Finite Group Databasebeta

← C3×#10615233 #14453197

Subgroups — C3×#10615233 #14453197

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C22×C3×#686C211yesmaximal, characteristic, complemented
4C3×D4×D20C211yesmaximal, characteristic, complemented
5C3×#65527C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65347C211yesmaximal, characteristic, complemented
8C3×#65346C211yesmaximal, characteristic, complemented
9C3×#65337C211yesmaximal, characteristic, complemented
10C3×#65335C211yesmaximal, characteristic, complemented
11C3×#65328C211yesmaximal, characteristic, complemented
12C3×#65325C211yesmaximal, characteristic, complemented
13C3×#65304C211yesmaximal, characteristic, complemented
14C3×#65303C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615233C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic, complemented
22C3×C5×#124C2211yescharacteristic, complemented
23C3×C5×#123—21no—
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25C3×C5×#121—21no—
26C3×C5×#121C2211yescharacteristic, complemented
27C3×C5×#120—21no—
28C3×C4×C5×D4C2211yescharacteristic
29C3×C4×C5×D4C2211yescharacteristic, complemented
30C2×C3×C5×C22⋊C4—21no—
31C3×#4095—24no—
32C2×C3×#688C2211yescharacteristic, complemented
33C2×C3×#688C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic, complemented
35C2×C3×#686—24no—
36C2×C3×#686C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#686C2211yescharacteristic, complemented
40C2×C3×#686C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic, complemented
42C3×#4076C2211yescharacteristic
43C3×#4076C2211yescharacteristic, complemented
44C2×C3×#681C2211yescharacteristic, complemented
45C22×C3×#168C2211yescharacteristic, complemented
46C3×#4041—21no—
47C3×#4028—21no—
48C3×#4028—21no—
49C3×#4020C2211yescharacteristic, complemented
50C3×C4×D20C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3940C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C5×#546C2×C311yescharacteristic, complemented
64C2×#4095C2×C311yescharacteristic, complemented
65C22×#686C2×C311yescharacteristic, complemented
66D4×D20C2×C311yescharacteristic, complemented
67#65527C2×C311yescharacteristic, complemented
68#65506C2×C311yescharacteristic, complemented
69#65347C2×C311yescharacteristic, complemented
70#65346C2×C311yescharacteristic, complemented
71#65337C2×C311yescharacteristic, complemented
72#65335C2×C311yescharacteristic, complemented
73#65328C2×C311yescharacteristic, complemented
74#65325C2×C311yescharacteristic, complemented
75#65304C2×C311yescharacteristic, complemented
76#65303C2×C311yescharacteristic, complemented
77#65300C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C3×C5×#41—22no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—41no—
89C2×C3×C5×D4D411yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C2×C3×C5×D4C2311yescharacteristic
92C22×C3×C4×C5—21no—
93C22×C3×C4×C5—21no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5—21no—
98C3×D4×D5—44no—
99C2×C3×D20—22no—
100C2×C3×D20—22no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—21no—
104C2×C3×D20—21no—
105C2×C3×D20—41no—
106C2×C3×D20—41no—
107C2×C3×D20C2311yescharacteristic
108C2×C3×D20C2311yescharacteristic
109C2×C3×D20C2311yescharacteristic
110C2×C3×C4×D5—21no—
111C3×C5×C4⋊C4—21no—
112C3×C5×C4⋊C4D411yescharacteristic
113C3×C5×C4⋊C4C2311yescharacteristic
114C3×C5×C22⋊C4—21no—
115C3×C5×C22⋊C4—21no—
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118C3×C5×C22⋊C4—21no—
119C3×C5×C22⋊C4D411yescharacteristic
120C3×C5×C22⋊C4D411yescharacteristic
121C3×C42×C5C2311yescharacteristic
122C3×#688—22no—
123C3×#688—22no—
124C3×#688—41no—
125C3×#686—22no—
126C3×#686—22no—
127C3×#686—22no—
