Finite Group Databasebeta

← C3×#10612298 #14453944

Subgroups — C3×#10612298 #14453944

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
1C2×C3×#4062C211yesmaximal, characteristic, complemented
2C2×C3×#4057C211yesmaximal, characteristic, complemented
3C3×#66010C211yesmaximal, characteristic, complemented
4C3×#65889C211yesmaximal, characteristic, complemented
5C3×C5×#463C211yesmaximal, characteristic, complemented
6C3×#65462C211yesmaximal, characteristic, complemented
7C3×#65447C211yesmaximal, characteristic, complemented
8C3×#65349C211yesmaximal, characteristic, complemented
9C3×#65303C211yesmaximal, characteristic, complemented
10C3×#65130C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65105C211yesmaximal, characteristic, complemented
13C3×#65099C211yesmaximal, characteristic, complemented
14C3×#65067C211yesmaximal, characteristic, complemented
15C3×#65065C211yesmaximal, characteristic, complemented
16#10612298C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic, complemented
22C2×C3×C5×D8C2211yescharacteristic
23C3×C5×#124C2211yescharacteristic
24C3×C4×C5×D4C2211yescharacteristic, complemented
25C3×#4092C2211yescharacteristic
26C2×C3×#689C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C3×#4084C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076—21no—
33C2×C3×C4⋊Dic5—21no—
34C3×#4062—24no—
35C3×#4057—24no—
36C2×C3×#677C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×#676C2211yescharacteristic
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4043C2211yescharacteristic
41C3×#4043C2211yescharacteristic, complemented
42C3×#4032—21no—
43C3×#4032—21no—
44C3×#4030—21no—
45C3×#4029—21no—
46C3×#4028—21no—
47C3×D5×C22⋊C4—21no—
48C3×C4×D20C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×#4015C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic
54C3×#3964C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic
56C3×#3952C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic
60C3×#3940C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4062C2×C311yescharacteristic, complemented
64C2×#4057C2×C311yescharacteristic, complemented
65#66010C2×C311yescharacteristic, complemented
66#65889C2×C311yescharacteristic, complemented
67C5×#463C2×C311yescharacteristic, complemented
68#65462C2×C311yescharacteristic, complemented
69#65447C2×C311yescharacteristic, complemented
70#65349C2×C311yescharacteristic, complemented
71#65303C2×C311yescharacteristic, complemented
72#65130C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65105C2×C311yescharacteristic, complemented
75#65099C2×C311yescharacteristic, complemented
76#65067C2×C311yescharacteristic, complemented
77#65065C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C22×C3×Dic5—21no—
88C22×C3×Dic5—21no—
89C3×#713—22no—
90C3×#713—41no—
91C3×#711—22no—
92C3×#711—22no—
93C3×#711—41no—
94C3×#711—41no—
95C3×D4×D5—22no—
96C3×D4×D5—41no—
97C2×C3×D20—21no—
98C2×C3×D20D411yescharacteristic
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5C2311yescharacteristic
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×SD16—22no—
107C3×C5×D8—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C42×C5C2311yescharacteristic
115C3×C22⋊Dic5—21no—
116C3×#689—22no—
117C3×#689—41no—
118C3×#687—22no—
119C3×#687—41no—
120C3×#686D414yescomplemented
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685D411yescharacteristic
126C3×#685D411yescharacteristic
127C3×C4⋊Dic5—21no—
128C3×C4⋊Dic5—21no—
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5—21no—
131C3×C4⋊Dic5D411yescharacteristic
132C3×C4⋊Dic5C2311yescharacteristic
133C3×#683—21no—
134C2×C3×#168C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C3×#677—22no—
137C3×#677—22no—
138C3×#676—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#470—51no—
146C3×#465—51no—
147C3×#463D511yescharacteristic, complemented
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×#713C22×C311yescharacteristic
156C2×#711C22×C311yescharacteristic
157C2×#711C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic, complemented
160C2×C5×D8C22×C311yescharacteristic
161C5×#124C22×C311yescharacteristic
162C4×C5×D4C22×C311yescharacteristic, complemented
163#4092C22×C311yescharacteristic
164C2×#689C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166#4084C22×C311yescharacteristic
167C2×#687C22×C311yescharacteristic
168C2×#687C22×C311yescharacteristic
