Finite Group Databasebeta

← C2×#11755025 #14480327

Subgroups — C2×#11755025 #14480327

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic, complemented
2C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#91826C211yesmaximal, characteristic, complemented
4C2×C5×#937C211yesmaximal, characteristic, complemented
5C2×C3×#4084C211yesmaximal, characteristic, complemented
6C2×#91573C211yesmaximal, characteristic, complemented
7C2×#91570C211yesmaximal, characteristic, complemented
8C2×#91562C211yesmaximal, characteristic, complemented
9C2×#91555C211yesmaximal, characteristic, complemented
10C2×#91550C211yesmaximal, characteristic, complemented
11C2×#91549C211yesmaximal, characteristic, complemented
12#11755025C2116yesmaximal, direct product factor
13C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#91448C211yesmaximal, characteristic, complemented
15C2×#91438C211yesmaximal, characteristic, complemented
16C2×#91427C211yesmaximal, characteristic, complemented
17C2×#65923—31nomaximal, Hall
18C24×D15C2211yescharacteristic, complemented
19C24×C5×D3C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C2×#6790—28no—
30C2×#6790C2218yescomplemented
31C2×D3×C22⋊D5—28no—
32C2×D3×C22⋊D5C2218yescomplemented
33C22×#1203C2211yescharacteristic
34C22×#1203C2211yescharacteristic
35C22×#1203C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic, complemented
37C22×#1201C2211yescharacteristic, complemented
38C22×#1200C2211yescharacteristic, complemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42#91826C2218yescomplemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#937C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
51C3×#4084C2218yescomplemented
52C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
53#91573C2218yescomplemented
54#91570C2218yescomplemented
55#91562C2218yescomplemented
56#91555C2218yescomplemented
57#91550C2218yescomplemented
58#91549C2218yescomplemented
59C2×Dic3⋊Dic5C2211yescharacteristic, complemented
60C2×#6669C2211yescharacteristic, complemented
61C2×#6668C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×#6667C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
66D5×(C2×D3)⋊C4C2218yescomplemented
67#91448C2218yescomplemented
68#91438C2218yescomplemented
69#91427C2218yescomplemented
70C2×#5605—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×D4×D5—31no—
73C2×C5×#120—31no—
74C2×#4099—31no—
75C2×#4084—31no—
76C2×#4084D311yescharacteristic, complemented
77C2×#4083—31no—
78C2×#4083—31no—
79C2×#4081—31no—
80#65923—316no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4030—31no—
84C2×#4029—31no—
85C2×#4029—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—42no—
91C23×D15—42no—
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yescomplemented
95C23×C5×D3—24no—
96C23×C5×D3—42no—
97C23×C5×D3—42no—
98C23×C5×D3C2311yescharacteristic
99C23×C5×D3C2311yescharacteristic
100C23×C5×D3C2314yescomplemented
101C23×C3×D5C2311yescharacteristic
102C22×D3×D5—42no—
103C22×D3×D5—42no—
104C22×D3×D5D418yescomplemented
105C22×D3×D5C2314yes—
106C2×C3×C5×D4—42no—
107C2×C3×C5×D4C2314yescomplemented
108C22×C3×C4×C5C2311yescharacteristic
109C2×#1220—24no—
110C2×#1220—42no—
111C2×#1220C2314yes—
112C2×#1220C2314yescomplemented
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C2×C5×#67—24no—
116C2×C5×#67—42no—
117C2×C5×#67C2314yes—
118C2×C5×#67C2314yescomplemented
119C22×C5×Dic3C2311yescharacteristic
120C22×C5×Dic3C2311yescharacteristic
121C2×C3×C22⋊D5—24no—
122C2×C3×C22⋊D5—24no—
123C2×C3×C22⋊D5C2314yescomplemented
124C2×C3×C22⋊D5C2314yescomplemented
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C2×C3×C4×D5—42no—
129C2×C3×C4×D5C2314yescomplemented
130#6790—232no—
131D3×C22⋊D5—232no—
132C2×#1203—24no—
133C2×#1203—24no—
134C2×#1203—42no—
135C2×#1203C2314yes—
136C2×#1203C2314yes—
137C2×#1203C2314yescomplemented
138C2×#1202—24no—
139C2×#1202C2314yescomplemented
140C2×#1201—24no—
141C2×#1201C2314yescomplemented
142C2×#1200—24no—
