Finite Group Databasebeta

← C3×#10611819 #14424805

Subgroups — C3×#10611819 #14424805

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C2×C3×#4061C211yesmaximal, characteristic, complemented
3C2×C3×#4058C211yesmaximal, characteristic, complemented
4C3×#65942C211yesmaximal, characteristic, complemented
5C3×C5×#449C211yesmaximal, characteristic, complemented
6C3×#65528C211yesmaximal, characteristic, complemented
7C3×#65459C211yesmaximal, characteristic, complemented
8C3×#65447C211yesmaximal, characteristic, complemented
9C3×#65329C211yesmaximal, characteristic, complemented
10C3×#65097C211yesmaximal, characteristic, complemented
11C3×D5×#103C211yesmaximal, characteristic, complemented
12C3×#65072C211yesmaximal, characteristic, complemented
13C3×#65060C211yesmaximal, characteristic, complemented
14C3×#65028C211yesmaximal, characteristic, complemented
15C3×#65016C211yesmaximal, characteristic, complemented
16#10611819C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C3×#4150—24no—
19C3×#4150—24no—
20C2×C3×Q8×D5C2211yescharacteristic
21C2×C3×Q8×D5C2211yescharacteristic
22C2×C3×#711—21no—
23C2×C3×#711—21no—
24C2×C3×#711C2211yescharacteristic
25C2×C3×#711C2211yescharacteristic
26C2×C3×#711C2211yescharacteristic
27C2×C3×#709—21no—
28C2×C3×#709C2211yescharacteristic
29C22×C3×Dic10—21no—
30C22×C3×Dic10C2211yescharacteristic
31C2×C3×C5×SD16C2211yescharacteristic
32C2×C3×C5×D8C2211yescharacteristic
33C3×C5×#121C2211yescharacteristic
34C2×C3×#689C2211yescharacteristic
35C3×#4085—21no—
36C3×#4084—21no—
37C3×#4084C2211yescharacteristic
38C2×C3×#687C2211yescharacteristic
39C2×C3×#687C2211yescharacteristic
40C2×C3×#687C2211yescharacteristic
41C3×#4070C2211yescharacteristic
42C3×#4061—24no—
43C3×#4058—24no—
44C2×C3×Dic20C2211yescharacteristic
45C2×C3×Dic20C2211yescharacteristic
46C2×C3×#676C2211yescharacteristic
47C2×C3×C8×D5C2211yescharacteristic
48C3×#4043C2211yescharacteristic
49C3×D5×C4⋊C4C2211yescharacteristic
50C3×#4030—21no—
51C3×#4024—21no—
52C3×C5×#103C2211yescharacteristic
53C3×C5×#102C2211yescharacteristic
54C3×C5×C22⋊C8C2211yescharacteristic
55C3×#3967C2211yescharacteristic
56C3×#3964C2211yescharacteristic
57C3×C22⋊#168C2211yescharacteristic
58C3×#3952C2211yescharacteristic
59C3×#3952C2211yescharacteristic
60C3×#3948C2211yescharacteristic
61C3×#3948C2211yescharacteristic
62C3×#3942C2211yescharacteristic
63C3×#3942C2211yescharacteristic
64C3×#3013—51nomaximal, Hall
65C2×#4150C2×C311yescharacteristic, complemented
66C2×#4061C2×C311yescharacteristic, complemented
67C2×#4058C2×C311yescharacteristic, complemented
68#65942C2×C311yescharacteristic, complemented
69C5×#449C2×C311yescharacteristic, complemented
