Finite Group Databasebeta

← C3×#10611226 #14453719

Subgroups — C3×#10611226 #14453719

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4055C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic, complemented
3C3×#65884C211yesmaximal, characteristic
4C3×D4×Dic10C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6C3×#65423C211yesmaximal, characteristic, complemented
7C3×#65405C211yesmaximal, characteristic, complemented
8C3×#65134C211yesmaximal, characteristic, complemented
9C3×#65130C211yesmaximal, characteristic, complemented
10C3×#65028C211yesmaximal, characteristic, complemented
11C3×#65027C211yesmaximal, characteristic, complemented
12C3×#65022C211yesmaximal, characteristic, complemented
13C3×#65020C211yesmaximal, characteristic, complemented
14C3×#65004C211yesmaximal, characteristic, complemented
15C3×#64999C211yesmaximal, characteristic, complemented
16#10611226C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×C3×C5×M16C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24C3×#4083—21no—
25C3×D4×Dic5—21no—
26C3×#4076C2211yescharacteristic
27C3×#4070C2211yescharacteristic
28C3×#4070C2211yescharacteristic
29C3×#4070C2211yescharacteristic, complemented
30C3×#4055—24no—
31C2×C3×Dic20C2211yescharacteristic, complemented
32C2×C3×Dic20C2211yescharacteristic, complemented
33C2×C3×Dic20C2211yescharacteristic, complemented
34C2×C3×#677—24no—
35C2×C3×#677C2211yescharacteristic
36C2×C3×#677C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×#677C2211yescharacteristic
39C2×C3×#677C2211yescharacteristic
40C2×C3×#677C2211yescharacteristic
41C3×#4040—21no—
42C3×#4034—21no—
43C3×#4030—21no—
44C3×D5×C22⋊C4—21no—
45C3×#4024—21no—
46C3×#4024—21no—
47C3×#4021C2211yescharacteristic
48C3×C4×D20C2211yescharacteristic
49C3×#4015C2211yescharacteristic, complemented
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic
56C3×#3953C2211yescharacteristic
57C3×#3950C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3948C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3266—51nomaximal, Hall
63C2×#4055C2×C311yescharacteristic, complemented
64C22×#677C2×C311yescharacteristic, complemented
65#65884C2×C311yescharacteristic
66D4×Dic10C2×C311yescharacteristic, complemented
67C5×#435C2×C311yescharacteristic, complemented
68#65423C2×C311yescharacteristic, complemented
69#65405C2×C311yescharacteristic, complemented
70#65134C2×C311yescharacteristic, complemented
71#65130C2×C311yescharacteristic, complemented
72#65028C2×C311yescharacteristic, complemented
73#65027C2×C311yescharacteristic, complemented
74#65022C2×C311yescharacteristic, complemented
75#65020C2×C311yescharacteristic, complemented
76#65004C2×C311yescharacteristic, complemented
77#64999C2×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—
84C22×C3×Dic5—21no—
85C22×C3×Dic5—21no—
86C3×#709—22no—
87C3×#709—41no—
88C2×C3×D20—22no—
89C2×C3×D20—21no—
90C2×C3×D20—41no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5—21no—
95C2×C3×Dic10—22no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10—21no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—41no—
100C2×C3×Dic10—41no—
101C2×C3×Dic10C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×M16—22no—
106C2×C3×C5×C8—22no—
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C2×C3×C5×C8C2311yescharacteristic
111C3×C5×C4⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C42×C5C2311yescharacteristic
115C3×C22⋊Dic5—21no—
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×#685—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×C4⋊Dic5—21no—
123C3×C4⋊Dic5—21no—
124C3×C4⋊Dic5C2311yescharacteristic
125C3×C4⋊Dic5C2311yescharacteristic
126C3×#683—21no—
127C3×#683—21no—
128C3×#683—21no—
129C3×#683—21no—
130C3×C4×Dic5—21no—
131C3×Dic20—22no—
