Finite Group Databasebeta

← C2×#11755029 #14480421

Subgroups — C2×#11755029 #14480421

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×D5×#67C211yesmaximal, characteristic, complemented
2C22×#6779C211yesmaximal, characteristic, complemented
3C2×#91829C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×C3×#4083C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91569C211yesmaximal, characteristic, complemented
8C2×#91567C211yesmaximal, characteristic, complemented
9C2×#91564C211yesmaximal, characteristic, complemented
10C2×#91557C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11755029C2116yesmaximal, direct product factor
13C2×#91476C211yesmaximal, characteristic, complemented
14C2×#91464C211yesmaximal, characteristic, complemented
15C2×#91459C211yesmaximal, characteristic, complemented
16C2×#91394C211yesmaximal, characteristic, complemented
17C2×#65941—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic, complemented
24C22×#1220C2211yescharacteristic, complemented
25C22×D60C2211yescharacteristic, complemented
26C22×C5×#67C2211yescharacteristic
27C22×C5×#67C2211yescharacteristic, complemented
28C23×C5×Dic3C2211yescharacteristic, complemented
29C22×C3×C22⋊D5C2211yescharacteristic
30C22×C3×C22⋊D5C2211yescharacteristic, complemented
31C2×D5×#67—28no—
32C2×D5×#67C2218yescomplemented
33C22×#1204C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic, complemented
35C22×#1202C2211yescharacteristic
36C22×#1202C2211yescharacteristic
37C22×#1202C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic
39C22×#1200C2211yescharacteristic, complemented
40C2×#6779—28no—
41C2×#6779C2218yescomplemented
42C22×D5×Dic3C2211yescharacteristic
43#91829C2218yescomplemented
44C2×C4×Dic15C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#939C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C3×#4083C2218yescomplemented
51C2×C3×#685C2211yescharacteristic
52C2×C3×#685C2211yescharacteristic, complemented
53#91577C2218yescomplemented
54#91569C2218yescomplemented
55#91567C2218yescomplemented
56#91564C2218yescomplemented
57#91557C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic
63C2×#6665C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91526C2218yescomplemented
66#91476C2218yescomplemented
67#91464C2218yescomplemented
68#91459C2218yescomplemented
69#91394C2218yescomplemented
70C2×#5592—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×#4083D311yescharacteristic, complemented
79C2×#4076—31no—
80#65941—316no—
81C2×#4041—31no—
82C2×#4038—31no—
83C2×#4031—31no—
84C2×#4031—31no—
85C2×#4028—31no—
86C2×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×D15C2311yescharacteristic
91C23×C5×D3C2311yescharacteristic
92C23×C3×D5—24no—
93C23×C3×D5—42no—
94C23×C3×D5—42no—
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2314yes—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5C2314yes—
102C2×C3×C5×D4—42no—
103C2×C3×C5×D4C2314yescomplemented
104C22×C3×C4×C5C2311yescharacteristic
105C2×#1220—24no—
106C2×#1220—24no—
107C2×#1220—42no—
108C2×#1220—42no—
109C2×#1220C2314yes—
110C2×#1220C2314yescomplemented
111C2×#1220C2314yescomplemented
112C2×#1220C2314yescomplemented
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C2×D60—42no—
116C2×D60C2314yescomplemented
117C2×C5×#67—24no—
118C2×C5×#67—42no—
119C2×C5×#67C2314yes—
120C2×C5×#67C2314yescomplemented
121C22×C5×Dic3—24no—
122C22×C5×Dic3C2311yescharacteristic
123C22×C5×Dic3C2311yescharacteristic
124C22×C5×Dic3C2311yescharacteristic
125C22×C5×Dic3C2314yescomplemented
126C2×C3×C22⋊D5—24no—
127C2×C3×C22⋊D5—42no—
128C2×C3×C22⋊D5C2314yes—
129C2×C3×C22⋊D5C2314yescomplemented
130C22×C3×Dic5C2311yescharacteristic
131C22×C3×Dic5C2311yescharacteristic
