Finite Group Databasebeta

← C2×#11753252 #14480432

Subgroups — C2×#11753252 #14480432

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91771C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4031C211yesmaximal, characteristic, complemented
6C2×#91573C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91475C211yesmaximal, characteristic, complemented
11C2×#91459C211yesmaximal, characteristic, complemented
12C2×#91454C211yesmaximal, characteristic, complemented
13C2×#91451C211yesmaximal, characteristic, complemented
14C2×#91402C211yesmaximal, characteristic, complemented
15C2×#91326C211yesmaximal, characteristic, complemented
16#11753252C2116yesmaximal, direct product factor
17C2×#65941—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic
22C22×D60C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C5×D12C2211yescharacteristic, complemented
26C22×C4×C5×D3C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×C3×Dic10C2211yescharacteristic, complemented
29C2×#6790—28no—
30C2×#6790C2218yescomplemented
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1203C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic
37C22×#1202C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic, complemented
39C22×#1200C2211yescharacteristic
40C22×#1200C2211yescharacteristic, complemented
41C2×#6769—28no—
42C2×#6769C2218yescomplemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic
45C2×#6714C2211yescharacteristic, complemented
46#91771C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C5×#884C2218yescomplemented
50C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×C4×Dic5C2211yescharacteristic, complemented
54C3×#4031C2218yescomplemented
55#91573C2218yescomplemented
56#91567C2218yescomplemented
57#91557C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64#91475C2218yescomplemented
65#91459C2218yescomplemented
66#91454C2218yescomplemented
67#91451C2218yescomplemented
68#91402C2218yescomplemented
69#91326C2218yescomplemented
70C2×#5674—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#121—31no—
74C2×#4086—31no—
75C2×#4086—31no—
76C2×#4084—31no—
77C2×#4083—31no—
78C2×#4083—31no—
79C2×#4076—31no—
80#65941—316no—
81C2×#4041—31no—
82C2×#4038—31no—
83C2×#4031—31no—
84C2×#4031D311yescharacteristic, complemented
85C2×#4028—31no—
86C2×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—42no—
90C23×D15—42no—
91C23×D15C2311yescharacteristic
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yes—
95C23×C5×D3C2311yescharacteristic
96C23×C5×D3C2311yescharacteristic
97C23×C3×D5C2311yescharacteristic
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5C2314yes—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—42no—
105C2×#1220C2314yescomplemented
106C22×Dic15C2311yescharacteristic
107C2×D60—24no—
108C2×D60—42no—
109C2×D60C2314yes—
110C2×D60C2314yescomplemented
111C2×C5×#67—24no—
112C2×C5×#67—42no—
113C2×C5×#67C2314yes—
114C2×C5×#67C2314yescomplemented
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C2×C5×D12—42no—
118C2×C5×D12C2314yescomplemented
119C2×C4×C5×D3—24no—
120C2×C4×C5×D3C2314yescomplemented
121C2×C3×C22⋊D5—24no—
122C2×C3×C22⋊D5C2314yes—
123C22×C3×Dic5C2311yescharacteristic
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C2×C3×Dic10—24no—
127C2×C3×Dic10C2314yescomplemented
128#6790—232no—
129C2×#1203—24no—
130C2×#1203—24no—
