Finite Group Databasebeta

← C3×#10615308 #14454217

Subgroups — C3×#10615308 #14454217

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, 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×#65363C211yesmaximal, characteristic, complemented
8C3×#65361C211yesmaximal, characteristic, complemented
9C3×#65331C211yesmaximal, characteristic, complemented
10C3×#65327C211yesmaximal, characteristic, complemented
11C3×#65326C211yesmaximal, characteristic, complemented
12C3×#65325C211yesmaximal, characteristic, complemented
13C3×#65317C211yesmaximal, characteristic, complemented
14C3×#65315C211yesmaximal, characteristic, complemented
15C3×#65300C211yesmaximal, characteristic, complemented
16#10615308C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C3×C5×#127—21no—
22C3×C5×#127C2211yescharacteristic, complemented
23C3×C5×#121—21no—
24C3×C5×#121—21no—
25C3×C5×#121C2211yescharacteristic
26C3×C5×#121C2211yescharacteristic, complemented
27C3×C4×C5×Q8C2211yescharacteristic, complemented
28C3×C4×C5×D4—21no—
29C3×C4×C5×D4C2211yescharacteristic
30C3×#4096—24no—
31C3×#4095—24no—
32C2×C3×#689C2211yescharacteristic, complemented
33C2×C3×#688C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35C3×#4083—21no—
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#687C2211yescharacteristic, complemented
38C2×C3×#686C2211yescharacteristic
39C2×C3×#686C2211yescharacteristic
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×#3964C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic
55C3×C22⋊#168C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3939C2211yescharacteristic, complemented
60C3×C4⋊#168C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C5×#550C2×C311yescharacteristic, complemented
64C2×#4096C2×C311yescharacteristic, complemented
65C2×#4095C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65527C2×C311yescharacteristic, complemented
69#65363C2×C311yescharacteristic, complemented
70#65361C2×C311yescharacteristic, complemented
71#65331C2×C311yescharacteristic, complemented
72#65327C2×C311yescharacteristic, complemented
73#65326C2×C311yescharacteristic, complemented
74#65325C2×C311yescharacteristic, complemented
75#65317C2×C311yescharacteristic, complemented
76#65315C2×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×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4—21no—
89C2×C3×C5×D4—21no—
90C2×C3×C5×D4D411yescharacteristic
91C2×C3×C5×D4C2311yescharacteristic
92C2×C3×C5×D4C2311yescharacteristic
93C22×C3×C4×C5—21no—
94C22×C3×C4×C5—21no—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—21no—
99C3×#709—22no—
100C3×#709—41no—
101C2×C3×D20—22no—
102C2×C3×D20—21no—
103C2×C3×D20—41no—
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5—21no—
108C2×C3×Dic10C2311yescharacteristic
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⋊C4D411yescharacteristic
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C42×C5—21no—
117C3×C42×C5C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×#689—22no—
120C3×#688—22no—
121C3×#688D414yescomplemented
122C3×#687—22no—
123C3×#687—41no—
124C3×#686—22no—
125C3×#686—22no—
126C3×#686—22no—
127C3×#686—41no—
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×#550D511yescharacteristic, complemented
143C3×#546—51no—
144C3×#496—51no—
145C3×#468—51no—
146C3×#466—51no—
147C3×#464—51no—
148C3×#459—51no—
149C3×#452—51no—
150C3×#449—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×C5×#41C22×C311yescharacteristic
156C2×C5×#41C22×C311yescharacteristic, complemented
157C2×#709C22×C311yescharacteristic
158C22×D20C22×C311yescharacteristic
159C5×#127—21no—
160C5×#127C22×C311yescharacteristic, complemented
161C5×#121—21no—
162C5×#121—21no—
