Finite Group Databasebeta

← C3×#10615237 #14453692

Subgroups — C3×#10615237 #14453692

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic
2C2×C3×#4097C211yesmaximal, characteristic, complemented
3C22×C3×#687C211yesmaximal, characteristic, complemented
4C3×D4×Dic10C211yesmaximal, characteristic, complemented
5C3×#65528C211yesmaximal, characteristic, complemented
6C3×#65507C211yesmaximal, characteristic, complemented
7C3×#65349C211yesmaximal, characteristic, complemented
8C3×#65343C211yesmaximal, characteristic, complemented
9C3×#65340C211yesmaximal, characteristic, complemented
10C3×#65339C211yesmaximal, characteristic, complemented
11C3×#65331C211yesmaximal, characteristic, complemented
12C3×#65329C211yesmaximal, characteristic, complemented
13C3×#65308C211yesmaximal, characteristic, complemented
14C3×#65307C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615237C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C3×C5×#124C2211yescharacteristic
22C3×C5×#123—21no—
23C3×C5×C22⋊Q8C2211yescharacteristic
24C3×C5×#121—21no—
25C3×C5×#121C2211yescharacteristic
26C3×C5×#120—21no—
27C3×C4×C5×D4C2211yescharacteristic
28C3×C4×C5×D4C2211yescharacteristic
29C2×C3×C5×C22⋊C4—21no—
30C3×#4097—24no—
31C2×C3×#689C2211yescharacteristic, complemented
32C2×C3×#689C2211yescharacteristic, complemented
33C2×C3×#689C2211yescharacteristic, complemented
34C3×D4×Dic5—21no—
35C2×C3×#687—24no—
36C2×C3×#687C2211yescharacteristic
37C2×C3×#687C2211yescharacteristic
38C2×C3×#687C2211yescharacteristic
39C2×C3×#687C2211yescharacteristic
40C2×C3×#687C2211yescharacteristic
41C2×C3×#687C2211yescharacteristic
42C3×#4070C2211yescharacteristic
43C3×#4070C2211yescharacteristic, complemented
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic
46C3×#4034—21no—
47C3×#4024—21no—
48C3×#4024—21no—
49C3×#4015C2211yescharacteristic, complemented
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic
53C3×#3964C2211yescharacteristic
54C3×C22⋊#168C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58C3×#3942C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63C5×#546C2×C311yescharacteristic
64C2×#4097C2×C311yescharacteristic, complemented
65C22×#687C2×C311yescharacteristic, complemented
66D4×Dic10C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65507C2×C311yescharacteristic, complemented
69#65349C2×C311yescharacteristic, complemented
70#65343C2×C311yescharacteristic, complemented
71#65340C2×C311yescharacteristic, complemented
72#65339C2×C311yescharacteristic, complemented
73#65331C2×C311yescharacteristic, complemented
74#65329C2×C311yescharacteristic, complemented
75#65308C2×C311yescharacteristic, complemented
76#65307C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4D411yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×Dic5—21no—
95C22×C3×Dic5—21no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10—22no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—21no—
100C2×C3×Dic10—41no—
101C2×C3×Dic10—41no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4D411yescharacteristic
107C3×C5×C4⋊C4C2311yescharacteristic
108C3×C5×C22⋊C4—21no—
109C3×C5×C22⋊C4—21no—
110C3×C5×C22⋊C4—21no—
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C42×C5C2311yescharacteristic
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×#689—22no—
119C3×#689—22no—
120C3×#689—41no—
121C3×#687—22no—
122C3×#687—22no—
123C3×#687—22no—
124C3×#687—22no—
125C3×#687—41no—
126C3×#687D414yescomplemented
127C3×C4⋊Dic5—21no—
128C3×C4⋊Dic5—21no—
129C3×C4⋊Dic5C2311yescharacteristic
130C3×#683—21no—
131C3×#683—21no—
132C3×#683—21no—
133C3×C4×Dic5—21no—
134C3×#681—22no—
135C2×C3×#168—22no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C2×C3×#137—51no—
