Finite Group Databasebeta

← C3×#10611171 #14458618

Subgroups — C3×#10611171 #14458618

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65884C211yesmaximal, characteristic
2C3×#65875C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4C3×#65405C211yesmaximal, characteristic, complemented
5C3×#65403C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7C2×C3×#3953C211yesmaximal, characteristic, complemented
8C3×#65136C211yesmaximal, characteristic, complemented
9C3×#65134C211yesmaximal, characteristic, complemented
10C3×#65026C211yesmaximal, characteristic, complemented
11C3×#65022C211yesmaximal, characteristic, complemented
12C3×#65020C211yesmaximal, characteristic, complemented
13C3×#65010C211yesmaximal, characteristic, complemented
14C3×#64986C211yesmaximal, characteristic, complemented
15C3×C4×#677C211yesmaximal, characteristic, complemented
16#10611171C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C3×#4083—21no—
23C3×#4081—21no—
24C3×#4076C2211yescharacteristic
25C3×#4072C2211yescharacteristic, complemented
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C3×#4070C2211yescharacteristic
28C3×#4070C2211yescharacteristic
29C3×#4070C2211yescharacteristic, complemented
30C2×C3×Dic20C2211yescharacteristic, complemented
31C2×C3×#677C2211yescharacteristic
32C2×C3×#677C2211yescharacteristic
33C3×#4040—21no—
34C3×#4035—21no—
35C3×#4030—21no—
36C3×D5×C22⋊C4—21no—
37C3×#4025—21no—
38C3×#4023—21no—
39C3×#4021C2211yescharacteristic
40C3×C4×D20C2211yescharacteristic
41C3×#4016C2211yescharacteristic, complemented
42C3×C4×Dic10C2211yescharacteristic, complemented
43C3×C5×C4⋊C8C2211yescharacteristic, complemented
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×C5×C22⋊C8C2211yescharacteristic, complemented
46C3×C4×C5×C8C2211yescharacteristic, complemented
47C3×#3953C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3953C2211yescharacteristic
53C3×#3950C2211yescharacteristic, complemented
54C3×#3949C2211yescharacteristic, complemented
55C3×#3949C2211yescharacteristic, complemented
56C3×#3948C2211yescharacteristic, complemented
57C3×#3948C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3948C2211yescharacteristic, complemented
60C3×#3296—51nomaximal, Hall
61#65884C2×C311yescharacteristic
62#65875C2×C311yescharacteristic, complemented
63C5×C8×D4C2×C311yescharacteristic, complemented
64#65405C2×C311yescharacteristic, complemented
65#65403C2×C311yescharacteristic, complemented
66#65402C2×C311yescharacteristic, complemented
67C2×#3953C2×C311yescharacteristic, complemented
68#65136C2×C311yescharacteristic, complemented
69#65134C2×C311yescharacteristic, complemented
70#65026C2×C311yescharacteristic, complemented
71#65022C2×C311yescharacteristic, complemented
72#65020C2×C311yescharacteristic, complemented
73#65010C2×C311yescharacteristic, complemented
74#64986C2×C311yescharacteristic, complemented
75C4×#677C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C3×#709—22no—
84C3×#709—41no—
85C2×C3×D20—22no—
86C2×C3×D20—21no—
87C2×C3×D20—41no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×C3×C5×C8—41no—
95C2×C3×C5×C8—41no—
96C2×C3×C5×C8C2311yescharacteristic
97C2×C3×C5×C8C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4D411yescharacteristic
101C3×C5×C22⋊C4D411yescharacteristic
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C42×C5C2311yescharacteristic
104C3×C22⋊Dic5—21no—
105C3×C22⋊Dic5—21no—
106C3×C22⋊Dic5—21no—
107C3×C22⋊Dic5—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683—21no—
119C3×#683—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×#683—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5—21no—
