Finite Group Databasebeta

← C2×#11754818 #14482590

Subgroups — C2×#11754818 #14482590

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic, complemented
2C22×#6779C211yesmaximal, characteristic, complemented
3C2×C5×#935C211yesmaximal, characteristic, complemented
4C2×C3×#4085C211yesmaximal, characteristic, complemented
5C2×#91572C211yesmaximal, characteristic, complemented
6C2×#91572C211yesmaximal, characteristic, complemented
7C2×#91561C211yesmaximal, characteristic, complemented
8C2×#91552C211yesmaximal, characteristic, complemented
9C2×#91550C211yesmaximal, characteristic, complemented
10C22×#6667C211yesmaximal, characteristic, complemented
11C2×#91526C211yesmaximal, characteristic, complemented
12#11754818C2116yesmaximal, direct product factor
13C2×#91459C211yesmaximal, characteristic, complemented
14C2×#91433C211yesmaximal, characteristic, complemented
15C2×#91396C211yesmaximal, characteristic, complemented
16C2×#91377C211yesmaximal, characteristic, complemented
17C2×#65988—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C24×D15C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C2×D4×D15—28no—
24C2×D4×D15C2218yescomplemented
25C22×D60C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic
27C23×C5×Dic3C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×C22⋊D5C2211yescharacteristic, complemented
30C23×C3×Dic5C2211yescharacteristic, complemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic, complemented
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C2×#6779—28no—
38C2×#6779C2218yescomplemented
39C22×D5×Dic3C2211yescharacteristic, complemented
40C2×C5×#217C2211yescharacteristic, complemented
41C2×C5×#217C2211yescharacteristic, complemented
42C2×C5×#217C2211yescharacteristic, complemented
43C5×#935C2218yescomplemented
44C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
47C3×#4085C2218yescomplemented
48C2×C3×#685C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50#91572C2218yescomplemented
51#91572C2218yescomplemented
52#91561C2218yescomplemented
53#91552C2218yescomplemented
54#91550C2218yescomplemented
55C2×#6669C2211yescharacteristic, complemented
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2218yescomplemented
60C2×#6667C2211yescharacteristic, complemented
61C2×#6667C2211yescharacteristic, complemented
62C2×#6667C2211yescharacteristic, complemented
63C2×#6667C2211yescharacteristic, complemented
64C2×Dic3×Dic5C2211yescharacteristic, complemented
65#91526C2218yescomplemented
66#91459C2218yescomplemented
67#91433C2218yescomplemented
68#91396C2218yescomplemented
69#91377C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085D311yescharacteristic, complemented
75C22×#685—31no—
76#65988—316no—
77C2×#4042—31no—
78C2×#4041—31no—
79C2×#4040—31no—
80C2×#4039—31no—
81C2×#4031—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—24no—
91C23×D15—24no—
92C23×D15—24no—
93C23×D15—42no—
94C23×D15—42no—
95C23×D15C2311yescharacteristic
96C23×D15C2314yes—
97C23×D15C2314yes—
98C23×D15C2311yescharacteristic
99C23×D15C2311yescharacteristic
100C23×C3×D5C2311yescharacteristic
101C2×C3×C5×D4—24no—
102C2×C3×C5×D4C2314yes—
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220D418yescomplemented
106C2×#1220C2314yes—
107C2×#1220C2314yes—
108C22×Dic15C2311yescharacteristic
109D4×D15—232no—
110C2×D60—24no—
111C2×D60C2314yes—
112C2×C4×D15—24no—
113C2×C4×D15C2314yes—
114C22×C5×Dic3—24no—
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2314yescomplemented
120C2×C3×C22⋊D5—24no—
121C2×C3×C22⋊D5—42no—
122C2×C3×C22⋊D5C2314yescomplemented
123C2×C3×C22⋊D5C2314yescomplemented
124C22×C3×Dic5—42no—
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2311yescharacteristic
128C22×C3×Dic5C2314yescomplemented
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1202—24no—
132C2×#1202—24no—
133C2×#1202—42no—
134C2×#1202C2314yes—
135C2×#1202C2314yescomplemented
136C2×#1202C2314yescomplemented
137C2×#1200—24no—
138C2×#1200—42no—
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141#6779—232no—
142C2×D5×Dic3—24no—
143C2×D5×Dic3C2314yescomplemented
144C5×#217C2314yescomplemented