132D5×#67—232no—
133C2×#1204—24no—
134C2×#1204C2314yescomplemented
135C2×#1203—42no—
136C2×#1203C2314yescomplemented
137C2×#1202—24no—
138C2×#1202—24no—
139C2×#1202—42no—
140C2×#1202C2314yes—
141C2×#1202C2314yes—
142C2×#1202C2314yescomplemented
143C2×#1201—24no—
144C2×#1201C2314yes—
145C2×#1200—24no—
146C2×#1200C2314yescomplemented
147#6779—232no—
148C2×D5×Dic3D418yescomplemented
149C2×D5×Dic3C2314yes—
150C4×Dic15C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×Dic3⋊C4C2314yescomplemented
154C3×C22⋊Dic5C2314yescomplemented
155C3×#685C2314yes—
156C3×#685C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
161#6665C2314yes—
162#6665C2314yescomplemented
163Dic3×Dic5C2314yescomplemented
164C23×#67—51no—
165C22×#237—51no—
166C2×C3×#120—51no—
167C2×#953—51no—
168C2×#940—51no—
169C2×#940—51no—
170C2×#939—51no—
171C2×#939D511yescharacteristic, complemented
172C2×#937—51no—
173#5592—516no—
174C2×#885—51no—
175C2×#885—51no—
176C2×#884—51no—
177C2×#884—51no—
178C2×#882—51no—
179C2×#877—51no—
180C24×D5—31no—
181C24×D5C2×D311yescharacteristic
182C22×C5×D4—31no—
183C22×C5×D4—31no—
184C22×C5×D4C2×D311yescharacteristic, complemented
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⋊D5C2×D311yescharacteristic
193C22×C22⋊D5C2×D311yescharacteristic, complemented
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×Dic10—31no—
205C5×#121—38no—
206C2×C5×C4⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5C2×D311yescharacteristic, complemented
211#4086—38no—
212#4086—38no—
213#4084—38no—
214#4083—38no—
215#4083C2×D318yescomplemented
216#4076—38no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685C2×D311yescharacteristic
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×C4×Dic5—31no—
225C2×C4×Dic5—31no—
226#4041—38no—
227#4038—38no—
228#4031—38no—
229#4031—38no—
230#4028—38no—
231#4028—38no—
232C2×#535—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—22no—
248C22×D15C2412yes—
249C22×D15C2412yes—
250C22×C5×D3—22no—
251C22×C5×D3—22no—
252C22×C5×D3—22no—
253C22×C5×D3C2412yes—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5—22no—
259C22×C3×D5—28no—
260C22×C3×D5—44no—
261C22×C3×D5—44no—
262C22×C3×D5—416no—
263C22×C3×D5C2×D414yes—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—416no—
270C3×C5×D4—44no—
271C2×C3×C4×C5—22no—
272C2×C3×C4×C5C2412yes—
273#1220—28no—
274#1220—28no—
275#1220—44no—
276#1220—44no—
277C2×Dic15—22no—
278C2×Dic15C2×D414yes—
279C2×Dic15C2412yes—
280C2×Dic15C2412yes—
281D60—44no—
282C5×#67—28no—
283C5×#67—44no—
284C2×C5×Dic3—22no—
285C2×C5×Dic3—22no—
286C2×C5×Dic3—28no—
287C2×C5×Dic3C2×D414yes—
288C2×C5×Dic3C2412yes—
289C2×C5×Dic3C2412yes—
290C2×C5×Dic3C2412yes—
291C3×C22⋊D5—28no—
292C3×C22⋊D5—44no—
293C2×C3×Dic5—22no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5C2412yes—
296C2×C3×Dic5C2412yes—
297#1204—28no—
298#1203—44no—
299#1202—28no—
300#1202—28no—
301#1202—44no—
302#1201—28no—
303#1200—28no—
304D5×Dic3C2×D4116yescomplemented
305C25×C3—51no—
306C24×D3—51no—
307C22×C3×D4—51no—
308C22×C3×D4—51no—
309C22×C3×D4C2×D511yescharacteristic, complemented
310C22×#67—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—58no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—108no—
320C22×#67C2×D511yescharacteristic
321C22×#67C2×D511yescharacteristic, complemented
322C23×Dic3—51no—
323C23×Dic3C2×D511yescharacteristic, complemented
324C2×#237—58no—
325C2×#237—108no—
326C22×D12—51no—
327C22×D12—51no—
328C22×C4×D3—51no—
329C22×Dic6—51no—
330C3×#120—58no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4—51no—
334#953—58no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217C2×D511yescharacteristic, complemented
338#940—58no—
339#940—58no—
340#939—58no—
