Finite Group Databasebeta

← C2×#11753225 #14482437

Subgroups — C2×#11753225 #14482437

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×D5×#67C211yesmaximal, characteristic, complemented
3C23×#1201C211yesmaximal, characteristic, complemented
4C22×#6777C211yesmaximal, characteristic, complemented
5C2×#91770C211yesmaximal, characteristic, complemented
6C2×C5×#882C211yesmaximal, characteristic, complemented
7C2×C3×#4028C211yesmaximal, characteristic, complemented
8C2×#91571C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91463C211yesmaximal, characteristic, complemented
12C2×#91461C211yesmaximal, characteristic, complemented
13C2×#91453C211yesmaximal, characteristic, complemented
14C2×#91442C211yesmaximal, characteristic, complemented
15C2×#91408C211yesmaximal, characteristic, complemented
16#11753225C2116yesmaximal, direct product factor
17C2×#65924—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic, complemented
19C24×C3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C23×D3×D5C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C23×Dic15C2211yescharacteristic, complemented
24C22×C4×D15C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C5×D12C2211yescharacteristic, complemented
27C22×C5×D12C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×D20C2211yescharacteristic, complemented
30C22×C3×D20C2211yescharacteristic, complemented
31C2×D3×C22⋊D5—28no—
32C2×D3×C22⋊D5C2218yescomplemented
33C2×D5×#67—28no—
34C2×D5×#67C2218yescomplemented
35C22×#1203C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic, complemented
37C22×#1201—28no—
38C22×#1201C2211yescharacteristic
39C22×#1201C2218yescomplemented
40C22×#1201C2211yescharacteristic, complemented
41C22×#1201C2211yescharacteristic, complemented
42C22×#1201C2211yescharacteristic, complemented
43C22×#1201C2211yescharacteristic, complemented
44C22×#1201C2211yescharacteristic, complemented
45C22×#1201C2211yescharacteristic, complemented
46C22×D3×Dic5C2211yescharacteristic, complemented
47C22×D5×Dic3C2211yescharacteristic, complemented
48C2×#6777—28no—
49C2×#6777C2218yescomplemented
50C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
51C2×#6714C2211yescharacteristic, complemented
52C2×#6712C2211yescharacteristic, complemented
53C2×C4×Dic15C2211yescharacteristic, complemented
54#91770C2218yescomplemented
55C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
56C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
57C5×#882C2218yescomplemented
58C2×C3×#685C2211yescharacteristic, complemented
59C2×C3×#685C2211yescharacteristic, complemented
60C3×#4028C2218yescomplemented
61#91571C2218yescomplemented
62C2×#6669C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
64C2×#6665C2211yescharacteristic, complemented
65#91475C2218yescomplemented
66#91474C2218yescomplemented
67#91463C2218yescomplemented
68#91461C2218yescomplemented
69#91453C2218yescomplemented
70#91442C2218yescomplemented
71#91408C2218yescomplemented
72C2×#5590—51nomaximal, Hall
73C23×C22⋊D5—31no—
74C23×C22⋊D5—31no—
75C22×D4×D5—31no—
76C22×D4×D5—31no—
77C2×C5×#120—31no—
78C2×#4086—31no—
79C2×#4085—31no—
80C2×#4085—31no—
81C2×#4083—31no—
82#65924—316no—
83C2×#4030—31no—
84C2×#4030—31no—
85C2×#4028—31no—
86C2×#4028D311yescharacteristic, complemented
87C2×#4027—31no—
88C2×#4027—31no—
89C24×C3×C5C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C23×C5×D3—24no—
92C23×C5×D3—24no—
93C23×C5×D3—42no—
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C5×D3C2311yescharacteristic
97C23×C5×D3C2314yescomplemented
98C23×C3×D5—24no—
99C23×C3×D5—24no—
100C23×C3×D5—42no—
101C23×C3×D5C2311yescharacteristic
102C23×C3×D5C2311yescharacteristic
103C23×C3×D5C2311yescharacteristic
104C23×C3×D5C2314yescomplemented
105C22×D3×D5—24no—
106C22×D3×D5—24no—