143C2×#1200C2314yescomplemented
144C2×D3×Dic5—24no—
145C2×D3×Dic5C2314yescomplemented
146C2×D5×Dic3—42no—
147C2×D5×Dic3C2314yescomplemented
148#6719C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C3×C22⋊Dic5C2314yescomplemented
155C3×C22⋊Dic5C2314yescomplemented
156C3×C4⋊Dic5C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6669C2314yescomplemented
159#6668C2314yescomplemented
160#6667C2314yescomplemented
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163(C2×D3)⋊Dic5C2314yescomplemented
164C22×D3×D4—51no—
165C22×D3×D4—51no—
166C2×C3×#121—51no—
167C2×#939—51no—
168C2×#939—51no—
169C2×#937—51no—
170C2×#937D511yescharacteristic, complemented
171C2×#930—51no—
172C22×(C2×D3)⋊C4—51no—
173#5605—516no—
174C2×#894—51no—
175C2×#894—51no—
176C2×#883—51no—
177C2×#883—51no—
178C2×#882—51no—
179C2×#882—51no—
180C25×C5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C5×D4C2×D311yescharacteristic, complemented
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—38no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—31no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5—68no—
194C22×C22⋊D5C2×D311yescharacteristic, complemented
195C22×C22⋊D5C2×D311yescharacteristic, complemented
196C23×Dic5—31no—
197C2×D4×D5—38no—
198C2×D4×D5—68no—
199C22×D20—31no—
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#120—38no—
204C2×C5×C22⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207#4099—38no—
208C2×C22⋊Dic5—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211C2×C22⋊Dic5C2×D311yescharacteristic, complemented
212C2×C22⋊Dic5C2×D311yescharacteristic, complemented
213#4084—38no—
214#4084C2×D318yescomplemented
215#4083—38no—
216#4083—38no—
217#4081—38no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685—31no—
222C2×C4⋊Dic5—31no—
223C2×C4⋊Dic5C2×D311yescharacteristic, complemented
224C2×#683—31no—
225C2×#683—31no—
226#4032—38no—
227#4030—38no—
228#4030—38no—
229#4029—38no—
230#4029—38no—
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5—22no—
239C23×C3×C5C2412yes—
240C23×C3×C5C2412yes—
241C23×C3×C5C2411yescharacteristic
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—22no—
247C22×D15—28no—
248C22×D15—44no—
249C22×D15—44no—
250C22×D15—416no—
251C22×D15C2×D414yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3—22no—
257C22×C5×D3—22no—
258C22×C5×D3—22no—
259C22×C5×D3—28no—
260C22×C5×D3—44no—
261C22×C5×D3—44no—
262C22×C5×D3—416no—
263C22×C5×D3C2×D414yes—
264C22×C5×D3C2412yes—
265C22×C5×D3C2412yes—
266C22×C3×D5—22no—
267C22×C3×D5—22no—
268C22×C3×D5C2×D414yes—
269C22×C3×D5C2412yes—
270C2×D3×D5—416no—
271C2×D3×D5—44no—
272C2×D3×D5—44no—
273C2×D3×D5C2×D4116yescomplemented
274C3×C5×D4—44no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277#1220—28no—
278#1220—44no—
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15C2412yes—
282C2×Dic15C2412yes—
283C5×#67—28no—
284C5×#67—44no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3C2412yes—
288C2×C5×Dic3C2412yes—
289C3×C22⋊D5—28no—
290C3×C22⋊D5—28no—
291C2×C3×Dic5—22no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5C2412yes—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297C3×C4×D5—44no—
298#1203—28no—
299#1203—28no—
300#1203—44no—
301#1202—28no—
302#1201—28no—
303#1200—28no—
304D3×Dic5—28no—
305D5×Dic3—44no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3C2×D511yescharacteristic, complemented
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4C2×D511yescharacteristic, complemented
312C23×C3×C4—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67C2×D511yescharacteristic
318C22×#67C2×D511yescharacteristic, complemented
319C23×Dic3—51no—
320C2×D3×D4—58no—
321C2×D3×D4—58no—
322C2×D3×D4—108no—
323C2×D3×D4—108no—
324C22×D12—51no—
325C22×D12—51no—
326C22×D12—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C3×#121—58no—
330C2×C3×C4⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×#217—51no—
334C2×#217C2×D511yescharacteristic, complemented
335#939—58no—
336#939—58no—
337#937—58no—