141C22×C3×SD16—51no—
142C3×D4×Q8—51no—
143C3×#546D511yescharacteristic
144C3×#497—51no—
145C3×#468—51no—
146C3×#467—51no—
147C3×#464—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#451—51no—
151C3×#450—51no—
152C3×#448—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C22×C5×D4C22×C311yescharacteristic
157C22×Dic10C22×C311yescharacteristic
158C22×Dic10C22×C311yescharacteristic, complemented
159C5×#124C22×C311yescharacteristic
160C5×#123—21no—
161C5×C22⋊Q8C22×C311yescharacteristic
162C5×#121—21no—
163C5×#121C22×C311yescharacteristic
164C5×#120—21no—
165C4×C5×D4C22×C311yescharacteristic
166C4×C5×D4C22×C311yescharacteristic
167C2×C5×C22⋊C4—21no—
168#4097—24no—
169C2×#689C22×C311yescharacteristic, complemented
170C2×#689C22×C311yescharacteristic, complemented
171C2×#689C22×C311yescharacteristic, complemented
172D4×Dic5—21no—
173C2×#687—24no—
174C2×#687C22×C311yescharacteristic
175C2×#687C22×C311yescharacteristic
176C2×#687C22×C311yescharacteristic
177C2×#687C22×C311yescharacteristic
178C2×#687C22×C311yescharacteristic
179C2×#687C22×C311yescharacteristic
180#4070C22×C311yescharacteristic
181#4070C22×C311yescharacteristic, complemented
182C2×#681C22×C311yescharacteristic, complemented
183C22×#168C22×C311yescharacteristic
184#4034—21no—
185#4024—21no—
186#4024—21no—
187#4015C22×C311yescharacteristic, complemented
188C4×Dic10C22×C311yescharacteristic, complemented
189#3967C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic
191#3964C22×C311yescharacteristic
192C22⋊#168C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic, complemented
194#3942C22×C311yescharacteristic, complemented
195#3942C22×C311yescharacteristic, complemented
196#3942C22×C311yescharacteristic, complemented
197#3939C22×C311yescharacteristic, complemented
198C4⋊#168C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3266—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—42no—
204C23×C3×C5—42no—
205C23×C3×C5—81no—
206C23×C3×C5C2×D411yescharacteristic
207C23×C3×C5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×D4—22no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—42no—
215C3×C5×D4—42no—
216C3×C5×D4—81no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—42no—
225C2×C3×C4×C5—81no—
226C2×C3×C4×C5C2×D411yescharacteristic
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—42no—
236C2×C3×Dic5—42no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yes—
245C3×#168—21no—
246C3×#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×C3×#41C2×D511yescharacteristic
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4C2×D511yescharacteristic
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16—51no—
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—104no—
264C2×C3×M16—51no—
265C22×C3×C8—51no—
266C3×C4⋊Q8—51no—
267C3×C4⋊Q8—101no—
268C3×#124C2×D511yescharacteristic
269C3×#123—21no—
270C3×C22⋊Q8—51no—
271C3×C22⋊Q8—51no—
272C3×C22⋊Q8—101no—
273C3×C22⋊Q8—101no—
274C3×C22⋊Q8C2×D511yescharacteristic
275C3×#121—21no—
276C3×#121C2×D511yescharacteristic
277C3×#120—21no—
278C3×C4×Q8—51no—
279C3×C4×D4—101no—
280C3×C4×D4C2×D511yescharacteristic
281C3×C4×D4C2×D511yescharacteristic
282C2×C3×C22⋊C4—21no—
283C3×#107—51no—
284C3×C4⋊C8—51no—
285C3×#103—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×C22⋊C8—51no—
292C3×C22⋊C8—51no—
293C3×#97—51no—
294C24×C5—21no—
295C5×#41—22no—
296C5×#41—41no—
297C2×C5×Q8C23×C311yescharacteristic
298C2×C5×D4—22no—
299C2×C5×D4—21no—
300C2×C5×D4—21no—
301C2×C5×D4—21no—
302C2×C5×D4—41no—
303C2×C5×D4C3×D411yescharacteristic
304C2×C5×D4C23×C311yescharacteristic
305C2×C5×D4C23×C311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C22×Dic5—21no—
