Finite Group Databasebeta

← C3×#10611526 #14453710

Subgroups — C3×#10611526 #14453710

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4061C211yesmaximal, characteristic, complemented
2C2×C3×D5×SD16C211yesmaximal, characteristic, complemented
3C3×Q8×D20C211yesmaximal, characteristic, complemented
4C3×#65888C211yesmaximal, characteristic
5C3×C5×#440C211yesmaximal, characteristic, complemented
6C3×#65317C211yesmaximal, characteristic, complemented
7C3×#65308C211yesmaximal, characteristic, complemented
8C3×#65176C211yesmaximal, characteristic, complemented
9C3×#65175C211yesmaximal, characteristic, complemented
10C3×#65097C211yesmaximal, characteristic, complemented
11C3×#65095C211yesmaximal, characteristic, complemented
12C3×#65072C211yesmaximal, characteristic, complemented
13C3×#65065C211yesmaximal, characteristic, complemented
14C3×#65004C211yesmaximal, characteristic, complemented
15C3×#64995C211yesmaximal, characteristic, complemented
16#10611526C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic, complemented
19C2×C3×#711C2211yescharacteristic
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×SD16C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic, complemented
23C3×C4×C5×D4C2211yescharacteristic
24C2×C3×#689C2211yescharacteristic, complemented
25C2×C3×#688C2211yescharacteristic
26C2×C3×#687C2211yescharacteristic
27C2×C3×#687C2211yescharacteristic
28C3×#4076—21no—
29C2×C3×#685—21no—
30C3×#4061—24no—
31C3×D5×SD16—24no—
32C2×C3×Dic20C2211yescharacteristic, complemented
33C2×C3×Dic20C2211yescharacteristic, complemented
34C2×C3×#677C2211yescharacteristic
35C2×C3×#677C2211yescharacteristic
36C2×C3×#676C2211yescharacteristic, complemented
37C2×C3×C8×D5C2211yescharacteristic
38C3×#4043—21no—
39C3×#4043—21no—
40C3×#4043C2211yescharacteristic
41C3×#4043C2211yescharacteristic
42C3×#4043C2211yescharacteristic, complemented
43C3×#4041C2211yescharacteristic
44C3×#4032—21no—
45C3×#4028—21no—
46C3×#4021C2211yescharacteristic
47C3×C4×D20—21no—
48C3×C4×D20C2211yescharacteristic
49C3×#4015—21no—
50C3×#4015C2211yescharacteristic, complemented
51C3×C5×#107C2211yescharacteristic, complemented
52C3×C5×#103C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic
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×#3266—51nomaximal, Hall
63C2×#4061C2×C311yescharacteristic, complemented
64C2×D5×SD16C2×C311yescharacteristic, complemented
65Q8×D20C2×C311yescharacteristic, complemented
66#65888C2×C311yescharacteristic
67C5×#440C2×C311yescharacteristic, complemented
68#65317C2×C311yescharacteristic, complemented
69#65308C2×C311yescharacteristic, complemented
70#65176C2×C311yescharacteristic, complemented
71#65175C2×C311yescharacteristic, complemented
72#65097C2×C311yescharacteristic, complemented
73#65095C2×C311yescharacteristic, complemented
74#65072C2×C311yescharacteristic, complemented
75#65065C2×C311yescharacteristic, complemented
76#65004C2×C311yescharacteristic, complemented
77#64995C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C3×Q8×D5—22no—
86C3×Q8×D5—22no—
87C3×Q8×D5—41no—
88C3×Q8×D5—41no—
89C3×#711—22no—
90C3×#711—41no—
91C3×D4×D5—22no—
92C3×D4×D5—41no—
93C2×C3×D20—21no—
94C2×C3×D20D411yescharacteristic
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5C2311yescharacteristic
