C2×D518yescomplemented
314C22×D12C2×D511yescharacteristic
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⋊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—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—51no—
338C2×(C2×D3)⋊C4—58no—
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—31no—
352C24×C5—34no—
353C24×C5—34no—
354C24×C5—64no—
355C24×C5—64no—
356C24×C5—64no—
357C24×C5—64no—
358C24×C5—122no—
359C24×C5—122no—
360C24×C5C22×D311yescharacteristic
361C24×C5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—24no—
364C2×C5×D4—38no—
365C2×C5×D4—34no—
366C2×C5×D4—34no—
367C2×C5×D4—34no—
368C2×C5×D4—64no—
369C2×C5×D4—64no—
370C2×C5×D4—632no—
371C2×C5×D4C22×D314yes—
372C22×C4×C5—31no—
373C22×C4×C5—34no—
374C22×C4×C5—64no—
375C22×C4×C5C22×D311yescharacteristic
376C2×C22⋊D5—24no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—34no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—42no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5—122no—
384C2×C22⋊D5C22×D314yescomplemented
385C2×C22⋊D5C22×D314yescomplemented
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—31no—
389C22×Dic5—31no—
390C22×Dic5—34no—
391C22×Dic5—34no—
392C22×Dic5—34no—
393C22×Dic5—42no—
394C22×Dic5—64no—
395C22×Dic5—64no—
396C22×Dic5—122no—
397C22×Dic5C22×D311yescharacteristic
398C22×Dic5C22×D311yescharacteristic
399C22×Dic5C22×D311yescharacteristic
400C22×Dic5C22×D314yescomplemented
401#711—632no—
402C2×C4×D5—34no—
403C2×C4×D5—64no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C22⋊Dic5—34no—
407C22⋊Dic5—34no—
408C22⋊Dic5—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413C22⋊Dic5—34no—
414C22⋊Dic5—34no—
415C22⋊Dic5—34no—
416C22⋊Dic5C22×D314yescomplemented
417#685C22×D314yescomplemented
418C4⋊Dic5—34no—
419#683—34no—
420#683—34no—
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—31no—
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—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
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×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×C5×D3—28no—
452C2×C5×D3—28no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—22no—
460C2×C5×D3—416no—
461C2×C5×D3—416no—
462C2×C5×D3—44no—
463C2×C5×D3C22×D414yes—
464C2×C5×D3C2×#4114yescomplemented
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—22no—
468C2×C3×D5—44no—
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C3×Dic5—22no—
476C3×Dic5—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C24×C3C22×D511yescharacteristic
481C23×D3—24no—
482C23×D3—24no—
483C23×D3—24no—
484C23×D3—24no—
485C23×D3—42no—
486C23×D3—42no—
487C23×D3C22×D511yescharacteristic
488C23×D3C22×D514yes—
489C23×D3C22×D514yes—
490C23×D3C22×D511yescharacteristic
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—24no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—202no—
497C2×C3×D4C22×D514yes—
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—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—104no—
510C2×#67—202no—
511C2×#67C22⋊D518yescomplemented
512C2×#67C22×D514yes—
513C2×#67C22×D514yes—
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—51no—
518C22×Dic3—54no—
519C22×Dic3—54no—
520C22×Dic3—104no—
521C22×Dic3—104no—
522C22×Dic3C22×D511yescharacteristic
523#237—1032no—
524D3×D4—232no—
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×D514yes—
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#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)⋊C4—54no—
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—34no—
558C23×C5—34no—
559C23×C5—32no—
560C23×C5—32no—
561C23×C5—32no—
562C23×C5—68no—
563C23×C5—68no—
564C23×C5—68no—
565C23×C5—62no—
566C23×C5—62no—
567C23×C5—62no—
568C23×C5—62no—
569C23×C5—68no—
570C23×C5—62no—
571C23×C5—62no—
572C23×C5—62no—
573C23×C5—124no—
574C23×C5—124no—
575C23×C5—1216no—
576C23×C5—1216no—
577C23×C5D3×D414yes—
578C23×C5C23×D312yes—
579C23×C5C23×D312yes—
580C23×C5C23×D311yescharacteristic
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5C23×D312yes—
585C5×D4—28no—
586C5×D4—316no—
587C5×D4—68no—
588C5×D4—68no—
589C2×C4×C5—22no—
590C2×C4×C5—34no—
591C2×C4×C5—32no—
592C2×C4×C5—68no—
593C2×C4×C5C23×D312yes—
594C22⋊D5—28no—
595C22⋊D5—44no—
596C22⋊D5—68no—
597C22⋊D5—68no—
598C22⋊D5—124no—
599C2×Dic5—22no—
600C2×Dic5—22no—
601C2×Dic5—22no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—32no—
606C2×Dic5—44no—
607C2×Dic5—68no—
608C2×Dic5—62no—
609C2×Dic5—62no—
610C2×Dic5—68no—
611C2×Dic5—62no—