145C5×#217C2314yescomplemented
146C5×#217C2314yescomplemented
147C5×Dic3⋊C4C2314yescomplemented
148C5×Dic3⋊C4C2314yescomplemented
149C3×C22⋊Dic5C2314yescomplemented
150C3×#685C2314yescomplemented
151C3×#683C2314yescomplemented
152#6669C2314yescomplemented
153#6667C2314yes—
154#6667C2314yes—
155#6667C2314yes—
156#6667C2314yescomplemented
157#6667C2314yescomplemented
158#6667C2314yescomplemented
159#6667C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4—51no—
163C2×C3×#121—51no—
164C2×#939—51no—
165C2×#937—51no—
166C2×#937—51no—
167C2×#935D511yescharacteristic, complemented
168C2×C4×#67—51no—
169C22×(C2×D3)⋊C4—51no—
170#5610—516no—
171C2×#896—51no—
172C2×#894—51no—
173C2×#885—51no—
174C2×#884—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4C2×D311yescharacteristic
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5C2×D311yescharacteristic, complemented
184C22×C22⋊D5C2×D311yescharacteristic, complemented
185C23×Dic5C2×D311yescharacteristic, complemented
186C2×D4×D5—38no—
187C2×D4×D5—68no—
188C2×#709—38no—
189C2×#709—68no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×D20—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#123—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C4⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4—31no—
204C2×C5×C22⋊C4—31no—
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085C2×D318yescomplemented
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—38no—
215C2×#685C2×D311yescharacteristic, complemented
216C2×#683—31no—
217C2×#683C2×D311yescharacteristic, complemented
218C2×C4×Dic5—31no—
219#4042—38no—
220#4041—38no—
221#4040—38no—
222#4039—38no—
223#4031—38no—
224#4030—38no—
225#4028—38no—
226#4028—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5C2×D414yes—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—28no—
245C22×D15—22no—
246C22×D15—22no—
247C22×D15—28no—
248C22×D15—28no—
249C22×D15—28no—
250C22×D15—44no—
251C22×D15—44no—
252C22×D15—416no—
253C22×D15—416no—
254C22×D15C2×D414yes—
255C22×D15#4114yescomplemented
256C22×D15C2412yes—
257C22×D15C2412yes—
258C22×D15C2412yes—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5C2412yes—
263C3×C5×D4—28no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220C2×D4116yescomplemented
268C2×Dic15C2×D414yes—
269C2×Dic15C2412yes—
270D60—28no—
271C4×D15—28no—
272C2×C5×Dic3—22no—
273C2×C5×Dic3—28no—
274C2×C5×Dic3—22no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C3×C22⋊D5—28no—
282C3×C22⋊D5—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—22no—
286C2×C3×Dic5—44no—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1202—28no—
292#1202—28no—
293#1202—44no—
294#1200—28no—
295#1200—44no—
296D5×Dic3—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4C2×D511yescharacteristic
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67—51no—
308C23×Dic3—51no—
309C23×Dic3C2×D511yescharacteristic, complemented
310C2×#237—58no—
311C2×#237—108no—
312C2×D3×D4—58no—
313C2×D3×D4—108no—
314C22×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6—51no—
319C3×#121—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×#217C2×D511yescharacteristic, complemented
324C2×#217C2×D511yescharacteristic, complemented
325C2×#217C2×D511yescharacteristic, complemented
326#939—58no—
327#937—58no—
328#937—58no—
329#935C2×D518yescomplemented
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—51no—
338C2×(C2×D3)⋊C4—58no—
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4C2×D511yescharacteristic, complemented
341C2×Dic3⋊C4C2×D511yescharacteristic, complemented
342C2×C4×Dic3—51no—
343#896—58no—
344#894—58no—
345#885—58no—
346#884—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5C22×D311yescharacteristic
350C24×C5C22×D311yescharacteristic
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—24no—
364C2×C5×D4C22×D314yes—
365C22×C4×C5—31no—
366C22×C4×C5—31no—
367C22×C4×C5—31no—
368C22×C4×C5—31no—
369C22×C4×C5—34no—
370C22×C4×C5—64no—
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—24no—
373C2×C22⋊D5—38no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—42no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5C22×D314yescomplemented
