Finite Group Databasebeta

← C3×#10615253 #14453962

Subgroups — C3×#10615253 #14453962

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic, complemented
4C3×#65884C211yesmaximal, characteristic, complemented
5C3×#65528C211yesmaximal, characteristic, complemented
6C3×#65527C211yesmaximal, characteristic, complemented
7C3×#65375C211yesmaximal, characteristic, complemented
8C3×#65372C211yesmaximal, characteristic, complemented
9C3×#65341C211yesmaximal, characteristic, complemented
10C3×#65337C211yesmaximal, characteristic, complemented
11C3×#65336C211yesmaximal, characteristic, complemented
12C3×#65335C211yesmaximal, characteristic, complemented
13C3×#65305C211yesmaximal, characteristic, complemented
14C3×#65303C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615253C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C3×C5×C4⋊Q8C2211yescharacteristic, complemented
22C3×C5×#123—21no—
23C3×C5×#123—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×C22⋊Q8C2211yescharacteristic, complemented
26C3×C5×#121—21no—
27C3×C4×C5×D4C2211yescharacteristic
28C3×C4×C5×D4C2211yescharacteristic, complemented
29C2×C3×C5×C4⋊C4—21no—
30C3×#4096—24no—
31C3×#4095—24no—
32C2×C3×#689C2211yescharacteristic, complemented
33C2×C3×#689C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic
35C2×C3×#688C2211yescharacteristic
36C2×C3×#688C2211yescharacteristic
37C2×C3×#688C2211yescharacteristic
38C3×#4083—21no—
39C2×C3×#687C2211yescharacteristic, complemented
40C2×C3×#686C2211yescharacteristic
41C2×C3×#686C2211yescharacteristic
42C3×#4076C2211yescharacteristic
43C3×#4070C2211yescharacteristic
44C2×C3×#681C2211yescharacteristic
45C22×C3×#168C2211yescharacteristic, complemented
46C3×#4040—21no—
47C3×#4030—21no—
48C3×D5×C22⋊C4—21no—
49C3×#4021C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3940C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C5×#547C2×C311yescharacteristic, complemented
64C2×#4096C2×C311yescharacteristic, complemented
65C2×#4095C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65527C2×C311yescharacteristic, complemented
69#65375C2×C311yescharacteristic, complemented
70#65372C2×C311yescharacteristic, complemented
71#65341C2×C311yescharacteristic, complemented
72#65337C2×C311yescharacteristic, complemented
73#65336C2×C311yescharacteristic, complemented
74#65335C2×C311yescharacteristic, complemented
75#65305C2×C311yescharacteristic, complemented
76#65303C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4D411yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C3×#709—22no—
97C3×#709—41no—
98C2×C3×D20—22no—
99C2×C3×D20—21no—
100C2×C3×D20—41no—
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5—21no—
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4—21no—
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×#689—22no—
120C3×#689—41no—
121C3×#688—22no—
122C3×#688—22no—
123C3×#688—22no—
124C3×#688—41no—
125C3×#687—22no—
126C3×#686—22no—
127C3×#686D414yescomplemented
128C3×#685—21no—
129C3×#685—21no—
130C3×#685—21no—
131C3×#685—21no—
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683—21no—
134C3×#681—22no—
135C2×C3×#168—22no—
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547D511yescharacteristic, complemented
143C3×#546—51no—
144C3×#497—51no—
145C3×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C2×C5×#41C22×C311yescharacteristic, complemented
157C2×#709C22×C311yescharacteristic
158C22×D20C22×C311yescharacteristic
159C5×C4⋊Q8C22×C311yescharacteristic, complemented
160C5×#123—21no—
161C5×#123—21no—
162C5×C22⋊Q8C22×C311yescharacteristic
163C5×C22⋊Q8C22×C311yescharacteristic, complemented
164C5×#121—21no—
165C4×C5×D4C22×C311yescharacteristic
166C4×C5×D4C22×C311yescharacteristic, complemented
167C2×C5×C4⋊C4—21no—
168#4096—24no—
169#4095—24no—
170C2×#689C22×C311yescharacteristic, complemented
171C2×#689C22×C311yescharacteristic, complemented
172C2×#688C22×C311yescharacteristic
173C2×#688C22×C311yescharacteristic
174C2×#688C22×C311yescharacteristic
175C2×#688C22×C311yescharacteristic
176#4083—21no—
177C2×#687C22×C311yescharacteristic, complemented
178C2×#686C22×C311yescharacteristic
179C2×#686C22×C311yescharacteristic
180#4076C22×C311yescharacteristic
181#4070C22×C311yescharacteristic
182C2×#681C22×C311yescharacteristic
183C22×#168C22×C311yescharacteristic, complemented
184#4040—21no—
185#4030—21no—
186D5×C22⋊C4—21no—
