Finite Group Databasebeta

← C3×C4×#4064 #14416830

Subgroups — C3×C4×#4064 #14416830

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4064C211yesmaximal, characteristic
2C3×C4×#713C211yesmaximal, characteristic
3C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
4C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
5C3×#65473C211yesmaximal, characteristic, complemented
6C3×C4×#689C211yesmaximal, characteristic, complemented
7C3×C4×#688C211yesmaximal, characteristic, complemented
8C3×#65178C211yesmaximal, characteristic, complemented
9C3×#65170C211yesmaximal, characteristic, complemented
10C3×#65106C211yesmaximal, characteristic, complemented
11C3×#65092C211yesmaximal, characteristic
12C3×#65091C211yesmaximal, characteristic, complemented
13C3×#65078C211yesmaximal, characteristic, complemented
14C3×C4×#677C211yesmaximal, characteristic, complemented
15C3×C4×#676C211yesmaximal, characteristic, complemented
16C4×#4064C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×C5×Q16C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21C3×C4×C5×Q8C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C2×C3×#689C2211yescharacteristic
25C2×C3×#688C2211yescharacteristic
26C3×#4064C418yesdirect product factor
27C2×C3×#677C2211yescharacteristic
28C2×C3×#676C2211yescharacteristic
29C2×C3×#676C2211yescharacteristic
30C3×#4039—21no—
31C3×#4039C2211yescharacteristic
32C3×#4038—21no—
33C3×#4038C2211yescharacteristic
34C3×D5×C4⋊C4—21no—
35C3×D5×C4⋊C4C2211yescharacteristic
36C3×#4033—21no—
37C3×#4033C2211yescharacteristic
38C3×C4×D20—21no—
39C3×C4×D20C2211yescharacteristic
40C3×C42×D5—21no—
41C3×C42×D5—21no—
42C3×C42×D5C2211yescharacteristic
43C3×C4×Dic10—21no—
44C3×C4×Dic10C2211yescharacteristic
45C3×C5×#107C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×#103C2211yescharacteristic
48C3×C4×C5×C8C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3967C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3949C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3947C2211yescharacteristic
55C3×#3947C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3940C2211yescharacteristic
59C3×#3939C2211yescharacteristic
60C3×C4×#168C2211yescharacteristic
61C3×C4×#137—51nomaximal, Hall
62C2×#4064C2×C311yescharacteristic
63C4×#713C2×C311yescharacteristic
64C4×Q8×D5C2×C311yescharacteristic, complemented
65C4×C5×Q16C2×C311yescharacteristic, complemented
66#65473C2×C311yescharacteristic, complemented
67C4×#689C2×C311yescharacteristic, complemented
68C4×#688C2×C311yescharacteristic, complemented
69#65178C2×C311yescharacteristic, complemented
70#65170C2×C311yescharacteristic, complemented
71#65106C2×C311yescharacteristic, complemented
72#65092C2×C311yescharacteristic
73#65091C2×C311yescharacteristic, complemented
74#65078C2×C311yescharacteristic, complemented
75C4×#677C2×C311yescharacteristic, complemented
76C4×#676C2×C311yescharacteristic, complemented
