Finite Group Databasebeta

← C3×#10615686 #14454196

Subgroups — C3×#10615686 #14454196

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
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#66168C211yesmaximal, characteristic, complemented
3C3×#66140C211yesmaximal, characteristic, complemented
4C2×C3×#4062C211yesmaximal, characteristic, complemented
5C3×#65528C211yesmaximal, characteristic, complemented
6C3×#65506C211yesmaximal, characteristic, complemented
7C3×#65461C211yesmaximal, characteristic, complemented
8C3×#65455C211yesmaximal, characteristic, complemented
9C3×#65453C211yesmaximal, characteristic, complemented
10C3×#65447C211yesmaximal, characteristic, complemented
11C3×#65446C211yesmaximal, characteristic, complemented
12C3×#65443C211yesmaximal, characteristic, complemented
13C3×#65439C211yesmaximal, characteristic, complemented
14C3×#65423C211yesmaximal, characteristic, complemented
15C3×#65416C211yesmaximal, characteristic, complemented
16#10615686C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic, complemented
20C2×C3×#711C2211yescharacteristic
21C3×C5×AGL(1,ℤ/8)—24no—
22C2×C3×C5×SD16C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×D8C2211yescharacteristic
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic
27C3×#4099—21no—
28C2×C3×C22⋊Dic5—21no—
29C3×Q8×Dic5C2211yescharacteristic, complemented
30C2×C3×#689C2211yescharacteristic, complemented
31C3×#4086—21no—
32C3×#4086C2211yescharacteristic, complemented
33C3×#4085—21no—
34C3×#4084—21no—
35C3×#4084C2211yescharacteristic
36C3×#4084C2211yescharacteristic, complemented
37C3×#4082C2211yescharacteristic
38C3×#4081—21no—
39C3×D4×Dic5C2211yescharacteristic
40C2×C3×#687C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic
42C2×C3×#686C2211yescharacteristic
43C3×#4076—21no—
44C3×#4076C2211yescharacteristic
45C3×C4×C22⋊D5—21no—
46C3×C4×C22⋊D5C2211yescharacteristic
47C3×#4070C2211yescharacteristic
48C3×#4062—24no—
49C2×C3×#677C2211yescharacteristic, complemented
50C2×C3×C8×D5C2211yescharacteristic, complemented
51C3×#3967C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic
53C3×#3964C2211yescharacteristic
54C3×#3964C2211yescharacteristic, complemented
55C3×C22⋊#168C2211yescharacteristic
56C3×#3953C2211yescharacteristic, complemented
57C3×#3952C2211yescharacteristic, complemented
58C3×#3950C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3947C2211yescharacteristic, complemented
61C3×#3946C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
64#66168C2×C311yescharacteristic, complemented
65#66140C2×C311yescharacteristic, complemented
66C2×#4062C2×C311yescharacteristic, complemented
67#65528C2×C311yescharacteristic, complemented
68#65506C2×C311yescharacteristic, complemented
69#65461C2×C311yescharacteristic, complemented
70#65455C2×C311yescharacteristic, complemented
71#65453C2×C311yescharacteristic, complemented
72#65447C2×C311yescharacteristic, complemented
73#65446C2×C311yescharacteristic, complemented
74#65443C2×C311yescharacteristic, complemented
75#65439C2×C311yescharacteristic, complemented
76#65423C2×C311yescharacteristic, complemented
77#65416C2×C311yescharacteristic, complemented
