Finite Group Databasebeta

← C3×#10611228 #14454229

Subgroups — C3×#10611228 #14454229

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4054C211yesmaximal, characteristic, complemented
2C2×C3×#4050C211yesmaximal, characteristic, complemented
3C3×#65887C211yesmaximal, characteristic, complemented
4C3×#65884C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6C3×#65423C211yesmaximal, characteristic, complemented
7C3×#65404C211yesmaximal, characteristic, complemented
8C3×#65134C211yesmaximal, characteristic, complemented
9C3×#65132C211yesmaximal, characteristic, complemented
10C3×#65023C211yesmaximal, characteristic, complemented
11C3×#65023C211yesmaximal, characteristic, complemented
12C3×#65022C211yesmaximal, characteristic, complemented
13C3×#65021C211yesmaximal, characteristic, complemented
14C3×#65001C211yesmaximal, characteristic, complemented
15C3×#64999C211yesmaximal, characteristic, complemented
16#10611228C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic, complemented
20C22×C3×D20C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C3×C4×C5×D4C2211yescharacteristic
24C3×#4086—21no—
25C3×#4083—21no—
26C3×#4076C2211yescharacteristic
27C3×#4076C2211yescharacteristic
28C3×#4076C2211yescharacteristic, complemented
29C3×#4070C2211yescharacteristic
30C3×#4054—24no—
31C2×C3×Dic20C2211yescharacteristic, complemented
32C3×#4050—24no—
33C2×C3×D40C2211yescharacteristic
34C2×C3×D40C2211yescharacteristic
35C2×C3×D40C2211yescharacteristic
36C2×C3×D40C2211yescharacteristic
37C2×C3×#677C2211yescharacteristic
38C2×C3×#677C2211yescharacteristic
39C2×C3×#677C2211yescharacteristic, complemented
40C2×C3×#677C2211yescharacteristic, complemented
41C3×#4040—21no—
42C3×#4039—21no—
43C3×#4030—21no—
44C3×#4030—21no—
45C3×#4030—21no—
46C3×D5×C22⋊C4—21no—
47C3×#4021C2211yescharacteristic
48C3×#4020C2211yescharacteristic, complemented
49C3×C4×D20C2211yescharacteristic
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55C3×#3953C2211yescharacteristic
56C3×#3953C2211yescharacteristic
57C3×#3953C2211yescharacteristic, complemented
58C3×#3953C2211yescharacteristic, complemented
59C3×#3950C2211yescharacteristic, complemented
60C3×#3948C2211yescharacteristic, complemented
61C3×#3948C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C2×#4054C2×C311yescharacteristic, complemented
64C2×#4050C2×C311yescharacteristic, complemented
65#65887C2×C311yescharacteristic, complemented
66#65884C2×C311yescharacteristic, complemented
67C5×#435C2×C311yescharacteristic, complemented
68#65423C2×C311yescharacteristic, complemented
69#65404C2×C311yescharacteristic, complemented
70#65134C2×C311yescharacteristic, complemented
71#65132C2×C311yescharacteristic, complemented
72#65023C2×C311yescharacteristic, complemented
73#65023C2×C311yescharacteristic, complemented
74#65022C2×C311yescharacteristic, complemented
75#65021C2×C311yescharacteristic, complemented
76#65001C2×C311yescharacteristic, complemented
77#64999C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C3×#709—22no—
89C3×#709—22no—
90C3×#709—22no—
91C3×#709—41no—
92C3×#709—41no—
93C3×#709—41no—
94C2×C3×D20—22no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20—21no—
98C2×C3×D20—41no—
99C2×C3×D20C2311yescharacteristic
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103C2×C3×C4×D5—21no—
104C2×C3×C4×D5—21no—
105C2×C3×C4×D5—21no—
106C2×C3×C4×D5—21no—
107C2×C3×Dic10C2311yescharacteristic
108C2×C3×Dic10C2311yescharacteristic
109C3×C5×M16—22no—
