Finite Group Databasebeta

← C3×#10611609 #14453200

Subgroups — C3×#10611609 #14453200

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
1C2×C3×#4057C211yesmaximal, characteristic, complemented
2C2×C3×D5×D8C211yesmaximal, characteristic, complemented
3C3×#65888C211yesmaximal, characteristic, complemented
4C3×D4×D20C211yesmaximal, characteristic, complemented
5C3×C5×#442C211yesmaximal, characteristic, complemented
6C3×#65305C211yesmaximal, characteristic, complemented
7C3×#65304C211yesmaximal, characteristic, complemented
8C3×#65154C211yesmaximal, characteristic, complemented
9C3×#65153C211yesmaximal, characteristic, complemented
10C3×#65070C211yesmaximal, characteristic, complemented
11C3×#65065C211yesmaximal, characteristic, complemented
12C3×#65062C211yesmaximal, characteristic, complemented
13C3×#65062C211yesmaximal, characteristic, complemented
14C3×#65001C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10611609C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic, complemented
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic, complemented
21C22×C3×D20—21no—
22C2×C3×C5×D8C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic, complemented
24C3×C4×C5×D4C2211yescharacteristic, complemented
25C2×C3×#687C2211yescharacteristic, complemented
26C2×C3×#686C2211yescharacteristic
27C2×C3×#686C2211yescharacteristic, complemented
28C2×C3×#686C2211yescharacteristic, complemented
29C3×#4076—21no—
30C3×#4076—21no—
31C2×C3×#685—21no—
32C3×#4057—24no—
33C3×D5×D8—24no—
34C2×C3×D40C2211yescharacteristic, complemented
35C2×C3×D40C2211yescharacteristic, complemented
36C2×C3×#677C2211yescharacteristic, complemented
37C2×C3×#677C2211yescharacteristic, complemented
38C2×C3×#676C2211yescharacteristic, complemented
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4043C2211yescharacteristic, complemented
41C3×#4041C2211yescharacteristic
42C3×#4041C2211yescharacteristic, complemented
43C3×#4041C2211yescharacteristic, complemented
44C3×#4032—21no—
45C3×#4028—21no—
46C3×#4028—21no—
47C3×#4028—21no—
48C3×#4021C2211yescharacteristic, complemented
49C3×#4020C2211yescharacteristic, complemented
50C3×C4×D20C2211yescharacteristic
51C3×C5×#106C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic, complemented
56C3×#3952C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58C3×#3941C2211yescharacteristic, complemented
59C3×#3941C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic, complemented
61C3×C4⋊#168C2211yescharacteristic, complemented
62C3×#3264—51nomaximal, Hall
63C2×#4057C2×C311yescharacteristic, complemented
64C2×D5×D8C2×C311yescharacteristic, complemented
65#65888C2×C311yescharacteristic, complemented
66D4×D20C2×C311yescharacteristic, complemented
67C5×#442C2×C311yescharacteristic, complemented
68#65305C2×C311yescharacteristic, complemented
69#65304C2×C311yescharacteristic, complemented
70#65154C2×C311yescharacteristic, complemented
71#65153C2×C311yescharacteristic, complemented
72#65070C2×C311yescharacteristic, complemented
73#65065C2×C311yescharacteristic, complemented
74#65062C2×C311yescharacteristic, complemented
75#65062C2×C311yescharacteristic, complemented
76#65001C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C23×C3×D5—21no—
