Finite Group Databasebeta

← D3×#65097 #14423366

Subgroups — D3×#65097 #14423366

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Q8×D5C211yesmaximal, characteristic
2C2×D3×#689C211yesmaximal, characteristic, complemented
3C2×D3×Dic20C211yesmaximal, characteristic, complemented
4D3×#4043C211yesmaximal, characteristic
5#11750910C211yesmaximal, characteristic, complemented
6C5×D3×#103C211yesmaximal, characteristic, complemented
7C3×#65097C211yesmaximal, characteristic, complemented
8#11749310C211yesmaximal, characteristic, complemented
9#11749291C211yesmaximal, characteristic, complemented
10#11748130C211yesmaximal, characteristic, complemented
11#11748126C211yesmaximal, characteristic, complemented
12D3×#3952C211yesmaximal, characteristic
13#11747496C211yesmaximal, characteristic, complemented
14#11747492C211yesmaximal, characteristic, complemented
15D3×#3942C211yesmaximal, characteristic, complemented
16C2×#65097—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20D3×Q8×D5—24no—
21D3×Q8×D5—24no—
22C2×C4×D3×D5—21no—
23C2×C4×D3×D5C2211yescharacteristic
24C2×D15⋊Q8—21no—
25C2×D15⋊Q8C2211yescharacteristic
26C2×D3×Dic10—21no—
27C2×D3×Dic10C2211yescharacteristic
28C2×D3×Dic10C2211yescharacteristic
29C2×D5×Dic6—21no—
30C2×D5×Dic6C2211yescharacteristic
31C2×#6718C2211yescharacteristic, complemented
32C2×Dic60C2211yescharacteristic, complemented
33#91786C2211yescharacteristic
34C2×C5×D3×C8C2211yescharacteristic
35C5×D3×C4⋊C4C2211yescharacteristic
36C2×C3×#689C2211yescharacteristic, complemented
37C2×C3×Dic20C2211yescharacteristic, complemented
38C3×#4043C2211yescharacteristic
39D3×#689—24no—
40D3×#685—21no—
41#91429—21no—
42D3×C4⋊Dic5—21no—
43#91422—21no—
44#91390C2211yescharacteristic
45#91360C2211yescharacteristic
46C2×#6663C2211yescharacteristic, complemented
47C2×#6662C2211yescharacteristic, complemented
48C2×#6662C2211yescharacteristic, complemented
49C2×#6661C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic
51D3×Dic20—24no—
52C3×C5×#103C2211yescharacteristic, complemented
53#91104C2211yescharacteristic
54#91094C2211yescharacteristic, complemented
55C5×#835C2211yescharacteristic, complemented
56C5×#816C2211yescharacteristic, complemented
57C5×#810C2211yescharacteristic, complemented
58C3×#3952C2211yescharacteristic
59C3×#3942C2211yescharacteristic, complemented
60#90975C2211yescharacteristic, complemented
61#90970C2211yescharacteristic, complemented
62#90957C2211yescharacteristic
63#90955C2211yescharacteristic
64D3×#451—51nomaximal, Hall
65C22×Q8×D5—31no—
66C22×#689—31no—
67C22×Dic20—31no—
68C2×#4043—31no—
69C2×C5×#103—31no—
70C2×#3952—31no—
71C2×#3942—31no—
72#65097—31no—
73#65097—31no—
74#65097—31no—
75#65097—31no—
76#65097—31no—
77#65097—31no—
78#65097—31no—
79#65097D311yescharacteristic, direct product factor
80C22×D3×D5D411yescharacteristic
81C2×C3×C5×Q8C2311yescharacteristic
82Q8×D15—22no—
