Finite Group Databasebeta

← C3×#10612176 #14453977

Subgroups — C3×#10612176 #14453977

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×#4060C211yesmaximal, characteristic, complemented
3C3×#66060C211yesmaximal, characteristic, complemented
4C3×#65888C211yesmaximal, characteristic, complemented
5C3×C5×#461C211yesmaximal, characteristic, complemented
6C3×#65462C211yesmaximal, characteristic, complemented
7C3×#65458C211yesmaximal, characteristic, complemented
8C3×#65375C211yesmaximal, characteristic, complemented
9C3×#65303C211yesmaximal, characteristic, complemented
10C3×#65133C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65105C211yesmaximal, characteristic, complemented
13C3×#65100C211yesmaximal, characteristic, complemented
14C3×#65099C211yesmaximal, characteristic, complemented
15C3×#65096C211yesmaximal, characteristic, complemented
16#10612176C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic, complemented
19C2×C3×#711C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic
23C3×C5×C4⋊Q8C2211yescharacteristic, complemented
24C3×C4×C5×D4C2211yescharacteristic
25C3×#4092C2211yescharacteristic
26C3×#4092C2211yescharacteristic, complemented
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#689C2211yescharacteristic, complemented
29C2×C3×#688C2211yescharacteristic
30C2×C3×#688C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×#4076—21no—
33C2×C3×#685—21no—
34C3×#4062—24no—
35C3×#4060—24no—
36C2×C3×D40C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic, complemented
38C2×C3×#676C2211yescharacteristic
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4043C2211yescharacteristic
41C3×#4041—21no—
42C3×#4041C2211yescharacteristic
43C3×#4040—21no—
44C3×#4040—21no—
45C3×D5×C4⋊C4—21no—
46C3×#4032—21no—
47C3×#4028—21no—
48C3×#4021C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×C4×D20C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#103C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic
55C3×#3953C2211yescharacteristic
56C3×#3952C2211yescharacteristic
57C3×#3952C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic, complemented
60C3×#3940C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4062C2×C311yescharacteristic, complemented
64C2×#4060C2×C311yescharacteristic, complemented
65#66060C2×C311yescharacteristic, complemented
66#65888C2×C311yescharacteristic, complemented
67C5×#461C2×C311yescharacteristic, complemented
68#65462C2×C311yescharacteristic, complemented
69#65458C2×C311yescharacteristic, complemented
70#65375C2×C311yescharacteristic, complemented
71#65303C2×C311yescharacteristic, complemented
72#65133C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65105C2×C311yescharacteristic, complemented
75#65100C2×C311yescharacteristic, complemented
76#65099C2×C311yescharacteristic, complemented
77#65096C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C22×C3×Dic5—21no—
86C3×#713—22no—
87C3×#713—22no—
88C3×#713—41no—
89C3×#713—41no—
90C3×#711—22no—
91C3×#711—41no—
92C3×D4×D5—22no—
93C3×D4×D5—41no—
94C2×C3×D20—21no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20D411yescharacteristic
98C2×C3×D20C2311yescharacteristic
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5C2311yescharacteristic
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×SD16—22no—
107C3×C5×SD16—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4—21no—
112C3×C5×C4⋊C4C2311yescharacteristic
113C3×C5×C22⋊C4—21no—
114C3×C42×C5C2311yescharacteristic
115C3×#689—22no—
116C3×#689—41no—
117C3×#688—22no—
118C3×#688—41no—
119C3×#686D414yescomplemented
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5D411yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683—21no—
134C2×C3×#168C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C3×D40—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×#463—51no—
148C3×#461D511yescharacteristic, complemented
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435—51no—
155C2×#713C22×C311yescharacteristic
156C2×#713C22×C311yescharacteristic, complemented