80C23×C3×D5—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C22×C3×Dic5—21no—
90C3×#711—22no—
91C3×#711—41no—
92C3×D4×D5—22no—
93C3×D4×D5—22no—
94C3×D4×D5—22no—
95C3×D4×D5—41no—
96C3×D4×D5—41no—
97C3×D4×D5—41no—
98C2×C3×D20—21no—
99C2×C3×D20—21no—
100C2×C3×D20—21no—
101C2×C3×D20—21no—
102C2×C3×D20—21no—
103C2×C3×D20—44no—
104C2×C3×D20D411yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×D20C2311yescharacteristic
107C2×C3×D20C2311yescharacteristic
108C2×C3×C4×D5C2311yescharacteristic
109C2×C3×C4×D5C2311yescharacteristic
110C2×C3×Dic10C2311yescharacteristic
111C3×C5×D8D414yescomplemented
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118C3×C42×C5C2311yescharacteristic
119C3×#687—22no—
120C3×#686—22no—
121C3×#686—22no—
122C3×#686—22no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685D411yescharacteristic
130C3×#685D411yescharacteristic
131C3×C4⋊Dic5—21no—
132C3×C4⋊Dic5D411yescharacteristic
133C2×C3×#168C2311yescharacteristic
134C2×C3×#168C2311yescharacteristic
135C3×D40—22no—
136C3×D40—41no—
137C3×#677—22no—
138C3×#677—41no—
139C3×#676—22no—
140C3×C8×D5—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142C22×C3×D8—51no—
143C3×#546—51no—
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×#442D511yescharacteristic, complemented
155C3×#435—51no—
156C2×#711C22×C311yescharacteristic, complemented
157C2×D4×D5C22×C311yescharacteristic
158C2×D4×D5C22×C311yescharacteristic, complemented
159C2×D4×D5C22×C311yescharacteristic, complemented
160C22×D20—21no—
161C2×C5×D8C22×C311yescharacteristic
162C4×C5×D4C22×C311yescharacteristic, complemented
163C4×C5×D4C22×C311yescharacteristic, complemented
164C2×#687C22×C311yescharacteristic, complemented
165C2×#686C22×C311yescharacteristic
166C2×#686C22×C311yescharacteristic, complemented
167C2×#686C22×C311yescharacteristic, complemented
168#4076—21no—
169#4076—21no—
170C2×#685—21no—
171#4057—24no—
172D5×D8—24no—
173C2×D40C22×C311yescharacteristic, complemented
174C2×D40C22×C311yescharacteristic, complemented
175C2×#677C22×C311yescharacteristic, complemented
176C2×#677C22×C311yescharacteristic, complemented
177C2×#676C22×C311yescharacteristic, complemented
178C2×C8×D5C22×C311yescharacteristic, complemented
179#4043C22×C311yescharacteristic, complemented
180#4041C22×C311yescharacteristic
181#4041C22×C311yescharacteristic, complemented
182#4041C22×C311yescharacteristic, complemented
183#4032—21no—
184#4028—21no—
185#4028—21no—
186#4028—21no—
187#4021C22×C311yescharacteristic, complemented
188#4020C22×C311yescharacteristic, complemented
189C4×D20C22×C311yescharacteristic
190C5×#106C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic, complemented
192C5×#102C22×C311yescharacteristic, complemented
193C5×#97C22×C311yescharacteristic, complemented
194#3952C22×C311yescharacteristic, complemented
195#3952C22×C311yescharacteristic, complemented
196#3942C22×C311yescharacteristic, complemented
197#3941C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic, complemented
199#3941C22×C311yescharacteristic, complemented
200C4⋊#168C22×C311yescharacteristic, complemented
201#3264—51noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—42no—
211C22×C3×D5—42no—
212C22×C3×D5—42no—
