Finite Group Databasebeta

← C2×D5×#878 #14479433

Subgroups — C2×D5×#878 #14479433

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D5×Dic3C211yesmaximal, characteristic
2C22×D5×Dic6C211yesmaximal, characteristic, complemented
3C2×#91767C211yesmaximal, characteristic, complemented
4C2×C5×#878C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
6C2×#91576C211yesmaximal, characteristic, complemented
7C2×#91575C211yesmaximal, characteristic, complemented
8C2×D5×#217C211yesmaximal, characteristic
9C2×#91431C211yesmaximal, characteristic, complemented
10C2×#91430C211yesmaximal, characteristic, complemented
11C2×#91422C211yesmaximal, characteristic, complemented
12C2×#91421C211yesmaximal, characteristic, complemented
13C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
14C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16D5×#878C2116yesmaximal, direct product factor
17C2×D5×C22⋊Q8—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C23×C5×Dic3C2211yescharacteristic
22C22×C5×Dic6C2211yescharacteristic, complemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204C2211yescharacteristic, complemented
26C22×#1204C2211yescharacteristic, complemented
27C22×D5×Dic3—28no—
28C22×D5×Dic3C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C22×D5×Dic3C2218yes—
31C22×D5×Dic3C2211yescharacteristic
32C22×D5×Dic3C2211yescharacteristic
33C22×D5×Dic3C2211yescharacteristic
34C22×D5×Dic3C2211yescharacteristic
35C2×D5×Dic6—28no—
36C2×D5×Dic6C2218yescomplemented
37C2×C3×C5×C22⋊C4C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×C4⋊Dic15C2211yescharacteristic, complemented
40C2×#6712C2211yescharacteristic, complemented
41C2×#6712C2211yescharacteristic, complemented
42#91767C2218yescomplemented
43C2×C5×#217C2211yescharacteristic
44C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
47C5×#878C2218yescomplemented
48C2×C3×C22⋊Dic5C2211yescharacteristic
49C2×C3×#685C2211yescharacteristic
50C2×C3×#685C2211yescharacteristic
51C3×D5×C22⋊C4C2218yes—
52#91576C2218yescomplemented
53#91575C2218yescomplemented
54D5×#217C2218yes—
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×#6669C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6668C2211yescharacteristic, complemented
60C2×#6668C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic
62C2×#6665C2211yescharacteristic
63#91431C2218yescomplemented
64#91430C2218yescomplemented
65#91422C2218yescomplemented
66#91421C2218yescomplemented
67D5×C4⋊Dic3C2218yescomplemented
68D5×Dic3⋊C4C2218yescomplemented
69D5×Dic3⋊C4C2218yescomplemented
70C22×#878—51nomaximal, Hall
71C22×Q8×D5—31no—
72C23×C4×D5—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4092—31no—
75C2×#4070—31no—
76D5×C22⋊Q8—316no—
77C2×#4043—31no—
78C2×#4042—31no—
79C2×#4042—31no—
80C2×D5×C4⋊C4—31no—
81C2×D5×C4⋊C4—31no—
