Finite Group Databasebeta

← C3×#10613552 #14439274

Subgroups — C3×#10613552 #14439274

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4064C211yesmaximal, characteristic, complemented
2C2×C3×#4061C211yesmaximal, characteristic, complemented
3C2×C3×#4060C211yesmaximal, characteristic, complemented
4C2×C3×#4057C211yesmaximal, characteristic, complemented
5C3×D5×#124C211yesmaximal, characteristic, complemented
6C3×#66002C211yesmaximal, characteristic, complemented
7C3×C5×#495C211yesmaximal, characteristic, complemented
8C3×#65479C211yesmaximal, characteristic, complemented
9C3×#65465C211yesmaximal, characteristic, complemented
10C3×#65456C211yesmaximal, characteristic, complemented
11C3×#65443C211yesmaximal, characteristic, complemented
12C3×#65348C211yesmaximal, characteristic, complemented
13C3×#65348C211yesmaximal, characteristic, complemented
14C3×#64985C211yesmaximal, characteristic, complemented
15C3×C4×#676C211yesmaximal, characteristic, complemented
16#10613552C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×Q16C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C2×C3×C5×D8C2211yescharacteristic
25C3×C5×#124C2211yescharacteristic
26C3×C5×#124C2211yescharacteristic, complemented
27C3×#4093C2211yescharacteristic
28C3×#4090C2211yescharacteristic, complemented
29C2×C3×#689C2211yescharacteristic, complemented
30C2×C3×#689C2211yescharacteristic, complemented
31C2×C3×#688C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic, complemented
33C3×#4086C2211yescharacteristic, complemented
34C3×#4082C2211yescharacteristic
35C2×C3×#687C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic
39C3×#4064—24no—
40C3×#4061—24no—
41C3×#4060—24no—
42C3×#4057—24no—
43C2×C3×Dic20C2211yescharacteristic, complemented
44C2×C3×D40C2211yescharacteristic
45C2×C3×#677C2211yescharacteristic
46C2×C3×#677C2211yescharacteristic, complemented
47C2×C3×#676C2211yescharacteristic
48C2×C3×#676C2211yescharacteristic
49C3×#4031—22no—
50C3×#4030—22no—
51C3×#4027—22no—
52C3×D5×C22⋊C4—22no—
53C3×#4021C2211yescharacteristic
54C3×#4021C2211yescharacteristic, complemented
55C3×C42×D5C2211yescharacteristic
56C3×C4×C5×C8C2211yescharacteristic, complemented
57C3×#3947C2211yescharacteristic, complemented
58C3×#3947C2211yescharacteristic, complemented
59C3×C4×#168C2211yescharacteristic, complemented
60C3×#3153—51nomaximal, Hall
61C2×#4064C2×C311yescharacteristic, complemented
62C2×#4061C2×C311yescharacteristic, complemented
63C2×#4060C2×C311yescharacteristic, complemented
64C2×#4057C2×C311yescharacteristic, complemented
65D5×#124C2×C311yescharacteristic, complemented
66#66002C2×C311yescharacteristic, complemented
67C5×#495C2×C311yescharacteristic, complemented
68#65479C2×C311yescharacteristic, complemented
69#65465C2×C311yescharacteristic, complemented
70#65456C2×C311yescharacteristic, complemented