78C24×C3×C5—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—41no—
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5D411yescharacteristic
98C22×C3×Dic5—21no—
99C22×C3×Dic5—21no—
100C3×#713—22no—
101C3×#713—41no—
102C3×#711—22no—
103C3×#711—41no—
104C2×C3×D20—21no—
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5C2311yescharacteristic
108C2×C3×Dic10C2311yescharacteristic
109C3×C5×SD16—22no—
110C3×C5×SD16D414yescomplemented
111C3×C5×D8—22no—
112C3×C5×D8—22no—
113C3×C5×M16—22no—
114C2×C3×C5×C8C2311yescharacteristic
115C2×C3×C5×C8C2311yescharacteristic
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×C22⋊Dic5—21no—
120C3×C22⋊Dic5—21no—
121C3×C22⋊Dic5—21no—
122C3×C22⋊Dic5D411yescharacteristic
123C3×#689—22no—
124C3×#687—41no—
125C3×#686—22no—
126C3×#686—41no—
127C3×#685—21no—
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5C2311yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683D411yescharacteristic
134C3×C4×Dic5—21no—
135C3×C4×Dic5C2311yescharacteristic
136C2×C3×#168C2311yescharacteristic
137C2×C3×#168C2311yescharacteristic
138C3×#677—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
141C2×C3×#135—51no—
142C3×#550—51no—
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
156C22×C5×D4C22×C311yescharacteristic
157C2×#713C22×C311yescharacteristic, complemented
158C2×#711C22×C311yescharacteristic
159C5×AGL(1,ℤ/8)—24no—
160C2×C5×SD16C22×C311yescharacteristic
161C2×C5×SD16C22×C311yescharacteristic
162C2×C5×D8C22×C311yescharacteristic
163C2×C5×D8C22×C311yescharacteristic
164C2×C5×M16C22×C311yescharacteristic
165#4099—21no—
166C2×C22⋊Dic5—21no—
167Q8×Dic5C22×C311yescharacteristic, complemented
168C2×#689C22×C311yescharacteristic, complemented
169#4086—21no—
170#4086C22×C311yescharacteristic, complemented
171#4085—21no—
172#4084—21no—
173#4084C22×C311yescharacteristic
174#4084C22×C311yescharacteristic, complemented
175#4082C22×C311yescharacteristic
176#4081—21no—
177D4×Dic5C22×C311yescharacteristic
178C2×#687C22×C311yescharacteristic, complemented
179C2×#686C22×C311yescharacteristic
180C2×#686C22×C311yescharacteristic
181#4076—21no—
182#4076C22×C311yescharacteristic
183C4×C22⋊D5—21no—
184C4×C22⋊D5C22×C311yescharacteristic
185#4070C22×C311yescharacteristic
186#4062—24no—
187C2×#677C22×C311yescharacteristic, complemented
188C2×C8×D5C22×C311yescharacteristic, complemented
189#3967C22×C311yescharacteristic, complemented
190#3964C22×C311yescharacteristic
191#3964C22×C311yescharacteristic
192#3964C22×C311yescharacteristic, complemented
193C22⋊#168C22×C311yescharacteristic
194#3953C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic, complemented
196#3950C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3947C22×C311yescharacteristic, complemented
199#3946C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C22×C3×D5—21no—
209C22×C3×D5C2×D411yescharacteristic
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—21no—
217C3×C5×D4—42no—
218C3×C5×D4—42no—
219C3×C5×D4C2×D412yes—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—42no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226C3×C22⋊D5—41no—
227C3×C22⋊D5—42no—
228C3×C22⋊D5—42no—
229C3×C22⋊D5—81no—
230C3×C22⋊D5—81no—
231C3×C22⋊D5—81no—