107C22×D3×D5—24no—
108C22×D3×D5—24no—
109C22×D3×D5—42no—
110C22×D3×D5—42no—
111C22×D3×D5C2314yescomplemented
112C22×D3×D5C2314yescomplemented
113C22×C3×C4×C5C2311yescharacteristic
114C22×C3×C4×C5C2311yescharacteristic
115C2×#1220D418yescomplemented
116C2×#1220C2314yes—
117C22×Dic15—24no—
118C22×Dic15C2311yescharacteristic
119C22×Dic15C2311yescharacteristic
120C22×Dic15C2311yescharacteristic
121C22×Dic15C2314yescomplemented
122C2×C4×D15—24no—
123C2×C4×D15C2314yescomplemented
124C2×C5×#67—24no—
125C2×C5×#67C2314yescomplemented
126C22×C5×Dic3C2311yescharacteristic
127C2×C5×D12—24no—
128C2×C5×D12—42no—
129C2×C5×D12C2314yescomplemented
130C2×C5×D12C2314yescomplemented
131C2×C3×C22⋊D5—24no—
132C2×C3×C22⋊D5C2314yescomplemented
133C22×C3×Dic5C2311yescharacteristic
134C2×C3×D20—24no—
135C2×C3×D20—42no—
136C2×C3×D20C2314yescomplemented
137C2×C3×D20C2314yescomplemented
138D3×C22⋊D5—232no—
139D5×#67—232no—
140C2×#1203—24no—
141C2×#1203C2314yescomplemented
142C2×#1202—24no—
143C2×#1202C2314yescomplemented
144C2×#1201—24no—
145C2×#1201—24no—
146C2×#1201—24no—
147C2×#1201—24no—
148C2×#1201—24no—
149C2×#1201—24no—
150C2×#1201—232no—
151C2×#1201D418yescomplemented
152C2×#1201C2314yes—
153C2×#1201C2314yescomplemented
154C2×#1201C2314yescomplemented
155C2×#1201C2314yescomplemented
156C2×#1201C2314yescomplemented
157C2×#1201C2314yescomplemented
158C2×#1201C2314yescomplemented
159C2×D3×Dic5—24no—
160C2×D3×Dic5C2314yescomplemented
161C2×D5×Dic3—24no—
162C2×D5×Dic3C2314yescomplemented
163#6777—232no—
164C3×C5×C22⋊C4C2314yescomplemented
165#6714C2314yescomplemented
166#6712C2314yescomplemented
167C4×Dic15C2314yescomplemented
168C5×(C2×D3)⋊C4C2314yescomplemented
169C5×(C2×D3)⋊C4C2314yescomplemented
170C3×#685C2314yescomplemented
171C3×#685C2314yescomplemented
172#6669C2314yescomplemented
173(C2×D3)⋊Dic5C2314yescomplemented
174#6665C2314yescomplemented
175C23×#67—51no—
176C23×#67—51no—
177C22×D3×D4—51no—
178C22×D3×D4—51no—
179C2×C3×#120—51no—
180C2×#940—51no—
181C2×#939—51no—
182C2×#939—51no—
183C2×#937—51no—
184#5590—516no—
185C2×#884—51no—
186C2×#884—51no—
187C2×#882—51no—
188C2×#882D511yescharacteristic, complemented
189C2×#67⋊C4—51no—
190C2×#67⋊C4—51no—
191C25×C5—31no—
192C24×D5—31no—
193C24×D5—31no—
194C24×D5C2×D311yescharacteristic, complemented
195C22×C5×D4—31no—
196C22×C5×D4—31no—
197C22×C5×D4—31no—
198C22×C22⋊D5—31no—
199C22×C22⋊D5—31no—
200C22×C22⋊D5—31no—
201C22×C22⋊D5—31no—
202C22×C22⋊D5—31no—
203C22×C22⋊D5—31no—
204C22×C22⋊D5—31no—
205C22×C22⋊D5—31no—
206C22×C22⋊D5—38no—
207C22×C22⋊D5—38no—
208C22×C22⋊D5—31no—
209C22×C22⋊D5—68no—
210C22×C22⋊D5—68no—
211C22×C22⋊D5C2×D311yescharacteristic, complemented
212C23×Dic5—31no—
213C23×Dic5—31no—
214C2×D4×D5—38no—
215C2×D4×D5—38no—
216C2×D4×D5—68no—
217C2×D4×D5—68no—
218C22×D20—31no—
219C22×D20C2×D311yescharacteristic, complemented
220C22×D20C2×D311yescharacteristic, complemented
221C22×C4×D5—31no—
222C22×C4×D5—31no—
223C5×#120—38no—
224C2×C5×C22⋊C4—31no—
225C2×C5×C22⋊C4—31no—
226C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
227C2×C22⋊Dic5—31no—
228#4086—38no—
229#4085—38no—
230#4085—38no—
231#4083—38no—
232C2×#685—31no—
233C2×#685—31no—
234C2×#685C2×D311yescharacteristic, complemented
235C2×#685C2×D311yescharacteristic, complemented
236C2×#683—31no—
237C2×#683—31no—
238C2×C4×Dic5—31no—
239#4030—38no—
240#4030—38no—
241#4028—38no—
242#4028C2×D318yescomplemented
243#4027—38no—
244#4027—38no—
245C2×D42—151noSylow
246C23×C3×C5—22no—
247C23×C3×C5—22no—
248C23×C3×C5C2×D414yescomplemented
249C23×C3×C5C2412yes—
250C23×C3×C5C2411yescharacteristic
251C22×D15—22no—
252C22×D15—22no—
253C22×D15C2×D414yescomplemented
254C22×D15C2412yes—
255C22×C5×D3—22no—
256C22×C5×D3—22no—
257C22×C5×D3—22no—
258C22×C5×D3—22no—
259C22×C5×D3—22no—