169C2×#686C22×C311yescharacteristic
170#4076—21no—
171C2×C4⋊Dic5—21no—
172#4062—24no—
173#4057—24no—
174C2×#677C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×#676C22×C311yescharacteristic
177C2×C8×D5C22×C311yescharacteristic, complemented
178#4043C22×C311yescharacteristic
179#4043C22×C311yescharacteristic, complemented
180#4032—21no—
181#4032—21no—
182#4030—21no—
183#4029—21no—
184#4028—21no—
185D5×C22⋊C4—21no—
186C4×D20C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188#4015C22×C311yescharacteristic, complemented
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×#103C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic
192#3964C22×C311yescharacteristic, complemented
193#3952C22×C311yescharacteristic
194#3952C22×C311yescharacteristic, complemented
195#3948C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic
198#3940C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—42no—
205C22×C3×D5—42no—
206C22×C3×D5—81no—
207C22×C3×D5C2×D411yescharacteristic
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4C2×D412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—42no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2411yescharacteristic
221C3×C22⋊D5—42no—
222C3×C22⋊D5—42no—
223C3×C22⋊D5—42no—
224C3×C22⋊D5—81no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—42no—
229C2×C3×Dic5—42no—
230C2×C3×Dic5C2×D411yescharacteristic
231C2×C3×Dic5C2×D411yescharacteristic
232C3×D20—21no—
233C3×D20—41no—
234C3×D20—42no—
235C3×D20C2×D412yes—
236C3×C4×D5—21no—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×C4×D5—42no—
241C3×C4×D5—81no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×#168—21no—
249C3×#168C2×D412yes—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41—51no—
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×SD16C2×D511yescharacteristic, complemented
263C2×C3×D8—51no—
264C2×C3×D8C2×D511yescharacteristic
265C2×C3×M16—51no—
266C22×C3×C8—51no—
267C3×C4⋊Q8—51no—
268C3×#124C2×D511yescharacteristic
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—51no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#121—101no—
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4—51no—
281C3×C4×D4C2×D511yescharacteristic, complemented
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106—51no—
285C3×C4⋊C8C2×D511yescharacteristic, complemented
286C3×#103—51no—
287C3×#103—51no—
288C3×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102—51no—
291C3×#102C2×D511yescharacteristic
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97—51no—
295C23×D5—21no—
296C2×C5×Q8C23×C311yescharacteristic
297C2×C5×D4C23×C311yescharacteristic
298C2×C5×D4C23×C311yescharacteristic
299C22×C4×C5—21no—
300C2×C22⋊D5—21no—
301C2×C22⋊D5—21no—
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304C22×Dic5—21no—
305C22×Dic5—21no—
306#713—22no—
307#713—41no—
308#711—22no—
309#711—22no—
310#711—41no—
311#711—41no—
312D4×D5—22no—
313D4×D5—41no—
314C2×D20—21no—
315C2×D20C3×D411yescharacteristic
316C2×D20C23×C311yescharacteristic
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5C23×C311yescharacteristic
320C2×C4×D5C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×SD16—22no—
324C5×D8—22no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4C23×C311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—21no—
330C5×C22⋊C4—21no—
331C42×C5C23×C311yescharacteristic
332C22⋊Dic5—21no—
333#689—22no—
334#689—41no—
335#687—22no—
336#687—41no—
337#686C3×D414yescomplemented
338#685—21no—
339#685—21no—
340#685—21no—
341#685—21no—
342#685C3×D411yescharacteristic
343#685C3×D411yescharacteristic
344C4⋊Dic5—21no—
345C4⋊Dic5—21no—
346C4⋊Dic5—21no—
347C4⋊Dic5—21no—
348C4⋊Dic5C3×D411yescharacteristic
349C4⋊Dic5C23×C311yescharacteristic
350#683—21no—
351C2×#168C23×C311yescharacteristic
352C2×#168C23×C311yescharacteristic
353#677—22no—
354#677—22no—
355#676—22no—
356C8×D5—22no—
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497—51no—
362#470—51no—
363#465—51no—
364#463C3×D511yescharacteristic, complemented
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435—51no—
372C22×C3×C5—22no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C22×D411yescharacteristic
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C2×C3×D5—22no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C2×C3×D5—21no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395C3×Dic5—21no—
