Finite Group Databasebeta

← C2×#11752860 #14482950

Subgroups — C2×#11752860 #14482950

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×D5×Dic6C211yesmaximal, characteristic, complemented
3C2×#91767C211yesmaximal, characteristic, complemented
4C2×C5×#878C211yesmaximal, characteristic, complemented
5C2×C3×#4027C211yesmaximal, characteristic
6C2×#91574C211yesmaximal, characteristic, complemented
7C2×#91559C211yesmaximal, characteristic
8C2×Dic3×C22⋊D5C211yesmaximal, characteristic
9C2×#91468C211yesmaximal, characteristic, complemented
10C2×#91430C211yesmaximal, characteristic, complemented
11C2×#91422C211yesmaximal, characteristic, complemented
12C2×#91349C211yesmaximal, characteristic, complemented
13C2×#91329C211yesmaximal, characteristic, complemented
14C2×#91328C211yesmaximal, characteristic, complemented
15C2×#91323C211yesmaximal, characteristic, complemented
16#11752860C2116yesmaximal, direct product factor
17C2×#65966—31nomaximal, Hall
18C23×Dic15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C22×C5×Dic6C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204—28no—
26C22×#1204C2211yescharacteristic
27C22×#1204C2211yescharacteristic
28C22×#1204C2211yescharacteristic
29C22×#1204C2211yescharacteristic
30C22×#1204C2211yescharacteristic
31C22×#1204C2218yescomplemented
32C22×D5×Dic3C2211yescharacteristic
33C22×D5×Dic3C2211yescharacteristic
34C2×D5×Dic6—28no—
35C2×D5×Dic6C2218yescomplemented
36C2×C3×C5×C22⋊C4C2211yescharacteristic
37C2×#6719C2211yescharacteristic
38C2×C4⋊Dic15C2211yescharacteristic
39C2×#6712C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41#91767C2218yescomplemented
42C2×C5×#217C2211yescharacteristic
43C2×C5×C4⋊Dic3C2211yescharacteristic
44C2×C5×Dic3⋊C4C2211yescharacteristic
45C2×C5×Dic3⋊C4C2211yescharacteristic
46C5×#878C2218yescomplemented
47C2×C3×#685C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic
49C2×C3×C4×Dic5C2211yescharacteristic
50C3×#4027C2218yes—
51#91574C2218yescomplemented
52#91559C2218yes—
53Dic3×C22⋊D5C2218yes—
54C2×Dic3⋊Dic5C2211yescharacteristic
55C2×#6669C2211yescharacteristic
56C2×#6668C2211yescharacteristic
57C2×#6668C2211yescharacteristic
58C2×#6668C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63#91468C2218yescomplemented
64#91430C2218yescomplemented
65#91422C2218yescomplemented
66#91349C2218yescomplemented
67#91329C2218yescomplemented
68#91328C2218yescomplemented
69#91323C2218yescomplemented
70C2×D4×Dic6—51nomaximal, Hall
71C22×Q8×D5—31no—
72C23×Dic10—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4090—31no—
75C2×C4×C22⋊D5—31no—
76#65966—316no—
77C2×#4043—31no—
78C2×#4042—31no—
79C2×#4042—31no—
80C2×#4034—31no—
81C2×#4034—31no—
82C2×#4033—31no—
83C2×#4027—31no—
84C2×#4027D311yescharacteristic
85C2×#4024—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
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—
99C22×C5×Dic3—24no—
100C22×C5×Dic3C2314yes—