125C3×Dic20—41no—
126C3×#677—22no—
127C3×#677—41no—
128C3×#552—51no—
129C3×#546—51no—
130C3×#488—51no—
131C3×#483—51no—
132C3×#482—51no—
133C3×#478—51no—
134C3×#467—51no—
135C3×#465—51no—
136C3×#464—51no—
137C3×#452—51no—
138C3×#450—51no—
139C3×C4×SD16—51no—
140C3×C8×D4D511yescharacteristic, complemented
141C3×#416—51no—
142C2×C3×#102—51no—
143C2×#709C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C22×C5×C8C22×C311yescharacteristic
146C22×C5×C8C22×C311yescharacteristic, complemented
147C4×C5×D4C22×C311yescharacteristic
148#4083—21no—
149#4081—21no—
150#4076C22×C311yescharacteristic
151#4072C22×C311yescharacteristic, complemented
152C2×C4⋊Dic5C22×C311yescharacteristic
153#4070C22×C311yescharacteristic
154#4070C22×C311yescharacteristic
155#4070C22×C311yescharacteristic, complemented
156C2×Dic20C22×C311yescharacteristic, complemented
157C2×#677C22×C311yescharacteristic
158C2×#677C22×C311yescharacteristic
159#4040—21no—
160#4035—21no—
161#4030—21no—
162D5×C22⋊C4—21no—
163#4025—21no—
164#4023—21no—
165#4021C22×C311yescharacteristic
166C4×D20C22×C311yescharacteristic
167#4016C22×C311yescharacteristic, complemented
168C4×Dic10C22×C311yescharacteristic, complemented
169C5×C4⋊C8C22×C311yescharacteristic, complemented
170C5×C22⋊C8C22×C311yescharacteristic
171C5×C22⋊C8C22×C311yescharacteristic, complemented
172C4×C5×C8C22×C311yescharacteristic, complemented
173#3953C22×C311yescharacteristic
174#3953C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3953C22×C311yescharacteristic
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3950C22×C311yescharacteristic, complemented
180#3949C22×C311yescharacteristic, complemented
181#3949C22×C311yescharacteristic, complemented
182#3948C22×C311yescharacteristic, complemented
183#3948C22×C311yescharacteristic, complemented
184#3948C22×C311yescharacteristic, complemented
185#3948C22×C311yescharacteristic, complemented
186#3296—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5—81no—
194C3×C5×D4—22no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C3×C22⋊D5—42no—
205C3×C22⋊D5—81no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—42no—
213C3×D20—21no—
214C3×D20—21no—
215C3×D20—21no—
216C3×D20—42no—
217C3×D20#4112yes—
218C3×C4×D5—42no—
219C3×C4×D5—81no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224C3×C5×C8—21no—
225C3×C5×C8—21no—
226C3×C5×C8—21no—
227C3×C5×C8—21no—
228C2×C3×#41—51no—
229C22×C3×D4—51no—
230C2×C3×Q16—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C22×C3×C8C2×D511yescharacteristic
234C22×C3×C8C2×D511yescharacteristic, complemented
235C3×#126—101no—
236C3×#125—51no—
237C3×#125—101no—
238C3×#124—51no—
239C3×#123—101no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8—51no—
243C3×C22⋊Q8—51no—
244C3×#121—51no—
245C3×#121—101no—
246C3×#120—101no—
247C3×C4×Q8—51no—
248C3×C4×D4—51no—
249C3×C4×D4C2×D511yescharacteristic
250C3×#117—51no—
251C3×#117—101no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—101no—
254C3×#107—51no—
255C3×#106—51no—
256C3×#106—51no—
257C3×C4⋊C8C2×D511yescharacteristic, complemented
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×#102—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×C22⋊C8C2×D511yescharacteristic
269C3×C22⋊C8C2×D511yescharacteristic, complemented
270C3×C4×C8C2×D511yescharacteristic, complemented
271C23×D5—21no—
272C2×C5×D4C3×D411yescharacteristic
273C22×C4×C5C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C2×C22⋊D5—21no—
276C2×C22⋊D5—21no—
277C22×Dic5—21no—
278#709—22no—
279#709—41no—
280C2×D20—22no—