82C2×D5×C4⋊C4—31no—
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4D311yescharacteristic
85C2×#4024—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C23×C3×D5—24no—
89C23×C3×D5—24no—
90C23×C3×D5Q818yescomplemented
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2314yes—
93C23×C3×D5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×Dic15—24no—
97C22×Dic15C2314yes—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×Dic30—24no—
103C2×Dic30C2314yescomplemented
104C22×C5×Dic3—24no—
105C22×C5×Dic3C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C5×Dic6—24no—
111C2×C5×Dic6C2314yescomplemented
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×C4×D5—24no—
115C2×C3×C4×D5—24no—
116C2×C3×C4×D5C2314yes—
117C2×C3×C4×D5C2314yes—
118C2×#1204—24no—
119C2×#1204—24no—
120C2×#1204C2314yescomplemented
121C2×#1204C2314yescomplemented
122C2×D5×Dic3—24no—
123C2×D5×Dic3—24no—
124C2×D5×Dic3—24no—
125C2×D5×Dic3—24no—
126C2×D5×Dic3—24no—
127C2×D5×Dic3—232no—
128C2×D5×Dic3D418yes—
129C2×D5×Dic3C2314yes—
130C2×D5×Dic3C2314yes—
131C2×D5×Dic3C2314yes—
132C2×D5×Dic3C2314yes—
133C2×D5×Dic3C2314yes—
134C2×D5×Dic3C2314yes—
135D5×Dic6—232no—
136C3×C5×C22⋊C4C2314yes—
137#6719C2314yes—
138C4⋊Dic15C2314yescomplemented
139#6712C2314yescomplemented
140#6712C2314yescomplemented
141C5×#217C2314yes—
142C5×C4⋊Dic3C2314yescomplemented
143C5×Dic3⋊C4C2314yescomplemented
144C5×Dic3⋊C4C2314yescomplemented
145C3×C22⋊Dic5C2314yes—
146C3×#685C2314yes—
147C3×#685C2314yes—
148Dic3⋊Dic5C2314yescomplemented
149Dic3⋊Dic5C2314yescomplemented
150#6669C2314yescomplemented
151#6669C2314yescomplemented
152#6668C2314yescomplemented
153#6668C2314yescomplemented
154#6665C2314yes—
155#6665C2314yes—
156C24×Dic3—51no—
157C23×Dic6—51no—
158C22×C3×C22⋊C4—51no—
159C22×#217—51no—
160C22×C4⋊Dic3—51no—
161C22×Dic3⋊C4—51no—
162C22×Dic3⋊C4—51no—
163C2×#878—51no—
164C2×#878—51no—
165C2×#878—51no—
166C2×#878—51no—
167C2×#878—51no—
168C2×#878—51no—
169C2×#878—51no—
170C2×#878—516no—
171C2×#878D511yescharacteristic, direct product factor
172C24×D5C2×D311yescharacteristic
173C22×C5×Q8—31no—
174C23×C4×C5—31no—
175C23×Dic5—31no—
176C2×Q8×D5—38no—
177C2×Q8×D5—68no—
178C22×C4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C22×C4×D5—31no—
182C22×C4×D5—31no—
183C22×C4×D5—31no—
184C22×C4×D5—38no—
185C22×C4×D5—68no—
186C22×C4×D5C2×D311yescharacteristic
187C22×C4×D5C2×D311yescharacteristic
188C22×Dic10—31no—
189C22×Dic10—31no—
190C22×Dic10—31no—
191C5×C22⋊Q8—38no—
192C2×C5×C4⋊C4—31no—
193C2×C5×C4⋊C4—31no—
194C2×C5×C4⋊C4—31no—
195C2×C5×C22⋊C4—31no—
196C2×C5×C22⋊C4C2×D311yescharacteristic
197C2×C22⋊Dic5—31no—
198C2×C22⋊Dic5C2×D311yescharacteristic
199#4092—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685C2×D311yescharacteristic
203C2×#685C2×D311yescharacteristic