187#4021C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic
189#3967C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic, complemented
192C22⋊#168C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic, complemented
194#3942C22×C311yescharacteristic, complemented
195#3941C22×C311yescharacteristic
196#3941C22×C311yescharacteristic
197#3940C22×C311yescharacteristic, complemented
198C4⋊#168C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—42no—
207C22×C3×D5—42no—
208C22×C3×D5—81no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×D4—21no—
214C3×C5×D4—41no—
215C3×C5×D4—42no—
216C3×C5×D4—42no—
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—21no—
225C2×C3×C4×C5—42no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2×D411yescharacteristic
232C2×C3×C4×C5C2411yescharacteristic
233C3×C22⋊D5—42no—
234C3×C22⋊D5—81no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—21no—
240C3×D20—42no—
241C3×D20C2×D412yes—
242C3×C4×D5—42no—
243C3×C4×D5—81no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×#168—21no—
247C3×#168—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×C3×#41—51no—
251C2×C3×#41C2×D511yescharacteristic
252C2×C3×#41C2×D511yescharacteristic, complemented
253C22×C3×D4—51no—
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×D8—51no—
264C2×C3×D8—51no—
265C2×C3×M16—51no—
266C22×C3×C8—51no—
267C3×C4⋊Q8C2×D511yescharacteristic, complemented
268C3×#124—51no—
269C3×#123—21no—
270C3×#123—21no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8C2×D511yescharacteristic
274C3×C22⋊Q8C2×D511yescharacteristic, complemented
275C3×#121—21no—
276C3×#121—51no—
277C3×#121—101no—
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4C2×D511yescharacteristic
281C3×C4×D4C2×D511yescharacteristic, complemented
282C2×C3×C4⋊C4—21no—
283C2×C3×C22⋊C4—101no—
284C3×#106—51no—
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97—51no—
295C23×D5—21no—
296C5×#41—22no—
297C5×#41—22no—
298C5×#41—41no—
299C5×#41—41no—
300C2×C5×Q8C23×C311yescharacteristic
301C2×C5×Q8C23×C311yescharacteristic
302C2×C5×D4—21no—
303C2×C5×D4—21no—
304C2×C5×D4C3×D411yescharacteristic
305C2×C5×D4C23×C311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—21no—
308C22×C4×C5—21no—
309C22×C4×C5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C2×C22⋊D5—21no—
312C2×C22⋊D5—21no—
313#709—22no—
314#709—41no—
315C2×D20—22no—
316C2×D20—21no—
317C2×D20—41no—
318C2×D20C23×C311yescharacteristic
319C2×D20C23×C311yescharacteristic
320C2×C4×D5—21no—
321C2×C4×D5—21no—
322C2×Dic10C23×C311yescharacteristic
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4—21no—
327C5×C4⋊C4C3×D411yescharacteristic
328C5×C4⋊C4C23×C311yescharacteristic
329C5×C22⋊C4—21no—
330C5×C22⋊C4—21no—
331C5×C22⋊C4—21no—
332C5×C22⋊C4C3×D411yescharacteristic
333C5×C22⋊C4C3×D411yescharacteristic
334C42×C5C23×C311yescharacteristic
335C22⋊Dic5—21no—
336#689—22no—
337#689—41no—
338#688—22no—
339#688—22no—
340#688—22no—
341#688—41no—
342#687—22no—
343#686—22no—
344#686C3×D414yescomplemented
345#685—21no—
346#685—21no—
347#685—21no—
348#685—21no—
349C4⋊Dic5C23×C311yescharacteristic
350#683—21no—
351#681—22no—
352C2×#168—22no—
353C2×#168C23×C311yescharacteristic
354C2×#168C23×C311yescharacteristic
355C2×#168C23×C311yescharacteristic
356C2×#168C23×C311yescharacteristic
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547C3×D511yescharacteristic, complemented
360#546—51no—
361#497—51no—
362#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—22no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C22×D411yescharacteristic
382C2×C3×D5—22no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—21no—
392C3×C4×C5—21no—
393C3×C4×C5—41no—
394C3×C4×C5—41no—
395C3×C4×C5—41no—
396C3×C4×C5C22×D411yescharacteristic
397C3×C4×C5H(5,𝔽2)11yescharacteristic
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—22no—
402C3×#41—22no—
403C3×#41—41no—
404C3×#41—41no—
405C3×#41—102no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—21no—
411C2×C3×D4—21no—
412C2×C3×D4—51no—
413C2×C3×D4—51no—
414C2×C3×D4—102no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—201no—
419C2×C3×D4C22⋊D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
421C22×C3×C4—21no—
422C22×C3×C4—21no—
423C22×C3×C4—21no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—54no—
436C3×D8—102no—
437C3×M16—102no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—51no—
441C2×C3×C8—51no—