163C5×#121C22×C311yescharacteristic
164C5×#121C22×C311yescharacteristic, complemented
165C4×C5×Q8C22×C311yescharacteristic, complemented
166C4×C5×D4—21no—
167C4×C5×D4C22×C311yescharacteristic
168#4096—24no—
169#4095—24no—
170C2×#689C22×C311yescharacteristic, complemented
171C2×#688C22×C311yescharacteristic
172C2×#688C22×C311yescharacteristic
173#4083—21no—
174C2×#687C22×C311yescharacteristic, complemented
175C2×#687C22×C311yescharacteristic, complemented
176C2×#686C22×C311yescharacteristic
177C2×#686C22×C311yescharacteristic
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#3964C22×C311yescharacteristic, complemented
191#3964C22×C311yescharacteristic, complemented
192C22⋊#168C22×C311yescharacteristic
193C22⋊#168C22×C311yescharacteristic, complemented
194#3942C22×C311yescharacteristic, complemented
195#3941C22×C311yescharacteristic
196#3941C22×C311yescharacteristic
197#3939C22×C311yescharacteristic, complemented
198C4⋊#168C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C23×C3×C5C2×D411yescharacteristic
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—81no—
210C3×C5×Q8—21no—
211C3×C5×Q8C2×D412yes—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—41no—
217C3×C5×D4—42no—
218C3×C5×D4—42no—
219C3×C5×D4—42no—
220C3×C5×D4—81no—
221C3×C5×D4—81no—
222C3×C5×D4—81no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—42no—
230C2×C3×C4×C5—42no—
231C2×C3×C4×C5C2×D411yescharacteristic
232C2×C3×C4×C5C2×D411yescharacteristic
233C2×C3×C4×C5C2×D411yescharacteristic
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2411yescharacteristic
236C3×C22⋊D5—42no—
237C3×C22⋊D5—81no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×D20C2×D412yes—
245C3×C4×D5—42no—
246C3×C4×D5—81no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3×#168—21no—
250C3×#168—21no—
251C3×#168—21no—
252C3×#168C2×D412yes—
253C2×C3×#41—51no—
254C2×C3×#41C2×D511yescharacteristic
255C2×C3×#41C2×D511yescharacteristic, complemented
256C22×C3×D4—51no—
257C3×AGL(1,ℤ/8)—104no—
258C3×#135—104no—
259C2×C3×Q16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C2×C3×M16—51no—
269C22×C3×C8—51no—
270C3×#127—21no—
271C3×#127C2×D511yescharacteristic, complemented
272C3×#124—51no—
273C3×#123—101no—
274C3×C22⋊Q8—51no—
275C3×#121—21no—
276C3×#121—21no—
277C3×#121—51no—
278C3×#121—101no—
279C3×#121C2×D511yescharacteristic
280C3×#121C2×D511yescharacteristic, complemented
281C3×#120—101no—
282C3×C4×Q8C2×D511yescharacteristic, complemented
283C3×C4×D4—21no—
284C3×C4×D4—51no—
285C3×C4×D4C2×D511yescharacteristic
286C2×C3×C22⋊C4—101no—
287C3×#107—51no—
288C3×C4⋊C8—51no—
289C3×#103—51no—
290C3×#103—51no—
291C3×#102—51no—
292C3×#102—51no—
293C3×#102—51no—
294C3×#102—51no—
295C3×C22⋊C8—51no—
296C3×C22⋊C8—51no—
297C3×#97—51no—
298C23×D5—21no—
299C5×#41—22no—
300C5×#41—22no—
301C5×#41—41no—
302C5×#41—41no—
303C2×C5×Q8C23×C311yescharacteristic
304C2×C5×D4—21no—
305C2×C5×D4—21no—
306C2×C5×D4—21no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—21no—
310C2×C5×D4C3×D411yescharacteristic
311C2×C5×D4C23×C311yescharacteristic
312C2×C5×D4C23×C311yescharacteristic
313C22×C4×C5—21no—
314C22×C4×C5—21no—
315C22×C4×C5C23×C311yescharacteristic
316C22×C4×C5C23×C311yescharacteristic
317C2×C22⋊D5—21no—
318C2×C22⋊D5—21no—
319#709—22no—
320#709—41no—
321C2×D20—22no—
322C2×D20—21no—
323C2×D20—41no—
324C2×D20C23×C311yescharacteristic
325C2×D20C23×C311yescharacteristic
326C2×C4×D5—21no—
327C2×C4×D5—21no—
328C2×Dic10C23×C311yescharacteristic
329C5×C4⋊C4—21no—
330C5×C4⋊C4C3×D411yescharacteristic
331C5×C4⋊C4C23×C311yescharacteristic
332C5×C22⋊C4—21no—
333C5×C22⋊C4—21no—
334C5×C22⋊C4C3×D411yescharacteristic
335C5×C22⋊C4C3×D411yescharacteristic
336C42×C5—21no—
337C42×C5C23×C311yescharacteristic