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5—31no—
206C2×C4⋊Dic5—31no—
207#4070—38no—
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×#683—31no—
213C2×#683—31no—
214#4043—38no—
215#4042—38no—
216#4042—38no—
217D5×C4⋊C4—38no—
218D5×C4⋊C4—38no—
219D5×C4⋊C4—38no—
220D5×C22⋊C4—38no—
221D5×C22⋊C4C2×D318yes—
222#4024—38no—
223#4024—38no—
224C22×C22⋊Q8—151noSylow
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5C2×Q814yescomplemented
228C23×C3×C5C2412yes—
229C23×C3×C5C2411yescharacteristic
230C22×C3×D5—22no—
231C22×C3×D5—22no—
232C22×C3×D5—232no—
233C22×C3×D5—28no—
234C22×C3×D5—28no—
235C22×C3×D5C2×D414yes—
236C22×C3×D5C2×Q814yes—
237C22×C3×D5C2×Q8116yescomplemented
238C22×C3×D5C2×Q814yescomplemented
239C22×C3×D5#4114yes—
240C22×C3×D5C2412yes—
241C22×C3×D5C2412yes—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—22no—
249C2×Dic15—28no—
250C2×Dic15C2×D414yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C2×Dic15C2412yes—
255Dic30—28no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3—28no—
260C2×C5×Dic3C2×D414yes—
261C2×C5×Dic3C2412yes—
262C2×C5×Dic3C2412yes—
263C2×C5×Dic3C2412yes—
264C2×C5×Dic3C2412yes—
265C5×Dic6—28no—
266C2×C3×Dic5—22no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C3×C4×D5—28no—
271C3×C4×D5—28no—
272#1204—28no—
273#1204—28no—
274D5×Dic3—28no—
275D5×Dic3—28no—
276D5×Dic3—28no—
277D5×Dic3—28no—
278D5×Dic3—28no—
279D5×Dic3C2×D4116yes—
280C25×C3—51no—
281C23×C3×C4—51no—
282C23×C3×C4—51no—
283C23×Dic3—51no—
284C23×Dic3—51no—
285C23×Dic3—51no—
286C23×Dic3—51no—
287C23×Dic3—58no—
288C23×Dic3—51no—
289C23×Dic3—51no—
290C23×Dic3—51no—
291C23×Dic3—108no—
292C23×Dic3C2×D511yescharacteristic
293C22×Dic6—51no—
294C22×Dic6—51no—
295C22×Dic6—51no—
296C22×Dic6—58no—
297C22×Dic6—108no—
298C22×Dic6C2×D511yescharacteristic, complemented
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—58no—
303C2×C3×C22⋊C4C2×D511yescharacteristic
304C2×#217—51no—
305C2×#217—51no—
306C2×#217—51no—
307C2×#217—58no—
308C2×#217C2×D511yescharacteristic
309C2×C4⋊Dic3—51no—
310C2×C4⋊Dic3—51no—
311C2×C4⋊Dic3—51no—
312C2×C4⋊Dic3—58no—
313C2×C4⋊Dic3C2×D511yescharacteristic, complemented
314C2×Dic3⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—58no—
321C2×Dic3⋊C4—58no—
322C2×Dic3⋊C4C2×D511yescharacteristic, complemented
323C2×Dic3⋊C4C2×D511yescharacteristic, complemented
324#878—58no—
325#878—58no—
326#878—58no—
327#878—58no—
328#878—58no—
329#878—58no—
330#878—58no—
331#878C2×D518yesdirect product factor
332C24×C5C22×D311yescharacteristic
333C23×D5—24no—
334C23×D5—24no—
335C23×D5Dic618yescomplemented
336C23×D5C22×D314yes—
337C23×D5C22×D311yescharacteristic
338C23×D5C22×D311yescharacteristic
339C2×C5×Q8—34no—
340C2×C5×Q8—64no—
341C22×C4×C5—31no—
342C22×C4×C5—31no—
343C22×C4×C5—31no—
344C22×C4×C5—31no—