83Q8×D15—22no—
84C2×C4×D15—21no—
85C2×C4×D15C2311yescharacteristic
86C2×Dic30—21no—
87C2×Dic30C2311yescharacteristic
88C2×Dic30C2311yescharacteristic
89C5×D3×Q8—22no—
90C5×D3×Q8D414yes—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3—21no—
93C2×C4×C5×D3C2311yescharacteristic
94C2×C5×Dic6—21no—
95C2×C5×Dic6C2311yescharacteristic
96C3×Q8×D5—22no—
97C3×Q8×D5—22no—
98C2×C3×C4×D5—21no—
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10—21no—
101C2×C3×Dic10C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103C2×#1204—21no—
104C2×#1204—21no—
105C2×#1204—21no—
106C2×#1204—21no—
107C2×#1200—21no—
108C2×#1200D411yescharacteristic
109C2×D3×Dic5—21no—
110C2×D3×Dic5—21no—
111C2×D3×Dic5D411yescharacteristic
112C2×D5×Dic3—21no—
113C2×D5×Dic3D411yescharacteristic
114C4×D3×D5—28no—
115C4×D3×D5—22no—
116C4×D3×D5—22no—
117D15⋊Q8—28no—
118D15⋊Q8—22no—
119D15⋊Q8—22no—
120D3×Dic10—28no—
121D3×Dic10—22no—
122D3×Dic10—22no—
123D3×Dic10—22no—
124D3×Dic10D414yes—
125D5×Dic6—28no—
126D5×Dic6—22no—
127D5×Dic6—22no—
128C2×C3×C5×C8C2311yescharacteristic
129C3×C5×C4⋊C4C2311yescharacteristic
130#6718—22no—
131#6714—21no—
132C4⋊Dic15—21no—
133C2×C3⋊#168C2311yescharacteristic
134Dic60—22no—
135C5×C4⋊Dic3C2311yescharacteristic
136C5×Dic3⋊C4—21no—
137C2×C5×C3⋊C8C2311yescharacteristic
138C5×D3×C8—22no—
139C3×#689—22no—
140C3×#685—21no—
141C3×C4⋊Dic5—21no—
142C2×C3×#168C2311yescharacteristic
143C3×Dic20—22no—
144Dic3⋊Dic5—21no—
145Dic3⋊Dic5—21no—
146#6667—21no—
147#6665—21no—
148#6663—22no—
149#6662—22no—
150#6662—22no—
151#6661—22no—
152D3×#168—22no—
153C22×D3×Q8—51no—
154C2×D3×Q16—51no—
155C2×D3×Q16—51no—
156D3×C22⋊Q8—51no—
157C3×#451—51no—
158#5228—51no—
159#5186—51no—
160#5186—51no—
161#5050—51no—
162#4809—51no—
163#4809—51no—
164D3×#103—51no—
165D3×#103D511yescharacteristic, complemented
166#4739—51no—
167D3×C22⋊C8—51no—
168C22×C5×Q8—31no—
169C2×Q8×D5—31no—
170C2×Q8×D5—31no—
171C2×Q8×D5—31no—
172C2×Q8×D5—61no—
173C2×Q8×D5—64no—
174C2×Q8×D5—61no—
175C2×Q8×D5—64no—
176C2×Q8×D5C2×D311yescharacteristic
177C22×C4×D5—31no—
178C22×C4×D5—61no—
179C22×Dic10—31no—
180C22×Dic10—31no—
181C22×Dic10—61no—
182C22×C5×C8—31no—
183C2×C5×C4⋊C4—31no—
184C2×#689—31no—
185C2×#689—31no—
186C2×#689—31no—
187C2×#689—64no—
188C2×#689C2×D311yescharacteristic, complemented
189C2×#685—61no—
190C2×C4⋊Dic5—61no—
191C22×#168—31no—
192C2×Dic20—31no—
193C2×Dic20—31no—
194C2×Dic20—31no—
195C2×Dic20—64no—
196C2×Dic20C2×D311yescharacteristic, complemented
197#4043—31no—
198#4043—31no—
199#4043—31no—
200#4043—61no—
201#4043—61no—
202#4043C2×D311yescharacteristic
203C5×#103—31no—
204C5×#103—31no—
205C5×#103—31no—
206C5×#103C2×D311yescharacteristic, complemented
207#3952—31no—
208#3952—31no—
209#3952—31no—
210#3952C2×D311yescharacteristic
211#3942—31no—
212#3942—31no—
213#3942—31no—
214#3942C2×D311yescharacteristic, complemented
215C2×#451—151noSylow