71#65443C2×C311yescharacteristic, complemented
72#65348C2×C311yescharacteristic, complemented
73#65348C2×C311yescharacteristic, complemented
74#64985C2×C311yescharacteristic, complemented
75C4×#676C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5—22no—
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C3×#713—22no—
86C3×#713—22no—
87C3×Q8×D5—22no—
88C3×Q8×D5—22no—
89C3×#711—22no—
90C3×#711—22no—
91C3×D4×D5—22no—
92C3×D4×D5—22no—
93C2×C3×D20—21no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5D412yes—
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10—21no—
101C2×C3×Dic10C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103C3×C5×Q16—22no—
104C3×C5×SD16—22no—
105C3×C5×SD16—22no—
106C3×C5×D8—22no—
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C3×C5×C22⋊C4—22no—
110C3×C5×C22⋊C4—22no—
111C3×C42×C5C2311yescharacteristic
112C3×C22⋊Dic5—22no—
113C3×#689—22no—
114C3×#689—22no—
115C3×#688—22no—
116C3×#688—22no—
117C3×#687—22no—
118C3×#687—22no—
119C3×#686—22no—
120C3×#686—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×#685—22no—
124C3×#683—22no—
125C3×C4×Dic5D412yes—
126C3×C4×Dic5C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129C3×Dic20—22no—
130C3×D40—22no—
131C3×#677—22no—
132C3×#677—22no—
133C3×#676D414yescomplemented
134C3×#676D414yescomplemented
135C2×C3×#137—51no—
136C2×C3×#137—51no—
137C2×C3×AGL(1,ℤ/8)—51no—
138C2×C3×AGL(1,ℤ/8)—51no—
139C3×#532—51no—
140C2×C3×#124—51no—
141C3×#497—51no—
142C3×#497—51no—
143C3×#496—51no—
144C3×#496—51no—
145C3×#495—51no—
146C3×#495—51no—
147C3×#495—51no—
148C3×#495D511yescharacteristic, complemented
149C3×C4×M16—51no—
150C2×#713C22×C311yescharacteristic
151C2×Q8×D5C22×C311yescharacteristic
152C2×#711C22×C311yescharacteristic
153C2×D4×D5C22×C311yescharacteristic
154C2×C5×Q16C22×C311yescharacteristic, complemented
155C2×C5×SD16C22×C311yescharacteristic
156C2×C5×SD16C22×C311yescharacteristic, complemented
157C2×C5×D8C22×C311yescharacteristic
158C5×#124C22×C311yescharacteristic
159C5×#124C22×C311yescharacteristic, complemented
160#4093C22×C311yescharacteristic
161#4090C22×C311yescharacteristic, complemented
162C2×#689C22×C311yescharacteristic, complemented
163C2×#689C22×C311yescharacteristic, complemented
164C2×#688C22×C311yescharacteristic
165C2×#688C22×C311yescharacteristic, complemented
166#4086C22×C311yescharacteristic, complemented
167#4082C22×C311yescharacteristic
168C2×#687C22×C311yescharacteristic
169C2×#687C22×C311yescharacteristic, complemented
170C2×#686C22×C311yescharacteristic
171C2×#686C22×C311yescharacteristic
172#4064—24no—
173#4061—24no—
174#4060—24no—
175#4057—24no—
176C2×Dic20C22×C311yescharacteristic, complemented
177C2×D40C22×C311yescharacteristic
178C2×#677C22×C311yescharacteristic
179C2×#677C22×C311yescharacteristic, complemented
180C2×#676C22×C311yescharacteristic
