Finite Group Databasebeta

← C2×#11752861 #14482952

Subgroups — C2×#11752861 #14482952

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1204C211yesmaximal, characteristic, complemented
2C22×D3×Dic10C211yesmaximal, characteristic, complemented
3C2×#91767C211yesmaximal, characteristic, complemented
4C2×C5×#67⋊C4C211yesmaximal, characteristic
5C2×C3×#4024C211yesmaximal, characteristic, complemented
6C2×#91575C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic5C211yesmaximal, characteristic
8C2×Dic5×#67C211yesmaximal, characteristic
9C2×#91469C211yesmaximal, characteristic, complemented
10C2×#91436C211yesmaximal, characteristic, complemented
11C2×#91417C211yesmaximal, characteristic, complemented
12C2×#91352C211yesmaximal, characteristic, complemented
13C2×#91328C211yesmaximal, characteristic, complemented
14C2×#91327C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11752861C2116yesmaximal, direct product factor
17C2×D4×Dic10—31nomaximal, Hall
18C23×Dic15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×Dic10C2211yescharacteristic
25C22×#1204—28no—
26C22×#1204C2211yescharacteristic
27C22×#1204C2211yescharacteristic
28C22×#1204C2211yescharacteristic
29C22×#1204C2211yescharacteristic
30C22×#1204C2211yescharacteristic
31C22×#1204C2218yescomplemented
32C22×D3×Dic5C2211yescharacteristic
33C22×D3×Dic5C2211yescharacteristic
34C2×D3×Dic10—28no—
35C2×D3×Dic10C2218yescomplemented
36C2×C3×C5×C22⋊C4C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41#91767C2218yescomplemented
42C2×C5×(C2×D3)⋊C4C2211yescharacteristic
43C2×C5×Dic3⋊C4C2211yescharacteristic
44C2×C4×C5×Dic3C2211yescharacteristic
45C5×#67⋊C4C2218yes—
46C2×C3×C22⋊Dic5C2211yescharacteristic
47C2×C3×C4⋊Dic5C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C3×#4024C2218yescomplemented
51#91575C2218yescomplemented
52#67⋊Dic5C2218yes—
53Dic5×#67C2218yes—
54C2×Dic3⋊Dic5C2211yescharacteristic
55C2×Dic3⋊Dic5C2211yescharacteristic
56C2×Dic3⋊Dic5C2211yescharacteristic
57C2×#6669C2211yescharacteristic
58C2×#6668C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63#91469C2218yescomplemented
64#91436C2218yescomplemented
65#91417C2218yescomplemented
66#91352C2218yescomplemented
67#91328C2218yescomplemented
68#91327C2218yescomplemented
69#91324C2218yescomplemented
70C2×#5632—51nomaximal, Hall
71C23×Dic10—31no—
72C23×Dic10—31no—
73C2×C4×C5×D4—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C2×#4070—31no—
77C2×#4070—31no—
78D4×Dic10—316no—
79C2×#4034—31no—
80C2×#4034—31no—
81C2×#4024—31no—
82C2×#4024—31no—
83C2×#4024—31no—
84C2×#4024D311yescharacteristic, complemented
85C2×#4015—31no—
86C2×C4×Dic10—31no—
87C24×C3×C5C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15—24no—
92C22×Dic15C2314yes—
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C2×Dic30—24no—
98C2×Dic30C2314yes—