260C22×C5×D3—22no—
261C22×C5×D3—28no—
262C22×C5×D3—22no—
263C22×C5×D3—22no—
264C22×C5×D3—28no—
265C22×C5×D3—44no—
266C22×C5×D3—416no—
267C22×C5×D3C2×D414yescomplemented
268C22×C5×D3C2412yes—
269C22×C5×D3C2412yes—
270C22×C5×D3C2412yes—
271C22×C3×D5—22no—
272C22×C3×D5—22no—
273C22×C3×D5—22no—
274C22×C3×D5—22no—
275C22×C3×D5—22no—
276C22×C3×D5—22no—
277C22×C3×D5—28no—
278C22×C3×D5—22no—
279C22×C3×D5—22no—
280C22×C3×D5—28no—
281C22×C3×D5—44no—
282C22×C3×D5—416no—
283C22×C3×D5C2×D414yescomplemented
284C22×C3×D5C2412yes—
285C22×C3×D5C2412yes—
286C22×C3×D5C2412yes—
287C2×D3×D5—28no—
288C2×D3×D5—28no—
289C2×D3×D5—28no—
290C2×D3×D5—28no—
291C2×D3×D5—44no—
292C2×D3×D5—44no—
293C2×D3×D5—416no—
294C2×D3×D5—416no—
295C2×C3×C4×C5—22no—
296C2×C3×C4×C5—22no—
297C2×C3×C4×C5C2412yes—
298C2×C3×C4×C5C2412yes—
299#1220C2×D4116yescomplemented
300C2×Dic15—22no—
301C2×Dic15—28no—
302C2×Dic15C2×D414yescomplemented
303C2×Dic15C2×D414yescomplemented
304C2×Dic15C2412yes—
305C2×Dic15C2412yes—
306C2×Dic15C2412yes—
307C4×D15—28no—
308C5×#67—28no—
309C2×C5×Dic3—22no—
310C2×C5×Dic3C2412yes—
311C5×D12—28no—
312C5×D12—44no—
313C3×C22⋊D5—28no—
314C2×C3×Dic5—22no—
315C2×C3×Dic5C2412yes—
316C3×D20—28no—
317C3×D20—44no—
318#1203—28no—
319#1202—28no—
320#1201—28no—
321#1201—28no—
322#1201—28no—
323#1201—28no—
324#1201—28no—
325#1201—28no—
326#1201C2×D4116yescomplemented
327D3×Dic5—28no—
328D5×Dic3—28no—
329C25×C3—51no—
330C24×D3—51no—
331C24×D3—51no—
332C24×D3C2×D511yescharacteristic, complemented
333C22×C3×D4—51no—
334C22×C3×D4—51no—
335C22×C3×D4—51no—
336C22×#67—51no—
337C22×#67—51no—
338C22×#67—51no—
339C22×#67—51no—
340C22×#67—51no—
341C22×#67—51no—
342C22×#67—51no—
343C22×#67—51no—
344C22×#67—58no—
345C22×#67—58no—
346C22×#67—51no—
347C22×#67—108no—
348C22×#67—108no—
349C22×#67C2×D511yescharacteristic, complemented
350C23×Dic3—51no—
351C23×Dic3—51no—
352C2×D3×D4—58no—
353C2×D3×D4—58no—
354C2×D3×D4—108no—
355C2×D3×D4—108no—
356C22×D12—51no—
357C22×D12C2×D511yescharacteristic, complemented
358C22×D12C2×D511yescharacteristic, complemented
359C22×C4×D3—51no—
360C22×C4×D3—51no—
361C3×#120—58no—
362C2×C3×C22⋊C4—51no—
363C2×C3×C22⋊C4—51no—
364C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
365C2×#217—51no—
366#940—58no—
367#939—58no—
368#939—58no—
369#937—58no—
370C2×(C2×D3)⋊C4—51no—
371C2×(C2×D3)⋊C4—51no—
372C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
373C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
374C2×Dic3⋊C4—51no—
375C2×Dic3⋊C4—51no—
376C2×C4×Dic3—51no—
377#884—58no—
378#884—58no—
379#882—58no—
380#882C2×D518yescomplemented
381#67⋊C4—58no—
382#67⋊C4—58no—
383C24×C5—31no—
384C24×C5—31no—
385C24×C5—31no—
386C24×C5—34no—
387C24×C5—64no—
388C24×C5—64no—
389C24×C5—122no—
390C24×C5C22×D311yescharacteristic
391C23×D5—24no—
392C23×D5—24no—
393C23×D5—31no—
394C23×D5—34no—
395C23×D5—34no—
396C23×D5—42no—
397C23×D5—64no—
398C23×D5—64no—
399C23×D5—64no—
400C23×D5—64no—
401C23×D5—122no—
402C23×D5—122no—
403C23×D5C22×D311yescharacteristic
404C23×D5C22×D311yescharacteristic
405C23×D5C22×D311yescharacteristic
406C23×D5C22×D314yescomplemented
407C2×C5×D4—34no—
408C2×C5×D4—34no—
409C2×C5×D4—34no—
410C2×C5×D4—64no—
411C2×C5×D4—64no—
412C2×C5×D4—122no—
413C22×C4×C5—31no—
414C22×C4×C5C22×D311yescharacteristic
415C22×C4×C5C22×D311yescharacteristic
416C2×C22⋊D5—24no—
417C2×C22⋊D5—38no—
418C2×C22⋊D5—34no—
419C2×C22⋊D5—38no—
420C2×C22⋊D5—34no—
421C2×C22⋊D5—34no—
422C2×C22⋊D5—34no—
423C2×C22⋊D5—34no—
424C2×C22⋊D5—34no—
425C2×C22⋊D5—34no—
426C2×C22⋊D5—34no—
427C2×C22⋊D5—34no—
428C2×C22⋊D5—64no—
429C2×C22⋊D5—64no—
430C2×C22⋊D5—64no—
431C2×C22⋊D5—64no—
432C2×C22⋊D5—64no—
433C2×C22⋊D5—632no—
434C2×C22⋊D5—632no—
435C2×C22⋊D5—64no—
436C2×C22⋊D5—64no—
437C2×C22⋊D5C22×D314yescomplemented
438C22×Dic5—31no—