131C2×#1203—24no—
132C2×#1203—42no—
133C2×#1203—42no—
134C2×#1203C2314yes—
135C2×#1203C2314yes—
136C2×#1203C2314yescomplemented
137C2×#1203C2314yescomplemented
138C2×#1203C2314yescomplemented
139C2×#1202—24no—
140C2×#1202—42no—
141C2×#1202C2314yes—
142C2×#1202C2314yescomplemented
143C2×#1201—42no—
144C2×#1201C2314yescomplemented
145C2×#1200—24no—
146C2×#1200D418yescomplemented
147C2×#1200C2314yes—
148C2×#1200C2314yescomplemented
149#6769—232no—
150C3×C5×C22⋊C4C2314yescomplemented
151#6714C2314yes—
152#6714C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C5×Dic3⋊C4C2314yescomplemented
155C3×C22⋊Dic5C2314yescomplemented
156C3×#685C2314yescomplemented
157C3×#685C2314yescomplemented
158C3×C4×Dic5C2314yescomplemented
159Dic3⋊Dic5C2314yescomplemented
160#6667C2314yes—
161#6667C2314yescomplemented
162(C2×D3)⋊Dic5C2314yescomplemented
163Dic3×Dic5C2314yescomplemented
164C22×#239—51no—
165C22×D3×D4—51no—
166C2×C3×#124—51no—
167C2×#947—51no—
168C2×#940—51no—
169#5674—516no—
170C2×#884—51no—
171C2×#884—51no—
172C2×#884—51no—
173C2×#884D511yescharacteristic, complemented
174C2×#882—51no—
175C2×#882—51no—
176C2×#882—51no—
177C2×#882—51no—
178C2×#874—51no—
179C2×#872—51no—
180C24×D5—31no—
181C24×D5—31no—
182C22×C5×D4—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C23×C4×C5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—31no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5C2×D311yescharacteristic
194C2×D4×D5—38no—
195C2×D4×D5—68no—
196C2×#709—38no—
197C2×#709—68no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20—31no—
201C22×D20—31no—
202C22×C4×D5—31no—
203C22×C4×D5—31no—
204C22×Dic10C2×D311yescharacteristic, complemented
205C5×#121—38no—
206C2×C5×C4⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5C2×D311yescharacteristic, complemented
211#4086—38no—
212#4086—38no—
213#4084—38no—
214#4083—38no—
215#4083—38no—
216#4076—38no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685C2×D311yescharacteristic, complemented
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×C4×Dic5—31no—
225C2×C4×Dic5C2×D311yescharacteristic, complemented
226#4041—38no—
227#4038—38no—
228#4031—38no—
229#4031C2×D318yescomplemented
230#4028—38no—
231#4028—38no—
232C2×#535—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—28no—
247C22×D15—44no—
248C22×D15—44no—
249C22×D15—416no—
250C22×D15C2×D414yes—
251C22×D15C2412yes—
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—22no—
260C22×C5×D3C2412yes—
261C22×C5×D3C2412yes—
262C22×C3×D5—22no—
263C22×C3×D5—22no—
264C22×C3×D5—22no—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—416no—
270C2×C3×C4×C5—22no—
271C2×C3×C4×C5—22no—
272C2×C3×C4×C5C2412yes—
273C2×C3×C4×C5C2412yes—
274#1220—44no—
275C2×Dic15—22no—
276C2×Dic15C2412yes—
277D60—28no—
278D60—44no—
279C5×#67—28no—
280C5×#67—44no—
281C2×C5×Dic3—22no—
282C2×C5×Dic3C2×D414yes—
283C2×C5×Dic3C2412yes—
284C2×C5×Dic3C2412yes—
285C5×D12—44no—
286C4×C5×D3—28no—
287C3×C22⋊D5—28no—
288C2×C3×Dic5—22no—
289C2×C3×Dic5—22no—
290C2×C3×Dic5C2×D414yes—
291C2×C3×Dic5C2412yes—
292C2×C3×Dic5C2412yes—
293C2×C3×Dic5C2412yes—
294C3×Dic10—28no—
295#1203—28no—
296#1203—28no—
297#1203—28no—
298#1203—44no—
299#1203—44no—
300#1202—28no—
301#1202—44no—
302#1201—44no—
303#1200—28no—
304#1200C2×D4116yescomplemented
305C24×D3—51no—
306C24×D3—51no—
307C22×C3×Q8—51no—