213C22×C3×D5—81no—
214C22×C3×D5—81no—
215C22×C3×D5—81no—
216C22×C3×D5C2×D411yescharacteristic
217C22×C3×D5C2×D411yescharacteristic
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4C2×D412yes—
221C3×C5×D4C2×D412yescomplemented
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—42no—
225C2×C3×C4×C5—81no—
226C2×C3×C4×C5C2×D411yescharacteristic
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2411yescharacteristic
229C3×C22⋊D5—42no—
230C3×C22⋊D5—42no—
231C3×C22⋊D5—42no—
232C3×C22⋊D5—42no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—42no—
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—22no—
238C3×D20—21no—
239C3×D20—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—42no—
245C3×D20—42no—
246C3×D20—42no—
247C3×D20—81no—
248C3×D20—81no—
249C3×C4×D5—21no—
250C3×C4×D5—21no—
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×Dic10—21no—
254C3×Dic10—21no—
255C3×C5×C8—21no—
256C3×C5×C8C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×C3×#41—51no—
260C22×C3×D4—51no—
261C22×C3×D4—51no—
262C22×C3×D4—51no—
263C22×C3×D4—101no—
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—104no—
274C2×C3×D8C2×D511yescharacteristic
275C2×C3×M16—51no—
276C22×C3×C8—51no—
277C3×#127—51no—
278C3×#124—51no—
279C3×#123—101no—
280C3×C22⋊Q8—51no—
281C3×#121—51no—
282C3×#121—51no—
283C3×#121—51no—
284C3×#121—101no—
285C3×#121—101no—
286C3×#120—101no—
287C3×#120—101no—
288C3×#120—101no—
289C3×C4×D4—51no—
290C3×C4×D4C2×D511yescharacteristic, complemented
291C3×C4×D4C2×D511yescharacteristic, complemented
292C2×C3×C22⋊C4—101no—
293C3×#106C2×D511yescharacteristic, complemented
294C3×C4⋊C8—51no—
295C3×#103—51no—
296C3×#102—51no—
297C3×#102—51no—
298C3×#102—51no—
299C3×#102C2×D511yescharacteristic, complemented
300C3×#102C2×D511yescharacteristic, complemented
301C3×C22⋊C8—51no—
302C3×C22⋊C8—51no—
303C3×#97C2×D511yescharacteristic, complemented
304C23×D5—21no—
305C23×D5—21no—
306C23×D5—21no—
307C2×C5×D4C23×C311yescharacteristic
308C2×C5×D4C23×C311yescharacteristic
309C22×C4×C5—21no—
310C22×C4×C5—21no—
311C2×C22⋊D5—21no—
312C2×C22⋊D5—21no—
313C2×C22⋊D5—21no—
314C2×C22⋊D5—21no—
315C22×Dic5—21no—
316#711—22no—
317#711—41no—
318D4×D5—22no—
319D4×D5—22no—
320D4×D5—22no—
321D4×D5—41no—
322D4×D5—41no—
323D4×D5—41no—
324C2×D20—21no—
325C2×D20—21no—
326C2×D20—21no—
327C2×D20—21no—
328C2×D20—21no—
329C2×D20—44no—
330C2×D20C3×D411yescharacteristic
331C2×D20C23×C311yescharacteristic
332C2×D20C23×C311yescharacteristic
333C2×D20C23×C311yescharacteristic
334C2×C4×D5C23×C311yescharacteristic
335C2×C4×D5C23×C311yescharacteristic
336C2×Dic10C23×C311yescharacteristic
337C5×D8C3×D414yescomplemented
338C2×C5×C8C23×C311yescharacteristic
339C2×C5×C8C23×C311yescharacteristic
340C5×C4⋊C4C23×C311yescharacteristic
341C5×C4⋊C4C23×C311yescharacteristic
342C5×C22⋊C4—21no—
343C5×C22⋊C4—21no—
344C42×C5C23×C311yescharacteristic
345#687—22no—
346#686—22no—
347#686—22no—
348#686—22no—
349#685—21no—
350#685—21no—
351#685—21no—
352#685—21no—
353#685—21no—
354#685—21no—
355#685C3×D411yescharacteristic
356#685C3×D411yescharacteristic
357C4⋊Dic5—21no—
358C4⋊Dic5C3×D411yescharacteristic
359C2×#168C23×C311yescharacteristic
360C2×#168C23×C311yescharacteristic
361D40—22no—
362D40—41no—
363#677—22no—