281C2×D20—21no—
282C2×D20—41no—
283C2×D20C23×C311yescharacteristic
284C2×D20C23×C311yescharacteristic
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×Dic10C23×C311yescharacteristic
288C2×Dic10C23×C311yescharacteristic
289C2×C5×C8—41no—
290C2×C5×C8—41no—
291C2×C5×C8C23×C311yescharacteristic
292C2×C5×C8C23×C311yescharacteristic
293C2×C5×C8C23×C311yescharacteristic
294C2×C5×C8C23×C311yescharacteristic
295C5×C4⋊C4C3×D411yescharacteristic
296C5×C22⋊C4C3×D411yescharacteristic
297C5×C22⋊C4C3×D411yescharacteristic
298C42×C5C23×C311yescharacteristic
299C22⋊Dic5—21no—
300C22⋊Dic5—21no—
301C22⋊Dic5—21no—
302C22⋊Dic5—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306#685—21no—
307C4⋊Dic5—21no—
308C4⋊Dic5C23×C311yescharacteristic
309C4⋊Dic5C23×C311yescharacteristic
310C4⋊Dic5C23×C311yescharacteristic
311C4⋊Dic5C23×C311yescharacteristic
312#683—21no—
313#683—21no—
314#683—21no—
315#683—21no—
316#683—21no—
317#683—21no—
318C4×Dic5—21no—
319C4×Dic5—21no—
320Dic20—41no—
321#677—22no—
322#677—41no—
323#552—51no—
324#546—51no—
325#488—51no—
326#483—51no—
327#482—51no—
328#478—51no—
329#467—51no—
330#465—51no—
331#464—51no—
332#452—51no—
333#450—51no—
334C4×SD16—51no—
335C8×D4C3×D511yescharacteristic, complemented
336#416—51no—
337C2×#102—51no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—22no—
346C2×C3×D5—41no—
347C2×C3×D5—41no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351C2×C3×D5—84no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358C3×Dic5—41no—
359C3×Dic5—41no—
360C3×Dic5—41no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C24×C3—101no—
365C3×#41—102no—
366C3×#41—201no—
367C2×C3×Q8—51no—
368C2×C3×Q8—51no—
369C2×C3×D4—51no—
370C2×C3×D4—51no—
371C2×C3×D4—102no—
372C2×C3×D4—101no—
373C2×C3×D4—101no—
374C2×C3×D4—101no—
375C2×C3×D4—201no—
376C2×C3×D4D2011yescharacteristic
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C3×Q16—201no—
383C3×SD16—102no—
384C3×SD16—201no—
385C2×C3×C8—41no—
386C2×C3×C8—41no—
387C2×C3×C8C22×D511yescharacteristic
388C2×C3×C8C22×D511yescharacteristic
389C2×C3×C8C22×D511yescharacteristic
390C2×C3×C8C22×D511yescharacteristic
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4—101no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4D2011yescharacteristic
403C3×C22⋊C4—101no—
404C3×C22⋊C4—101no—
405C3×C22⋊C4—101no—
406C3×C22⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4D2011yescharacteristic
412C3×C22⋊C4D2011yescharacteristic
413C3×C42—101no—
414C3×C42—101no—
415C3×C42C22×D511yescharacteristic
416C23×C5C2×C3×D411yescharacteristic
417C23×C5C2×C3×D411yescharacteristic
418C22×D5—21no—
419C22×D5—21no—
420C22×D5—42no—
421C22×D5—42no—
422C22×D5—81no—
423C5×D4—22no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5C2×C3×D411yescharacteristic
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C2×C3×D411yescharacteristic
431C2×C4×C5C2×C3×D411yescharacteristic
432C2×C4×C5C24×C311yescharacteristic
433C22⋊D5—42no—
434C22⋊D5—81no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—42no—
442D20—21no—
443D20—21no—
444D20—21no—
445D20—42no—
446D20C3×#4112yes—
447C4×D5—42no—
448C4×D5—81no—
449Dic10—21no—
450Dic10—21no—
451Dic10—21no—
452Dic10—21no—
453C5×C8—21no—
454C5×C8—21no—
455C5×C8—21no—
456C5×C8—21no—
457C2×#41—51no—
458C22×D4—51no—
459C2×Q16—51no—
460C2×SD16—51no—
461C2×SD16—51no—
462C22×C8C2×C3×D511yescharacteristic
463C22×C8C2×C3×D511yescharacteristic, complemented
464#126—101no—
465#125—51no—
466#125—101no—
467#124—51no—
468#123—101no—
469#123—101no—
470C22⋊Q8—51no—
471C22⋊Q8—51no—
472C22⋊Q8—51no—
473#121—51no—
474#121—101no—
475#120—101no—