379C2×C22⋊D5C22×D314yescomplemented
380C22×Dic5—31no—
381C22×Dic5—42no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385C22×Dic5C22×D314yescomplemented
386D4×D5—632no—
387#709—632no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—34no—
392C2×D20—64no—
393C2×D20—64no—
394C2×D20—64no—
395C2×D20—122no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C4⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4—34no—
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685—34no—
419#685C22×D314yescomplemented
420#683—34no—
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—31no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—51no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—28no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5C22×D414yes—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—28no—
452C2×D15—28no—
453C2×D15—22no—
454C2×D15—22no—
455C2×D15—22no—
456C2×D15—22no—
457C2×D15—22no—
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—416no—
461C2×D15—416no—
462C2×D15—44no—
463C2×D15C22×D414yes—
464C2×D15C2×#4114yescomplemented
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—22no—
468C2×C3×D5—44no—
469C3×C4×C5—22no—
470Dic15C22×D414yes—
471C3×Dic5—22no—
472C3×Dic5—22no—
473C3×Dic5—22no—
474C5×Dic3—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C24×C3C22×D511yescharacteristic
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—51no—
484C23×D3—54no—
485C23×D3—54no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3—202no—
492C2×C3×D4—24no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—202no—
497C2×C3×D4C22×D514yes—
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4—51no—
501C22×C3×C4—54no—
502C22×C3×C4—202no—
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—58no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—202no—
514C22×Dic3—24no—
515C22×Dic3—51no—
516C22×Dic3—54no—
517C22×Dic3—104no—
518C22×Dic3C22×D511yescharacteristic
519C22×Dic3C22×D511yescharacteristic
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522C22×Dic3C22×D514yescomplemented
523#237—1032no—
524D3×D4—1032no—
525C2×D12—54no—
526C2×D12—104no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538#217C22×D514yescomplemented
539#217C22×D514yescomplemented
540#217C22×D514yescomplemented
541(C2×D3)⋊C4—54no—
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548Dic3⋊C4—54no—
549Dic3⋊C4C22×D514yescomplemented
550Dic3⋊C4C22×D514yescomplemented
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5D3×D414yes—
558C23×C5C23×D312yes—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—34no—
565C22×D5—34no—
566C22×D5—32no—
567C22×D5—32no—
568C22×D5—32no—
569C22×D5—68no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—62no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—124no—
581C22×D5—124no—
582C22×D5—1216no—
583C22×D5—1216no—
584C22×D5C23×D312yes—
585C5×D4—28no—
586C2×C4×C5—22no—
587C2×C4×C5—32no—
588C2×C4×C5—32no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—62no—
592C2×C4×C5—62no—
593C2×C4×C5—68no—
594C2×C4×C5—62no—
595C2×C4×C5—62no—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—316no—
599C22⋊D5—44no—
600C22⋊D5—68no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—34no—
605C2×Dic5—32no—
606C2×Dic5—44no—
607C2×Dic5C23×D312yes—
608C2×Dic5C23×D312yes—
609C2×Dic5C23×D312yes—
610D20—68no—
611D20—68no—
612D20—68no—
613D20—124no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—51no—
625C22×D4—51no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—158no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4D3×D511yescharacteristic
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—38no—
643#123—158no—
644C22⋊Q8—158no—
645#121—58no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—31no—
654C2×C4⋊C4—51no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—158no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5—24no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—24no—
678D15—24no—
679D15—42no—
680C3×D5—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—52no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3D4×D514yes—