439C22×Dic5—31no—
440C22×Dic5—31no—
441C22×Dic5—34no—
442C22×Dic5—34no—
443C22×Dic5—64no—
444C22×Dic5—64no—
445C22×Dic5C22×D311yescharacteristic
446D4×D5—632no—
447D4×D5—632no—
448C2×D20—24no—
449C2×D20—34no—
450C2×D20—42no—
451C2×D20—64no—
452C2×D20C22×D314yescomplemented
453C2×D20C22×D314yescomplemented
454C2×C4×D5—34no—
455C2×C4×D5—34no—
456C2×C4×D5—64no—
457C2×C4×D5—64no—
458C5×C22⋊C4—34no—
459C5×C22⋊C4—34no—
460C5×C22⋊C4C22×D314yescomplemented
461C22⋊Dic5—34no—
462#685—34no—
463#685—34no—
464#685C22×D314yescomplemented
465#685C22×D314yescomplemented
466#683—34no—
467#683—34no—
468C4×Dic5—34no—
469C23×D4—151no—
470C23×D4—151no—
471C23×D4—151no—
472C23×D4—151no—
473D42—1516no—
474C2×#127—151no—
475C2×#121—151no—
476C2×#121—151no—
477C2×#121—151no—
478C2×#121—151no—
479C2×#120—31no—
480C2×#120—51no—
481C2×#120—151no—
482C2×#120—151no—
483C2×C4×D4—151no—
484C2×C4×D4—151no—
485C22×C3×C5—28no—
486C22×C3×C5—22no—
487C22×C3×C5—22no—
488C22×C3×C5C22×D412yes—
489C22×C3×C5C22×D412yes—
490C22×C3×C5C22×D414yescomplemented
491C22×C3×C5H(5,𝔽2)12yes—
492C22×C3×C5C2511yescharacteristic
493C2×D15—28no—
494C2×D15—22no—
495C2×D15—22no—
496C2×D15C22×D414yescomplemented
497C2×C5×D3—28no—
498C2×C5×D3—22no—
499C2×C5×D3—22no—
500C2×C5×D3—22no—
501C2×C5×D3—22no—
502C2×C5×D3—22no—
503C2×C5×D3—22no—
504C2×C5×D3—22no—
505C2×C5×D3—22no—
506C2×C5×D3—416no—
507C2×C5×D3—44no—
508C2×C5×D3—44no—
509C2×C5×D3C22×D414yescomplemented
510C2×C3×D5—28no—
511C2×C3×D5—22no—
512C2×C3×D5—22no—
513C2×C3×D5—22no—
514C2×C3×D5—22no—
515C2×C3×D5—22no—
516C2×C3×D5—22no—
517C2×C3×D5—22no—
518C2×C3×D5—22no—
519C2×C3×D5—416no—
520C2×C3×D5—44no—
521C2×C3×D5—44no—
522C2×C3×D5C22×D414yescomplemented
523D3×D5—416no—
524D3×D5—416no—
525C3×C4×C5—22no—
526C3×C4×C5—22no—
527Dic15—22no—
528Dic15C22×D414yescomplemented
529Dic15C22×D414yescomplemented
530C3×Dic5—22no—
531C5×Dic3—22no—
532C24×C3—51no—
533C24×C3—51no—
534C24×C3—51no—
535C24×C3—54no—
536C24×C3—104no—
537C24×C3—104no—
538C24×C3—202no—
539C24×C3C22×D511yescharacteristic
540C23×D3—24no—
541C23×D3—24no—
542C23×D3—42no—
543C23×D3—51no—
544C23×D3—54no—
545C23×D3—54no—
546C23×D3—104no—
547C23×D3—104no—
548C23×D3—104no—
549C23×D3—104no—
550C23×D3—202no—
551C23×D3—202no—
552C23×D3C22×D511yescharacteristic
553C23×D3C22×D511yescharacteristic
554C23×D3C22×D511yescharacteristic
555C23×D3C22×D514yescomplemented
556C2×C3×D4—54no—
557C2×C3×D4—54no—
558C2×C3×D4—54no—
559C2×C3×D4—104no—
560C2×C3×D4—104no—
561C2×C3×D4—202no—
562C22×C3×C4—51no—
563C22×C3×C4C22×D511yescharacteristic
564C22×C3×C4C22×D511yescharacteristic
565C2×#67—24no—
566C2×#67—58no—
567C2×#67—54no—
568C2×#67—58no—
569C2×#67—54no—
570C2×#67—54no—
571C2×#67—54no—
572C2×#67—54no—
573C2×#67—54no—
574C2×#67—54no—
575C2×#67—54no—
576C2×#67—54no—
577C2×#67—104no—
578C2×#67—104no—
579C2×#67—104no—
580C2×#67—104no—
581C2×#67—104no—
582C2×#67—1032no—
583C2×#67—1032no—
584C2×#67—104no—
585C2×#67—104no—
586C2×#67C22×D514yescomplemented
587C22×Dic3—51no—
588C22×Dic3—51no—
589C22×Dic3—54no—
590C22×Dic3—51no—
591C22×Dic3—54no—
592C22×Dic3—104no—
593C22×Dic3—104no—
594C22×Dic3C22×D511yescharacteristic
595D3×D4—1032no—
596D3×D4—1032no—
597C2×D12—24no—
598C2×D12—42no—
599C2×D12—54no—
600C2×D12—104no—
601C2×D12C22×D514yescomplemented
602C2×D12C22×D514yescomplemented
603C2×C4×D3—54no—
604C2×C4×D3—54no—
605C2×C4×D3—104no—
606C2×C4×D3—104no—
607C3×C22⋊C4—54no—
608C3×C22⋊C4—54no—
609C3×C22⋊C4C22×D514yescomplemented
610#217—54no—
611(C2×D3)⋊C4—54no—
612(C2×D3)⋊C4—54no—
613(C2×D3)⋊C4C22×D514yescomplemented
614(C2×D3)⋊C4C22×D514yescomplemented
615Dic3⋊C4—54no—
616Dic3⋊C4—54no—
617C4×Dic3—54no—
618C23×C5—22no—
619C23×C5—22no—
620C23×C5—34no—
621C23×C5—32no—
622C23×C5—32no—
623C23×C5—32no—
624C23×C5—68no—
625C23×C5—62no—
626C23×C5—62no—
