Finite Group Databasebeta

← C2×#11753849 #14480357

Subgroups — C2×#11753849 #14480357

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×#6777C211yesmaximal, characteristic, complemented
2C22×D3×D20C211yesmaximal, characteristic, complemented
3C2×#91783C211yesmaximal, characteristic, complemented
4C2×C5×#894C211yesmaximal, characteristic, complemented
5C2×C3×#4041C211yesmaximal, characteristic, complemented
6C2×#91476C211yesmaximal, characteristic, complemented
7C2×#91475C211yesmaximal, characteristic, complemented
8C2×#91474C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91452C211yesmaximal, characteristic, complemented
12C2×#91448C211yesmaximal, characteristic, complemented
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91354C211yesmaximal, characteristic, complemented
16#11753849C2116yesmaximal, direct product factor
17C2×#65987—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×C4×D15C2211yescharacteristic, complemented
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic, complemented
25C22×C3×D20C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic, complemented
28C22×C3×C4×D5C2211yescharacteristic, complemented
29C22×#1203C2211yescharacteristic, complemented
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic, complemented
33C22×#1201C2211yescharacteristic
34C22×#1201C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic, complemented
36C22×D5×Dic3C2211yescharacteristic, complemented
37C2×#6777—28no—
38C2×#6777C2218yescomplemented
39C2×D3×D20—28no—
40C2×D3×D20C2218yescomplemented
41C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46#91783C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
51C5×#894C2218yescomplemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#685C2211yescharacteristic, complemented
54C3×#4041C2218yescomplemented
55C2×#6668C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
58C2×#6665C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91475C2218yescomplemented
62#91474C2218yescomplemented
63#91474C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91452C2218yescomplemented
66#91448C2218yescomplemented
67#91409C2218yescomplemented
68#91408C2218yescomplemented
69#91354C2218yescomplemented
70C2×#5605—51nomaximal, Hall
71C22×D4×D5—31no—
72C23×D20—31no—
73C2×C5×#123—31no—
74C2×#4083—31no—
75C2×#4075—31no—
76#65987—316no—
77C2×#4041—31no—
78C2×#4041D311yescharacteristic, complemented
79C2×#4040—31no—
80C2×#4040—31no—
81C2×#4030—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4028—31no—
86C2×D5×C22⋊C4—31no—
87C23×D15C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C22×D3×D5—24no—
95C22×D3×D5—24no—
96C22×D3×D5—42no—
97C22×D3×D5—42no—
98C22×D3×D5—42no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5—42no—
102C22×D3×D5D418yescomplemented
103C22×D3×D5C2314yes—
104C22×D3×D5C2314yescomplemented
105C22×D3×D5C2314yescomplemented
106C22×C3×C4×C5C2311yescharacteristic
107C22×C3×C4×C5C2311yescharacteristic
108C22×C3×C4×C5C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C2×D60—24no—
112C2×D60C2314yes—
113C2×C4×D15—24no—
114C2×C4×D15C2314yescomplemented
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C2×C5×D12—24no—
118C2×C5×D12C2314yes—
119C2×C4×C5×D3—24no—
120C2×C4×C5×D3C2314yescomplemented
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×D20—24no—
123C2×C3×D20—24no—
124C2×C3×D20—42no—
125C2×C3×D20C2314yescomplemented
126C2×C3×D20C2314yescomplemented
127C2×C3×D20C2314yescomplemented
128C2×C3×C4×D5—42no—
129C2×C3×C4×D5C2314yescomplemented
130C2×#1203—42no—
131C2×#1203C2314yescomplemented
132C2×#1202—24no—
133C2×#1202—24no—
134C2×#1202—42no—
135C2×#1202C2314yes—
136C2×#1202C2314yescomplemented
137C2×#1202C2314yescomplemented
138C2×#1201—24no—
139C2×#1201—24no—
140C2×#1201—42no—