128C3×#686—22no—
129C3×#686—41no—
130C3×#686D414yescomplemented
131C3×#685—21no—
132C3×#685—21no—
133C3×#685—21no—
134C3×C4⋊Dic5C2311yescharacteristic
135C3×#681—22no—
136C2×C3×#168—22no—
137C2×C3×#168C2311yescharacteristic
138C2×C3×#168C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C2×C3×#168C2311yescharacteristic
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×D8—51no—
143C3×#546D511yescharacteristic, complemented
144C3×D42—51no—
145C3×#496—51no—
146C3×#469—51no—
147C3×#465—51no—
148C3×#463—51no—
149C3×#459—51no—
150C3×#450—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#447—51no—
154C3×#442—51no—
155C3×#435—51no—
156C2×C5×#41C22×C311yescharacteristic, complemented
157C22×C5×D4C22×C311yescharacteristic, complemented
158C2×D4×D5—21no—
159C22×D20C22×C311yescharacteristic
160C22×D20C22×C311yescharacteristic, complemented
161C5×#124C22×C311yescharacteristic, complemented
162C5×#123—21no—
163C5×C22⋊Q8C22×C311yescharacteristic, complemented
164C5×#121—21no—
165C5×#121C22×C311yescharacteristic, complemented
166C5×#120—21no—
167C4×C5×D4C22×C311yescharacteristic
168C4×C5×D4C22×C311yescharacteristic, complemented
169C2×C5×C22⋊C4—21no—
170#4095—24no—
171C2×#688C22×C311yescharacteristic, complemented
172C2×#688C22×C311yescharacteristic, complemented
173C2×#688C22×C311yescharacteristic, complemented
174C2×#686—24no—
175C2×#686C22×C311yescharacteristic
176C2×#686C22×C311yescharacteristic
177C2×#686C22×C311yescharacteristic, complemented
178C2×#686C22×C311yescharacteristic, complemented
179C2×#686C22×C311yescharacteristic, complemented
180C2×#686C22×C311yescharacteristic, complemented
181#4076C22×C311yescharacteristic
182#4076C22×C311yescharacteristic, complemented
183C2×#681C22×C311yescharacteristic, complemented
184C22×#168C22×C311yescharacteristic, complemented
185#4041—21no—
186#4028—21no—
187#4028—21no—
188#4020C22×C311yescharacteristic, complemented
189C4×D20C22×C311yescharacteristic, complemented
190#3967C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic, complemented
194C22⋊#168C22×C311yescharacteristic, complemented
195#3941C22×C311yescharacteristic, complemented
196#3941C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic, complemented
198#3940C22×C311yescharacteristic, complemented
199C4⋊#168C22×C311yescharacteristic, complemented
200#3935C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C23×C3×C5C2×D411yescharacteristic
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—42no—
215C22×C3×D5—42no—
216C22×C3×D5—81no—
217C22×C3×D5—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—22no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—21no—
224C3×C5×D4—42no—
225C3×C5×D4—42no—
226C3×C5×D4—81no—
227C3×C5×D4C2×D412yescomplemented
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—42no—
235C2×C3×C4×C5—81no—
236C2×C3×C4×C5C2×D411yescharacteristic
237C2×C3×C4×C5C2×D411yescharacteristic
238C2×C3×C4×C5C2×D411yescharacteristic
239C2×C3×C4×C5C2×D411yescharacteristic
240C2×C3×C4×C5C2411yescharacteristic
241C3×C22⋊D5—42no—
242C3×C22⋊D5—42no—
243C2×C3×Dic5—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×D20—42no—
250C3×D20—42no—
251C3×D20—42no—
252C3×D20—81no—
253C3×D20C2×D412yes—
254C3×C4×D5—42no—
255C3×#168—21no—
256C3×#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×C3×#41C2×D511yescharacteristic, complemented
260C22×C3×D4—51no—
261C22×C3×D4—51no—
262C22×C3×D4—101no—
263C22×C3×D4C2×D511yescharacteristic, complemented
264C3×AGL(1,ℤ/8)—104no—
265C2×C3×SD16—51no—
266C2×C3×SD16—51no—
267C2×C3×SD16—51no—
268C2×C3×D8—51no—
269C2×C3×D8—51no—
270C2×C3×D8—51no—
271C2×C3×D8—51no—
272C2×C3×D8—51no—
273C2×C3×D8—51no—
274C2×C3×D8—104no—