442C2×C3×C8—102no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—21no—
446C3×C4⋊C4—21no—
447C3×C4⋊C4—51no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4C22⋊D511yescharacteristic
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—21no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4C22⋊D511yescharacteristic
460C3×C22⋊C4C22⋊D511yescharacteristic
461C3×C42C22×D511yescharacteristic
462C23×C5—21no—
463C23×C5C2×C3×D411yescharacteristic
464C23×C5C2×C3×D411yescharacteristic
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—42no—
468C22×D5—42no—
469C22×D5—81no—
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—21no—
473C5×Q8—21no—
474C5×D4—21no—
475C5×D4—41no—
476C5×D4—42no—
477C5×D4—42no—
478C5×D4C2×C3×D412yes—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—42no—
487C2×C4×C5—42no—
488C2×C4×C5—42no—
489C2×C4×C5C2×C3×D411yescharacteristic
490C2×C4×C5C2×C3×D411yescharacteristic
491C2×C4×C5C2×C3×D411yescharacteristic
492C2×C4×C5C2×C3×D411yescharacteristic
493C2×C4×C5C24×C311yescharacteristic
494C22⋊D5—42no—
495C22⋊D5—81no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498D20—21no—
499D20—21no—
500D20—21no—
501D20—42no—
502D20C2×C3×D412yes—
503C4×D5—42no—
504C4×D5—81no—
505Dic10—21no—
506Dic10—21no—
507#168—21no—
508#168—21no—
509#168—21no—
510#168C2×C3×D412yes—
511C2×#41—51no—
512C2×#41C2×C3×D511yescharacteristic
513C2×#41C2×C3×D511yescharacteristic, complemented
514C22×D4—51no—
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16—51no—
523C2×SD16—51no—
524C2×D8—51no—
525C2×D8—51no—
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8C2×C3×D511yescharacteristic, complemented
529#124—51no—
530#123—21no—
531#123—21no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8C2×C3×D511yescharacteristic
535C22⋊Q8C2×C3×D511yescharacteristic, complemented
536#121—21no—
537#121—51no—
538#121—101no—
539#120—101no—
540C4×D4—51no—
541C4×D4C2×C3×D511yescharacteristic
542C4×D4C2×C3×D511yescharacteristic, complemented
543C2×C4⋊C4—21no—
544C2×C22⋊C4—101no—
545#106—51no—
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103—51no—
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97—51no—
556C2×C3×C5—41no—
557C2×C3×C5—41no—
558C2×C3×C5—42no—
559C2×C3×C5D4211yescharacteristic
560C2×C3×C5#57511yescharacteristic
561C2×C3×C5#57711yescharacteristic
562C3×D5—42no—
563C3×D5—81no—
564C23×C3—21no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—202no—
568C23×C3—202no—
569C23×C3—401no—
570C23×C3C2×C22⋊D511yescharacteristic
571C23×C3C2×C22⋊D511yescharacteristic
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—52no—
583C3×D4—101no—
584C3×D4—101no—
585C3×D4—101no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—401no—
589C3×D4D4×D512yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—42no—
598C2×C3×C4—42no—
599C2×C3×C4—42no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—202no—
603C2×C3×C4—401no—
604C2×C3×C4C2×C22⋊D511yescharacteristic
605C2×C3×C4C2×C22⋊D511yescharacteristic
606C2×C3×C4C2×C22⋊D511yescharacteristic
607C2×C3×C4C2×C22⋊D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—52no—
610C3×C8—101no—
611C3×C8—101no—
612C3×C8—101no—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—21no—
617C22×C5—21no—
618C22×C5—21no—
619C22×C5—22no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5C22×C3×D411yescharacteristic
623C2×D5—22no—
624C2×D5—41no—
625C2×D5—41no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—21no—
633C4×C5—21no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5C22×C3×D411yescharacteristic
638C4×C5C3×H(5,𝔽2)11yescharacteristic
639Dic5—41no—
640Dic5—41no—
641C24—101no—
642#41—22no—
643#41—22no—
644#41—41no—
645#41—41no—
646#41—102no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8C22×C3×D511yescharacteristic
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—51no—
654C2×D4—51no—
655C2×D4—102no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—201no—
660C2×D4C3×C22⋊D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4C22×C3×D511yescharacteristic
668C22×C4C22×C3×D511yescharacteristic
669Q16—102no—
670Q16—201no—
671SD16—102no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—54no—
677D8—102no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—51no—
682C2×C8—51no—
683C2×C8—102no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—51no—
689C4⋊C4—101no—
690C4⋊C4C3×C22⋊D511yescharacteristic