627C23×C5—62no—
628C23×C5—62no—
629C23×C5—62no—
630C23×C5—62no—
631C23×C5—68no—
632C23×C5—62no—
633C23×C5—62no—
634C23×C5—124no—
635C23×C5—1216no—
636C23×C5D3×D414yescomplemented
637C23×C5C23×D312yes—
638C23×C5C23×D311yescharacteristic
639C22×D5—22no—
640C22×D5—22no—
641C22×D5—22no—
642C22×D5—22no—
643C22×D5—22no—
644C22×D5—22no—
645C22×D5—28no—
646C22×D5—22no—
647C22×D5—22no—
648C22×D5—28no—
649C22×D5—34no—
650C22×D5—32no—
651C22×D5—44no—
652C22×D5—416no—
653C22×D5—68no—
654C22×D5—68no—
655C22×D5—68no—
656C22×D5—62no—
657C22×D5—62no—
658C22×D5—68no—
659C22×D5—124no—
660C22×D5—124no—
661C22×D5—1216no—
662C22×D5—1216no—
663C22×D5D3×D414yescomplemented
664C22×D5C23×D312yes—
665C22×D5C23×D312yes—
666C22×D5C23×D312yes—
667C5×D4—68no—
668C5×D4—68no—
669C5×D4—124no—
670C2×C4×C5—22no—
671C2×C4×C5—22no—
672C2×C4×C5—32no—
673C2×C4×C5—62no—
674C2×C4×C5C23×D312yes—
675C2×C4×C5C23×D312yes—
676C22⋊D5—28no—
677C22⋊D5—316no—
678C22⋊D5—316no—
679C22⋊D5—68no—
680C22⋊D5—68no—
681C22⋊D5—68no—
682C22⋊D5—68no—
683C22⋊D5—68no—
684C22⋊D5—68no—
685C22⋊D5—68no—
686C2×Dic5—22no—
687C2×Dic5—34no—
688C2×Dic5—34no—
689C2×Dic5—32no—
690C2×Dic5—32no—
691C2×Dic5—32no—
692C2×Dic5—68no—
693C2×Dic5—68no—
694C2×Dic5—62no—
695C2×Dic5C23×D312yes—
696D20—28no—
697D20—44no—
698D20—68no—
699C4×D5—68no—
700C4×D5—68no—
701C25—31no—
702C25—51no—
703C25—151no—
704C25—151no—
705C22×D4—31no—
706C22×D4—31no—
707C22×D4—31no—
708C22×D4—51no—
709C22×D4—51no—
710C22×D4—51no—
711C22×D4—151no—
712C22×D4—151no—
713C22×D4—158no—
714C22×D4—158no—
715C22×D4—158no—
716C22×D4—151no—
717C22×D4—151no—
718C22×D4—151no—
719C22×D4—151no—
720C22×D4—151no—
721C22×D4—151no—
722C22×D4—151no—
723C22×D4—151no—
724C22×D4—158no—
725C22×D4—308no—
726C22×D4—308no—
727C22×D4—308no—
728C22×D4—308no—
729C23×C4—151no—
730C23×C4—151no—
731C23×C4—151no—
732C23×C4—151no—
733#127—158no—
734#121—158no—
735#121—158no—
736#121—158no—
737#121—158no—
738#120—38no—
739#120—58no—
740#120—158no—
741#120—158no—
742C4×D4—158no—
743C4×D4—158no—
744C2×C4⋊C4—151no—
745C2×C4⋊C4—151no—
746C2×C22⋊C4—31no—
747C2×C22⋊C4—31no—
748C2×C22⋊C4—51no—
749C2×C22⋊C4—51no—
750C2×C22⋊C4—151no—
751C2×C22⋊C4—151no—
752C2×C22⋊C4—151no—
753C2×C22⋊C4D3×D511yescharacteristic, complemented
754C2×C42—151no—
755C2×C3×C5—24no—
756C2×C3×C5D4214yescomplemented
757C2×C3×C5C23×D411yescharacteristic
758C2×C3×C5C23×D411yescharacteristic
759C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
760D15—24no—
761C3×D5—24no—
762C3×D5—42no—
763C3×D5—42no—
764C5×D3—24no—
765C5×D3—42no—
766C5×D3—42no—
767C23×C3—22no—
768C23×C3—22no—
769C23×C3—54no—
770C23×C3—52no—
771C23×C3—52no—
772C23×C3—52no—
773C23×C3—108no—
774C23×C3—102no—
775C23×C3—102no—
776C23×C3—102no—
777C23×C3—102no—
778C23×C3—102no—
779C23×C3—102no—
780C23×C3—108no—
781C23×C3—102no—
782C23×C3—102no—
783C23×C3—204no—
784C23×C3—2016no—
785C23×C3D4×D514yescomplemented
786C23×C3C23×D512yes—
787C23×C3C23×D511yescharacteristic
788C22×D3—22no—
789C22×D3—22no—
790C22×D3—22no—
791C22×D3—22no—
792C22×D3—22no—
793C22×D3—22no—
794C22×D3—28no—
795C22×D3—22no—
796C22×D3—22no—
797C22×D3—28no—
798C22×D3—44no—
799C22×D3—416no—
800C22×D3—54no—
801C22×D3—52no—
802C22×D3—108no—
803C22×D3—108no—
804C22×D3—108no—
805C22×D3—102no—
806C22×D3—102no—
807C22×D3—108no—
808C22×D3—204no—
809C22×D3—204no—
810C22×D3—2016no—
811C22×D3—2016no—
812C22×D3D4×D514yescomplemented
813C22×D3C23×D512yes—
814C22×D3C23×D512yes—
815C22×D3C23×D512yes—
816C3×D4—108no—
817C3×D4—108no—
818C3×D4—204no—
819C2×C3×C4—22no—
820C2×C3×C4—22no—
821C2×C3×C4—52no—
822C2×C3×C4—102no—
823C2×C3×C4C23×D512yes—
824C2×C3×C4C23×D512yes—
825#67—28no—
826#67—516no—
827#67—516no—
828#67—108no—
829#67—108no—
830#67—108no—
831#67—108no—
832#67—108no—
833#67—108no—
834#67—108no—
835C2×Dic3—22no—
