Finite Group Databasebeta

← C2×#11753243 #14482618

Subgroups — C2×#11753243 #14482618

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×#6790C211yesmaximal, characteristic, complemented
2C22×#6766C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91572C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91548C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#91461C211yesmaximal, characteristic, complemented
12C2×C4×#1202C211yesmaximal, characteristic, complemented
13C2×#91424C211yesmaximal, characteristic, complemented
14C2×#91395C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16#11753243C2116yesmaximal, direct product factor
17C2×#66010—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic, complemented
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×#6790—28no—
29C2×#6790C2218yescomplemented
30C22×#1203C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic, complemented
35C22×#1200C2211yescharacteristic
36C22×D5×Dic3C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6766—28no—
39C2×#6766C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic
44C22⋊C4×D15C2218yescomplemented
45C2×C5×#217C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C4×C5×Dic3C2211yescharacteristic, complemented
49C5×#885C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52C3×#4030C2218yescomplemented
53#91572C2218yescomplemented
54#91549C2218yescomplemented
55#91548C2218yescomplemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91474C2218yescomplemented
64D5×(C2×D3)⋊C4C2218yescomplemented
65#91461C2218yescomplemented
66C4×#1202C2218yescomplemented
67#91424C2218yescomplemented
68#91395C2218yescomplemented
69#91355C2218yescomplemented
70C2×#5610—51nomaximal, Hall
71C22×#713—31no—
72C22×D4×D5—31no—
73C2×C5×#124—31no—
74C2×#4092—31no—
75C2×#4084—31no—
76#66010—316no—
77C2×#4030—31no—
78C2×#4030D311yescharacteristic, complemented
79C2×#4029—31no—
80C2×#4029—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4—31no—
85C2×C4×D20—31no—
86C2×C4×D20—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15—24no—
89C23×D15—24no—
90C23×D15—42no—
91C23×D15C2314yes—
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×C4×D15—24no—
106C2×C4×D15—42no—
107C2×C4×D15C2314yescomplemented
108C2×C4×D15C2314yescomplemented
109C2×C5×#67—24no—
110C2×C5×#67C2314yes—
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C2×C5×Dic6—24no—
115C2×C5×Dic6C2314yescomplemented
116C2×C3×C22⋊D5—24no—
117C2×C3×C22⋊D5—42no—
118C2×C3×C22⋊D5C2314yes—
119C2×C3×C22⋊D5C2314yescomplemented
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×D20—24no—
123C2×C3×D20C2314yescomplemented
124C2×C3×C4×D5—42no—
125C2×C3×C4×D5C2314yescomplemented
126#6790—232no—
127C2×#1203—24no—
128C2×#1203C2314yes—
129C2×#1202—24no—
130C2×#1202—24no—
131C2×#1202D418yescomplemented
132C2×#1202C2314yes—
133C2×#1202C2314yes—
134C2×#1202C2314yescomplemented
135C2×#1201—42no—
136C2×#1201C2314yescomplemented
137C2×#1200—24no—
138C2×#1200C2314yes—
139C2×D5×Dic3—24no—
140C2×D5×Dic3—24no—
141C2×D5×Dic3C2314yescomplemented
142C2×D5×Dic3C2314yescomplemented
143#6766—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yes—
147#6714C2314yes—
148C5×#217C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C4×C5×Dic3C2314yescomplemented
152C3×#685C2314yescomplemented
153C3×#683C2314yescomplemented
154Dic3⋊Dic5C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6669C2314yescomplemented
157#6667C2314yes—
158#6667C2314yescomplemented
159(C2×D3)⋊Dic5C2314yescomplemented
160#6665C2314yescomplemented
161C22×#237—51no—
162C22×D3×D4—51no—
163C2×C3×#121—51no—
164C2×#939—51no—
165C2×#937—51no—
166C2×#937—51no—
167C2×#935—51no—
168C2×C4×#67—51no—
169C22×(C2×D3)⋊C4—51no—
170#5610—516no—
171C2×#896—51no—
172C2×#894—51no—
173C2×#885D511yescharacteristic, complemented
174C2×#884—51no—
175C2×#67⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×Q8—31no—
180C22×C5×D4—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5C2×D311yescharacteristic
184C22×C22⋊D5C2×D311yescharacteristic, complemented
185C2×#713—38no—
186C2×#713—68no—
187C2×D4×D5—38no—
188C2×D4×D5—68no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20C2×D311yescharacteristic, complemented
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×C4×D5C2×D311yescharacteristic, complemented
199C5×#124—38no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
204C2×C42×C5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5—31no—
207#4092—38no—
208#4084—38no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685C2×D311yescharacteristic, complemented
215C2×C4⋊Dic5—31no—
216C2×C4⋊Dic5—31no—
217C2×#683—31no—
218C2×#683C2×D311yescharacteristic, complemented