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×Q8C2311yescharacteristic
79C3×#713—22no—
80C3×#713C2×C414yes—
81C3×Q8×D5—22no—
82C3×Q8×D5C2×C414yescomplemented
83C2×C3×D20—21no—
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5D411yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10—21no—
94C2×C3×Dic10C2311yescharacteristic
95C3×C5×Q16C2×C414yescomplemented
96C2×C3×C5×C8C2311yescharacteristic
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C42×C5—21no—
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×#689C2×C414yescomplemented
106C3×#688C2×C414yescomplemented
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×C4⋊Dic5—21no—
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5—21no—
122C3×C4×Dic5D411yescharacteristic
123C3×C4×Dic5D411yescharacteristic
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×#677C2×C414yescomplemented
128C3×#676—22no—
129C3×#676C2×C414yescomplemented
130C2×C3×#137—51no—
131C3×C4×#41—51no—
132C2×C3×C4×Q8—51no—
133C3×#441—51no—
134C3×#441—51no—
135C3×#440—51no—
136C3×#440—51no—
137C3×C4×Q16—51no—
138C3×C4×Q16D511yescharacteristic, complemented
139C3×C4×SD16—51no—
140C3×C4×SD16—51no—
141C3×#428—51no—
142C3×#419—51no—
143C3×#417—51no—
144C3×C4×M16—51no—
145C2×#713C22×C311yescharacteristic
146C2×Q8×D5C22×C311yescharacteristic
147C2×C5×Q16C22×C311yescharacteristic
148C4×C5×Q8C22×C311yescharacteristic
149C4×C5×Q8C22×C311yescharacteristic
150Q8×Dic5C22×C311yescharacteristic
151Q8×Dic5C22×C311yescharacteristic
152C2×#689C22×C311yescharacteristic
153C2×#688C22×C311yescharacteristic
154#4064C3×C418yesdirect product factor
155C2×#677C22×C311yescharacteristic
156C2×#676C22×C311yescharacteristic
157C2×#676C22×C311yescharacteristic
158#4039—21no—
159#4039C22×C311yescharacteristic
160#4038—21no—
161#4038C22×C311yescharacteristic
162D5×C4⋊C4—21no—
163D5×C4⋊C4C22×C311yescharacteristic
164#4033—21no—
165#4033C22×C311yescharacteristic
166C4×D20—21no—
167C4×D20C22×C311yescharacteristic
168C42×D5—21no—
169C42×D5—21no—
170C42×D5C22×C311yescharacteristic
171C4×Dic10—21no—
172C4×Dic10C22×C311yescharacteristic
173C5×#107C22×C311yescharacteristic
174C5×#103C22×C311yescharacteristic
175C5×#103C22×C311yescharacteristic
176C4×C5×C8C22×C311yescharacteristic
177#3967C22×C311yescharacteristic
178#3967C22×C311yescharacteristic
179#3953C22×C311yescharacteristic
180#3949C22×C311yescharacteristic
181#3948C22×C311yescharacteristic
182#3947C22×C311yescharacteristic
183#3947C22×C311yescharacteristic
184#3942C22×C311yescharacteristic
185#3941C22×C311yescharacteristic
186#3940C22×C311yescharacteristic
187#3939C22×C311yescharacteristic
188C4×#168C22×C311yescharacteristic
189C4×#137—51noSylow
190C22×C3×D5—21no—
191C22×C3×D5C2×D411yescharacteristic
192C3×C5×Q8—21no—
193C3×C5×Q8—21no—
194C3×C5×Q8C22×C412yes—
195C3×C5×Q8C22×C412yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C3×D20—24no—
210C3×D20—21no—
211C3×D20C22×C412yes—
212C3×C4×D5—24no—
213C3×C4×D5—22no—
214C3×C4×D5—24no—