311C22×Dic5—21no—
312C2×Dic10—22no—
313C2×Dic10—22no—
314C2×Dic10—21no—
315C2×Dic10—21no—
316C2×Dic10—41no—
317C2×Dic10—41no—
318C2×Dic10C23×C311yescharacteristic
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×C4⋊C4—21no—
322C5×C4⋊C4C3×D411yescharacteristic
323C5×C4⋊C4C23×C311yescharacteristic
324C5×C22⋊C4—21no—
325C5×C22⋊C4—21no—
326C5×C22⋊C4—21no—
327C5×C22⋊C4—21no—
328C5×C22⋊C4—21no—
329C5×C22⋊C4C3×D411yescharacteristic
330C5×C22⋊C4C3×D411yescharacteristic
331C42×C5C23×C311yescharacteristic
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334#689—22no—
335#689—22no—
336#689—41no—
337#687—22no—
338#687—22no—
339#687—22no—
340#687—22no—
341#687—41no—
342#687C3×D414yescomplemented
343C4⋊Dic5—21no—
344C4⋊Dic5—21no—
345C4⋊Dic5C23×C311yescharacteristic
346#683—21no—
347#683—21no—
348#683—21no—
349C4×Dic5—21no—
350#681—22no—
351C2×#168—22no—
352C2×#168C23×C311yescharacteristic
353C2×#168C23×C311yescharacteristic
354C2×#168C23×C311yescharacteristic
355C2×#168C23×C311yescharacteristic
356C2×#137—51no—
357C22×SD16—51no—
358D4×Q8—51no—
359#546C3×D511yescharacteristic
360#497—51no—
361#468—51no—
362#467—51no—
363#464—51no—
364#461—51no—
365#452—51no—
366#451—51no—
367#450—51no—
368#448—51no—
369#440—51no—
370#435—51no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—22no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—84no—
383C22×C3×C5#13712yescomplemented
384C22×C3×C5C22×D411yescharacteristic
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5—41no—
390C3×C4×C5—41no—
391C3×C4×C5C22×D411yescharacteristic
392C3×C4×C5H(5,𝔽2)11yescharacteristic
393C3×Dic5—22no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—21no—
398C3×#41—22no—
399C3×#41—41no—
400C2×C3×Q8—51no—
401C2×C3×Q8—51no—
402C2×C3×Q8—51no—
403C2×C3×Q8—102no—
404C2×C3×Q8—102no—
405C2×C3×Q8—101no—
406C2×C3×Q8—101no—
407C2×C3×Q8—201no—
408C2×C3×Q8—201no—
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—22no—
411C2×C3×D4—21no—
412C2×C3×D4—21no—
413C2×C3×D4—21no—
414C2×C3×D4—41no—
415C2×C3×D4C22⋊D511yescharacteristic
416C2×C3×D4C22×D511yescharacteristic
417C2×C3×D4C22×D511yescharacteristic
418C22×C3×C4—21no—
419C22×C3×C4—21no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—102no—
425C3×Q16—102no—
426C3×Q16—201no—
427C3×SD16—54no—
428C3×SD16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—201no—
433C3×M16—102no—
434C2×C3×C8—51no—
435C2×C3×C8—51no—
436C2×C3×C8—51no—
437C2×C3×C8—51no—
438C2×C3×C8—102no—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—51no—
441C3×C4⋊C4—101no—
442C3×C4⋊C4—101no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4C22⋊D511yescharacteristic
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C22⋊C4—21no—
450C3×C22⋊C4—21no—
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4C22⋊D511yescharacteristic
456C3×C22⋊C4C22⋊D511yescharacteristic
457C3×C42—101no—
458C3×C42C22×D511yescharacteristic
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—42no—
462C23×C5—42no—
463C23×C5—81no—
464C23×C5C2×C3×D411yescharacteristic
465C23×C5C2×C3×D411yescharacteristic
466C5×Q8—21no—
467C5×Q8—21no—
468C5×D4—22no—
469C5×D4—21no—
470C5×D4—21no—
471C5×D4—21no—
472C5×D4—42no—
473C5×D4—42no—
474C5×D4—81no—
475C5×D4C2×C3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—42no—
483C2×C4×C5—81no—
484C2×C4×C5C2×C3×D411yescharacteristic
485C2×C4×C5C2×C3×D411yescharacteristic
486C2×C4×C5C2×C3×D411yescharacteristic
487C2×C4×C5C2×C3×D411yescharacteristic
488C2×C4×C5C24×C311yescharacteristic
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—42no—
494C2×Dic5—42no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—21no—
499Dic10—21no—