345C22×C4×C5—34no—
346C22×C4×C5—64no—
347C22×C4×C5C22×D311yescharacteristic
348C22×C4×C5C22×D311yescharacteristic
349C22×Dic5—31no—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—34no—
353C22×Dic5—31no—
354C22×Dic5—64no—
355C22×Dic5C22×D311yescharacteristic
356C22×Dic5C22×D311yescharacteristic
357Q8×D5—632no—
358C2×C4×D5—24no—
359C2×C4×D5—24no—
360C2×C4×D5—38no—
361C2×C4×D5—34no—
362C2×C4×D5—34no—
363C2×C4×D5—34no—
364C2×C4×D5—34no—
365C2×C4×D5—34no—
366C2×C4×D5—34no—
367C2×C4×D5—632no—
368C2×C4×D5—64no—
369C2×C4×D5—64no—
370C2×C4×D5—64no—
371C2×C4×D5—64no—
372C2×C4×D5—64no—
373C2×C4×D5C22×D314yes—
374C2×C4×D5C22×D314yes—
375C2×Dic10—34no—
376C2×Dic10—34no—
377C2×Dic10—34no—
378C2×Dic10—64no—
379C2×Dic10—64no—
380C2×Dic10—64no—
381C5×C4⋊C4—34no—
382C5×C4⋊C4—34no—
383C5×C4⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4C22×D314yes—
386C22⋊Dic5—34no—
387C22⋊Dic5C22×D314yes—
388#685—34no—
389#685—34no—
390#685C22×D314yes—
391#685C22×D314yes—
392C4⋊Dic5—34no—
393C4⋊Dic5—34no—
394C4⋊Dic5—34no—
395#683—34no—
396#683—34no—
397#683—34no—
398#683—34no—
399#683—34no—
400#683—34no—
401C23×Q8—151no—
402C24×C4—151no—
403C2×C22⋊Q8—31no—
404C2×C22⋊Q8—151no—
405C2×C22⋊Q8—151no—
406C2×C22⋊Q8—151no—
407C2×C22⋊Q8—151no—
408C2×C22⋊Q8—1516no—
409C2×C22⋊Q8—151no—
410C2×C22⋊Q8—151no—
411C2×C22⋊Q8—151no—
412C22×C4⋊C4—151no—
413C22×C4⋊C4—151no—
414C22×C4⋊C4—151no—
415C22×C22⋊C4—51no—
416C22×C22⋊C4—151no—
417C22×C3×C5—28no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5C22×D412yes—
421C22×C3×C5C22×Q812yes—
422C22×C3×C5C22×Q814yescomplemented
423C22×C3×C5C2×#4112yes—
424C22×C3×C5C2511yescharacteristic
425C2×C3×D5—28no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—232no—
429C2×C3×D5C22⋊Q8116yescomplemented
430C2×C3×D5C22×D414yes—
431C2×C3×D5C22×Q814yes—
432C2×C3×D5C22×Q814yescomplemented
433C2×C3×D5C2×#4114yes—
434C3×C4×C5—22no—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
439Dic15C22×D414yes—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C5×Dic3—22no—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3C22×D414yes—
446C24×C3—51no—
447C24×C3—58no—
448C24×C3—54no—
449C24×C3—51no—
450C24×C3—104no—
451C24×C3—104no—
452C24×C3C22×D511yescharacteristic
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—54no—
456C22×C3×C4—54no—
457C22×C3×C4—104no—
458C22×C3×C4—104no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×Dic3—24no—
462C22×Dic3—51no—
463C22×Dic3—58no—
464C22×Dic3—54no—
465C22×Dic3—54no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—51no—
469C22×Dic3—54no—
470C22×Dic3—54no—
471C22×Dic3—54no—
472C22×Dic3—54no—
473C22×Dic3—54no—
474C22×Dic3—104no—
475C22×Dic3—1032no—
476C22×Dic3—104no—
477C22×Dic3—104no—
478C22×Dic3—104no—
479C22×Dic3—104no—
480C22×Dic3—104no—
481C22×Dic3C22×D514yes—