132C3×Dic20—22no—
133C3×Dic20—41no—
134C3×#677—22no—
135C3×#677—22no—
136C3×#677—22no—
137C3×#677—22no—
138C3×#677—41no—
139C3×#677D414yescomplemented
140C2×C3×#137—51no—
141C22×C3×SD16—51no—
142C3×D4×Q8—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#468—51no—
146C3×#467—51no—
147C3×#464—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#451—51no—
151C3×#450—51no—
152C3×#448—51no—
153C3×#440—51no—
154C3×#435D511yescharacteristic, complemented
155C2×#709C22×C311yescharacteristic
156C22×D20C22×C311yescharacteristic
157C22×Dic10C22×C311yescharacteristic
158C22×Dic10C22×C311yescharacteristic, complemented
159C2×C5×M16C22×C311yescharacteristic, complemented
160C22×C5×C8C22×C311yescharacteristic
161C4×C5×D4C22×C311yescharacteristic
162#4083—21no—
163D4×Dic5—21no—
164#4076C22×C311yescharacteristic
165#4070C22×C311yescharacteristic
166#4070C22×C311yescharacteristic
167#4070C22×C311yescharacteristic, complemented
168#4055—24no—
169C2×Dic20C22×C311yescharacteristic, complemented
170C2×Dic20C22×C311yescharacteristic, complemented
171C2×Dic20C22×C311yescharacteristic, complemented
172C2×#677—24no—
173C2×#677C22×C311yescharacteristic
174C2×#677C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×#677C22×C311yescharacteristic
177C2×#677C22×C311yescharacteristic
178C2×#677C22×C311yescharacteristic
179#4040—21no—
180#4034—21no—
181#4030—21no—
182D5×C22⋊C4—21no—
183#4024—21no—
184#4024—21no—
185#4021C22×C311yescharacteristic
186C4×D20C22×C311yescharacteristic
187#4015C22×C311yescharacteristic, complemented
188C4×Dic10C22×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#3950C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3948C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199#3948C22×C311yescharacteristic, complemented
200#3266—51noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
208C3×C5×D4—22no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218C3×C22⋊D5—42no—
219C3×C22⋊D5—81no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—42no—
227C2×C3×Dic5—42no—
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—21no—
231C3×D20—42no—
232C3×D20C2×D412yes—
233C3×C4×D5—42no—
234C3×C4×D5—81no—
235C3×Dic10—21no—
236C3×Dic10—21no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yes—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×C5×C8C2×D412yes—
249C2×C3×#41—51no—
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4—51no—
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16—51no—
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—104no—
264C2×C3×M16C2×D511yescharacteristic, complemented
265C22×C3×C8C2×D511yescharacteristic
266C3×C4⋊Q8—51no—
267C3×C4⋊Q8—101no—
268C3×#124—51no—
269C3×#123—101no—
270C3×C22⋊Q8—51no—
271C3×C22⋊Q8—51no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—101no—
274C3×C22⋊Q8—101no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#120—101no—
278C3×C4×Q8—51no—
279C3×C4×D4—51no—
280C3×C4×D4—101no—
281C3×C4×D4C2×D511yescharacteristic
282C2×C3×C22⋊C4—101no—
283C3×#107—51no—
284C3×C4⋊C8C2×D511yescharacteristic, complemented
285C3×#103—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102—51no—
291C3×C22⋊C8C2×D511yescharacteristic
292C3×C22⋊C8C2×D511yescharacteristic, complemented
293C3×#97C2×D511yescharacteristic, complemented
294C23×D5—21no—
295C2×C5×D4C3×D411yescharacteristic
296C22×C4×C5C23×C311yescharacteristic
297C22×C4×C5C23×C311yescharacteristic
298C2×C22⋊D5—21no—
299C2×C22⋊D5—21no—
300C22×Dic5—21no—
301C22×Dic5—21no—
302#709—22no—
303#709—41no—
304C2×D20—22no—
305C2×D20—21no—
306C2×D20—41no—
307C2×D20C23×C311yescharacteristic
308C2×D20C23×C311yescharacteristic
309C2×C4×D5—21no—
310C2×C4×D5—21no—
311C2×Dic10—22no—
312C2×Dic10—22no—
313C2×Dic10—21no—
314C2×Dic10—21no—