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2311yescharacteristic
105C2×C5×Dic6—24no—
106C2×C5×Dic6C2314yes—
107C2×C3×C22⋊D5Q818yescomplemented
108C2×C3×C22⋊D5C2314yes—
109C22×C3×Dic5—24no—
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×C4×D5—24no—
115C2×C3×C4×D5C2314yes—
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×D5×Dic3—24no—
128C2×D5×Dic3—24no—
129C2×D5×Dic3C2314yes—
130C2×D5×Dic3C2314yes—
131D5×Dic6—232no—
132C3×C5×C22⋊C4C2314yes—
133#6719C2314yes—
134C4⋊Dic15C2314yes—
135#6712C2314yes—
136#6712C2314yes—
137C5×#217C2314yes—
138C5×C4⋊Dic3C2314yes—
139C5×Dic3⋊C4C2314yes—
140C5×Dic3⋊C4C2314yes—
141C3×#685C2314yes—
142C3×#683C2314yes—
143C3×C4×Dic5C2314yes—
144Dic3⋊Dic5C2314yes—
145#6669C2314yes—
146#6668C2314yes—
147#6668C2314yes—
148#6668C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151Dic3×Dic5C2314yes—
152Dic3×Dic5C2314yes—
153C23×Dic6—51no—
154C23×Dic6—51no—
155C2×C3×C4×D4—51no—
156C2×D4×Dic3—51no—
157C2×D4×Dic3—51no—
158C2×#924—51no—
159C2×#924—51no—
160D4×Dic6—516no—
161C2×#888—51no—
162C2×#888—51no—
163C2×#878—51no—
164C2×#878—51no—
165C2×#878—51no—
166C2×#878D511yescharacteristic, complemented
167C2×#869—51no—
168C2×C4×Dic6—51no—
169C22×C5×Q8—31no—
170C23×C4×C5—31no—
171C22×C22⋊D5C2×D311yescharacteristic
172C23×Dic5—31no—
173C23×Dic5C2×D311yescharacteristic
174C2×Q8×D5—38no—
175C2×Q8×D5—68no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×C4×D5C2×D311yescharacteristic
179C22×Dic10—31no—
180C22×Dic10—31no—
181C22×Dic10—31no—
182C22×Dic10—31no—
183C22×Dic10—31no—
184C22×Dic10—31no—
185C22×Dic10—38no—
186C22×Dic10—68no—
187C5×C22⋊Q8—38no—
188C2×C5×C4⋊C4—31no—
189C2×C5×C4⋊C4—31no—
190C2×C5×C4⋊C4—31no—
191C2×C5×C22⋊C4—31no—
192C2×C5×C22⋊C4C2×D311yescharacteristic
193C2×C22⋊Dic5—31no—
194#4090—38no—
195C4×C22⋊D5—38no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685C2×D311yescharacteristic
199C2×C4⋊Dic5—31no—
200C2×C4⋊Dic5—31no—
201C2×#683—31no—
202C2×#683—31no—
203C2×#683—31no—
204C2×#683—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic
208C2×C4×Dic5—31no—
209C2×C4×Dic5—31no—
210C2×C4×Dic5C2×D311yescharacteristic
211#4043—38no—
212#4042—38no—
213#4042—38no—
214#4034—38no—
215#4034—38no—
216#4033—38no—
217#4027—38no—
218#4027C2×D318yes—
219#4024—38no—
220#4024—38no—
221C2×D4×Q8—151noSylow
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5C2×Q814yescomplemented
225C23×C3×C5C2412yes—
226C23×C3×C5C2411yescharacteristic
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5C2×Q814yescomplemented
230C22×C3×D5C2412yes—
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—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—22no—
247C2×C5×Dic3—22no—
248C2×C5×Dic3—28no—
249C2×C5×Dic3C2×D414yes—
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C5×Dic6—28no—
255C3×C22⋊D5C2×Q8116yescomplemented
256C2×C3×Dic5—22no—
257C2×C3×Dic5—28no—
258C2×C3×Dic5C2×D414yes—
259C2×C3×Dic5C2×Q814yescomplemented
