Finite Group Databasebeta

← C2×D3×#4024 #14479435

Subgroups — C2×D3×#4024 #14479435

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×D3×Dic5C211yesmaximal, characteristic
2C22×D3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91767C211yesmaximal, characteristic, complemented
4C2×C5×D3×C22⋊C4C211yesmaximal, characteristic
5C2×C3×#4024C211yesmaximal, characteristic, complemented
6C2×#91576C211yesmaximal, characteristic, complemented
7C2×#91574C211yesmaximal, characteristic, complemented
8C2×D3×C22⋊Dic5C211yesmaximal, characteristic
9C2×#91436C211yesmaximal, characteristic, complemented
10C2×#91432C211yesmaximal, characteristic, complemented
11C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
12C2×#91417C211yesmaximal, characteristic, complemented
13C2×#91410C211yesmaximal, characteristic, complemented
14C2×D3×#683C211yesmaximal, characteristic, complemented
15C2×D3×#683C211yesmaximal, characteristic, complemented
16D3×#4024C2116yesmaximal, direct product factor
17C22×#4024—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C22×C4×C5×D3C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic, complemented
25C22×#1204C2211yescharacteristic, complemented
26C22×#1204C2211yescharacteristic, complemented
27C22×D3×Dic5—28no—
28C22×D3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic
31C22×D3×Dic5C2218yes—
32C22×D3×Dic5C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic
34C22×D3×Dic5C2211yescharacteristic
35C2×D3×Dic10—28no—
36C2×D3×Dic10C2218yescomplemented
37C2×C3×C5×C22⋊C4C2211yescharacteristic
38C2×#6719C2211yescharacteristic
39C2×C4⋊Dic15C2211yescharacteristic, complemented
40C2×#6712C2211yescharacteristic, complemented
41C2×#6712C2211yescharacteristic, complemented
42#91767C2218yescomplemented
43C2×C5×#217C2211yescharacteristic
44C2×C5×(C2×D3)⋊C4C2211yescharacteristic
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic
46C5×D3×C22⋊C4C2218yes—
47C2×C3×C22⋊Dic5C2211yescharacteristic
48C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
49C2×C3×#683C2211yescharacteristic, complemented
50C2×C3×#683C2211yescharacteristic, complemented
51C3×#4024C2218yescomplemented
52#91576C2218yescomplemented
53#91574C2218yescomplemented
54D3×C22⋊Dic5C2218yes—
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×#6669C2211yescharacteristic, complemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6668C2211yescharacteristic, complemented
60C2×#6668C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic
62C2×(C2×D3)⋊Dic5C2211yescharacteristic
63#91436C2218yescomplemented
64#91432C2218yescomplemented
65D3×C4⋊Dic5C2218yescomplemented
66#91417C2218yescomplemented
67#91410C2218yescomplemented
68D3×#683C2218yescomplemented
69D3×#683C2218yescomplemented
70C2×D3×C22⋊Q8—51nomaximal, Hall
71C24×Dic5—31no—
72C23×Dic10—31no—
73C22×C5×C22⋊C4—31no—
74C22×C22⋊Dic5—31no—
75C22×C4⋊Dic5—31no—
76C22×#683—31no—
77C22×#683—31no—
78C2×#4024—31no—
