Finite Group Databasebeta

← C3×#10611610 #14453965

Subgroups — C3×#10611610 #14453965

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4058C211yesmaximal, characteristic, complemented
2C2×C3×#4057C211yesmaximal, characteristic, complemented
3C3×#65889C211yesmaximal, characteristic, complemented
4C3×#65888C211yesmaximal, characteristic, complemented
5C3×C5×#442C211yesmaximal, characteristic, complemented
6C3×#65308C211yesmaximal, characteristic, complemented
7C3×#65305C211yesmaximal, characteristic, complemented
8C3×#65157C211yesmaximal, characteristic, complemented
9C3×#65153C211yesmaximal, characteristic, complemented
10C3×#65072C211yesmaximal, characteristic, complemented
11C3×#65072C211yesmaximal, characteristic, complemented
12C3×#65070C211yesmaximal, characteristic, complemented
13C3×#65065C211yesmaximal, characteristic, complemented
14C3×#65004C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10611610C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×D8C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic, complemented
24C2×C3×#687C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C2×C3×#687C2211yescharacteristic, complemented
27C2×C3×#686C2211yescharacteristic
28C3×#4076—21no—
29C3×#4076—21no—
30C2×C3×#685—21no—
31C2×C3×C4⋊Dic5—21no—
32C3×#4058—24no—
33C3×#4057—24no—
34C2×C3×Dic20C2211yescharacteristic, complemented
35C2×C3×Dic20C2211yescharacteristic, complemented
36C2×C3×#677C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×#676C2211yescharacteristic
39C2×C3×C8×D5C2211yescharacteristic, complemented
40C3×#4043C2211yescharacteristic
41C3×#4043C2211yescharacteristic
42C3×#4043C2211yescharacteristic, complemented
43C3×#4041C2211yescharacteristic
44C3×#4032—21no—
45C3×#4032—21no—
46C3×#4032—21no—
47C3×#4028—21no—
48C3×#4021C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×#4015C2211yescharacteristic, complemented
51C3×C5×#106C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic
53C3×C5×#102C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic
56C3×#3952C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58C3×#3942C2211yescharacteristic, complemented
59C3×#3942C2211yescharacteristic, complemented
60C3×#3941C2211yescharacteristic
61C3×C4⋊#168C2211yescharacteristic, complemented
62C3×#3267—51nomaximal, Hall
63C2×#4058C2×C311yescharacteristic, complemented
64C2×#4057C2×C311yescharacteristic, complemented
65#65889C2×C311yescharacteristic, complemented
66#65888C2×C311yescharacteristic, complemented
67C5×#442C2×C311yescharacteristic, complemented
68#65308C2×C311yescharacteristic, complemented
69#65305C2×C311yescharacteristic, complemented
70#65157C2×C311yescharacteristic, complemented
71#65153C2×C311yescharacteristic, complemented
72#65072C2×C311yescharacteristic, complemented
73#65072C2×C311yescharacteristic, complemented
74#65070C2×C311yescharacteristic, complemented
75#65065C2×C311yescharacteristic, complemented
76#65004C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C22×C3×Dic5—21no—
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C3×#711—22no—
91C3×#711—22no—
92C3×#711—22no—
93C3×#711—41no—
94C3×#711—41no—
95C3×#711—41no—
96C3×D4×D5—22no—
97C3×D4×D5—41no—
98C2×C3×D20—21no—
99C2×C3×D20D411yescharacteristic
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×C4×D5C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C3×C5×D8D414yescomplemented