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10—21no—
101C2×C3×Dic10—21no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×SD16D414yescomplemented
106C2×C3×C5×C8C2311yescharacteristic
107C2×C3×C5×C8C2311yescharacteristic
108C3×C5×C4⋊C4—21no—
109C3×C5×C4⋊C4C2311yescharacteristic
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112C3×C42×C5—21no—
113C3×C42×C5C2311yescharacteristic
114C3×#689—22no—
115C3×#688—22no—
116C3×#687—22no—
117C3×#687—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×#137—51no—
141C22×C3×SD16—51no—
142C3×D4×Q8—51no—
143C3×#546—51no—
144C3×#497—51no—
145C3×#468—51no—
146C3×#467—51no—
147C3×#464—51no—
148C3×#461—51no—
149C3×#452—51no—
150C3×#451—51no—
151C3×#450—51no—
152C3×#448—51no—
153C3×#440D511yescharacteristic, complemented
154C3×#435—51no—
155C2×Q8×D5C22×C311yescharacteristic
156C2×Q8×D5C22×C311yescharacteristic, complemented
157C2×#711C22×C311yescharacteristic
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×SD16C22×C311yescharacteristic
160C4×C5×Q8C22×C311yescharacteristic, complemented
161C4×C5×D4C22×C311yescharacteristic
162C2×#689C22×C311yescharacteristic, complemented
163C2×#688C22×C311yescharacteristic
164C2×#687C22×C311yescharacteristic
165C2×#687C22×C311yescharacteristic
166#4076—21no—
167C2×#685—21no—
168#4061—24no—
169D5×SD16—24no—
170C2×Dic20C22×C311yescharacteristic, complemented
171C2×Dic20C22×C311yescharacteristic, complemented
172C2×#677C22×C311yescharacteristic
173C2×#677C22×C311yescharacteristic
174C2×#676C22×C311yescharacteristic, complemented
175C2×C8×D5C22×C311yescharacteristic
176#4043—21no—
177#4043—21no—
178#4043C22×C311yescharacteristic
179#4043C22×C311yescharacteristic
180#4043C22×C311yescharacteristic, complemented
181#4041C22×C311yescharacteristic
182#4032—21no—
183#4028—21no—
184#4021C22×C311yescharacteristic
185C4×D20—21no—
186C4×D20C22×C311yescharacteristic
187#4015—21no—
188#4015C22×C311yescharacteristic, complemented
189C5×#107C22×C311yescharacteristic, complemented
190C5×#103C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic
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#3266—51noSylow
201C23×C3×C5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—42no—
204C22×C3×D5—42no—
205C22×C3×D5—81no—
206C22×C3×D5C2×D411yescharacteristic
207C22×C3×D5C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8C2×D412yes—
210C3×C5×D4—21no—
211C3×C5×D4C2×D412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—81no—
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2411yescharacteristic
219C3×C22⋊D5—42no—
220C3×C22⋊D5—42no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—42no—
225C2×C3×Dic5C2×D411yescharacteristic
226C2×C3×Dic5C2×D411yescharacteristic
227C3×D20—22no—
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—81no—
231C3×C4×D5—21no—
232C3×C4×D5—21no—
233C3×C4×D5—21no—
234C3×C4×D5—21no—
235C3×C4×D5—42no—
236C3×C4×D5—42no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—21no—
243C3×Dic10—42no—
244C3×Dic10—42no—
245C3×C5×C8—21no—
246C3×C5×C8C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C2×C3×#41—51no—
250C22×C3×Q8—51no—
251C22×C3×Q8—51no—
252C22×C3×D4—51no—
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×Q16—51no—
257C2×C3×SD16—51no—
258C2×C3×SD16—51no—