79C2×#4024—31no—
80C2×#4024—31no—
81C2×#4024—316no—
82C2×#4024—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C2×#4024—31no—
86C2×#4024D311yescharacteristic, direct product factor
87C24×C3×C5C2311yescharacteristic
88C23×C5×D3—24no—
89C23×C5×D3—24no—
90C23×C5×D3Q818yescomplemented
91C23×C5×D3C2314yes—
92C23×C5×D3C2311yescharacteristic
93C23×C5×D3C2311yescharacteristic
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×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C2×C4×C5×D3—24no—
107C2×C4×C5×D3—24no—
108C2×C4×C5×D3C2314yes—
109C2×C4×C5×D3C2314yes—
110C22×C3×Dic5—24no—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2314yes—
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×Dic10—24no—
117C2×C3×Dic10C2314yescomplemented
118C2×#1204—24no—
119C2×#1204—24no—
120C2×#1204C2314yescomplemented
121C2×#1204C2314yescomplemented
122C2×D3×Dic5—24no—
123C2×D3×Dic5—24no—
124C2×D3×Dic5—24no—
125C2×D3×Dic5—24no—
126C2×D3×Dic5—24no—
127C2×D3×Dic5—232no—
128C2×D3×Dic5D418yes—
129C2×D3×Dic5C2314yes—
130C2×D3×Dic5C2314yes—
131C2×D3×Dic5C2314yes—
132C2×D3×Dic5C2314yes—
133C2×D3×Dic5C2314yes—
134C2×D3×Dic5C2314yes—
135D3×Dic10—232no—
136C3×C5×C22⋊C4C2314yes—
137#6719C2314yes—
138C4⋊Dic15C2314yescomplemented
139#6712C2314yescomplemented
140#6712C2314yescomplemented
141C5×#217C2314yes—
142C5×(C2×D3)⋊C4C2314yes—
143C5×(C2×D3)⋊C4C2314yes—
144C3×C22⋊Dic5C2314yes—
145C3×C4⋊Dic5C2314yescomplemented
146C3×#683C2314yescomplemented
147C3×#683C2314yescomplemented
148Dic3⋊Dic5C2314yescomplemented
149Dic3⋊Dic5C2314yescomplemented
150#6669C2314yescomplemented
151#6669C2314yescomplemented
152#6668C2314yescomplemented
153#6668C2314yescomplemented
154(C2×D3)⋊Dic5C2314yes—
155(C2×D3)⋊Dic5C2314yes—
156C22×D3×Q8—51no—
157C23×C4×D3—51no—
158C2×C3×C22⋊Q8—51no—
159C2×#946—51no—
160C2×#924—51no—
161D3×C22⋊Q8—516no—
162C2×#897—51no—
163C2×#896—51no—
164C2×#896—51no—
165C2×D3×C4⋊C4—51no—
166C2×D3×C4⋊C4—51no—
167C2×D3×C4⋊C4—51no—
168C2×D3×C22⋊C4—51no—
169C2×D3×C22⋊C4D511yescharacteristic
170C2×#878—51no—
171C2×#878—51no—
172C25×C5—31no—
173C23×C4×C5—31no—
174C23×C4×C5—31no—
175C23×Dic5—31no—
176C23×Dic5—31no—
177C23×Dic5—31no—
178C23×Dic5—38no—
179C23×Dic5—31no—
180C23×Dic5—31no—
181C23×Dic5—31no—
182C23×Dic5—31no—
183C23×Dic5—68no—
184C23×Dic5C2×D311yescharacteristic
185C22×Dic10—31no—
186C22×Dic10—31no—
187C22×Dic10—31no—
188C22×Dic10—38no—
189C22×Dic10—68no—
190C22×Dic10C2×D311yescharacteristic, complemented
191C2×C5×C22⋊C4—31no—
192C2×C5×C22⋊C4—31no—
193C2×C5×C22⋊C4—31no—
194C2×C5×C22⋊C4—38no—
195C2×C5×C22⋊C4C2×D311yescharacteristic
196C2×C22⋊Dic5—31no—
197C2×C22⋊Dic5—31no—
198C2×C22⋊Dic5—31no—
199C2×C22⋊Dic5—38no—
200C2×C22⋊Dic5C2×D311yescharacteristic
201C2×C4⋊Dic5—31no—
202C2×C4⋊Dic5—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—38no—
205C2×C4⋊Dic5C2×D311yescharacteristic, complemented
206C2×#683—31no—
207C2×#683—31no—