181C2×#676C22×C311yescharacteristic
182#4031—22no—
183#4030—22no—
184#4027—22no—
185D5×C22⋊C4—22no—
186#4021C22×C311yescharacteristic
187#4021C22×C311yescharacteristic, complemented
188C42×D5C22×C311yescharacteristic
189C4×C5×C8C22×C311yescharacteristic, complemented
190#3947C22×C311yescharacteristic, complemented
191#3947C22×C311yescharacteristic, complemented
192C4×#168C22×C311yescharacteristic, complemented
193#3153—51noSylow
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—44no—
199C22×C3×D5—42no—
200C22×C3×D5C2×D411yescharacteristic
201C3×C5×Q8—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8—21no—
204C3×C5×Q8—21no—
205C3×C5×D4—21no—
206C3×C5×D4—21no—
207C3×C5×D4—21no—
208C3×C5×D4—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C2×D412yes—
212C2×C3×C4×C5C2411yescharacteristic
213C3×C22⋊D5—44no—
214C3×C22⋊D5—42no—
215C3×C22⋊D5—42no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—42no—
219C2×C3×Dic5C2×D412yes—
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20—21no—
223C3×D20—21no—
224C3×D20—21no—
225C3×D20—42no—
226C3×C4×D5—42no—
227C3×C4×D5—42no—
228C3×C4×D5—42no—
229C3×C4×D5C2×D412yes—
230C3×C4×D5C2×D412yes—
231C3×Dic10—21no—
232C3×Dic10—21no—
233C3×Dic10—21no—
234C3×Dic10—21no—
235C3×Dic10—42no—
236C3×C5×C8C2×D412yes—
237C3×C5×C8C2×D412yes—
238C3×#168C2×D412yes—
239C3×#168C2×D412yes—
240C2×C3×#41—51no—
241C2×C3×#41—51no—
242C22×C3×Q8—51no—
243C22×C3×D4—51no—
244C3×#137—104no—
245C3×#137—104no—
246C3×AGL(1,ℤ/8)—104no—
247C3×AGL(1,ℤ/8)—104no—
248C2×C3×Q16—51no—
249C2×C3×Q16—51no—
250C2×C3×Q16—51no—
251C2×C3×Q16C2×D511yescharacteristic, complemented
252C2×C3×SD16—51no—
253C2×C3×SD16—51no—
254C2×C3×SD16—51no—
255C2×C3×SD16—51no—
256C2×C3×SD16—51no—
257C2×C3×SD16—51no—
258C2×C3×SD16C2×D511yescharacteristic
259C2×C3×SD16C2×D511yescharacteristic, complemented
260C2×C3×D8—51no—
261C2×C3×D8—51no—
262C2×C3×D8—51no—
263C2×C3×D8C2×D511yescharacteristic
264C2×C3×M16—51no—
265C2×C3×M16—51no—
266C3×C4⋊Q8—51no—
267C3×#127—51no—
268C3×#124—51no—
269C3×#124—51no—
270C3×#124—51no—
271C3×#124—51no—
272C3×#124—102no—
273C3×#124C2×D511yescharacteristic
274C3×#124C2×D511yescharacteristic, complemented
275C3×#121—102no—
276C3×C4×D4—102no—
277C2×C3×C22⋊C4—102no—
278C2×C3×C42—51no—
279C3×#97—51no—
280C3×#97—51no—
281C3×C4×C8—51no—
282C3×C4×C8C2×D511yescharacteristic, complemented
283C23×D5—21no—
284C2×C5×Q8C23×C311yescharacteristic
285C2×C5×Q8C23×C311yescharacteristic
286C2×C5×D4C23×C311yescharacteristic
287C2×C5×D4C23×C311yescharacteristic
288C2×C22⋊D5—21no—
289C2×C22⋊D5—21no—
290C2×C22⋊D5—22no—
291C22×Dic5—21no—
292#713—22no—
293#713—22no—
294Q8×D5—22no—
295Q8×D5—22no—
296#711—22no—
297#711—22no—
298D4×D5—22no—
299D4×D5—22no—
300C2×D20—21no—
301C2×D20C23×C311yescharacteristic
302C2×D20C23×C311yescharacteristic
303C2×C4×D5—21no—
304C2×C4×D5—21no—
305C2×C4×D5C3×D412yes—