612C2×Dic5—62no—
613C2×Dic5—124no—
614C2×Dic5C23×D312yes—
615C2×Dic5C23×D312yes—
616C2×Dic5C23×D312yes—
617C4×D5—68no—
618Dic10—68no—
619C25—31no—
620C25—31no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—38no—
627C22×D4—31no—
628C22×D4—51no—
629C22×D4—51no—
630C22×D4—68no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4D3×D511yescharacteristic
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—158no—
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—51no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—158no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—158no—
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—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677C3×D5—42no—
678C5×D3—24no—
679C5×D3—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—52no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3C2×C22⋊D514yes—
691C23×C3C23×D512yes—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—28no—
702C22×D3—28no—
703C22×D3—28no—
704C22×D3—28no—
705C22×D3—44no—
706C22×D3—44no—
707C22×D3—416no—
708C22×D3—416no—
709C22×D3#71114yescomplemented
710C22×D3C2×C22⋊D514yes—
711C22×D3C23×D512yes—
712C22×D3C23×D512yes—
713C22×D3C23×D512yes—
714C3×D4—28no—
715C3×D4—108no—
716C3×D4—204no—
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—108no—
728#67—108no—
729#67—204no—
730#67C2×C22⋊D5116yescomplemented
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3—102no—
739C2×Dic3—108no—
740C2×Dic3—108no—
741C2×Dic3C2×C22⋊D514yes—
742C2×Dic3C23×D512yes—
743D12—28no—
744C4×D3—28no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—28no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—34no—
755C22×C5—34no—
756C22×C5—44no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—62no—
760C22×C5—62no—
761C22×C5—68no—
762C22×C5—68no—
763C22×C5—62no—
764C22×C5—62no—
765C22×C5—62no—
766C22×C5—1216no—
767C22×C5—1216no—
768C22×C5—124no—
769C22×C5C2×D3×D414yes—
770C22×C5C2×D3×D412yes—
771C22×C5#100412yes—
772C22×C5D3×#4112yes—
773C22×C5C24×D311yescharacteristic
774C2×D5—22no—
775C2×D5—22no—
776C2×D5—22no—
777C2×D5—44no—
778C4×C5—22no—
779C4×C5—34no—
780Dic5—22no—
781Dic5—22no—
782Dic5—22no—
783Dic5—62no—
784Dic5—62no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—31no—
789C24—31no—
790C24—34no—
791C24—34no—
792C24—51no—
793C24—64no—
794C24—64no—
795C24—64no—
796C24—64no—
797C24—122no—
798C24—122no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—38no—
806C2×D4—34no—
807C2×D4—34no—
808C2×D4—34no—
809C2×D4—54no—
810C2×D4—54no—
811C2×D4—64no—
812C2×D4—64no—
813C2×D4—632no—
814C2×D4—104no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—154no—
818C2×D4—202no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4C2×D3×D514yes—
823C22×C4—31no—
824C22×C4—34no—
825C22×C4—51no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—64no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—151no—
837C22×C4—151no—
838C22×C4—202no—
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—54no—
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⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—204no—
873C22×C3C2×#71112yes—
874C22×C3#414412yes—
875C22×C3C22×C22⋊D514yes—
876C22×C3C22×C22⋊D512yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—28no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—416no—
888C2×D3—416no—
889C2×D3—44no—
890C2×D3C2×#71114yescomplemented
891C2×D3C22×C22⋊D514yes—
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—102no—
897Dic3—102no—
898Dic3—102no—
899Dic3—102no—
900Dic3C22×C22⋊D514yes—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5—64no—
904C2×C5—64no—
905C2×C5—122no—
906C2×C5#561014yescomplemented
907C2×C5C22×D3×D411yescharacteristic
908C2×C5C2×#100411yescharacteristic
909C2×C5C2×D3×#4111yescharacteristic
910D5—42no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—34no—
917C23—34no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—52no—
922C23—68no—
923C23—68no—
924C23—68no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—68no—
932C23—62no—
933C23—102no—
934C23—102no—
935C23—102no—
936C23—124no—
937C23—124no—
938C23—1216no—
939C23—1216no—
940C23D3×C22⋊D514yes—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—316no—
947D4—68no—
948D4—68no—
949D4—108no—
950D4—204no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—34no—
956C2×C4—32no—
957C2×C4—52no—
958C2×C4—52no—
959C2×C4—52no—
960C2×C4—68no—
961C2×C4—102no—
962C2×C4—102no—
963C2×C4—102no—
964C2×C4—152no—