275C2×C3×M16—51no—
276C22×C3×C8—51no—
277C3×#127—51no—
278C3×#124C2×D511yescharacteristic, complemented
279C3×#123—21no—
280C3×C22⋊Q8C2×D511yescharacteristic, complemented
281C3×#121—21no—
282C3×#121—51no—
283C3×#121—51no—
284C3×#121—101no—
285C3×#121C2×D511yescharacteristic, complemented
286C3×#120—21no—
287C3×#120—101no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4C2×D511yescharacteristic
291C3×C4×D4C2×D511yescharacteristic, complemented
292C2×C3×C22⋊C4—21no—
293C3×#106—51no—
294C3×C4⋊C8—51no—
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102—51no—
300C3×#102—51no—
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97—51no—
304C24×C5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C5×#41—22no—
308C5×#41—41no—
309C2×C5×Q8C23×C311yescharacteristic
310C2×C5×D4—22no—
311C2×C5×D4—21no—
312C2×C5×D4—21no—
313C2×C5×D4—21no—
314C2×C5×D4—41no—
315C2×C5×D4C3×D411yescharacteristic
316C2×C5×D4C23×C311yescharacteristic
317C2×C5×D4C23×C311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5—21no—
320C22×C4×C5C23×C311yescharacteristic
321C22×C4×C5C23×C311yescharacteristic
322C2×C22⋊D5—21no—
323C2×C22⋊D5—21no—
324D4×D5—44no—
325C2×D20—22no—
326C2×D20—22no—
327C2×D20—21no—
328C2×D20—21no—
329C2×D20—21no—
330C2×D20—21no—
331C2×D20—41no—
332C2×D20—41no—
333C2×D20C23×C311yescharacteristic
334C2×D20C23×C311yescharacteristic
335C2×D20C23×C311yescharacteristic
336C2×C4×D5—21no—
337C5×C4⋊C4—21no—
338C5×C4⋊C4C3×D411yescharacteristic
339C5×C4⋊C4C23×C311yescharacteristic
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—21no—
343C5×C22⋊C4—21no—
344C5×C22⋊C4—21no—
345C5×C22⋊C4C3×D411yescharacteristic
346C5×C22⋊C4C3×D411yescharacteristic
347C42×C5C23×C311yescharacteristic
348#688—22no—
349#688—22no—
350#688—41no—
351#686—22no—
352#686—22no—
353#686—22no—
354#686—22no—
355#686—41no—
356#686C3×D414yescomplemented
357#685—21no—
358#685—21no—
359#685—21no—
360C4⋊Dic5C23×C311yescharacteristic
361#681—22no—
362C2×#168—22no—
363C2×#168C23×C311yescharacteristic
364C2×#168C23×C311yescharacteristic
365C2×#168C23×C311yescharacteristic
366C2×#168C23×C311yescharacteristic
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546C3×D511yescharacteristic, complemented
370D42—51no—
371#496—51no—
372#469—51no—
373#465—51no—
374#463—51no—
375#459—51no—
376#450—51no—
377#449—51no—
378#447—51no—
379#447—51no—
380#442—51no—
381#435—51no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—22no—
386C22×C3×C5—21no—
387C22×C3×C5—21no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—84no—
394C22×C3×C5AGL(1,ℤ/8)12yescomplemented
395C22×C3×C5C22×D411yescharacteristic
396C2×C3×D5—22no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—84no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—21no—
410C3×C4×C5—21no—
411C3×C4×C5—41no—
412C3×C4×C5—41no—
413C3×C4×C5C22×D411yescharacteristic
414C3×C4×C5H(5,𝔽2)11yescharacteristic
415C3×Dic5—41no—
416C24×C3—21no—
417C24×C3—101no—
418C24×C3—101no—
419C3×#41—22no—
420C3×#41—41no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—22no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—21no—
426C2×C3×D4—41no—
427C2×C3×D4—51no—
428C2×C3×D4—51no—
429C2×C3×D4—51no—
430C2×C3×D4—102no—
431C2×C3×D4—102no—
432C2×C3×D4—101no—
433C2×C3×D4—101no—
434C2×C3×D4—101no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—201no—
439C2×C3×D4—201no—
440C2×C3×D4—204no—
441C2×C3×D4C22⋊D511yescharacteristic
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—21no—
445C22×C3×C4—21no—
446C22×C3×C4—101no—
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—54no—
453C3×D8—102no—
454C3×D8—102no—
455C3×D8—102no—
456C3×D8—102no—
457C3×D8—201no—
458C3×M16—102no—
459C2×C3×C8—51no—