232C3×C22⋊D5—81no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—42no—
237C2×C3×Dic5—81no—
238C2×C3×Dic5C2×D411yescharacteristic
239C2×C3×Dic5C2×D411yescharacteristic
240C2×C3×Dic5C2×D411yescharacteristic
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×C4×D5—21no—
245C3×C4×D5—21no—
246C3×C4×D5—42no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3×C5×C8—21no—
250C3×C5×C8C2×D412yes—
251C3×#168—21no—
252C3×#168—21no—
253C2×C3×#41—51no—
254C2×C3×#41—51no—
255C2×C3×#41C2×D511yescharacteristic
256C22×C3×D4C2×D511yescharacteristic
257C3×AGL(1,ℤ/8)—24no—
258C3×#135—104no—
259C2×C3×Q16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8C2×D511yescharacteristic
267C2×C3×D8C2×D511yescharacteristic
268C2×C3×M16C2×D511yescharacteristic
269C22×C3×C8—51no—
270C3×#127—51no—
271C3×#127—101no—
272C3×#124—51no—
273C3×#123—101no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—51no—
277C3×#121—51no—
278C3×#121—101no—
279C3×#121—101no—
280C3×#121—101no—
281C3×#120—101no—
282C3×C4×Q8—51no—
283C3×C4×D4—51no—
284C3×C4×D4—51no—
285C3×C4×D4—101no—
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—
298C24×C5—21no—
299C5×#41—22no—
300C5×#41—41no—
301C2×C5×Q8C23×C311yescharacteristic
302C2×C5×D4—22no—
303C2×C5×D4—21no—
304C2×C5×D4—21no—
305C2×C5×D4—41no—
306C2×C5×D4C23×C311yescharacteristic
307C2×C5×D4C23×C311yescharacteristic
308C2×C5×D4C23×C311yescharacteristic
309C22×C4×C5—21no—
310C22×C4×C5C23×C311yescharacteristic
311C2×C22⋊D5—21no—
312C2×C22⋊D5—21no—
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315C2×C22⋊D5—21no—
316C2×C22⋊D5—21no—
317C2×C22⋊D5C3×D411yescharacteristic
318C22×Dic5—21no—
319C22×Dic5—21no—
320#713—22no—
321#713—41no—
322#711—22no—
323#711—41no—
324C2×D20—21no—
325C2×D20C23×C311yescharacteristic
326C2×C4×D5—21no—
327C2×C4×D5C23×C311yescharacteristic
328C2×Dic10C23×C311yescharacteristic
329C5×SD16—22no—
330C5×SD16C3×D414yescomplemented
331C5×D8—22no—
332C5×D8—22no—
333C5×M16—22no—
334C2×C5×C8C23×C311yescharacteristic
335C2×C5×C8C23×C311yescharacteristic
336C22⋊Dic5—21no—
337C22⋊Dic5—21no—
338C22⋊Dic5—21no—
339C22⋊Dic5—21no—
340C22⋊Dic5—21no—
341C22⋊Dic5—21no—
342C22⋊Dic5C3×D411yescharacteristic
343#689—22no—
344#687—41no—
345#686—22no—
346#686—41no—
347#685—21no—
348#685C3×D411yescharacteristic
349C4⋊Dic5—21no—
350C4⋊Dic5C23×C311yescharacteristic
351C4⋊Dic5C23×C311yescharacteristic
352#683—21no—
353#683C3×D411yescharacteristic
354C4×Dic5—21no—
355C4×Dic5C23×C311yescharacteristic
356C2×#168C23×C311yescharacteristic
357C2×#168C23×C311yescharacteristic
358#677—22no—
359C8×D5—22no—
360C2×AGL(1,ℤ/8)C3×D511yescharacteristic, complemented
361C2×#135—51no—
362#550—51no—
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—22no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
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×C5—84no—
388C22×C3×C5C22×D411yescharacteristic
389C2×C3×D5—21no—
390C2×C3×D5—21no—
391C2×C3×D5—21no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C3×C4×C5—22no—
396C3×C4×C5—21no—
397C3×C4×C5C22×D411yescharacteristic
398C3×C4×C5H(5,𝔽2)11yescharacteristic
399C3×Dic5—21no—
400C3×Dic5—21no—
401C3×Dic5—21no—