215C3×C4×D5—41no—
216C3×C4×D5—42no—
217C3×C4×D5—42no—
218C3×C4×D5—42no—
219C3×C4×D5C22×C412yes—
220C3×C4×D5#4112yes—
221C3×Dic10—21no—
222C3×Dic10—24no—
223C3×Dic10C22×C412yes—
224C3×C5×C8—21no—
225C3×C5×C8C22×C412yes—
226C3×#168—21no—
227C3×#168C22×C412yes—
228C2×C3×#41—51no—
229C22×C3×Q8—51no—
230C3×#137—58no—
231C2×C3×Q16—51no—
232C2×C3×Q16C2×D511yescharacteristic
233C2×C3×SD16—51no—
234C2×C3×SD16—51no—
235C2×C3×M16—51no—
236C2×C3×M16—51no—
237C3×C4×Q8—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
244C3×C4×Q8C2×D511yescharacteristic
245C3×C4×D4—51no—
246C3×C4×D4—51no—
247C3×C4×D4—101no—
248C3×C4×D4—101no—
249C3×#117—51no—
250C3×#117—101no—
251C2×C3×C4⋊C4—51no—
252C2×C3×C4⋊C4—101no—
253C2×C3×C42—51no—
254C2×C3×C42—101no—
255C2×C3×C42—101no—
256C3×#107—51no—
257C3×#107C2×D511yescharacteristic
258C3×#106—51no—
259C3×#106—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#103—51no—
263C3×#103—51no—
264C3×#103C2×D511yescharacteristic
265C3×#103C2×D511yescharacteristic
266C3×#102—51no—
267C3×#102—51no—
268C3×#97—51no—
269C3×#97—51no—
270C3×C4×C8—51no—
271C3×C4×C8C2×D511yescharacteristic
272C2×C5×Q8C23×C311yescharacteristic
273C2×C5×Q8C23×C311yescharacteristic
274#713—22no—
275#713C2×C3×C414yes—
276Q8×D5—22no—
277Q8×D5C2×C3×C414yescomplemented
278C2×D20—21no—
279C2×D20C23×C311yescharacteristic
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5—21no—
283C2×C4×D5—21no—
284C2×C4×D5—21no—
285C2×C4×D5C3×D411yescharacteristic
286C2×C4×D5C3×D411yescharacteristic
287C2×C4×D5C23×C311yescharacteristic
288C2×Dic10—21no—
289C2×Dic10C23×C311yescharacteristic
290C5×Q16C2×C3×C414yescomplemented
291C2×C5×C8C23×C311yescharacteristic
292C2×C5×C8C23×C311yescharacteristic
293C5×C4⋊C4—21no—
294C5×C4⋊C4—21no—
295C5×C4⋊C4C23×C311yescharacteristic
296C5×C4⋊C4C23×C311yescharacteristic
297C42×C5—21no—
298C42×C5—21no—
299C42×C5C23×C311yescharacteristic
300#689C2×C3×C414yescomplemented
301#688C2×C3×C414yescomplemented
302#685—21no—
303#685—21no—
304#685—21no—
305C4⋊Dic5—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5C23×C311yescharacteristic
308C4⋊Dic5C23×C311yescharacteristic
309#683—21no—
310#683—21no—
311#683—21no—
312C4×Dic5—21no—
313C4×Dic5—21no—
314C4×Dic5—21no—
315C4×Dic5—21no—
316C4×Dic5—21no—
317C4×Dic5C3×D411yescharacteristic
318C4×Dic5C3×D411yescharacteristic
319C4×Dic5C23×C311yescharacteristic
320C2×#168C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322#677C2×C3×C414yescomplemented
323#676—22no—
324#676C2×C3×C414yescomplemented
325C2×#137—51no—
326C4×#41—51no—
327C2×C4×Q8—51no—
328#441—51no—
329#441—51no—
330#440—51no—
331#440—51no—
332C4×Q16—51no—
333C4×Q16C3×D511yescharacteristic, complemented
334C4×SD16—51no—
335C4×SD16—51no—
336#428—51no—
337#419—51no—
338#417—51no—
339C4×M16—51no—
340C22×C3×C5C22×D411yescharacteristic
341C2×C3×D5—21no—
342C2×C3×D5—21no—
343C2×C3×D5—22no—
344C2×C3×D5—41no—
345C2×C3×D5—41no—
346C2×C3×D5C4×D412yes—
347C3×C4×C5—22no—
