Finite Group Databasebeta

← C3×#10611380 #14417408

Subgroups — C3×#10611380 #14417408

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×SD16C211yesmaximal, characteristic
2C3×#65906C211yesmaximal, characteristic, complemented
3C3×#65879C211yesmaximal, characteristic
4C3×C4×C5×SD16C211yesmaximal, characteristic, complemented
5C3×SD16×Dic5C211yesmaximal, characteristic, complemented
6C3×#65315C211yesmaximal, characteristic, complemented
7C3×#65307C211yesmaximal, characteristic, complemented
8C3×#65149C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65106C211yesmaximal, characteristic, complemented
11C3×#65091C211yesmaximal, characteristic, complemented
12C3×#65059C211yesmaximal, characteristic
13C3×#65046C211yesmaximal, characteristic, complemented
14C3×C4×#677C211yesmaximal, characteristic, complemented
15C3×#64978C211yesmaximal, characteristic, complemented
16#10611380C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic, complemented
23C2×C3×#688C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C2×C3×#685—21no—
28C3×D5×SD16C418yescomplemented
29C2×C3×#677C2211yescharacteristic
30C2×C3×#676C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic
32C3×#4039C2211yescharacteristic
33C3×#4038—21no—
34C3×#4038C2211yescharacteristic
35C3×#4038C2211yescharacteristic
36C3×#4033—21no—
37C3×#4033C2211yescharacteristic, complemented
38C3×#4027—21no—
39C3×D5×C22⋊C4—21no—
40C3×C4×D20C2211yescharacteristic
41C3×#4018—21no—
42C3×#4018C2211yescharacteristic
43C3×C4×Dic10—21no—
44C3×C4×Dic10C2211yescharacteristic, complemented
45C3×C5×#106C2211yescharacteristic, complemented
46C3×C5×#103C2211yescharacteristic, complemented
47C3×C5×#102C2211yescharacteristic
48C3×C4×C5×C8C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3964C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3949C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3947C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic
58C3×#3939C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3935C2211yescharacteristic, complemented
61C3×#2949—51nomaximal, Hall
62C2×D5×SD16C2×C311yescharacteristic
63#65906C2×C311yescharacteristic, complemented
64#65879C2×C311yescharacteristic
65C4×C5×SD16C2×C311yescharacteristic, complemented
66SD16×Dic5C2×C311yescharacteristic, complemented
67#65315C2×C311yescharacteristic, complemented
68#65307C2×C311yescharacteristic, complemented
69#65149C2×C311yescharacteristic, complemented
70#65141C2×C311yescharacteristic, complemented
71#65106C2×C311yescharacteristic, complemented
72#65091C2×C311yescharacteristic, complemented
73#65059C2×C311yescharacteristic
74#65046C2×C311yescharacteristic, complemented
75C4×#677C2×C311yescharacteristic, complemented
76#64978C2×C311yescharacteristic, complemented
77C23×C3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C3×Q8×D5—22no—
84C3×Q8×D5C2×C414yescomplemented
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yes—
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×Dic10—21no—
93C2×C3×Dic10C2311yescharacteristic
94C3×C5×SD16C2×C414yescomplemented
95C2×C3×C5×C8C2311yescharacteristic
96C2×C3×C5×C8C2311yescharacteristic
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C42×C5—21no—