396C3×Dic5—21no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—102no—
402C3×#41—102no—
403C3×#41—102no—
404C3×#41—201no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8—51no—
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—101no—
413C2×C3×D4—101no—
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—51no—
423C22×C3×C4—51no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4—101no—
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—22no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—22no—
436C3×D8—54no—
437C3×M16—102no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—51no—
444C3×C4⋊C4—51no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—21no—
454C3×C22⋊C4—51no—
455C3×C22⋊C4—51no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C42C22×D511yescharacteristic
462C23×C5—21no—
463C23×C5—21no—
464C22×D5—21no—
465C22×D5—42no—
466C22×D5—42no—
467C22×D5—81no—
468C22×D5C2×C3×D411yescharacteristic
469C22×D5C2×C3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×D4—21no—
473C5×D4—21no—
474C5×D4—21no—
475C5×D4C2×C3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—42no—
479C2×C4×C5C2×C3×D411yescharacteristic
480C2×C4×C5C2×C3×D411yescharacteristic
481C2×C4×C5C24×C311yescharacteristic
482C22⋊D5—42no—
483C22⋊D5—42no—
484C22⋊D5—42no—
485C22⋊D5—81no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—42no—
490C2×Dic5—42no—
491C2×Dic5C2×C3×D411yescharacteristic
492C2×Dic5C2×C3×D411yescharacteristic
493D20—21no—
494D20—41no—
495D20—42no—
496D20C2×C3×D412yes—
497C4×D5—21no—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—21no—
501C4×D5—42no—
502C4×D5—81no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8—21no—
509#168—21no—
510#168C2×C3×D412yes—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41—51no—
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×SD16C2×C3×D511yescharacteristic, complemented
524C2×D8—51no—
525C2×D8C2×C3×D511yescharacteristic
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8—51no—
529#124C2×C3×D511yescharacteristic
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
535C22⋊Q8—51no—
536#121—51no—
537#121—101no—
538#121—101no—
539#120—101no—
540C4×D4—51no—
541C4×D4—51no—
542C4×D4C2×C3×D511yescharacteristic, complemented
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106—51no—
546C4⋊C8C2×C3×D511yescharacteristic, complemented
547#103—51no—
548#103—51no—
549#103C2×C3×D511yescharacteristic, complemented
550#102—51no—
551#102—51no—
552#102C2×C3×D511yescharacteristic
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97—51no—
556C2×C3×C5—42no—
557C2×C3×C5—81no—
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#57511yescharacteristic
560C2×C3×C5#57711yescharacteristic
561C3×D5—41no—
562C3×D5—41no—
563C3×D5—42no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—51no—
567C23×C3—51no—
568C23×C3—101no—
569C23×C3—202no—
570C23×C3—202no—
571C23×C3—401no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—52no—
582C3×D4—101no—
583C3×D4—201no—
584C3×D4—202no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—401no—
589C3×D4D4×D512yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—42no—
593C2×C3×C4—51no—
594C2×C3×C4—51no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—202no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—401no—
606C2×C3×C4D4×D511yescharacteristic
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—52no—
612C3×C8—101no—
613C22×C5—22no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5C22×C3×D411yescharacteristic
620C2×D5—21no—
621C2×D5—21no—
622C2×D5—21no—
623C2×D5—21no—
624C2×D5—21no—
625C2×D5—21no—
626C2×D5—22no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5C22×C3×D411yescharacteristic
635C4×C5C3×H(5,𝔽2)11yescharacteristic
636Dic5—21no—
637Dic5—21no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641C24—101no—
642#41—102no—
643#41—102no—
644#41—102no—
645#41—201no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8—51no—
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—101no—
654C2×D4—101no—
655C2×D4—102no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—201no—
660C2×D4C22×C3×D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669Q16—102no—
670Q16—201no—
671SD16—22no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—22no—
677D8—54no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—51no—
685C4⋊C4—51no—