216C22×D15C2×D411yescharacteristic
217C22×C5×D3C2×D411yescharacteristic
218C22×C3×D5C2×D411yescharacteristic
219C2×D3×D5—22no—
220C2×D3×D5—22no—
221C2×D3×D5Q1614yescomplemented
222C3×C5×Q8—21no—
223C3×C5×Q8C2×D412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5C2411yescharacteristic
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15C2×D411yescharacteristic
230C4×D15—24no—
231C4×D15—21no—
232C4×D15—21no—
233Dic30—24no—
234Dic30—21no—
235Dic30—21no—
236Dic30—21no—
237Dic30C2×D412yes—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3C2×D411yescharacteristic
241C4×C5×D3—24no—
242C4×C5×D3—42no—
243C4×C5×D3C2×D412yes—
244C4×C5×D3C2×D412yes—
245C5×Dic6—21no—
246C5×Dic6—24no—
247C5×Dic6C2×D412yes—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5C2×D411yescharacteristic
251C3×C4×D5—24no—
252C3×C4×D5—21no—
253C3×C4×D5—21no—
254C3×Dic10—24no—
255C3×Dic10—21no—
256C3×Dic10—21no—
257C3×Dic10—21no—
258C3×Dic10C2×D412yes—
259#1204—24no—
260#1204—24no—
261#1204—24no—
262#1204—42no—
263#1200—24no—
264#1200—22no—
265D3×Dic5—22no—
266D3×Dic5—24no—
267D3×Dic5—42no—
268D5×Dic3—24no—
269D5×Dic3—22no—
270C3×C5×C8—21no—
271C3⋊#168—21no—
272C3×#168—21no—
273C5×C3⋊C8—21no—
274C22×C3×Q8—51no—
275C2×D3×Q8—51no—
276C2×D3×Q8—51no—
277C2×D3×Q8—51no—
278C2×D3×Q8—51no—
279C2×D3×Q8—101no—
280C2×D3×Q8—101no—
281C2×D3×Q8—104no—
282C2×D3×Q8—104no—
283C2×D3×Q8C2×D511yescharacteristic
284C22×C4×D3—51no—
285C22×C4×D3—101no—
286C22×Dic6—51no—
287C22×Dic6—101no—
288C2×C3×Q16—51no—
289C2×C3×Q16—51no—
290C3×C22⋊Q8—51no—
291#946—51no—
292C2×#216—51no—
293C2×#216—51no—
294C2×#216—51no—
295C2×#216—51no—
296#924—51no—
297D3×Q16—104no—
298D3×Q16—104no—
299C2×Dic12—51no—
300C2×Dic12—51no—
301C2×D3×C8—51no—
302C2×D3×C8C2×D511yescharacteristic
303#897—51no—
304#896—101no—
305D3×C4⋊C4—101no—
306D3×C4⋊C4C2×D511yescharacteristic
307D3×C22⋊C4—101no—
308#878—101no—
309C3×#103—51no—
310C3×#103C2×D511yescharacteristic, complemented
311C3×C22⋊C8—51no—
312#835—51no—
313#835C2×D511yescharacteristic, complemented
314#830—51no—
315(C2×D3)⋊C8—51no—
316(C2×D3)⋊C8—51no—
317#816—51no—
318#816C2×D511yescharacteristic, complemented
319#810—51no—
320#810C2×D511yescharacteristic, complemented
321C23×D5—31no—
322C2×C5×Q8—34no—
323C2×C5×Q8—31no—
324C2×C5×Q8—61no—
325C2×C5×Q8—62no—
326C2×C5×Q8C22×D311yescharacteristic
327C22×C4×C5—31no—
328C22×C4×C5—61no—
329C22×C4×C5—61no—
330C22×Dic5—31no—
331C22×Dic5—61no—
332C22×Dic5—61no—
333Q8×D5—22no—
334Q8×D5—22no—
335Q8×D5—62no—
336Q8×D5—68no—
337Q8×D5—62no—
338Q8×D5—62no—
339Q8×D5—62no—
340Q8×D5—68no—
341Q8×D5—62no—
342Q8×D5—62no—
343C2×C4×D5—21no—
344C2×C4×D5—31no—
345C2×C4×D5—31no—
346C2×C4×D5—31no—
347C2×C4×D5—62no—
348C2×C4×D5—62no—
349C2×C4×D5—68no—
350C2×C4×D5—61no—
351C2×C4×D5—61no—
352C2×C4×D5—61no—
353C2×C4×D5C22×D311yescharacteristic
354C2×Dic10—21no—
355C2×Dic10—31no—
356C2×Dic10—34no—
357C2×Dic10—31no—
358C2×Dic10—62no—