70#65528C2×C311yescharacteristic, complemented
71#65459C2×C311yescharacteristic, complemented
72#65447C2×C311yescharacteristic, complemented
73#65329C2×C311yescharacteristic, complemented
74#65097C2×C311yescharacteristic, complemented
75D5×#103C2×C311yescharacteristic, complemented
76#65072C2×C311yescharacteristic, complemented
77#65060C2×C311yescharacteristic, complemented
78#65028C2×C311yescharacteristic, complemented
79#65016C2×C311yescharacteristic, complemented
80C3×C5×#41—22no—
81C3×C5×#41—22no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4C2311yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C22×C3×C4×C5—21no—
88C22×C3×C4×C5C2311yescharacteristic
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5D411yescharacteristic
94C2×C3×C22⋊D5D411yescharacteristic
95C22×C3×Dic5—21no—
96C22×C3×Dic5—21no—
97C22×C3×Dic5—21no—
98C22×C3×Dic5—21no—
99C3×Q8×D5—22no—
100C3×Q8×D5—22no—
101C3×Q8×D5—22no—
102C3×Q8×D5D414yescomplemented
103C3×#711—28no—
104C3×#711—28no—
105C3×#711—22no—
106C3×#711—22no—
107C3×#711—22no—
108C3×#711—22no—
109C3×#711—22no—
110C3×#711D414yescomplemented
111C3×#709—28no—
112C3×#709—22no—
113C3×#709—22no—
114C2×C3×D20D411yescharacteristic
115C2×C3×C4×D5—21no—
116C2×C3×C4×D5—21no—
117C2×C3×C4×D5—21no—
118C2×C3×C4×D5C2311yescharacteristic
119C2×C3×C4×D5C2311yescharacteristic
120C2×C3×Dic10—28no—
121C2×C3×Dic10—21no—
122C2×C3×Dic10—21no—
123C2×C3×Dic10—21no—
124C2×C3×Dic10—22no—
125C2×C3×Dic10—22no—
126C2×C3×Dic10D411yescharacteristic
127C2×C3×Dic10C2311yescharacteristic
128C2×C3×Dic10C2311yescharacteristic
129C2×C3×Dic10C2311yescharacteristic
130C3×C5×SD16—22no—
131C3×C5×D8—22no—
132C2×C3×C5×C8C2311yescharacteristic
133C2×C3×C5×C8C2311yescharacteristic
134C3×C5×C4⋊C4C2311yescharacteristic
135C3×C5×C22⋊C4—21no—
136C3×C22⋊Dic5—21no—
137C3×C22⋊Dic5—21no—
138C3×#689—22no—
139C3×#687—22no—
140C3×#687—22no—
141C3×#687—22no—
142C3×#685—21no—
143C3×C4⋊Dic5—21no—
144C3×C4⋊Dic5C2311yescharacteristic
145C3×#683—21no—
146C3×#683—21no—
147C2×C3×#168C2311yescharacteristic
148C2×C3×#168C2311yescharacteristic
149C3×Dic20—22no—
150C3×Dic20—22no—
151C3×#676—22no—
152C3×C8×D5—22no—
153C2×C3×2−1+4—51no—
154C2×C3×#137—51no—
155C2×C3×#135—51no—
156C3×#537—51no—
157C3×#452—51no—
158C3×#452—51no—
159C3×#451—51no—
160C3×#451—51no—
161C3×#449—51no—
162C3×#449D511yescharacteristic, complemented
163C3×#448—51no—
164C3×#448—51no—
165C3×#417—51no—
166C2×C3×#103—51no—
167C3×#408—51no—
168C2×C5×#41C22×C311yescharacteristic
169#4150—24no—
170#4150—24no—
171C2×Q8×D5C22×C311yescharacteristic
172C2×Q8×D5C22×C311yescharacteristic
173C2×#711—21no—
174C2×#711—21no—
175C2×#711C22×C311yescharacteristic