460C2×C3×C8—51no—
461C2×C3×C8—51no—
462C2×C3×C8—51no—
463C2×C3×C8—102no—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—51no—
466C3×C4⋊C4C22⋊D511yescharacteristic
467C3×C4⋊C4C22×D511yescharacteristic
468C3×C22⋊C4—21no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—21no—
471C3×C22⋊C4—21no—
472C3×C22⋊C4—21no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4C22⋊D511yescharacteristic
477C3×C22⋊C4C22⋊D511yescharacteristic
478C3×C42C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—42no—
482C23×C5—42no—
483C23×C5—81no—
484C23×C5C2×C3×D411yescharacteristic
485C23×C5C2×C3×D411yescharacteristic
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—42no—
490C22×D5—42no—
491C22×D5—42no—
492C22×D5—42no—
493C22×D5—81no—
494C22×D5—81no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—22no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—42no—
502C5×D4—42no—
503C5×D4—81no—
504C5×D4C2×C3×D412yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—42no—
512C2×C4×C5—81no—
513C2×C4×C5C2×C3×D411yescharacteristic
514C2×C4×C5C2×C3×D411yescharacteristic
515C2×C4×C5C2×C3×D411yescharacteristic
516C2×C4×C5C2×C3×D411yescharacteristic
517C2×C4×C5C24×C311yescharacteristic
518C22⋊D5—42no—
519C22⋊D5—42no—
520C2×Dic5—21no—
521D20—21no—
522D20—21no—
523D20—21no—
524D20—21no—
525D20—21no—
526D20—42no—
527D20—42no—
528D20—42no—
529D20—81no—
530D20C2×C3×D412yes—
531C4×D5—42no—
532#168—21no—
533#168—21no—
534#168—21no—
535#168C2×C3×D412yescomplemented
536C2×#41C2×C3×D511yescharacteristic, complemented
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—101no—
540C22×D4C2×C3×D511yescharacteristic, complemented
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—51no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8—51no—
549C2×D8—51no—
550C2×D8—51no—
551C2×D8—104no—
552C2×M16—51no—
553C22×C8—51no—
554#127—51no—
555#124C2×C3×D511yescharacteristic, complemented
556#123—21no—
557C22⋊Q8C2×C3×D511yescharacteristic, complemented
558#121—21no—
559#121—51no—
560#121—51no—
561#121—101no—
562#121C2×C3×D511yescharacteristic, complemented
563#120—21no—
564#120—101no—
565#120—101no—
566C4×D4—51no—
567C4×D4C2×C3×D511yescharacteristic
568C4×D4C2×C3×D511yescharacteristic, complemented
569C2×C22⋊C4—21no—
570#106—51no—
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102—51no—
577#102—51no—
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97—51no—
581C2×C3×C5—22no—
582C2×C3×C5—41no—
583C2×C3×C5—42no—
584C2×C3×C5—81no—
585C2×C3×C5D4211yescharacteristic
586C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
587C2×C3×C5#57611yescharacteristic
588C3×D5—42no—
589C3×D5—81no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—81no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—202no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—202no—
603C23×C3—401no—
604C23×C3—401no—
605C23×C3C2×C22⋊D511yescharacteristic
606C23×C3C2×C22⋊D511yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—22no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—42no—
614C3×D4—42no—
615C3×D4—52no—
616C3×D4—81no—
617C3×D4—101no—
618C3×D4—101no—
619C3×D4—101no—
620C3×D4—101no—
621C3×D4—101no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—202no—
626C3×D4—202no—
627C3×D4—401no—
628C3×D4D4×D512yescomplemented
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—42no—
636C2×C3×C4—81no—
637C2×C3×C4—101no—
638C2×C3×C4—202no—
639C2×C3×C4C2×C22⋊D511yescharacteristic
640C2×C3×C4C2×C22⋊D511yescharacteristic
641C2×C3×C4C2×C22⋊D511yescharacteristic
642C2×C3×C4C2×C22⋊D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—52no—
645C3×C8—101no—
646C3×C8—101no—
647C3×C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—21no—