141C2×#1201C2314yes—
142C2×#1201C2314yescomplemented
143C2×#1201C2314yescomplemented
144C2×D5×Dic3—42no—
145C2×D5×Dic3C2314yescomplemented
146#6777—232no—
147D3×D20—232no—
148C3×C5×C4⋊C4C2314yescomplemented
149#6714C2314yescomplemented
150#6714C2314yescomplemented
151#6714C2314yescomplemented
152#6712C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C5×(C2×D3)⋊C4C2314yescomplemented
156C5×Dic3⋊C4C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×#685C2314yescomplemented
159#6668C2314yescomplemented
160#6667C2314yescomplemented
161(C2×D3)⋊Dic5C2314yescomplemented
162#6665C2314yescomplemented
163#6665C2314yescomplemented
164C22×D3×D4—51no—
165C22×D3×D4—51no—
166C2×C3×#121—51no—
167C2×#939—51no—
168C2×#939—51no—
169C2×#937—51no—
170C2×#937—51no—
171C2×#930—51no—
172C22×(C2×D3)⋊C4—51no—
173#5605—516no—
174C2×#894—51no—
175C2×#894D511yescharacteristic, complemented
176C2×#883—51no—
177C2×#883—51no—
178C2×#882—51no—
179C2×#882—51no—
180C24×D5—31no—
181C24×D5—31no—
182C24×D5—31no—
183C22×C5×D4—31no—
184C23×C4×C5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C2×D4×D5—38no—
190C2×D4×D5—68no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×D20—31no—
195C22×D20—38no—
196C22×D20—68no—
197C22×D20C2×D311yescharacteristic, complemented
198C22×D20C2×D311yescharacteristic, complemented
199C22×D20C2×D311yescharacteristic, complemented
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#123—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4—31no—
209C2×C22⋊Dic5—31no—
210#4083—38no—
211#4075—38no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×#685C2×D311yescharacteristic, complemented
220C2×#683—31no—
221C2×#683—31no—
222#4041—38no—
223#4041C2×D318yescomplemented
224#4040—38no—
225#4040—38no—
226#4030—38no—
227#4030—38no—
228#4028—38no—
229#4028—38no—
230#4028—38no—
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5C2411yescharacteristic
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15C2×D414yes—
240C22×D15C2412yes—
241C22×D15C2412yes—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3C2×D414yes—
248C22×C5×D3C2412yes—
249C22×C5×D3C2412yes—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5—22no—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5C2×D414yes—
259C22×C3×D5C2412yes—
260C22×C3×D5C2412yes—
261C22×C3×D5C2412yes—
262C2×D3×D5—28no—
263C2×D3×D5—28no—
264C2×D3×D5—416no—
265C2×D3×D5—44no—
266C2×D3×D5—44no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—44no—
270C2×D3×D5—44no—
271C2×D3×D5—416no—
272C2×D3×D5—416no—
273C2×D3×D5C2×D4116yescomplemented
274C2×C3×C4×C5—22no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5—22no—
277C2×C3×C4×C5C2412yes—
278C2×C3×C4×C5C2412yes—
279C2×C3×C4×C5C2412yes—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284D60—28no—
285C4×D15—28no—
286C2×C5×Dic3—22no—
287C2×C5×Dic3—22no—
288C2×C5×Dic3C2412yes—
289C2×C5×Dic3C2412yes—
290C5×D12—28no—
291C4×C5×D3—28no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5C2412yes—
294C3×D20—28no—
295C3×D20—28no—
296C3×D20—44no—
297C3×C4×D5—44no—
298#1203—44no—
299#1202—28no—
300#1202—28no—
301#1202—44no—
302#1201—28no—
303#1201—28no—
304#1201—44no—
305D5×Dic3—44no—
306C24×D3—51no—
307C24×D3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—51no—
312C23×C3×C4—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
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×D12C2×D511yescharacteristic
327C22×C4×D3—51no—
328C22×C4×D3C2×D511yescharacteristic, complemented
329C3×#121—58no—
330C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×#217—51no—
334C2×#217—51no—
335#939—58no—
336#939—58no—
337#937—58no—
338#937—58no—
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—58no—
346C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