402C3×Dic5—41no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C24×C3—21no—
406C3×#41—22no—
407C3×#41—41no—
408C3×#41—102no—
409C3×#41—102no—
410C3×#41—201no—
411C3×#41—201no—
412C2×C3×Q8—51no—
413C2×C3×Q8C22×D511yescharacteristic
414C2×C3×D4—22no—
415C2×C3×D4—21no—
416C2×C3×D4—21no—
417C2×C3×D4—41no—
418C2×C3×D4—51no—
419C2×C3×D4—51no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4C22×D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—51no—
432C22×C3×C4—101no—
433C22×C3×C4—101no—
434C22×C3×C4—101no—
435C22×C3×C4C22×D511yescharacteristic
436C3×Q16—102no—
437C3×SD16—22no—
438C3×SD16—102no—
439C3×SD16—201no—
440C3×SD16C22⋊D514yescomplemented
441C3×D8—22no—
442C3×D8—22no—
443C3×D8—102no—
444C3×D8—201no—
445C3×M16—22no—
446C2×C3×C8—51no—
447C2×C3×C8—51no—
448C2×C3×C8—102no—
449C2×C3×C8C22×D511yescharacteristic
450C2×C3×C8C22×D511yescharacteristic
451C3×C4⋊C4—51no—
452C3×C4⋊C4—51no—
453C3×C4⋊C4—51no—
454C3×C4⋊C4—101no—
455C3×C4⋊C4—101no—
456C3×C22⋊C4—51no—
457C3×C22⋊C4—51no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4—101no—
464C3×C22⋊C4—101no—
465C3×C42—51no—
466C3×C42—101no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C23×C5—42no—
471C23×C5—42no—
472C23×C5—81no—
473C23×C5C2×C3×D411yescharacteristic
474C22×D5—21no—
475C22×D5C2×C3×D411yescharacteristic
476C5×Q8—21no—
477C5×Q8C2×C3×D412yes—
478C5×D4—21no—
479C5×D4—21no—
480C5×D4—21no—
481C5×D4—21no—
482C5×D4—21no—
483C5×D4—42no—
484C5×D4—42no—
485C5×D4C2×C3×D412yes—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—42no—
490C2×C4×C5C2×C3×D411yescharacteristic
491C2×C4×C5C24×C311yescharacteristic
492C22⋊D5—41no—
493C22⋊D5—42no—
494C22⋊D5—42no—
495C22⋊D5—81no—
496C22⋊D5—81no—
497C22⋊D5—81no—
498C22⋊D5—81no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—42no—
503C2×Dic5—81no—
504C2×Dic5C2×C3×D411yescharacteristic
505C2×Dic5C2×C3×D411yescharacteristic
506C2×Dic5C2×C3×D411yescharacteristic
507D20—21no—
508D20—21no—
509D20—42no—
510C4×D5—21no—
511C4×D5—21no—
512C4×D5—42no—
513Dic10—21no—
514Dic10—21no—
515C5×C8—21no—
516C5×C8C2×C3×D412yes—
517#168—21no—
518#168—21no—
519C2×#41—51no—
520C2×#41—51no—
521C2×#41C2×C3×D511yescharacteristic
522C22×D4C2×C3×D511yescharacteristic
523AGL(1,ℤ/8)—24no—
524#135—104no—
525C2×Q16—51no—
526C2×SD16—51no—
527C2×SD16—51no—
528C2×SD16C2×C3×D511yescharacteristic
529C2×SD16C2×C3×D511yescharacteristic
530C2×D8—51no—
531C2×D8—51no—
532C2×D8C2×C3×D511yescharacteristic
533C2×D8C2×C3×D511yescharacteristic
534C2×M16C2×C3×D511yescharacteristic
535C22×C8—51no—
536#127—51no—
537#127—101no—
538#124—51no—
539#123—101no—
540C22⋊Q8—51no—
541#121—51no—
542#121—51no—
543#121—51no—
544#121—101no—
545#121—101no—
546#121—101no—
547#120—101no—
548C4×Q8—51no—
549C4×D4—51no—
550C4×D4—51no—
551C4×D4—101no—
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—42no—
566C2×C3×C5—81no—
567C2×C3×C5—81no—
568C2×C3×C5D4211yescharacteristic
569C2×C3×C5#57511yescharacteristic
570C2×C3×C5#57611yescharacteristic
571C3×D5—41no—
572C3×D5—81no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—51no—
579C23×C3—81no—
580C23×C3—101no—
581C23×C3D4×D511yescharacteristic
582C3×Q8—21no—
583C3×Q8—101no—
584C3×Q8—101no—
585C3×Q8C2×C22⋊D512yes—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—101no—