338#937C2×D518yescomplemented
339#930—58no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4—58no—
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
349C2×C4⋊Dic3—51no—
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4—51no—
352#894—58no—
353#894—58no—
354#883—58no—
355#883—58no—
356#882—58no—
357#882—58no—
358C24×C5—31no—
359C24×C5—31no—
360C24×C5—34no—
361C24×C5—64no—
362C24×C5—122no—
363C24×C5—122no—
364C24×C5C22×D311yescharacteristic
365C24×C5C22×D311yescharacteristic
366C23×D5—31no—
367C23×D5—38no—
368C23×D5—34no—
369C23×D5—31no—
370C23×D5—34no—
371C23×D5—64no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5—122no—
375C23×D5—122no—
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—34no—
378C2×C5×D4—34no—
379C2×C5×D4—42no—
380C2×C5×D4—64no—
381C2×C5×D4—122no—
382C2×C5×D4C22×D314yescomplemented
383C22×C4×C5—31no—
384C22×C4×C5—31no—
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—24no—
387C2×C22⋊D5—24no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—34no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—632no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—64no—
399C2×C22⋊D5—122no—
400C2×C22⋊D5—122no—
401C2×C22⋊D5C22×D314yescomplemented
402C2×C22⋊D5C22×D314yescomplemented
403C22×Dic5—31no—
404C22×Dic5—31no—
405C22×Dic5—34no—
406C22×Dic5—64no—
407C22×Dic5C22×D311yescharacteristic
408C22×Dic5C22×D311yescharacteristic
409C22×Dic5C22×D311yescharacteristic
410D4×D5—632no—
411C2×D20—34no—
412C2×D20—64no—
413C2×C4×D5—34no—
414C2×C4×D5—34no—
415C2×C4×D5—42no—
416C2×C4×D5—64no—
417C2×C4×D5—122no—
418C2×C4×D5C22×D314yescomplemented
419C5×C22⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C22⋊Dic5—34no—
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425C22⋊Dic5C22×D314yescomplemented
426C22⋊Dic5C22×D314yescomplemented
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431C4⋊Dic5—34no—
432C4⋊Dic5C22×D314yescomplemented
433#683—34no—
434#683—34no—
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—151no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—51no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—31no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—22no—
457C22×C3×C5—44no—
458C22×C3×C5—44no—
459C22×C3×C5C22×D412yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5H(5,𝔽2)12yes—
462C22×C3×C5C2511yescharacteristic
463C2×D15—28no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—22no—
469C2×D15—416no—
470C2×D15—44no—
471C2×D15C22×D414yes—
472C2×C5×D3—28no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3—22no—
476C2×C5×D3—22no—
477C2×C5×D3—22no—
478C2×C5×D3—416no—
479C2×C5×D3—44no—
480C2×C5×D3C22×D414yes—
481C2×C3×D5—28no—
482C2×C3×D5—22no—
483C2×C3×D5—22no—
484C2×C3×D5C22×D414yes—
485D3×D5—416no—
486C3×C4×C5—22no—
487Dic15—22no—
488Dic15—22no—
489C3×Dic5—22no—
490C3×Dic5—22no—
491C3×Dic5—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3C22×D511yescharacteristic
496C24×C3C22×D511yescharacteristic
497C23×D3—24no—
498C23×D3—42no—
499C23×D3—42no—
500C23×D3—51no—
501C23×D3—58no—
502C23×D3—54no—
503C23×D3—51no—
504C23×D3—54no—
505C23×D3—104no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3C22×D511yescharacteristic
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D514yescomplemented
513C2×C3×D4—42no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—104no—
518C2×C3×D4C22×D514yescomplemented
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4—51no—
522C22×C3×C4—54no—
523C22×C3×C4—202no—
524C22×C3×C4C22×D511yescharacteristic
525C2×#67—24no—
526C2×#67—42no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—202no—
535C2×#67C22×D514yes—
536C2×#67C22×D514yescomplemented
537C22×Dic3—51no—
538C22×Dic3—51no—
539C22×Dic3—54no—
540C22×Dic3—202no—
541C22×Dic3C22×D511yescharacteristic
542C22×Dic3C22×D511yescharacteristic
543D3×D4—1032no—
544D3×D4—1032no—
545C2×D12—54no—
546C2×D12—54no—
547C2×D12—54no—
548C2×D12—104no—
549C2×D12—104no—
550C2×D12—202no—