686C4⋊C4—101no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—51no—
696C22⋊C4—51no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42C22×C3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—101no—
711C22×C3—101no—
712C22×C3—101no—
713C22×C3—101no—
714C22×C3—101no—
715C22×C3—101no—
716C22×C3—102no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—101no—
726C3×C4—101no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414911yescharacteristic
732C2×C5—42no—
733C2×C5—81no—
734C2×C5C3×D4211yescharacteristic
735C2×C5C3×#57511yescharacteristic
736C2×C5C3×#57711yescharacteristic
737D5—41no—
738D5—41no—
739D5—42no—
740C23—21no—
741C23—21no—
742C23—51no—
743C23—51no—
744C23—101no—
745C23—202no—
746C23—202no—
747C23—401no—
748Q8—21no—
749Q8—21no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—52no—
758D4—101no—
759D4—201no—
760D4—202no—
761D4—202no—
762D4—202no—
763D4—202no—
764D4—401no—
765D4C3×D4×D512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—42no—
769C2×C4—51no—
770C2×C4—51no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—401no—
782C2×C4C3×D4×D511yescharacteristic
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—21no—
787C8—52no—
788C8—101no—
789C2×C3—42no—
790C2×C3—81no—
791C2×C3—201no—
792C2×C3—201no—
793C2×C3—202no—
794C2×C3#6594311yescharacteristic
795C2×C3#6610411yescharacteristic
796C2×C3#6610711yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—101no—
805C22—101no—
806C22—101no—
807C22—101no—
808C22—101no—
809C22—101no—
810C22—102no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—101no—
820C4—101no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414911yescharacteristic
826C3#1061229811yescharacteristic, direct product factor, Sylow
827C2—42no—
828C2—81no—
829C2—201no—
830C2—201no—
831C2—202no—
832C2C3×#6594311yescharacteristic
833C2C3×#6610411yescharacteristic
834C2C3×#6610711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#463C2
socleC22×C3×C5C22×D4
hypercenterC3×#463D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4062C2semidirect
2. C2×C3×#4057C2semidirect
3. C3×#66010C2semidirect
4. C3×#65889C2semidirect
5. C3×C5×#463C2semidirect
6. C3×#65462C2semidirect
7. C3×#65447C2semidirect
8. C3×#65349C2semidirect
9. C3×#65303C2semidirect
10. C3×#65130C2semidirect
11. C3×#65125C2semidirect
12. C3×#65105C2semidirect
13. C3×#65099C2semidirect
14. C3×#65067C2semidirect
15. C3×#65065C2semidirect
16. #10612298C3direct (N × H)
19. C2×C3×#711C22semidirect
21. C2×C3×C5×SD16C22semidirect
24. C3×C4×C5×D4C22semidirect
26. C2×C3×#689C22semidirect
27. C2×C3×#689C22semidirect
39. C2×C3×C8×D5C22semidirect
41. C3×#4043C22semidirect
50. C3×#4015C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#103C22semidirect
54. C3×#3964C22semidirect
56. C3×#3952C22semidirect
57. C3×#3948C22semidirect
58. C3×#3948C22semidirect
60. C3×#3940C22semidirect
61. C3×#3935C22semidirect
63. C2×#4062C2×C3semidirect
64. C2×#4057C2×C3semidirect
65. #66010C2×C3semidirect
66. #65889C2×C3semidirect
67. C5×#463C2×C3semidirect
68. #65462C2×C3semidirect
69. #65447C2×C3semidirect
70. #65349C2×C3semidirect
71. #65303C2×C3semidirect
72. #65130C2×C3semidirect
73. #65125C2×C3semidirect
74. #65105C2×C3semidirect
75. #65099C2×C3semidirect
76. #65067C2×C3semidirect
77. #65065C2×C3semidirect
120. C3×#686D4semidirect
147. C3×#463D5semidirect
157. C2×#711C22×C3semidirect
159. C2×C5×SD16C22×C3semidirect
162. C4×C5×D4C22×C3semidirect
164. C2×#689C22×C3semidirect
165. C2×#689C22×C3semidirect
177. C2×C8×D5C22×C3semidirect
179. #4043C22×C3semidirect
188. #4015C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
190. C5×#103C22×C3semidirect
192. #3964C22×C3semidirect
194. #3952C22×C3semidirect
195. #3948C22×C3semidirect
196. #3948C22×C3semidirect
198. #3940C22×C3semidirect
199. #3935C22×C3semidirect
262. C2×C3×SD16C2×D5semidirect
281. C3×C4×D4C2×D5semidirect
285. C3×C4⋊C8C2×D5semidirect
288. C3×#103C2×D5semidirect
337. #686C3×D4semidirect
364. #463C3×D5semidirect
523. C2×SD16C2×C3×D5semidirect
542. C4×D4C2×C3×D5semidirect
546. C4⋊C8C2×C3×D5semidirect
549. #103C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10612298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40622
C2×C3×#40572
C3×#660102
C3×#658892
C3×C5×#4632
C3×#654622
C3×#654472
C3×#653492
C3×#653032
C3×#651302
C3×#651252
C3×#651052
C3×#650992
C3×#650672
C3×#650652
#106122983
C3×#32675