691C23×C3C23×D512yes—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—54no—
695C22×D3—54no—
696C22×D3—52no—
697C22×D3—52no—
698C22×D3—52no—
699C22×D3—108no—
700C22×D3—108no—
701C22×D3—108no—
702C22×D3—102no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—108no—
708C22×D3—102no—
709C22×D3—102no—
710C22×D3—204no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3—2016no—
714C3×D4—28no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—102no—
724C2×C3×C4—204no—
725C2×C3×C4C23×D512yes—
726#67—516no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—28no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—54no—
737C2×Dic3—52no—
738C2×Dic3—108no—
739C2×Dic3C23×D512yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742C2×Dic3C23×D512yes—
743D12—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—28no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—44no—
755C22×C5C2×D3×D414yes—
756C22×C5C2×D3×D412yes—
757C22×C5#100412yes—
758C22×C5D3×#4112yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—34no—
764C2×D5—34no—
765C2×D5—44no—
766C2×D5—62no—
767C2×D5—62no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—68no—
771C2×D5—68no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—62no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5—124no—
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—22no—
786Dic5—34no—
787C24—51no—
788C24—151no—
789C24—151no—
790C24—151no—
791C24—154no—
792C24—154no—
793C24—304no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—602no—
798C24—602no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—24no—
805C2×D4—54no—
806C2×D4—54no—
807C2×D4—104no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—158no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—202no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—3032no—
821C2×D4—602no—
822C2×D4C2×D3×D514yes—
823C22×C4—34no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—31no—
827C22×C4—31no—
828C22×C4—51no—
829C22×C4—51no—
830C22×C4—51no—
831C22×C4—54no—
832C22×C4—64no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—151no—
837C22×C4—154no—
838C22×C4—202no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—34no—
846C4⋊C4—54no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—28no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—204no—
873C22×C3C2×D4×D514yes—
874C22×C3C2×D4×D512yes—
875C22×C3D5×#4112yes—
876C22×C3#414912yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—54no—
879C2×D3—54no—
880C2×D3—108no—
881C2×D3—108no—
882C2×D3—102no—
883C2×D3—102no—
884C2×D3—102no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—102no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—22no—
900Dic3—54no—
901C2×C5—24no—
902C2×C5—42no—
903C2×C5#561014yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×#100411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907D5—42no—
908D5—64no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—52no—
917C23—102no—
918C23—102no—
919C23—102no—
920C23—154no—
921C23—154no—
922C23—152no—
923C23—152no—
924C23—152no—
925C23—308no—
926C23—308no—
927C23—308no—
928C23—302no—
929C23—302no—
930C23—302no—
931C23—302no—
932C23—302no—
933C23—302no—
934C23—308no—
935C23—302no—
936C23—604no—
937C23—604no—
938C23—6016no—
939C23—6016no—
940C23#679014yes—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—28no—
946D4—108no—
947D4—1516no—
948D4—204no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—68no—
967C2×C4—102no—
968C2×C4—102no—
969C2×C4—102no—
970C2×C4—154no—
971C2×C4—152no—
972C2×C4—204no—
973C2×C4—308no—
974C2×C4—308no—
975C2×C4—308no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—24no—
979C2×C3—42no—
980C2×C3—202no—
981C2×C3#6598814yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—104no—
986D3—104no—
987D3—202no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—28no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—44no—
996C22—102no—
997C22—102no—
998C22—102no—
999C22—154no—
1000C22—154no—
1001C22—204no—
1002C22—302no—
1003C22—308no—
1004C22—308no—
1005C22—302no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—6016no—