102C3×C42×C5C2311yescharacteristic
103C3×C22⋊Dic5—21no—
104C3×#688C2×C414yescomplemented
105C3×#687C2×C414yescomplemented
106C3×#685—21no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685D411yescharacteristic
111C3×#685D411yescharacteristic
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683D411yescharacteristic
118C3×#683D411yescharacteristic
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×#677C2×C414yescomplemented
128C3×#676—22no—
129C3×C8×D5C2×C414yescomplemented
130C22×C3×SD16—51no—
131C3×#519—51no—
132C3×#518—51no—
133C3×#440—51no—
134C3×#440—51no—
135C3×#440—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×SD16—51no—
139C3×C4×SD16—51no—
140C3×C4×SD16D511yescharacteristic, complemented
141C3×#427—51no—
142C3×#419—51no—
143C3×#418—51no—
144C3×#405—51no—
145C2×Q8×D5C22×C311yescharacteristic
146C2×D4×D5C22×C311yescharacteristic
147C2×C5×SD16C22×C311yescharacteristic
148C4×C5×Q8C22×C311yescharacteristic, complemented
149C4×C5×D4C22×C311yescharacteristic
150Q8×Dic5C22×C311yescharacteristic, complemented
151C2×#688C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153C2×#687C22×C311yescharacteristic
154C4×C22⋊D5—21no—
155C2×#685—21no—
156D5×SD16C3×C418yescomplemented
157C2×#677C22×C311yescharacteristic
158C2×#676C22×C311yescharacteristic
159C2×C8×D5C22×C311yescharacteristic
160#4039C22×C311yescharacteristic
161#4038—21no—
162#4038C22×C311yescharacteristic
163#4038C22×C311yescharacteristic
164#4033—21no—
165#4033C22×C311yescharacteristic, complemented
166#4027—21no—
167D5×C22⋊C4—21no—
168C4×D20C22×C311yescharacteristic
169#4018—21no—
170#4018C22×C311yescharacteristic
171C4×Dic10—21no—
172C4×Dic10C22×C311yescharacteristic, complemented
173C5×#106C22×C311yescharacteristic, complemented
174C5×#103C22×C311yescharacteristic, complemented
175C5×#102C22×C311yescharacteristic
176C4×C5×C8C22×C311yescharacteristic, complemented
177#3967C22×C311yescharacteristic, complemented
178#3964C22×C311yescharacteristic
179#3953C22×C311yescharacteristic
180#3949C22×C311yescharacteristic, complemented
181#3948C22×C311yescharacteristic, complemented
182#3947C22×C311yescharacteristic, complemented
183C8×Dic5C22×C311yescharacteristic, complemented
184#3942C22×C311yescharacteristic, complemented
185#3941C22×C311yescharacteristic
186#3939C22×C311yescharacteristic, complemented
187#3939C22×C311yescharacteristic, complemented
188#3935C22×C311yescharacteristic, complemented
189#2949—51noSylow
190C23×C3×C5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—24no—
193C22×C3×D5—81no—
194C22×C3×D5—81no—
195C22×C3×D5C2×D411yescharacteristic
196C3×C5×Q8—21no—
197C3×C5×Q8C22×C412yes—
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207C3×C22⋊D5—24no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5C2×D411yescharacteristic
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C3×D20—21no—
216C3×D20C22×C412yes—
217C3×C4×D5—24no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3×C4×D5C22×C412yes—
221C3×C4×D5#4112yes—
222C3×Dic10—21no—
223C3×Dic10—24no—
224C3×Dic10C22×C412yes—
225C3×C5×C8—21no—
226C3×C5×C8C22×C412yes—
227C3×#168—21no—
228C3×#168C22×C412yes—
229C22×C3×Q8—51no—
230C22×C3×D4—51no—