500Dic10—42no—
501Dic10—42no—
502Dic10C2×C3×D412yes—
503#168—21no—
504#168—21no—
505#168—21no—
506#168C2×C3×D412yes—
507C2×#41C2×C3×D511yescharacteristic
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4C2×C3×D511yescharacteristic
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16—51no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—104no—
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124C2×C3×D511yescharacteristic
527#123—21no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—101no—
531C22⋊Q8—101no—
532C22⋊Q8C2×C3×D511yescharacteristic
533#121—21no—
534#121C2×C3×D511yescharacteristic
535#120—21no—
536C4×Q8—51no—
537C4×D4—101no—
538C4×D4C2×C3×D511yescharacteristic
539C4×D4C2×C3×D511yescharacteristic
540C2×C22⋊C4—21no—
541#107—51no—
542C4⋊C8—51no—
543#103—51no—
544#103—51no—
545#103—51no—
546#103—51no—
547#102—51no—
548#102—51no—
549C22⋊C8—51no—
550C22⋊C8—51no—
551#97—51no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5—42no—
555C2×C3×C5—81no—
556C2×C3×C5D4211yescharacteristic
557C2×C3×C5C2×#13711yescharacteristic
558C2×C3×C5#57711yescharacteristic
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—81no—
564C23×C3C2×C22⋊D511yescharacteristic
565C23×C3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—52no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8—202no—
576C3×D4—22no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—81no—
583C3×D4D4×D512yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—42no—
591C2×C3×C4—81no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—202no—
597C2×C3×C4—202no—
598C2×C3×C4C2×C22⋊D511yescharacteristic
599C2×C3×C4C2×C22⋊D511yescharacteristic
600C2×C3×C4C2×C22⋊D511yescharacteristic
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603C3×C8—52no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5—22no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—84no—
619C22×C5C3×#13712yescomplemented
620C22×C5C22×C3×D411yescharacteristic
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—41no—
626C4×C5—41no—
627C4×C5C22×C3×D411yescharacteristic
628C4×C5C3×H(5,𝔽2)11yescharacteristic
629Dic5—22no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—21no—
634#41—22no—
635#41—41no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—102no—
640C2×Q8—102no—
641C2×Q8—101no—
642C2×Q8—101no—
643C2×Q8—201no—
644C2×Q8—201no—
645C2×Q8C22×C3×D511yescharacteristic
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—41no—
651C2×D4C3×C22⋊D511yescharacteristic
652C2×D4C22×C3×D511yescharacteristic
653C2×D4C22×C3×D511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4C22×C3×D511yescharacteristic
659C22×C4C22×C3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—54no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—102no—
668SD16—201no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—51no—
673C2×C8—51no—
674C2×C8—102no—
675C4⋊C4—21no—
676C4⋊C4—51no—
677C4⋊C4—101no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4C3×C22⋊D511yescharacteristic
683C4⋊C4C22×C3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4C3×C22⋊D511yescharacteristic
692C22⋊C4C3×C22⋊D511yescharacteristic
693C42—101no—
694C42C22×C3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—84no—
708C22×C3#409712yescomplemented
709C22×C3C22×C22⋊D511yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—102no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C2×D4×D511yescharacteristic
721C3×C4#414411yescharacteristic
722C2×C5—22no—
723C2×C5—41no—
724C2×C5—42no—
725C2×C5—81no—
726C2×C5C3×D4211yescharacteristic
727C2×C5C2×C3×#13711yescharacteristic
728C2×C5C3×#57711yescharacteristic
729C23—21no—
730C23—21no—
731C23—42no—
732C23—42no—