551C2×C4×D3—54no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3—104no—
555C3×C4⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217C22×D514yescomplemented
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4C22×D514yescomplemented
567(C2×D3)⋊C4C22×D514yescomplemented
568C4⋊Dic3—54no—
569Dic3⋊C4—54no—
570Dic3⋊C4—54no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—22no—
577C23×C5—34no—
578C23×C5—32no—
579C23×C5—32no—
580C23×C5—68no—
581C23×C5—62no—
582C23×C5—62no—
583C23×C5—62no—
584C23×C5—62no—
585C23×C5—62no—
586C23×C5—124no—
587C23×C5—124no—
588C23×C5—1216no—
589C23×C5C23×D312yes—
590C23×C5C23×D312yes—
591C23×C5C23×D311yescharacteristic
592C22×D5—22no—
593C22×D5—22no—
594C22×D5—34no—
595C22×D5—32no—
596C22×D5—316no—
597C22×D5—32no—
598C22×D5—68no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—62no—
602C22×D5—62no—
603C22×D5—62no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—1216no—
607C22×D5—124no—
608C22×D5—124no—
609C22×D5—1216no—
610C22×D5D3×D414yes—
611C22×D5C23×D312yes—
612C5×D4—44no—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—62no—
619C2×C4×C5—62no—
620C2×C4×C5C23×D312yes—
621C22⋊D5—28no—
622C22⋊D5—28no—
623C22⋊D5—68no—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—124no—
628C22⋊D5—124no—
629C2×Dic5—22no—
630C2×Dic5—22no—
631C2×Dic5—22no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—68no—
635C2×Dic5—62no—
636C2×Dic5—62no—
637C2×Dic5C23×D312yes—
638C2×Dic5C23×D312yes—
639C2×Dic5C23×D312yes—
640D20—68no—
641C4×D5—44no—
642C4×D5—68no—
643C4×D5—124no—
644C25—31no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—158no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—308no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—51no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667#123—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—58no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—38no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—51no—
680C2×C4⋊C4—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—31no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—51no—
688C2×C22⋊C4—158no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4—151no—
696C2×C3×C5—42no—
697C2×C3×C5—42no—
698C2×C3×C5#53414yescomplemented
699C2×C3×C5C23×D411yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
702D15—24no—
703D15—42no—
704C3×D5—24no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—54no—
714C23×C3—52no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3C23×D512yes—
718C23×C3C23×D512yes—
719C23×C3C23×D511yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—28no—
726C22×D3—44no—
727C22×D3—44no—
728C22×D3—416no—
729C22×D3—54no—
730C22×D3—52no—
731C22×D3—516no—
732C22×D3—52no—
733C22×D3—108no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—102no—
738C22×D3—102no—
739C22×D3—2016no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—204no—
743C22×D3—204no—
744C22×D3—2016no—
745C22×D3D4×D514yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—44no—
749C3×D4—108no—
750C3×D4—108no—
751C2×C3×C4—22no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—52no—
755C2×C3×C4—102no—
756C2×C3×C4—102no—
757C2×C3×C4—102no—
758C2×C3×C4—204no—
759C2×C3×C4C23×D512yes—
760#67—28no—
761#67—44no—
762#67—108no—
763#67—108no—
764#67—108no—
765#67—204no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—52no—
769C2×Dic3—52no—
770C2×Dic3—102no—
771C2×Dic3—102no—
772C2×Dic3—204no—
773C2×Dic3C23×D512yes—
774C2×Dic3C23×D512yes—
775D12—108no—
776D12—108no—
777D12—204no—
778C4×D3—108no—
779C4×D3—108no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—22no—
784C22×C5—22no—
785C22×C5—22no—
786C22×C5—34no—
787C22×C5—44no—
788C22×C5—44no—
789C22×C5—62no—
790C22×C5—62no—
791C22×C5—68no—
792C22×C5—62no—
793C22×C5—62no—
794C22×C5—62no—
795C22×C5—1216no—
796C22×C5—124no—
797C22×C5C2×D3×D412yes—
798C22×C5#100412yes—
799C22×C5#100912yes—
800C22×C5C24×D311yescharacteristic
801C2×D5—22no—
802C2×D5—22no—
803C2×D5—28no—