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—101no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4C3×C22⋊D511yescharacteristic
701C22⋊C4C3×C22⋊D511yescharacteristic
702C42C22×C3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—102no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C22×C22⋊D511yescharacteristic
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414411yescharacteristic
732C2×C5—41no—
733C2×C5—41no—
734C2×C5—42no—
735C2×C5C3×D4211yescharacteristic
736C2×C5C3×#57511yescharacteristic
737C2×C5C3×#57711yescharacteristic
738D5—42no—
739D5—81no—
740C23—21no—
741C23—101no—
742C23—101no—
743C23—202no—
744C23—202no—
745C23—401no—
746C23C2×C3×C22⋊D511yescharacteristic
747C23C2×C3×C22⋊D511yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—41no—
756D4—42no—
757D4—42no—
758D4—52no—
759D4—101no—
760D4—101no—
761D4—101no—
762D4—202no—
763D4—202no—
764D4—401no—
765D4C3×D4×D512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—202no—
779C2×C4—401no—
780C2×C4C2×C3×C22⋊D511yescharacteristic
781C2×C4C2×C3×C22⋊D511yescharacteristic
782C2×C4C2×C3×C22⋊D511yescharacteristic
783C2×C4C2×C3×C22⋊D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—52no—
786C8—101no—
787C8—101no—
788C8—101no—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—42no—
792C2×C3—202no—
793C2×C3—401no—
794C2×C3D4×C22⋊D511yescharacteristic
795C2×C3#6615611yescharacteristic
796C2×C3#6617111yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—22no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—102no—
808C22—201no—
809C22—201no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C22×C3×C22⋊D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414411yescharacteristic
826C3#1061525311yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—41no—
829C2—42no—
830C2—202no—
831C2—401no—
832C2C3×D4×C22⋊D511yescharacteristic
833C2C3×#6615611yescharacteristic
834C2C3×#6617111yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#547C2
socleC22×C3×C5C22×D4
hypercenterC3×#547D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
1. C3×C5×#547C2semidirect
2. C2×C3×#4096C2semidirect
3. C2×C3×#4095C2semidirect
4. C3×#65884C2semidirect
5. C3×#65528C2semidirect
6. C3×#65527C2semidirect
7. C3×#65375C2semidirect
8. C3×#65372C2semidirect
9. C3×#65341C2semidirect
10. C3×#65337C2semidirect
11. C3×#65336C2semidirect
12. C3×#65335C2semidirect
13. C3×#65305C2semidirect
14. C3×#65303C2semidirect
15. C3×#65300C2semidirect
16. #10615253C3direct (N × H)
18. C2×C3×C5×#41C22semidirect
21. C3×C5×C4⋊Q8C22semidirect
25. C3×C5×C22⋊Q8C22semidirect
28. C3×C4×C5×D4C22semidirect
32. C2×C3×#689C22semidirect
33. C2×C3×#689C22semidirect
39. C2×C3×#687C22semidirect
45. C22×C3×#168C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
53. C3×#3964C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
59. C3×#3940C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×#547C2×C3semidirect
64. C2×#4096C2×C3semidirect
65. C2×#4095C2×C3semidirect
66. #65884C2×C3semidirect
67. #65528C2×C3semidirect
68. #65527C2×C3semidirect
69. #65375C2×C3semidirect
70. #65372C2×C3semidirect
71. #65341C2×C3semidirect
72. #65337C2×C3semidirect
73. #65336C2×C3semidirect
74. #65335C2×C3semidirect
75. #65305C2×C3semidirect
76. #65303C2×C3semidirect
77. #65300C2×C3semidirect
127. C3×#686D4semidirect
142. C3×#547D5semidirect
156. C2×C5×#41C22×C3semidirect
159. C5×C4⋊Q8C22×C3semidirect
163. C5×C22⋊Q8C22×C3semidirect
166. C4×C5×D4C22×C3semidirect
170. C2×#689C22×C3semidirect
171. C2×#689C22×C3semidirect
177. C2×#687C22×C3semidirect
183. C22×#168C22×C3semidirect
189. #3967C22×C3semidirect
190. #3967C22×C3semidirect
191. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. #3942C22×C3semidirect
197. #3940C22×C3semidirect
198. C4⋊#168C22×C3semidirect
199. #3935C22×C3semidirect
252. C2×C3×#41C2×D5semidirect
267. C3×C4⋊Q8C2×D5semidirect
274. C3×C22⋊Q8C2×D5semidirect
281. C3×C4×D4C2×D5semidirect
344. #686C3×D4semidirect
359. #547C3×D5semidirect
513. C2×#41C2×C3×D5semidirect
528. C4⋊Q8C2×C3×D5semidirect
535. C22⋊Q8C2×C3×D5semidirect
542. C4×D4C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10615253direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5472
C2×C3×#40962
C2×C3×#40952
C3×#658842
C3×#655282
C3×#655272
C3×#653752
C3×#653722
C3×#653412
C3×#653372
C3×#653362
C3×#653352
C3×#653052
C3×#653032
C3×#653002
#106152533
C3×#32675