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×#683—38no—
213C2×#683—38no—
214C2×#683C2×D311yescharacteristic, complemented
215C2×#683C2×D311yescharacteristic, complemented
216#4024—38no—
217#4024—38no—
218#4024—38no—
219#4024—38no—
220#4024—38no—
221#4024—38no—
222#4024—38no—
223#4024C2×D318yesdirect product factor
224C22×C22⋊Q8—151noSylow
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5C2×Q814yescomplemented
228C23×C3×C5C2412yes—
229C23×C3×C5C2411yescharacteristic
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3—232no—
233C22×C5×D3—28no—
234C22×C5×D3—28no—
235C22×C5×D3C2×D414yes—
236C22×C5×D3C2×Q814yes—
237C22×C5×D3C2×Q8116yescomplemented
238C22×C5×D3C2×Q814yescomplemented
239C22×C5×D3#4114yes—
240C22×C5×D3C2412yes—
241C22×C5×D3C2412yes—
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×Dic3C2412yes—
259C2×C5×Dic3C2412yes—
260C4×C5×D3—28no—
261C4×C5×D3—28no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—22no—
265C2×C3×Dic5—28no—
266C2×C3×Dic5C2×D414yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C3×Dic10—28no—
272#1204—28no—
273#1204—28no—
274D3×Dic5—28no—
275D3×Dic5—28no—
276D3×Dic5—28no—
277D3×Dic5—28no—
278D3×Dic5—28no—
279D3×Dic5C2×D4116yes—
280C24×D3C2×D511yescharacteristic
281C22×C3×Q8—51no—
282C23×C3×C4—51no—
283C23×Dic3—51no—
284C2×D3×Q8—58no—
285C2×D3×Q8—108no—
286C22×C4×D3—51no—
287C22×C4×D3—51no—
288C22×C4×D3—51no—
289C22×C4×D3—51no—
290C22×C4×D3—58no—
291C22×C4×D3—51no—
292C22×C4×D3—51no—
293C22×C4×D3—108no—
294C22×C4×D3C2×D511yescharacteristic
295C22×C4×D3C2×D511yescharacteristic
296C22×Dic6—51no—
297C22×Dic6—51no—
298C22×Dic6—51no—
299C3×C22⋊Q8—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C4⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4C2×D511yescharacteristic
305C2×#217—51no—
306C2×#217C2×D511yescharacteristic
307#946—58no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4C2×D511yescharacteristic
311C2×(C2×D3)⋊C4C2×D511yescharacteristic
312C2×C4⋊Dic3—51no—
313C2×C4⋊Dic3—51no—
314C2×C4⋊Dic3—51no—
315#924—58no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—51no—
321C2×Dic3⋊C4—51no—
322#897—58no—
323#896—58no—
324#896—58no—
325D3×C4⋊C4—58no—
326D3×C4⋊C4—58no—
327D3×C4⋊C4—58no—
328D3×C22⋊C4—58no—
329D3×C22⋊C4C2×D518yes—
330#878—58no—
331#878—58no—
332C24×C5—31no—
333C24×C5—38no—
334C24×C5—34no—
335C24×C5—31no—
336C24×C5—64no—
337C24×C5—64no—
338C24×C5C22×D311yescharacteristic
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5—34no—
342C22×C4×C5—34no—
343C22×C4×C5—64no—
344C22×C4×C5—64no—
345C22×C4×C5C22×D311yescharacteristic
346C22×C4×C5C22×D311yescharacteristic
347C22×Dic5—24no—
348C22×Dic5—31no—
349C22×Dic5—38no—
350C22×Dic5—34no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353C22×Dic5—34no—
354C22×Dic5—31no—
355C22×Dic5—34no—
356C22×Dic5—34no—
357C22×Dic5—34no—
358C22×Dic5—34no—
359C22×Dic5—34no—
360C22×Dic5—64no—
361C22×Dic5—632no—
362C22×Dic5—64no—
363C22×Dic5—64no—
364C22×Dic5—64no—
