Finite Group Databasebeta

← C3×#10611227 #14453974

Subgroups — C3×#10611227 #14453974

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×#4054C211yesmaximal, characteristic, complemented
2C2×C3×#4050C211yesmaximal, characteristic, complemented
3C3×#65885C211yesmaximal, characteristic, complemented
4C3×#65884C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6C3×#65426C211yesmaximal, characteristic, complemented
7C3×#65403C211yesmaximal, characteristic, complemented
8C3×#65133C211yesmaximal, characteristic, complemented
9C3×#65130C211yesmaximal, characteristic, complemented
10C3×#65023C211yesmaximal, characteristic, complemented
11C3×#65022C211yesmaximal, characteristic, complemented
12C3×#65022C211yesmaximal, characteristic, complemented
13C3×#65020C211yesmaximal, characteristic, complemented
14C3×#65004C211yesmaximal, characteristic, complemented
15C3×#65000C211yesmaximal, characteristic, complemented
16#10611227C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic, complemented
20C22×C3×D20C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C3×C4×C5×D4C2211yescharacteristic
24C3×#4084—21no—
25C3×#4083—21no—
26C3×#4076C2211yescharacteristic
27C3×#4070C2211yescharacteristic
28C3×#4070C2211yescharacteristic
29C3×#4070C2211yescharacteristic, complemented
30C3×#4054—24no—
31C2×C3×Dic20C2211yescharacteristic, complemented
32C2×C3×Dic20C2211yescharacteristic, complemented
33C3×#4050—24no—
34C2×C3×D40C2211yescharacteristic
35C2×C3×D40C2211yescharacteristic
36C2×C3×#677C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×#677C2211yescharacteristic
39C2×C3×#677C2211yescharacteristic
40C2×C3×#677C2211yescharacteristic, complemented
41C3×#4040—21no—
42C3×D5×C4⋊C4—21no—
43C3×#4030—21no—
44C3×#4029—21no—
45C3×#4029—21no—
46C3×D5×C22⋊C4—21no—
47C3×#4021C2211yescharacteristic
48C3×C4×D20C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic, complemented
50C3×#4015C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic
56C3×#3953C2211yescharacteristic
57C3×#3953C2211yescharacteristic, complemented
58C3×#3949C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3948C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4054C2×C311yescharacteristic, complemented
64C2×#4050C2×C311yescharacteristic, complemented
65#65885C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic, complemented
67C5×#435C2×C311yescharacteristic, complemented
68#65426C2×C311yescharacteristic, complemented
69#65403C2×C311yescharacteristic, complemented
70#65133C2×C311yescharacteristic, complemented
71#65130C2×C311yescharacteristic, complemented
72#65023C2×C311yescharacteristic, complemented
73#65022C2×C311yescharacteristic, complemented
74#65022C2×C311yescharacteristic, complemented
75#65020C2×C311yescharacteristic, complemented
76#65004C2×C311yescharacteristic, complemented
77#65000C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C3×#709—22no—
87C3×#709—22no—
88C3×#709—22no—
89C3×#709—41no—
90C3×#709—41no—
91C3×#709—41no—
92C2×C3×D20—22no—
93C2×C3×D20—21no—
94C2×C3×D20—41no—
95C2×C3×D20C2311yescharacteristic
96C2×C3×D20C2311yescharacteristic
97C2×C3×D20C2311yescharacteristic
98C2×C3×C4×D5—21no—
99C2×C3×C4×D5—21no—
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5—21no—
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×M16—22no—
107C2×C3×C5×C8—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112C3×C5×C4⋊C4D411yescharacteristic
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C42×C5C2311yescharacteristic
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×C22⋊Dic5—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×C4⋊Dic5—21no—
125C3×C4⋊Dic5—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C3×C4⋊Dic5C2311yescharacteristic
128C3×#683—21no—
129C3×#683—21no—
130C3×#683—21no—
131C3×Dic20—22no—
132C3×Dic20—41no—
133C3×D40—22no—
134C3×D40D414yescomplemented
135C3×#677—22no—
136C3×#677—22no—
137C3×#677—22no—
138C3×#677—22no—
139C3×#677—41no—
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×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442—51no—
154C3×#435D511yescharacteristic, complemented
155C2×#709C22×C311yescharacteristic
156C2×#709C22×C311yescharacteristic
157C2×#709C22×C311yescharacteristic, complemented
158C22×D20C22×C311yescharacteristic