157C2×#711C22×C311yescharacteristic
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic
160C2×C5×SD16C22×C311yescharacteristic
161C5×C4⋊Q8C22×C311yescharacteristic, complemented
162C4×C5×D4C22×C311yescharacteristic
163#4092C22×C311yescharacteristic
164#4092C22×C311yescharacteristic, complemented
165C2×#689C22×C311yescharacteristic, complemented
166C2×#689C22×C311yescharacteristic, complemented
167C2×#688C22×C311yescharacteristic
168C2×#688C22×C311yescharacteristic
169C2×#686C22×C311yescharacteristic
170#4076—21no—
171C2×#685—21no—
172#4062—24no—
173#4060—24no—
174C2×D40C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic, complemented
176C2×#676C22×C311yescharacteristic
177C2×C8×D5C22×C311yescharacteristic, complemented
178#4043C22×C311yescharacteristic
179#4041—21no—
180#4041C22×C311yescharacteristic
181#4040—21no—
182#4040—21no—
183D5×C4⋊C4—21no—
184#4032—21no—
185#4028—21no—
186#4021C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188C4×D20C22×C311yescharacteristic, complemented
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×#103C22×C311yescharacteristic, complemented
191C5×#103C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic
193#3953C22×C311yescharacteristic
194#3952C22×C311yescharacteristic
195#3952C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic, complemented
198#3940C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C22×C3×D5—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×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×D4—21no—
214C3×C5×D4C2×D412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—81no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222C3×C22⋊D5—42no—
223C3×C22⋊D5—42no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—42no—
227C2×C3×Dic5C2×D411yescharacteristic
228C2×C3×Dic5C2×D411yescharacteristic
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—21no—
232C3×D20—41no—
233C3×D20—42no—
234C3×D20—42no—
235C3×D20—81no—
236C3×D20C2×D412yes—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×C4×D5—21no—
241C3×C4×D5—42no—
242C3×C4×D5—42no—
243C3×C4×D5—42no—
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×SD16C2×D511yescharacteristic
262C2×C3×SD16C2×D511yescharacteristic
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—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
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106—51no—
285C3×C4⋊C8C2×D511yescharacteristic, complemented
286C3×#103—51no—
287C3×#103C2×D511yescharacteristic, complemented
288C3×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97—51no—
295C23×D5—21no—
296C2×C5×Q8C23×C311yescharacteristic
297C2×C5×Q8C23×C311yescharacteristic
298C2×C5×D4C23×C311yescharacteristic
299C22×C4×C5—21no—
300C2×C22⋊D5—21no—
301C2×C22⋊D5—21no—
302C22×Dic5—21no—
303#713—22no—
304#713—22no—
305#713—41no—
306#713—41no—
307#711—22no—
308#711—41no—
309D4×D5—22no—
310D4×D5—41no—
311C2×D20—21no—
312C2×D20—21no—
313C2×D20—21no—
314C2×D20C3×D411yescharacteristic
315C2×D20C23×C311yescharacteristic
316C2×D20C23×C311yescharacteristic
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×C4×D5C23×C311yescharacteristic
321C2×C4×D5C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×SD16—22no—
324C5×SD16—22no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4—21no—
328C5×C4⋊C4—21no—
329C5×C4⋊C4C23×C311yescharacteristic
330C5×C22⋊C4—21no—
331C42×C5C23×C311yescharacteristic
332#689—22no—
333#689—41no—
334#688—22no—
335#688—41no—
336#686C3×D414yescomplemented
337#685—21no—
338#685—21no—
339#685—21no—
340#685—21no—
341#685—21no—
342#685—21no—
343#685—21no—
344#685C3×D411yescharacteristic
345#685C3×D411yescharacteristic
346C4⋊Dic5—21no—
347C4⋊Dic5C3×D411yescharacteristic
348C4⋊Dic5C23×C311yescharacteristic
349#683—21no—
350#683—21no—
351C2×#168C23×C311yescharacteristic
352C2×#168C23×C311yescharacteristic
353D40—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#463—51no—
365#461C3×D511yescharacteristic, complemented
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×C5C22×D411yescharacteristic