176C2×#711C22×C311yescharacteristic
177C2×#711C22×C311yescharacteristic
178C2×#709—21no—
179C2×#709C22×C311yescharacteristic
180C22×Dic10—21no—
181C22×Dic10C22×C311yescharacteristic
182C2×C5×SD16C22×C311yescharacteristic
183C2×C5×D8C22×C311yescharacteristic
184C5×#121C22×C311yescharacteristic
185C2×#689C22×C311yescharacteristic
186#4085—21no—
187#4084—21no—
188#4084C22×C311yescharacteristic
189C2×#687C22×C311yescharacteristic
190C2×#687C22×C311yescharacteristic
191C2×#687C22×C311yescharacteristic
192#4070C22×C311yescharacteristic
193#4061—24no—
194#4058—24no—
195C2×Dic20C22×C311yescharacteristic
196C2×Dic20C22×C311yescharacteristic
197C2×#676C22×C311yescharacteristic
198C2×C8×D5C22×C311yescharacteristic
199#4043C22×C311yescharacteristic
200D5×C4⋊C4C22×C311yescharacteristic
201#4030—21no—
202#4024—21no—
203C5×#103C22×C311yescharacteristic
204C5×#102C22×C311yescharacteristic
205C5×C22⋊C8C22×C311yescharacteristic
206#3967C22×C311yescharacteristic
207#3964C22×C311yescharacteristic
208C22⋊#168C22×C311yescharacteristic
209#3952C22×C311yescharacteristic
210#3952C22×C311yescharacteristic
211#3948C22×C311yescharacteristic
212#3948C22×C311yescharacteristic
213#3942C22×C311yescharacteristic
214#3942C22×C311yescharacteristic
215#3013—51noSylow
216C23×C3×C5—21no—
217C23×C3×C5—21no—
218C23×C3×C5C2×D411yescharacteristic
219C22×C3×D5C2×D411yescharacteristic
220C22×C3×D5C2×D411yescharacteristic
221C3×C5×Q8—21no—
222C3×C5×Q8C2×D412yes—
223C3×C5×D4—24no—
224C3×C5×D4—21no—
225C3×C5×D4—21no—
226C3×C5×D4—21no—
227C3×C5×D4—81no—
228C3×C5×D4C2×D412yes—
229C2×C3×C4×C5—24no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2411yescharacteristic
236C3×C22⋊D5—24no—
237C3×C22⋊D5—22no—
238C3×C22⋊D5—24no—
239C3×C22⋊D5—22no—
240C3×C22⋊D5—42no—
241C3×C22⋊D5—81no—
242C2×C3×Dic5—24no—
243C2×C3×Dic5—24no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—24no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—42no—
250C2×C3×Dic5C2×D411yescharacteristic
251C2×C3×Dic5C2×D411yescharacteristic
252C3×D20—22no—
253C3×C4×D5—24no—
254C3×C4×D5—24no—
255C3×C4×D5—21no—
256C3×C4×D5—21no—
257C3×C4×D5—81no—
258C3×C4×D5C2×D412yes—
259C3×C4×D5C2×D412yes—
260C3×Dic10—24no—
261C3×Dic10—24no—
262C3×Dic10—21no—
263C3×Dic10—21no—
264C3×Dic10—22no—
265C3×Dic10—24no—
266C3×Dic10—21no—
267C3×Dic10—21no—
268C3×Dic10C2×D412yes—
269C3×Dic10C2×D412yes—
270C3×C5×C8—21no—
271C3×C5×C8—21no—
272C3×#168—21no—
273C3×#168—21no—
274C3×2−1+4—104no—
275C3×2−1+4—104no—
276C2×C3×#41—51no—
277C2×C3×#41—51no—
278C2×C3×#41—51no—
279C2×C3×#41—51no—
280C2×C3×#41—101no—
281C2×C3×#41—101no—
282C2×C3×#41—101no—
283C2×C3×#41C2×D511yescharacteristic
284C22×C3×Q8—51no—
285C22×C3×Q8—51no—