159C2×C5×M16C22×C311yescharacteristic
160C22×C5×C8C22×C311yescharacteristic, complemented
161C4×C5×D4C22×C311yescharacteristic
162#4084—21no—
163#4083—21no—
164#4076C22×C311yescharacteristic
165#4070C22×C311yescharacteristic
166#4070C22×C311yescharacteristic
167#4070C22×C311yescharacteristic, complemented
168#4054—24no—
169C2×Dic20C22×C311yescharacteristic, complemented
170C2×Dic20C22×C311yescharacteristic, complemented
171#4050—24no—
172C2×D40C22×C311yescharacteristic
173C2×D40C22×C311yescharacteristic
174C2×#677C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×#677C22×C311yescharacteristic
177C2×#677C22×C311yescharacteristic
178C2×#677C22×C311yescharacteristic, complemented
179#4040—21no—
180D5×C4⋊C4—21no—
181#4030—21no—
182#4029—21no—
183#4029—21no—
184D5×C22⋊C4—21no—
185#4021C22×C311yescharacteristic
186C4×D20C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic, complemented
188#4015C22×C311yescharacteristic, complemented
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×C22⋊C8C22×C311yescharacteristic
191C5×C22⋊C8C22×C311yescharacteristic, complemented
192C5×#97C22×C311yescharacteristic, complemented
193#3953C22×C311yescharacteristic
194#3953C22×C311yescharacteristic
195#3953C22×C311yescharacteristic, complemented
196#3949C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199#3948C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—42no—
207C22×C3×D5—42no—
208C22×C3×D5—81no—
209C3×C5×D4—41no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2411yescharacteristic
219C3×C22⋊D5—42no—
220C3×C22⋊D5—42no—
221C3×C22⋊D5—42no—
222C3×C22⋊D5—81no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—21no—
232C3×D20—42no—
233C3×D20C2×D412yes—
234C3×D20C2×D412yes—
235C3×C4×D5—42no—
236C3×C4×D5—42no—
237C3×C4×D5—42no—
238C3×C4×D5—42no—
239C3×C4×D5—81no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×C5×C8—21no—
249C3×C5×C8C2×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×SD16—51no—
263C2×C3×D8—51no—
264C2×C3×D8—51no—
265C2×C3×M16C2×D511yescharacteristic
266C22×C3×C8C2×D511yescharacteristic, complemented
267C3×C4⋊Q8—51no—
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×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8C2×D511yescharacteristic
293C3×C22⋊C8C2×D511yescharacteristic, complemented
294C3×#97C2×D511yescharacteristic, complemented
295C23×D5—21no—
296C2×C5×D4C3×D411yescharacteristic
297C22×C4×C5C23×C311yescharacteristic
298C22×C4×C5C23×C311yescharacteristic
299C2×C22⋊D5—21no—
300C2×C22⋊D5—21no—
301C2×C22⋊D5—21no—
302C2×C22⋊D5—21no—
303#709—22no—
304#709—22no—
305#709—22no—
306#709—41no—
307#709—41no—
308#709—41no—
309C2×D20—22no—
310C2×D20—21no—
311C2×D20—41no—
312C2×D20C23×C311yescharacteristic
313C2×D20C23×C311yescharacteristic
314C2×D20C23×C311yescharacteristic
315C2×C4×D5—21no—
316C2×C4×D5—21no—
317C2×C4×D5—21no—
318C2×C4×D5—21no—
319C2×C4×D5—21no—
320C2×Dic10C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×M16—22no—
324C2×C5×C8—22no—
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C2×C5×C8C23×C311yescharacteristic
328C2×C5×C8C23×C311yescharacteristic
329C5×C4⋊C4C3×D411yescharacteristic
330C5×C22⋊C4C3×D411yescharacteristic
331C5×C22⋊C4C3×D411yescharacteristic
332C42×C5C23×C311yescharacteristic
333C22⋊Dic5—21no—
334C22⋊Dic5—21no—
335C22⋊Dic5—21no—
336#685—21no—
337#685—21no—
338#685—21no—
339#685—21no—
340#685—21no—
341C4⋊Dic5—21no—
342C4⋊Dic5—21no—
343C4⋊Dic5C23×C311yescharacteristic
344C4⋊Dic5C23×C311yescharacteristic
345#683—21no—
346#683—21no—
347#683—21no—
348Dic20—22no—
349Dic20—41no—
350D40—22no—
351D40C3×D414yescomplemented
352#677—22no—
353#677—22no—
354#677—22no—
355#677—22no—
356#677—41no—
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#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442—51no—
371#435C3×D511yescharacteristic, complemented
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5C22×D411yescharacteristic
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
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—21no—
392C3×C4×C5—21no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395C3×Dic5—41no—
396C3×Dic5—41no—
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×Q8—51no—
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—51no—