308C22×C3×D4—51no—
309C22×#67—51no—
310C22×#67—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67C2×D511yescharacteristic
314C22×#67C2×D511yescharacteristic, complemented
315C2×#239—58no—
316C2×#239—108no—
317C2×D3×D4—58no—
318C2×D3×D4—108no—
319C22×D12—51no—
320C22×D12—51no—
321C22×D12—51no—
322C22×D12—51no—
323C22×D12—51no—
324C22×D12—51no—
325C22×D12—51no—
326C22×D12C2×D511yescharacteristic, complemented
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C22×C4×D3C2×D511yescharacteristic, complemented
330C3×#124—58no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4—51no—
334C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
335C2×C3×C42—51no—
336#947—58no—
337#940—58no—
338C2×(C2×D3)⋊C4—51no—
339C2×(C2×D3)⋊C4—51no—
340C2×(C2×D3)⋊C4—51no—
341C2×(C2×D3)⋊C4—51no—
342C2×(C2×D3)⋊C4—51no—
343C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
344C2×Dic3⋊C4—51no—
345C2×Dic3⋊C4C2×D511yescharacteristic, complemented
346C2×C4×Dic3—51no—
347#884—58no—
348#884—58no—
349#884—58no—
350#884C2×D518yescomplemented
351#882—58no—
352#882—58no—
353#882—58no—
354#882—58no—
355#874—58no—
356#872—58no—
357C24×C5—31no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C23×D5—31no—
361C23×D5—31no—
362C23×D5—31no—
363C23×D5—34no—
364C23×D5—34no—
365C23×D5—64no—
366C23×D5—64no—
367C23×D5—122no—
368C23×D5—122no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5C22×D311yescharacteristic
372C2×C5×D4—34no—
373C2×C5×D4—34no—
374C2×C5×D4—34no—
375C2×C5×D4—64no—
376C2×C5×D4—122no—
377C2×C5×D4—122no—
378C22×C4×C5—31no—
379C22×C4×C5—31no—
380C22×C4×C5—34no—
381C22×C4×C5—64no—
382C22×C4×C5C22×D311yescharacteristic
383C22×C4×C5C22×D311yescharacteristic
384C2×C22⋊D5—24no—
385C2×C22⋊D5—34no—
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—64no—
393C2×C22⋊D5—64no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—122no—
396C2×C22⋊D5—122no—
397C2×C22⋊D5—122no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5C22×D314yes—
400C22×Dic5—31no—
401C22×Dic5C22×D311yescharacteristic
402C22×Dic5C22×D311yescharacteristic
403C22×Dic5C22×D311yescharacteristic
404D4×D5—632no—
405#709—632no—
406C2×D20—34no—
407C2×D20—34no—
408C2×D20—34no—
409C2×D20—34no—
410C2×D20—64no—
411C2×D20—64no—
412C2×D20—122no—
413C2×D20—122no—
414C2×C4×D5—38no—
415C2×C4×D5—34no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×Dic10—24no—
419C2×Dic10C22×D314yescomplemented
420C5×C4⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4C22×D314yescomplemented
423C22⋊Dic5—34no—
424C22⋊Dic5C22×D314yescomplemented
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yescomplemented
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4×Dic5—34no—
433C4×Dic5C22×D314yescomplemented
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—51no—
440C2×#124—151no—
441C2×#121—31no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#117—151no—
450C22×C3×C5—22no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—44no—
454C22×C3×C5C22×D412yes—
455C22×C3×C5H(5,𝔽2)12yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5C2511yescharacteristic
458C2×D15—28no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—416no—
468C2×D15—44no—
469C2×D15—44no—
470C2×D15C22×D414yes—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—22no—
474C2×C5×D3—22no—
475C2×C5×D3—22no—
476C2×C5×D3—22no—
477C2×C5×D3—44no—