965C2×C4—152no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—204no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—308no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3—202no—
981C2×C3#6614014yescomplemented
982C2×C3C22×#71111yescharacteristic
983C2×C3C2×#414411yescharacteristic
984C2×C3C23×C22⋊D511yescharacteristic
985D3—24no—
986D3—24no—
987D3—42no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—28no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—34no—
996C22—34no—
997C22—44no—
998C22—62no—
999C22—68no—
1000C22—68no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—102no—
1008C22—102no—
1009C22—102no—
1010C22—1216no—
1011C22—1216no—
1012C22—124no—
1013C22—204no—
1014C22D3×#71112yes—
1015C22#9202512yes—
1016C22C2×D3×C22⋊D514yes—
1017C22C2×D3×C22⋊D512yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—34no—
1021C4—102no—
1022C4—102no—
1023C4—102no—
1024C4—302no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6614011yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—64no—
1032C2—64no—
1033C2—122no—
1034C2—202no—
1035C2#1175494214yesdirect product factor
1036C2C2×D3×#71111yescharacteristic
1037C2C2×#9202511yescharacteristic
1038C2C22×D3×C22⋊D511yescharacteristic
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×C5×D3×D4C2semidirect
2. C22×#6780C2semidirect
3. C2×#91824C2semidirect
4. C2×C3×#4085C2semidirect
5. C2×#91568C2semidirect
6. C2×#91568C2semidirect
7. C2×D3×C22⋊Dic5C2semidirect
8. C2×Dic5×#67C2semidirect
9. C2×#91549C2semidirect
10. C22×(C2×D3)⋊Dic5C2semidirect
11. C2×#91525C2semidirect
12. #11754942C2direct (N × H)
13. C2×#91453C2semidirect
14. C2×#91441C2semidirect
15. C2×#91423C2semidirect
16. C2×#91352C2semidirect
21. C23×Dic15C22semidirect
25. C2×C5×D3×D4C22semidirect
28. C22×C3×C22⋊D5C22semidirect
29. C22×C3×C22⋊D5C22semidirect
30. C23×C3×Dic5C22semidirect
31. C22×#1204C22semidirect
33. C22×#1201C22semidirect
34. C22×#1201C22semidirect
35. C22×D3×Dic5C22semidirect
36. C22×D3×Dic5C22semidirect
38. C2×#6780C22semidirect
39. C22×D5×Dic3C22semidirect
40. C2×#6719C22semidirect
41. C2×#6719C22semidirect
42. C2×#6719C22semidirect
43. #91824C22semidirect
44. C2×#6712C22semidirect
45. C2×#6712C22semidirect
46. C2×C3×C22⋊Dic5C22semidirect
47. C3×#4085C22semidirect
48. C2×C3×#685C22semidirect
49. C2×C3×#683C22semidirect
50. #91568C22semidirect
51. #91568C22semidirect
52. D3×C22⋊Dic5C22semidirect
53. Dic5×#67C22semidirect
54. #91549C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×(C2×D3)⋊Dic5C22semidirect
63. C2×(C2×D3)⋊Dic5C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91525C22semidirect
66. #91453C22semidirect
67. #91441C22semidirect
68. #91423C22semidirect
69. #91352C22semidirect
79. C2×#4085D3semidirect
109. C22×Dic15C23semidirect
111. C2×C5×#67D4semidirect
122. C2×C3×C22⋊D5C23semidirect
123. C2×C3×C22⋊D5C23semidirect
128. C22×C3×Dic5C23semidirect
130. C2×#1204C23semidirect
135. C2×#1201C23semidirect
136. C2×#1201C23semidirect
139. C2×D3×Dic5C23semidirect
140. C2×D3×Dic5C23semidirect
143. C2×D5×Dic3C23semidirect
144. #6719C23semidirect
145. #6719C23semidirect
146. #6719C23semidirect
147. #6712C23semidirect
148. #6712C23semidirect
149. C3×C22⋊Dic5C23semidirect
150. C3×#685C23semidirect
151. C3×#683C23semidirect
152. Dic3⋊Dic5C23semidirect
156. (C2×D3)⋊Dic5C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. Dic3×Dic5C23semidirect
162. C22×D3×D4D5semidirect
189. C22×C22⋊D5C2×D3semidirect
190. C22×C22⋊D5C2×D3semidirect
194. C23×Dic5C2×D3semidirect
213. C2×C22⋊Dic5C2×D3semidirect
215. #4085C2×D3semidirect
222. C2×#685C2×D3semidirect
227. C2×#683C2×D3semidirect
255. C22×C5×D3#41semidirect
276. C5×#67C2×D4semidirect
313. C2×D3×D4C2×D5semidirect
384. C2×C22⋊D5C22×D3semidirect
385. C2×C22⋊D5C22×D3semidirect
400. C22×Dic5C22×D3semidirect
416. C22⋊Dic5C22×D3semidirect
417. #685C22×D3semidirect
421. #683C22×D3semidirect
464. C2×C5×D3C2×#41semidirect
511. C2×#67C22⋊D5semidirect
673. C2×C3×C5#546semidirect
709. C22×D3#711semidirect
730. #67C2×C22⋊D5semidirect
861. C3×C5C2×#546semidirect
890. C2×D3C2×#711semidirect
906. C2×C5#5610semidirect
981. C2×C3#66140semidirect
988. C5C2×#5610semidirect
1028. C3C2×#66140semidirect
1035. C2#11754942direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D3×D42
C22×#67802
C2×#918242
C2×C3×#40852
C2×#915682
C2×D3×C22⋊Dic52
C2×Dic5×#672
C2×#915492
C22×(C2×D3)⋊Dic52
C2×#915252
#117549422
C2×#914532
C2×#914412
C2×#914232
C2×#913522
C2×#661403
C2×#56105