341#939C2×D518yescomplemented
342#937—58no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
347C2×Dic3⋊C4—51no—
348C2×Dic3⋊C4C2×D511yescharacteristic, complemented
349C2×C4×Dic3—51no—
350C2×C4×Dic3—51no—
351#885—58no—
352#885—58no—
353#884—58no—
354#884—58no—
355#882—58no—
356#877—58no—
357C24×C5—31no—
358C24×C5C22×D311yescharacteristic
359C24×C5C22×D311yescharacteristic
360C23×D5—24no—
361C23×D5—31no—
362C23×D5—31no—
363C23×D5—34no—
364C23×D5—42no—
365C23×D5—42no—
366C23×D5—64no—
367C23×D5—122no—
368C23×D5—122no—
369C23×D5C22×D311yescharacteristic
370C23×D5C22×D311yescharacteristic
371C23×D5C22×D314yes—
372C2×C5×D4—34no—
373C2×C5×D4—34no—
374C2×C5×D4—42no—
375C2×C5×D4—64no—
376C2×C5×D4—122no—
377C2×C5×D4C22×D314yescomplemented
378C22×C4×C5—31no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—34no—
382C22×C4×C5—64no—
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—42no—
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⋊D5C22×D314yes—
399C2×C22⋊D5C22×D314yescomplemented
400C22×Dic5—31no—
401C22×Dic5—31no—
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—34no—
419C2×Dic10—64no—
420C5×C4⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C22⋊Dic5—34no—
424C22⋊Dic5C22×D314yescomplemented
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yes—
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4×Dic5—34no—
433C4×Dic5—34no—
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—151no—
440C2×#124—151no—
441C2×#121—31no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—51no—
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—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—44no—
457C22×C3×C5—44no—
458C22×C3×C5C22×D412yes—
459C22×C3×C5H(5,𝔽2)12yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5C2511yescharacteristic
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—44no—
469C2×D15—44no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—44no—
474C2×C3×D5—28no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—416no—
481C2×C3×D5—44no—
482C2×C3×D5C22×D414yes—
483D3×D5—416no—
484C3×C4×C5—22no—
485Dic15—22no—
486Dic15C22×D414yes—
487C3×Dic5—22no—
488C3×Dic5—22no—
489C5×Dic3—22no—
490C5×Dic3—22no—
491C5×Dic3C22×D414yes—
492C24×C3—51no—
493C24×C3—51no—
494C24×C3—54no—
495C24×C3—104no—
496C24×C3—202no—
497C24×C3—202no—
498C24×C3C22×D511yescharacteristic
499C24×C3C22×D511yescharacteristic
500C23×D3—51no—
501C23×D3—51no—
502C23×D3—54no—
503C23×D3—104no—
504C23×D3—202no—
505C23×D3—202no—
506C23×D3C22×D511yescharacteristic
507C2×C3×D4—42no—
508C2×C3×D4—54no—
509C2×C3×D4—54no—
510C2×C3×D4—104no—
511C2×C3×D4—202no—
512C2×C3×D4C22×D514yescomplemented
513C22×C3×C4—51no—
514C22×C3×C4—51no—
515C22×C3×C4C22×D511yescharacteristic
516C2×#67—24no—
517C2×#67—42no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—54no—
522C2×#67—54no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—104no—
527C2×#67—1032no—
528C2×#67—104no—
529C2×#67—104no—
530C2×#67—104no—
531C2×#67—104no—
532C2×#67—202no—
533C2×#67—202no—
534C2×#67—202no—
535C2×#67C22×D514yes—
536C2×#67C22×D514yescomplemented
537C22×Dic3—24no—
538C22×Dic3—51no—
539C22×Dic3—58no—
540C22×Dic3—54no—
541C22×Dic3—51no—
542C22×Dic3C22×D511yescharacteristic
543C22×Dic3C22×D511yescharacteristic
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D514yescomplemented
546#237—1032no—
547C2×D12—54no—
548C2×D12—54no—
549C2×D12—202no—
550C2×D12—202no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×Dic6—54no—
554C2×Dic6—104no—
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217—54no—
560#217C22×D514yescomplemented
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4C22×D514yescomplemented
565Dic3⋊C4—54no—