478C2×C5×D3—44no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—22no—
482C2×C3×D5—44no—
483D3×D5—416no—
484C3×C4×C5—22no—
485C3×C4×C5—22no—
486Dic15—22no—
487C3×Dic5—22no—
488C3×Dic5—22no—
489C3×Dic5C22×D414yes—
490C5×Dic3—22no—
491C5×Dic3C22×D414yes—
492C24×C3—51no—
493C24×C3C22×D511yescharacteristic
494C23×D3—51no—
495C23×D3—51no—
496C23×D3—51no—
497C23×D3—54no—
498C23×D3—54no—
499C23×D3—104no—
500C23×D3—104no—
501C23×D3—202no—
502C23×D3—202no—
503C23×D3—202no—
504C23×D3—202no—
505C23×D3C22×D511yescharacteristic
506C23×D3C22×D511yescharacteristic
507C2×C3×Q8—54no—
508C2×C3×Q8—104no—
509C2×C3×D4—54no—
510C2×C3×D4—104no—
511C22×C3×C4—51no—
512C22×C3×C4—51no—
513C22×C3×C4—51no—
514C22×C3×C4C22×D511yescharacteristic
515C22×C3×C4C22×D511yescharacteristic
516C2×#67—24no—
517C2×#67—42no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—54no—
522C2×#67—104no—
523C2×#67—202no—
524C2×#67—202no—
525C2×#67—202no—
526C2×#67C22×D514yes—
527C2×#67C22×D514yescomplemented
528C22×Dic3—51no—
529C22×Dic3C22×D511yescharacteristic
530C22×Dic3C22×D511yescharacteristic
531#239—1032no—
532D3×D4—1032no—
533C2×D12—42no—
534C2×D12—54no—
535C2×D12—54no—
536C2×D12—54no—
537C2×D12—54no—
538C2×D12—54no—
539C2×D12—54no—
540C2×D12—54no—
541C2×D12—104no—
542C2×D12—104no—
543C2×D12—104no—
544C2×D12—104no—
545C2×D12—202no—
546C2×D12—202no—
547C2×D12—202no—
548C2×D12C22×D514yescomplemented
549C2×C4×D3—24no—
550C2×C4×D3—58no—
551C2×C4×D3—54no—
552C2×C4×D3—54no—
553C2×C4×D3—104no—
554C2×C4×D3C22×D514yescomplemented
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558C3×C22⋊C4C22×D514yescomplemented
559C3×C42—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
566Dic3⋊C4—54no—
567Dic3⋊C4C22×D514yescomplemented
568C4×Dic3—54no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—32no—
573C23×C5—32no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5C23×D312yes—
581C23×C5C23×D311yescharacteristic
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—34no—
586C22×D5—32no—
587C22×D5—32no—
588C22×D5—32no—
589C22×D5—68no—
590C22×D5—68no—
591C22×D5—62no—
592C22×D5—62no—
593C22×D5—62no—
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—1216no—
605C22×D5C23×D312yes—
606C5×D4—68no—
607C5×D4—124no—
608C5×D4—124no—
609C2×C4×C5—22no—
610C2×C4×C5—22no—
611C2×C4×C5—34no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—68no—
615C2×C4×C5—62no—
616C2×C4×C5C23×D312yes—
617C2×C4×C5C23×D312yes—
618C22⋊D5—28no—
619C22⋊D5—68no—
620C22⋊D5—68no—
621C22⋊D5—68no—
622C22⋊D5—124no—
623C22⋊D5—124no—
624C22⋊D5—124no—
625C22⋊D5—124no—
626C2×Dic5—22no—
627C2×Dic5—22no—
628C2×Dic5—32no—
629C2×Dic5—62no—
630C2×Dic5D3×D414yes—
631C2×Dic5C23×D312yes—
632C2×Dic5C23×D312yes—
633C2×Dic5C23×D312yes—
634D20—68no—
635D20—68no—
636D20—124no—
637D20—124no—
638C4×D5—316no—
639C4×D5—68no—
640Dic10—28no—
641C25—151no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—51no—
646C22×D4—31no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—151no—
662C22×D4—308no—
663C23×C4—31no—
664C23×C4—151no—
665C23×C4—151no—
666#127—158no—
667#127—158no—
668#124—58no—
669#124—158no—
670#121—38no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#117—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—151no—
681C2×C22⋊C4—31no—
682C2×C22⋊C4—51no—
683C2×C22⋊C4—51no—
684C2×C22⋊C4—51no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4D3×D511yescharacteristic, complemented