482C22×Dic3C22×D511yescharacteristic
483C22×Dic3C22×D511yescharacteristic
484C22×Dic3C22×D511yescharacteristic
485C22×Dic3C22×D511yescharacteristic
486C2×Dic6—24no—
487C2×Dic6—54no—
488C2×Dic6—54no—
489C2×Dic6—54no—
490C2×Dic6—1032no—
491C2×Dic6—104no—
492C2×Dic6—104no—
493C2×Dic6—104no—
494C2×Dic6C22×D514yescomplemented
495C3×C22⋊C4—54no—
496C3×C22⋊C4—54no—
497C3×C22⋊C4—54no—
498C3×C22⋊C4C22×D514yes—
499#217—54no—
500#217—54no—
501#217—54no—
502#217C22×D514yes—
503C4⋊Dic3—54no—
504C4⋊Dic3—54no—
505C4⋊Dic3—54no—
506C4⋊Dic3C22×D514yescomplemented
507Dic3⋊C4—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4—54no—
513Dic3⋊C4C22×D514yescomplemented
514Dic3⋊C4C22×D514yescomplemented
515C23×C5—22no—
516C23×C5—22no—
517C23×C5C2×Dic614yescomplemented
518C23×C5C23×D312yes—
519C23×C5C23×D311yescharacteristic
520C22×D5—22no—
521C22×D5—22no—
522C22×D5—232no—
523C22×D5—28no—
524C22×D5—28no—
525C22×D5C2×Dic614yes—
526C22×D5C2×Dic6116yescomplemented
527C22×D5C2×Dic614yescomplemented
528C22×D5D3×D414yes—
529C22×D5#23714yes—
530C22×D5C23×D312yes—
531C22×D5C23×D312yes—
532C5×Q8—68no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—34no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—32no—
539C2×C4×C5—32no—
540C2×C4×C5—68no—
541C2×C4×C5—62no—
542C2×C4×C5—62no—
543C2×C4×C5—62no—
544C2×C4×C5C23×D312yes—
545C2×C4×C5C23×D312yes—
546C2×Dic5—22no—
547C2×Dic5—22no—
548C2×Dic5—34no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—32no—
553C2×Dic5—68no—
554C2×Dic5—62no—
555C2×Dic5—62no—
556C2×Dic5—62no—
557C2×Dic5C23×D312yes—
558C2×Dic5C23×D312yes—
559C4×D5—28no—
560C4×D5—28no—
561C4×D5—316no—
562C4×D5—68no—
563C4×D5—68no—
564C4×D5—68no—
565C4×D5—68no—
566C4×D5—68no—
567Dic10—68no—
568Dic10—68no—
569Dic10—68no—
570C25—51no—
571C22×Q8—31no—
572C22×Q8—151no—
573C22×Q8—151no—
574C22×Q8—158no—
575C22×Q8—151no—
576C22×Q8—308no—
577C23×C4—31no—
578C23×C4—51no—
579C23×C4—51no—
580C23×C4—151no—
581C23×C4—151no—
582C23×C4—151no—
583C23×C4—151no—
584C23×C4—151no—
585C23×C4—158no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—308no—
589C22⋊Q8—38no—
590C22⋊Q8—158no—
591C22⋊Q8—158no—
592C22⋊Q8—158no—
593C22⋊Q8—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596C22⋊Q8—158no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—31no—
599C2×C4⋊C4—31no—
600C2×C4⋊C4—158no—
601C2×C4⋊C4—158no—
602C2×C4⋊C4—158no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—51no—
614C2×C22⋊C4—51no—
615C2×C22⋊C4—51no—
616C2×C22⋊C4—58no—
617C2×C22⋊C4—158no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C22⋊C4—151no—
621C2×C22⋊C4D3×D511yescharacteristic
622C2×C3×C5—24no—
623C2×C3×C5C2×C22⋊Q814yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C23×Q811yescharacteristic
626C2×C3×C5C22×#4111yescharacteristic
627C3×D5—24no—
628C3×D5C2×C22⋊Q818yescomplemented