365C22×Dic5—64no—
366C22×Dic5—64no—
367C22×Dic5C22×D311yescharacteristic
368C22×Dic5C22×D311yescharacteristic
369C22×Dic5C22×D314yes—
370C22×Dic5C22×D311yescharacteristic
371C22×Dic5C22×D311yescharacteristic
372C2×Dic10—24no—
373C2×Dic10—34no—
374C2×Dic10—34no—
375C2×Dic10—34no—
376C2×Dic10—632no—
377C2×Dic10—64no—
378C2×Dic10—64no—
379C2×Dic10—64no—
380C2×Dic10C22×D314yescomplemented
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C5×C22⋊C4C22×D314yes—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387C22⋊Dic5—34no—
388C22⋊Dic5C22×D314yes—
389C4⋊Dic5—34no—
390C4⋊Dic5—34no—
391C4⋊Dic5—34no—
392C4⋊Dic5C22×D314yescomplemented
393#683—34no—
394#683—34no—
395#683—34no—
396#683—34no—
397#683—34no—
398#683—34no—
399#683C22×D314yescomplemented
400#683C22×D314yescomplemented
401C23×Q8—151no—
402C24×C4—151no—
403C2×C22⋊Q8—51no—
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—31no—
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×C5×D3—28no—
426C2×C5×D3—22no—
427C2×C5×D3—22no—
428C2×C5×D3—232no—
429C2×C5×D3C22⋊Q8116yescomplemented
430C2×C5×D3C22×D414yes—
431C2×C5×D3C22×Q814yes—
432C2×C5×D3C22×Q814yescomplemented
433C2×C5×D3C2×#4114yes—
434C3×C4×C5—22no—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15—22no—
439Dic15C22×D414yes—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5—22no—
443C3×Dic5C22×D414yes—
444C5×Dic3—22no—
445C5×Dic3—22no—
446C24×C3C22×D511yescharacteristic
447C23×D3—24no—
448C23×D3—24no—
449C23×D3Dic1018yescomplemented
450C23×D3C22×D514yes—
451C23×D3C22×D511yescharacteristic
452C23×D3C22×D511yescharacteristic
453C2×C3×Q8—54no—
454C2×C3×Q8—104no—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—54no—
460C22×C3×C4—104no—
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×Dic3—51no—
464C22×Dic3—54no—
465C22×Dic3—51no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—104no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471D3×Q8—1032no—
472C2×C4×D3—24no—
473C2×C4×D3—24no—
474C2×C4×D3—58no—
475C2×C4×D3—54no—
476C2×C4×D3—54no—
477C2×C4×D3—54no—
478C2×C4×D3—54no—
479C2×C4×D3—54no—
480C2×C4×D3—54no—
481C2×C4×D3—1032no—
482C2×C4×D3—104no—
483C2×C4×D3—104no—
484C2×C4×D3—104no—
485C2×C4×D3—104no—
486C2×C4×D3—104no—
487C2×C4×D3C22×D514yes—
488C2×C4×D3C22×D514yes—
489C2×Dic6—54no—
490C2×Dic6—54no—
491C2×Dic6—54no—
492C2×Dic6—104no—
493C2×Dic6—104no—
494C2×Dic6—104no—
495C3×C4⋊C4—54no—
496C3×C4⋊C4—54no—
497C3×C4⋊C4—54no—
498C3×C22⋊C4—54no—
499C3×C22⋊C4C22×D514yes—
500#217—54no—
501#217C22×D514yes—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4C22×D514yes—
505(C2×D3)⋊C4C22×D514yes—
506C4⋊Dic3—54no—
507C4⋊Dic3—54no—
508C4⋊Dic3—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4—54no—
513Dic3⋊C4—54no—
514Dic3⋊C4—54no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—34no—
518C23×C5—34no—
519C23×C5—34no—
520C23×C5—32no—
521C23×C5—34no—
522C23×C5—316no—
523C23×C5—32no—
524C23×C5—68no—