349C2×C4⋊Dic3—51no—
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4C2×D511yescharacteristic, complemented
352#894—58no—
353#894C2×D518yescomplemented
354#883—58no—
355#883—58no—
356#882—58no—
357#882—58no—
358C24×C5—31no—
359C24×C5—31no—
360C23×D5—31no—
361C23×D5—38no—
362C23×D5—34no—
363C23×D5—31no—
364C23×D5—34no—
365C23×D5—34no—
366C23×D5—64no—
367C23×D5—64no—
368C23×D5—122no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5—122no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5C22×D311yescharacteristic
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D311yescharacteristic
377C2×C5×D4—34no—
378C2×C5×D4—64no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—34no—
382C22×C4×C5—64no—
383C22×C4×C5C22×D311yescharacteristic
384C22×C4×C5C22×D311yescharacteristic
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—64no—
391C2×C22⋊D5—64no—
392C2×C22⋊D5—122no—
393C2×C22⋊D5—122no—
394C22×Dic5—31no—
395C22×Dic5—31no—
396C22×Dic5C22×D311yescharacteristic
397D4×D5—632no—
398C2×D20—24no—
399C2×D20—24no—
400C2×D20—34no—
401C2×D20—34no—
402C2×D20—34no—
403C2×D20—34no—
404C2×D20—42no—
405C2×D20—632no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—122no—
410C2×D20C22×D314yescomplemented
411C2×D20C22×D314yescomplemented
412C2×D20C22×D314yescomplemented
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×C4⋊C4—34no—
420C5×C4⋊C4C22×D314yescomplemented
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4—34no—
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431#685C22×D314yescomplemented
432#685C22×D314yescomplemented
433#683—34no—
434#683—34no—
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—31no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—51no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5C22×D412yes—
452C22×C3×C5H(5,𝔽2)12yes—
453C22×C3×C5H(5,𝔽2)12yes—
454C22×C3×C5C2511yescharacteristic
455C2×D15—28no—
456C2×D15—22no—
457C2×D15—22no—
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—44no—
462C2×D15C22×D414yes—
463C2×C5×D3—28no—
464C2×C5×D3—22no—
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—44no—
470C2×C5×D3C22×D414yes—
471C2×C3×D5—28no—
472C2×C3×D5—22no—
473C2×C3×D5—22no—
474C2×C3×D5—22no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—44no—
481C2×C3×D5—44no—
482C2×C3×D5C22×D414yes—
483D3×D5—416no—
484D3×D5—416no—
485D3×D5—416no—
486C3×C4×C5—22no—
487C3×C4×C5—22no—
488C3×C4×C5—22no—
489Dic15—22no—
490Dic15—22no—
491C3×Dic5—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3—51no—
497C23×D3—51no—
498C23×D3—58no—
499C23×D3—54no—
500C23×D3—51no—
501C23×D3—54no—
502C23×D3—54no—
503C23×D3—104no—
504C23×D3—104no—
505C23×D3—202no—
506C23×D3—202no—
507C23×D3—202no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3—202no—
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—54no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—104no—
518C2×C3×D4—202no—
519C22×C3×C4—51no—
520C22×C3×C4—54no—
521C22×C3×C4—202no—
522C22×C3×C4C22×D511yescharacteristic
523C22×C3×C4C22×D511yescharacteristic
524C22×C3×C4C22×D511yescharacteristic
525C2×#67—54no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—104no—
535C2×#67—202no—
536C2×#67—202no—
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—24no—
546C2×D12—54no—
547C2×D12—54no—
548C2×D12—104no—
549C2×D12—202no—
550C2×D12C22×D514yes—
551C2×C4×D3—24no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3C22×D514yescomplemented
555C3×C4⋊C4C22×D514yescomplemented
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217—54no—
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)⋊C4C22×D514yescomplemented
566(C2×D3)⋊C4C22×D514yescomplemented
567(C2×D3)⋊C4C22×D514yescomplemented
568C4⋊Dic3—54no—
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—34no—
572C23×C5—32no—