306C2×C4×D5C23×C311yescharacteristic
307C2×Dic10—21no—
308C2×Dic10C23×C311yescharacteristic
309C2×Dic10C23×C311yescharacteristic
310C5×Q16—22no—
311C5×SD16—22no—
312C5×SD16—22no—
313C5×D8—22no—
314C2×C5×C8C23×C311yescharacteristic
315C2×C5×C8C23×C311yescharacteristic
316C5×C22⋊C4—22no—
317C5×C22⋊C4—22no—
318C42×C5C23×C311yescharacteristic
319C22⋊Dic5—22no—
320#689—22no—
321#689—22no—
322#688—22no—
323#688—22no—
324#687—22no—
325#687—22no—
326#686—22no—
327#686—22no—
328#685—22no—
329#685—22no—
330#685—22no—
331#683—22no—
332C4×Dic5C3×D412yes—
333C4×Dic5C23×C311yescharacteristic
334C2×#168C23×C311yescharacteristic
335C2×#168C23×C311yescharacteristic
336Dic20—22no—
337D40—22no—
338#677—22no—
339#677—22no—
340#676C3×D414yescomplemented
341#676C3×D414yescomplemented
342C2×#137—51no—
343C2×#137—51no—
344C2×AGL(1,ℤ/8)—51no—
345C2×AGL(1,ℤ/8)—51no—
346#532—51no—
347C2×#124—51no—
348#497—51no—
349#497—51no—
350#496—51no—
351#496—51no—
352#495—51no—
353#495—51no—
354#495—51no—
355#495C3×D511yescharacteristic, complemented
356C4×M16—51no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—42no—
360C22×C3×C5—42no—
361C22×C3×C5C22×D411yescharacteristic
362C2×C3×D5—22no—
363C2×C3×D5—41no—
364C2×C3×D5—41no—
365C2×C3×D5—42no—
366C2×C3×D5—42no—
367C2×C3×D5—84no—
368C2×C3×D5#12712yes—
369C3×C4×C5—22no—
370C3×C4×C5—41no—
371C3×C4×C5—41no—
372C3×C4×C5C22×D411yescharacteristic
373C3×C4×C5C22×D411yescharacteristic
374C3×Dic5—22no—
375C3×Dic5—41no—
376C3×Dic5—41no—
377C3×Dic5#12712yes—
378C24×C3—101no—
379C3×#41—102no—
380C3×#41—102no—
381C3×#41—102no—
382C3×#41—102no—
383C2×C3×Q8—51no—
384C2×C3×Q8—51no—
385C2×C3×Q8—101no—
386C2×C3×Q8—102no—
387C2×C3×Q8—102no—
388C2×C3×Q8C22×D511yescharacteristic
389C2×C3×Q8C22×D511yescharacteristic
390C2×C3×D4—51no—
391C2×C3×D4—51no—
392C2×C3×D4—101no—
393C2×C3×D4—102no—
394C2×C3×D4—102no—
395C2×C3×D4—102no—
396C2×C3×D4—101no—
397C2×C3×D4—101no—
398C2×C3×D4C22×D511yescharacteristic
399C2×C3×D4C22×D511yescharacteristic
400C22×C3×C4—51no—
401C22×C3×C4—52no—
402C22×C3×C4—101no—
403C22×C3×C4—101no—
404C22×C3×C4—101no—
405C3×Q16—22no—
406C3×Q16—102no—
407C3×Q16—102no—
408C3×Q16—102no—
409C3×SD16—22no—
410C3×SD16—22no—
411C3×SD16—102no—
412C3×SD16—102no—
413C3×SD16—102no—
414C3×SD16—102no—
415C3×SD16—102no—
416C3×SD16—102no—
417C3×D8—22no—
418C3×D8—102no—
419C3×D8—102no—
420C3×D8—102no—
421C3×M16—54no—
422C3×M16—54no—
423C2×C3×C8—51no—
424C2×C3×C8—51no—
425C2×C3×C8C22×D511yescharacteristic
426C2×C3×C8C22×D511yescharacteristic
427C3×C4⋊C4—102no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—102no—
431C3×C22⋊C4—102no—
432C3×C22⋊C4—102no—
433C3×C22⋊C4—102no—
434C3×C42—52no—
435C3×C42—51no—
436C3×C42C22×D511yescharacteristic
437C23×C5—21no—
438C23×C5—21no—
439C22×D5—21no—
440C22×D5—21no—
441C22×D5—44no—
442C22×D5—42no—
443C22×D5C2×C3×D411yescharacteristic
444C5×Q8—21no—