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C3×C5×C4⋊C4C2311yescharacteristic
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C42×C5C2311yescharacteristic
114C3×#687—22no—
115C3×#687—22no—
116C3×#687—22no—
117C3×#686—22no—
118C3×#685—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685D411yescharacteristic
125C3×#685D411yescharacteristic
126C3×C4⋊Dic5—21no—
127C3×C4⋊Dic5—21no—
128C3×C4⋊Dic5—21no—
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5—21no—
131C3×C4⋊Dic5D411yescharacteristic
132C2×C3×#168C2311yescharacteristic
133C2×C3×#168C2311yescharacteristic
134C3×Dic20—22no—
135C3×Dic20—41no—
136C3×#677—22no—
137C3×#677—41no—
138C3×#676—22no—
139C3×C8×D5—22no—
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#547—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#470—51no—
146C3×#465—51no—
147C3×#463—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#452—51no—
151C3×#450—51no—
152C3×#449—51no—
153C3×#442D511yescharacteristic, complemented
154C3×#435—51no—
155C2×#711C22×C311yescharacteristic
156C2×#711C22×C311yescharacteristic
157C2×#711C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×D8C22×C311yescharacteristic
160C4×C5×D4C22×C311yescharacteristic
161C4×C5×D4C22×C311yescharacteristic, complemented
162C2×#687C22×C311yescharacteristic
163C2×#687C22×C311yescharacteristic
164C2×#687C22×C311yescharacteristic, complemented
165C2×#686C22×C311yescharacteristic
166#4076—21no—
167#4076—21no—
168C2×#685—21no—
169C2×C4⋊Dic5—21no—
170#4058—24no—
171#4057—24no—
172C2×Dic20C22×C311yescharacteristic, complemented
173C2×Dic20C22×C311yescharacteristic, complemented
174C2×#677C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×#676C22×C311yescharacteristic
177C2×C8×D5C22×C311yescharacteristic, complemented
178#4043C22×C311yescharacteristic
179#4043C22×C311yescharacteristic
180#4043C22×C311yescharacteristic, complemented
181#4041C22×C311yescharacteristic
182#4032—21no—
183#4032—21no—
184#4032—21no—
185#4028—21no—
186#4021C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188#4015C22×C311yescharacteristic, complemented
189C5×#106C22×C311yescharacteristic, complemented
190C5×#102C22×C311yescharacteristic
191C5×#102C22×C311yescharacteristic, complemented
192C5×#97C22×C311yescharacteristic, complemented
193#3952C22×C311yescharacteristic
194#3952C22×C311yescharacteristic, complemented
195#3942C22×C311yescharacteristic, complemented
196#3942C22×C311yescharacteristic, complemented
197#3942C22×C311yescharacteristic, complemented
198#3941C22×C311yescharacteristic
199C4⋊#168C22×C311yescharacteristic, complemented
200#3267—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—42no—
205C22×C3×D5—42no—
206C22×C3×D5—81no—
207C22×C3×D5C2×D411yescharacteristic
208C22×C3×D5C2×D411yescharacteristic
209C3×C5×D4—21no—
210C3×C5×D4—21no—
211C3×C5×D4C2×D412yes—
212C3×C5×D4C2×D412yes—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—42no—
216C2×C3×C4×C5—81no—
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2411yescharacteristic
220C3×C22⋊D5—42no—
221C3×C22⋊D5—42no—
222C3×C22⋊D5—42no—
223C3×C22⋊D5—42no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—42no—
228C2×C3×Dic5—42no—
229C2×C3×Dic5—42no—
230C2×C3×Dic5C2×D411yescharacteristic
231C2×C3×Dic5C2×D411yescharacteristic
232C3×D20—21no—
233C3×D20—21no—
234C3×D20—41no—
235C3×D20—81no—