573C23×C5—32no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5C23×D311yescharacteristic
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—34no—
589C22×D5—32no—
590C22×D5—316no—
591C22×D5—32no—
592C22×D5—68no—
593C22×D5—68no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—124no—
600C22×D5—124no—
601C22×D5—1216no—
602C22×D5—124no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—124no—
606C22×D5—1216no—
607C22×D5—1216no—
608C22×D5D3×D414yes—
609C22×D5C23×D312yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—68no—
613C2×C4×C5—22no—
614C2×C4×C5—22no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—68no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5C23×D312yes—
622C2×C4×C5C23×D312yes—
623C2×C4×C5C23×D312yes—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—124no—
627C22⋊D5—124no—
628C2×Dic5—22no—
629C2×Dic5—32no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5—62no—
633C2×Dic5C23×D312yes—
634D20—28no—
635D20—28no—
636D20—44no—
637D20—68no—
638D20—68no—
639D20—68no—
640D20—124no—
641C4×D5—44no—
642C4×D5—68no—
643C4×D5—124no—
644C25—151no—
645C25—151no—
646C25—151no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—158no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4—308no—
663C23×C4—31no—
664C23×C4—51no—
665C23×C4—151no—
666C23×C4—151no—
667#123—38no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—58no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4D3×D511yescharacteristic, complemented
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#53414yescomplemented
697C2×C3×C5C23×D411yescharacteristic
698C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
699C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
700D15—24no—
701D15—42no—
702C3×D5—24no—
703C3×D5—42no—
704C3×D5—42no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—54no—
708C23×C3—52no—
709C23×C3—52no—
710C23×C3—52no—
711C23×C3—102no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3C23×D511yescharacteristic
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—22no—
725C22×D3—54no—
726C22×D3—52no—
727C22×D3—516no—
728C22×D3—52no—
729C22×D3—108no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—108no—
736C22×D3—2016no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—204no—
740C22×D3—204no—
741C22×D3—204no—
742C22×D3—204no—
743C22×D3—2016no—
744C22×D3—2016no—
745C22×D3D4×D514yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—108no—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—52no—
755C2×C3×C4—102no—
756C2×C3×C4—204no—
757C2×C3×C4C23×D512yes—
758C2×C3×C4C23×D512yes—
759C2×C3×C4C23×D512yes—
760#67—108no—
761#67—108no—
762#67—108no—
763#67—108no—
764#67—204no—
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—28no—
776D12—108no—
777D12—204no—
778C4×D3—28no—
779C4×D3—108no—
780C22×C5—34no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—68no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100912yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—28no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—34no—
802C2×D5—44no—
803C2×D5—44no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—68no—
807C2×D5—62no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—1216no—
811C2×D5—1216no—
812C2×D5—1216no—
813C2×D5—124no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—22no—
817C4×C5—22no—
818C4×C5—62no—
819C4×C5—62no—
820Dic5—22no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—51no—
826C24—51no—
827C24—51no—
828C24—154no—
829C24—158no—
830C24—154no—
831C24—154no—
832C24—151no—
833C24—151no—
834C24—304no—
835C24—304no—
836C24—602no—
837C24—602no—
838C24—602no—
839C24—602no—
840C24—602no—
841C24—602no—
842C2×D4—34no—
843C2×D4—54no—
844C2×D4—54no—
845C2×D4—54no—
846C2×D4—64no—
847C2×D4—104no—