525C23×C5—68no—
526C23×C5—632no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5D3×Q814yescomplemented
530C23×C5C23×D312yes—
531C23×C5C23×D311yescharacteristic
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—68no—
537C2×C4×C5—68no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D312yes—
542C2×Dic5—22no—
543C2×Dic5—22no—
544C2×Dic5—22no—
545C2×Dic5—28no—
546C2×Dic5—34no—
547C2×Dic5—32no—
548C2×Dic5—316no—
549C2×Dic5—32no—
550C2×Dic5—32no—
551C2×Dic5—32no—
552C2×Dic5—68no—
553C2×Dic5—68no—
554C2×Dic5—68no—
555C2×Dic5—68no—
556C2×Dic5—68no—
557C2×Dic5—62no—
558C2×Dic5—62no—
559C2×Dic5—62no—
560C2×Dic5—68no—
561C2×Dic5D3×D414yes—
562C2×Dic5C23×D312yes—
563C2×Dic5C23×D312yes—
564C2×Dic5C23×D312yes—
565C2×Dic5C23×D312yes—
566Dic10—28no—
567Dic10—68no—
568Dic10—68no—
569Dic10—68no—
570C25—31no—
571C22×Q8—51no—
572C22×Q8—151no—
573C22×Q8—151no—
574C22×Q8—158no—
575C22×Q8—151no—
576C22×Q8—308no—
577C23×C4—31no—
578C23×C4—31no—
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—58no—
590C22⋊Q8—158no—
591C22⋊Q8—158no—
592C22⋊Q8—158no—
593C22⋊Q8—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596C22⋊Q8—158no—
597C2×C4⋊C4—51no—
598C2×C4⋊C4—51no—
599C2×C4⋊C4—51no—
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—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—38no—
616C2×C22⋊C4—51no—
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
627C5×D3—24no—
628C5×D3C2×C22⋊Q818yescomplemented
629C23×C3—22no—
630C23×C3—22no—
631C23×C3C2×Dic1014yescomplemented
632C23×C3C23×D512yes—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—28no—
637C22×D3—28no—
638C22×D3—232no—
639C22×D3C2×Dic1014yes—
640C22×D3C2×Dic10116yescomplemented
641C22×D3C2×Dic1014yescomplemented
642C22×D3D4×D514yes—
643C22×D3#71114yes—
644C22×D3C23×D512yes—
645C22×D3C23×D512yes—
646C3×Q8—108no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—54no—
650C2×C3×C4—52no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—108no—
655C2×C3×C4—102no—
656C2×C3×C4—102no—
657C2×C3×C4—102no—
658C2×C3×C4C23×D512yes—
659C2×C3×C4C23×D512yes—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—54no—
663C2×Dic3—52no—
664C2×Dic3—52no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—108no—
668C2×Dic3—102no—
669C2×Dic3—102no—
670C2×Dic3—102no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C4×D3—28no—
674C4×D3—28no—
675C4×D3—516no—
676C4×D3—108no—
677C4×D3—108no—
678C4×D3—108no—
679C4×D3—108no—
680C4×D3—108no—
681Dic6—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—34no—
688C22×C5—34no—
689C22×C5—34no—
690C22×C5—316no—
691C22×C5—34no—
692C22×C5—632no—
693C22×C5—62no—
694C22×C5—62no—
695C22×C5—68no—
696C22×C5C2×D3×D412yes—
697C22×C5C2×D3×Q812yes—
698C22×C5C2×D3×Q814yescomplemented
699C22×C5D3×#4112yes—
700C22×C5C24×D311yescharacteristic
701C4×C5—22no—
702C4×C5—22no—
703C4×C5—62no—
704C4×C5—62no—
705Dic5—22no—
706Dic5—22no—
707Dic5—22no—
708Dic5—34no—
709Dic5—62no—