236C3×C4×D5—21no—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—21no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C3×Dic10—21no—
246C3×C5×C8—21no—
247C3×C5×C8C2×D412yes—
248C3×#168—21no—
249C3×#168—21no—
250C2×C3×#41—51no—
251C2×C3×#41—51no—
252C2×C3×#41—51no—
253C22×C3×D4—51no—
254C3×AGL(1,ℤ/8)—104no—
255C3×#135—104no—
256C2×C3×Q16—51no—
257C2×C3×Q16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×D8—51no—
264C2×C3×D8C2×D511yescharacteristic
265C2×C3×M16—51no—
266C22×C3×C8—51no—
267C3×C4⋊Q8—51no—
268C3×#124—51no—
269C3×#123—101no—
270C3×#123—101no—
271C3×#123—101no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—51no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#121—101no—
278C3×#120—101no—
279C3×C4×D4—51no—
280C3×C4×D4C2×D511yescharacteristic
281C3×C4×D4C2×D511yescharacteristic, complemented
282C2×C3×C4⋊C4—101no—
283C2×C3×C22⋊C4—101no—
284C3×#106C2×D511yescharacteristic, complemented
285C3×C4⋊C8—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103—51no—
289C3×#102—51no—
290C3×#102C2×D511yescharacteristic
291C3×#102C2×D511yescharacteristic, complemented
292C3×C22⋊C8—51no—
293C3×C22⋊C8—51no—
294C3×#97C2×D511yescharacteristic, complemented
295C23×D5—21no—
296C2×C5×D4C23×C311yescharacteristic
297C2×C5×D4C23×C311yescharacteristic
298C22×C4×C5—21no—
299C22×C4×C5—21no—
300C2×C22⋊D5—21no—
301C2×C22⋊D5—21no—
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304C22×Dic5—21no—
305C22×Dic5—21no—
306C22×Dic5—21no—
307#711—22no—
308#711—22no—
309#711—22no—
310#711—41no—
311#711—41no—
312#711—41no—
313D4×D5—22no—
314D4×D5—41no—
315C2×D20—21no—
316C2×D20C3×D411yescharacteristic
317C2×D20C23×C311yescharacteristic
318C2×C4×D5C23×C311yescharacteristic
319C2×C4×D5C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C2×Dic10C23×C311yescharacteristic
322C2×Dic10C23×C311yescharacteristic
323C5×D8C3×D414yescomplemented
324C2×C5×C8C23×C311yescharacteristic
325C2×C5×C8C23×C311yescharacteristic
326C5×C4⋊C4C23×C311yescharacteristic
327C5×C4⋊C4C23×C311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—21no—
330C42×C5C23×C311yescharacteristic
331#687—22no—
332#687—22no—
333#687—22no—
334#686—22no—
335#685—21no—
336#685—21no—
337#685—21no—
338#685—21no—
339#685—21no—
340#685—21no—
341#685C3×D411yescharacteristic
342#685C3×D411yescharacteristic
343C4⋊Dic5—21no—
344C4⋊Dic5—21no—
345C4⋊Dic5—21no—
346C4⋊Dic5—21no—
347C4⋊Dic5—21no—
348C4⋊Dic5C3×D411yescharacteristic
349C2×#168C23×C311yescharacteristic
350C2×#168C23×C311yescharacteristic
351Dic20—22no—
352Dic20—41no—
353#677—22no—
354#677—41no—
355#676—22no—
356C8×D5—22no—
357C2×AGL(1,ℤ/8)—51no—
358C2×#135—51no—
359#547—51no—
360#546—51no—
361#497—51no—
362#470—51no—
363#465—51no—
364#463—51no—
365#461—51no—
366#452—51no—
367#452—51no—
368#450—51no—
369#449—51no—
370#442C3×D511yescharacteristic, complemented
371#435—51no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C22×D411yescharacteristic
379C2×C3×D5—21no—
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
383C2×C3×D5—21no—
384C2×C3×D5—21no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395C3×Dic5—21no—
396C3×Dic5—21no—
397C3×Dic5—41no—
398C3×Dic5—41no—
399C3×Dic5—41no—
400C24×C3—101no—
401C3×#41—102no—
402C3×#41—102no—
403C3×#41—102no—
404C3×#41—201no—
405C3×#41—201no—
406C3×#41—201no—
407C2×C3×Q8—51no—
408C2×C3×Q8—51no—
409C2×C3×Q8—51no—
410C2×C3×D4—51no—
411C2×C3×D4—51no—
412C2×C3×D4—101no—
413C2×C3×D4—101no—