315C2×Dic10—41no—
316C2×Dic10—41no—
317C2×Dic10C23×C311yescharacteristic
318C2×Dic10C23×C311yescharacteristic
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×M16—22no—
322C2×C5×C8—22no—
323C2×C5×C8C23×C311yescharacteristic
324C2×C5×C8C23×C311yescharacteristic
325C2×C5×C8C23×C311yescharacteristic
326C2×C5×C8C23×C311yescharacteristic
327C5×C4⋊C4C3×D411yescharacteristic
328C5×C22⋊C4C3×D411yescharacteristic
329C5×C22⋊C4C3×D411yescharacteristic
330C42×C5C23×C311yescharacteristic
331C22⋊Dic5—21no—
332C22⋊Dic5—21no—
333C22⋊Dic5—21no—
334#685—21no—
335#685—21no—
336#685—21no—
337#685—21no—
338C4⋊Dic5—21no—
339C4⋊Dic5—21no—
340C4⋊Dic5C23×C311yescharacteristic
341C4⋊Dic5C23×C311yescharacteristic
342#683—21no—
343#683—21no—
344#683—21no—
345#683—21no—
346C4×Dic5—21no—
347Dic20—22no—
348Dic20—22no—
349Dic20—41no—
350#677—22no—
351#677—22no—
352#677—22no—
353#677—22no—
354#677—41no—
355#677C3×D414yescomplemented
356C2×#137—51no—
357C22×SD16—51no—
358D4×Q8—51no—
359#546—51no—
360#497—51no—
361#468—51no—
362#467—51no—
363#464—51no—
364#461—51no—
365#452—51no—
366#451—51no—
367#450—51no—
368#448—51no—
369#440—51no—
370#435C3×D511yescharacteristic, complemented
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×C3×D5—22no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391C3×Dic5—22no—
392C3×Dic5—41no—
393C3×Dic5—41no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—51no—
401C2×C3×Q8—51no—
402C2×C3×Q8—51no—
403C2×C3×Q8—51no—
404C2×C3×Q8—102no—
405C2×C3×Q8—102no—
406C2×C3×Q8—101no—
407C2×C3×Q8—101no—
408C2×C3×Q8—201no—
409C2×C3×Q8—201no—
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—102no—
413C2×C3×D4—101no—
414C2×C3×D4—101no—
415C2×C3×D4—101no—
416C2×C3×D4—201no—
417C2×C3×D4D2011yescharacteristic
418C22×C3×C4—101no—
419C22×C3×C4—101no—
420C22×C3×C4—101no—
421C22×C3×C4—101no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C3×Q16—102no—
425C3×Q16—102no—
426C3×Q16—201no—
427C3×SD16—54no—
428C3×SD16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—201no—
433C3×M16—22no—
434C2×C3×C8—22no—
435C2×C3×C8C22×D511yescharacteristic
436C2×C3×C8C22×D511yescharacteristic
437C2×C3×C8C22×D511yescharacteristic
438C2×C3×C8C22×D511yescharacteristic
439C3×C4⋊C4—51no—
440C3×C4⋊C4—51no—
441C3×C4⋊C4—101no—
442C3×C4⋊C4—101no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4D2011yescharacteristic
448C3×C22⋊C4—101no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4D2011yescharacteristic
456C3×C22⋊C4D2011yescharacteristic
457C3×C42—101no—
458C3×C42C22×D511yescharacteristic
459C23×C5C2×C3×D411yescharacteristic
460C23×C5C2×C3×D411yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—42no—
464C22×D5—42no—
465C22×D5—81no—
466C5×D4—22no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5C2×C3×D411yescharacteristic
472C2×C4×C5C2×C3×D411yescharacteristic
473C2×C4×C5C2×C3×D411yescharacteristic
474C2×C4×C5C2×C3×D411yescharacteristic
475C2×C4×C5C24×C311yescharacteristic
476C22⋊D5—42no—
477C22⋊D5—81no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—21no—
483C2×Dic5—21no—
484C2×Dic5—42no—
485C2×Dic5—42no—
486D20—21no—
487D20—21no—
488D20—21no—
489D20—42no—
490D20C2×C3×D412yes—
491C4×D5—42no—
492C4×D5—81no—
493Dic10—21no—
494Dic10—21no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—21no—
499Dic10—21no—
500Dic10—42no—
501Dic10—42no—
502Dic10C2×C3×D412yes—
503C5×C8—21no—
504C5×C8—21no—
505C5×C8—21no—
506C5×C8C2×C3×D412yes—
507C2×#41—51no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—51no—
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16—51no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—104no—
522C2×M16C2×C3×D511yescharacteristic, complemented
523C22×C8C2×C3×D511yescharacteristic
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—51no—