231C2×C3×SD16—51no—
232C2×C3×SD16—51no—
233C2×C3×SD16—58no—
234C2×C3×SD16—51no—
235C2×C3×SD16C2×D511yescharacteristic
236C2×C3×M16—51no—
237C22×C3×C8—51no—
238C3×C4×Q8—51no—
239C3×C4×Q8—51no—
240C3×C4×Q8—51no—
241C3×C4×Q8—101no—
242C3×C4×Q8—101no—
243C3×C4×Q8C2×D511yescharacteristic, complemented
244C3×C4×D4—51no—
245C3×C4×D4—51no—
246C3×C4×D4—51no—
247C3×C4×D4—101no—
248C3×C4×D4—101no—
249C3×C4×D4C2×D511yescharacteristic
250C3×#117—51no—
251C3×#117—51no—
252C3×#117—51no—
253C3×#117—101no—
254C3×#117—101no—
255C2×C3×C22⋊C4—101no—
256C2×C3×C22⋊C4—101no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#106—51no—
260C3×#106C2×D511yescharacteristic, complemented
261C3×#103—51no—
262C3×#103—51no—
263C3×#103—51no—
264C3×#103C2×D511yescharacteristic, complemented
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102C2×D511yescharacteristic
269C3×#97—51no—
270C3×#97—51no—
271C3×C4×C8—51no—
272C3×C4×C8C2×D511yescharacteristic, complemented
273C23×D5—21no—
274C2×C5×Q8C23×C311yescharacteristic
275C2×C5×D4C23×C311yescharacteristic
276C22×C4×C5—21no—
277C2×C22⋊D5—21no—
278C22×Dic5—21no—
279Q8×D5—22no—
280Q8×D5C2×C3×C414yescomplemented
281D4×D5—22no—
282D4×D5C2×C3×C414yes—
283C2×D20C23×C311yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×C4×D5C23×C311yescharacteristic
288C2×Dic10—21no—
289C2×Dic10C23×C311yescharacteristic
290C5×SD16C2×C3×C414yescomplemented
291C2×C5×C8C23×C311yescharacteristic
292C2×C5×C8C23×C311yescharacteristic
293C5×C4⋊C4—21no—
294C5×C4⋊C4C23×C311yescharacteristic
295C5×C4⋊C4C23×C311yescharacteristic
296C5×C22⋊C4—21no—
297C42×C5—21no—
298C42×C5C23×C311yescharacteristic
299C22⋊Dic5—21no—
300#688C2×C3×C414yescomplemented
301#687C2×C3×C414yescomplemented
302#685—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306#685C3×D411yescharacteristic
307#685C3×D411yescharacteristic
308C4⋊Dic5—21no—
309C4⋊Dic5C23×C311yescharacteristic
310C4⋊Dic5C23×C311yescharacteristic
311#683—21no—
312#683—21no—
313#683C3×D411yescharacteristic
314#683C3×D411yescharacteristic
315C4×Dic5—21no—
316C4×Dic5—21no—
317C4×Dic5—21no—
318C4×Dic5—21no—
319C4×Dic5—21no—
320C4×Dic5C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323#677C2×C3×C414yescomplemented
324#676—22no—
325C8×D5C2×C3×C414yescomplemented
326C22×SD16—51no—
327#519—51no—
328#518—51no—
329#440—51no—
330#440—51no—
331#440—51no—
332#440—51no—
333C4×SD16—51no—
334C4×SD16—51no—
335C4×SD16—51no—
336C4×SD16C3×D511yescharacteristic, complemented
337#427—51no—
338#419—51no—
339#418—51no—
340#405—51no—
341C22×C3×C5—22no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—22no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—84no—
351C2×C3×D5C4×D412yes—
352C3×C4×C5—22no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—41no—
356C3×C4×C5—41no—
357C3×C4×C5C23×C411yescharacteristic
358C3×C4×C5C2×#4111yescharacteristic
359C3×Dic5—22no—
360C3×Dic5—21no—
361C3×Dic5—21no—
362C3×Dic5—41no—
363C3×Dic5—41no—
364C3×Dic5C4×D412yes—
365C24×C3—101no—
366C2×C3×Q8—54no—
367C2×C3×Q8—51no—
368C2×C3×Q8—101no—
369C2×C3×Q8—102no—
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4—54no—
372C2×C3×D4—51no—
373C2×C3×D4—102no—
374C2×C3×D4—101no—
375C2×C3×D4C22×D511yescharacteristic