691C2×C42—51no—
692C2×C42—151no—
693C2×C3×C5—42no—
694C2×C3×C5#53514yescomplemented
695C2×C3×C5C23×D411yescharacteristic
696C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
697C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
698D15—24no—
699D15—42no—
700D15—42no—
701C3×D5—42no—
702C5×D3—42no—
703C5×D3—42no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—52no—
708C23×C3—102no—
709C23×C3—102no—
710C23×C3—102no—
711C23×C3C23×D512yes—
712C23×C3C23×D511yescharacteristic
713C22×D3—22no—
714C22×D3—22no—
715C22×D3—22no—
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—54no—
720C22×D3—52no—
721C22×D3—52no—
722C22×D3—52no—
723C22×D3—108no—
724C22×D3—108no—
725C22×D3—102no—
726C22×D3—102no—
727C22×D3—102no—
728C22×D3—102no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—204no—
734C22×D3—204no—
735C22×D3—2016no—
736C22×D3—204no—
737C22×D3—204no—
738C22×D3—2016no—
739C22×D3C23×D512yes—
740C22×D3C23×D512yes—
741C3×Q8—108no—
742C3×D4—108no—
743C2×C3×C4—22no—
744C2×C3×C4—22no—
745C2×C3×C4—54no—
746C2×C3×C4—52no—
747C2×C3×C4—52no—
748C2×C3×C4—52no—
749C2×C3×C4—102no—
750C2×C3×C4—102no—
751C2×C3×C4C23×D512yes—
752C2×C3×C4C23×D512yes—
753#67—28no—
754#67—44no—
755#67—108no—
756#67—204no—
757#67—204no—
758#67—204no—
759C2×Dic3—22no—
760C2×Dic3—52no—
761C2×Dic3—102no—
762C2×Dic3D4×D514yes—
763C2×Dic3C23×D512yes—
764C2×Dic3C23×D512yes—
765D12—44no—
766D12—108no—
767D12—108no—
768D12—108no—
769D12—108no—
770D12—204no—
771D12—204no—
772D12—204no—
773C4×D3—28no—
774C4×D3—516no—
775C4×D3—108no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—44no—
780C22×C5—62no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—62no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—124no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100912yes—
790C22×C5#100912yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—22no—
795C2×D5—34no—
796C2×D5—44no—
797C2×D5—68no—
798C2×D5—62no—
799C2×D5—62no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—1216no—
807C2×D5—1216no—
808C2×D5—124no—
809C2×D5—124no—
810C4×C5—22no—
811C4×C5—22no—
812C4×C5—34no—
813C4×C5—62no—
814Dic5—22no—
815Dic5—22no—
816Dic5—62no—
817Dic5C2×D3×D414yes—
818C24—31no—
819C24—31no—
820C24—51no—
821C24—154no—
822C24—151no—
823C24—151no—
824C24—151no—
825C24—154no—
826C24—304no—
827C24—304no—
828C24—602no—
829C24—602no—
830C24—602no—
831C24—602no—
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—54no—
835C2×Q8—104no—
836C2×D4—34no—
837C2×D4—34no—
838C2×D4—34no—
839C2×D4—54no—
840C2×D4—64no—
841C2×D4—104no—
842C2×D4—122no—
843C2×D4—122no—
844C2×D4—154no—
845C2×D4—154no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—304no—
856C2×D4—304no—
857C2×D4—304no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—3032no—
861C2×D4—602no—
862C2×D4—602no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C22×C4—31no—
868C22×C4—31no—
869C22×C4—34no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—64no—
874C22×C4—154no—
875C22×C4—158no—
876C22×C4—154no—
877C22×C4—151no—
878C22×C4—304no—
879C22×C4C2×D3×D511yescharacteristic
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—34no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—54no—
885C22⋊C4—54no—
886C22⋊C4—54no—
887C22⋊C4—154no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4C2×D3×D514yescomplemented