848C2×D4—104no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—202no—
858C2×D4—304no—
859C2×D4—3032no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—3032no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4—602no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—34no—
871C22×C4—51no—
872C22×C4—54no—
873C22×C4—64no—
874C22×C4—154no—
875C22×C4—151no—
876C22×C4—151no—
877C22×C4—154no—
878C22×C4—202no—
879C22×C4—304no—
880C22×C4—602no—
881C22×C4C2×D3×D511yescharacteristic
882C22×C4C2×D3×D511yescharacteristic
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4C2×D3×D514yescomplemented
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—54no—
902C22×C3—108no—
903C22×C3—102no—
904C22×C3—102no—
905C22×C3—102no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—204no—
912C22×C3—204no—
913C22×C3C2×D4×D512yes—
914C22×C3#414912yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—44no—
924C2×D3—54no—
925C2×D3—108no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—102no—
929C2×D3—102no—
930C2×D3—102no—
931C2×D3—2016no—
932C2×D3—2016no—
933C2×D3—2016no—
934C2×D3—204no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—102no—
940Dic3—22no—
941Dic3—22no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—64no—
945C2×C5—122no—
946C2×C5#560514yescomplemented
947C2×C5C22×D3×D411yescharacteristic
948C2×C5C2×#100411yescharacteristic
949C2×C5C2×#100911yescharacteristic
950D5—24no—
951D5—42no—
952D5—42no—
953D5—64no—
954D5—122no—
955C23—34no—
956C23—32no—
957C23—32no—
958C23—54no—
959C23—52no—
960C23—52no—
961C23—52no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—102no—
974C23—102no—
975C23—1516no—
976C23—154no—
977C23—152no—
978C23—152no—
979C23—308no—
980C23—308no—
981C23—302no—
982C23—302no—
983C23—302no—
984C23—302no—
985C23—302no—
986C23—6016no—
987C23—604no—
988C23—604no—
989C23—604no—
990C23—604no—
991C23—604no—
992C23—604no—
993C23—6016no—
994C23—6016no—
995C23C22×D3×D511yescharacteristic
996D4—68no—
997D4—108no—
998D4—108no—
999D4—204no—
1000D4—308no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—604no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—52no—
1014C2×C4—68no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—102no—
1018C2×C4—152no—
1019C2×C4—152no—
1020C2×C4—204no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—604no—
1025C2×C4C22×D3×D512yes—
1026C2×C4C22×D3×D512yes—
1027C2×C4C22×D3×D512yes—
1028C2×C3—104no—
1029C2×C3—202no—
1030C2×C3—202no—
1031C2×C3#6598714yescomplemented
1032C2×C3C22×D4×D511yescharacteristic
1033C2×C3C2×#414911yescharacteristic
1034C2×C3C2×#414911yescharacteristic
1035D3—24no—
1036D3—42no—
1037D3—104no—
1038D3—202no—
1039C5C2×#560511yescharacteristic, complemented, Sylow
1040C22—34no—
1041C22—54no—
1042C22—68no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—108no—
1049C22—102no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—102no—
1054C22—102no—
1055C22—102no—
1056C22—102no—
1057C22—124no—
1058C22—154no—
1059C22—204no—
1060C22—204no—
1061C22—308no—
1062C22—302no—
1063C22—302no—
1064C22—302no—
1065C22—302no—
1066C22—302no—
1067C22—6016no—
1068C22—6016no—
1069C22—6016no—
1070C22—604no—
1071C22#9201712yes—
1072C22D3×D4×D512yes—
1073C22#9203512yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—22no—
1077C4—22no—
1078C4—62no—
1079C4—62no—
1080C4—102no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6598711yescharacteristic, complemented, Sylow
1084C2—64no—
1085C2—104no—
1086C2—122no—
1087C2—202no—
1088C2—202no—
1089C2—304no—
1090C2—602no—
1091C2#1175384914yesdirect product factor
1092C2C2×#9201711yescharacteristic
1093C2C2×D3×D4×D511yescharacteristic
1094C2C2×#9203511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6777C2semidirect
2. C22×D3×D20C2semidirect