376C22×C3×C4—21no—
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C22×C3×C4—101no—
382C3×SD16—54no—
383C3×SD16—54no—
384C3×SD16—54no—
385C3×SD16C4×D514yescomplemented
386C3×M16—102no—
387C2×C3×C8—51no—
388C2×C3×C8—54no—
389C2×C3×C8—51no—
390C2×C3×C8C22×D511yescharacteristic
391C2×C3×C8C22×D511yescharacteristic
392C3×C4⋊C4—21no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—51no—
396C3×C4⋊C4—51no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—51no—
404C3×C22⋊C4—51no—
405C3×C22⋊C4—101no—
406C3×C22⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C42—21no—
411C3×C42—51no—
412C3×C42—101no—
413C3×C42—101no—
414C3×C42—101no—
415C3×C42—101no—
416C3×C42—101no—
417C3×C42C22×D511yescharacteristic
418C23×C5—21no—
419C22×D5—21no—
420C22×D5—24no—
421C22×D5—81no—
422C22×D5—81no—
423C22×D5C2×C3×D411yescharacteristic
424C5×Q8—21no—
425C5×Q8C22×C3×C412yes—
426C5×D4—21no—
427C5×D4C22×C3×C412yes—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—81no—
432C2×C4×C5C2×C3×D411yescharacteristic
433C2×C4×C5C2×C3×D411yescharacteristic
434C2×C4×C5C24×C311yescharacteristic
435C22⋊D5—24no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—81no—
440C2×Dic5C2×C3×D411yescharacteristic
441C2×Dic5C2×C3×D411yescharacteristic
442C2×Dic5C2×C3×D411yescharacteristic
443D20—21no—
444D20C22×C3×C412yes—
445C4×D5—24no—
446C4×D5—81no—
447C4×D5—81no—
448C4×D5C22×C3×C412yes—
449C4×D5C3×#4112yes—
450Dic10—21no—
451Dic10—24no—
452Dic10C22×C3×C412yes—
453C5×C8—21no—
454C5×C8C22×C3×C412yes—
455#168—21no—
456#168C22×C3×C412yes—
457C22×Q8—51no—
458C22×D4—51no—
459C2×SD16—51no—
460C2×SD16—51no—
461C2×SD16—58no—
462C2×SD16—51no—
463C2×SD16C2×C3×D511yescharacteristic
464C2×M16—51no—
465C22×C8—51no—
466C4×Q8—51no—
467C4×Q8—51no—
468C4×Q8—51no—
469C4×Q8—101no—
470C4×Q8—101no—
471C4×Q8C2×C3×D511yescharacteristic, complemented
472C4×D4—51no—
473C4×D4—51no—
474C4×D4—51no—
475C4×D4—101no—
476C4×D4—101no—
477C4×D4C2×C3×D511yescharacteristic
478#117—51no—
479#117—51no—
480#117—51no—
481#117—101no—
482#117—101no—
483C2×C22⋊C4—101no—
484C2×C22⋊C4—101no—
485#107—51no—
486#107—51no—
487#106—51no—
488#106C2×C3×D511yescharacteristic, complemented
489#103—51no—
490#103—51no—
491#103—51no—
492#103C2×C3×D511yescharacteristic, complemented
493#102—51no—
494#102—51no—
495#102—51no—
496#102C2×C3×D511yescharacteristic
497#97—51no—
498#97—51no—
499C4×C8—51no—
500C4×C8C2×C3×D511yescharacteristic, complemented
501C2×C3×C5—42no—
502C2×C3×C5C2×C4×D411yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C3×D5—22no—
506C3×D5—42no—
507C23×C3—21no—
508C23×C3—51no—
509C23×C3—104no—
510C23×C3—101no—
511C23×C3—401no—
512C23×C3—401no—
513C3×Q8—21no—
514C3×Q8—52no—
515C3×Q8—104no—
516C3×Q8—101no—
517C3×Q8C2×C4×D512yes—
518C3×D4—21no—
519C3×D4—52no—
520C3×D4—104no—
521C3×D4—101no—
522C3×D4C2×C4×D512yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—51no—
527C2×C3×C4—52no—
528C2×C3×C4—52no—
529C2×C3×C4—51no—
530C2×C3×C4—51no—
531C2×C3×C4—81no—
532C2×C3×C4—104no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—401no—
537C2×C3×C4—401no—
538C2×C3×C4—401no—
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4D4×D511yescharacteristic