653C22×C5—22no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—84no—
660C22×C5C3×AGL(1,ℤ/8)12yescomplemented
661C22×C5C22×C3×D411yescharacteristic
662C2×D5—22no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—84no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—21no—
676C4×C5—21no—
677C4×C5—41no—
678C4×C5—41no—
679C4×C5C22×C3×D411yescharacteristic
680C4×C5C3×H(5,𝔽2)11yescharacteristic
681Dic5—41no—
682C24—21no—
683C24—101no—
684C24—101no—
685#41—22no—
686#41—41no—
687C2×Q8C22×C3×D511yescharacteristic
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—51no—
694C2×D4—51no—
695C2×D4—51no—
696C2×D4—102no—
697C2×D4—102no—
698C2×D4—101no—
699C2×D4—101no—
700C2×D4—101no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—201no—
705C2×D4—201no—
706C2×D4—204no—
707C2×D4C3×C22⋊D511yescharacteristic
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—101no—
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715SD16—102no—
716SD16—102no—
717SD16—201no—
718D8—54no—
719D8—102no—
720D8—102no—
721D8—102no—
722D8—102no—
723D8—201no—
724M16—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—51no—
728C2×C8—51no—
729C2×C8—102no—
730C4⋊C4—21no—
731C4⋊C4—51no—
732C4⋊C4C3×C22⋊D511yescharacteristic
733C4⋊C4C22×C3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4C3×C22⋊D511yescharacteristic
743C22⋊C4C3×C22⋊D511yescharacteristic
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—84no—
758C22×C3—102no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3—201no—
762C22×C3—201no—
763C22×C3—201no—
764C22×C3—201no—
765C22×C3—201no—
766C22×C3—201no—
767C22×C3—404no—
768C22×C3—404no—
769C22×C3#409512yescomplemented
770C22×C3C22×C22⋊D511yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—201no—
778C3×C4C2×D4×D511yescharacteristic
779C3×C4#414411yescharacteristic
780C2×C5—22no—
781C2×C5—41no—
782C2×C5—42no—
783C2×C5—81no—
784C2×C5C3×D4211yescharacteristic
785C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
786C2×C5C3×#57611yescharacteristic
787D5—42no—
788D5—81no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—81no—
795C23—101no—
796C23—101no—
797C23—101no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—401no—
803C23—401no—
804C23C2×C3×C22⋊D511yescharacteristic
805C23C2×C3×C22⋊D511yescharacteristic
806Q8—21no—
807Q8—21no—
808D4—22no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—42no—
814D4—52no—
815D4—81no—
816D4—101no—
817D4—101no—
818D4—101no—
819D4—101no—
820D4—101no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—202no—
825D4—202no—
826D4—401no—
827D4C3×D4×D512yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—42no—
835C2×C4—81no—
836C2×C4—101no—
837C2×C4—202no—
838C2×C4C2×C3×C22⋊D511yescharacteristic
839C2×C4C2×C3×C22⋊D511yescharacteristic
840C2×C4C2×C3×C22⋊D511yescharacteristic
841C2×C4C2×C3×C22⋊D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—101no—
846C8—101no—
847C2×C3—22no—
848C2×C3—41no—
849C2×C3—42no—
850C2×C3—81no—
851C2×C3—202no—
852C2×C3—401no—
853C2×C3—401no—
854C2×C3D4×C22⋊D511yescharacteristic
855C2×C3C2×#409511yescharacteristic
856C2×C3#6616911yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—84no—
870C22—102no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—404no—
880C22—404no—
881C22C3×#409512yescomplemented
882C22C22×C3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—41no—
889C4—201no—
890C4C2×C3×D4×D511yescharacteristic
891C4C3×#414411yescharacteristic
892C3#1061523311yescharacteristic, direct product factor, Sylow
893C2—22no—
894C2—41no—
895C2—42no—
896C2—81no—
897C2—202no—
898C2—401no—
899C2—401no—
900C2C3×D4×C22⋊D511yescharacteristic
901C2C2×C3×#409511yescharacteristic