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C3×C4×D5—28no—
264#1204—28no—
265#1204—28no—
266#1204—28no—
267#1204—28no—
268#1204C2×D4116yescomplemented
269D5×Dic3—28no—
270D5×Dic3—28no—
271C22×C3×D4—51no—
272C23×C3×C4—51no—
273C23×C3×C4—51no—
274C23×Dic3—51no—
275C23×Dic3—51no—
276C23×Dic3—51no—
277C23×Dic3C2×D511yescharacteristic
278C22×Dic6—51no—
279C22×Dic6—51no—
280C22×Dic6—51no—
281C22×Dic6—51no—
282C22×Dic6—51no—
283C22×Dic6—51no—
284C22×Dic6—58no—
285C22×Dic6—58no—
286C22×Dic6—108no—
287C22×Dic6—108no—
288C22×Dic6C2×D511yescharacteristic
289C3×C4×D4—58no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4C2×D511yescharacteristic
293C2×C3×C42—51no—
294C2×#217—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×#217C2×D511yescharacteristic
298D4×Dic3—58no—
299D4×Dic3—58no—
300C2×C4⋊Dic3—51no—
301C2×C4⋊Dic3—51no—
302C2×C4⋊Dic3—51no—
303C2×C4⋊Dic3—51no—
304C2×C4⋊Dic3C2×D511yescharacteristic
305#924—58no—
306#924—58no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4C2×D511yescharacteristic
312C2×Dic3⋊C4C2×D511yescharacteristic
313C2×C4×Dic3—51no—
314C2×C4×Dic3—51no—
315#888—58no—
316#888—58no—
317#878—58no—
318#878—58no—
319#878—58no—
320#878C2×D518yescomplemented
321#869—58no—
322C4×Dic6—58no—
323C24×C5C22×D311yescharacteristic
324C23×D5C22×D311yescharacteristic
325C2×C5×Q8—34no—
326C2×C5×Q8—64no—
327C22×C4×C5—31no—
328C22×C4×C5—31no—
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—34no—
332C22×C4×C5—64no—
333C22×C4×C5C22×D311yescharacteristic
334C22×C4×C5C22×D311yescharacteristic
335C2×C22⋊D5Dic618yescomplemented
336C2×C22⋊D5C22×D314yes—
337C22×Dic5—24no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—31no—
343C22×Dic5—64no—
344C22×Dic5C22×D314yes—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348Q8×D5—632no—
349C2×C4×D5—24no—
350C2×C4×D5—34no—
351C2×C4×D5—34no—
352C2×C4×D5—64no—
353C2×C4×D5—64no—
354C2×C4×D5C22×D314yes—
355C2×Dic10—38no—
356C2×Dic10—34no—
357C2×Dic10—34no—
358C2×Dic10—34no—
359C2×Dic10—34no—
360C2×Dic10—34no—
361C2×Dic10—34no—
362C2×Dic10—632no—
363C2×Dic10—64no—
364C2×Dic10—64no—
365C2×Dic10—64no—
366C2×Dic10—64no—
367C2×Dic10—64no—
368C5×C4⋊C4—34no—
369C5×C4⋊C4—34no—
370C5×C4⋊C4—34no—
371C5×C22⋊C4—34no—
372C5×C22⋊C4C22×D314yes—
373C22⋊Dic5—34no—
374#685—34no—
375#685—34no—
376#685C22×D314yes—
377C4⋊Dic5—34no—
378C4⋊Dic5—34no—
379#683—34no—
380#683—34no—
381#683—34no—
382#683—34no—
383#683—34no—
384#683—34no—
385#683C22×D314yes—
386C4×Dic5—34no—
387C4×Dic5—34no—
388C4×Dic5C22×D314yes—
389C23×Q8—151no—
390C23×Q8—151no—
391D4×Q8—1516no—
392C2×C4⋊Q8—151no—
393C2×C4⋊Q8—151no—
394C2×C4⋊Q8—151no—
395C2×C22⋊Q8—31no—
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—51no—
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×C3×D5—28no—
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5C22×Q814yescomplemented
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419Dic15—22no—