566Dic3⋊C4C22×D514yescomplemented
567C4×Dic3—54no—
568C4×Dic3—54no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—32no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5C23×D312yes—
580C23×C5C23×D312yes—
581C23×C5C23×D311yescharacteristic
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—28no—
588C22×D5—32no—
589C22×D5—32no—
590C22×D5—44no—
591C22×D5—44no—
592C22×D5—416no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—62no—
599C22×D5—68no—
600C22×D5—124no—
601C22×D5—124no—
602C22×D5—1216no—
603C22×D5D3×D414yes—
604C22×D5C23×D312yes—
605C22×D5C23×D312yes—
606C5×D4—44no—
607C5×D4—68no—
608C5×D4—124no—
609C2×C4×C5—22no—
610C2×C4×C5—34no—
611C2×C4×C5—32no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—68no—
615C2×C4×C5—62no—
616C2×C4×C5—62no—
617C2×C4×C5C23×D312yes—
618C22⋊D5—28no—
619C22⋊D5—44no—
620C22⋊D5—68no—
621C22⋊D5—68no—
622C22⋊D5—68no—
623C22⋊D5—124no—
624C22⋊D5—124no—
625C22⋊D5—124no—
626C2×Dic5—22no—
627C2×Dic5—22no—
628C2×Dic5—34no—
629C2×Dic5—32no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5C23×D312yes—
633C2×Dic5C23×D312yes—
634D20—68no—
635D20—68no—
636D20—124no—
637D20—124no—
638C4×D5—316no—
639C4×D5—68no—
640Dic10—68no—
641C25—51no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—151no—
646C22×D4—31no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—158no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—31no—
664C23×C4—151no—
665C23×C4—151no—
666#127—158no—
667#127—158no—
668#124—158no—
669#124—158no—
670#121—38no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—58no—
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—31no—
683C2×C22⋊C4—51no—
684C2×C22⋊C4—51no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—151no—
691C2×C42—151no—
692C2×C42—151no—
693C2×C3×C5—42no—
694C2×C3×C5—42no—
695C2×C3×C5#53514yescomplemented
696C2×C3×C5C23×D411yescharacteristic
697C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
698C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
699D15—42no—
700D15—42no—
701C3×D5—24no—
702C3×D5—42no—
703C5×D3—42no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—54no—
711C23×C3—52no—
712C23×C3—52no—
713C23×C3—108no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3—204no—
720C23×C3—204no—
721C23×C3—2016no—
722C23×C3C23×D512yes—
723C23×C3C23×D512yes—
724C23×C3C23×D511yescharacteristic
725C22×D3—22no—
726C22×D3—22no—
727C22×D3—22no—
728C22×D3—52no—
729C22×D3—52no—
730C22×D3—108no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—2016no—
740C22×D3C23×D512yes—
741C3×D4—44no—
742C3×D4—108no—
743C3×D4—204no—
744C2×C3×C4—22no—
745C2×C3×C4—52no—
746C2×C3×C4—52no—
747C2×C3×C4—102no—
748C2×C3×C4—102no—
749C2×C3×C4C23×D512yes—
750#67—28no—
751#67—44no—
752#67—108no—
753#67—108no—
754#67—108no—
755#67—108no—
756#67—108no—
757#67—204no—
758#67—204no—
759#67—204no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—28no—
763C2×Dic3—54no—
764C2×Dic3—52no—
765C2×Dic3—516no—
766C2×Dic3—52no—
767C2×Dic3—102no—
768C2×Dic3D4×D514yes—
769C2×Dic3C23×D512yes—
770C2×Dic3C23×D512yes—
771C2×Dic3C23×D512yes—
772D12—204no—
773D12—204no—
774C4×D3—108no—
775Dic6—108no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—22no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—44no—
783C22×C5—44no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100412yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—28no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—416no—
799C2×D5—44no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—1216no—
807C2×D5—124no—
808C2×D5—124no—
809C2×D5C2×D3×D414yes—
810C4×C5—22no—
811C4×C5—34no—
812C4×C5—62no—
813C4×C5—62no—
814Dic5—22no—
815Dic5—22no—
816Dic5—34no—
817Dic5—62no—
818C24—31no—