359C2×Dic10—68no—
360C2×Dic10—62no—
361C2×Dic10—62no—
362C2×Dic10—61no—
363C2×Dic10—61no—
364C2×Dic10—61no—
365C2×Dic10—61no—
366C2×Dic10—61no—
367C2×Dic10C22×D311yescharacteristic
368C2×Dic10C22×D311yescharacteristic
369C2×C5×C8—31no—
370C2×C5×C8—62no—
371C2×C5×C8C22×D311yescharacteristic
372C5×C4⋊C4—31no—
373C5×C4⋊C4—61no—
374C5×C4⋊C4C22×D311yescharacteristic
375#689—22no—
376#689—62no—
377#689—62no—
378#689—62no—
379#685—21no—
380#685—61no—
381#685—61no—
382#685—61no—
383C4⋊Dic5—21no—
384C4⋊Dic5—61no—
385C4⋊Dic5—61no—
386C4⋊Dic5—61no—
387C2×#168—31no—
388C2×#168—62no—
389C2×#168C22×D311yescharacteristic
390Dic20—22no—
391Dic20—62no—
392Dic20—62no—
393Dic20—62no—
394C23×Q8—151no—
395C22×Q16—151no—
396C22×Q16—151no—
397C2×C22⋊Q8—151no—
398#451—51no—
399#451—151no—
400#451—151no—
401#451—151no—
402#451—151no—
403#451—151no—
404#451—151no—
405#451—151no—
406C2×#103—31no—
407C2×#103—151no—
408C2×C22⋊C8—151no—
409C22×C3×C5C22×D411yescharacteristic
410C2×D15—21no—
411C2×D15—21no—
412C2×D15C2×Q1612yescomplemented
413C2×C5×D3#12012yes—
414C2×C5×D3C2×Q1612yes—
415C2×C5×D3#13712yes—
416C2×C3×D5—21no—
417C2×C3×D5—21no—
418C2×C3×D5C2×Q1612yescomplemented
419D3×D5—28no—
420C3×C4×C5—22no—
421C3×C4×C5—41no—
422C3×C4×C5C22×D411yescharacteristic
423C3×C4×C5C22×D411yescharacteristic
424Dic15—21no—
425Dic15—22no—
426Dic15—41no—
427C3×Dic5—21no—
428C3×Dic5—22no—
429C3×Dic5—41no—
430C5×Dic3—22no—
431C5×Dic3—41no—
432C5×Dic3#12012yes—
433C23×D3—51no—
434C2×C3×Q8—51no—
435C2×C3×Q8—51no—
436C2×C3×Q8—101no—
437C2×C3×Q8—102no—
438C2×C3×Q8—102no—
439C2×C3×Q8C22×D511yescharacteristic
440C22×C3×C4—51no—
441C22×C3×C4—101no—
442C22×Dic3—51no—
443C22×Dic3—101no—
444D3×Q8—22no—
445D3×Q8—54no—
446D3×Q8—102no—
447D3×Q8—108no—
448D3×Q8—102no—
449D3×Q8—108no—
450D3×Q8—102no—
451D3×Q8—102no—
452D3×Q8—102no—
453D3×Q8—102no—
454D3×Q8—102no—
455D3×Q8D2014yes—
456C2×C4×D3—21no—
457C2×C4×D3—21no—
458C2×C4×D3—51no—
459C2×C4×D3—51no—
460C2×C4×D3—51no—
461C2×C4×D3—108no—
462C2×C4×D3—101no—
463C2×C4×D3—101no—
464C2×C4×D3—101no—
465C2×C4×D3—102no—
466C2×C4×D3—102no—
467C2×C4×D3—101no—
468C2×C4×D3C22×D511yescharacteristic
469C2×Dic6—21no—
470C2×Dic6—51no—
471C2×Dic6—51no—
472C2×Dic6—102no—
473C2×Dic6—108no—
474C2×Dic6—101no—
475C2×Dic6—101no—
476C2×Dic6—101no—
477C2×Dic6—101no—
478C2×Dic6—102no—
479C2×Dic6—101no—
480C2×Dic6C22×D511yescharacteristic
481C3×Q16—102no—
482C3×Q16—102no—
483C2×C3×C8—51no—
484C2×C3×C8C22×D511yescharacteristic
485C3×C4⋊C4—101no—
486C3×C4⋊C4C22×D511yescharacteristic
487C3×C22⋊C4—101no—
488#217—101no—
489#216—102no—
490#216—102no—
491#216—102no—
492#216—102no—
493(C2×D3)⋊C4—101no—
494(C2×D3)⋊C4—101no—
495C4⋊Dic3—101no—
496C4⋊Dic3C22×D511yescharacteristic
497Dic3⋊C4—21no—
498Dic3⋊C4—101no—
499Dic3⋊C4—101no—
500C2×C3⋊C8—51no—
501C2×C3⋊C8C22×D511yescharacteristic
502Dic12—102no—
503Dic12—102no—
504D3×C8—22no—
505D3×C8—102no—