804C2×D5—34no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—68no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—62no—
817C4×C5—62no—
818Dic5—22no—
819Dic5—22no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—34no—
826C24—51no—
827C24—64no—
828C24—122no—
829C24—122no—
830C24—154no—
831C24—158no—
832C24—151no—
833C24—151no—
834C24—154no—
835C24—304no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24C2×D3×D511yescharacteristic
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—34no—
844C2×D4—42no—
845C2×D4—54no—
846C2×D4—54no—
847C2×D4—64no—
848C2×D4—104no—
849C2×D4—104no—
850C2×D4—122no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—154no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—3032no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4C2×D3×D514yescomplemented
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—54no—
874C22×C4—154no—
875C22×C4—154no—
876C22×C4—154no—
877C22×C4—151no—
878C22×C4—151no—
879C22×C4—202no—
880C22×C4—304no—
881C22×C4—304no—
882C22×C4—602no—
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—54no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—34no—
891C22⋊C4—54no—
892C22⋊C4—54no—
893C22⋊C4—154no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4—154no—
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—44no—
908C22×C3—44no—
909C22×C3—54no—
910C22×C3—108no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3C2×D4×D512yes—
914C22×C3#414412yes—
915C22×C3#414412yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—416no—
924C2×D3—44no—
925C2×D3—54no—
926C2×D3—108no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—102no—
932C2×D3—2016no—
933C2×D3—2016no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—102no—
938C3×C4—102no—
939C3×C4—102no—
940Dic3—22no—
941Dic3—22no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—42no—
946C2×C5—64no—
947C2×C5—122no—
948C2×C5#560514yescomplemented
949C2×C5C22×D3×D411yescharacteristic
950C2×C5C2×#100411yescharacteristic
951C2×C5C2×#100911yescharacteristic
952D5—24no—
953D5—64no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—34no—
962C23—32no—
963C23—32no—
964C23—54no—
965C23—52no—
966C23—68no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—102no—
973C23—102no—
974C23—124no—
975C23—124no—
976C23—1216no—
977C23—1516no—
978C23—154no—
979C23—152no—
980C23—152no—
981C23—308no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—302no—
987C23—604no—
988C23—604no—
989C23—6016no—
990C23—6016no—
991C23—604no—
992C23—604no—
993C23C22×D3×D512yes—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—44no—
997D4—68no—
998D4—108no—
999D4—108no—
1000D4—124no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—52no—
1012C2×C4—52no—
1013C2×C4—52no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—102no—
1017C2×C4—102no—
1018C2×C4—102no—
1019C2×C4—152no—
1020C2×C4—152no—
1021C2×C4—204no—
1022C2×C4—308no—
1023C2×C4—308no—
1024C2×C4—302no—
1025C2×C4—302no—
1026C2×C4—604no—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—42no—
1030C2×C3—104no—
1031C2×C3#6592314yescomplemented
1032C2×C3C22×D4×D511yescharacteristic
1033C2×C3C2×#414411yescharacteristic
1034C2×C3C2×#414411yescharacteristic
1035D3—24no—
1036D3—42no—
1037D3—104no—
1038D3—202no—
1039C5C2×#560511yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—34no—
1047C22—44no—
1048C22—44no—
1049C22—54no—
1050C22—68no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—108no—
1057C22—102no—
1058C22—102no—
1059C22—1216no—
1060C22—124no—
1061C22—154no—
1062C22—308no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22D3×D4×D512yes—
1072C22#9202712yes—
1073C22#9204912yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—62no—
1077C4—62no—
1078C4—102no—
1079C4—102no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6592311yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—42no—
1086C2—64no—
1087C2—104no—
1088C2—122no—
1089C2—304no—
1090C2—602no—
1091C2#1175502514yesdirect product factor