99C2×C5×#67Q818yescomplemented
100C2×C5×#67C2314yes—
101C22×C5×Dic3—24no—
102C22×C5×Dic3C2314yes—
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C22×C5×Dic3C2311yescharacteristic
106C2×C4×C5×D3—24no—
107C2×C4×C5×D3C2314yes—
108C22×C3×Dic5—24no—
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2314yes—
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×Dic10—24no—
115C2×C3×Dic10C2314yes—
116C2×#1204—24no—
117C2×#1204—24no—
118C2×#1204—24no—
119C2×#1204—24no—
120C2×#1204—232no—
121C2×#1204D418yescomplemented
122C2×#1204C2314yes—
123C2×#1204C2314yes—
124C2×#1204C2314yes—
125C2×#1204C2314yes—
126C2×#1204C2314yes—
127C2×D3×Dic5—24no—
128C2×D3×Dic5—24no—
129C2×D3×Dic5C2314yes—
130C2×D3×Dic5C2314yes—
131D3×Dic10—232no—
132C3×C5×C22⋊C4C2314yes—
133#6719C2314yes—
134C4⋊Dic15C2314yes—
135#6712C2314yes—
136#6712C2314yes—
137C5×(C2×D3)⋊C4C2314yes—
138C5×Dic3⋊C4C2314yes—
139C4×C5×Dic3C2314yes—
140C3×C22⋊Dic5C2314yes—
141C3×C4⋊Dic5C2314yes—
142C3×#683C2314yes—
143C3×#683C2314yes—
144Dic3⋊Dic5C2314yes—
145Dic3⋊Dic5C2314yes—
146Dic3⋊Dic5C2314yes—
147#6669C2314yes—
148#6668C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150(C2×D3)⋊Dic5C2314yes—
151Dic3×Dic5C2314yes—
152Dic3×Dic5C2314yes—
153C22×D3×Q8—51no—
154C23×Dic6—51no—
155C2×C3×C22⋊Q8—51no—
156C2×#944—51no—
157C2×C4×#67—51no—
158#5632—516no—
159C2×#897—51no—
160C2×#896—51no—
161C2×#896—51no—
162C2×#888—51no—
163C2×#888—51no—
164C2×#887—51no—
165C2×#67⋊C4—51no—
166C2×#67⋊C4D511yescharacteristic
167C2×#878—51no—
168C2×#878—51no—
169C22×C5×D4—31no—
170C23×C4×C5—31no—
171C23×C4×C5—31no—
172C23×Dic5—31no—
173C23×Dic5—31no—
174C23×Dic5—31no—
175C23×Dic5C2×D311yescharacteristic
176C22×Dic10—31no—
177C22×Dic10—31no—
178C22×Dic10—31no—
179C22×Dic10—31no—
180C22×Dic10—31no—
181C22×Dic10—31no—
182C22×Dic10—38no—
183C22×Dic10—38no—
184C22×Dic10—68no—
185C22×Dic10—68no—
186C22×Dic10C2×D311yescharacteristic
187C4×C5×D4—38no—
188C2×C5×C4⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4C2×D311yescharacteristic
191C2×C42×C5—31no—
192C2×C22⋊Dic5—31no—
193C2×C22⋊Dic5—31no—
194C2×C22⋊Dic5—31no—
195C2×C22⋊Dic5C2×D311yescharacteristic
196D4×Dic5—38no—
197D4×Dic5—38no—
198C2×C4⋊Dic5—31no—
199C2×C4⋊Dic5—31no—
200C2×C4⋊Dic5—31no—
201C2×C4⋊Dic5—31no—
202C2×C4⋊Dic5C2×D311yescharacteristic
203#4070—38no—
204#4070—38no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×#683—31no—
209C2×#683C2×D311yescharacteristic
210C2×#683C2×D311yescharacteristic
211C2×C4×Dic5—31no—
212C2×C4×Dic5—31no—
213#4034—38no—
214#4034—38no—
215#4024—38no—
216#4024—38no—
217#4024—38no—
218#4024C2×D318yescomplemented
219#4015—38no—
220C4×Dic10—38no—
221C2×D4×Q8—151noSylow
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5C2×Q814yescomplemented
225C23×C3×C5C2412yes—
226C23×C3×C5C2411yescharacteristic
227C22×C5×D3—22no—
228C22×C5×D3—22no—