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—104no—
263C2×C3×SD16C2×D511yescharacteristic
264C2×C3×M16—51no—
265C22×C3×C8—51no—
266C3×C4⋊Q8—51no—
267C3×C4⋊Q8—101no—
268C3×#124—51no—
269C3×#123—101no—
270C3×C22⋊Q8—51no—
271C3×C22⋊Q8—51no—
272C3×C22⋊Q8—51no—
273C3×C22⋊Q8—101no—
274C3×C22⋊Q8—101no—
275C3×#121—51no—
276C3×#121—101no—
277C3×#120—101no—
278C3×C4×Q8C2×D511yescharacteristic, complemented
279C3×C4×D4—51no—
280C3×C4×D4—101no—
281C3×C4×D4C2×D511yescharacteristic
282C2×C3×C22⋊C4—101no—
283C3×#107C2×D511yescharacteristic, complemented
284C3×C4⋊C8—51no—
285C3×#103—51no—
286C3×#103—51no—
287C3×#103—51no—
288C3×#103C2×D511yescharacteristic, complemented
289C3×#102—51no—
290C3×#102C2×D511yescharacteristic
291C3×C22⋊C8—51no—
292C3×C22⋊C8—51no—
293C3×#97C2×D511yescharacteristic, complemented
294C23×D5—21no—
295C2×C5×Q8C23×C311yescharacteristic
296C2×C5×D4C23×C311yescharacteristic
297C22×C4×C5—21no—
298C2×C22⋊D5—21no—
299C2×C22⋊D5—21no—
300C22×Dic5—21no—
301Q8×D5—22no—
302Q8×D5—22no—
303Q8×D5—41no—
304Q8×D5—41no—
305#711—22no—
306#711—41no—
307D4×D5—22no—
308D4×D5—41no—
309C2×D20—21no—
310C2×D20C3×D411yescharacteristic
311C2×D20C23×C311yescharacteristic
312C2×C4×D5—21no—
313C2×C4×D5—21no—
314C2×C4×D5C23×C311yescharacteristic
315C2×C4×D5C23×C311yescharacteristic
316C2×Dic10—21no—
317C2×Dic10—21no—
318C2×Dic10C23×C311yescharacteristic
319C2×Dic10C23×C311yescharacteristic
320C2×Dic10C23×C311yescharacteristic
321C5×SD16C3×D414yescomplemented
322C2×C5×C8C23×C311yescharacteristic
323C2×C5×C8C23×C311yescharacteristic
324C5×C4⋊C4—21no—
325C5×C4⋊C4C23×C311yescharacteristic
326C5×C4⋊C4C23×C311yescharacteristic
327C5×C22⋊C4—21no—
328C42×C5—21no—
329C42×C5C23×C311yescharacteristic
330#689—22no—
331#688—22no—
332#687—22no—
333#687—22no—
334#685—21no—
335#685—21no—
336#685—21no—
337#685—21no—
338#685—21no—
339#685—21no—
340#685C3×D411yescharacteristic
341#685C3×D411yescharacteristic
342C4⋊Dic5—21no—
343C4⋊Dic5—21no—
344C4⋊Dic5—21no—
345C4⋊Dic5—21no—
346C4⋊Dic5—21no—
347C4⋊Dic5C3×D411yescharacteristic
348C2×#168C23×C311yescharacteristic
349C2×#168C23×C311yescharacteristic
350Dic20—22no—
351Dic20—41no—
352#677—22no—
353#677—41no—
354#676—22no—
355C8×D5—22no—
356C2×#137—51no—
357C22×SD16—51no—
358D4×Q8—51no—
359#546—51no—
360#497—51no—
361#468—51no—
362#467—51no—
363#464—51no—
364#461—51no—
365#452—51no—
366#451—51no—
367#450—51no—
368#448—51no—
369#440C3×D511yescharacteristic, complemented
370#435—51no—
371C22×C3×C5—22no—
372C22×C3×C5—41no—
373C22×C3×C5—41no—
374C22×C3×C5C22×D411yescharacteristic
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—84no—
384C2×C3×D5#13712yescomplemented
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×C4×C5C22×D411yescharacteristic
391C3×C4×C5H(5,𝔽2)11yescharacteristic
392C3×Dic5—21no—
393C3×Dic5—21no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—51no—
401C2×C3×Q8—51no—
402C2×C3×Q8—51no—
403C2×C3×Q8—101no—
404C2×C3×Q8—101no—
405C2×C3×Q8—102no—
406C2×C3×Q8—102no—
407C2×C3×Q8—201no—
408C2×C3×Q8—201no—
409C2×C3×Q8C22×D511yescharacteristic
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—201no—
417C2×C3×D4C22×D511yescharacteristic
418C22×C3×C4—21no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—101no—
422C22×C3×C4—101no—
423C22×C3×C4—101no—
424C3×Q16—102no—
425C3×Q16—102no—