733C23—81no—
734C23C2×C3×C22⋊D511yescharacteristic
735C23C2×C3×C22⋊D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—52no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8—202no—
746D4—22no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—42no—
752D4—81no—
753D4C3×D4×D512yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—81no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—202no—
767C2×C4—202no—
768C2×C4C2×C3×C22⋊D511yescharacteristic
769C2×C4C2×C3×C22⋊D511yescharacteristic
770C2×C4C2×C3×C22⋊D511yescharacteristic
771C2×C4C2×C3×C22⋊D511yescharacteristic
772C2×C4C23×C3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—101no—
776C8—101no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3—42no—
780C2×C3—81no—
781C2×C3D4×C22⋊D511yescharacteristic
782C2×C3C2×#409711yescharacteristic
783C2×C3#6617011yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—84no—
797C22C3×#409712yescomplemented
798C22C22×C3×C22⋊D511yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—41no—
804C4—41no—
805C4—102no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C2×C3×D4×D511yescharacteristic
810C4C3×#414411yescharacteristic
811C3#1061523711yescharacteristic, direct product factor, Sylow
812C2—22no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2C3×D4×C22⋊D511yescharacteristic
817C2C2×C3×#409711yescharacteristic
818C2C3×#6617011yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenterC3×#546D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#546

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4097C2semidirect
3. C22×C3×#687C2semidirect
4. C3×D4×Dic10C2semidirect
5. C3×#65528C2semidirect
6. C3×#65507C2semidirect
7. C3×#65349C2semidirect
8. C3×#65343C2semidirect
9. C3×#65340C2semidirect
10. C3×#65339C2semidirect
11. C3×#65331C2semidirect
12. C3×#65329C2semidirect
13. C3×#65308C2semidirect
14. C3×#65307C2semidirect
15. C3×#65300C2semidirect
16. #10615237C3direct (N × H)
20. C22×C3×Dic10C22semidirect
31. C2×C3×#689C22semidirect
32. C2×C3×#689C22semidirect
33. C2×C3×#689C22semidirect
43. C3×#4070C22semidirect
44. C2×C3×#681C22semidirect
49. C3×#4015C22semidirect
50. C3×C4×Dic10C22semidirect
51. C3×#3967C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
57. C3×#3942C22semidirect
58. C3×#3942C22semidirect
59. C3×#3939C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
64. C2×#4097C2×C3semidirect
65. C22×#687C2×C3semidirect
66. D4×Dic10C2×C3semidirect
67. #65528C2×C3semidirect
68. #65507C2×C3semidirect
69. #65349C2×C3semidirect
70. #65343C2×C3semidirect
71. #65340C2×C3semidirect
72. #65339C2×C3semidirect
73. #65331C2×C3semidirect
74. #65329C2×C3semidirect
75. #65308C2×C3semidirect
76. #65307C2×C3semidirect
77. #65300C2×C3semidirect
126. C3×#687D4semidirect
158. C22×Dic10C22×C3semidirect
169. C2×#689C22×C3semidirect
170. C2×#689C22×C3semidirect
171. C2×#689C22×C3semidirect
181. #4070C22×C3semidirect
182. C2×#681C22×C3semidirect
187. #4015C22×C3semidirect
188. C4×Dic10C22×C3semidirect
189. #3967C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. #3942C22×C3semidirect
195. #3942C22×C3semidirect
196. #3942C22×C3semidirect
197. #3939C22×C3semidirect
198. C4⋊#168C22×C3semidirect
199. #3935C22×C3semidirect
342. #687C3×D4semidirect
383. C22×C3×C5#137semidirect
619. C22×C5C3×#137semidirect
695. C3×C5#3266semidirect
708. C22×C3#4097semidirect
784. C5C3×#3266semidirect
797. C22C3×#4097semidirect
811. C3#10615237direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5462
C2×C3×#40972
C22×C3×#6872
C3×D4×Dic102
C3×#655282
C3×#655072
C3×#653492
C3×#653432
C3×#653402
C3×#653392
C3×#653312
C3×#653292
C3×#653082
C3×#653072
C3×#653002
#106152373
C3×#32665