594C3×D4—101no—
595C3×D4—202no—
596C3×D4—201no—
597C3×D4—202no—
598C3×D4—202no—
599C3×D4—401no—
600C3×D4—401no—
601C3×D4—401no—
602C3×D4—401no—
603C3×D4C2×C22⋊D512yes—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—42no—
608C2×C3×C4—51no—
609C2×C3×C4—51no—
610C2×C3×C4—51no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—202no—
617C2×C3×C4—202no—
618C2×C3×C4—401no—
619C2×C3×C4D4×D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—21no—
622C3×C8—101no—
623C3×C8—101no—
624C3×C8C2×C22⋊D512yes—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—22no—
628C22×C5—21no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—84no—
638C22×C5C22×C3×D411yescharacteristic
639C2×D5—21no—
640C2×D5—21no—
641C2×D5—21no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—41no—
645C4×C5—22no—
646C4×C5—21no—
647C4×C5C22×C3×D411yescharacteristic
648C4×C5C3×H(5,𝔽2)11yescharacteristic
649Dic5—21no—
650Dic5—21no—
651Dic5—21no—
652Dic5—41no—
653Dic5—41no—
654Dic5—41no—
655C24—21no—
656#41—22no—
657#41—41no—
658#41—102no—
659#41—102no—
660#41—201no—
661#41—201no—
662C2×Q8—51no—
663C2×Q8C22×C3×D511yescharacteristic
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—51no—
669C2×D4—51no—
670C2×D4—101no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—101no—
677C2×D4C22×C3×D511yescharacteristic
678C2×D4C22×C3×D511yescharacteristic
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—21no—
681C22×C4—51no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4C22×C3×D511yescharacteristic
686Q16—102no—
687SD16—22no—
688SD16—102no—
689SD16—201no—
690SD16C3×C22⋊D514yescomplemented
691D8—22no—
692D8—22no—
693D8—102no—
694D8—201no—
695M16—22no—
696C2×C8—51no—
697C2×C8—51no—
698C2×C8—102no—
699C2×C8C22×C3×D511yescharacteristic
700C2×C8C22×C3×D511yescharacteristic
701C4⋊C4—51no—
702C4⋊C4—51no—
703C4⋊C4—51no—
704C4⋊C4—101no—
705C4⋊C4—101no—
706C22⋊C4—51no—
707C22⋊C4—51no—
708C22⋊C4—101no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4—101no—
714C22⋊C4—101no—
715C42—51no—
716C42—101no—
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—84no—
731C22×C3—101no—
732C22×C3—101no—
733C22×C3—101no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3C2×D4×D511yescharacteristic
738C3×C4—21no—
739C3×C4—22no—
740C3×C4—101no—
741C3×C4—101no—
742C3×C4—101no—
743C3×C4—201no—
744C3×C4—201no—
745C3×C4—201no—
746C3×C4#414411yescharacteristic
747C3×C4C22×C22⋊D511yescharacteristic
748C2×C5—41no—
749C2×C5—42no—
750C2×C5—81no—
751C2×C5—81no—
752C2×C5C3×D4211yescharacteristic
753C2×C5C3×#57511yescharacteristic
754C2×C5C3×#57611yescharacteristic
755D5—41no—
756D5—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—42no—
761C23—42no—
762C23—51no—
763C23—81no—
764C23—101no—
765C23C3×D4×D511yescharacteristic
766Q8—21no—
767Q8—101no—
768Q8—101no—
769Q8C2×C3×C22⋊D512yes—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—21no—
775D4—42no—
776D4—42no—
777D4—101no—
778D4—101no—
779D4—202no—
780D4—201no—
781D4—202no—
782D4—202no—
783D4—401no—
784D4—401no—
785D4—401no—
786D4—401no—
787D4C2×C3×C22⋊D512yes—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—42no—
792C2×C4—51no—
793C2×C4—51no—