541C2×C3×C4C23×D511yescharacteristic
542C3×C8—21no—
543C3×C8—52no—
544C3×C8—101no—
545C3×C8C2×C4×D512yes—
546C22×C5—22no—
547C22×C5—41no—
548C22×C5—41no—
549C22×C5C22×C3×D411yescharacteristic
550C2×D5—21no—
551C2×D5—21no—
552C2×D5—22no—
553C2×D5—41no—
554C2×D5—41no—
555C2×D5—84no—
556C2×D5C3×C4×D412yes—
557C4×C5—21no—
558C4×C5—21no—
559C4×C5—22no—
560C4×C5—41no—
561C4×C5—41no—
562C4×C5C23×C3×C411yescharacteristic
563C4×C5C2×C3×#4111yescharacteristic
564Dic5—21no—
565Dic5—21no—
566Dic5—22no—
567Dic5—41no—
568Dic5—41no—
569Dic5C3×C4×D412yes—
570C24—101no—
571C2×Q8—54no—
572C2×Q8—51no—
573C2×Q8—101no—
574C2×Q8—102no—
575C2×Q8C22×C3×D511yescharacteristic
576C2×D4—54no—
577C2×D4—51no—
578C2×D4—102no—
579C2×D4—101no—
580C2×D4C22×C3×D511yescharacteristic
581C22×C4—21no—
582C22×C4—51no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587SD16—54no—
588SD16—54no—
589SD16—54no—
590SD16C3×C4×D514yescomplemented
591M16—102no—
592C2×C8—51no—
593C2×C8—54no—
594C2×C8—51no—
595C2×C8C22×C3×D511yescharacteristic
596C2×C8C22×C3×D511yescharacteristic
597C4⋊C4—21no—
598C4⋊C4—51no—
599C4⋊C4—51no—
600C4⋊C4—51no—
601C4⋊C4—51no—
602C4⋊C4—101no—
603C4⋊C4—101no—
604C4⋊C4—101no—
605C4⋊C4C22×C3×D511yescharacteristic
606C4⋊C4C22×C3×D511yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—51no—
609C22⋊C4—51no—
610C22⋊C4—101no—
611C22⋊C4—101no—
612C22⋊C4—101no—
613C22⋊C4—101no—
614C22⋊C4—101no—
615C42—21no—
616C42—51no—
617C42—101no—
618C42—101no—
619C42—101no—
620C42—101no—
621C42—101no—
622C42C22×C3×D511yescharacteristic
623C3×C5#294911yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—52no—
628C22×C3—101no—
629C22×C3—101no—
630C22×C3—102no—
631C22×C3—201no—
632C22×C3—201no—
633C22×C3—404no—
634C22×C3C2×D4×D511yescharacteristic
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—22no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—52no—
641C3×C4—101no—
642C3×C4—101no—
643C3×C4—102no—
644C3×C4—201no—
645C3×C4—201no—
646C3×C4C22×C4×D511yescharacteristic
647C3×C4D5×#4111yescharacteristic
648C2×C5—42no—
649C2×C5C2×C3×C4×D411yescharacteristic
650C2×C5C3×#57711yescharacteristic
651C2×C5C3×#57711yescharacteristic
652D5—22no—
653D5—42no—
654C23—21no—
655C23—51no—
656C23—104no—
657C23—101no—
658C23—401no—
659C23—401no—
660Q8—21no—
661Q8—52no—
662Q8—104no—
663Q8—101no—
664Q8C2×C3×C4×D512yes—
665D4—21no—
666D4—52no—
667D4—104no—
668D4—101no—
669D4C2×C3×C4×D512yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—51no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—51no—
677C2×C4—51no—
678C2×C4—81no—
679C2×C4—104no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—401no—
684C2×C4—401no—
685C2×C4—401no—
686C2×C4C3×D4×D511yescharacteristic
687C2×C4C3×D4×D511yescharacteristic
688C2×C4C23×C3×D511yescharacteristic
689C8—21no—
690C8—52no—
691C8—101no—
692C8C2×C3×C4×D512yes—
693C2×C3—42no—
694C2×C3—102no—
695C2×C3—202no—
696C2×C3C4×D4×D511yescharacteristic
697C2×C3#6609611yescharacteristic
698C2×C3#6610411yescharacteristic
699C5C3×#294911yescharacteristic, complemented, Sylow
700C22—22no—
701C22—41no—
702C22—41no—
703C22—52no—
704C22—101no—
705C22—101no—
706C22—102no—
707C22—201no—
708C22—201no—
709C22—404no—
710C22C2×C3×D4×D511yescharacteristic