414C2×C3×D4—102no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4—201no—
419C2×C3×D4C22×D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
421C22×C3×C4—21no—
422C22×C3×C4—21no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—101no—
426C22×C3×C4—101no—
427C22×C3×C4—101no—
428C3×Q16—102no—
429C3×Q16—201no—
430C3×SD16—102no—
431C3×SD16—102no—
432C3×SD16—102no—
433C3×SD16—102no—
434C3×SD16—201no—
435C3×D8—102no—
436C3×D8D2014yescomplemented
437C3×M16—102no—
438C2×C3×C8—51no—
439C2×C3×C8—51no—
440C2×C3×C8—102no—
441C2×C3×C8C22×D511yescharacteristic
442C2×C3×C8C22×D511yescharacteristic
443C3×C4⋊C4—51no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4—101no—
447C3×C4⋊C4—101no—
448C3×C4⋊C4—101no—
449C3×C4⋊C4C22×D511yescharacteristic
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—21no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—51no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C42C22×D511yescharacteristic
462C23×C5—21no—
463C23×C5—21no—
464C22×D5—21no—
465C22×D5—42no—
466C22×D5—42no—
467C22×D5—81no—
468C22×D5C2×C3×D411yescharacteristic
469C22×D5C2×C3×D411yescharacteristic
470C5×D4—21no—
471C5×D4—21no—
472C5×D4C2×C3×D412yes—
473C5×D4C2×C3×D412yes—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—42no—
477C2×C4×C5—81no—
478C2×C4×C5C2×C3×D411yescharacteristic
479C2×C4×C5C2×C3×D411yescharacteristic
480C2×C4×C5C24×C311yescharacteristic
481C22⋊D5—42no—
482C22⋊D5—42no—
483C22⋊D5—42no—
484C22⋊D5—42no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—42no—
489C2×Dic5—42no—
490C2×Dic5—42no—
491C2×Dic5C2×C3×D411yescharacteristic
492C2×Dic5C2×C3×D411yescharacteristic
493D20—21no—
494D20—21no—
495D20—41no—
496D20—81no—
497C4×D5—21no—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—21no—
501Dic10—21no—
502Dic10—21no—
503Dic10—21no—
504Dic10—21no—
505Dic10—21no—
506Dic10—21no—
507C5×C8—21no—
508C5×C8C2×C3×D412yes—
509#168—21no—
510#168—21no—
511C2×#41—51no—
512C2×#41—51no—
513C2×#41—51no—
514C22×D4—51no—
515AGL(1,ℤ/8)—104no—
516#135—104no—
517C2×Q16—51no—
518C2×Q16—51no—
519C2×SD16—51no—
520C2×SD16—51no—
521C2×SD16—51no—
522C2×SD16—51no—
523C2×SD16—51no—
524C2×D8—51no—
525C2×D8C2×C3×D511yescharacteristic
526C2×M16—51no—
527C22×C8—51no—
528C4⋊Q8—51no—
529#124—51no—
530#123—101no—
531#123—101no—
532#123—101no—
533C22⋊Q8—51no—
534C22⋊Q8—51no—
535C22⋊Q8—51no—
536#121—51no—
537#121—101no—
538#121—101no—
539#120—101no—
540C4×D4—51no—
541C4×D4C2×C3×D511yescharacteristic
542C4×D4C2×C3×D511yescharacteristic, complemented
543C2×C4⋊C4—101no—
544C2×C22⋊C4—101no—
545#106C2×C3×D511yescharacteristic, complemented
546C4⋊C8—51no—
547#103—51no—
548#103—51no—
549#103—51no—
550#102—51no—
551#102C2×C3×D511yescharacteristic
552#102C2×C3×D511yescharacteristic, complemented
553C22⋊C8—51no—
554C22⋊C8—51no—
555#97C2×C3×D511yescharacteristic, complemented
556C2×C3×C5—42no—
557C2×C3×C5—42no—
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#57511yescharacteristic
560C2×C3×C5#57711yescharacteristic
561C3×D5—41no—
562C3×D5—41no—
563C3×D5—81no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—51no—
567C23×C3—51no—
568C23×C3—101no—
569C23×C3—202no—
570C23×C3—202no—
571C23×C3—401no—
572C3×Q8—101no—
573C3×Q8—101no—
574C3×Q8—101no—
575C3×Q8—101no—
576C3×Q8—101no—
577C3×Q8—101no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—101no—
581C3×D4—101no—
582C3×D4—201no—
583C3×D4—202no—