286C22×C3×Q8—51no—
287C22×C3×Q8—101no—
288C3×#137—104no—
289C3×#135—104no—
290C2×C3×Q16—51no—
291C2×C3×Q16—51no—
292C2×C3×Q16—51no—
293C2×C3×SD16—51no—
294C2×C3×SD16—51no—
295C2×C3×SD16—51no—
296C2×C3×SD16C2×D511yescharacteristic
297C2×C3×D8C2×D511yescharacteristic
298C2×C3×M16—51no—
299C22×C3×C8—51no—
300C3×C22⋊Q8—51no—
301C3×C22⋊Q8—51no—
302C3×C22⋊Q8—101no—
303C3×#121—51no—
304C3×#121—101no—
305C3×#121—101no—
306C3×#121—101no—
307C3×#121C2×D511yescharacteristic
308C2×C3×C4⋊C4—51no—
309C3×#103—51no—
310C3×#103—51no—
311C3×#103—51no—
312C3×#103—51no—
313C3×#103—51no—
314C3×#103C2×D511yescharacteristic
315C3×#102—51no—
316C3×#102C2×D511yescharacteristic
317C3×C22⋊C8—51no—
318C3×C22⋊C8—51no—
319C3×C22⋊C8—51no—
320C3×C22⋊C8C2×D511yescharacteristic
321C5×#41—22no—
322C5×#41—22no—
323C2×C5×Q8C23×C311yescharacteristic
324C2×C5×D4—21no—
325C2×C5×D4—21no—
326C2×C5×D4C23×C311yescharacteristic
327C2×C5×D4C23×C311yescharacteristic
328C22×C4×C5—21no—
329C22×C4×C5C23×C311yescharacteristic
330C2×C22⋊D5—21no—
331C2×C22⋊D5—21no—
332C2×C22⋊D5—21no—
333C2×C22⋊D5—21no—
334C2×C22⋊D5C3×D411yescharacteristic
335C2×C22⋊D5C3×D411yescharacteristic
336C22×Dic5—21no—
337C22×Dic5—21no—
338C22×Dic5—21no—
339C22×Dic5—21no—
340Q8×D5—22no—
341Q8×D5—22no—
342Q8×D5—22no—
343Q8×D5C3×D414yescomplemented
344#711—28no—
345#711—28no—
346#711—22no—
347#711—22no—
348#711—22no—
349#711—22no—
350#711—22no—
351#711C3×D414yescomplemented
352#709—28no—
353#709—22no—
354#709—22no—
355C2×D20C3×D411yescharacteristic
356C2×C4×D5—21no—
357C2×C4×D5—21no—
358C2×C4×D5—21no—
359C2×C4×D5C23×C311yescharacteristic
360C2×C4×D5C23×C311yescharacteristic
361C2×Dic10—28no—
362C2×Dic10—21no—
363C2×Dic10—21no—
364C2×Dic10—21no—
365C2×Dic10—22no—
366C2×Dic10—22no—
367C2×Dic10C3×D411yescharacteristic
368C2×Dic10C23×C311yescharacteristic
369C2×Dic10C23×C311yescharacteristic
370C2×Dic10C23×C311yescharacteristic
371C5×SD16—22no—
372C5×D8—22no—
373C2×C5×C8C23×C311yescharacteristic
374C2×C5×C8C23×C311yescharacteristic
375C5×C4⋊C4C23×C311yescharacteristic
376C5×C22⋊C4—21no—
377C22⋊Dic5—21no—
378C22⋊Dic5—21no—
379#689—22no—
380#687—22no—
381#687—22no—
382#687—22no—
383#685—21no—
384C4⋊Dic5—21no—
385C4⋊Dic5C23×C311yescharacteristic
386#683—21no—
387#683—21no—
388C2×#168C23×C311yescharacteristic
389C2×#168C23×C311yescharacteristic
390Dic20—22no—
391Dic20—22no—
392#676—22no—
393C8×D5—22no—
394C2×2−1+4—51no—
395C2×#137—51no—
396C2×#135—51no—
397#537—51no—
398#452—51no—
399#452—51no—
400#451—51no—
401#451—51no—
402#449—51no—
403#449C3×D511yescharacteristic, complemented
404#448—51no—
405#448—51no—
406#417—51no—
407C2×#103—51no—
408#408—51no—
409C22×C3×C5—21no—