426C3×Q16—201no—
427C3×SD16—102no—
428C3×SD16—102no—
429C3×SD16—102no—
430C3×SD16—102no—
431C3×SD16—201no—
432C3×SD16D2014yescomplemented
433C3×M16—102no—
434C2×C3×C8—51no—
435C2×C3×C8—51no—
436C2×C3×C8—102no—
437C2×C3×C8C22×D511yescharacteristic
438C2×C3×C8C22×D511yescharacteristic
439C3×C4⋊C4—21no—
440C3×C4⋊C4—51no—
441C3×C4⋊C4—101no—
442C3×C4⋊C4—101no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4—101no—
446C3×C4⋊C4C22×D511yescharacteristic
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C22⋊C4—51no—
450C3×C22⋊C4—51no—
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453C3×C22⋊C4—101no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C42—21no—
458C3×C42C22×D511yescharacteristic
459C23×C5—21no—
460C22×D5—21no—
461C22×D5—42no—
462C22×D5—42no—
463C22×D5—81no—
464C22×D5C2×C3×D411yescharacteristic
465C22×D5C2×C3×D411yescharacteristic
466C5×Q8—21no—
467C5×Q8C2×C3×D412yes—
468C5×D4—21no—
469C5×D4C2×C3×D412yes—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—81no—
474C2×C4×C5C2×C3×D411yescharacteristic
475C2×C4×C5C2×C3×D411yescharacteristic
476C2×C4×C5C24×C311yescharacteristic
477C22⋊D5—42no—
478C22⋊D5—42no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—42no—
483C2×Dic5C2×C3×D411yescharacteristic
484C2×Dic5C2×C3×D411yescharacteristic
485D20—22no—
486D20—21no—
487D20—21no—
488D20—81no—
489C4×D5—21no—
490C4×D5—21no—
491C4×D5—21no—
492C4×D5—21no—
493C4×D5—42no—
494C4×D5—42no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—21no—
499Dic10—21no—
500Dic10—21no—
501Dic10—42no—
502Dic10—42no—
503C5×C8—21no—
504C5×C8C2×C3×D412yes—
505#168—21no—
506#168—21no—
507C2×#41—51no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—51no—
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
514C2×Q16—51no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—51no—
520C2×SD16—104no—
521C2×SD16C2×C3×D511yescharacteristic
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—51no—
525C4⋊Q8—101no—
526#124—51no—
527#123—101no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—51no—
531C22⋊Q8—101no—
532C22⋊Q8—101no—
533#121—51no—
534#121—101no—
535#120—101no—
536C4×Q8C2×C3×D511yescharacteristic, complemented
537C4×D4—51no—
538C4×D4—101no—
539C4×D4C2×C3×D511yescharacteristic
540C2×C22⋊C4—101no—
541#107C2×C3×D511yescharacteristic, complemented
542C4⋊C8—51no—
543#103—51no—
544#103—51no—
545#103—51no—
546#103C2×C3×D511yescharacteristic, complemented
547#102—51no—
548#102C2×C3×D511yescharacteristic
549C22⋊C8—51no—
550C22⋊C8—51no—
551#97C2×C3×D511yescharacteristic, complemented
552C2×C3×C5—42no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556C3×D5—22no—
557C3×D5—41no—
558C3×D5—81no—
559C23×C3—21no—
560C23×C3—51no—
561C23×C3—51no—
562C23×C3—101no—
563C23×C3—202no—
564C23×C3—202no—
565C23×C3—401no—
566C3×Q8—21no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—101no—
573C3×Q8—202no—
574C3×Q8—202no—
575C3×Q8C2×D2012yes—
576C3×D4—21no—
577C3×D4—102no—
578C3×D4—101no—
579C3×D4—101no—
580C3×D4—202no—
581C3×D4—202no—
582C3×D4—401no—
583C3×D4C2×D2012yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—51no—
588C2×C3×C4—51no—
589C2×C3×C4—81no—
590C2×C3×C4—101no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—202no—
598C2×C3×C4—202no—
599C2×C3×C4—202no—
600C2×C3×C4D4×D511yescharacteristic