584C3×D4—202no—
585C3×D4—202no—
586C3×D4—202no—
587C3×D4—401no—
588C3×D4C2×D2012yes—
589C3×D4C2×D2012yes—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—42no—
593C2×C3×C4—51no—
594C2×C3×C4—51no—
595C2×C3×C4—81no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4—101no—
602C2×C3×C4—101no—
603C2×C3×C4—202no—
604C2×C3×C4—202no—
605C2×C3×C4—202no—
606C2×C3×C4D4×D511yescharacteristic
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609C3×C8—21no—
610C3×C8—101no—
611C3×C8—101no—
612C3×C8C2×D2012yes—
613C22×C5—22no—
614C22×C5—22no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5C22×C3×D411yescharacteristic
620C2×D5—21no—
621C2×D5—21no—
622C2×D5—21no—
623C2×D5—21no—
624C2×D5—21no—
625C2×D5—21no—
626C2×D5—41no—
627C2×D5—41no—
628C2×D5—41no—
629C2×D5—84no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5C22×C3×D411yescharacteristic
635C4×C5C3×H(5,𝔽2)11yescharacteristic
636Dic5—21no—
637Dic5—21no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641C24—101no—
642#41—102no—
643#41—102no—
644#41—102no—
645#41—201no—
646#41—201no—
647#41—201no—
648C2×Q8—51no—
649C2×Q8—51no—
650C2×Q8—51no—
651C2×D4—51no—
652C2×D4—51no—
653C2×D4—101no—
654C2×D4—101no—
655C2×D4—102no—
656C2×D4—101no—
657C2×D4—101no—
658C2×D4—101no—
659C2×D4—201no—
660C2×D4C22×C3×D511yescharacteristic
661C2×D4C22×C3×D511yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669Q16—102no—
670Q16—201no—
671SD16—102no—
672SD16—102no—
673SD16—102no—
674SD16—102no—
675SD16—201no—
676D8—102no—
677D8C3×D2014yescomplemented
678M16—102no—
679C2×C8—51no—
680C2×C8—51no—
681C2×C8—102no—
682C2×C8C22×C3×D511yescharacteristic
683C2×C8C22×C3×D511yescharacteristic
684C4⋊C4—51no—
685C4⋊C4—101no—
686C4⋊C4—101no—
687C4⋊C4—101no—
688C4⋊C4—101no—
689C4⋊C4—101no—
690C4⋊C4C22×C3×D511yescharacteristic
691C4⋊C4C22×C3×D511yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—51no—
695C22⋊C4—51no—
696C22⋊C4—101no—
697C22⋊C4—101no—
698C22⋊C4—101no—
699C22⋊C4—101no—
700C22⋊C4—101no—
701C22⋊C4—101no—
702C42C22×C3×D511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—101no—
711C22×C3—101no—
712C22×C3—101no—
713C22×C3—101no—
714C22×C3—101no—
715C22×C3—101no—
716C22×C3—201no—
717C22×C3—201no—
718C22×C3—201no—
719C22×C3—404no—
720C22×C3C2×D4×D511yescharacteristic
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—101no—
726C3×C4—101no—
727C3×C4—201no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4C22×D2011yescharacteristic
731C3×C4#414911yescharacteristic
732C2×C5—42no—
733C2×C5—42no—
734C2×C5C3×D4211yescharacteristic
735C2×C5C3×#57511yescharacteristic
736C2×C5C3×#57711yescharacteristic
737D5—41no—
738D5—41no—
739D5—81no—
740C23—21no—
741C23—21no—
742C23—51no—
743C23—51no—
744C23—101no—
745C23—202no—
746C23—202no—
747C23—401no—
748Q8—101no—
749Q8—101no—
750Q8—101no—
751Q8—101no—
752Q8—101no—
753Q8—101no—
754D4—21no—
755D4—21no—
756D4—101no—
757D4—101no—
758D4—201no—
759D4—202no—
760D4—202no—
761D4—202no—
762D4—202no—
763D4—401no—
764D4C2×C3×D2012yes—
765D4C2×C3×D2012yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—42no—
769C2×C4—51no—
770C2×C4—51no—
771C2×C4—81no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—202no—
782C2×C4C3×D4×D511yescharacteristic
783C2×C4C3×D4×D511yescharacteristic
784C2×C4C23×C3×D511yescharacteristic
785C8—21no—
786C8—101no—
787C8—101no—
788C8C2×C3×D2012yes—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—201no—