338C22⋊Dic5—21no—
339#689—22no—
340#688—22no—
341#688C3×D414yescomplemented
342#687—22no—
343#687—41no—
344#686—22no—
345#686—22no—
346#686—22no—
347#686—41no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—21no—
352C4⋊Dic5C23×C311yescharacteristic
353#683—21no—
354#681—22no—
355C2×#168—22no—
356C2×#168C23×C311yescharacteristic
357C2×#168C23×C311yescharacteristic
358C2×#168C23×C311yescharacteristic
359C2×#168C23×C311yescharacteristic
360C2×AGL(1,ℤ/8)—51no—
361C2×#135—51no—
362#550C3×D511yescharacteristic, complemented
363#546—51no—
364#496—51no—
365#468—51no—
366#466—51no—
367#464—51no—
368#459—51no—
369#452—51no—
370#449—51no—
371#449—51no—
372#447—51no—
373#440—51no—
374#435—51no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5C22×D411yescharacteristic
388C2×C3×D5—22no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—84no—
395C3×C4×C5—21no—
396C3×C4×C5—21no—
397C3×C4×C5—22no—
398C3×C4×C5—21no—
399C3×C4×C5—21no—
400C3×C4×C5—41no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403C3×Dic5—41no—
404C3×Dic5—41no—
405C24×C3—101no—
406C3×#41—22no—
407C3×#41—22no—
408C3×#41—41no—
409C3×#41—41no—
410C3×#41—102no—
411C3×#41—201no—
412C2×C3×Q8—51no—
413C2×C3×Q8C22×D511yescharacteristic
414C2×C3×D4—21no—
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4—21no—
419C2×C3×D4—21no—
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—102no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—201no—
427C2×C3×D4C22⋊D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—21no—
432C22×C3×C4—101no—
433C22×C3×C4—101no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C3×Q16—102no—
437C3×SD16—54no—
438C3×SD16—102no—
439C3×SD16—102no—
440C3×SD16—201no—
441C3×D8—102no—
442C3×D8—102no—
443C3×D8—102no—
444C3×D8—201no—
445C3×M16—102no—
446C2×C3×C8—51no—
447C2×C3×C8—51no—
448C2×C3×C8—51no—
449C2×C3×C8—51no—
450C2×C3×C8—102no—
451C3×C4⋊C4—21no—
452C3×C4⋊C4—51no—
453C3×C4⋊C4—101no—
454C3×C4⋊C4C22⋊D511yescharacteristic
455C3×C4⋊C4C22×D511yescharacteristic
456C3×C22⋊C4—21no—
457C3×C22⋊C4—21no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4C22⋊D511yescharacteristic
464C3×C22⋊C4C22⋊D511yescharacteristic
465C3×C42—21no—
466C3×C42C22×D511yescharacteristic
467C23×C5—21no—
468C23×C5—21no—
469C23×C5C2×C3×D411yescharacteristic
470C23×C5C2×C3×D411yescharacteristic
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—42no—
474C22×D5—42no—
475C22×D5—81no—
476C5×Q8—21no—
477C5×Q8C2×C3×D412yes—
478C5×D4—21no—
479C5×D4—21no—
480C5×D4—21no—
481C5×D4—21no—
482C5×D4—41no—
483C5×D4—42no—
484C5×D4—42no—
485C5×D4—42no—
486C5×D4—81no—
487C5×D4—81no—
488C5×D4—81no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—42no—
496C2×C4×C5—42no—
497C2×C4×C5C2×C3×D411yescharacteristic
498C2×C4×C5C2×C3×D411yescharacteristic
499C2×C4×C5C2×C3×D411yescharacteristic
500C2×C4×C5C2×C3×D411yescharacteristic
501C2×C4×C5C24×C311yescharacteristic
502C22⋊D5—42no—
503C22⋊D5—81no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506D20—21no—
507D20—21no—
508D20—21no—
509D20—42no—
510D20C2×C3×D412yes—
511C4×D5—42no—
512C4×D5—81no—
513Dic10—21no—
514Dic10—21no—
515#168—21no—
516#168—21no—
517#168—21no—
518#168C2×C3×D412yes—
519C2×#41—51no—
520C2×#41C2×C3×D511yescharacteristic
521C2×#41C2×C3×D511yescharacteristic, complemented
522C22×D4—51no—
523AGL(1,ℤ/8)—104no—
524#135—104no—
525C2×Q16—51no—
526C2×SD16—51no—
527C2×SD16—51no—
528C2×SD16—51no—
529C2×SD16—51no—
530C2×D8—51no—
531C2×D8—51no—
532C2×D8—51no—
533C2×D8—51no—
534C2×M16—51no—
535C22×C8—51no—
536#127—21no—
537#127C2×C3×D511yescharacteristic, complemented
538#124—51no—
539#123—101no—
540C22⋊Q8—51no—
541#121—21no—
542#121—21no—
543#121—51no—
544#121—101no—
545#121C2×C3×D511yescharacteristic