229C22×C5×D3C2×Q814yescomplemented
230C22×C5×D3C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5C2412yes—
234C2×C3×C4×C5C2412yes—
235C2×Dic15—22no—
236C2×Dic15—22no—
237C2×Dic15—22no—
238C2×Dic15—28no—
239C2×Dic15C2×D414yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C2×Dic15C2412yes—
244Dic30—28no—
245C5×#67C2×Q8116yescomplemented
246C2×C5×Dic3—22no—
247C2×C5×Dic3—28no—
248C2×C5×Dic3C2×D414yes—
249C2×C5×Dic3C2×Q814yescomplemented
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C4×C5×D3—28no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5—28no—
258C2×C3×Dic5C2×D414yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C3×Dic10—28no—
264#1204—28no—
265#1204—28no—
266#1204—28no—
267#1204—28no—
268#1204C2×D4116yescomplemented
269D3×Dic5—28no—
270D3×Dic5—28no—
271C22×C3×Q8—51no—
272C23×C3×C4—51no—
273C22×#67C2×D511yescharacteristic
274C23×Dic3—51no—
275C23×Dic3C2×D511yescharacteristic
276C2×D3×Q8—58no—
277C2×D3×Q8—108no—
278C22×C4×D3—51no—
279C22×C4×D3—51no—
280C22×C4×D3C2×D511yescharacteristic
281C22×Dic6—51no—
282C22×Dic6—51no—
283C22×Dic6—58no—
284C22×Dic6—51no—
285C22×Dic6—51no—
286C22×Dic6—51no—
287C22×Dic6—51no—
288C22×Dic6—108no—
289C3×C22⋊Q8—58no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C22⋊C4C2×D511yescharacteristic
295C2×#217—51no—
296#944—58no—
297C4×#67—58no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×C4⋊Dic3—51no—
302C2×C4⋊Dic3—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×Dic3⋊C4—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4C2×D511yescharacteristic
310C2×C4×Dic3—51no—
311C2×C4×Dic3—51no—
312C2×C4×Dic3C2×D511yescharacteristic
313#897—58no—
314#896—58no—
315#896—58no—
316#888—58no—
317#888—58no—
318#887—58no—
319#67⋊C4—58no—
320#67⋊C4C2×D518yes—
321#878—58no—
322#878—58no—
323C24×C5—31no—
324C24×C5C22×D311yescharacteristic
325C2×C5×D4—38no—
326C2×C5×D4—34no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—34no—
331C22×C4×C5—34no—
332C22×C4×C5—64no—
333C22×C4×C5—64no—
334C22×C4×C5C22×D311yescharacteristic
335C22×C4×C5C22×D311yescharacteristic
336C22×Dic5—24no—
337C22×Dic5—31no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—34no—
343C22×Dic5—34no—
344C22×Dic5—64no—
345C22×Dic5—64no—
346C22×Dic5—64no—
347C22×Dic5C22×D311yescharacteristic
348C22×Dic5C22×D311yescharacteristic
349C22×Dic5C22×D311yescharacteristic
350C22×Dic5C22×D314yes—
351C22×Dic5C22×D311yescharacteristic
352C2×Dic10—24no—
353C2×Dic10—38no—
354C2×Dic10—34no—
355C2×Dic10—34no—
356C2×Dic10—34no—
357C2×Dic10—34no—
358C2×Dic10—34no—
359C2×Dic10—34no—
360C2×Dic10—632no—
361C2×Dic10—632no—
362C2×Dic10—64no—
363C2×Dic10—64no—
364C2×Dic10—64no—
365C2×Dic10—64no—
366C2×Dic10—64no—
367C2×Dic10C22×D314yes—
368C5×C4⋊C4—34no—
369C5×C22⋊C4—34no—
370C5×C22⋊C4C22×D314yes—
371C42×C5—34no—
372C22⋊Dic5—34no—
373C22⋊Dic5—34no—
374C22⋊Dic5—34no—