3. C2×#91783C2semidirect
4. C2×C5×#894C2semidirect
5. C2×C3×#4041C2semidirect
6. C2×#91476C2semidirect
7. C2×#91475C2semidirect
8. C2×#91474C2semidirect
9. C2×#91474C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91452C2semidirect
12. C2×#91448C2semidirect
13. C2×#91409C2semidirect
14. C2×#91408C2semidirect
15. C2×#91354C2semidirect
16. #11753849C2direct (N × H)
19. C23×D3×D5C22semidirect
20. C23×D3×D5C22semidirect
22. C22×C4×D15C22semidirect
24. C22×C4×C5×D3C22semidirect
25. C22×C3×D20C22semidirect
26. C22×C3×D20C22semidirect
27. C22×C3×D20C22semidirect
28. C22×C3×C4×D5C22semidirect
29. C22×#1203C22semidirect
31. C22×#1202C22semidirect
32. C22×#1202C22semidirect
34. C22×#1201C22semidirect
35. C22×#1201C22semidirect
36. C22×D5×Dic3C22semidirect
38. C2×#6777C22semidirect
40. C2×D3×D20C22semidirect
41. C2×C3×C5×C4⋊C4C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6714C22semidirect
45. C2×#6712C22semidirect
46. #91783C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×(C2×D3)⋊C4C22semidirect
50. C2×C5×Dic3⋊C4C22semidirect
51. C5×#894C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#685C22semidirect
54. C3×#4041C22semidirect
55. C2×#6668C22semidirect
56. C2×#6667C22semidirect
57. C2×(C2×D3)⋊Dic5C22semidirect
58. C2×#6665C22semidirect
59. C2×#6665C22semidirect
60. #91476C22semidirect
61. #91475C22semidirect
62. #91474C22semidirect
63. #91474C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91452C22semidirect
66. #91448C22semidirect
67. #91409C22semidirect
68. #91408C22semidirect
69. #91354C22semidirect
78. C2×#4041D3semidirect
102. C22×D3×D5D4semidirect
104. C22×D3×D5C23semidirect
105. C22×D3×D5C23semidirect
114. C2×C4×D15C23semidirect
120. C2×C4×C5×D3C23semidirect
125. C2×C3×D20C23semidirect
126. C2×C3×D20C23semidirect
127. C2×C3×D20C23semidirect
129. C2×C3×C4×D5C23semidirect
131. C2×#1203C23semidirect
136. C2×#1202C23semidirect
137. C2×#1202C23semidirect
142. C2×#1201C23semidirect
143. C2×#1201C23semidirect
145. C2×D5×Dic3C23semidirect
148. C3×C5×C4⋊C4C23semidirect
149. #6714C23semidirect
150. #6714C23semidirect
151. #6714C23semidirect
152. #6712C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C5×(C2×D3)⋊C4C23semidirect
156. C5×Dic3⋊C4C23semidirect
157. C3×#685C23semidirect
158. C3×#685C23semidirect
159. #6668C23semidirect
160. #6667C23semidirect
161. (C2×D3)⋊Dic5C23semidirect
162. #6665C23semidirect
163. #6665C23semidirect
175. C2×#894D5semidirect
197. C22×D20C2×D3semidirect
198. C22×D20C2×D3semidirect
199. C22×D20C2×D3semidirect
202. C22×C4×D5C2×D3semidirect
205. C2×C5×C4⋊C4C2×D3semidirect
218. C2×#685C2×D3semidirect
219. C2×#685C2×D3semidirect
223. #4041C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
328. C22×C4×D3C2×D5semidirect
330. C2×C3×C4⋊C4C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
348. C2×(C2×D3)⋊C4C2×D5semidirect
351. C2×Dic3⋊C4C2×D5semidirect
353. #894C2×D5semidirect
410. C2×D20C22×D3semidirect
411. C2×D20C22×D3semidirect
412. C2×D20C22×D3semidirect
418. C2×C4×D5C22×D3semidirect
420. C5×C4⋊C4C22×D3semidirect
431. #685C22×D3semidirect
432. #685C22×D3semidirect
554. C2×C4×D3C22×D5semidirect
555. C3×C4⋊C4C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
567. (C2×D3)⋊C4C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
682. C2×C4⋊C4D3×D5semidirect
696. C2×C3×C5#534semidirect
887. C4⋊C4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
946. C2×C5#5605semidirect
1031. C2×C3#65987semidirect
1039. C5C2×#5605semidirect
1083. C3C2×#65987semidirect
1091. C2#11753849direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67772
C22×D3×D202
C2×#917832
C2×C5×#8942
C2×C3×#40412
C2×#914762
C2×#914752
C2×#914742
C2×D5×(C2×D3)⋊C42
C2×#914522
C2×#914482
C2×#914092
C2×#914082
C2×#913542
#117538492
C2×#659873
C2×#56055