420Dic15—22no—
421Dic15—22no—
422Dic15C22×D414yes—
423C3×Dic5—22no—
424C3×Dic5C22×D414yes—
425C3×Dic5C22×Q814yescomplemented
426C5×Dic3—22no—
427C5×Dic3—22no—
428C5×Dic3—22no—
429C5×Dic3C22×D414yes—
430C24×C3—51no—
431C24×C3C22×D511yescharacteristic
432C2×C3×D4—58no—
433C2×C3×D4—54no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×C3×C4—54no—
438C22×C3×C4—54no—
439C22×C3×C4—104no—
440C22×C3×C4—104no—
441C22×C3×C4C22×D511yescharacteristic
442C22×C3×C4C22×D511yescharacteristic
443C22×Dic3—24no—
444C22×Dic3—51no—
445C22×Dic3—54no—
446C22×Dic3—51no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—54no—
450C22×Dic3—54no—
451C22×Dic3—104no—
452C22×Dic3—104no—
453C22×Dic3—104no—
454C22×Dic3C22×D514yes—
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D511yescharacteristic
457C22×Dic3C22×D511yescharacteristic
458C22×Dic3C22×D511yescharacteristic
459C2×Dic6—24no—
460C2×Dic6—58no—
461C2×Dic6—54no—
462C2×Dic6—54no—
463C2×Dic6—54no—
464C2×Dic6—54no—
465C2×Dic6—54no—
466C2×Dic6—54no—
467C2×Dic6—1032no—
468C2×Dic6—1032no—
469C2×Dic6—104no—
470C2×Dic6—104no—
471C2×Dic6—104no—
472C2×Dic6—104no—
473C2×Dic6—104no—
474C2×Dic6C22×D514yes—
475C3×C4⋊C4—54no—
476C3×C22⋊C4—54no—
477C3×C22⋊C4C22×D514yes—
478C3×C42—54no—
479#217—54no—
480#217—54no—
481#217—54no—
482#217C22×D514yes—
483C4⋊Dic3—54no—
484C4⋊Dic3—54no—
485C4⋊Dic3—54no—
486C4⋊Dic3—54no—
487C4⋊Dic3C22×D514yes—
488Dic3⋊C4—54no—
489Dic3⋊C4—54no—
490Dic3⋊C4—54no—
491Dic3⋊C4—54no—
492Dic3⋊C4C22×D514yes—
493Dic3⋊C4C22×D514yes—
494C4×Dic3—54no—
495C4×Dic3—54no—
496C23×C5—22no—
497C23×C5—22no—
498C23×C5C2×Dic614yescomplemented
499C23×C5C23×D312yes—
500C23×C5C23×D311yescharacteristic
501C22×D5—22no—
502C22×D5—22no—
503C22×D5C2×Dic614yescomplemented
504C22×D5C23×D312yes—
505C5×Q8—68no—
506C2×C4×C5—22no—
507C2×C4×C5—22no—
508C2×C4×C5—34no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—68no—
514C2×C4×C5—62no—
515C2×C4×C5—62no—
516C2×C4×C5—62no—
517C2×C4×C5C23×D312yes—
518C2×C4×C5C23×D312yes—
519C22⋊D5C2×Dic6116yescomplemented
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—62no—
529C2×Dic5—62no—
530C2×Dic5—62no—
531C2×Dic5C2×Dic614yescomplemented
532C2×Dic5D3×D414yes—
533C2×Dic5C23×D312yes—
534C2×Dic5C23×D312yes—
535C2×Dic5C23×D312yes—
536C4×D5—28no—
537C4×D5—68no—
538C4×D5—68no—
539Dic10—316no—
540Dic10—68no—
541Dic10—68no—
542Dic10—68no—
543Dic10—68no—
544Dic10—68no—
545C22×Q8—31no—
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—51no—
557C23×C4—31no—
558C23×C4—51no—
559C23×C4—51no—
560C23×C4—151no—
561C23×C4—151no—
562C23×C4—151no—
563C4⋊Q8—158no—
564C4⋊Q8—158no—
565C4⋊Q8—158no—
566C22⋊Q8—38no—
567C22⋊Q8—158no—
568C22⋊Q8—158no—
569C22⋊Q8—158no—
570C22⋊Q8—158no—
571C22⋊Q8—158no—
572C4×Q8—158no—
573C4×D4—58no—
574C4×D4—158no—
575C4×D4—158no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—31no—
578C2×C4⋊C4—31no—
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—51no—