364#677—41no—
365#676—22no—
366C8×D5—22no—
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—51no—
369#546—51no—
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#442C3×D511yescharacteristic, complemented
381#435—51no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×C3×D5—21no—
390C2×C3×D5—21no—
391C2×C3×D5—21no—
392C2×C3×D5—21no—
393C2×C3×D5—21no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
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—84no—
404C2×C3×D5—84no—
405C2×C3×D5—84no—
406C2×C3×D5AGL(1,ℤ/8)12yescomplemented
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—41no—
410C3×C4×C5—41no—
411C3×C4×C5C22×D411yescharacteristic
412C3×C4×C5H(5,𝔽2)11yescharacteristic
413C3×Dic5—21no—
414C3×Dic5—21no—
415C3×Dic5—41no—
416C24×C3—101no—
417C24×C3—101no—
418C24×C3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—51no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—101no—
429C2×C3×D4—101no—
430C2×C3×D4—101no—
431C2×C3×D4—101no—
432C2×C3×D4—102no—
433C2×C3×D4—102no—
434C2×C3×D4—102no—
435C2×C3×D4—101no—
436C2×C3×D4—101no—
437C2×C3×D4—101no—
438C2×C3×D4—204no—
439C2×C3×D4—201no—
440C2×C3×D4—201no—
441C2×C3×D4—201no—
442C2×C3×D4C22×D511yescharacteristic
443C2×C3×D4C22×D511yescharacteristic
444C22×C3×C4—21no—
445C22×C3×C4—21no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—101no—
449C3×SD16—102no—
450C3×SD16—102no—
451C3×SD16—201no—
452C3×D8—102no—
453C3×D8—102no—
454C3×D8—102no—
455C3×D8—102no—
456C3×D8—201no—
457C3×D8D2014yescomplemented
458C3×M16—102no—
459C2×C3×C8—51no—
460C2×C3×C8—51no—
461C2×C3×C8—102no—
462C2×C3×C8C22×D511yescharacteristic
463C2×C3×C8C22×D511yescharacteristic
464C3×C4⋊C4—51no—
465C3×C4⋊C4—101no—
466C3×C4⋊C4C22×D511yescharacteristic
467C3×C4⋊C4C22×D511yescharacteristic
468C3×C22⋊C4—21no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—51no—
471C3×C22⋊C4—51no—
472C3×C22⋊C4—101no—
473C3×C22⋊C4—101no—
474C3×C22⋊C4—101no—
475C3×C22⋊C4—101no—
476C3×C22⋊C4—101no—
477C3×C22⋊C4—101no—
478C3×C42C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—42no—
485C22×D5—42no—
486C22×D5—42no—
487C22×D5—42no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—81no—
491C22×D5—81no—
492C22×D5—81no—
493C22×D5C2×C3×D411yescharacteristic
494C22×D5C2×C3×D411yescharacteristic
495C5×D4—21no—
496C5×D4—21no—
497C5×D4C2×C3×D412yes—
498C5×D4C2×C3×D412yescomplemented
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—42no—
502C2×C4×C5—81no—
503C2×C4×C5C2×C3×D411yescharacteristic
504C2×C4×C5C2×C3×D411yescharacteristic
505C2×C4×C5C24×C311yescharacteristic
506C22⋊D5—42no—
507C22⋊D5—42no—
508C22⋊D5—42no—
509C22⋊D5—42no—
510C2×Dic5—21no—
511C2×Dic5—42no—
512C2×Dic5C2×C3×D411yescharacteristic
513C2×Dic5C2×C3×D411yescharacteristic
514D20—22no—
515D20—21no—
516D20—21no—
517D20—21no—
518D20—21no—
519D20—21no—
520D20—21no—
521D20—42no—
522D20—42no—
523D20—42no—
524D20—81no—
525D20—81no—
526C4×D5—21no—
527C4×D5—21no—
528C4×D5—21no—
529C4×D5—21no—
530Dic10—21no—
531Dic10—21no—
532C5×C8—21no—
533C5×C8C2×C3×D412yescomplemented
534#168—21no—
535#168—21no—
536C2×#41—51no—
537C22×D4—51no—
538C22×D4—51no—
539C22×D4—51no—
540C22×D4—101no—
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—104no—
551C2×D8C2×C3×D511yescharacteristic