836C2×Dic3—54no—
837C2×Dic3—54no—
838C2×Dic3—52no—
839C2×Dic3—52no—
840C2×Dic3—52no—
841C2×Dic3—108no—
842C2×Dic3—108no—
843C2×Dic3—102no—
844C2×Dic3C23×D512yes—
845D12—28no—
846D12—44no—
847D12—108no—
848C4×D3—108no—
849C4×D3—108no—
850C22×C5—22no—
851C22×C5—22no—
852C22×C5—28no—
853C22×C5—34no—
854C22×C5—62no—
855C22×C5—62no—
856C22×C5—68no—
857C22×C5—62no—
858C22×C5—62no—
859C22×C5—62no—
860C22×C5—62no—
861C22×C5—62no—
862C22×C5—62no—
863C22×C5—1216no—
864C22×C5—124no—
865C22×C5—124no—
866C22×C5C2×D3×D412yes—
867C22×C5C2×D3×D412yes—
868C22×C5C2×D3×D414yescomplemented
869C22×C5#100412yes—
870C22×C5C24×D311yescharacteristic
871C2×D5—22no—
872C2×D5—22no—
873C2×D5—28no—
874C2×D5—22no—
875C2×D5—22no—
876C2×D5—22no—
877C2×D5—22no—
878C2×D5—22no—
879C2×D5—22no—
880C2×D5—34no—
881C2×D5—416no—
882C2×D5—44no—
883C2×D5—44no—
884C2×D5—62no—
885C2×D5—62no—
886C2×D5—68no—
887C2×D5—1216no—
888C2×D5—1216no—
889C2×D5C2×D3×D414yescomplemented
890C4×C5—22no—
891C4×C5—22no—
892C4×C5—62no—
893Dic5—22no—
894Dic5—34no—
895Dic5—34no—
896Dic5—62no—
897C24—31no—
898C24—31no—
899C24—31no—
900C24—34no—
901C24—51no—
902C24—51no—
903C24—51no—
904C24—54no—
905C24—64no—
906C24—64no—
907C24—104no—
908C24—104no—
909C24—122no—
910C24—154no—
911C24—154no—
912C24—151no—
913C24—202no—
914C24—304no—
915C24—304no—
916C24—304no—
917C24—304no—
918C24—602no—
919C24—602no—
920C24C2×D3×D511yescharacteristic
921C2×D4—34no—
922C2×D4—34no—
923C2×D4—34no—
924C2×D4—54no—
925C2×D4—54no—
926C2×D4—54no—
927C2×D4—64no—
928C2×D4—64no—
929C2×D4—104no—
930C2×D4—104no—
931C2×D4—122no—
932C2×D4—154no—
933C2×D4—154no—
934C2×D4—154no—
935C2×D4—158no—
936C2×D4—158no—
937C2×D4—154no—
938C2×D4—154no—
939C2×D4—154no—
940C2×D4—154no—
941C2×D4—154no—
942C2×D4—154no—
943C2×D4—154no—
944C2×D4—202no—
945C2×D4—304no—
946C2×D4—304no—
947C2×D4—304no—
948C2×D4—304no—
949C2×D4—304no—
950C2×D4—304no—
951C2×D4—3032no—
952C2×D4—3032no—
953C2×D4—3032no—
954C2×D4—3032no—
955C2×D4—304no—
956C2×D4—304no—
957C22×C4—31no—
958C22×C4—51no—
959C22×C4—154no—
960C22×C4—154no—
961C22×C4—151no—
962C22×C4—151no—
963C22×C4—154no—
964C22×C4—151no—
965C22×C4—154no—
966C22×C4—304no—
967C22×C4—304no—
968C22×C4—304no—
969C22×C4—304no—
970C22×C4C2×D3×D511yescharacteristic
971C22×C4C2×D3×D511yescharacteristic
972C4⋊C4—154no—
973C4⋊C4—154no—
974C22⋊C4—34no—
975C22⋊C4—34no—
976C22⋊C4—54no—
977C22⋊C4—54no—
978C22⋊C4—154no—
979C22⋊C4—154no—
980C22⋊C4—154no—
981C22⋊C4C2×D3×D514yescomplemented
982C42—154no—
983C3×C5C2×D4211yescharacteristic, complemented, Hall
984C22×C3—28no—
985C22×C3—22no—
986C22×C3—22no—
987C22×C3—54no—
988C22×C3—108no—
989C22×C3—102no—
990C22×C3—102no—
991C22×C3—102no—
992C22×C3—102no—
993C22×C3—102no—
994C22×C3—102no—
995C22×C3—102no—
996C22×C3—102no—
997C22×C3—2016no—
998C22×C3—204no—
999C22×C3—204no—
1000C22×C3C2×D4×D512yes—
1001C22×C3C2×D4×D512yes—
1002C22×C3C2×D4×D514yescomplemented
1003C22×C3#414412yes—
1004C22×C3C24×D511yescharacteristic
1005C2×D3—28no—
1006C2×D3—22no—
1007C2×D3—22no—
1008C2×D3—22no—
1009C2×D3—22no—
1010C2×D3—22no—
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—416no—
1015C2×D3—44no—
1016C2×D3—44no—
1017C2×D3—54no—
1018C2×D3—108no—
1019C2×D3—102no—
1020C2×D3—102no—
1021C2×D3—2016no—
1022C2×D3—2016no—
1023C2×D3C2×D4×D514yescomplemented
1024C3×C4—22no—
1025C3×C4—22no—
1026C3×C4—102no—
1027Dic3—22no—
1028Dic3—54no—
1029Dic3—54no—
1030Dic3—102no—
1031C2×C5—24no—
1032C2×C5—64no—
1033C2×C5—122no—
1034C2×C5—122no—
1035C2×C5#559014yescomplemented
1036C2×C5C22×D3×D411yescharacteristic
1037C2×C5C22×D3×D411yescharacteristic
1038C2×C5C2×#100411yescharacteristic
1039D5—24no—
1040D5—42no—
1041D5—42no—
1042D5—64no—
1043C23—22no—
1044C23—22no—
1045C23—34no—
1046C23—32no—
1047C23—32no—
1048C23—32no—
1049C23—54no—
1050C23—52no—