819C24—51no—
820C24—51no—
821C24—54no—
822C24—104no—
823C24—154no—
824C24—151no—
825C24—151no—
826C24—202no—
827C24—202no—
828C24—304no—
829C24—602no—
830C24—602no—
831C24C2×D3×D511yescharacteristic
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—154no—
835C2×Q8—304no—
836C2×D4—34no—
837C2×D4—34no—
838C2×D4—42no—
839C2×D4—54no—
840C2×D4—54no—
841C2×D4—64no—
842C2×D4—104no—
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—202no—
855C2×D4—304no—
856C2×D4—304no—
857C2×D4—3032no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—602no—
862C2×D4—602no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4C2×D3×D514yescomplemented
867C22×C4—31no—
868C22×C4—34no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—64no—
874C22×C4—154no—
875C22×C4—154no—
876C22×C4—158no—
877C22×C4—151no—
878C22×C4—151no—
879C22×C4—304no—
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—34no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—54no—
886C22⋊C4—54no—
887C22⋊C4—54no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4—154no—
893C42—154no—
894C42—154no—
895C3×C5C2×#53511yescharacteristic, complemented, Hall
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—44no—
903C22×C3—44no—
904C22×C3—54no—
905C22×C3—108no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—102no—
911C22×C3—2016no—
912C22×C3—204no—
913C22×C3C2×D4×D512yes—
914C22×C3#414412yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—44no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—2016no—
928C2×D3—204no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—102no—
932C3×C4—102no—
933Dic3—22no—
934Dic3—22no—
935Dic3—54no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—42no—
940C2×C5—122no—
941C2×C5#559214yescomplemented
942C2×C5C22×D3×D411yescharacteristic
943C2×C5C2×#100411yescharacteristic
944C2×C5C2×#100411yescharacteristic
945D5—24no—
946D5—42no—
947D5—122no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—32no—
956C23—54no—
957C23—52no—
958C23—52no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—108no—
963C23—102no—
964C23—102no—
965C23—102no—
966C23—102no—
967C23—102no—
968C23—152no—
969C23—152no—
970C23—204no—
971C23—204no—
972C23—2016no—
973C23—308no—
974C23—302no—
975C23—302no—
976C23—302no—
977C23—302no—
978C23—302no—
979C23—302no—
980C23—604no—
981C23—604no—
982C23—6016no—
983C23C22×D3×D512yes—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—308no—
987D4—44no—
988D4—68no—
989D4—108no—
990D4—124no—
991D4—204no—
992D4—308no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—308no—
997D4—604no—
998D4—604no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—34no—
1004C2×C4—32no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—52no—
1008C2×C4—52no—
1009C2×C4—68no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—102no—
1013C2×C4—102no—
1014C2×C4—1516no—
1015C2×C4—154no—
1016C2×C4—152no—
1017C2×C4—152no—
1018C2×C4—308no—
1019C2×C4—302no—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—42no—
1023C2×C3—104no—
1024C2×C3—202no—
1025C2×C3#6594114yescomplemented
1026C2×C3C22×D4×D511yescharacteristic
1027C2×C3C2×#414411yescharacteristic
1028C2×C3C2×#414911yescharacteristic
1029D3—42no—
1030D3—202no—
1031D3—202no—
1032C5C2×#559211yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—44no—
1040C22—44no—
1041C22—54no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—108no—
1046C22—102no—
1047C22—102no—
1048C22—102no—
1049C22—102no—
1050C22—102no—
1051C22—124no—
1052C22—2016no—
1053C22—204no—
1054C22—302no—
1055C22—302no—
1056C22—302no—
1057C22—302no—
1058C22—302no—
1059C22—302no—
1060C22—6016no—
1061C22—604no—
1062C22—604no—
1063C22D3×D4×D512yes—
1064C22#9202612yes—