552C2×M16—51no—
553C22×C8—51no—
554#127—51no—
555#124—51no—
556#123—101no—
557C22⋊Q8—51no—
558#121—51no—
559#121—51no—
560#121—51no—
561#121—101no—
562#121—101no—
563#120—101no—
564#120—101no—
565#120—101no—
566C4×D4—51no—
567C4×D4C2×C3×D511yescharacteristic, complemented
568C4×D4C2×C3×D511yescharacteristic, complemented
569C2×C22⋊C4—101no—
570#106C2×C3×D511yescharacteristic, complemented
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—51no—
575#102—51no—
576#102C2×C3×D511yescharacteristic, complemented
577#102C2×C3×D511yescharacteristic, complemented
578C22⋊C8—51no—
579C22⋊C8—51no—
580#97C2×C3×D511yescharacteristic, complemented
581C2×C3×C5—42no—
582C2×C3×C5—42no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586C3×D5—22no—
587C3×D5—41no—
588C3×D5—81no—
589C3×D5—81no—
590C3×D5—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—51no—
594C23×C3—51no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—202no—
601C23×C3—202no—
602C23×C3—202no—
603C23×C3—202no—
604C23×C3—401no—
605C23×C3—401no—
606C23×C3—401no—
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—102no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—101no—
615C3×D4—101no—
616C3×D4—101no—
617C3×D4—101no—
618C3×D4—202no—
619C3×D4—202no—
620C3×D4—202no—
621C3×D4—202no—
622C3×D4—202no—
623C3×D4—202no—
624C3×D4—202no—
625C3×D4—401no—
626C3×D4—401no—
627C3×D4C2×D2012yes—
628C3×D4C2×D2012yescomplemented
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—42no—
632C2×C3×C4—51no—
633C2×C3×C4—51no—
634C2×C3×C4—81no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—202no—
641C2×C3×C4D4×D511yescharacteristic
642C2×C3×C4D4×D511yescharacteristic
643C2×C3×C4C23×D511yescharacteristic
644C3×C8—21no—
645C3×C8—101no—
646C3×C8—101no—
647C3×C8C2×D2012yescomplemented
648C22×C5—22no—
649C22×C5—22no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5C22×C3×D411yescharacteristic
655C2×D5—21no—
656C2×D5—21no—
657C2×D5—21no—
658C2×D5—21no—
659C2×D5—21no—
660C2×D5—41no—
661C2×D5—41no—
662C2×D5—41no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—84no—
670C2×D5—84no—
671C2×D5—84no—
672C2×D5C3×AGL(1,ℤ/8)12yescomplemented
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5—41no—
677C4×C5C22×C3×D411yescharacteristic
678C4×C5C3×H(5,𝔽2)11yescharacteristic
679Dic5—21no—
680Dic5—21no—
681Dic5—41no—
682C24—101no—
683C24—101no—
684C24—101no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—51no—
689C2×D4—51no—
690C2×D4—51no—
691C2×D4—51no—
692C2×D4—101no—
693C2×D4—101no—
694C2×D4—101no—
695C2×D4—101no—
696C2×D4—101no—
697C2×D4—101no—
698C2×D4—102no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—101no—
702C2×D4—101no—
703C2×D4—101no—
704C2×D4—204no—
705C2×D4—201no—
706C2×D4—201no—
707C2×D4—201no—
708C2×D4C22×C3×D511yescharacteristic
709C2×D4C22×C3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—51no—
713C22×C4—51no—
714C22×C4—101no—
715SD16—102no—
716SD16—102no—
717SD16—201no—
718D8—102no—
719D8—102no—
720D8—102no—
721D8—102no—
722D8—201no—
723D8C3×D2014yescomplemented
724M16—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—102no—
728C2×C8C22×C3×D511yescharacteristic
729C2×C8C22×C3×D511yescharacteristic
730C4⋊C4—51no—
731C4⋊C4—101no—