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—22no—
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
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—41no—
392C3×C4×C5—41no—
393C3×C4×C5—41no—
394C3×C4×C5C22×D411yescharacteristic
395C3×C4×C5H(5,𝔽2)11yescharacteristic
396C3×Dic5—21no—
397C3×Dic5—21no—
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×Q8C22×D511yescharacteristic
409C2×C3×Q8C22×D511yescharacteristic
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—51no—
413C2×C3×D4—101no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—102no—
418C2×C3×D4—101no—
419C2×C3×D4—201no—
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—22no—
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—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—51no—
446C3×C4⋊C4—51no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4—101no—
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
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—
463C22×D5—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×Q8—21no—
473C5×Q8—21no—
474C5×D4—21no—
475C5×D4C2×C3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—81no—
480C2×C4×C5C2×C3×D411yescharacteristic
481C2×C4×C5C2×C3×D411yescharacteristic
482C2×C4×C5C24×C311yescharacteristic
483C22⋊D5—42no—
484C22⋊D5—42no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—42no—
488C2×Dic5C2×C3×D411yescharacteristic
489C2×Dic5C2×C3×D411yescharacteristic
490D20—21no—
491D20—21no—
492D20—21no—
493D20—41no—
494D20—42no—
495D20—42no—
496D20—81no—
497D20C2×C3×D412yes—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—21no—
501C4×D5—21no—
502C4×D5—42no—
503C4×D5—42no—
504C4×D5—42no—
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×SD16C2×C3×D511yescharacteristic
523C2×SD16C2×C3×D511yescharacteristic
524C2×D8—51no—
525C2×D8—51no—
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8C2×C3×D511yescharacteristic, complemented
529#124—51no—
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
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106—51no—
546C4⋊C8C2×C3×D511yescharacteristic, complemented
547#103—51no—
548#103C2×C3×D511yescharacteristic, complemented
549#103C2×C3×D511yescharacteristic, complemented
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97—51no—
556C2×C3×C5—42no—
557C2×C3×C5D4211yescharacteristic
558C2×C3×C5#57511yescharacteristic
559C2×C3×C5#57711yescharacteristic
560C3×D5—41no—
561C3×D5—41no—
562C3×D5—42no—
563C3×D5—81no—
564C23×C3—21no—
565C23×C3—51no—
566C23×C3—51no—
567C23×C3—101no—
568C23×C3—101no—
569C23×C3—202no—
570C23×C3—202no—
571C23×C3—401no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—52no—
580C3×D4—101no—
581C3×D4—101no—
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—21no—
593C2×C3×C4—51no—
594C2×C3×C4—51no—
595C2×C3×C4—81no—
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—202no—
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×C5C22×C3×D411yescharacteristic
617C2×D5—21no—
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C2×D5—21no—
622C2×D5—21no—
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—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5C22×C3×D411yescharacteristic
636C4×C5C3×H(5,𝔽2)11yescharacteristic
637Dic5—21no—
638Dic5—21no—
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×Q8C22×C3×D511yescharacteristic
650C2×Q8C22×C3×D511yescharacteristic
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—51no—
654C2×D4—101no—
655C2×D4—101no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—102no—
659C2×D4—101no—
660C2×D4—201no—
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—22no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—54no—
677D8—102no—
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—51no—
687C4⋊C4—51no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4—101no—
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—51no—
694C22⋊C4—51no—
695C22⋊C4—101no—
696C22⋊C4—101no—
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—101no—
708C22×C3—101no—
709C22×C3—101no—
710C22×C3—101no—