375C22⋊Dic5C22×D314yes—
376C4⋊Dic5—34no—
377C4⋊Dic5—34no—
378C4⋊Dic5—34no—
379C4⋊Dic5—34no—
380C4⋊Dic5C22×D314yes—
381#683—34no—
382#683—34no—
383#683—34no—
384#683—34no—
385#683C22×D314yes—
386#683C22×D314yes—
387C4×Dic5—34no—
388C4×Dic5—34no—
389C23×Q8—151no—
390C23×Q8—151no—
391D4×Q8—1516no—
392C2×C4⋊Q8—151no—
393C2×C4⋊Q8—151no—
394C2×C4⋊Q8—151no—
395C2×C22⋊Q8—51no—
396C2×C22⋊Q8—151no—
397C2×C22⋊Q8—151no—
398C2×C22⋊Q8—151no—
399C2×C22⋊Q8—151no—
400C2×C22⋊Q8—151no—
401C2×C4×Q8—151no—
402C2×C4×D4—31no—
403C2×C4×D4—151no—
404C2×C4×D4—151no—
405C22×C3×C5—28no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5C22×D412yes—
409C22×C3×C5C22×Q812yes—
410C22×C3×C5C22×Q814yescomplemented
411C22×C3×C52−1+412yes—
412C22×C3×C5C2511yescharacteristic
413C2×C5×D3—28no—
414C2×C5×D3—22no—
415C2×C5×D3—22no—
416C2×C5×D3C22×Q814yescomplemented
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419Dic15—22no—
420Dic15—22no—
421Dic15—22no—
422Dic15C22×D414yes—
423C3×Dic5—22no—
424C3×Dic5—22no—
425C3×Dic5—22no—
426C3×Dic5C22×D414yes—
427C5×Dic3—22no—
428C5×Dic3C22×D414yes—
429C5×Dic3C22×Q814yescomplemented
430C24×C3C22×D511yescharacteristic
431C23×D3C22×D511yescharacteristic
432C2×C3×Q8—54no—
433C2×C3×Q8—104no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×C3×C4—51no—
438C22×C3×C4—54no—
439C22×C3×C4—104no—
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C2×#67Dic1018yescomplemented
443C2×#67C22×D514yes—
444C22×Dic3—24no—
445C22×Dic3—51no—
446C22×Dic3—54no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—104no—
451C22×Dic3C22×D514yes—
452C22×Dic3C22×D511yescharacteristic
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455D3×Q8—1032no—
456C2×C4×D3—24no—
457C2×C4×D3—54no—
458C2×C4×D3—54no—
459C2×C4×D3—104no—
460C2×C4×D3—104no—
461C2×C4×D3C22×D514yes—
462C2×Dic6—58no—
463C2×Dic6—54no—
464C2×Dic6—54no—
465C2×Dic6—54no—
466C2×Dic6—54no—
467C2×Dic6—54no—
468C2×Dic6—54no—
469C2×Dic6—1032no—
470C2×Dic6—104no—
471C2×Dic6—104no—
472C2×Dic6—104no—
473C2×Dic6—104no—
474C2×Dic6—104no—
475C3×C4⋊C4—54no—
476C3×C4⋊C4—54no—
477C3×C4⋊C4—54no—
478C3×C22⋊C4—54no—
479C3×C22⋊C4C22×D514yes—
480#217—54no—
481(C2×D3)⋊C4—54no—
482(C2×D3)⋊C4—54no—
483(C2×D3)⋊C4C22×D514yes—
484C4⋊Dic3—54no—
485C4⋊Dic3—54no—
486Dic3⋊C4—54no—
487Dic3⋊C4—54no—
488Dic3⋊C4—54no—
489Dic3⋊C4—54no—
490Dic3⋊C4—54no—
491Dic3⋊C4—54no—
492Dic3⋊C4C22×D514yes—
493C4×Dic3—54no—
494C4×Dic3—54no—
495C4×Dic3C22×D514yes—
496C23×C5—22no—
497C23×C5—22no—
498C23×C5—34no—
499C23×C5—32no—
500C23×C5—62no—
501C23×C5—62no—
502C23×C5D3×Q814yescomplemented
503C23×C5C23×D312yes—
504C23×C5C23×D311yescharacteristic
505C5×D4—316no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—34no—
509C2×C4×C5—34no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—68no—
514C2×C4×C5—68no—
515C2×C4×C5—62no—
516C2×C4×C5C23×D312yes—
517C2×C4×C5C23×D312yes—