732C4⋊C4C22×C3×D511yescharacteristic
733C4⋊C4C22×C3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—51no—
737C22⋊C4—51no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—101no—
742C22⋊C4—101no—
743C22⋊C4—101no—
744C42C22×C3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—52no—
753C22×C3—101no—
754C22×C3—101no—
755C22×C3—101no—
756C22×C3—101no—
757C22×C3—101no—
758C22×C3—201no—
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—404no—
770C22×C3C2×D4×D511yescharacteristic
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—101no—
776C3×C4—101no—
777C3×C4—201no—
778C3×C4C22×D2011yescharacteristic
779C3×C4#414911yescharacteristic
780C2×C5—42no—
781C2×C5—42no—
782C2×C5C3×D4211yescharacteristic
783C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
784C2×C5C3×#57611yescharacteristic
785D5—22no—
786D5—41no—
787D5—81no—
788D5—81no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—51no—
793C23—51no—
794C23—101no—
795C23—101no—
796C23—101no—
797C23—202no—
798C23—202no—
799C23—202no—
800C23—202no—
801C23—202no—
802C23—202no—
803C23—401no—
804C23—401no—
805C23—401no—
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—102no—
811D4—101no—
812D4—101no—
813D4—101no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—202no—
818D4—202no—
819D4—202no—
820D4—202no—
821D4—202no—
822D4—202no—
823D4—202no—
824D4—401no—
825D4—401no—
826D4C2×C3×D2012yes—
827D4C2×C3×D2012yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—42no—
831C2×C4—51no—
832C2×C4—51no—
833C2×C4—81no—
834C2×C4—101no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—101no—
839C2×C4—202no—
840C2×C4C3×D4×D511yescharacteristic
841C2×C4C3×D4×D511yescharacteristic
842C2×C4C23×C3×D511yescharacteristic
843C8—21no—
844C8—101no—
845C8—101no—
846C8C2×C3×D2012yescomplemented
847C2×C3—42no—
848C2×C3—42no—
849C2×C3—102no—
850C2×C3—201no—
851C2×C3—401no—
852C2×C3—401no—
853C2×C3—401no—
854C2×C3D4×D2011yescharacteristic
855C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
856C2×C3#6610811yescharacteristic
857C5C3×#326411yescharacteristic, complemented, Sylow
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—52no—
865C22—101no—
866C22—101no—
867C22—101no—
868C22—101no—
869C22—101no—
870C22—201no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—404no—
880C22—404no—
881C22—404no—
882C22C2×C3×D4×D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—101no—
888C4—101no—
889C4—201no—
890C4C22×C3×D2011yescharacteristic
891C4C3×#414911yescharacteristic
892C3#1061160911yescharacteristic, direct product factor, Sylow
893C2—42no—
894C2—42no—
895C2—102no—
896C2—201no—
897C2—401no—
898C2—401no—
899C2—401no—
900C2C3×D4×D2011yescharacteristic
901C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
902C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#442C2
socleC22×C3×C5C22×D4
hypercenterC3×#442D5
hypocenterC5C3×#3264
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4057C2semidirect
2. C2×C3×D5×D8C2semidirect
3. C3×#65888C2semidirect
4. C3×D4×D20C2semidirect
5. C3×C5×#442C2semidirect
6. C3×#65305C2semidirect
7. C3×#65304C2semidirect
8. C3×#65154C2semidirect
9. C3×#65153C2semidirect
10. C3×#65070C2semidirect
11. C3×#65065C2semidirect
12. C3×#65062C2semidirect
13. C3×#65062C2semidirect