410C22×C3×C5—22no—
411C22×C3×C5—21no—
412C22×C3×C5—21no—
413C22×C3×C5—41no—
414C22×C3×C5—41no—
415C22×C3×C5—41no—
416C22×C3×C5—41no—
417C22×C3×C5—41no—
418C22×C3×C5C22×D411yescharacteristic
419C2×C3×D5—21no—
420C2×C3×D5—21no—
421C2×C3×D5—21no—
422C2×C3×D5—21no—
423C2×C3×D5—21no—
424C2×C3×D5#12012yes—
425C3×C4×C5—21no—
426C3×C4×C5—22no—
427C3×C4×C5—41no—
428C3×C4×C5C22×D411yescharacteristic
429C3×C4×C5C22×D411yescharacteristic
430C3×Dic5—21no—
431C3×Dic5—22no—
432C3×Dic5—22no—
433C3×Dic5—41no—
434C3×Dic5—41no—
435C3×Dic5#12012yes—
436C3×#41—22no—
437C3×#41—22no—
438C3×#41—54no—
439C3×#41—102no—
440C3×#41—102no—
441C3×#41—108no—
442C3×#41—102no—
443C3×#41—102no—
444C3×#41—102no—
445C3×#41—102no—
446C3×#41—108no—
447C3×#41—108no—
448C3×#41—102no—
449C2×C3×Q8—51no—
450C2×C3×Q8—54no—
451C2×C3×Q8—51no—
452C2×C3×Q8—51no—
453C2×C3×Q8—51no—
454C2×C3×Q8—101no—
455C2×C3×Q8—101no—
456C2×C3×Q8—102no—
457C2×C3×Q8—102no—
458C2×C3×Q8—108no—
459C2×C3×Q8—102no—
460C2×C3×Q8—102no—
461C2×C3×Q8—102no—
462C2×C3×Q8—101no—
463C2×C3×Q8C22×D511yescharacteristic
464C2×C3×D4—21no—
465C2×C3×D4—21no—
466C2×C3×D4—51no—
467C2×C3×D4—51no—
468C2×C3×D4—51no—
469C2×C3×D4—101no—
470C2×C3×D4—101no—
471C2×C3×D4—101no—
472C2×C3×D4—101no—
473C2×C3×D4C22×D511yescharacteristic
474C2×C3×D4C22×D511yescharacteristic
475C22×C3×C4—21no—
476C22×C3×C4—51no—
477C22×C3×C4—51no—
478C22×C3×C4—101no—
479C22×C3×C4—101no—
480C22×C3×C4—101no—
481C22×C3×C4—101no—
482C22×C3×C4—101no—
483C22×C3×C4—101no—
484C22×C3×C4—101no—
485C22×C3×C4C22×D511yescharacteristic
486C3×Q16—102no—
487C3×Q16—102no—
488C3×Q16—102no—
489C3×SD16—22no—
490C3×SD16—102no—
491C3×SD16—102no—
492C3×SD16—102no—
493C3×D8—22no—
494C3×M16—102no—
495C2×C3×C8—51no—
496C2×C3×C8—51no—
497C2×C3×C8—102no—
498C2×C3×C8C22×D511yescharacteristic
499C2×C3×C8C22×D511yescharacteristic
500C3×C4⋊C4—51no—
501C3×C4⋊C4—101no—
502C3×C4⋊C4—101no—
503C3×C4⋊C4—101no—
504C3×C4⋊C4C22×D511yescharacteristic
505C3×C22⋊C4—21no—
506C3×C22⋊C4—101no—
507C3×C22⋊C4—101no—
508C3×C22⋊C4—101no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5C2×C3×D411yescharacteristic
512C22×D5C2×C3×D411yescharacteristic
513C22×D5C2×C3×D411yescharacteristic
514C5×Q8—21no—
515C5×Q8C2×C3×D412yes—
516C5×D4—24no—
517C5×D4—21no—
518C5×D4—21no—
519C5×D4—21no—
520C5×D4—81no—
521C5×D4C2×C3×D412yes—
522C2×C4×C5—24no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5C2×C3×D411yescharacteristic
528C2×C4×C5C24×C311yescharacteristic
529C22⋊D5—24no—
530C22⋊D5—22no—
531C22⋊D5—24no—
532C22⋊D5—22no—
533C22⋊D5—42no—
534C22⋊D5—81no—
535C2×Dic5—24no—
536C2×Dic5—24no—
537C2×Dic5—21no—
538C2×Dic5—21no—
539C2×Dic5—24no—
540C2×Dic5—21no—
541C2×Dic5—21no—
542C2×Dic5—42no—