792C2×C3—201no—
793C2×C3—401no—
794C2×C3D4×D2011yescharacteristic
795C2×C3#6610711yescharacteristic
796C2×C3#6610911yescharacteristic
797C5C3×#326711yescharacteristic, complemented, Sylow
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—101no—
805C22—101no—
806C22—101no—
807C22—101no—
808C22—101no—
809C22—101no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—404no—
814C22C2×C3×D4×D511yescharacteristic
815C4—21no—
816C4—21no—
817C4—41no—
818C4—41no—
819C4—101no—
820C4—101no—
821C4—201no—
822C4—201no—
823C4—201no—
824C4C22×C3×D2011yescharacteristic
825C4C3×#414911yescharacteristic
826C3#1061161011yescharacteristic, direct product factor, Sylow
827C2—42no—
828C2—42no—
829C2—201no—
830C2—201no—
831C2—401no—
832C2C3×D4×D2011yescharacteristic
833C2C3×#6610711yescharacteristic
834C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#442C2
socleC22×C3×C5C22×D4
hypercenterC3×#442D5
hypocenterC5C3×#3267
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4058C2semidirect
2. C2×C3×#4057C2semidirect
3. C3×#65889C2semidirect
4. C3×#65888C2semidirect
5. C3×C5×#442C2semidirect
6. C3×#65308C2semidirect
7. C3×#65305C2semidirect
8. C3×#65157C2semidirect
9. C3×#65153C2semidirect
10. C3×#65072C2semidirect
11. C3×#65072C2semidirect
12. C3×#65070C2semidirect
13. C3×#65065C2semidirect
14. C3×#65004C2semidirect
15. C3×#64995C2semidirect
16. #10611610C3direct (N × H)
19. C2×C3×#711C22semidirect
23. C3×C4×C5×D4C22semidirect
26. C2×C3×#687C22semidirect
34. C2×C3×Dic20C22semidirect
35. C2×C3×Dic20C22semidirect
39. C2×C3×C8×D5C22semidirect
42. C3×#4043C22semidirect
50. C3×#4015C22semidirect
51. C3×C5×#106C22semidirect
53. C3×C5×#102C22semidirect
54. C3×C5×#97C22semidirect
56. C3×#3952C22semidirect
57. C3×#3942C22semidirect
58. C3×#3942C22semidirect
59. C3×#3942C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4058C2×C3semidirect
64. C2×#4057C2×C3semidirect
65. #65889C2×C3semidirect
66. #65888C2×C3semidirect
67. C5×#442C2×C3semidirect
68. #65308C2×C3semidirect
69. #65305C2×C3semidirect
70. #65157C2×C3semidirect
71. #65153C2×C3semidirect
72. #65072C2×C3semidirect
73. #65072C2×C3semidirect
74. #65070C2×C3semidirect
75. #65065C2×C3semidirect
76. #65004C2×C3semidirect
77. #64995C2×C3semidirect
106. C3×C5×D8D4semidirect
153. C3×#442D5semidirect
157. C2×#711C22×C3semidirect
161. C4×C5×D4C22×C3semidirect
164. C2×#687C22×C3semidirect
172. C2×Dic20C22×C3semidirect
173. C2×Dic20C22×C3semidirect
177. C2×C8×D5C22×C3semidirect
180. #4043C22×C3semidirect
188. #4015C22×C3semidirect
189. C5×#106C22×C3semidirect
191. C5×#102C22×C3semidirect
192. C5×#97C22×C3semidirect
194. #3952C22×C3semidirect
195. #3942C22×C3semidirect
196. #3942C22×C3semidirect
197. #3942C22×C3semidirect
199. C4⋊#168C22×C3semidirect
281. C3×C4×D4C2×D5semidirect
284. C3×#106C2×D5semidirect
291. C3×#102C2×D5semidirect
294. C3×#97C2×D5semidirect
323. C5×D8C3×D4semidirect
370. #442C3×D5semidirect
436. C3×D8D20semidirect
542. C4×D4C2×C3×D5semidirect
545. #106C2×C3×D5semidirect
552. #102C2×C3×D5semidirect
555. #97C2×C3×D5semidirect
677. D8C3×D20semidirect
703. C3×C5#3267semidirect
797. C5C3×#3267semidirect
826. C3#10611610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40582
C2×C3×#40572
C3×#658892
C3×#658882
C3×C5×#4422
C3×#653082
C3×#653052
C3×#651572
C3×#651532
C3×#650722
C3×#650702
C3×#650652
C3×#650042
C3×#649952
#106116103
C3×#32675