14. C3×#65001C2semidirect
15. C3×#64995C2semidirect
16. #10611609C3direct (N × H)
17. C2×C3×#711C22semidirect
19. C2×C3×D4×D5C22semidirect
20. C2×C3×D4×D5C22semidirect
23. C3×C4×C5×D4C22semidirect
24. C3×C4×C5×D4C22semidirect
25. C2×C3×#687C22semidirect
27. C2×C3×#686C22semidirect
28. C2×C3×#686C22semidirect
34. C2×C3×D40C22semidirect
35. C2×C3×D40C22semidirect
36. C2×C3×#677C22semidirect
37. C2×C3×#677C22semidirect
38. C2×C3×#676C22semidirect
39. C2×C3×C8×D5C22semidirect
40. C3×#4043C22semidirect
42. C3×#4041C22semidirect
43. C3×#4041C22semidirect
48. C3×#4021C22semidirect
49. C3×#4020C22semidirect
51. C3×C5×#106C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×#97C22semidirect
55. C3×#3952C22semidirect
56. C3×#3952C22semidirect
57. C3×#3942C22semidirect
58. C3×#3941C22semidirect
59. C3×#3941C22semidirect
60. C3×#3941C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4057C2×C3semidirect
64. C2×D5×D8C2×C3semidirect
65. #65888C2×C3semidirect
66. D4×D20C2×C3semidirect
67. C5×#442C2×C3semidirect
68. #65305C2×C3semidirect
69. #65304C2×C3semidirect
70. #65154C2×C3semidirect
71. #65153C2×C3semidirect
72. #65070C2×C3semidirect
73. #65065C2×C3semidirect
74. #65062C2×C3semidirect
75. #65062C2×C3semidirect
76. #65001C2×C3semidirect
77. #64995C2×C3semidirect
111. C3×C5×D8D4semidirect
154. C3×#442D5semidirect
156. C2×#711C22×C3semidirect
158. C2×D4×D5C22×C3semidirect
159. C2×D4×D5C22×C3semidirect
162. C4×C5×D4C22×C3semidirect
163. C4×C5×D4C22×C3semidirect
164. C2×#687C22×C3semidirect
166. C2×#686C22×C3semidirect
167. C2×#686C22×C3semidirect
173. C2×D40C22×C3semidirect
174. C2×D40C22×C3semidirect
175. C2×#677C22×C3semidirect
176. C2×#677C22×C3semidirect
177. C2×#676C22×C3semidirect
178. C2×C8×D5C22×C3semidirect
179. #4043C22×C3semidirect
181. #4041C22×C3semidirect
182. #4041C22×C3semidirect
187. #4021C22×C3semidirect
188. #4020C22×C3semidirect
190. C5×#106C22×C3semidirect
191. C5×#102C22×C3semidirect
192. C5×#102C22×C3semidirect
193. C5×#97C22×C3semidirect
194. #3952C22×C3semidirect
195. #3952C22×C3semidirect
196. #3942C22×C3semidirect
197. #3941C22×C3semidirect
198. #3941C22×C3semidirect
199. #3941C22×C3semidirect
200. C4⋊#168C22×C3semidirect
221. C3×C5×D4C2×D4semidirect
256. C3×C5×C8C2×D4semidirect
290. C3×C4×D4C2×D5semidirect
291. C3×C4×D4C2×D5semidirect
293. C3×#106C2×D5semidirect
299. C3×#102C2×D5semidirect
300. C3×#102C2×D5semidirect
303. C3×#97C2×D5semidirect
337. C5×D8C3×D4semidirect
380. #442C3×D5semidirect
406. C2×C3×D5AGL(1,ℤ/8)semidirect
457. C3×D8D20semidirect
498. C5×D4C2×C3×D4semidirect
533. C5×C8C2×C3×D4semidirect
567. C4×D4C2×C3×D5semidirect
568. C4×D4C2×C3×D5semidirect
570. #106C2×C3×D5semidirect
576. #102C2×C3×D5semidirect
577. #102C2×C3×D5semidirect
580. #97C2×C3×D5semidirect
628. C3×D4C2×D20semidirect
647. C3×C8C2×D20semidirect
672. C2×D5C3×AGL(1,ℤ/8)semidirect
723. D8C3×D20semidirect
745. C3×C5#3264semidirect
827. D4C2×C3×D20semidirect
846. C8C2×C3×D20semidirect
857. C5C3×#3264semidirect
892. C3#10611609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40572
C2×C3×D5×D82
C3×#658882
C3×D4×D202
C3×C5×#4422
C3×#653052
C3×#653042
C3×#651542
C3×#651532
C3×#650702
C3×#650652
C3×#650622
C3×#650012
C3×#649952
#106116093
C3×#32645