506C23×C5—31no—
507C22×D5—31no—
508C22×D5—34no—
509C22×D5—62no—
510C22×D5—62no—
511C22×D5D3×D411yescharacteristic
512C5×Q8—21no—
513C5×Q8—32no—
514C5×Q8—64no—
515C5×Q8—61no—
516C5×Q8D3×D412yes—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—31no—
520C2×C4×C5—32no—
521C2×C4×C5—32no—
522C2×C4×C5—64no—
523C2×C4×C5—61no—
524C2×C4×C5—61no—
525C2×C4×C5—122no—
526C2×C4×C5C23×D311yescharacteristic
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—31no—
530C2×Dic5—64no—
531C2×Dic5—62no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—122no—
535C2×Dic5D3×D411yescharacteristic
536C4×D5—24no—
537C4×D5—21no—
538C4×D5—21no—
539C4×D5—62no—
540C4×D5—64no—
541C4×D5—64no—
542C4×D5—62no—
543C4×D5—64no—
544C4×D5—61no—
545C4×D5—61no—
546Dic10—24no—
547Dic10—21no—
548Dic10—21no—
549Dic10—21no—
550Dic10—32no—
551Dic10—64no—
552Dic10—64no—
553Dic10—64no—
554Dic10—64no—
555Dic10—61no—
556Dic10—61no—
557Dic10—61no—
558Dic10—122no—
559Dic10D3×D412yes—
560C5×C8—21no—
561C5×C8—61no—
562#168—21no—
563#168—61no—
564C22×Q8—31no—
565C22×Q8—51no—
566C22×Q8—151no—
567C22×Q8—151no—
568C22×Q8—151no—
569C22×Q8—151no—
570C22×Q8—151no—
571C22×Q8—301no—
572C22×Q8—301no—
573C22×Q8—301no—
574C22×Q8—304no—
575C22×Q8—304no—
576C23×C4—151no—
577C23×C4—301no—
578C2×Q16—51no—
579C2×Q16—51no—
580C2×Q16—151no—
581C2×Q16—151no—
582C2×Q16—151no—
583C2×Q16—151no—
584C2×Q16—151no—
585C2×Q16—151no—
586C2×Q16—304no—
587C2×Q16—304no—
588C22×C8—31no—
589C22×C8—151no—
590C22⋊Q8—51no—
591C22⋊Q8—151no—
592C22⋊Q8—151no—
593C22⋊Q8—151no—
594C22⋊Q8—301no—
595C22⋊Q8—301no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—301no—
598C2×C22⋊C4—301no—
599#103—31no—
600#103—31no—
601#103—31no—
602#103—51no—
603#103—151no—
604#103—151no—
605#103—151no—
606#103D3×D511yescharacteristic, complemented
607C22⋊C8—51no—
608C22⋊C8—151no—
609C22⋊C8—151no—
610C22⋊C8—151no—
611C2×C3×C5C2×#12011yescharacteristic
612C2×C3×C5C22×Q1611yescharacteristic
613C2×C3×C5C2×#13711yescharacteristic
614D15—22no—
615C3×D5—22no—
616C5×D3#45114yescomplemented
617C23×C3—51no—
618C22×D3—51no—
619C22×D3—54no—
620C22×D3—102no—
621C22×D3—102no—
622C22×D3D4×D511yescharacteristic
623C3×Q8—21no—
624C3×Q8—52no—
625C3×Q8—104no—
626C3×Q8—101no—
627C3×Q8—101no—
628C3×Q8—101no—
629C3×Q8C2×D2012yes—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—51no—
633C2×C3×C4—104no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4C23×D511yescharacteristic
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—51no—
642C2×Dic3—104no—
643C2×Dic3—101no—
644C2×Dic3—102no—
645C2×Dic3—101no—
646C2×Dic3D4×D511yescharacteristic
647C4×D3—24no—
648C4×D3—42no—
649C4×D3—104no—
650C4×D3—104no—
651C4×D3—102no—
652C4×D3—104no—
653C4×D3—101no—
654C4×D3—101no—
655C4×D3—102no—
656C4×D3—202no—
657C4×D3C2×D2012yes—
658C4×D3D4×D512yes—
659Dic6—21no—
660Dic6—24no—
661Dic6—52no—
662Dic6—104no—
663Dic6—104no—
664Dic6—104no—