1012C22—6016no—
1013C22—604no—
1014C22#9202412yes—
1015C22#9202612yes—
1016C22C2×#679014yes—
1017C22C2×#679012yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—62no—
1021C4—62no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—102no—
1027C4—154no—
1028C3C2×#6598811yescharacteristic, complemented, Sylow
1029C2—24no—
1030C2—42no—
1031C2—202no—
1032C2—304no—
1033C2—304no—
1034C2—602no—
1035C2#1175481814yesdirect product factor
1036C2C2×#9202411yescharacteristic
1037C2C2×#9202611yescharacteristic
1038C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
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×D4×D15C2semidirect
2. C22×#6779C2semidirect
3. C2×C5×#935C2semidirect
4. C2×C3×#4085C2semidirect
5. C2×#91572C2semidirect
6. C2×#91572C2semidirect
7. C2×#91561C2semidirect
8. C2×#91552C2semidirect
9. C2×#91550C2semidirect
10. C22×#6667C2semidirect
11. C2×#91526C2semidirect
12. #11754818C2direct (N × H)
13. C2×#91459C2semidirect
14. C2×#91433C2semidirect
15. C2×#91396C2semidirect
16. C2×#91377C2semidirect
24. C2×D4×D15C22semidirect
27. C23×C5×Dic3C22semidirect
28. C22×C3×C22⋊D5C22semidirect
29. C22×C3×C22⋊D5C22semidirect
30. C23×C3×Dic5C22semidirect
31. C22×#1204C22semidirect
33. C22×#1202C22semidirect
34. C22×#1202C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
38. C2×#6779C22semidirect
39. C22×D5×Dic3C22semidirect
40. C2×C5×#217C22semidirect
41. C2×C5×#217C22semidirect
42. C2×C5×#217C22semidirect
43. C5×#935C22semidirect
44. C2×C5×Dic3⋊C4C22semidirect
45. C2×C5×Dic3⋊C4C22semidirect
46. C2×C3×C22⋊Dic5C22semidirect
47. C3×#4085C22semidirect
48. C2×C3×#685C22semidirect
49. C2×C3×#683C22semidirect
50. #91572C22semidirect
51. #91572C22semidirect
52. #91561C22semidirect
53. #91552C22semidirect
54. #91550C22semidirect
55. C2×#6669C22semidirect
59. C2×#6667C22semidirect
60. C2×#6667C22semidirect
61. C2×#6667C22semidirect
62. C2×#6667C22semidirect
63. C2×#6667C22semidirect
64. C2×Dic3×Dic5C22semidirect
65. #91526C22semidirect
66. #91459C22semidirect
67. #91433C22semidirect
68. #91396C22semidirect
69. #91377C22semidirect
74. C2×#4085D3semidirect
105. C2×#1220D4semidirect
119. C22×C5×Dic3C23semidirect
122. C2×C3×C22⋊D5C23semidirect
123. C2×C3×C22⋊D5C23semidirect
128. C22×C3×Dic5C23semidirect
130. C2×#1204C23semidirect
135. C2×#1202C23semidirect
136. C2×#1202C23semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
143. C2×D5×Dic3C23semidirect
144. C5×#217C23semidirect
145. C5×#217C23semidirect
146. C5×#217C23semidirect
147. C5×Dic3⋊C4C23semidirect
148. C5×Dic3⋊C4C23semidirect
149. C3×C22⋊Dic5C23semidirect
150. C3×#685C23semidirect
151. C3×#683C23semidirect
152. #6669C23semidirect
156. #6667C23semidirect
157. #6667C23semidirect
158. #6667C23semidirect
159. #6667C23semidirect
160. Dic3×Dic5C23semidirect
167. C2×#935D5semidirect
183. C22×C22⋊D5C2×D3semidirect
184. C22×C22⋊D5C2×D3semidirect
185. C23×Dic5C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
206. #4085C2×D3semidirect
215. C2×#685C2×D3semidirect
217. C2×#683C2×D3semidirect
255. C22×D15#41semidirect
267. #1220C2×D4semidirect
309. C23×Dic3C2×D5semidirect
323. C2×#217C2×D5semidirect
324. C2×#217C2×D5semidirect
325. C2×#217C2×D5semidirect
329. #935C2×D5semidirect
340. C2×Dic3⋊C4C2×D5semidirect
341. C2×Dic3⋊C4C2×D5semidirect
378. C2×C22⋊D5C22×D3semidirect
379. C2×C22⋊D5C22×D3semidirect
385. C22×Dic5C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
419. #685C22×D3semidirect
421. #683C22×D3semidirect
464. C2×D15C2×#41semidirect
522. C22×Dic3C22×D5semidirect
538. #217C22×D5semidirect
539. #217C22×D5semidirect
540. #217C22×D5semidirect
549. Dic3⋊C4C22×D5semidirect
550. Dic3⋊C4C22×D5semidirect
673. C2×C3×C5#546semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5610semidirect
981. C2×C3#65988semidirect
988. C5C2×#5610semidirect
1028. C3C2×#65988semidirect
1035. C2#11754818direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×#67792
C2×C5×#9352
C2×C3×#40852
C2×#915722
C2×#915612
C2×#915522
C2×#915502
C22×#66672
C2×#915262
#117548182
C2×#914592
C2×#914332
C2×#913962
C2×#913772
C2×#659883
C2×#56105