348C3×C4×C5—22no—
349C3×C4×C5—21no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5#13712yescomplemented
353C3×C4×C5C23×C411yescharacteristic
354C3×C4×C5C2×#4111yescharacteristic
355C3×Dic5—22no—
356C3×Dic5—21no—
357C3×Dic5—21no—
358C3×Dic5—41no—
359C3×Dic5—41no—
360C3×Dic5C4×D412yes—
361C3×#41—54no—
362C3×#41—102no—
363C2×C3×Q8—54no—
364C2×C3×Q8—51no—
365C2×C3×Q8—101no—
366C2×C3×Q8—102no—
367C2×C3×Q8C22×D511yescharacteristic
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—51no—
370C2×C3×D4—101no—
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—101no—
375C22×C3×C4—101no—
376C22×C3×C4—101no—
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C3×Q16—54no—
380C3×Q16C4×D514yescomplemented
381C3×SD16—54no—
382C3×SD16—54no—
383C3×M16—54no—
384C3×M16—102no—
385C2×C3×C8—51no—
386C2×C3×C8—51no—
387C2×C3×C8C22×D511yescharacteristic
388C2×C3×C8C22×D511yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4C22×D511yescharacteristic
399C3×C4⋊C4C22×D511yescharacteristic
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—51no—
406C3×C42—51no—
407C3×C42—51no—
408C3×C42—101no—
409C3×C42—101no—
410C3×C42—101no—
411C3×C42—101no—
412C3×C42—101no—
413C3×C42C22×D511yescharacteristic
414C22×D5—21no—
415C22×D5C2×C3×D411yescharacteristic
416C5×Q8—21no—
417C5×Q8—21no—
418C5×Q8C22×C3×C412yes—
419C5×Q8C22×C3×C412yes—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5C2×C3×D411yescharacteristic
425C2×C4×C5C2×C3×D411yescharacteristic
426C2×C4×C5C24×C311yescharacteristic
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5C2×C3×D411yescharacteristic
431C2×Dic5C2×C3×D411yescharacteristic
432C2×Dic5C2×C3×D411yescharacteristic
433D20—24no—
434D20—21no—
435D20C22×C3×C412yes—
436C4×D5—24no—
437C4×D5—22no—
438C4×D5—24no—
439C4×D5—41no—
440C4×D5—42no—
441C4×D5—42no—
442C4×D5—42no—
443C4×D5C22×C3×C412yes—
444C4×D5C3×#4112yes—
445Dic10—21no—
446Dic10—24no—
447Dic10C22×C3×C412yes—
448C5×C8—21no—
449C5×C8C22×C3×C412yes—
450#168—21no—
451#168C22×C3×C412yes—
452C2×#41—51no—
453C22×Q8—51no—
454#137—58no—
455C2×Q16—51no—
456C2×Q16C2×C3×D511yescharacteristic
457C2×SD16—51no—
458C2×SD16—51no—
459C2×M16—51no—
460C2×M16—51no—
461C4×Q8—51no—
462C4×Q8—51no—
463C4×Q8—51no—
464C4×Q8—51no—
465C4×Q8—101no—
466C4×Q8—101no—
467C4×Q8C2×C3×D511yescharacteristic
468C4×Q8C2×C3×D511yescharacteristic
469C4×D4—51no—
470C4×D4—51no—
471C4×D4—101no—
472C4×D4—101no—
473#117—51no—
474#117—101no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—101no—
477C2×C42—51no—
478C2×C42—101no—
479C2×C42—101no—
480#107—51no—
481#107C2×C3×D511yescharacteristic
482#106—51no—
483#106—51no—
484#103—51no—
485#103—51no—
486#103—51no—
487#103—51no—
488#103C2×C3×D511yescharacteristic
489#103C2×C3×D511yescharacteristic
490#102—51no—
491#102—51no—
492#97—51no—
493#97—51no—
494C4×C8—51no—
495C4×C8C2×C3×D511yescharacteristic
496C2×C3×C5C2×C4×D411yescharacteristic
497C2×C3×C5C2×#13711yescharacteristic
498C2×C3×C5#57511yescharacteristic