527#123—101no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—51no—
531C22⋊Q8—101no—
532C22⋊Q8—101no—
533#121—51no—
534#121—101no—
535#120—101no—
536C4×Q8—51no—
537C4×D4—51no—
538C4×D4—101no—
539C4×D4C2×C3×D511yescharacteristic
540C2×C22⋊C4—101no—
541#107—51no—
542C4⋊C8C2×C3×D511yescharacteristic, complemented
543#103—51no—
544#103—51no—
545#103—51no—
546#103—51no—
547#102—51no—
548#102—51no—
549C22⋊C8C2×C3×D511yescharacteristic
550C22⋊C8C2×C3×D511yescharacteristic, complemented
551#97C2×C3×D511yescharacteristic, complemented
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C3×D5—42no—
558C3×D5—81no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—202no—
562C23×C3—202no—
563C23×C3—401no—
564C23×C3C2×D2011yescharacteristic
565C23×C3C2×D2011yescharacteristic
566C3×Q8—52no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—202no—
575C3×Q8—202no—
576C3×D4—22no—
577C3×D4—52no—
578C3×D4—101no—
579C3×D4—101no—
580C3×D4—101no—
581C3×D4—202no—
582C3×D4—202no—
583C3×D4—401no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—202no—
595C2×C3×C4—202no—
596C2×C3×C4—202no—
597C2×C3×C4—401no—
598C2×C3×C4C2×D2011yescharacteristic
599C2×C3×C4C2×D2011yescharacteristic
600C2×C3×C4C2×D2011yescharacteristic
601C2×C3×C4C2×D2011yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8D4×D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5C3×#13712yescomplemented
613C22×C5C22×C3×D411yescharacteristic
614C2×D5—22no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—41no—
620C2×D5—84no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5C22×C3×D411yescharacteristic
626C4×C5C3×H(5,𝔽2)11yescharacteristic
627Dic5—22no—
628Dic5—41no—
629Dic5—41no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—101no—
634#41—102no—
635#41—201no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—51no—
640C2×Q8—102no—
641C2×Q8—102no—
642C2×Q8—101no—
643C2×Q8—101no—
644C2×Q8—201no—
645C2×Q8—201no—
646C2×D4—51no—
647C2×D4—51no—
648C2×D4—102no—
649C2×D4—101no—
650C2×D4—101no—
651C2×D4—101no—
652C2×D4—201no—
653C2×D4C3×D2011yescharacteristic
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4C22×C3×D511yescharacteristic
659C22×C4C22×C3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—54no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—102no—
668SD16—201no—
669M16—22no—
670C2×C8—22no—
671C2×C8C22×C3×D511yescharacteristic
672C2×C8C22×C3×D511yescharacteristic
673C2×C8C22×C3×D511yescharacteristic
674C2×C8C22×C3×D511yescharacteristic
675C4⋊C4—51no—
676C4⋊C4—51no—
677C4⋊C4—101no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4—101no—
683C4⋊C4C3×D2011yescharacteristic
684C22⋊C4—101no—
685C22⋊C4—101no—
686C22⋊C4—101no—
687C22⋊C4—101no—
688C22⋊C4—101no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4C3×D2011yescharacteristic
692C22⋊C4C3×D2011yescharacteristic
693C42—101no—
694C42C22×C3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—102no—
702C22×C3—201no—
703C22×C3—201no—
704C22×C3—201no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—404no—
708C22×C3#405512yescomplemented
709C22×C3C22×D2011yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—102no—
715C3×C4—201no—
716C3×C4—201no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C2×D4×D511yescharacteristic
721C3×C4#414911yescharacteristic
722C2×C5—22no—
723C2×C5—41no—
724C2×C5C3×D4211yescharacteristic
725C2×C5C2×C3×#13711yescharacteristic
726C2×C5C3×#57711yescharacteristic
727D5—42no—
728D5—81no—
729C23—101no—
730C23—101no—
731C23—202no—
732C23—202no—
733C23—401no—
734C23C2×C3×D2011yescharacteristic
735C23C2×C3×D2011yescharacteristic
736Q8—52no—
737Q8—101no—
738Q8—101no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—101no—
744Q8—202no—
745Q8—202no—
746D4—22no—
747D4—52no—