665Dic6—101no—
666Dic6—104no—
667Dic6—101no—
668Dic6—101no—
669Dic6—202no—
670Dic6C2×D2012yes—
671C3×C8—21no—
672C3×C8—101no—
673C3⋊C8—21no—
674C3⋊C8—101no—
675C22×C5—32no—
676C22×C5—32no—
677C22×C5—32no—
678C22×C5C2×D3×D411yescharacteristic
679C2×D5—21no—
680C2×D5—21no—
681C2×D5—32no—
682C2×D5—68no—
683C2×D5—61no—
684C2×D5—61no—
685C2×D5D3×Q1612yescomplemented
686C4×C5—22no—
687C4×C5—32no—
688C4×C5—41no—
689C4×C5—62no—
690C4×C5—121no—
691C4×C5C2×D3×D411yescharacteristic
692C4×C5C2×D3×D411yescharacteristic
693Dic5—21no—
694Dic5—22no—
695Dic5—41no—
696Dic5—62no—
697Dic5—61no—
698Dic5—121no—
699C24—151no—
700C2×Q8—34no—
701C2×Q8—31no—
702C2×Q8—51no—
703C2×Q8—51no—
704C2×Q8—61no—
705C2×Q8—62no—
706C2×Q8—101no—
707C2×Q8—102no—
708C2×Q8—102no—
709C2×Q8—154no—
710C2×Q8—151no—
711C2×Q8—151no—
712C2×Q8—301no—
713C2×Q8—301no—
714C2×Q8—301no—
715C2×Q8—302no—
716C2×Q8—302no—
717C2×Q8—302no—
718C2×Q8—301no—
719C2×Q8—301no—
720C2×Q8—308no—
721C2×Q8—302no—
722C2×Q8—302no—
723C2×Q8—308no—
724C2×Q8—302no—
725C2×Q8—302no—
726C2×Q8—302no—
727C2×Q8—308no—
728C2×Q8—302no—
729C2×Q8C2×D3×D511yescharacteristic
730C22×C4—31no—
731C22×C4—51no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—101no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—301no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—301no—
743C22×C4—308no—
744C22×C4—301no—
745C22×C4—301no—
746C22×C4—301no—
747Q16—102no—
748Q16—102no—
749Q16—302no—
750Q16—302no—
751Q16—302no—
752Q16—302no—
753Q16—302no—
754Q16—302no—
755C2×C8—31no—
756C2×C8—51no—
757C2×C8—62no—
758C2×C8—151no—
759C2×C8—302no—
760C2×C8C2×D3×D511yescharacteristic
761C4⋊C4—31no—
762C4⋊C4—61no—
763C4⋊C4—101no—
764C4⋊C4—301no—
765C4⋊C4—301no—
766C4⋊C4—301no—
767C4⋊C4C2×D3×D511yescharacteristic
768C22⋊C4—101no—
769C22⋊C4—301no—
770C22⋊C4—301no—
771C22⋊C4—301no—
772C3×C5C2×#45111yescharacteristic, complemented, Hall
773C22×C3—52no—
774C22×C3—101no—
775C22×C3—101no—
776C22×C3C2×D4×D511yescharacteristic
777C2×D3—52no—
778C2×D3—101no—
779C2×D3—101no—
780C2×D3—108no—
781C2×D3#402812yes—
782C2×D3#406112yes—
783C2×D3D5×Q1612yes—
784C3×C4—22no—
785C3×C4—41no—
786C3×C4—101no—
787C3×C4—102no—
788C3×C4—201no—
789C3×C4C22×D2011yescharacteristic
790C3×C4C2×D4×D511yescharacteristic
791Dic3—22no—
792Dic3—41no—
793Dic3—102no—
794Dic3—101no—
795Dic3—201no—
796Dic3#402812yes—
797C2×C5—34no—
798C2×C5D3×#12011yescharacteristic
799C2×C5C2×D3×Q1611yescharacteristic
800C2×C5D3×#13711yescharacteristic
801D5—22no—
802D5—62no—
803C23—31no—
804C23—51no—
805C23—154no—
806C23—151no—
807C23—302no—
808C23—302no—
809Q8—21no—
810Q8—32no—
811Q8—52no—
812Q8—64no—
813Q8—61no—
814Q8—104no—
815Q8—101no—
816Q8—101no—
817Q8—101no—
818Q8—152no—
819Q8—304no—
820Q8—304no—
821Q8—304no—
822Q8—304no—
823Q8—301no—
824Q8—301no—
825Q8—301no—
826Q8—602no—
827Q8D3×D2012yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—31no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—51no—