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—54no—
632C23×C3—54no—
633C23×C3—54no—
634C23×C3—52no—
635C23×C3—54no—
636C23×C3—516no—
637C23×C3—52no—
638C23×C3—108no—
639C23×C3—1032no—
640C23×C3—108no—
641C23×C3—102no—
642C23×C3—102no—
643C23×C3Q8×D514yescomplemented
644C23×C3C23×D512yes—
645C23×C3C23×D511yescharacteristic
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—52no—
649C2×C3×C4—52no—
650C2×C3×C4—108no—
651C2×C3×C4—108no—
652C2×C3×C4—102no—
653C2×C3×C4—102no—
654C2×C3×C4C23×D512yes—
655C2×C3×C4C23×D512yes—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—28no—
660C2×Dic3—54no—
661C2×Dic3—52no—
662C2×Dic3—516no—
663C2×Dic3—52no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—108no—
667C2×Dic3—108no—
668C2×Dic3—108no—
669C2×Dic3—108no—
670C2×Dic3—108no—
671C2×Dic3—102no—
672C2×Dic3—102no—
673C2×Dic3—102no—
674C2×Dic3—108no—
675C2×Dic3D4×D514yes—
676C2×Dic3C23×D512yes—
677C2×Dic3C23×D512yes—
678C2×Dic3C23×D512yes—
679C2×Dic3C23×D512yes—
680Dic6—28no—
681Dic6—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5C22×Dic612yes—
688C22×C5C22×Dic614yescomplemented
689C22×C5C2×D3×D412yes—
690C22×C5C2×#23712yes—
691C22×C5C24×D311yescharacteristic
692C2×D5—22no—
693C2×D5—22no—
694C2×D5—28no—
695C2×D5—232no—
696C2×D5#878116yesdirect product factor
697C2×D5C22×Dic614yes—
698C2×D5C22×Dic614yescomplemented
699C2×D5C2×D3×D414yes—
700C2×D5C2×#23714yes—
701C4×C5—22no—
702C4×C5—22no—
703C4×C5—34no—
704C4×C5—62no—
705C4×C5—62no—
706C4×C5—62no—
707Dic5—22no—
708Dic5—22no—
709Dic5—34no—
710Dic5—62no—
711Dic5—62no—
712Dic5—62no—
713C24—51no—
714C24—58no—
715C24—54no—
716C24—51no—
717C24—104no—
718C24—104no—
719C24C2×D3×D511yescharacteristic
720C2×Q8—34no—
721C2×Q8—64no—
722C2×Q8—154no—
723C2×Q8—154no—
724C2×Q8—154no—
725C2×Q8—304no—
726C2×Q8—304no—
727C2×Q8—304no—
728C2×Q8—3032no—
729C22×C4—31no—
730C22×C4—34no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—51no—
735C22×C4—51no—
736C22×C4—54no—
737C22×C4—54no—
738C22×C4—64no—
739C22×C4—104no—
740C22×C4—104no—
741C22×C4—154no—
742C22×C4—158no—
743C22×C4—154no—
744C22×C4—154no—
745C22×C4—154no—
746C22×C4—154no—
747C22×C4—154no—
748C22×C4—151no—
749C22×C4—154no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—304no—
754C22×C4—3032no—
755C22×C4—304no—
756C22×C4—304no—
757C22×C4—304no—
758C22×C4—304no—
759C22×C4—304no—
760C22×C4C2×D3×D511yescharacteristic
761C22×C4C2×D3×D511yescharacteristic
762C4⋊C4—34no—
763C4⋊C4—34no—
764C4⋊C4—34no—
765C4⋊C4—154no—
766C4⋊C4—154no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4—154no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4—154no—
773C4⋊C4—154no—
774C22⋊C4—34no—
775C22⋊C4—54no—
776C22⋊C4—54no—
777C22⋊C4—54no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4C2×D3×D514yes—