518C2×Dic5—22no—
519C2×Dic5—22no—
520C2×Dic5—22no—
521C2×Dic5—28no—
522C2×Dic5—34no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—68no—
528C2×Dic5—68no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5—62no—
532C2×Dic5—68no—
533C2×Dic5D3×D414yes—
534C2×Dic5C23×D312yes—
535C2×Dic5C23×D312yes—
536C2×Dic5C23×D312yes—
537C2×Dic5C23×D312yes—
538Dic10—28no—
539Dic10—316no—
540Dic10—68no—
541Dic10—68no—
542Dic10—68no—
543Dic10—68no—
544Dic10—68no—
545C22×Q8—51no—
546C22×Q8—151no—
547C22×Q8—151no—
548C22×Q8—151no—
549C22×Q8—151no—
550C22×Q8—151no—
551C22×Q8—158no—
552C22×Q8—158no—
553C22×Q8—151no—
554C22×Q8—308no—
555C22×Q8—308no—
556C22×D4—31no—
557C23×C4—31no—
558C23×C4—31no—
559C23×C4—51no—
560C23×C4—151no—
561C23×C4—151no—
562C23×C4—151no—
563C4⋊Q8—158no—
564C4⋊Q8—158no—
565C4⋊Q8—158no—
566C22⋊Q8—58no—
567C22⋊Q8—158no—
568C22⋊Q8—158no—
569C22⋊Q8—158no—
570C22⋊Q8—158no—
571C22⋊Q8—158no—
572C4×Q8—158no—
573C4×D4—38no—
574C4×D4—158no—
575C4×D4—158no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—51no—
578C2×C4⋊C4—51no—
579C2×C4⋊C4—51no—
580C2×C4⋊C4—151no—
581C2×C4⋊C4—151no—
582C2×C4⋊C4—151no—
583C2×C4⋊C4—151no—
584C2×C4⋊C4—151no—
585C2×C4⋊C4—151no—
586C2×C4⋊C4—151no—
587C2×C4⋊C4—151no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—51no—
590C2×C22⋊C4—151no—
591C2×C22⋊C4—151no—
592C2×C22⋊C4—151no—
593C2×C22⋊C4D3×D511yescharacteristic
594C2×C42—31no—
595C2×C42—151no—
596C2×C42—151no—
597C2×C3×C5—24no—
598C2×C3×C5D4×Q814yescomplemented
599C2×C3×C5C23×D411yescharacteristic
600C2×C3×C5C23×Q811yescharacteristic
601C2×C3×C5C2×2−1+411yescharacteristic
602C5×D3—24no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3C2×Dic1014yescomplemented
606C23×C3C23×D512yes—
607C23×C3C23×D511yescharacteristic
608C22×D3—22no—
609C22×D3—22no—
610C22×D3C2×Dic1014yescomplemented
611C22×D3C23×D512yes—
612C3×Q8—108no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—54no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—108no—
621C2×C3×C4—102no—
622C2×C3×C4—102no—
623C2×C3×C4—102no—
624C2×C3×C4C23×D512yes—
625C2×C3×C4C23×D512yes—
626#67C2×Dic10116yescomplemented
627C2×Dic3—22no—
628C2×Dic3—28no—
629C2×Dic3—54no—
630C2×Dic3—52no—
631C2×Dic3—52no—
632C2×Dic3—52no—
633C2×Dic3—52no—
634C2×Dic3—108no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3C2×Dic1014yescomplemented
639C2×Dic3D4×D514yes—
640C2×Dic3C23×D512yes—
641C2×Dic3C23×D512yes—
642C2×Dic3C23×D512yes—
643C4×D3—28no—
644C4×D3—108no—
645C4×D3—108no—
646Dic6—516no—
647Dic6—108no—
648Dic6—108no—
649Dic6—108no—
650Dic6—108no—
651Dic6—108no—
652C22×C5—28no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—34no—
656C22×C5—68no—
657C22×C5—62no—
658C22×C5—62no—
659C22×C5C2×D3×D412yes—
660C22×C5C2×D3×Q812yes—
661C22×C5C2×D3×Q814yescomplemented
662C22×C5#101012yes—
663C22×C5C24×D311yescharacteristic