1051C23—52no—
1052C23—52no—
1053C23—68no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—68no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—108no—
1064C23—102no—
1065C23—102no—
1066C23—102no—
1067C23—102no—
1068C23—108no—
1069C23—102no—
1070C23—102no—
1071C23—102no—
1072C23—102no—
1073C23—124no—
1074C23—1216no—
1075C23—154no—
1076C23—152no—
1077C23—204no—
1078C23—2016no—
1079C23—308no—
1080C23—308no—
1081C23—308no—
1082C23—308no—
1083C23—302no—
1084C23—302no—
1085C23—604no—
1086C23—604no—
1087C23—6016no—
1088C23—6016no—
1089C23#677714yescomplemented
1090C23C22×D3×D512yes—
1091C23C22×D3×D511yescharacteristic
1092D4—68no—
1093D4—68no—
1094D4—108no—
1095D4—108no—
1096D4—124no—
1097D4—1516no—
1098D4—1516no—
1099D4—204no—
1100D4—308no—
1101D4—308no—
1102D4—308no—
1103D4—308no—
1104D4—308no—
1105D4—308no—
1106D4—308no—
1107D4—308no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—32no—
1111C2×C4—52no—
1112C2×C4—62no—
1113C2×C4—102no—
1114C2×C4—154no—
1115C2×C4—154no—
1116C2×C4—152no—
1117C2×C4—152no—
1118C2×C4—152no—
1119C2×C4—308no—
1120C2×C4—308no—
1121C2×C4—308no—
1122C2×C4—308no—
1123C2×C4—302no—
1124C2×C4C22×D3×D512yes—
1125C2×C4C22×D3×D512yes—
1126C2×C3—24no—
1127C2×C3—104no—
1128C2×C3—202no—
1129C2×C3—202no—
1130C2×C3#6592414yescomplemented
1131C2×C3C22×D4×D511yescharacteristic
1132C2×C3C22×D4×D511yescharacteristic
1133C2×C3C2×#414411yescharacteristic
1134D3—24no—
1135D3—42no—
1136D3—42no—
1137D3—104no—
1138C5C2×#559011yescharacteristic, complemented, Sylow
1139C22—28no—
1140C22—22no—
1141C22—22no—
1142C22—34no—
1143C22—54no—
1144C22—68no—
1145C22—62no—
1146C22—62no—
1147C22—62no—
1148C22—62no—
1149C22—62no—
1150C22—62no—
1151C22—62no—
1152C22—62no—
1153C22—108no—
1154C22—102no—
1155C22—102no—
1156C22—102no—
1157C22—102no—
1158C22—102no—
1159C22—102no—
1160C22—102no—
1161C22—102no—
1162C22—1216no—
1163C22—124no—
1164C22—124no—
1165C22—154no—
1166C22—2016no—
1167C22—204no—
1168C22—204no—
1169C22—308no—
1170C22—302no—
1171C22—302no—
1172C22—6016no—
1173C22—6016no—
1174C22C2×#677712yes—
1175C22C2×#677714yescomplemented
1176C22D3×D4×D512yes—
1177C22#9202512yes—
1178C22C23×D3×D511yescharacteristic
1179C4—22no—
1180C4—22no—
1181C4—62no—
1182C4—102no—
1183C4—154no—
1184C4—154no—
1185C4—302no—
1186C3C2×#6592411yescharacteristic, complemented, Sylow
1187C2—24no—
1188C2—64no—
1189C2—104no—
1190C2—122no—
1191C2—122no—
1192C2—202no—
1193C2—202no—
1194C2—304no—
1195C2#1175322514yesdirect product factor
1196C2C22×#677711yescharacteristic
1197C2C2×D3×D4×D511yescharacteristic
1198C2C2×#9202511yescharacteristic
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×D42
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×D3×C22⋊D5C2semidirect
2. C22×D5×#67C2semidirect
3. C23×#1201C2semidirect
4. C22×#6777C2semidirect
5. C2×#91770C2semidirect
6. C2×C5×#882C2semidirect
7. C2×C3×#4028C2semidirect
8. C2×#91571C2semidirect
9. C2×#91475C2semidirect
10. C2×#91474C2semidirect
11. C2×#91463C2semidirect
12. C2×#91461C2semidirect
13. C2×#91453C2semidirect
14. C2×#91442C2semidirect
15. C2×#91408C2semidirect
16. #11753225C2direct (N × H)
18. C24×C5×D3C22semidirect
19. C24×C3×D5C22semidirect
20. C23×D3×D5C22semidirect
21. C23×D3×D5C22semidirect
23. C23×Dic15C22semidirect
24. C22×C4×D15C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C5×D12C22semidirect
27. C22×C5×D12C22semidirect
28. C22×C3×C22⋊D5C22semidirect
29. C22×C3×D20C22semidirect
30. C22×C3×D20C22semidirect
32. C2×D3×C22⋊D5C22semidirect
34. C2×D5×#67C22semidirect
35. C22×#1203C22semidirect
36. C22×#1202C22semidirect
39. C22×#1201C22semidirect
40. C22×#1201C22semidirect
41. C22×#1201C22semidirect
42. C22×#1201C22semidirect
43. C22×#1201C22semidirect
44. C22×#1201C22semidirect
45. C22×#1201C22semidirect