476C4×Q8—51no—
477C4×D4—51no—
478C4×D4C2×C3×D511yescharacteristic
479#117—51no—
480#117—101no—
481C2×C4⋊C4—51no—
482C2×C22⋊C4—101no—
483#107—51no—
484#106—51no—
485#106—51no—
486C4⋊C8C2×C3×D511yescharacteristic, complemented
487#103—51no—
488#103—51no—
489#103—51no—
490#103—51no—
491#102—51no—
492#102—51no—
493#102—51no—
494#102—51no—
495#102—51no—
496#102—51no—
497C22⋊C8C2×C3×D511yescharacteristic
498C22⋊C8C2×C3×D511yescharacteristic, complemented
499C4×C8C2×C3×D511yescharacteristic, complemented
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C3×D5—42no—
506C3×D5—81no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3—202no—
510C23×C3—202no—
511C23×C3—401no—
512C23×C3C2×D2011yescharacteristic
513C23×C3C2×D2011yescharacteristic
514C3×Q8—101no—
515C3×Q8—101no—
516C3×Q8—101no—
517C3×Q8—101no—
518C3×D4—22no—
519C3×D4—52no—
520C3×D4—101no—
521C3×D4—101no—
522C3×D4—101no—
523C3×D4—202no—
524C3×D4—202no—
525C3×D4—401no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—202no—
537C2×C3×C4—202no—
538C2×C3×C4—401no—
539C2×C3×C4C2×D2011yescharacteristic
540C2×C3×C4C2×D2011yescharacteristic
541C2×C3×C4C2×D2011yescharacteristic
542C2×C3×C4C2×D2011yescharacteristic
543C2×C3×C4C23×D511yescharacteristic
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—21no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—21no—
553C22×C5C3×#13512yes—
554C22×C5C22×C3×D411yescharacteristic
555C2×D5—22no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—41no—
559C2×D5—41no—
560C2×D5—41no—
561C2×D5—84no—
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5C2×C3×#4111yescharacteristic
567C4×C5C3×H(5,𝔽2)11yescharacteristic
568Dic5—41no—
569Dic5—41no—
570Dic5—41no—
571Dic5—41no—
572Dic5—41no—
573Dic5—41no—
574C24—101no—
575#41—102no—
576#41—201no—
577C2×Q8—51no—
578C2×Q8—51no—
579C2×D4—51no—
580C2×D4—51no—
581C2×D4—102no—
582C2×D4—101no—
583C2×D4—101no—
584C2×D4—101no—
585C2×D4—201no—
586C2×D4C3×D2011yescharacteristic
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4C22×C3×D511yescharacteristic
591C22×C4C22×C3×D511yescharacteristic
592Q16—201no—
593SD16—102no—
594SD16—201no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8C22×C3×D511yescharacteristic
598C2×C8C22×C3×D511yescharacteristic
599C2×C8C22×C3×D511yescharacteristic
600C2×C8C22×C3×D511yescharacteristic
601C4⋊C4—51no—
602C4⋊C4—51no—
603C4⋊C4—51no—
604C4⋊C4—51no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4—101no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4—101no—
612C4⋊C4C3×D2011yescharacteristic
613C22⋊C4—101no—
614C22⋊C4—101no—
615C22⋊C4—101no—
616C22⋊C4—101no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C22⋊C4C3×D2011yescharacteristic
622C22⋊C4C3×D2011yescharacteristic
623C42—101no—
624C42—101no—
625C42C22×C3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—102no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3—201no—
636C22×C3—201no—
637C22×C3—201no—
638C22×C3—404no—
639C22×C3#405012yes—
640C22×C3C22×D2011yescharacteristic
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—201no—
646C3×C4—201no—
647C3×C4—201no—
648C3×C4—201no—
649C3×C4—201no—
650C3×C4—201no—
651C3×C4#414411yescharacteristic
652C3×C4D5×#4111yescharacteristic
653C2×C5—22no—
654C2×C5—41no—
655C2×C5C3×#54611yescharacteristic
656C2×C5C2×C3×#13511yescharacteristic
657C2×C5C3×#57711yescharacteristic
658D5—42no—
659D5—81no—
660C23—101no—
661C23—101no—
662C23—202no—
663C23—202no—
664C23—401no—
665C23C2×C3×D2011yescharacteristic
666C23C2×C3×D2011yescharacteristic
667Q8—101no—
668Q8—101no—
669Q8—101no—
670Q8—101no—
671D4—22no—
672D4—52no—