711C4—21no—
712C4—22no—
713C4—21no—
714C4—41no—
715C4—41no—
716C4—52no—
717C4—101no—
718C4—102no—
719C4—101no—
720C4—201no—
721C4—201no—
722C4C22×C3×C4×D511yescharacteristic
723C4C3×D5×#4111yescharacteristic
724C3#1061138011yescharacteristic, direct product factor, Sylow
725C2—42no—
726C2—102no—
727C2—202no—
728C2C3×C4×D4×D511yescharacteristic
729C2C3×#6609611yescharacteristic
730C2C3×#6610411yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C4×C5C24×C3
hypercenterC3×C4×SD16D5
hypocenterC5C3×#2949
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C3×#65906C2semidirect
4. C3×C4×C5×SD16C2semidirect
5. C3×SD16×Dic5C2semidirect
6. C3×#65315C2semidirect
7. C3×#65307C2semidirect
8. C3×#65149C2semidirect
9. C3×#65141C2semidirect
10. C3×#65106C2semidirect
11. C3×#65091C2semidirect
13. C3×#65046C2semidirect
14. C3×C4×#677C2semidirect
15. C3×#64978C2semidirect
16. #10611380C3direct (N × H)
20. C3×C4×C5×Q8C22semidirect
22. C3×Q8×Dic5C22semidirect
28. C3×D5×SD16C4semidirect
37. C3×#4033C22semidirect
44. C3×C4×Dic10C22semidirect
45. C3×C5×#106C22semidirect
46. C3×C5×#103C22semidirect
48. C3×C4×C5×C8C22semidirect
49. C3×#3967C22semidirect
52. C3×#3949C22semidirect
53. C3×#3948C22semidirect
54. C3×#3947C22semidirect
55. C3×C8×Dic5C22semidirect
56. C3×#3942C22semidirect
58. C3×#3939C22semidirect
59. C3×#3939C22semidirect
60. C3×#3935C22semidirect
63. #65906C2×C3semidirect
65. C4×C5×SD16C2×C3semidirect
66. SD16×Dic5C2×C3semidirect
67. #65315C2×C3semidirect
68. #65307C2×C3semidirect
69. #65149C2×C3semidirect
70. #65141C2×C3semidirect
71. #65106C2×C3semidirect
72. #65091C2×C3semidirect
74. #65046C2×C3semidirect
75. C4×#677C2×C3semidirect
76. #64978C2×C3semidirect
84. C3×Q8×D5C2×C4semidirect
94. C3×C5×SD16C2×C4semidirect
104. C3×#688C2×C4semidirect
105. C3×#687C2×C4semidirect
127. C3×#677C2×C4semidirect
129. C3×C8×D5C2×C4semidirect
140. C3×C4×SD16D5semidirect
148. C4×C5×Q8C22×C3semidirect
150. Q8×Dic5C22×C3semidirect
156. D5×SD16C3×C4semidirect
165. #4033C22×C3semidirect
172. C4×Dic10C22×C3semidirect
173. C5×#106C22×C3semidirect
174. C5×#103C22×C3semidirect
176. C4×C5×C8C22×C3semidirect
177. #3967C22×C3semidirect
180. #3949C22×C3semidirect
181. #3948C22×C3semidirect
182. #3947C22×C3semidirect
183. C8×Dic5C22×C3semidirect
184. #3942C22×C3semidirect
186. #3939C22×C3semidirect
187. #3939C22×C3semidirect
188. #3935C22×C3semidirect
243. C3×C4×Q8C2×D5semidirect
260. C3×#106C2×D5semidirect
264. C3×#103C2×D5semidirect
272. C3×C4×C8C2×D5semidirect
280. Q8×D5C2×C3×C4semidirect
290. C5×SD16C2×C3×C4semidirect
300. #688C2×C3×C4semidirect
301. #687C2×C3×C4semidirect
323. #677C2×C3×C4semidirect
325. C8×D5C2×C3×C4semidirect
336. C4×SD16C3×D5semidirect
385. C3×SD16C4×D5semidirect
471. C4×Q8C2×C3×D5semidirect
488. #106C2×C3×D5semidirect
492. #103C2×C3×D5semidirect
500. C4×C8C2×C3×D5semidirect
590. SD16C3×C4×D5semidirect
623. C3×C5#2949semidirect
699. C5C3×#2949semidirect
724. C3#10611380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×SD162
C3×#659062
C3×#658792
C3×C4×C5×SD162
C3×SD16×Dic52
C3×#653152
C3×#653072
C3×#651492
C3×#651412
C3×#651062
C3×#650912
C3×#650592
C3×#650462
C3×C4×#6772
C3×#649782
#106113803
C3×#29495