546#121C2×C3×D511yescharacteristic, complemented
547#120—101no—
548C4×Q8C2×C3×D511yescharacteristic, complemented
549C4×D4—21no—
550C4×D4—51no—
551C4×D4C2×C3×D511yescharacteristic
552C2×C22⋊C4—101no—
553#107—51no—
554C4⋊C8—51no—
555#103—51no—
556#103—51no—
557#102—51no—
558#102—51no—
559#102—51no—
560#102—51no—
561C22⋊C8—51no—
562C22⋊C8—51no—
563#97—51no—
564C2×C3×C5—41no—
565C2×C3×C5—41no—
566C2×C3×C5—81no—
567C2×C3×C5—81no—
568C2×C3×C5D4211yescharacteristic
569C2×C3×C5#57511yescharacteristic
570C2×C3×C5#57611yescharacteristic
571C3×D5—42no—
572C3×D5—81no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—202no—
578C23×C3—202no—
579C23×C3—401no—
580C23×C3C2×C22⋊D511yescharacteristic
581C23×C3C2×C22⋊D511yescharacteristic
582C3×Q8—21no—
583C3×Q8—101no—
584C3×Q8—101no—
585C3×Q8D4×D512yes—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—41no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—42no—
594C3×D4—52no—
595C3×D4—81no—
596C3×D4—81no—
597C3×D4—81no—
598C3×D4—101no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—202no—
602C3×D4—202no—
603C3×D4—401no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—202no—
615C2×C3×C4—401no—
616C2×C3×C4C2×C22⋊D511yescharacteristic
617C2×C3×C4C2×C22⋊D511yescharacteristic
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C2×C22⋊D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—52no—
622C3×C8—101no—
623C3×C8—101no—
624C3×C8—101no—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—21no—
628C22×C5—21no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5C22×C3×D411yescharacteristic
638C2×D5—22no—
639C2×D5—41no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—21no—
648C4×C5—21no—
649C4×C5—22no—
650C4×C5—41no—
651C4×C5C22×C3×D411yescharacteristic
652C4×C5C3×H(5,𝔽2)11yescharacteristic
653Dic5—41no—
654Dic5—41no—
655C24—101no—
656#41—22no—
657#41—22no—
658#41—41no—
659#41—41no—
660#41—102no—
661#41—201no—
662C2×Q8—51no—
663C2×Q8C22×C3×D511yescharacteristic
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—51no—
671C2×D4—51no—
672C2×D4—102no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—201no—
677C2×D4C3×C22⋊D511yescharacteristic
678C2×D4C22×C3×D511yescharacteristic
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4C22×C3×D511yescharacteristic
685C22×C4C22×C3×D511yescharacteristic
686Q16—102no—
687SD16—54no—
688SD16—102no—
689SD16—102no—
690SD16—201no—
691D8—102no—
692D8—102no—
693D8—102no—
694D8—201no—
695M16—102no—
696C2×C8—51no—
697C2×C8—51no—
698C2×C8—51no—
699C2×C8—51no—
700C2×C8—102no—
701C4⋊C4—21no—
702C4⋊C4—51no—
703C4⋊C4—101no—
704C4⋊C4C3×C22⋊D511yescharacteristic
705C4⋊C4C22×C3×D511yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—101no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4C3×C22⋊D511yescharacteristic
714C22⋊C4C3×C22⋊D511yescharacteristic
715C42—21no—
716C42C22×C3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—102no—
731C22×C3—201no—
732C22×C3—201no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—404no—
737C22×C3C22×C22⋊D511yescharacteristic
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—201no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414411yescharacteristic
748C2×C5—41no—
749C2×C5—41no—
750C2×C5—81no—
751C2×C5—81no—
752C2×C5C3×D4211yescharacteristic
753C2×C5C3×#57511yescharacteristic
754C2×C5C3×#57611yescharacteristic
755D5—42no—
756D5—81no—
757C23—21no—
758C23—21no—
759C23—101no—
760C23—101no—
761C23—202no—
762C23—202no—
763C23—401no—
764C23C2×C3×C22⋊D511yescharacteristic
765C23C2×C3×C22⋊D511yescharacteristic
766Q8—21no—
767Q8—101no—
768Q8—101no—
769Q8C3×D4×D512yes—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—41no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—52no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—101no—