893C42—54no—
894C42—154no—
895C3×C5C2×#53511yescharacteristic, complemented, Hall
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—44no—
900C22×C3—102no—
901C22×C3—102no—
902C22×C3—102no—
903C22×C3—204no—
904C22×C3C2×D4×D512yes—
905C22×C3#414412yes—
906C22×C3#414912yes—
907C22×C3C24×D511yescharacteristic
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—44no—
915C2×D3—44no—
916C2×D3—54no—
917C2×D3—108no—
918C2×D3—102no—
919C2×D3—102no—
920C2×D3—102no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—2016no—
927C2×D3—2016no—
928C2×D3—204no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—54no—
933C3×C4—102no—
934C3×C4—102no—
935Dic3—22no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—122no—
940C2×C5—122no—
941C2×C5#567414yescomplemented
942C2×C5C22×D3×D411yescharacteristic
943C2×C5C2×#100911yescharacteristic
944C2×C5C2×#100911yescharacteristic
945D5—42no—
946D5—64no—
947D5—122no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—32no—
953C23—32no—
954C23—52no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—102no—
962C23—102no—
963C23—102no—
964C23—154no—
965C23—152no—
966C23—152no—
967C23—152no—
968C23—308no—
969C23—308no—
970C23—302no—
971C23—302no—
972C23—302no—
973C23—302no—
974C23—302no—
975C23—302no—
976C23—302no—
977C23—302no—
978C23—604no—
979C23—604no—
980C23—6016no—
981C23—604no—
982C23—604no—
983C23—6016no—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—108no—
987D4—68no—
988D4—108no—
989D4—124no—
990D4—124no—
991D4—308no—
992D4—308no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—604no—
997D4—604no—
998D4—604no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—34no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—54no—
1008C2×C4—52no—
1009C2×C4—52no—
1010C2×C4—52no—
1011C2×C4—68no—
1012C2×C4—62no—
1013C2×C4—102no—
1014C2×C4—102no—
1015C2×C4—1516no—
1016C2×C4—152no—
1017C2×C4—308no—
1018C2×C4—302no—
1019C2×C4C22×D3×D512yes—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—202no—
1023C2×C3#6594114yescomplemented
1024C2×C3C22×D4×D511yescharacteristic
1025C2×C3C2×#414411yescharacteristic
1026C2×C3C2×#414911yescharacteristic
1027D3—42no—
1028D3—42no—
1029D3—104no—
1030D3—202no—
1031D3—202no—
1032C5C2×#567411yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—44no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—102no—
1044C22—102no—
1045C22—102no—
1046C22—124no—
1047C22—124no—
1048C22—154no—
1049C22—204no—
1050C22—308no—
1051C22—302no—
1052C22—302no—
1053C22—302no—
1054C22—302no—
1055C22—302no—
1056C22—302no—
1057C22—302no—
1058C22—302no—
1059C22—6016no—
1060C22—6016no—
1061C22—604no—
1062C22—604no—
1063C22#9201912yes—
1064C22D3×D4×D512yes—
1065C22#9202712yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—34no—
1070C4—54no—
1071C4—62no—
1072C4—102no—
1073C4—102no—
1074C4—302no—
1075C3C2×#6594111yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—122no—
1078C2—122no—
1079C2—202no—
1080C2—304no—
1081C2—602no—
1082C2—602no—
1083C2#1175325214yesdirect product factor
1084C2C2×#9201911yescharacteristic
1085C2C2×D3×D4×D511yescharacteristic
1086C2C2×#9202711yescharacteristic
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×#535
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×#6790C2semidirect
2. C22×#6769C2semidirect