445C5×Q8—21no—
446C5×Q8—21no—
447C5×Q8—21no—
448C5×D4—21no—
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5C2×C3×D412yes—
455C2×C4×C5C24×C311yescharacteristic
456C22⋊D5—44no—
457C22⋊D5—42no—
458C22⋊D5—42no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—42no—
462C2×Dic5C2×C3×D412yes—
463C2×Dic5C2×C3×D411yescharacteristic
464D20—21no—
465D20—21no—
466D20—21no—
467D20—21no—
468D20—42no—
469C4×D5—42no—
470C4×D5—42no—
471C4×D5—42no—
472C4×D5C2×C3×D412yes—
473C4×D5C2×C3×D412yes—
474Dic10—21no—
475Dic10—21no—
476Dic10—21no—
477Dic10—21no—
478Dic10—42no—
479C5×C8C2×C3×D412yes—
480C5×C8C2×C3×D412yes—
481#168C2×C3×D412yes—
482#168C2×C3×D412yes—
483C2×#41—51no—
484C2×#41—51no—
485C22×Q8—51no—
486C22×D4—51no—
487#137—104no—
488#137—104no—
489AGL(1,ℤ/8)—104no—
490AGL(1,ℤ/8)—104no—
491C2×Q16—51no—
492C2×Q16—51no—
493C2×Q16—51no—
494C2×Q16C2×C3×D511yescharacteristic, complemented
495C2×SD16—51no—
496C2×SD16—51no—
497C2×SD16—51no—
498C2×SD16—51no—
499C2×SD16—51no—
500C2×SD16—51no—
501C2×SD16C2×C3×D511yescharacteristic
502C2×SD16C2×C3×D511yescharacteristic, complemented
503C2×D8—51no—
504C2×D8—51no—
505C2×D8—51no—
506C2×D8C2×C3×D511yescharacteristic
507C2×M16—51no—
508C2×M16—51no—
509C4⋊Q8—51no—
510#127—51no—
511#124—51no—
512#124—51no—
513#124—51no—
514#124—51no—
515#124—102no—
516#124C2×C3×D511yescharacteristic
517#124C2×C3×D511yescharacteristic, complemented
518#121—102no—
519C4×D4—102no—
520C2×C22⋊C4—102no—
521C2×C42—51no—
522#97—51no—
523#97—51no—
524C4×C8—51no—
525C4×C8C2×C3×D511yescharacteristic, complemented
526C2×C3×C5—81no—
527C2×C3×C5—81no—
528C2×C3×C5C2×#12711yescharacteristic
529C2×C3×C5#57512yes—
530C3×D5—22no—
531C3×D5—81no—
532C3×D5—81no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—51no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3—202no—
539C23×C3—204no—
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—101no—
545C3×Q8—101no—
546C3×Q8—101no—
547C3×Q8—101no—
548C3×Q8—202no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—101no—
554C3×D4—101no—
555C3×D4—101no—
556C3×D4—101no—
557C3×D4—202no—
558C3×D4—202no—
559C3×D4—204no—
560C3×D4—202no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—51no—
564C2×C3×C4—52no—
565C2×C3×C4—52no—
566C2×C3×C4—52no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—202no—
570C2×C3×C4—202no—
571C2×C3×C4—202no—
572C2×C3×C4—202no—
573C2×C3×C4D4×D512yes—
574C2×C3×C4C23×D511yescharacteristic
575C3×C8—52no—
576C3×C8—52no—
577C3×C8D4×D512yes—
578C3×C8D4×D512yes—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—41no—
582C22×C5—41no—
583C22×C5C22×C3×D411yescharacteristic
584C2×D5—22no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—41no—
588C2×D5—41no—
589C2×D5—84no—
590C2×D5C3×#12712yes—
591C4×C5—22no—
592C4×C5—41no—
593C4×C5—41no—
594C4×C5C22×C3×D411yescharacteristic
595C4×C5C22×C3×D411yescharacteristic