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
602C3×D5—24no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—54no—
606C23×C3—52no—
607C23×C3—102no—
608C23×C3—102no—
609C23×C3Q8×D514yescomplemented
610C23×C3C23×D512yes—
611C23×C3C23×D511yescharacteristic
612C3×D4—516no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—54no—
616C2×C3×C4—54no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—108no—
621C2×C3×C4—108no—
622C2×C3×C4—102no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625C2×Dic3—22no—
626C2×Dic3—22no—
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—108no—
636C2×Dic3—102no—
637C2×Dic3—102no—
638C2×Dic3—102no—
639C2×Dic3—108no—
640C2×Dic3D4×D514yes—
641C2×Dic3C23×D512yes—
642C2×Dic3C23×D512yes—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645Dic6—28no—
646Dic6—516no—
647Dic6—108no—
648Dic6—108no—
649Dic6—108no—
650Dic6—108no—
651Dic6—108no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—28no—
655C22×C5C22×Dic612yes—
656C22×C5C22×Dic614yescomplemented
657C22×C5C2×D3×D412yes—
658C22×C5#101012yes—
659C22×C5C24×D311yescharacteristic
660C2×D5—22no—
661C2×D5—22no—
662C2×D5—28no—
663C2×D5C22×Dic614yescomplemented
664C4×C5—22no—
665C4×C5—22no—
666C4×C5—34no—
667C4×C5—62no—
668C4×C5—62no—
669C4×C5—62no—
670Dic5—22no—
671Dic5—34no—
672Dic5—62no—
673Dic5—62no—
674Dic5—62no—
675Dic5C22×Dic614yescomplemented
676Dic5C2×D3×D414yes—
677C24—51no—
678C24C2×D3×D511yescharacteristic
679C2×Q8—34no—
680C2×Q8—64no—
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—58no—
696C2×D4—54no—
697C22×C4—31no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—54no—
705C22×C4—51no—
706C22×C4—54no—
707C22×C4—64no—
708C22×C4—104no—
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—34no—
724C4⋊C4—34no—
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—54no—
741C42—154no—
742C42—154no—
743C3×C5C2×D4×Q811yescharacteristic, complemented, Hall
744C22×C3—28no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—54no—
748C22×C3—108no—
749C22×C3—102no—
750C22×C3—102no—
751C22×C3C2×D4×D512yes—
752C22×C3C2×Q8×D512yes—
753C22×C3C2×Q8×D514yescomplemented
754C22×C3#415012yes—
755C22×C3C24×D511yescharacteristic
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—54no—
759C3×C4—54no—
760C3×C4—102no—
761Dic3—22no—
762Dic3—22no—
763Dic3—22no—
764Dic3—54no—
765Dic3—102no—
766Dic3—102no—
767Dic3—102no—
768Dic3C2×D4×D514yes—
769C2×C5—24no—
770C2×C5D4×Dic614yescomplemented
771C2×C5C23×Dic611yescharacteristic
772C2×C5C22×D3×D411yescharacteristic
773C2×C5C2×#101011yescharacteristic
774D5—24no—
775C23—22no—
776C23—22no—
777C23—54no—
778C23—52no—
779C23—102no—
780C23—102no—
781C23D5×Dic614yescomplemented
782C23C22×D3×D512yes—
783C23C22×D3×D511yescharacteristic
784Q8—68no—
785Q8—1516no—
786Q8—308no—
787Q8—308no—
788Q8—308no—
789Q8—308no—
790Q8—308no—