710Dic5—62no—
711Dic5—62no—
712Dic5C2×D3×D414yes—
713C24—31no—
714C24—38no—
715C24—34no—
716C24—31no—
717C24—64no—
718C24—64no—
719C24C2×D3×D511yescharacteristic
720C2×Q8—54no—
721C2×Q8—104no—
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—31no—
731C22×C4—34no—
732C22×C4—34no—
733C22×C4—51no—
734C22×C4—54no—
735C22×C4—51no—
736C22×C4—51no—
737C22×C4—51no—
738C22×C4—64no—
739C22×C4—64no—
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—54no—
763C4⋊C4—54no—
764C4⋊C4—54no—
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—34no—
776C22⋊C4—34no—
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×C3C22×Dic1012yes—
787C22×C3C22×Dic1014yescomplemented
788C22×C3C2×D4×D512yes—
789C22×C3C2×#71112yes—
790C22×C3C24×D511yescharacteristic
791C2×D3—28no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—232no—
795C2×D3#4024116yesdirect product factor
796C2×D3C22×Dic1014yes—
797C2×D3C22×Dic1014yescomplemented
798C2×D3C2×D4×D514yes—
799C2×D3C2×#71114yes—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—54no—
803C3×C4—102no—
804C3×C4—102no—
805C3×C4—102no—
806Dic3—22no—
807Dic3—22no—
808Dic3—54no—
809Dic3—102no—
810Dic3—102no—
811Dic3—102no—
812C2×C5—24no—
813C2×C5—38no—
814C2×C5—64no—
815C2×C5D3×C22⋊Q814yescomplemented
816C2×C5C22×D3×D411yescharacteristic
817C2×C5C22×D3×Q811yescharacteristic
818C2×C5C2×D3×#4111yescharacteristic
819C23—22no—
820C23—22no—
821C23—34no—
822C23—34no—
823C23—34no—
824C23—32no—
825C23—34no—
826C23—316no—
827C23—32no—
828C23—68no—
829C23—632no—
830C23—68no—
831C23—62no—
832C23—62no—
833C23D3×Dic1014yescomplemented
834C23C22×D3×D512yes—
835C23C22×D3×D511yescharacteristic
836Q8—108no—
837Q8—308no—
838Q8—308no—
839Q8—308no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—54no—
845C2×C4—52no—
846C2×C4—52no—
847C2×C4—52no—
848C2×C4—52no—
849C2×C4—68no—
850C2×C4—68no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—108no—
854C2×C4—102no—
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×C3C2×#402414yescomplemented
876C2×C3C23×Dic1011yescharacteristic
877C2×C3C22×D4×D511yescharacteristic
878C2×C3C22×#71111yescharacteristic
879D3—24no—
880D3C2×#402418yesdirect product factor
881C5C2×D3×C22⋊Q811yescharacteristic, complemented, Sylow
882C22—28no—
883C22—22no—
884C22—22no—
885C22—316no—
886C22—34no—
887C22—34no—
888C22—34no—
889C22—34no—
890C22—632no—
891C22—68no—
892C22—62no—
893C22—62no—
894C22C2×D3×Dic1012yes—
895C22C2×D3×Dic1014yescomplemented
896C22D3×D4×D512yes—
897C22D3×#71112yes—
898C22C23×D3×D511yescharacteristic
899C4—22no—
900C4—22no—
901C4—54no—
902C4—62no—
903C4—62no—
904C4—102no—
905C4—102no—
906C4—102no—
907C4—154no—
908C4—302no—
909C4—302no—
910C4—302no—
911C3C22×#402411yescharacteristic, complemented, Sylow
912C2—24no—
913C2—38no—
914C2—64no—
915C2D3×#402414yesdirect product factor
916C2C22×D3×Dic1011yescharacteristic
917C2C2×D3×D4×D511yescharacteristic
918C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC24×C5×D3C22