596Dic5—22no—
597Dic5—41no—
598Dic5—41no—
599Dic5C3×#12712yes—
600C24—101no—
601#41—102no—
602#41—102no—
603#41—102no—
604#41—102no—
605C2×Q8—51no—
606C2×Q8—51no—
607C2×Q8—101no—
608C2×Q8—102no—
609C2×Q8—102no—
610C2×Q8C22×C3×D511yescharacteristic
611C2×Q8C22×C3×D511yescharacteristic
612C2×D4—51no—
613C2×D4—51no—
614C2×D4—101no—
615C2×D4—102no—
616C2×D4—102no—
617C2×D4—102no—
618C2×D4—101no—
619C2×D4—101no—
620C2×D4C22×C3×D511yescharacteristic
621C2×D4C22×C3×D511yescharacteristic
622C22×C4—51no—
623C22×C4—52no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627Q16—22no—
628Q16—102no—
629Q16—102no—
630Q16—102no—
631SD16—22no—
632SD16—22no—
633SD16—102no—
634SD16—102no—
635SD16—102no—
636SD16—102no—
637SD16—102no—
638SD16—102no—
639D8—22no—
640D8—102no—
641D8—102no—
642D8—102no—
643M16—54no—
644M16—54no—
645C2×C8—51no—
646C2×C8—51no—
647C2×C8C22×C3×D511yescharacteristic
648C2×C8C22×C3×D511yescharacteristic
649C4⋊C4—102no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—102no—
653C22⋊C4—102no—
654C22⋊C4—102no—
655C22⋊C4—102no—
656C42—52no—
657C42—51no—
658C42C22×C3×D511yescharacteristic
659C3×C5#315311yescharacteristic, complemented, Hall
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—52no—
665C22×C3—102no—
666C22×C3—201no—
667C22×C3—201no—
668C22×C3—202no—
669C22×C3—202no—
670C22×C3—404no—
671C22×C3C2×D4×D511yescharacteristic
672C3×C4—22no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—52no—
676C3×C4—102no—
677C3×C4—201no—
678C3×C4—201no—
679C3×C4C2×D4×D511yescharacteristic
680C3×C4C2×D4×D511yescharacteristic
681C2×C5—81no—
682C2×C5—81no—
683C2×C5C2×C3×#12711yescharacteristic
684C2×C5C3×#57512yes—
685D5—22no—
686D5—81no—
687D5—81no—
688C23—21no—
689C23—21no—
690C23—51no—
691C23—101no—
692C23—101no—
693C23—202no—
694C23—204no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—101no—
700Q8—101no—
701Q8—101no—
702Q8—101no—
703Q8—202no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—101no—
709D4—101no—
710D4—101no—
711D4—101no—
712D4—202no—
713D4—202no—
714D4—204no—
715D4—202no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—51no—
719C2×C4—52no—
720C2×C4—52no—
721C2×C4—52no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4C3×D4×D512yes—
729C2×C4C23×C3×D511yescharacteristic
730C8—52no—
731C8—52no—
732C8C3×D4×D512yes—
733C8C3×D4×D512yes—
734C2×C3—81no—
735C2×C3—81no—
736C2×C3—102no—
737C2×C3—401no—
738C2×C3—401no—
739C2×C3D5×#12711yescharacteristic
740C2×C3#6610212yes—
741C5C3×#315311yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—41no—
745C22—41no—
746C22—52no—
747C22—102no—
748C22—202no—
749C22—202no—
750C22—201no—
751C22—201no—
752C22—404no—
753C22C2×C3×D4×D511yescharacteristic
754C4—22no—
755C4—41no—
756C4—41no—
757C4—52no—
758C4—102no—
759C4—201no—
760C4—201no—
761C4C2×C3×D4×D511yescharacteristic
762C4C2×C3×D4×D511yescharacteristic