748D4—101no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—202no—
753D4—401no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—202no—
765C2×C4—202no—
766C2×C4—202no—
767C2×C4—401no—
768C2×C4C2×C3×D2011yescharacteristic
769C2×C4C2×C3×D2011yescharacteristic
770C2×C4C2×C3×D2011yescharacteristic
771C2×C4C2×C3×D2011yescharacteristic
772C2×C4C23×C3×D511yescharacteristic
773C8—21no—
774C8—21no—
775C8—21no—
776C8C3×D4×D512yes—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3—202no—
780C2×C3—401no—
781C2×C3D4×D2011yescharacteristic
782C2×C3C2×#405511yescharacteristic
783C2×C3#6608511yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—102no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—404no—
797C22C3×#405512yescomplemented
798C22C22×C3×D2011yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—102no—
804C4—201no—
805C4—201no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C2×C3×D4×D511yescharacteristic
810C4C3×#414911yescharacteristic
811C3#1061122611yescharacteristic, direct product factor, Sylow
812C2—22no—
813C2—41no—
814C2—202no—
815C2—401no—
816C2C3×D4×D2011yescharacteristic
817C2C2×C3×#405511yescharacteristic
818C2C3×#6608511yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
prime radicalC3×#65884C2
hypercenterC3×#435D5
hypocenterC5C3×#3266
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×#4055C2semidirect
2. C22×C3×#677C2semidirect
4. C3×D4×Dic10C2semidirect
5. C3×C5×#435C2semidirect
6. C3×#65423C2semidirect
7. C3×#65405C2semidirect
8. C3×#65134C2semidirect
9. C3×#65130C2semidirect
10. C3×#65028C2semidirect
11. C3×#65027C2semidirect
12. C3×#65022C2semidirect
13. C3×#65020C2semidirect
14. C3×#65004C2semidirect
15. C3×#64999C2semidirect
16. #10611226C3direct (N × H)
20. C22×C3×Dic10C22semidirect
21. C2×C3×C5×M16C22semidirect
29. C3×#4070C22semidirect
31. C2×C3×Dic20C22semidirect
32. C2×C3×Dic20C22semidirect
33. C2×C3×Dic20C22semidirect
49. C3×#4015C22semidirect
50. C3×C4×Dic10C22semidirect
51. C3×C5×C4⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
57. C3×#3950C22semidirect
58. C3×#3948C22semidirect
59. C3×#3948C22semidirect
60. C3×#3948C22semidirect
61. C3×#3948C22semidirect
63. C2×#4055C2×C3semidirect
64. C22×#677C2×C3semidirect
66. D4×Dic10C2×C3semidirect
67. C5×#435C2×C3semidirect
68. #65423C2×C3semidirect
69. #65405C2×C3semidirect
70. #65134C2×C3semidirect
71. #65130C2×C3semidirect
72. #65028C2×C3semidirect
73. #65027C2×C3semidirect
74. #65022C2×C3semidirect
75. #65020C2×C3semidirect
76. #65004C2×C3semidirect
77. #64999C2×C3semidirect
139. C3×#677D4semidirect
154. C3×#435D5semidirect
158. C22×Dic10C22×C3semidirect
159. C2×C5×M16C22×C3semidirect
167. #4070C22×C3semidirect
169. C2×Dic20C22×C3semidirect
170. C2×Dic20C22×C3semidirect
171. C2×Dic20C22×C3semidirect
187. #4015C22×C3semidirect
188. C4×Dic10C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
192. C5×#97C22×C3semidirect
195. #3950C22×C3semidirect
196. #3948C22×C3semidirect
197. #3948C22×C3semidirect
198. #3948C22×C3semidirect
199. #3948C22×C3semidirect
264. C2×C3×M16C2×D5semidirect
284. C3×C4⋊C8C2×D5semidirect
292. C3×C22⋊C8C2×D5semidirect
293. C3×#97C2×D5semidirect
355. #677C3×D4semidirect
370. #435C3×D5semidirect
376. C22×C3×C5#137semidirect
522. C2×M16C2×C3×D5semidirect
542. C4⋊C8C2×C3×D5semidirect
550. C22⋊C8C2×C3×D5semidirect
551. #97C2×C3×D5semidirect
612. C22×C5C3×#137semidirect
695. C3×C5#3266semidirect
708. C22×C3#4055semidirect
784. C5C3×#3266semidirect
797. C22C3×#4055semidirect
811. C3#10611226direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40552
C22×C3×#6772
C3×#658842
C3×D4×Dic102
C3×C5×#4352
C3×#654232
C3×#654052
C3×#651342
C3×#651302
C3×#650282
C3×#650272
C3×#650222
C3×#650202
C3×#650042
C3×#649992
#106112263
C3×#32665