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×D3×Dic10C2semidirect
3. C2×#91767C2semidirect
5. C2×C3×#4024C2semidirect
6. C2×#91576C2semidirect
7. C2×#91574C2semidirect
9. C2×#91436C2semidirect
10. C2×#91432C2semidirect
11. C2×D3×C4⋊Dic5C2semidirect
12. C2×#91417C2semidirect
13. C2×#91410C2semidirect
14. C2×D3×#683C2semidirect
15. C2×D3×#683C2semidirect
16. D3×#4024C2direct (N × H)
20. C22×Dic30C22semidirect
24. C22×C3×Dic10C22semidirect
25. C22×#1204C22semidirect
26. C22×#1204C22semidirect
36. C2×D3×Dic10C22semidirect
39. C2×C4⋊Dic15C22semidirect
40. C2×#6712C22semidirect
41. C2×#6712C22semidirect
42. #91767C22semidirect
48. C2×C3×C4⋊Dic5C22semidirect
49. C2×C3×#683C22semidirect
50. C2×C3×#683C22semidirect
51. C3×#4024C22semidirect
52. #91576C22semidirect
53. #91574C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×#6669C22semidirect
58. C2×#6669C22semidirect
59. C2×#6668C22semidirect
60. C2×#6668C22semidirect
63. #91436C22semidirect
64. #91432C22semidirect
65. D3×C4⋊Dic5C22semidirect
66. #91417C22semidirect
67. #91410C22semidirect
68. D3×#683C22semidirect
69. D3×#683C22semidirect
86. C2×#4024D3direct (N × H)
90. C23×C5×D3Q8semidirect
103. C2×Dic30C23semidirect
117. C2×C3×Dic10C23semidirect
120. C2×#1204C23semidirect
121. C2×#1204C23semidirect
138. C4⋊Dic15C23semidirect
139. #6712C23semidirect
140. #6712C23semidirect
145. C3×C4⋊Dic5C23semidirect
146. C3×#683C23semidirect
147. C3×#683C23semidirect
148. Dic3⋊Dic5C23semidirect
149. Dic3⋊Dic5C23semidirect
150. #6669C23semidirect
151. #6669C23semidirect
152. #6668C23semidirect
153. #6668C23semidirect
190. C22×Dic10C2×D3semidirect
205. C2×C4⋊Dic5C2×D3semidirect
214. C2×#683C2×D3semidirect
215. C2×#683C2×D3semidirect
223. #4024C2×D3direct (N × H)
227. C23×C3×C5C2×Q8semidirect
237. C22×C5×D3C2×Q8semidirect
238. C22×C5×D3C2×Q8semidirect
380. C2×Dic10C22×D3semidirect
392. C4⋊Dic5C22×D3semidirect
399. #683C22×D3semidirect
400. #683C22×D3semidirect
422. C22×C3×C5C22×Q8semidirect
429. C2×C5×D3C22⋊Q8semidirect
432. C2×C5×D3C22×Q8semidirect
449. C23×D3Dic10semidirect
529. C23×C5D3×Q8semidirect
623. C2×C3×C5C2×C22⋊Q8semidirect
628. C5×D3C2×C22⋊Q8semidirect
631. C23×C3C2×Dic10semidirect
640. C22×D3C2×Dic10semidirect
641. C22×D3C2×Dic10semidirect
698. C22×C5C2×D3×Q8semidirect
782. C3×C5C22×C22⋊Q8semidirect
787. C22×C3C22×Dic10semidirect
795. C2×D3#4024direct (N × H)
797. C2×D3C22×Dic10semidirect
815. C2×C5D3×C22⋊Q8semidirect
833. C23D3×Dic10semidirect
875. C2×C3C2×#4024semidirect
880. D3C2×#4024direct (N × H)
881. C5C2×D3×C22⋊Q8semidirect
895. C22C2×D3×Dic10semidirect
911. C3C22×#4024semidirect
915. C2D3×#4024direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×Dic52
C22×D3×Dic102
C2×#917672
C2×C5×D3×C22⋊C42
C2×C3×#40242
C2×#915762
C2×#915742
C2×D3×C22⋊Dic52
C2×#914362
C2×#914322
C2×D3×C4⋊Dic52
C2×#914172
C2×#914102
C2×D3×#6832
D3×#40242
C22×#40243
C2×D3×C22⋊Q85