783D4—101no—
784D4—101no—
785D4—202no—
786D4—202no—
787D4—401no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—202no—
799C2×C4—401no—
800C2×C4C2×C3×C22⋊D511yescharacteristic
801C2×C4C2×C3×C22⋊D511yescharacteristic
802C2×C4C2×C3×C22⋊D511yescharacteristic
803C2×C4C2×C3×C22⋊D511yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—52no—
806C8—101no—
807C8—101no—
808C8—101no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—81no—
812C2×C3—81no—
813C2×C3—202no—
814C2×C3—401no—
815C2×C3D4×C22⋊D511yescharacteristic
816C2×C3#6615611yescharacteristic
817C2×C3#6616911yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—102no—
832C22—201no—
833C22—201no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C22×C3×C22⋊D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—41no—
845C4—201no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414411yescharacteristic
849C3#1061530811yescharacteristic, direct product factor, Sylow
850C2—41no—
851C2—41no—
852C2—81no—
853C2—81no—
854C2—202no—
855C2—401no—
856C2C3×D4×C22⋊D511yescharacteristic
857C2C3×#6615611yescharacteristic
858C2C3×#6616911yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#550C2
socleC22×C3×C5C22×D4
hypercenterC3×#550D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C3×C5×#550C2semidirect
2. C2×C3×#4096C2semidirect
3. C2×C3×#4095C2semidirect
4. C3×#65884C2semidirect
5. C3×#65528C2semidirect
6. C3×#65527C2semidirect
7. C3×#65363C2semidirect
8. C3×#65361C2semidirect
9. C3×#65331C2semidirect
10. C3×#65327C2semidirect
11. C3×#65326C2semidirect
12. C3×#65325C2semidirect
13. C3×#65317C2semidirect
14. C3×#65315C2semidirect
15. C3×#65300C2semidirect
16. #10615308C3direct (N × H)
18. C2×C3×C5×#41C22semidirect
22. C3×C5×#127C22semidirect
26. C3×C5×#121C22semidirect
27. C3×C4×C5×Q8C22semidirect
32. C2×C3×#689C22semidirect
36. C2×C3×#687C22semidirect
37. C2×C3×#687C22semidirect
45. C22×C3×#168C22semidirect
51. C3×#3967C22semidirect
52. C3×#3964C22semidirect
53. C3×#3964C22semidirect
55. C3×C22⋊#168C22semidirect
56. C3×#3942C22semidirect
59. C3×#3939C22semidirect
60. C3×C4⋊#168C22semidirect
61. C3×#3935C22semidirect
63. C5×#550C2×C3semidirect
64. C2×#4096C2×C3semidirect
65. C2×#4095C2×C3semidirect
66. #65884C2×C3semidirect
67. #65528C2×C3semidirect
68. #65527C2×C3semidirect
69. #65363C2×C3semidirect
70. #65361C2×C3semidirect
71. #65331C2×C3semidirect
72. #65327C2×C3semidirect
73. #65326C2×C3semidirect
74. #65325C2×C3semidirect
75. #65317C2×C3semidirect
76. #65315C2×C3semidirect
77. #65300C2×C3semidirect
121. C3×#688D4semidirect
142. C3×#550D5semidirect
156. C2×C5×#41C22×C3semidirect
160. C5×#127C22×C3semidirect
164. C5×#121C22×C3semidirect
165. C4×C5×Q8C22×C3semidirect
170. C2×#689C22×C3semidirect
174. C2×#687C22×C3semidirect
175. C2×#687C22×C3semidirect
183. C22×#168C22×C3semidirect
189. #3967C22×C3semidirect
190. #3964C22×C3semidirect
191. #3964C22×C3semidirect
193. C22⋊#168C22×C3semidirect
194. #3942C22×C3semidirect
197. #3939C22×C3semidirect
198. C4⋊#168C22×C3semidirect
199. #3935C22×C3semidirect
255. C2×C3×#41C2×D5semidirect
271. C3×#127C2×D5semidirect
280. C3×#121C2×D5semidirect
282. C3×C4×Q8C2×D5semidirect
341. #688C3×D4semidirect
362. #550C3×D5semidirect
521. C2×#41C2×C3×D5semidirect
537. #127C2×C3×D5semidirect
546. #121C2×C3×D5semidirect
548. C4×Q8C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10615308direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5502
C2×C3×#40962
C2×C3×#40952
C3×#658842
C3×#655282
C3×#655272
C3×#653632
C3×#653612
C3×#653312
C3×#653272
C3×#653262
C3×#653252
C3×#653172
C3×#653152
C3×#653002
#106153083
C3×#32685