664C4×C5—22no—
665C4×C5—22no—
666C4×C5—34no—
667C4×C5—34no—
668C4×C5—62no—
669Dic5—22no—
670Dic5—22no—
671Dic5—22no—
672Dic5—34no—
673Dic5—62no—
674Dic5—62no—
675Dic5—62no—
676Dic5C2×D3×D414yes—
677C24—31no—
678C24C2×D3×D511yescharacteristic
679C2×Q8—54no—
680C2×Q8—104no—
681C2×Q8—154no—
682C2×Q8—158no—
683C2×Q8—154no—
684C2×Q8—154no—
685C2×Q8—154no—
686C2×Q8—154no—
687C2×Q8—154no—
688C2×Q8—304no—
689C2×Q8—304no—
690C2×Q8—304no—
691C2×Q8—304no—
692C2×Q8—304no—
693C2×Q8—3032no—
694C2×Q8—3032no—
695C2×D4—38no—
696C2×D4—34no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—34no—
700C22×C4—31no—
701C22×C4—34no—
702C22×C4—51no—
703C22×C4—54no—
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—51no—
707C22×C4—64no—
708C22×C4—64no—
709C22×C4—104no—
710C22×C4—154no—
711C22×C4—154no—
712C22×C4—151no—
713C22×C4—154no—
714C22×C4—151no—
715C22×C4—151no—
716C22×C4—151no—
717C22×C4—304no—
718C22×C4—304no—
719C22×C4—304no—
720C22×C4C2×D3×D511yescharacteristic
721C22×C4C2×D3×D511yescharacteristic
722C4⋊C4—34no—
723C4⋊C4—54no—
724C4⋊C4—54no—
725C4⋊C4—54no—
726C4⋊C4—154no—
727C4⋊C4—154no—
728C4⋊C4—154no—
729C4⋊C4—154no—
730C4⋊C4—154no—
731C4⋊C4—154no—
732C4⋊C4—154no—
733C4⋊C4—154no—
734C22⋊C4—34no—
735C22⋊C4—54no—
736C22⋊C4—154no—
737C22⋊C4—154no—
738C22⋊C4—154no—
739C22⋊C4C2×D3×D514yes—
740C42—34no—
741C42—154no—
742C42—154no—
743C3×C5C2×D4×Q811yescharacteristic, complemented, Hall
744C22×C3—28no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3C22×Dic1012yes—
748C22×C3C22×Dic1014yescomplemented
749C22×C3C2×D4×D512yes—
750C22×C3#415012yes—
751C22×C3C24×D511yescharacteristic
752C2×D3—28no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3C22×Dic1014yescomplemented
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—54no—
759C3×C4—102no—
760C3×C4—102no—
761C3×C4—102no—
762Dic3—22no—
763Dic3—54no—
764Dic3—102no—
765Dic3—102no—
766Dic3—102no—
767Dic3C22×Dic1014yescomplemented
768Dic3C2×D4×D514yes—
769C2×C5—24no—
770C2×C5—64no—
771C2×C5#563214yescomplemented
772C2×C5C22×D3×D411yescharacteristic
773C2×C5C22×D3×Q811yescharacteristic
774C2×C5C2×#101011yescharacteristic
775C23—22no—
776C23—22no—
777C23—34no—
778C23—32no—
779C23—62no—
780C23—62no—
781C23D3×Dic1014yescomplemented
782C23C22×D3×D512yes—
783C23C22×D3×D511yescharacteristic
784Q8—108no—
785Q8—1516no—
786Q8—308no—
787Q8—308no—
788Q8—308no—
789Q8—308no—
790Q8—308no—
791D4—316no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—34no—
795C2×C4—34no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—54no—
800C2×C4—52no—
801C2×C4—52no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—68no—
805C2×C4—68no—
806C2×C4—62no—
807C2×C4—108no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—154no—
812C2×C4—152no—
813C2×C4—152no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—308no—
817C2×C4—308no—