1092C2C2×D3×D4×D511yescharacteristic
1093C2C2×#9202711yescharacteristic
1094C2C2×#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×#534
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×#6790C2semidirect
2. C22×D3×C22⋊D5C2semidirect
3. C2×#91826C2semidirect
4. C2×C5×#937C2semidirect
5. C2×C3×#4084C2semidirect
6. C2×#91573C2semidirect
7. C2×#91570C2semidirect
8. C2×#91562C2semidirect
9. C2×#91555C2semidirect
10. C2×#91550C2semidirect
11. C2×#91549C2semidirect
12. #11755025C2direct (N × H)
13. C2×D5×(C2×D3)⋊C4C2semidirect
14. C2×#91448C2semidirect
15. C2×#91438C2semidirect
16. C2×#91427C2semidirect
18. C24×D15C22semidirect
19. C24×C5×D3C22semidirect
21. C22×C3×C5×D4C22semidirect
23. C22×#1220C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C3×C22⋊D5C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C4×D5C22semidirect
30. C2×#6790C22semidirect
32. C2×D3×C22⋊D5C22semidirect
35. C22×#1203C22semidirect
36. C22×#1202C22semidirect
37. C22×#1201C22semidirect
38. C22×#1200C22semidirect
39. C22×D3×Dic5C22semidirect
40. C22×D5×Dic3C22semidirect
41. C2×#6719C22semidirect
42. #91826C22semidirect
43. C2×#6714C22semidirect
44. C2×#6714C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#937C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C2×C3×C22⋊Dic5C22semidirect
51. C3×#4084C22semidirect
52. C2×C3×C4⋊Dic5C22semidirect
53. #91573C22semidirect
54. #91570C22semidirect
55. #91562C22semidirect
56. #91555C22semidirect
57. #91550C22semidirect
58. #91549C22semidirect
59. C2×Dic3⋊Dic5C22semidirect
60. C2×#6669C22semidirect
61. C2×#6668C22semidirect
62. C2×#6667C22semidirect
63. C2×#6667C22semidirect
64. C2×(C2×D3)⋊Dic5C22semidirect
65. C2×(C2×D3)⋊Dic5C22semidirect
66. D5×(C2×D3)⋊C4C22semidirect
67. #91448C22semidirect
68. #91438C22semidirect
69. #91427C22semidirect
76. C2×#4084D3semidirect
94. C23×D15C23semidirect
100. C23×C5×D3C23semidirect
104. C22×D3×D5D4semidirect
107. C2×C3×C5×D4C23semidirect
112. C2×#1220C23semidirect
118. C2×C5×#67C23semidirect
123. C2×C3×C22⋊D5C23semidirect
124. C2×C3×C22⋊D5C23semidirect
129. C2×C3×C4×D5C23semidirect
137. C2×#1203C23semidirect
139. C2×#1202C23semidirect
141. C2×#1201C23semidirect
143. C2×#1200C23semidirect
145. C2×D3×Dic5C23semidirect
147. C2×D5×Dic3C23semidirect
148. #6719C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C3×C22⋊Dic5C23semidirect
155. C3×C22⋊Dic5C23semidirect
156. C3×C4⋊Dic5C23semidirect
157. Dic3⋊Dic5C23semidirect
158. #6669C23semidirect
159. #6668C23semidirect
160. #6667C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. (C2×D3)⋊Dic5C23semidirect
170. C2×#937D5semidirect
185. C22×C5×D4C2×D3semidirect
194. C22×C22⋊D5C2×D3semidirect
195. C22×C22⋊D5C2×D3semidirect
202. C22×C4×D5C2×D3semidirect
211. C2×C22⋊Dic5C2×D3semidirect
212. C2×C22⋊Dic5C2×D3semidirect
214. #4084C2×D3semidirect
223. C2×C4⋊Dic5C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
308. C24×D3C2×D5semidirect
311. C22×C3×D4C2×D5semidirect
318. C22×#67C2×D5semidirect
334. C2×#217C2×D5semidirect
338. #937C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
348. C2×(C2×D3)⋊C4C2×D5semidirect
382. C2×C5×D4C22×D3semidirect
401. C2×C22⋊D5C22×D3semidirect
402. C2×C22⋊D5C22×D3semidirect
418. C2×C4×D5C22×D3semidirect
425. C22⋊Dic5C22×D3semidirect
426. C22⋊Dic5C22×D3semidirect
432. C4⋊Dic5C22×D3semidirect
512. C23×D3C22×D5semidirect
518. C2×C3×D4C22×D5semidirect
536. C2×#67C22×D5semidirect
559. #217C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
662. C22×D4D3×D5semidirect
698. C2×C3×C5#534semidirect
867. C2×D4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
948. C2×C5#5605semidirect
1031. C2×C3#65923semidirect
1039. C5C2×#5605semidirect
1083. C3C2×#65923semidirect
1091. C2#11755025direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C22×D3×C22⋊D52
C2×#918262
C2×C5×#9372
C2×C3×#40842
C2×#915732
C2×#915702
C2×#915622
C2×#915552
C2×#915502
C2×#915492
#117550252
C2×D5×(C2×D3)⋊C42
C2×#914482
C2×#914382
C2×#914272
C2×#659233
C2×#56055