834C2×C4—64no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—104no—
838C2×C4—101no—
839C2×C4—101no—
840C2×C4—101no—
841C2×C4—101no—
842C2×C4—122no—
843C2×C4—151no—
844C2×C4—304no—
845C2×C4—302no—
846C2×C4—302no—
847C2×C4—304no—
848C2×C4—304no—
849C2×C4—302no—
850C2×C4—304no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—602no—
856C2×C4C22×D3×D511yescharacteristic
857C8—21no—
858C8—61no—
859C8—101no—
860C8—301no—
861C2×C3—102no—
862C2×C3C2×#402811yescharacteristic
863C2×C3C2×#406111yescharacteristic
864C2×C3C2×D5×Q1611yescharacteristic
865D3—102no—
866D3#6509714yesdirect product factor
867C5D3×#45111yescharacteristic, complemented, Sylow
868C22—32no—
869C22—32no—
870C22—32no—
871C22—52no—
872C22—101no—
873C22—101no—
874C22—152no—
875C22—308no—
876C22—301no—
877C22—301no—
878C22D3×D4×D511yescharacteristic
879C4—22no—
880C4—32no—
881C4—41no—
882C4—62no—
883C4—101no—
884C4—102no—
885C4—121no—
886C4—201no—
887C4—301no—
888C4—302no—
889C4—601no—
890C4C2×D3×D2011yescharacteristic
891C4D3×D4×D511yescharacteristic
892C3C2×#6509711yescharacteristic, complemented, Sylow
893C2—34no—
894C2—102no—
895C2—302no—
896C2D3×#402811yescharacteristic
897C2D3×#406111yescharacteristic
898C2D3×D5×Q1611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC22×D3×D5D4
hypercenter#103D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D3×#689C2semidirect
3. C2×D3×Dic20C2semidirect
5. #11750910C2semidirect
6. C5×D3×#103C2semidirect
7. C3×#65097C2semidirect
8. #11749310C2semidirect
9. #11749291C2semidirect
10. #11748130C2semidirect
11. #11748126C2semidirect
13. #11747496C2semidirect
14. #11747492C2semidirect
15. D3×#3942C2semidirect
31. C2×#6718C22semidirect
32. C2×Dic60C22semidirect
36. C2×C3×#689C22semidirect
37. C2×C3×Dic20C22semidirect
46. C2×#6663C22semidirect
47. C2×#6662C22semidirect
48. C2×#6662C22semidirect
49. C2×#6661C22semidirect
52. C3×C5×#103C22semidirect
54. #91094C22semidirect
55. C5×#835C22semidirect
56. C5×#816C22semidirect
57. C5×#810C22semidirect
59. C3×#3942C22semidirect
60. #90975C22semidirect
61. #90970C22semidirect
79. #65097D3direct (N × H)
165. D3×#103D5semidirect
188. C2×#689C2×D3semidirect
196. C2×Dic20C2×D3semidirect
206. C5×#103C2×D3semidirect
214. #3942C2×D3semidirect
221. C2×D3×D5Q16semidirect
310. C3×#103C2×D5semidirect
313. #835C2×D5semidirect
318. #816C2×D5semidirect
320. #810C2×D5semidirect
412. C2×D15C2×Q16semidirect
418. C2×C3×D5C2×Q16semidirect
606. #103D3×D5semidirect
616. C5×D3#451semidirect
685. C2×D5D3×Q16semidirect
772. C3×C5C2×#451semidirect
866. D3#65097direct (N × H)
867. C5D3×#451semidirect
892. C3C2×#65097semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q8×D52
C2×D3×#6892
C2×D3×Dic202
D3×#40432
#117509102
C5×D3×#1032
C3×#650972
#117493102
#117492912
#117481302
#117481262
D3×#39522
#117474962
#117474922
D3×#39422
C2×#650973
D3×#4515