219#4030—38no—
220#4030C2×D318yescomplemented
221#4029—38no—
222#4029—38no—
223#4028—38no—
224#4028—38no—
225D5×C22⋊C4—38no—
226D5×C22⋊C4—38no—
227C4×D20—38no—
228C4×D20—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—28no—
240C22×D15—28no—
241C22×D15—44no—
242C22×D15—416no—
243C22×D15C2×D414yes—
244C22×D15#4114yescomplemented
245C22×D15C2412yes—
246C22×D15C2412yes—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3C2412yes—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5—22no—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5C2×D414yes—
257C22×C3×D5C2412yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267C2×Dic15—22no—
268C2×Dic15—22no—
269C2×Dic15C2412yes—
270C2×Dic15C2412yes—
271C4×D15—28no—
272C4×D15—44no—
273C5×#67—28no—
274C2×C5×Dic3—22no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3C2×D414yes—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C5×Dic6—28no—
281C3×C22⋊D5—28no—
282C3×C22⋊D5—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×D20—28no—
288C3×C4×D5—44no—
289#1203—28no—
290#1202—28no—
291#1202—28no—
292#1202C2×D4116yescomplemented
293#1201—44no—
294#1200—28no—
295D5×Dic3—28no—
296D5×Dic3—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4—51no—
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67C2×D511yescharacteristic
308C23×Dic3—51no—
309C23×Dic3—51no—
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×Dic6C2×D511yescharacteristic, complemented
319C3×#121—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
323C2×#217—51no—
324C2×#217—51no—
325C2×#217C2×D511yescharacteristic, complemented
326#939—58no—
327#937—58no—
328#937—58no—
329#935—58no—
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—58no—
337C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
338C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
339C2×Dic3⋊C4—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3C2×D511yescharacteristic, complemented
343#896—58no—
344#894—58no—
345#885C2×D518yescomplemented
346#884—58no—
347#67⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C23×D5—31no—
352C23×D5—31no—
353C23×D5—34no—
354C23×D5—34no—
355C23×D5—64no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5—122no—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×Q8—34no—
364C2×C5×Q8—64no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C22×C4×C5—31no—
368C22×C4×C5—31no—
369C22×C4×C5—31no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—24no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—42no—
376C2×C22⋊D5—64no—
377C2×C22⋊D5—122no—
378C2×C22⋊D5C22×D314yes—
379C2×C22⋊D5C22×D314yescomplemented
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384#713—632no—
385D4×D5—632no—
386C2×D20—24no—
387C2×D20—38no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—64no—
392C2×D20—64no—
393C2×D20C22×D314yescomplemented
394C2×C4×D5—34no—
395C2×C4×D5—34no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—42no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—64no—
404C2×C4×D5—122no—
405C2×C4×D5C22×D314yescomplemented
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4C22×D314yescomplemented
410C42×C5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yescomplemented
419C4⋊Dic5—34no—
420C4⋊Dic5—34no—
421#683—34no—
422#683C22×D314yescomplemented
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—31no—
427C2×#123—151no—
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—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—28no—
448C2×D15—28no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—416no—
454C2×D15C22×D414yes—
455C2×D15C2×#4114yescomplemented
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—22no—
459C2×C5×D3—44no—
460C2×C3×D5—28no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—44no—
467C2×C3×D5C22×D414yes—
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3C22×D511yescharacteristic
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4—202no—
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4—54no—
501C22×C3×C4—202no—
502C22×C3×C4C22×D511yescharacteristic
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—24no—
505C2×#67—54no—
506C2×#67—58no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—54no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—202no—
513C2×#67C22×D514yes—
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—54no—
517C22×Dic3—54no—
518C22×Dic3—104no—
519C22×Dic3—104no—
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522C22×Dic3C22×D511yescharacteristic
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—24no—
534C2×Dic6C22×D514yescomplemented