601C2×C3×C4D4×D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603C3×C8—21no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8C2×D2012yes—
607C22×C5—22no—
608C22×C5—41no—
609C22×C5—41no—
610C22×C5C22×C3×D411yescharacteristic
611C2×D5—21no—
612C2×D5—21no—
613C2×D5—21no—
614C2×D5—21no—
615C2×D5—21no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—84no—
620C2×D5C3×#13712yescomplemented
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—22no—
624C4×C5—41no—
625C4×C5—41no—
626C4×C5C22×C3×D411yescharacteristic
627C4×C5C3×H(5,𝔽2)11yescharacteristic
628Dic5—21no—
629Dic5—21no—
630Dic5—41no—
631Dic5—41no—
632Dic5—41no—
633C24—101no—
634#41—102no—
635#41—201no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—101no—
640C2×Q8—101no—
641C2×Q8—102no—
642C2×Q8—102no—
643C2×Q8—201no—
644C2×Q8—201no—
645C2×Q8C22×C3×D511yescharacteristic
646C2×D4—51no—
647C2×D4—51no—
648C2×D4—101no—
649C2×D4—101no—
650C2×D4—102no—
651C2×D4—101no—
652C2×D4—201no—
653C2×D4C22×C3×D511yescharacteristic
654C22×C4—21no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—101no—
660Q16—102no—
661Q16—102no—
662Q16—201no—
663SD16—102no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—201no—
668SD16C3×D2014yescomplemented
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—102no—
673C2×C8C22×C3×D511yescharacteristic
674C2×C8C22×C3×D511yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—51no—
677C4⋊C4—101no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—101no—
682C4⋊C4C22×C3×D511yescharacteristic
683C4⋊C4C22×C3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—51no—
686C22⋊C4—51no—
687C22⋊C4—101no—
688C22⋊C4—101no—
689C22⋊C4—101no—
690C22⋊C4—101no—
691C22⋊C4—101no—
692C22⋊C4—101no—
693C42—21no—
694C42C22×C3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—22no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—52no—
700C22×C3—101no—
701C22×C3—101no—
702C22×C3—101no—
703C22×C3—101no—
704C22×C3—101no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—201no—
708C22×C3—404no—
709C22×C3C2×D4×D511yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—22no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—101no—
716C3×C4—101no—
717C3×C4—201no—
718C3×C4—201no—
719C3×C4—201no—
720C3×C4C22×D2011yescharacteristic
721C3×C4#414911yescharacteristic
722C2×C5—42no—
723C2×C5C3×D4211yescharacteristic
724C2×C5C2×C3×#13711yescharacteristic
725C2×C5C3×#57711yescharacteristic
726D5—22no—
727D5—41no—
728D5—81no—
729C23—21no—
730C23—51no—
731C23—51no—
732C23—101no—
733C23—202no—
734C23—202no—
735C23—401no—
736Q8—21no—
737Q8—101no—
738Q8—101no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—101no—
743Q8—202no—
744Q8—202no—
745Q8C2×C3×D2012yes—
746D4—21no—
747D4—102no—
748D4—101no—
749D4—101no—
750D4—202no—
751D4—202no—
752D4—401no—
753D4C2×C3×D2012yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—51no—
758C2×C4—51no—
759C2×C4—81no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—202no—
768C2×C4—202no—
769C2×C4—202no—
770C2×C4C3×D4×D511yescharacteristic
771C2×C4C3×D4×D511yescharacteristic
772C2×C4C23×C3×D511yescharacteristic
773C8—21no—
774C8—101no—
775C8—101no—
776C8C2×C3×D2012yes—
777C2×C3—42no—
778C2×C3—102no—
779C2×C3—201no—
780C2×C3—401no—
781C2×C3D4×D2011yescharacteristic
782C2×C3#6610911yescharacteristic