543C2×Dic5C2×C3×D411yescharacteristic
544C2×Dic5C2×C3×D411yescharacteristic
545D20—22no—
546C4×D5—24no—
547C4×D5—24no—
548C4×D5—21no—
549C4×D5—21no—
550C4×D5—81no—
551C4×D5C2×C3×D412yes—
552C4×D5C2×C3×D412yes—
553Dic10—24no—
554Dic10—24no—
555Dic10—21no—
556Dic10—21no—
557Dic10—22no—
558Dic10—24no—
559Dic10—21no—
560Dic10—21no—
561Dic10C2×C3×D412yes—
562Dic10C2×C3×D412yes—
563C5×C8—21no—
564C5×C8—21no—
565#168—21no—
566#168—21no—
5672−1+4—104no—
5682−1+4—104no—
569C2×#41—51no—
570C2×#41—51no—
571C2×#41—51no—
572C2×#41—51no—
573C2×#41—101no—
574C2×#41—101no—
575C2×#41—101no—
576C2×#41C2×C3×D511yescharacteristic
577C22×Q8—51no—
578C22×Q8—51no—
579C22×Q8—51no—
580C22×Q8—101no—
581#137—104no—
582#135—104no—
583C2×Q16—51no—
584C2×Q16—51no—
585C2×Q16—51no—
586C2×SD16—51no—
587C2×SD16—51no—
588C2×SD16—51no—
589C2×SD16C2×C3×D511yescharacteristic
590C2×D8C2×C3×D511yescharacteristic
591C2×M16—51no—
592C22×C8—51no—
593C22⋊Q8—51no—
594C22⋊Q8—51no—
595C22⋊Q8—101no—
596#121—51no—
597#121—101no—
598#121—101no—
599#121—101no—
600#121C2×C3×D511yescharacteristic
601C2×C4⋊C4—51no—
602#103—51no—
603#103—51no—
604#103—51no—
605#103—51no—
606#103—51no—
607#103C2×C3×D511yescharacteristic
608#102—51no—
609#102C2×C3×D511yescharacteristic
610C22⋊C8—51no—
611C22⋊C8—51no—
612C22⋊C8—51no—
613C22⋊C8C2×C3×D511yescharacteristic
614C2×C3×C5—41no—
615C2×C3×C5—42no—
616C2×C3×C5—81no—
617C2×C3×C5C2×#12011yescharacteristic
618C2×C3×C5#57711yescharacteristic
619C2×C3×C5#57811yescharacteristic
620C3×D5—22no—
621C3×D5—41no—
622C23×C3—21no—
623C23×C3—21no—
624C23×C3—51no—
625C23×C3—51no—
626C23×C3D4×D511yescharacteristic
627C3×Q8—21no—
628C3×Q8—52no—
629C3×Q8—52no—
630C3×Q8—102no—
631C3×Q8—104no—
632C3×Q8—104no—
633C3×Q8—104no—
634C3×Q8—101no—
635C3×Q8—101no—
636C3×Q8—101no—
637C3×Q8—101no—
638C3×Q8D4×D512yes—
639C3×D4—24no—
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—81no—
644C3×D4—102no—
645C3×D4—102no—
646C3×D4—102no—
647C3×D4—104no—
648C3×D4—104no—
649C3×D4—202no—
650C3×D4—401no—
651C3×D4D4×D512yes—
652C2×C3×C4—24no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—51no—
658C2×C3×C4—52no—
659C2×C3×C4—52no—
660C2×C3×C4—51no—
661C2×C3×C4—104no—
662C2×C3×C4—104no—
663C2×C3×C4—104no—
664C2×C3×C4—104no—
665C2×C3×C4—104no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—202no—
673C2×C3×C4—401no—
674C2×C3×C4D4×D511yescharacteristic
675C2×C3×C4C23×D511yescharacteristic
676C3×C8—21no—
677C3×C8—21no—
678C3×C8—101no—
679C3×C8—101no—
680C22×C5—21no—
681C22×C5—21no—
682C22×C5—21no—
683C22×C5—22no—
684C22×C5—41no—
685C22×C5—41no—
686C22×C5—41no—
687C22×C5—41no—
688C22×C5—41no—
689C22×C5C22×C3×D411yescharacteristic
690C2×D5—21no—