782C3×C5C22×C22⋊Q811yescharacteristic, complemented, Hall
783C22×C3—28no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—516no—
787C22×C3—54no—
788C22×C3—54no—
789C22×C3—54no—
790C22×C3—54no—
791C22×C3—1032no—
792C22×C3—108no—
793C22×C3—102no—
794C22×C3—102no—
795C22×C3C2×D4×D512yes—
796C22×C3C2×Q8×D512yes—
797C22×C3C2×Q8×D514yescomplemented
798C22×C3D5×#4112yes—
799C22×C3C24×D511yescharacteristic
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—102no—
803C3×C4—102no—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—54no—
808Dic3—102no—
809Dic3—102no—
810Dic3—102no—
811Dic3C2×D4×D514yes—
812C2×C5—24no—
813C2×C5C2×#87814yescomplemented
814C2×C5C23×Dic611yescharacteristic
815C2×C5C22×D3×D411yescharacteristic
816C2×C5C22×#23711yescharacteristic
817D5—24no—
818D5C2×#87818yesdirect product factor
819C23—22no—
820C23—22no—
821C23—54no—
822C23—54no—
823C23—54no—
824C23—52no—
825C23—54no—
826C23—516no—
827C23—52no—
828C23—108no—
829C23—1032no—
830C23—108no—
831C23—102no—
832C23—102no—
833C23D5×Dic614yescomplemented
834C23C22×D3×D512yes—
835C23C22×D3×D511yescharacteristic
836Q8—68no—
837Q8—308no—
838Q8—308no—
839Q8—308no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—34no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—52no—
848C2×C4—52no—
849C2×C4—68no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—108no—
854C2×C4—108no—
855C2×C4—102no—
856C2×C4—102no—
857C2×C4—1516no—
858C2×C4—154no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—152no—
863C2×C4—308no—
864C2×C4—308no—
865C2×C4—308no—
866C2×C4—308no—
867C2×C4—308no—
868C2×C4—308no—
869C2×C4—302no—
870C2×C4—302no—
871C2×C4—302no—
872C2×C4C22×D3×D512yes—
873C2×C4C22×D3×D512yes—
874C2×C3—24no—
875C2×C3—58no—
876C2×C3—104no—
877C2×C3D5×C22⋊Q814yescomplemented
878C2×C3C22×D4×D511yescharacteristic
879C2×C3C22×Q8×D511yescharacteristic
880C2×C3C2×D5×#4111yescharacteristic
881C5C22×#87811yescharacteristic, complemented, Sylow
882C22—28no—
883C22—22no—
884C22—22no—
885C22—516no—
886C22—54no—
887C22—54no—
888C22—54no—
889C22—54no—
890C22—1032no—
891C22—108no—
892C22—102no—
893C22—102no—
894C22C2×D5×Dic612yes—
895C22C2×D5×Dic614yescomplemented
896C22D3×D4×D512yes—
897C22D5×#23712yes—
898C22C23×D3×D511yescharacteristic
899C4—22no—
900C4—22no—
901C4—34no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—102no—
906C4—102no—
907C4—154no—
908C4—302no—
909C4—302no—
910C4—302no—
911C3C2×D5×C22⋊Q811yescharacteristic, complemented, Sylow
912C2—24no—
913C2—58no—
914C2—104no—
915C2D5×#87814yesdirect product factor
916C2C22×D5×Dic611yescharacteristic
917C2C2×D3×D4×D511yescharacteristic
918C2C2×D5×#23711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C22×C22⋊Q8
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
2. C22×D5×Dic6C2semidirect
3. C2×#91767C2semidirect