818C2×C4—308no—
819C2×C4—302no—
820C2×C4—302no—
821C2×C4—302no—
822C2×C4C22×D3×D512yes—
823C2×C4C22×D3×D512yes—
824C2×C3—24no—
825C2×C3D4×Dic1014yescomplemented
826C2×C3C23×Dic1011yescharacteristic
827C2×C3C22×D4×D511yescharacteristic
828C2×C3C2×#415011yescharacteristic
829D3—24no—
830C5C2×#563211yescharacteristic, complemented, Sylow
831C22—28no—
832C22—22no—
833C22—22no—
834C22—34no—
835C22—68no—
836C22—62no—
837C22—62no—
838C22C2×D3×Dic1012yes—
839C22C2×D3×Dic1014yescomplemented
840C22#9202012yes—
841C22D3×D4×D512yes—
842C22C23×D3×D511yescharacteristic
843C4—22no—
844C4—22no—
845C4—34no—
846C4—34no—
847C4—54no—
848C4—62no—
849C4—102no—
850C4—102no—
851C4—102no—
852C4—154no—
853C4—302no—
854C4—302no—
855C4—302no—
856C3C2×D4×Dic1011yescharacteristic, complemented, Sylow
857C2—24no—
858C2—64no—
859C2#1175286114yesdirect product factor
860C2C22×D3×Dic1011yescharacteristic
861C2C2×#9202011yescharacteristic
862C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×D4×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
1. C23×#1204C2semidirect
2. C22×D3×Dic10C2semidirect
3. C2×#91767C2semidirect
5. C2×C3×#4024C2semidirect
6. C2×#91575C2semidirect
9. C2×#91469C2semidirect
10. C2×#91436C2semidirect
11. C2×#91417C2semidirect
12. C2×#91352C2semidirect
13. C2×#91328C2semidirect
14. C2×#91327C2semidirect
15. C2×#91324C2semidirect
16. #11752861C2direct (N × H)
31. C22×#1204C22semidirect
35. C2×D3×Dic10C22semidirect
41. #91767C22semidirect
50. C3×#4024C22semidirect
51. #91575C22semidirect
63. #91469C22semidirect
64. #91436C22semidirect
65. #91417C22semidirect
66. #91352C22semidirect
67. #91328C22semidirect
68. #91327C22semidirect
69. #91324C22semidirect
84. C2×#4024D3semidirect
99. C2×C5×#67Q8semidirect
121. C2×#1204D4semidirect
218. #4024C2×D3semidirect
224. C23×C3×C5C2×Q8semidirect
229. C22×C5×D3C2×Q8semidirect
245. C5×#67C2×Q8semidirect
249. C2×C5×Dic3C2×Q8semidirect
268. #1204C2×D4semidirect
410. C22×C3×C5C22×Q8semidirect
416. C2×C5×D3C22×Q8semidirect
429. C5×Dic3C22×Q8semidirect
442. C2×#67Dic10semidirect
502. C23×C5D3×Q8semidirect
598. C2×C3×C5D4×Q8semidirect
605. C23×C3C2×Dic10semidirect
610. C22×D3C2×Dic10semidirect
626. #67C2×Dic10semidirect
638. C2×Dic3C2×Dic10semidirect
661. C22×C5C2×D3×Q8semidirect
743. C3×C5C2×D4×Q8semidirect
748. C22×C3C22×Dic10semidirect
755. C2×D3C22×Dic10semidirect
767. Dic3C22×Dic10semidirect
771. C2×C5#5632semidirect
781. C23D3×Dic10semidirect
825. C2×C3D4×Dic10semidirect
830. C5C2×#5632semidirect
839. C22C2×D3×Dic10semidirect
856. C3C2×D4×Dic10semidirect
859. C2#11752861direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12042
C22×D3×Dic102
C2×#917672
C2×C5×#67⋊C42
C2×C3×#40242
C2×#915752
C2×#67⋊Dic52
C2×Dic5×#672
C2×#914692
C2×#914362
C2×#914172
C2×#913522
C2×#913282
C2×#913272
C2×#913242
#117528612
C2×D4×Dic103
C2×#56325