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4C22×D514yescomplemented
538#217—54no—
539#217—54no—
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)⋊C4C22×D514yescomplemented
547(C2×D3)⋊C4C22×D514yescomplemented
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3C22×D514yescomplemented
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—32no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—34no—
567C22×D5—34no—
568C22×D5—32no—
569C22×D5—32no—
570C22×D5—68no—
571C22×D5—68no—
572C22×D5—68no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—124no—
579C22×D5—1216no—
580C22×D5—124no—
581C22×D5—1216no—
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×Q8—68no—
586C5×D4—68no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—44no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—62no—
606C2×Dic5—62no—
607C2×Dic5C23×D312yes—
608C2×Dic5C23×D312yes—
609D20—28no—
610D20—316no—
611D20—68no—
612D20—68no—
613C4×D5—44no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—68no—
618C4×D5—124no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—31no—
625C22×D4—51no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—158no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—51no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—38no—
642#123—158no—
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—51no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—158no—
661C2×C22⋊C4—151no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—158no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—31no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677D15—24no—
678C3×D5—24no—
679C3×D5—42no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—52no—
686C23×C3—52no—
687C23×C3—102no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—54no—
698C22×D3—54no—
699C22×D3—52no—
700C22×D3—52no—
701C22×D3—108no—
702C22×D3—108no—
703C22×D3—108no—
704C22×D3—108no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—204no—
710C22×D3—2016no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—102no—
722C2×C3×C4—102no—
723C2×C3×C4—204no—
724C2×C3×C4C23×D512yes—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—516no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—108no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3—108no—
739C2×Dic3D4×D514yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742C2×Dic3C23×D512yes—
743D12—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—28no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—44no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×D3×D412yes—
757C22×C5#100412yes—
758C22×C5D3×#4112yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—28no—
763C2×D5—22no—
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—34no—
767C2×D5—34no—
768C2×D5—44no—
769C2×D5—62no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—68no—
774C2×D5—68no—
775C2×D5—1216no—
776C2×D5—1216no—
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—34no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—154no—
791C24—151no—
792C24—151no—
793C24—154no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—304no—
798C24—602no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—34no—
803C2×Q8—64no—
804C2×D4—34no—
805C2×D4—54no—
806C2×D4—54no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—104no—
810C2×D4—104no—
811C2×D4—154no—
812C2×D4—158no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—202no—
818C2×D4—304no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—3032no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—151no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—202no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—54no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—34no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—108no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—204no—
874C22×C3C2×D4×D512yes—
875C22×C3D5×#4112yes—
876C22×C3#414912yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—44no—
882C2×D3—54no—
883C2×D3—54no—
884C2×D3—108no—
885C2×D3—108no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—2016no—
891C2×D3—2016no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—122no—
903C2×C5#561014yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C2×#100411yescharacteristic
906C2×C5C2×D3×#4111yescharacteristic
907D5—24no—
908D5—42no—
909D5—64no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—32no—
915C23—54no—
916C23—52no—
917C23—52no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—102no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—102no—
926C23—154no—
927C23—154no—
928C23—152no—