691C2×D5—21no—
692C2×D5—21no—
693C2×D5—21no—
694C2×D5—21no—
695C2×D5C3×#12012yes—
696C4×C5—21no—
697C4×C5—22no—
698C4×C5—41no—
699C4×C5C22×C3×D411yescharacteristic
700C4×C5C22×C3×D411yescharacteristic
701Dic5—21no—
702Dic5—22no—
703Dic5—22no—
704Dic5—41no—
705Dic5—41no—
706Dic5C3×#12012yes—
707#41—22no—
708#41—22no—
709#41—54no—
710#41—102no—
711#41—102no—
712#41—108no—
713#41—102no—
714#41—102no—
715#41—102no—
716#41—102no—
717#41—108no—
718#41—108no—
719#41—102no—
720C2×Q8—51no—
721C2×Q8—54no—
722C2×Q8—51no—
723C2×Q8—51no—
724C2×Q8—51no—
725C2×Q8—101no—
726C2×Q8—101no—
727C2×Q8—102no—
728C2×Q8—102no—
729C2×Q8—108no—
730C2×Q8—102no—
731C2×Q8—102no—
732C2×Q8—102no—
733C2×Q8—101no—
734C2×Q8C22×C3×D511yescharacteristic
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—51no—
738C2×D4—51no—
739C2×D4—51no—
740C2×D4—101no—
741C2×D4—101no—
742C2×D4—101no—
743C2×D4—101no—
744C2×D4C22×C3×D511yescharacteristic
745C2×D4C22×C3×D511yescharacteristic
746C22×C4—21no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—101no—
750C22×C4—101no—
751C22×C4—101no—
752C22×C4—101no—
753C22×C4—101no—
754C22×C4—101no—
755C22×C4—101no—
756C22×C4C22×C3×D511yescharacteristic
757Q16—102no—
758Q16—102no—
759Q16—102no—
760SD16—22no—
761SD16—102no—
762SD16—102no—
763SD16—102no—
764D8—22no—
765M16—102no—
766C2×C8—51no—
767C2×C8—51no—
768C2×C8—102no—
769C2×C8C22×C3×D511yescharacteristic
770C2×C8C22×C3×D511yescharacteristic
771C4⋊C4—51no—
772C4⋊C4—101no—
773C4⋊C4—101no—
774C4⋊C4—101no—
775C4⋊C4C22×C3×D511yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—101no—
778C22⋊C4—101no—
779C22⋊C4—101no—
780C3×C5#301311yescharacteristic, complemented, Hall
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—22no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—52no—
791C22×C3—101no—
792C22×C3—101no—
793C22×C3—101no—
794C22×C3—101no—
795C22×C3—101no—
796C22×C3C2×D4×D511yescharacteristic
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—41no—
800C3×C4—52no—
801C3×C4—101no—
802C3×C4—102no—
803C3×C4—102no—
804C3×C4—201no—
805C3×C4—201no—
806C3×C4C2×D4×D511yescharacteristic
807C3×C4C2×D4×D511yescharacteristic
808C2×C5—41no—
809C2×C5—42no—
810C2×C5—81no—
811C2×C5C2×C3×#12011yescharacteristic
812C2×C5C3×#57711yescharacteristic
813C2×C5C3×#57811yescharacteristic
814D5—22no—
815D5—41no—
816C23—21no—
817C23—21no—
818C23—51no—
819C23—51no—
820C23C3×D4×D511yescharacteristic
821Q8—21no—
822Q8—52no—
823Q8—52no—
824Q8—102no—
825Q8—104no—
826Q8—104no—
827Q8—104no—
828Q8—101no—
829Q8—101no—
830Q8—101no—
831Q8—101no—
832Q8C3×D4×D512yes—
833D4—24no—
834D4—21no—
835D4—21no—
836D4—21no—
837D4—81no—
838D4—102no—
839D4—102no—
840D4—102no—
841D4—104no—