763C3#1061355211yescharacteristic, direct product factor, Sylow
764C2—81no—
765C2—81no—
766C2—102no—
767C2—401no—
768C2—401no—
769C2C3×D5×#12711yescharacteristic
770C2C3×#6610212yes—
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#495C2
socleC22×C3×C5C22×D4
hypercenterC3×#495D5
hypocenterC5C3×#3153
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#495

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4064C2semidirect
2. C2×C3×#4061C2semidirect
3. C2×C3×#4060C2semidirect
4. C2×C3×#4057C2semidirect
5. C3×D5×#124C2semidirect
6. C3×#66002C2semidirect
7. C3×C5×#495C2semidirect
8. C3×#65479C2semidirect
9. C3×#65465C2semidirect
10. C3×#65456C2semidirect
11. C3×#65443C2semidirect
12. C3×#65348C2semidirect
13. C3×#65348C2semidirect
14. C3×#64985C2semidirect
15. C3×C4×#676C2semidirect
16. #10613552C3direct (N × H)
21. C2×C3×C5×Q16C22semidirect
23. C2×C3×C5×SD16C22semidirect
26. C3×C5×#124C22semidirect
28. C3×#4090C22semidirect
29. C2×C3×#689C22semidirect
30. C2×C3×#689C22semidirect
32. C2×C3×#688C22semidirect
33. C3×#4086C22semidirect
36. C2×C3×#687C22semidirect
43. C2×C3×Dic20C22semidirect
46. C2×C3×#677C22semidirect
54. C3×#4021C22semidirect
56. C3×C4×C5×C8C22semidirect
57. C3×#3947C22semidirect
58. C3×#3947C22semidirect
59. C3×C4×#168C22semidirect
61. C2×#4064C2×C3semidirect
62. C2×#4061C2×C3semidirect
63. C2×#4060C2×C3semidirect
64. C2×#4057C2×C3semidirect
65. D5×#124C2×C3semidirect
66. #66002C2×C3semidirect
67. C5×#495C2×C3semidirect
68. #65479C2×C3semidirect
69. #65465C2×C3semidirect
70. #65456C2×C3semidirect
71. #65443C2×C3semidirect
72. #65348C2×C3semidirect
73. #65348C2×C3semidirect
74. #64985C2×C3semidirect
75. C4×#676C2×C3semidirect
133. C3×#676D4semidirect
134. C3×#676D4semidirect
148. C3×#495D5semidirect
154. C2×C5×Q16C22×C3semidirect
156. C2×C5×SD16C22×C3semidirect
159. C5×#124C22×C3semidirect
161. #4090C22×C3semidirect
162. C2×#689C22×C3semidirect
163. C2×#689C22×C3semidirect
165. C2×#688C22×C3semidirect
166. #4086C22×C3semidirect
169. C2×#687C22×C3semidirect
176. C2×Dic20C22×C3semidirect
179. C2×#677C22×C3semidirect
187. #4021C22×C3semidirect
189. C4×C5×C8C22×C3semidirect
190. #3947C22×C3semidirect
191. #3947C22×C3semidirect
192. C4×#168C22×C3semidirect
251. C2×C3×Q16C2×D5semidirect
259. C2×C3×SD16C2×D5semidirect
274. C3×#124C2×D5semidirect
282. C3×C4×C8C2×D5semidirect
340. #676C3×D4semidirect
341. #676C3×D4semidirect
355. #495C3×D5semidirect
494. C2×Q16C2×C3×D5semidirect
502. C2×SD16C2×C3×D5semidirect
517. #124C2×C3×D5semidirect
525. C4×C8C2×C3×D5semidirect
659. C3×C5#3153semidirect
741. C5C3×#3153semidirect
763. C3#10613552direct (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
C2×C3×#40612
C2×C3×#40602
C2×C3×#40572
C3×D5×#1242
C3×#660022
C3×C5×#4952
C3×#654792
C3×#654652
C3×#654562
C3×#654432
C3×#653482
C3×#649852
C3×C4×#6762
#106135523
C3×#31535