499C3×D5—22no—
500C3×D5—42no—
501C23×C3—51no—
502C23×C3—101no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—52no—
506C3×Q8—104no—
507C3×Q8—101no—
508C3×Q8C2×C4×D512yes—
509C3×Q8C2×C4×D512yes—
510C3×D4—52no—
511C3×D4—104no—
512C3×D4—101no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—51no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—51no—
521C2×C3×C4—51no—
522C2×C3×C4—104no—
523C2×C3×C4—104no—
524C2×C3×C4—101no—
525C2×C3×C4—102no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—201no—
529C2×C3×C4—202no—
530C2×C3×C4—202no—
531C2×C3×C4—202no—
532C2×C3×C4D4×D511yescharacteristic
533C2×C3×C4D4×D511yescharacteristic
534C2×C3×C4C23×D511yescharacteristic
535C3×C8—21no—
536C3×C8—52no—
537C3×C8—101no—
538C3×C8C2×C4×D512yes—
539C22×C5C22×C3×D411yescharacteristic
540C2×D5—21no—
541C2×D5—21no—
542C2×D5—22no—
543C2×D5—41no—
544C2×D5—41no—
545C2×D5C3×C4×D412yes—
546C4×C5—21no—
547C4×C5—22no—
548C4×C5—22no—
549C4×C5—41no—
550C4×C5—41no—
551C4×C5C3×#13712yescomplemented
552C4×C5C23×C3×C411yescharacteristic
553C4×C5C2×C3×#4111yescharacteristic
554Dic5—21no—
555Dic5—21no—
556Dic5—22no—
557Dic5—41no—
558Dic5—41no—
559Dic5C3×C4×D412yes—
560#41—54no—
561#41—102no—
562C2×Q8—54no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×Q8—102no—
566C2×Q8C22×C3×D511yescharacteristic
567C2×Q8C22×C3×D511yescharacteristic
568C2×D4—51no—
569C2×D4—101no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578Q16—54no—
579Q16C3×C4×D514yescomplemented
580SD16—54no—
581SD16—54no—
582M16—54no—
583M16—102no—
584C2×C8—51no—
585C2×C8—51no—
586C2×C8C22×C3×D511yescharacteristic
587C2×C8C22×C3×D511yescharacteristic
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—51no—
591C4⋊C4—51no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4—101no—
595C4⋊C4—101no—
596C4⋊C4—101no—
597C4⋊C4C22×C3×D511yescharacteristic
598C4⋊C4C22×C3×D511yescharacteristic
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C42—21no—
603C42—21no—
604C42—51no—
605C42—51no—
606C42—51no—
607C42—101no—
608C42—101no—
609C42—101no—
610C42—101no—
611C42—101no—
612C42C22×C3×D511yescharacteristic
613C3×C5C4×#13711yescharacteristic, complemented, Hall
614C22×C3—52no—
615C22×C3—101no—
616C22×C3—101no—
617C22×C3—102no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3C2×D4×D511yescharacteristic
621C3×C4—21no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—52no—
627C3×C4—101no—
628C3×C4—101no—
629C3×C4—102no—
630C3×C4—201no—
631C3×C4—201no—
632C3×C4#406412yesdirect product factor
633C3×C4C22×C4×D511yescharacteristic
634C3×C4D5×#4111yescharacteristic
635C2×C5C2×C3×C4×D411yescharacteristic
636C2×C5C2×C3×#13711yescharacteristic
637C2×C5C3×#57511yescharacteristic
638D5—22no—
639D5—42no—
640C23—51no—
641C23—101no—
642Q8—21no—
643Q8—21no—
644Q8—52no—
645Q8—104no—
646Q8—101no—
647Q8C2×C3×C4×D512yes—
648Q8C2×C3×C4×D512yes—
649D4—52no—
650D4—104no—
651D4—101no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—51no—