711C22×C3—101no—
712C22×C3—101no—
713C22×C3—102no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
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—41no—
726C3×C4—101no—
727C3×C4—101no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414911yescharacteristic
732C2×C5—42no—
733C2×C5C3×D4211yescharacteristic
734C2×C5C3×#57511yescharacteristic
735C2×C5C3×#57711yescharacteristic
736D5—41no—
737D5—41no—
738D5—42no—
739D5—81no—
740C23—21no—
741C23—51no—
742C23—51no—
743C23—101no—
744C23—101no—
745C23—202no—
746C23—202no—
747C23—401no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—52no—
756D4—101no—
757D4—101no—
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—21no—
769C2×C4—51no—
770C2×C4—51no—
771C2×C4—81no—
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—202no—
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—201no—
791C2×C3—201no—
792C2×C3—202no—
793C2×C3—401no—
794C2×C3#6594311yescharacteristic
795C2×C3#6609611yescharacteristic
796C2×C3#6611111yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—22no—
799C22—41no—
800C22—41no—
801C22—101no—
802C22—101no—
803C22—101no—
804C22—101no—
805C22—102no—
806C22—101no—
807C22—101no—
808C22—201no—
809C22—201no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—101no—
821C4—101no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414911yescharacteristic
826C3#1061217611yescharacteristic, direct product factor, Sylow
827C2—42no—
828C2—201no—
829C2—201no—
830C2—202no—
831C2—401no—
832C2C3×#6594311yescharacteristic
833C2C3×#6609611yescharacteristic
834C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#461C2
socleC22×C3×C5C22×D4
hypercenterC3×#461D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4062C2semidirect
2. C2×C3×#4060C2semidirect
3. C3×#66060C2semidirect
4. C3×#65888C2semidirect
5. C3×C5×#461C2semidirect
6. C3×#65462C2semidirect
7. C3×#65458C2semidirect
8. C3×#65375C2semidirect
9. C3×#65303C2semidirect
10. C3×#65133C2semidirect
11. C3×#65125C2semidirect
12. C3×#65105C2semidirect
13. C3×#65100C2semidirect
14. C3×#65099C2semidirect
15. C3×#65096C2semidirect
16. #10612176C3direct (N × H)
18. C2×C3×#713C22semidirect
23. C3×C5×C4⋊Q8C22semidirect
26. C3×#4092C22semidirect
27. C2×C3×#689C22semidirect
28. C2×C3×#689C22semidirect
37. C2×C3×#677C22semidirect
39. C2×C3×C8×D5C22semidirect
50. C3×C4×D20C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#103C22semidirect
53. C3×C5×#103C22semidirect
57. C3×#3952C22semidirect
58. C3×#3948C22semidirect
59. C3×#3941C22semidirect
60. C3×#3940C22semidirect
61. C3×#3935C22semidirect
63. C2×#4062C2×C3semidirect
64. C2×#4060C2×C3semidirect
65. #66060C2×C3semidirect
66. #65888C2×C3semidirect
67. C5×#461C2×C3semidirect
68. #65462C2×C3semidirect
69. #65458C2×C3semidirect
70. #65375C2×C3semidirect
71. #65303C2×C3semidirect
72. #65133C2×C3semidirect
73. #65125C2×C3semidirect
74. #65105C2×C3semidirect
75. #65100C2×C3semidirect
76. #65099C2×C3semidirect
77. #65096C2×C3semidirect
119. C3×#686D4semidirect
148. C3×#461D5semidirect
156. C2×#713C22×C3semidirect
161. C5×C4⋊Q8C22×C3semidirect
164. #4092C22×C3semidirect
165. C2×#689C22×C3semidirect
166. C2×#689C22×C3semidirect
175. C2×#677C22×C3semidirect
177. C2×C8×D5C22×C3semidirect
188. C4×D20C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
190. C5×#103C22×C3semidirect
191. C5×#103C22×C3semidirect
195. #3952C22×C3semidirect
196. #3948C22×C3semidirect
197. #3941C22×C3semidirect
198. #3940C22×C3semidirect
199. #3935C22×C3semidirect
267. C3×C4⋊Q8C2×D5semidirect
285. C3×C4⋊C8C2×D5semidirect
287. C3×#103C2×D5semidirect
288. C3×#103C2×D5semidirect
336. #686C3×D4semidirect
365. #461C3×D5semidirect
528. C4⋊Q8C2×C3×D5semidirect
546. C4⋊C8C2×C3×D5semidirect
548. #103C2×C3×D5semidirect
549. #103C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10612176direct (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×#40602
C3×#660602
C3×#658882
C3×C5×#4612
C3×#654622
C3×#654582
C3×#653752
C3×#653032
C3×#651332
C3×#651252
C3×#651052
C3×#651002
C3×#650992
C3×#650962
#106121763
C3×#32675