413C2×C3×D4—102no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—101no—
419C2×C3×D4—201no—
420C2×C3×D4D2011yescharacteristic
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—54no—
436C3×D8—102no—
437C3×M16—22no—
438C2×C3×C8—22no—
439C2×C3×C8C22×D511yescharacteristic
440C2×C3×C8C22×D511yescharacteristic
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⋊C4D2011yescharacteristic
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4D2011yescharacteristic
460C3×C22⋊C4D2011yescharacteristic
461C3×C42C22×D511yescharacteristic
462C23×C5C2×C3×D411yescharacteristic
463C23×C5C2×C3×D411yescharacteristic
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—42no—
468C22×D5—42no—
469C22×D5—81no—
470C5×D4—41no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5C2×C3×D411yescharacteristic
476C2×C4×C5C2×C3×D411yescharacteristic
477C2×C4×C5C2×C3×D411yescharacteristic
478C2×C4×C5C2×C3×D411yescharacteristic
479C2×C4×C5C24×C311yescharacteristic
480C22⋊D5—42no—
481C22⋊D5—42no—
482C22⋊D5—42no—
483C22⋊D5—81no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489D20—21no—
490D20—21no—
491D20—21no—
492D20—21no—
493D20—42no—
494D20C2×C3×D412yes—
495D20C2×C3×D412yes—
496C4×D5—42no—
497C4×D5—42no—
498C4×D5—42no—
499C4×D5—42no—
500C4×D5—81no—
501Dic10—21no—
502Dic10—21no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8—21no—
509C5×C8—21no—
510C5×C8C2×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×SD16—51no—
524C2×D8—51no—
525C2×D8—51no—
526C2×M16C2×C3×D511yescharacteristic
527C22×C8C2×C3×D511yescharacteristic, complemented
528C4⋊Q8—51no—
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#103—51no—
549#103—51no—
550#102—51no—
551#102—51no—
552#102—51no—
553C22⋊C8C2×C3×D511yescharacteristic
554C22⋊C8C2×C3×D511yescharacteristic, complemented
555#97C2×C3×D511yescharacteristic, complemented
556C2×C3×C5—41no—
557C2×C3×C5—41no—
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#57511yescharacteristic
560C2×C3×C5#57711yescharacteristic
561C3×D5—42no—
562C3×D5—42no—
563C3×D5—81no—
564C23×C3—101no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—202no—
568C23×C3—202no—
569C23×C3—401no—
570C23×C3C2×D2011yescharacteristic
571C23×C3C2×D2011yescharacteristic
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—41no—
579C3×D4—52no—
580C3×D4—52no—
581C3×D4—101no—
582C3×D4—101no—
583C3×D4—101no—
584C3×D4—101no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—202no—
588C3×D4—202no—
589C3×D4—401no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—202no—
600C2×C3×C4—202no—
601C2×C3×C4—202no—
602C2×C3×C4—202no—
603C2×C3×C4—401no—
604C2×C3×C4C2×D2011yescharacteristic
605C2×C3×C4C2×D2011yescharacteristic
606C2×C3×C4C2×D2011yescharacteristic
607C2×C3×C4C2×D2011yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8D4×D512yes—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—21no—
617C22×C5—21no—
618C22×C5—21no—
619C22×C5C22×C3×D411yescharacteristic
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—41no—
623C2×D5—41no—
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—21no—
633C4×C5—21no—
634C4×C5C22×C3×D411yescharacteristic
635C4×C5C3×H(5,𝔽2)11yescharacteristic
636Dic5—41no—
637Dic5—41no—
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×Q8—51no—
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—51no—
654C2×D4—102no—
655C2×D4—101no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—101no—
660C2×D4—201no—
661C2×D4C3×D2011yescharacteristic
662C22×C4—101no—
663C22×C4—101no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4C22×C3×D511yescharacteristic
668C22×C4C22×C3×D511yescharacteristic
669Q16—102no—
670Q16—201no—
671SD16—102no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—54no—
677D8—102no—
678M16—22no—
679C2×C8—22no—
680C2×C8C22×C3×D511yescharacteristic
681C2×C8C22×C3×D511yescharacteristic
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⋊C4C3×D2011yescharacteristic
692C22⋊C4—101no—
693C22⋊C4—101no—
694C22⋊C4—101no—
695C22⋊C4—101no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4C3×D2011yescharacteristic
701C22⋊C4C3×D2011yescharacteristic
702C42C22×C3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—201no—
713C22×C3—201no—
714C22×C3—201no—
715C22×C3—201no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C22×D2011yescharacteristic