794C2×C4—51no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—202no—
801C2×C4—202no—
802C2×C4—401no—
803C2×C4C3×D4×D511yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—21no—
806C8—101no—
807C8—101no—
808C8C2×C3×C22⋊D512yes—
809C2×C3—41no—
810C2×C3—42no—
811C2×C3—81no—
812C2×C3—81no—
813C2×C3—201no—
814C2×C3—401no—
815C2×C3#6610711yescharacteristic
816C2×C3#6610811yescharacteristic
817C2×C3D4×C22⋊D511yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—84no—
832C22—101no—
833C22—101no—
834C22—101no—
835C22—201no—
836C22—201no—
837C22—201no—
838C22C2×C3×D4×D511yescharacteristic
839C4—21no—
840C4—22no—
841C4—101no—
842C4—101no—
843C4—101no—
844C4—201no—
845C4—201no—
846C4—201no—
847C4C3×#414411yescharacteristic
848C4C22×C3×C22⋊D511yescharacteristic
849C3#1061568611yescharacteristic, direct product factor, Sylow
850C2—41no—
851C2—42no—
852C2—81no—
853C2—81no—
854C2—201no—
855C2—401no—
856C2C3×#6610711yescharacteristic
857C2C3×#6610811yescharacteristic
858C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
2. C3×#66168C2semidirect
3. C3×#66140C2semidirect
4. C2×C3×#4062C2semidirect
5. C3×#65528C2semidirect
6. C3×#65506C2semidirect
7. C3×#65461C2semidirect
8. C3×#65455C2semidirect
9. C3×#65453C2semidirect
10. C3×#65447C2semidirect
11. C3×#65446C2semidirect
12. C3×#65443C2semidirect
13. C3×#65439C2semidirect
14. C3×#65423C2semidirect
15. C3×#65416C2semidirect
16. #10615686C3direct (N × H)
19. C2×C3×#713C22semidirect
29. C3×Q8×Dic5C22semidirect
30. C2×C3×#689C22semidirect
32. C3×#4086C22semidirect
36. C3×#4084C22semidirect
40. C2×C3×#687C22semidirect
49. C2×C3×#677C22semidirect
50. C2×C3×C8×D5C22semidirect
51. C3×#3967C22semidirect
54. C3×#3964C22semidirect
56. C3×#3953C22semidirect
57. C3×#3952C22semidirect
58. C3×#3950C22semidirect
59. C3×#3948C22semidirect
60. C3×#3947C22semidirect
61. C3×#3946C22semidirect
63. C2×C5×AGL(1,ℤ/8)C2×C3semidirect
64. #66168C2×C3semidirect
65. #66140C2×C3semidirect
66. C2×#4062C2×C3semidirect
67. #65528C2×C3semidirect
68. #65506C2×C3semidirect
69. #65461C2×C3semidirect
70. #65455C2×C3semidirect
71. #65453C2×C3semidirect
72. #65447C2×C3semidirect
73. #65446C2×C3semidirect
74. #65443C2×C3semidirect
75. #65439C2×C3semidirect
76. #65423C2×C3semidirect
77. #65416C2×C3semidirect
110. C3×C5×SD16D4semidirect
140. C2×C3×AGL(1,ℤ/8)D5semidirect
157. C2×#713C22×C3semidirect
167. Q8×Dic5C22×C3semidirect
168. C2×#689C22×C3semidirect
170. #4086C22×C3semidirect
174. #4084C22×C3semidirect
178. C2×#687C22×C3semidirect
187. C2×#677C22×C3semidirect
188. C2×C8×D5C22×C3semidirect
189. #3967C22×C3semidirect
192. #3964C22×C3semidirect
194. #3953C22×C3semidirect
195. #3952C22×C3semidirect
196. #3950C22×C3semidirect
197. #3948C22×C3semidirect
198. #3947C22×C3semidirect
199. #3946C22×C3semidirect
330. C5×SD16C3×D4semidirect
360. C2×AGL(1,ℤ/8)C3×D5semidirect
440. C3×SD16C22⋊D5semidirect
690. SD16C3×C22⋊D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10615686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
C3×#661682
C3×#661402
C2×C3×#40622
C3×#655282
C3×#655062
C3×#654612
C3×#654552
C3×#654532
C3×#654472
C3×#654462
C3×#654432
C3×#654392
C3×#654232
C3×#654162
#106156863
C3×#32685