673D4—101no—
674D4—101no—
675D4—101no—
676D4—202no—
677D4—202no—
678D4—401no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—401no—
692C2×C4C2×C3×D2011yescharacteristic
693C2×C4C2×C3×D2011yescharacteristic
694C2×C4C2×C3×D2011yescharacteristic
695C2×C4C2×C3×D2011yescharacteristic
696C2×C4C23×C3×D511yescharacteristic
697C8—21no—
698C8—21no—
699C8—21no—
700C8—21no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3—202no—
704C2×C3—401no—
705C2×C3#6588811yescharacteristic
706C2×C3C2×#405011yescharacteristic
707C2×C3#6608511yescharacteristic
708C5C3×#329611yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—102no—
715C22—201no—
716C22—201no—
717C22—201no—
718C22—201no—
719C22—201no—
720C22—404no—
721C22C3×#405012yes—
722C22C22×C3×D2011yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—201no—
728C4—201no—
729C4—201no—
730C4—201no—
731C4—201no—
732C4—201no—
733C4C3×#414411yescharacteristic
734C4C3×D5×#4111yescharacteristic
735C3#1061117111yescharacteristic, direct product factor, Sylow
736C2—22no—
737C2—41no—
738C2—202no—
739C2—401no—
740C2C3×#6588811yescharacteristic
741C2C2×C3×#405011yescharacteristic
742C2C3×#6608511yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
prime radicalC3×#65884C2
hypercenterC3×C8×D4D5
hypocenterC5C3×#3296
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65875C2semidirect
3. C3×C5×C8×D4C2semidirect
4. C3×#65405C2semidirect
5. C3×#65403C2semidirect
6. C3×#65402C2semidirect
7. C2×C3×#3953C2semidirect
8. C3×#65136C2semidirect
9. C3×#65134C2semidirect
10. C3×#65026C2semidirect
11. C3×#65022C2semidirect
12. C3×#65020C2semidirect
13. C3×#65010C2semidirect
14. C3×#64986C2semidirect
15. C3×C4×#677C2semidirect
16. #10611171C3direct (N × H)
20. C22×C3×C5×C8C22semidirect
25. C3×#4072C22semidirect
29. C3×#4070C22semidirect
30. C2×C3×Dic20C22semidirect
41. C3×#4016C22semidirect
42. C3×C4×Dic10C22semidirect
43. C3×C5×C4⋊C8C22semidirect
45. C3×C5×C22⋊C8C22semidirect
46. C3×C4×C5×C8C22semidirect
53. C3×#3950C22semidirect
54. C3×#3949C22semidirect
55. C3×#3949C22semidirect
56. C3×#3948C22semidirect
57. C3×#3948C22semidirect
58. C3×#3948C22semidirect
59. C3×#3948C22semidirect
62. #65875C2×C3semidirect
63. C5×C8×D4C2×C3semidirect
64. #65405C2×C3semidirect
65. #65403C2×C3semidirect
66. #65402C2×C3semidirect
67. C2×#3953C2×C3semidirect
68. #65136C2×C3semidirect
69. #65134C2×C3semidirect
70. #65026C2×C3semidirect
71. #65022C2×C3semidirect
72. #65020C2×C3semidirect
73. #65010C2×C3semidirect
74. #64986C2×C3semidirect
75. C4×#677C2×C3semidirect
140. C3×C8×D4D5semidirect
146. C22×C5×C8C22×C3semidirect
151. #4072C22×C3semidirect
155. #4070C22×C3semidirect
156. C2×Dic20C22×C3semidirect
167. #4016C22×C3semidirect
168. C4×Dic10C22×C3semidirect
169. C5×C4⋊C8C22×C3semidirect
171. C5×C22⋊C8C22×C3semidirect
172. C4×C5×C8C22×C3semidirect
179. #3950C22×C3semidirect
180. #3949C22×C3semidirect
181. #3949C22×C3semidirect
182. #3948C22×C3semidirect
183. #3948C22×C3semidirect
184. #3948C22×C3semidirect
185. #3948C22×C3semidirect
234. C22×C3×C8C2×D5semidirect
257. C3×C4⋊C8C2×D5semidirect
269. C3×C22⋊C8C2×D5semidirect
270. C3×C4×C8C2×D5semidirect
335. C8×D4C3×D5semidirect
463. C22×C8C2×C3×D5semidirect
486. C4⋊C8C2×C3×D5semidirect
498. C22⋊C8C2×C3×D5semidirect
499. C4×C8C2×C3×D5semidirect
626. C3×C5#3296semidirect
708. C5C3×#3296semidirect
735. C3#10611171direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658842
C3×#658752
C3×C5×C8×D42
C3×#654052
C3×#654032
C3×#654022
C2×C3×#39532
C3×#651362
C3×#651342
C3×#650262
C3×#650222
C3×#650202
C3×#650102
C3×#649862
C3×C4×#6772
#106111713
C3×#32965