46. C22×D3×Dic5C22semidirect
47. C22×D5×Dic3C22semidirect
49. C2×#6777C22semidirect
50. C2×C3×C5×C22⋊C4C22semidirect
51. C2×#6714C22semidirect
52. C2×#6712C22semidirect
53. C2×C4×Dic15C22semidirect
54. #91770C22semidirect
55. C2×C5×(C2×D3)⋊C4C22semidirect
56. C2×C5×(C2×D3)⋊C4C22semidirect
57. C5×#882C22semidirect
58. C2×C3×#685C22semidirect
59. C2×C3×#685C22semidirect
60. C3×#4028C22semidirect
61. #91571C22semidirect
62. C2×#6669C22semidirect
63. C2×(C2×D3)⋊Dic5C22semidirect
64. C2×#6665C22semidirect
65. #91475C22semidirect
66. #91474C22semidirect
67. #91463C22semidirect
68. #91461C22semidirect
69. #91453C22semidirect
70. #91442C22semidirect
71. #91408C22semidirect
86. C2×#4028D3semidirect
97. C23×C5×D3C23semidirect
104. C23×C3×D5C23semidirect
111. C22×D3×D5C23semidirect
112. C22×D3×D5C23semidirect
115. C2×#1220D4semidirect
121. C22×Dic15C23semidirect
123. C2×C4×D15C23semidirect
125. C2×C5×#67C23semidirect
129. C2×C5×D12C23semidirect
130. C2×C5×D12C23semidirect
132. C2×C3×C22⋊D5C23semidirect
136. C2×C3×D20C23semidirect
137. C2×C3×D20C23semidirect
141. C2×#1203C23semidirect
143. C2×#1202C23semidirect
151. C2×#1201D4semidirect
153. C2×#1201C23semidirect
154. C2×#1201C23semidirect
155. C2×#1201C23semidirect
156. C2×#1201C23semidirect
157. C2×#1201C23semidirect
158. C2×#1201C23semidirect
160. C2×D3×Dic5C23semidirect
162. C2×D5×Dic3C23semidirect
164. C3×C5×C22⋊C4C23semidirect
165. #6714C23semidirect
166. #6712C23semidirect
167. C4×Dic15C23semidirect
168. C5×(C2×D3)⋊C4C23semidirect
169. C5×(C2×D3)⋊C4C23semidirect
170. C3×#685C23semidirect
171. C3×#685C23semidirect
172. #6669C23semidirect
173. (C2×D3)⋊Dic5C23semidirect
174. #6665C23semidirect
188. C2×#882D5semidirect
194. C24×D5C2×D3semidirect
211. C22×C22⋊D5C2×D3semidirect
219. C22×D20C2×D3semidirect
220. C22×D20C2×D3semidirect
226. C2×C5×C22⋊C4C2×D3semidirect
234. C2×#685C2×D3semidirect
235. C2×#685C2×D3semidirect
242. #4028C2×D3semidirect
248. C23×C3×C5C2×D4semidirect
253. C22×D15C2×D4semidirect
267. C22×C5×D3C2×D4semidirect
283. C22×C3×D5C2×D4semidirect
299. #1220C2×D4semidirect
302. C2×Dic15C2×D4semidirect
303. C2×Dic15C2×D4semidirect
326. #1201C2×D4semidirect
332. C24×D3C2×D5semidirect
349. C22×#67C2×D5semidirect
357. C22×D12C2×D5semidirect
358. C22×D12C2×D5semidirect
364. C2×C3×C22⋊C4C2×D5semidirect
372. C2×(C2×D3)⋊C4C2×D5semidirect
373. C2×(C2×D3)⋊C4C2×D5semidirect
380. #882C2×D5semidirect
406. C23×D5C22×D3semidirect
437. C2×C22⋊D5C22×D3semidirect
452. C2×D20C22×D3semidirect
453. C2×D20C22×D3semidirect
460. C5×C22⋊C4C22×D3semidirect
464. #685C22×D3semidirect
465. #685C22×D3semidirect
490. C22×C3×C5C22×D4semidirect
496. C2×D15C22×D4semidirect
509. C2×C5×D3C22×D4semidirect
522. C2×C3×D5C22×D4semidirect
528. Dic15C22×D4semidirect
529. Dic15C22×D4semidirect
555. C23×D3C22×D5semidirect
586. C2×#67C22×D5semidirect
601. C2×D12C22×D5semidirect
602. C2×D12C22×D5semidirect
609. C3×C22⋊C4C22×D5semidirect
613. (C2×D3)⋊C4C22×D5semidirect
614. (C2×D3)⋊C4C22×D5semidirect
636. C23×C5D3×D4semidirect
663. C22×D5D3×D4semidirect
753. C2×C22⋊C4D3×D5semidirect
756. C2×C3×C5D42semidirect
785. C23×C3D4×D5semidirect
812. C22×D3D4×D5semidirect
868. C22×C5C2×D3×D4semidirect
889. C2×D5C2×D3×D4semidirect
981. C22⋊C4C2×D3×D5semidirect
983. C3×C5C2×D42semidirect
1002. C22×C3C2×D4×D5semidirect
1023. C2×D3C2×D4×D5semidirect
1035. C2×C5#5590semidirect
1089. C23#6777semidirect
1130. C2×C3#65924semidirect
1138. C5C2×#5590semidirect
1175. C22C2×#6777semidirect
1186. C3C2×#65924semidirect
1195. C2#11753225direct (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×D5×#672
C23×#12012
C22×#67772
C2×#917702
C2×C5×#8822
C2×C3×#40282
C2×#915712
C2×#914752
C2×#914742
C2×#914632
C2×#914612
C2×#914532
C2×#914422
C2×#914082
#117532252
C2×#659243
C2×#55905