3. C2×#91771C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4031C2semidirect
6. C2×#91573C2semidirect
7. C2×#91567C2semidirect
8. C2×#91557C2semidirect
9. C2×#91476C2semidirect
10. C2×#91475C2semidirect
11. C2×#91459C2semidirect
12. C2×#91454C2semidirect
13. C2×#91451C2semidirect
14. C2×#91402C2semidirect
15. C2×#91326C2semidirect
16. #11753252C2direct (N × H)
20. C22×#1220C22semidirect
22. C22×D60C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C5×D12C22semidirect
26. C22×C4×C5×D3C22semidirect
28. C22×C3×Dic10C22semidirect
30. C2×#6790C22semidirect
33. C22×#1203C22semidirect
34. C22×#1203C22semidirect
35. C22×#1203C22semidirect
37. C22×#1202C22semidirect
38. C22×#1201C22semidirect
40. C22×#1200C22semidirect
42. C2×#6769C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
45. C2×#6714C22semidirect
46. #91771C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C5×#884C22semidirect
50. C2×C3×C22⋊Dic5C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×C4×Dic5C22semidirect
54. C3×#4031C22semidirect
55. #91573C22semidirect
56. #91567C22semidirect
57. #91557C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91476C22semidirect
64. #91475C22semidirect
65. #91459C22semidirect
66. #91454C22semidirect
67. #91451C22semidirect
68. #91402C22semidirect
69. #91326C22semidirect
84. C2×#4031D3semidirect
105. C2×#1220C23semidirect
110. C2×D60C23semidirect
114. C2×C5×#67C23semidirect
118. C2×C5×D12C23semidirect
120. C2×C4×C5×D3C23semidirect
127. C2×C3×Dic10C23semidirect
136. C2×#1203C23semidirect
137. C2×#1203C23semidirect
138. C2×#1203C23semidirect
142. C2×#1202C23semidirect
144. C2×#1201C23semidirect
146. C2×#1200D4semidirect
148. C2×#1200C23semidirect
150. C3×C5×C22⋊C4C23semidirect
152. #6714C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C5×Dic3⋊C4C23semidirect
155. C3×C22⋊Dic5C23semidirect
156. C3×#685C23semidirect
157. C3×#685C23semidirect
158. C3×C4×Dic5C23semidirect
159. Dic3⋊Dic5C23semidirect
161. #6667C23semidirect
162. (C2×D3)⋊Dic5C23semidirect
163. Dic3×Dic5C23semidirect
173. C2×#884D5semidirect
204. C22×Dic10C2×D3semidirect
208. C2×C5×C22⋊C4C2×D3semidirect
210. C2×C22⋊Dic5C2×D3semidirect
221. C2×#685C2×D3semidirect
222. C2×#685C2×D3semidirect
225. C2×C4×Dic5C2×D3semidirect
229. #4031C2×D3semidirect
304. #1200C2×D4semidirect
314. C22×#67C2×D5semidirect
326. C22×D12C2×D5semidirect
329. C22×C4×D3C2×D5semidirect
334. C2×C3×C22⋊C4C2×D5semidirect
343. C2×(C2×D3)⋊C4C2×D5semidirect
345. C2×Dic3⋊C4C2×D5semidirect
350. #884C2×D5semidirect
419. C2×Dic10C22×D3semidirect
422. C5×C22⋊C4C22×D3semidirect
424. C22⋊Dic5C22×D3semidirect
429. #685C22×D3semidirect
430. #685C22×D3semidirect
433. C4×Dic5C22×D3semidirect
527. C2×#67C22×D5semidirect
548. C2×D12C22×D5semidirect
554. C2×C4×D3C22×D5semidirect
558. C3×C22⋊C4C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
567. Dic3⋊C4C22×D5semidirect
690. C2×C22⋊C4D3×D5semidirect
694. C2×C3×C5#535semidirect
892. C22⋊C4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
941. C2×C5#5674semidirect
1023. C2×C3#65941semidirect
1032. C5C2×#5674semidirect
1075. C3C2×#65941semidirect
1083. C2#11753252direct (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×#67692
C2×#917712
C2×C5×#8842
C2×C3×#40312
C2×#915732
C2×#915672
C2×#915572
C2×#914762
C2×#914752
C2×#914592
C2×#914542
C2×#914512
C2×#914022
C2×#913262
#117532522
C2×#659413
C2×#56745