902C2C3×#6616911yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenterC3×#546D5
hypocenterC5C3×#3264
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
1. C3×C5×#546C2semidirect
2. C2×C3×#4095C2semidirect
3. C22×C3×#686C2semidirect
4. C3×D4×D20C2semidirect
5. C3×#65527C2semidirect
6. C3×#65506C2semidirect
7. C3×#65347C2semidirect
8. C3×#65346C2semidirect
9. C3×#65337C2semidirect
10. C3×#65335C2semidirect
11. C3×#65328C2semidirect
12. C3×#65325C2semidirect
13. C3×#65304C2semidirect
14. C3×#65303C2semidirect
15. C3×#65300C2semidirect
16. #10615233C3direct (N × H)
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×D4C22semidirect
21. C22×C3×D20C22semidirect
22. C3×C5×#124C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
26. C3×C5×#121C22semidirect
29. C3×C4×C5×D4C22semidirect
32. C2×C3×#688C22semidirect
33. C2×C3×#688C22semidirect
34. C2×C3×#688C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
40. C2×C3×#686C22semidirect
41. C2×C3×#686C22semidirect
43. C3×#4076C22semidirect
44. C2×C3×#681C22semidirect
45. C22×C3×#168C22semidirect
49. C3×#4020C22semidirect
50. C3×C4×D20C22semidirect
51. C3×#3967C22semidirect
52. C3×#3964C22semidirect
53. C3×#3964C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3941C22semidirect
57. C3×#3941C22semidirect
58. C3×#3941C22semidirect
59. C3×#3940C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×#546C2×C3semidirect
64. C2×#4095C2×C3semidirect
65. C22×#686C2×C3semidirect
66. D4×D20C2×C3semidirect
67. #65527C2×C3semidirect
68. #65506C2×C3semidirect
69. #65347C2×C3semidirect
70. #65346C2×C3semidirect
71. #65337C2×C3semidirect
72. #65335C2×C3semidirect
73. #65328C2×C3semidirect
74. #65325C2×C3semidirect
75. #65304C2×C3semidirect
76. #65303C2×C3semidirect
77. #65300C2×C3semidirect
130. C3×#686D4semidirect
143. C3×#546D5semidirect
156. C2×C5×#41C22×C3semidirect
157. C22×C5×D4C22×C3semidirect
160. C22×D20C22×C3semidirect
161. C5×#124C22×C3semidirect
163. C5×C22⋊Q8C22×C3semidirect
165. C5×#121C22×C3semidirect
168. C4×C5×D4C22×C3semidirect
171. C2×#688C22×C3semidirect
172. C2×#688C22×C3semidirect
173. C2×#688C22×C3semidirect
177. C2×#686C22×C3semidirect
178. C2×#686C22×C3semidirect
179. C2×#686C22×C3semidirect
180. C2×#686C22×C3semidirect
182. #4076C22×C3semidirect
183. C2×#681C22×C3semidirect
184. C22×#168C22×C3semidirect
188. #4020C22×C3semidirect
189. C4×D20C22×C3semidirect
190. #3967C22×C3semidirect
191. #3964C22×C3semidirect
192. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. C22⋊#168C22×C3semidirect
195. #3941C22×C3semidirect
196. #3941C22×C3semidirect
197. #3941C22×C3semidirect
198. #3940C22×C3semidirect
199. C4⋊#168C22×C3semidirect
200. #3935C22×C3semidirect
227. C3×C5×D4C2×D4semidirect
258. C3×#168C2×D4semidirect
259. C2×C3×#41C2×D5semidirect
263. C22×C3×D4C2×D5semidirect
278. C3×#124C2×D5semidirect
280. C3×C22⋊Q8C2×D5semidirect
285. C3×#121C2×D5semidirect
291. C3×C4×D4C2×D5semidirect
356. #686C3×D4semidirect
369. #546C3×D5semidirect
394. C22×C3×C5AGL(1,ℤ/8)semidirect
504. C5×D4C2×C3×D4semidirect
535. #168C2×C3×D4semidirect
536. C2×#41C2×C3×D5semidirect
540. C22×D4C2×C3×D5semidirect
555. #124C2×C3×D5semidirect
557. C22⋊Q8C2×C3×D5semidirect
562. #121C2×C3×D5semidirect
568. C4×D4C2×C3×D5semidirect
628. C3×D4D4×D5semidirect
660. C22×C5C3×AGL(1,ℤ/8)semidirect
745. C3×C5#3264semidirect
769. C22×C3#4095semidirect
827. D4C3×D4×D5semidirect
857. C5C3×#3264semidirect
881. C22C3×#4095semidirect
892. C3#10615233direct (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×#40952
C22×C3×#6862
C3×D4×D202
C3×#655272
C3×#655062
C3×#653472
C3×#653462
C3×#653372
C3×#653352
C3×#653282
C3×#653252
C3×#653042
C3×#653032
C3×#653002
#106152333
C3×#32645