791D4—516no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—34no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—54no—
800C2×C4—54no—
801C2×C4—52no—
802C2×C4—52no—
803C2×C4—52no—
804C2×C4—68no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4—108no—
809C2×C4—108no—
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×C3—104no—
826C2×C3#6596614yescomplemented
827C2×C3C22×D4×D511yescharacteristic
828C2×C3C22×Q8×D511yescharacteristic
829C2×C3C2×#415011yescharacteristic
830C5C2×D4×Dic611yescharacteristic, complemented, Sylow
831C22—28no—
832C22—22no—
833C22—22no—
834C22—54no—
835C22—108no—
836C22—102no—
837C22—102no—
838C22C2×D5×Dic612yes—
839C22C2×D5×Dic614yescomplemented
840C22#9202012yes—
841C22D3×D4×D512yes—
842C22C23×D3×D511yescharacteristic
843C4—22no—
844C4—22no—
845C4—34no—
846C4—54no—
847C4—54no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—102no—
852C4—154no—
853C4—302no—
854C4—302no—
855C4—302no—
856C3C2×#6596611yescharacteristic, complemented, Sylow
857C2—24no—
858C2—104no—
859C2#1175286014yesdirect product factor
860C2C22×D5×Dic611yescharacteristic
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×C3×C22⋊D5C22
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×D5×Dic6C2semidirect
3. C2×#91767C2semidirect
4. C2×C5×#878C2semidirect
6. C2×#91574C2semidirect
9. C2×#91468C2semidirect
10. C2×#91430C2semidirect
11. C2×#91422C2semidirect
12. C2×#91349C2semidirect
13. C2×#91329C2semidirect
14. C2×#91328C2semidirect
15. C2×#91323C2semidirect
16. #11752860C2direct (N × H)
31. C22×#1204C22semidirect
35. C2×D5×Dic6C22semidirect
41. #91767C22semidirect
46. C5×#878C22semidirect
51. #91574C22semidirect
63. #91468C22semidirect
64. #91430C22semidirect
65. #91422C22semidirect
66. #91349C22semidirect
67. #91329C22semidirect
68. #91328C22semidirect
69. #91323C22semidirect
107. C2×C3×C22⋊D5Q8semidirect
121. C2×#1204D4semidirect
166. C2×#878D5semidirect
224. C23×C3×C5C2×Q8semidirect
229. C22×C3×D5C2×Q8semidirect
255. C3×C22⋊D5C2×Q8semidirect
259. C2×C3×Dic5C2×Q8semidirect
268. #1204C2×D4semidirect
320. #878C2×D5semidirect
335. C2×C22⋊D5Dic6semidirect
410. C22×C3×C5C22×Q8semidirect
416. C2×C3×D5C22×Q8semidirect
425. C3×Dic5C22×Q8semidirect
498. C23×C5C2×Dic6semidirect
503. C22×D5C2×Dic6semidirect
519. C22⋊D5C2×Dic6semidirect
531. C2×Dic5C2×Dic6semidirect
598. C2×C3×C5D4×Q8semidirect
609. C23×C3Q8×D5semidirect
656. C22×C5C22×Dic6semidirect
663. C2×D5C22×Dic6semidirect
675. Dic5C22×Dic6semidirect
743. C3×C5C2×D4×Q8semidirect
753. C22×C3C2×Q8×D5semidirect
770. C2×C5D4×Dic6semidirect
781. C23D5×Dic6semidirect
826. C2×C3#65966semidirect
830. C5C2×D4×Dic6semidirect
839. C22C2×D5×Dic6semidirect
856. C3C2×#65966semidirect
859. C2#11752860direct (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×D5×Dic62
C2×#917672
C2×C5×#8782
C2×C3×#40272
C2×#915742
C2×#915592
C2×Dic3×C22⋊D52
C2×#914682
C2×#914302
C2×#914222
C2×#913492
C2×#913292
C2×#913282
C2×#913232
#117528602
C2×#659663
C2×D4×Dic65