1065C22#9204912yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—34no—
1069C4—62no—
1070C4—62no—
1071C4—102no—
1072C4—102no—
1073C4—154no—
1074C4—302no—
1075C3C2×#6594111yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—42no—
1078C2—104no—
1079C2—122no—
1080C2—202no—
1081C2—602no—
1082C2—602no—
1083C2#1175502914yesdirect product factor
1084C2C2×D3×D4×D511yescharacteristic
1085C2C2×#9202611yescharacteristic
1086C2C2×#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×#535
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×D5×#67C2semidirect
2. C22×#6779C2semidirect
3. C2×#91829C2semidirect
4. C2×C5×#939C2semidirect
5. C2×C3×#4083C2semidirect
6. C2×#91577C2semidirect
7. C2×#91569C2semidirect
8. C2×#91567C2semidirect
9. C2×#91564C2semidirect
10. C2×#91557C2semidirect
11. C2×#91526C2semidirect
12. #11755029C2direct (N × H)
13. C2×#91476C2semidirect
14. C2×#91464C2semidirect
15. C2×#91459C2semidirect
16. C2×#91394C2semidirect
20. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
23. C22×#1220C22semidirect
24. C22×#1220C22semidirect
25. C22×D60C22semidirect
27. C22×C5×#67C22semidirect
28. C23×C5×Dic3C22semidirect
30. C22×C3×C22⋊D5C22semidirect
32. C2×D5×#67C22semidirect
33. C22×#1204C22semidirect
34. C22×#1203C22semidirect
37. C22×#1202C22semidirect
39. C22×#1200C22semidirect
41. C2×#6779C22semidirect
43. #91829C22semidirect
44. C2×C4×Dic15C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#939C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C3×#4083C22semidirect
52. C2×C3×#685C22semidirect
53. #91577C22semidirect
54. #91569C22semidirect
55. #91567C22semidirect
56. #91564C22semidirect
57. #91557C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
63. C2×#6665C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91526C22semidirect
66. #91476C22semidirect
67. #91464C22semidirect
68. #91459C22semidirect
69. #91394C22semidirect
78. C2×#4083D3semidirect
103. C2×C3×C5×D4C23semidirect
110. C2×#1220C23semidirect
111. C2×#1220C23semidirect
112. C2×#1220C23semidirect
116. C2×D60C23semidirect
120. C2×C5×#67C23semidirect
125. C22×C5×Dic3C23semidirect
129. C2×C3×C22⋊D5C23semidirect
134. C2×#1204C23semidirect
136. C2×#1203C23semidirect
142. C2×#1202C23semidirect
146. C2×#1200C23semidirect
148. C2×D5×Dic3D4semidirect
150. C4×Dic15C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×Dic3⋊C4C23semidirect
154. C3×C22⋊Dic5C23semidirect
156. C3×#685C23semidirect
157. Dic3⋊Dic5C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
171. C2×#939D5semidirect
184. C22×C5×D4C2×D3semidirect
193. C22×C22⋊D5C2×D3semidirect
210. C2×C22⋊Dic5C2×D3semidirect
215. #4083C2×D3semidirect
222. C2×#685C2×D3semidirect
304. D5×Dic3C2×D4semidirect
309. C22×C3×D4C2×D5semidirect
321. C22×#67C2×D5semidirect
323. C23×Dic3C2×D5semidirect
337. C2×#217C2×D5semidirect
341. #939C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
348. C2×Dic3⋊C4C2×D5semidirect
377. C2×C5×D4C22×D3semidirect
399. C2×C22⋊D5C22×D3semidirect
424. C22⋊Dic5C22×D3semidirect
430. #685C22×D3semidirect
512. C2×C3×D4C22×D5semidirect
536. C2×#67C22×D5semidirect
545. C22×Dic3C22×D5semidirect
560. #217C22×D5semidirect
564. (C2×D3)⋊C4C22×D5semidirect
566. Dic3⋊C4C22×D5semidirect
662. C22×D4D3×D5semidirect
695. C2×C3×C5#535semidirect
866. C2×D4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
941. C2×C5#5592semidirect
1025. C2×C3#65941semidirect
1032. C5C2×#5592semidirect
1075. C3C2×#65941semidirect
1083. C2#11755029direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#672
C22×#67792
C2×#918292
C2×C5×#9392
C2×C3×#40832
C2×#915772
C2×#915692
C2×#915672
C2×#915642
C2×#915572
C2×#915262
#117550292
C2×#914762
C2×#914642
C2×#914592
C2×#913942
C2×#659413
C2×#55925