657C2×C4—52no—
658C2×C4—52no—
659C2×C4—51no—
660C2×C4—51no—
661C2×C4—104no—
662C2×C4—104no—
663C2×C4—101no—
664C2×C4—102no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—201no—
668C2×C4—202no—
669C2×C4—202no—
670C2×C4—202no—
671C2×C4C3×D4×D511yescharacteristic
672C2×C4C3×D4×D511yescharacteristic
673C2×C4C23×C3×D511yescharacteristic
674C8—21no—
675C8—52no—
676C8—101no—
677C8C2×C3×C4×D512yes—
678C2×C3—102no—
679C2×C3—202no—
680C2×C3C4×D4×D511yescharacteristic
681C2×C3C2×#406411yescharacteristic
682C2×C3#6610211yescharacteristic
683C5C3×C4×#13711yescharacteristic, complemented, Sylow
684C22—52no—
685C22—101no—
686C22—101no—
687C22—102no—
688C22—201no—
689C22—201no—
690C22C2×C3×D4×D511yescharacteristic
691C4—21no—
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—52no—
697C4—101no—
698C4—102no—
699C4—101no—
700C4—201no—
701C4—201no—
702C4C3×#406412yesdirect product factor
703C4C22×C3×C4×D511yescharacteristic
704C4C3×D5×#4111yescharacteristic
705C3C4×#406411yescharacteristic, direct product factor, Sylow
706C2—102no—
707C2—202no—
708C2C3×C4×D4×D511yescharacteristic
709C2C2×C3×#406411yescharacteristic
710C2C3×#6610211yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
cosocleC2×C4×C5C24×C3
hypercenterC3×C4×Q16D5
hypocenterC5C3×C4×#137
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C3×C4×Q8×D5C2semidirect
4. C3×C4×C5×Q16C2semidirect
5. C3×#65473C2semidirect
6. C3×C4×#689C2semidirect
7. C3×C4×#688C2semidirect
8. C3×#65178C2semidirect
9. C3×#65170C2semidirect
10. C3×#65106C2semidirect
12. C3×#65091C2semidirect
13. C3×#65078C2semidirect
14. C3×C4×#677C2semidirect
15. C3×C4×#676C2semidirect
16. C4×#4064C3direct (N × H)
26. C3×#4064C4direct (N × H)
64. C4×Q8×D5C2×C3semidirect
65. C4×C5×Q16C2×C3semidirect
66. #65473C2×C3semidirect
67. C4×#689C2×C3semidirect
68. C4×#688C2×C3semidirect
69. #65178C2×C3semidirect
70. #65170C2×C3semidirect
71. #65106C2×C3semidirect
73. #65091C2×C3semidirect
74. #65078C2×C3semidirect
75. C4×#677C2×C3semidirect
76. C4×#676C2×C3semidirect
82. C3×Q8×D5C2×C4semidirect
95. C3×C5×Q16C2×C4semidirect
105. C3×#689C2×C4semidirect
106. C3×#688C2×C4semidirect
127. C3×#677C2×C4semidirect
129. C3×#676C2×C4semidirect
138. C3×C4×Q16D5semidirect
154. #4064C3×C4direct (N × H)
277. Q8×D5C2×C3×C4semidirect
290. C5×Q16C2×C3×C4semidirect
300. #689C2×C3×C4semidirect
301. #688C2×C3×C4semidirect
322. #677C2×C3×C4semidirect
324. #676C2×C3×C4semidirect
333. C4×Q16C3×D5semidirect
352. C3×C4×C5#137semidirect
380. C3×Q16C4×D5semidirect
551. C4×C5C3×#137semidirect
579. Q16C3×C4×D5semidirect
613. C3×C5C4×#137semidirect
632. C3×C4#4064direct (N × H)
683. C5C3×C4×#137semidirect
702. C4C3×#4064direct (N × H)
705. C3C4×#4064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40642
C3×C4×#7132
C3×C4×Q8×D52
C3×C4×C5×Q162
C3×#654732
C3×C4×#6892
C3×C4×#6882
C3×#651782
C3×#651702
C3×#651062
C3×#650922
C3×#650912
C3×#650782
C3×C4×#6772
C3×C4×#6762
C4×#40643
C3×C4×#1375