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—201no—
726C3×C4—201no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C2×D4×D511yescharacteristic
731C3×C4#414911yescharacteristic
732C2×C5—41no—
733C2×C5—41no—
734C2×C5C3×D4211yescharacteristic
735C2×C5C3×#57511yescharacteristic
736C2×C5C3×#57711yescharacteristic
737D5—42no—
738D5—42no—
739D5—81no—
740C23—101no—
741C23—101no—
742C23—101no—
743C23—202no—
744C23—202no—
745C23—401no—
746C23C2×C3×D2011yescharacteristic
747C23C2×C3×D2011yescharacteristic
748Q8—101no—
749Q8—101no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—41no—
755D4—52no—
756D4—52no—
757D4—101no—
758D4—101no—
759D4—101no—
760D4—101no—
761D4—202no—
762D4—202no—
763D4—202no—
764D4—202no—
765D4—401no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—202no—
776C2×C4—202no—
777C2×C4—202no—
778C2×C4—202no—
779C2×C4—401no—
780C2×C4C2×C3×D2011yescharacteristic
781C2×C4C2×C3×D2011yescharacteristic
782C2×C4C2×C3×D2011yescharacteristic
783C2×C4C2×C3×D2011yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—21no—
787C8—21no—
788C8C3×D4×D512yes—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3—202no—
792C2×C3—202no—
793C2×C3—401no—
794C2×C3D4×D2011yescharacteristic
795C2×C3#6608211yescharacteristic
796C2×C3#6608511yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—102no—
805C22—102no—
806C22—201no—
807C22—201no—
808C22—201no—
809C22—201no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C22×C3×D2011yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—201no—
820C4—201no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C2×C3×D4×D511yescharacteristic
825C4C3×#414911yescharacteristic
826C3#1061122711yescharacteristic, direct product factor, Sylow
827C2—41no—
828C2—41no—
829C2—202no—
830C2—202no—
831C2—401no—
832C2C3×D4×D2011yescharacteristic
833C2C3×#6608211yescharacteristic
834C2C3×#6608511yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
hypercenterC3×#435D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4054C2semidirect
2. C2×C3×#4050C2semidirect
3. C3×#65885C2semidirect
4. C3×#65884C2semidirect
5. C3×C5×#435C2semidirect
6. C3×#65426C2semidirect
7. C3×#65403C2semidirect
8. C3×#65133C2semidirect
9. C3×#65130C2semidirect
10. C3×#65023C2semidirect
11. C3×#65022C2semidirect
12. C3×#65022C2semidirect
13. C3×#65020C2semidirect
14. C3×#65004C2semidirect
15. C3×#65000C2semidirect
16. #10611227C3direct (N × H)
19. C2×C3×#709C22semidirect
22. C22×C3×C5×C8C22semidirect
29. C3×#4070C22semidirect
31. C2×C3×Dic20C22semidirect
32. C2×C3×Dic20C22semidirect
40. C2×C3×#677C22semidirect
49. C3×C4×D20C22semidirect
50. C3×#4015C22semidirect
51. C3×C5×C4⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
57. C3×#3953C22semidirect
58. C3×#3949C22semidirect
59. C3×#3948C22semidirect
60. C3×#3948C22semidirect
61. C3×#3948C22semidirect
63. C2×#4054C2×C3semidirect
64. C2×#4050C2×C3semidirect
65. #65885C2×C3semidirect
66. #65884C2×C3semidirect
67. C5×#435C2×C3semidirect
68. #65426C2×C3semidirect
69. #65403C2×C3semidirect
70. #65133C2×C3semidirect
71. #65130C2×C3semidirect
72. #65023C2×C3semidirect
73. #65022C2×C3semidirect
74. #65022C2×C3semidirect
75. #65020C2×C3semidirect
76. #65004C2×C3semidirect
77. #65000C2×C3semidirect
134. C3×D40D4semidirect
154. C3×#435D5semidirect
157. C2×#709C22×C3semidirect
160. C22×C5×C8C22×C3semidirect
167. #4070C22×C3semidirect
169. C2×Dic20C22×C3semidirect
170. C2×Dic20C22×C3semidirect
178. C2×#677C22×C3semidirect
187. C4×D20C22×C3semidirect
188. #4015C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
192. C5×#97C22×C3semidirect
195. #3953C22×C3semidirect
196. #3949C22×C3semidirect
197. #3948C22×C3semidirect
198. #3948C22×C3semidirect
199. #3948C22×C3semidirect
266. C22×C3×C8C2×D5semidirect
285. C3×C4⋊C8C2×D5semidirect
293. C3×C22⋊C8C2×D5semidirect
294. C3×#97C2×D5semidirect
351. D40C3×D4semidirect
371. #435C3×D5semidirect
527. C22×C8C2×C3×D5semidirect
546. C4⋊C8C2×C3×D5semidirect
554. C22⋊C8C2×C3×D5semidirect
555. #97C2×C3×D5semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10611227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C2×C3×#40502
C3×#658852
C3×#658842
C3×C5×#4352
C3×#654262
C3×#654032
C3×#651332
C3×#651302
C3×#650232
C3×#650222
C3×#650202
C3×#650042
C3×#650002
#106112273
C3×#32675