4. C2×C5×#878C2semidirect
6. C2×#91576C2semidirect
7. C2×#91575C2semidirect
9. C2×#91431C2semidirect
10. C2×#91430C2semidirect
11. C2×#91422C2semidirect
12. C2×#91421C2semidirect
13. C2×D5×C4⋊Dic3C2semidirect
14. C2×D5×Dic3⋊C4C2semidirect
15. C2×D5×Dic3⋊C4C2semidirect
16. D5×#878C2direct (N × H)
20. C22×Dic30C22semidirect
22. C22×C5×Dic6C22semidirect
25. C22×#1204C22semidirect
26. C22×#1204C22semidirect
36. C2×D5×Dic6C22semidirect
39. C2×C4⋊Dic15C22semidirect
40. C2×#6712C22semidirect
41. C2×#6712C22semidirect
42. #91767C22semidirect
44. C2×C5×C4⋊Dic3C22semidirect
45. C2×C5×Dic3⋊C4C22semidirect
46. C2×C5×Dic3⋊C4C22semidirect
47. C5×#878C22semidirect
52. #91576C22semidirect
53. #91575C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×#6669C22semidirect
58. C2×#6669C22semidirect
59. C2×#6668C22semidirect
60. C2×#6668C22semidirect
63. #91431C22semidirect
64. #91430C22semidirect
65. #91422C22semidirect
66. #91421C22semidirect
67. D5×C4⋊Dic3C22semidirect
68. D5×Dic3⋊C4C22semidirect
69. D5×Dic3⋊C4C22semidirect
90. C23×C3×D5Q8semidirect
103. C2×Dic30C23semidirect
111. C2×C5×Dic6C23semidirect
120. C2×#1204C23semidirect
121. C2×#1204C23semidirect
138. C4⋊Dic15C23semidirect
139. #6712C23semidirect
140. #6712C23semidirect
142. C5×C4⋊Dic3C23semidirect
143. C5×Dic3⋊C4C23semidirect
144. C5×Dic3⋊C4C23semidirect
148. Dic3⋊Dic5C23semidirect
149. Dic3⋊Dic5C23semidirect
150. #6669C23semidirect
151. #6669C23semidirect
152. #6668C23semidirect
153. #6668C23semidirect
171. C2×#878D5direct (N × H)
227. C23×C3×C5C2×Q8semidirect
237. C22×C3×D5C2×Q8semidirect
238. C22×C3×D5C2×Q8semidirect
298. C22×Dic6C2×D5semidirect
313. C2×C4⋊Dic3C2×D5semidirect
322. C2×Dic3⋊C4C2×D5semidirect
323. C2×Dic3⋊C4C2×D5semidirect
331. #878C2×D5direct (N × H)
335. C23×D5Dic6semidirect
422. C22×C3×C5C22×Q8semidirect
429. C2×C3×D5C22⋊Q8semidirect
432. C2×C3×D5C22×Q8semidirect
494. C2×Dic6C22×D5semidirect
506. C4⋊Dic3C22×D5semidirect
513. Dic3⋊C4C22×D5semidirect
514. Dic3⋊C4C22×D5semidirect
517. C23×C5C2×Dic6semidirect
526. C22×D5C2×Dic6semidirect
527. C22×D5C2×Dic6semidirect
623. C2×C3×C5C2×C22⋊Q8semidirect
628. C3×D5C2×C22⋊Q8semidirect
643. C23×C3Q8×D5semidirect
688. C22×C5C22×Dic6semidirect
696. C2×D5#878direct (N × H)
698. C2×D5C22×Dic6semidirect
782. C3×C5C22×C22⋊Q8semidirect
797. C22×C3C2×Q8×D5semidirect
813. C2×C5C2×#878semidirect
818. D5C2×#878direct (N × H)
833. C23D5×Dic6semidirect
877. C2×C3D5×C22⋊Q8semidirect
881. C5C22×#878semidirect
895. C22C2×D5×Dic6semidirect
911. C3C2×D5×C22⋊Q8semidirect
915. C2D5×#878direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5×Dic32
C22×D5×Dic62
C2×#917672
C2×C5×#8782
C2×C3×D5×C22⋊C42
C2×#915762
C2×#915752
C2×D5×#2172
C2×#914312
C2×#914302
C2×#914222
C2×#914212
C2×D5×C4⋊Dic32
C2×D5×Dic3⋊C42
D5×#8782
C2×D5×C22⋊Q83
C22×#8785