929C23—152no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—308no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—604no—
939C23—6016no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—68no—
945D4—68no—
946D4—108no—
947D4—108no—
948D4—1516no—
949D4—204no—
950D4—308no—
951D4—308no—
952D4—308no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—102no—
965C2×C4—102no—
966C2×C4—152no—
967C2×C4—152no—
968C2×C4—204no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—202no—
981C2×C3#6601014yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—42no—
986D3—104no—
987D3—104no—
988C5C2×#561011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—54no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—108no—
998C22—102no—
999C22—102no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—124no—
1004C22—154no—
1005C22—154no—
1006C22—204no—
1007C22—308no—
1008C22—308no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22#9201612yes—
1016C22D3×D4×D512yes—
1017C22#9202612yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6601011yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—104no—
1031C2—122no—
1032C2—202no—
1033C2—304no—
1034C2—304no—
1035C2#1175324314yesdirect product factor
1036C2C2×#9201611yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#9202611yescharacteristic
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×#546
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×#6766C2semidirect
3. C2×C22⋊C4×D15C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91572C2semidirect
7. C2×#91549C2semidirect
8. C2×#91548C2semidirect
9. C2×#91474C2semidirect
10. C2×D5×(C2×D3)⋊C4C2semidirect
11. C2×#91461C2semidirect
12. C2×C4×#1202C2semidirect
13. C2×#91424C2semidirect
14. C2×#91395C2semidirect
15. C2×#91355C2semidirect
16. #11753243C2direct (N × H)
20. C22×C4×D15C22semidirect
21. C22×C4×D15C22semidirect
23. C22×C5×Dic6C22semidirect
25. C22×C3×C22⋊D5C22semidirect
26. C22×C3×D20C22semidirect
27. C22×C3×C4×D5C22semidirect
29. C2×#6790C22semidirect
33. C22×#1202C22semidirect
34. C22×#1201C22semidirect
36. C22×D5×Dic3C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6766C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
44. C22⋊C4×D15C22semidirect
45. C2×C5×#217C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C4×C5×Dic3C22semidirect
49. C5×#885C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#683C22semidirect
52. C3×#4030C22semidirect
53. #91572C22semidirect
54. #91549C22semidirect
55. #91548C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6669C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91474C22semidirect
64. D5×(C2×D3)⋊C4C22semidirect
65. #91461C22semidirect
66. C4×#1202C22semidirect
67. #91424C22semidirect
68. #91395C22semidirect
69. #91355C22semidirect
78. C2×#4030D3semidirect
107. C2×C4×D15C23semidirect
108. C2×C4×D15C23semidirect
115. C2×C5×Dic6C23semidirect
119. C2×C3×C22⋊D5C23semidirect
123. C2×C3×D20C23semidirect
125. C2×C3×C4×D5C23semidirect
131. C2×#1202D4semidirect
134. C2×#1202C23semidirect
136. C2×#1201C23semidirect
141. C2×D5×Dic3C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
148. C5×#217C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C4×C5×Dic3C23semidirect
152. C3×#685C23semidirect
153. C3×#683C23semidirect
154. Dic3⋊Dic5C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6669C23semidirect
158. #6667C23semidirect
159. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
173. C2×#885D5semidirect
184. C22×C22⋊D5C2×D3semidirect
192. C22×D20C2×D3semidirect
198. C22×C4×D5C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
214. C2×#685C2×D3semidirect
218. C2×#683C2×D3semidirect
220. #4030C2×D3semidirect
244. C22×D15#41semidirect
292. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
325. C2×#217C2×D5semidirect
337. C2×(C2×D3)⋊C4C2×D5semidirect
338. C2×(C2×D3)⋊C4C2×D5semidirect
342. C2×C4×Dic3C2×D5semidirect
345. #885C2×D5semidirect
379. C2×C22⋊D5C22×D3semidirect
393. C2×D20C22×D3semidirect
405. C2×C4×D5C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
418. #685C22×D3semidirect
422. #683C22×D3semidirect
455. C2×D15C2×#41semidirect
534. C2×Dic6C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
540. #217C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
547. (C2×D3)⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5610semidirect
981. C2×C3#66010semidirect
988. C5C2×#5610semidirect
1028. C3C2×#66010semidirect
1035. C2#11753243direct (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×#67662
C2×C22⋊C4×D152
C2×C5×#8852
C2×C3×#40302
C2×#915722
C2×#915492
C2×#915482
C2×#914742
C2×D5×(C2×D3)⋊C42
C2×#914612
C2×C4×#12022
C2×#914242
C2×#913952
C2×#913552
#117532432
C2×#660103
C2×#56105