842D4—104no—
843D4—202no—
844D4—401no—
845D4C3×D4×D512yes—
846C2×C4—24no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—51no—
852C2×C4—52no—
853C2×C4—52no—
854C2×C4—51no—
855C2×C4—104no—
856C2×C4—104no—
857C2×C4—104no—
858C2×C4—104no—
859C2×C4—104no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—202no—
867C2×C4—401no—
868C2×C4C3×D4×D511yescharacteristic
869C2×C4C23×C3×D511yescharacteristic
870C8—21no—
871C8—21no—
872C8—101no—
873C8—101no—
874C2×C3—41no—
875C2×C3—42no—
876C2×C3—81no—
877C2×C3—102no—
878C2×C3—201no—
879C2×C3D5×#12011yescharacteristic
880C2×C3#6610511yescharacteristic
881C2×C3#6610911yescharacteristic
882C5C3×#301311yescharacteristic, complemented, Sylow
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—52no—
893C22—101no—
894C22—101no—
895C22—101no—
896C22—101no—
897C22—101no—
898C22C2×C3×D4×D511yescharacteristic
899C4—21no—
900C4—22no—
901C4—41no—
902C4—52no—
903C4—101no—
904C4—102no—
905C4—102no—
906C4—201no—
907C4—201no—
908C4C2×C3×D4×D511yescharacteristic
909C4C2×C3×D4×D511yescharacteristic
910C3#1061181911yescharacteristic, direct product factor, Sylow
911C2—41no—
912C2—42no—
913C2—81no—
914C2—102no—
915C2—201no—
916C2C3×D5×#12011yescharacteristic
917C2C3×#6610511yescharacteristic
918C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenterC3×#449D5
hypocenterC5C3×#3013
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4150C2semidirect
2. C2×C3×#4061C2semidirect
3. C2×C3×#4058C2semidirect
4. C3×#65942C2semidirect
5. C3×C5×#449C2semidirect
6. C3×#65528C2semidirect
7. C3×#65459C2semidirect
8. C3×#65447C2semidirect
9. C3×#65329C2semidirect
10. C3×#65097C2semidirect
11. C3×D5×#103C2semidirect
12. C3×#65072C2semidirect
13. C3×#65060C2semidirect
14. C3×#65028C2semidirect
15. C3×#65016C2semidirect
16. #10611819C3direct (N × H)
65. C2×#4150C2×C3semidirect
66. C2×#4061C2×C3semidirect
67. C2×#4058C2×C3semidirect
68. #65942C2×C3semidirect
69. C5×#449C2×C3semidirect
70. #65528C2×C3semidirect
71. #65459C2×C3semidirect
72. #65447C2×C3semidirect
73. #65329C2×C3semidirect
74. #65097C2×C3semidirect
75. D5×#103C2×C3semidirect
76. #65072C2×C3semidirect
77. #65060C2×C3semidirect
78. #65028C2×C3semidirect
79. #65016C2×C3semidirect
102. C3×Q8×D5D4semidirect
110. C3×#711D4semidirect
162. C3×#449D5semidirect
343. Q8×D5C3×D4semidirect
351. #711C3×D4semidirect
403. #449C3×D5semidirect
780. C3×C5#3013semidirect
882. C5C3×#3013semidirect
910. C3#10611819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×C3×#40612
C2×C3×#40582
C3×#659422
C3×C5×#4492
C3×#655282
C3×#654592
C3×#654472
C3×#653292
C3×#650972
C3×D5×#1032
C3×#650722
C3×#650602
C3×#650282
C3×#650162
#106118193
C3×#30135