783C2×C3D5×#13711yescharacteristic
784C5C3×#326611yescharacteristic, complemented, Sylow
785C22—22no—
786C22—41no—
787C22—41no—
788C22—52no—
789C22—101no—
790C22—101no—
791C22—101no—
792C22—101no—
793C22—101no—
794C22—201no—
795C22—201no—
796C22—201no—
797C22—404no—
798C22C2×C3×D4×D511yescharacteristic
799C4—21no—
800C4—21no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—101no—
805C4—101no—
806C4—201no—
807C4—201no—
808C4—201no—
809C4C22×C3×D2011yescharacteristic
810C4C3×#414911yescharacteristic
811C3#1061152611yescharacteristic, direct product factor, Sylow
812C2—42no—
813C2—102no—
814C2—201no—
815C2—401no—
816C2C3×D4×D2011yescharacteristic
817C2C3×#6610911yescharacteristic
818C2C3×D5×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC3×#65888C2
hypercenterC3×#440D5
hypocenterC5C3×#3266
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4061C2semidirect
2. C2×C3×D5×SD16C2semidirect
3. C3×Q8×D20C2semidirect
5. C3×C5×#440C2semidirect
6. C3×#65317C2semidirect
7. C3×#65308C2semidirect
8. C3×#65176C2semidirect
9. C3×#65175C2semidirect
10. C3×#65097C2semidirect
11. C3×#65095C2semidirect
12. C3×#65072C2semidirect
13. C3×#65065C2semidirect
14. C3×#65004C2semidirect
15. C3×#64995C2semidirect
16. #10611526C3direct (N × H)
18. C2×C3×Q8×D5C22semidirect
22. C3×C4×C5×Q8C22semidirect
24. C2×C3×#689C22semidirect
32. C2×C3×Dic20C22semidirect
33. C2×C3×Dic20C22semidirect
36. C2×C3×#676C22semidirect
42. C3×#4043C22semidirect
50. C3×#4015C22semidirect
51. C3×C5×#107C22semidirect
52. C3×C5×#103C22semidirect
54. C3×C5×#97C22semidirect
56. C3×#3952C22semidirect
57. C3×#3942C22semidirect
58. C3×#3942C22semidirect
59. C3×#3942C22semidirect
61. C3×C4⋊#168C22semidirect
63. C2×#4061C2×C3semidirect
64. C2×D5×SD16C2×C3semidirect
65. Q8×D20C2×C3semidirect
67. C5×#440C2×C3semidirect
68. #65317C2×C3semidirect
69. #65308C2×C3semidirect
70. #65176C2×C3semidirect
71. #65175C2×C3semidirect
72. #65097C2×C3semidirect
73. #65095C2×C3semidirect
74. #65072C2×C3semidirect
75. #65065C2×C3semidirect
76. #65004C2×C3semidirect
77. #64995C2×C3semidirect
105. C3×C5×SD16D4semidirect
153. C3×#440D5semidirect
156. C2×Q8×D5C22×C3semidirect
160. C4×C5×Q8C22×C3semidirect
162. C2×#689C22×C3semidirect
170. C2×Dic20C22×C3semidirect
171. C2×Dic20C22×C3semidirect
174. C2×#676C22×C3semidirect
180. #4043C22×C3semidirect
188. #4015C22×C3semidirect
189. C5×#107C22×C3semidirect
190. C5×#103C22×C3semidirect
192. C5×#97C22×C3semidirect
194. #3952C22×C3semidirect
195. #3942C22×C3semidirect
196. #3942C22×C3semidirect
197. #3942C22×C3semidirect
199. C4⋊#168C22×C3semidirect
278. C3×C4×Q8C2×D5semidirect
283. C3×#107C2×D5semidirect
288. C3×#103C2×D5semidirect
293. C3×#97C2×D5semidirect
321. C5×SD16C3×D4semidirect
369. #440C3×D5semidirect
384. C2×C3×D5#137semidirect
432. C3×SD16D20semidirect
536. C4×Q8C2×C3×D5semidirect
541. #107C2×C3×D5semidirect
546. #103C2×C3×D5semidirect
551. #97C2×C3×D5semidirect
620. C2×D5C3×#137semidirect
668. SD16C3×D20semidirect
695. C3×C5#3266semidirect
784. C5C3×#3266semidirect
811. C3#10611526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40612
C2×C3×D5×SD162
C3×Q8×D202
C3×#658882
C3×C5×#4402
C3×#653172
C3×#653082
C3×#651762
C3×#651752
C3×#650972
C3×#650952
C3×#650722
C3×#650652
C3×#650042
C3×#649952
#106115263
C3×#32665