110C2×C3×C5×C8—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C4⋊C4D411yescharacteristic
116C3×C5×C22⋊C4D411yescharacteristic
117C3×C5×C22⋊C4D411yescharacteristic
118C3×C42×C5C2311yescharacteristic
119C3×C22⋊Dic5—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C3×C4⋊Dic5C2311yescharacteristic
128C3×#683—21no—
129C3×#683—21no—
130C3×C4×Dic5—21no—
131C3×Dic20—22no—
132C3×D40—22no—
133C3×D40—22no—
134C3×D40—22no—
135C3×D40—41no—
136C3×#677—22no—
137C3×#677—22no—
138C3×#677—41no—
139C3×#677D414yescomplemented
140C2×C3×AGL(1,ℤ/8)—51no—
141C2×C3×#135—51no—
142C3×#550—51no—
143C3×#546—51no—
144C3×#496—51no—
145C3×#468—51no—
146C3×#466—51no—
147C3×#464—51no—
148C3×#459—51no—
149C3×#452—51no—
150C3×#449—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#440—51no—
154C3×#435D511yescharacteristic, complemented
155C2×#709C22×C311yescharacteristic
156C2×#709C22×C311yescharacteristic
157C2×#709C22×C311yescharacteristic, complemented
158C22×D20C22×C311yescharacteristic
159C2×C5×M16C22×C311yescharacteristic
160C22×C5×C8C22×C311yescharacteristic, complemented
161C4×C5×D4C22×C311yescharacteristic
162#4086—21no—
163#4083—21no—
164#4076C22×C311yescharacteristic
165#4076C22×C311yescharacteristic
166#4076C22×C311yescharacteristic, complemented
167#4070C22×C311yescharacteristic
168#4054—24no—
169C2×Dic20C22×C311yescharacteristic, complemented
170#4050—24no—
171C2×D40C22×C311yescharacteristic
172C2×D40C22×C311yescharacteristic
173C2×D40C22×C311yescharacteristic
174C2×D40C22×C311yescharacteristic
175C2×#677C22×C311yescharacteristic
176C2×#677C22×C311yescharacteristic
177C2×#677C22×C311yescharacteristic, complemented
178C2×#677C22×C311yescharacteristic, complemented
179#4040—21no—
180#4039—21no—
181#4030—21no—
182#4030—21no—
183#4030—21no—
184D5×C22⋊C4—21no—
185#4021C22×C311yescharacteristic
186#4020C22×C311yescharacteristic, complemented
187C4×D20C22×C311yescharacteristic
188C4×Dic10C22×C311yescharacteristic, complemented
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×C22⋊C8C22×C311yescharacteristic
191C5×C22⋊C8C22×C311yescharacteristic, complemented
192C5×#97C22×C311yescharacteristic, complemented
193#3953C22×C311yescharacteristic
194#3953C22×C311yescharacteristic
195#3953C22×C311yescharacteristic, complemented
196#3953C22×C311yescharacteristic, complemented
197#3950C22×C311yescharacteristic, complemented
198#3948C22×C311yescharacteristic, complemented
199#3948C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—81no—
210C3×C5×D4—41no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
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—81no—
224C3×C22⋊D5—81no—
225C3×C22⋊D5—81no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C3×D20—21no—
231C3×D20—21no—
232C3×D20—21no—
233C3×D20—21no—
234C3×D20—21no—
235C3×D20—21no—
236C3×D20—21no—
237C3×D20—42no—
238C3×D20—42no—
239C3×D20—81no—
240C3×D20C2×D412yes—
241C3×C4×D5—42no—
242C3×C4×D5—42no—
243C3×C4×D5—42no—
244C3×C4×D5—81no—
245C3×Dic10—21no—
246C3×Dic10—21no—
247C3×Dic10—21no—
248C3×Dic10C2×D412yes—
249C3×C5×C8—21no—
250C3×C5×C8—21no—
251C3×C5×C8—21no—
252C3×C5×C8C2×D412yes—
253C2×C3×#41—51no—
254C2×C3×#41—51no—
255C2×C3×#41—51no—
256C22×C3×D4—51no—
257C3×AGL(1,ℤ/8)—104no—
258C3×#135—104no—
259C2×C3×Q16—51no—
260C2×C3×SD16—51no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C2×C3×M16C2×D511yescharacteristic
269C22×C3×C8C2×D511yescharacteristic, complemented
270C3×#127—51no—
271C3×#127—101no—
272C3×#124—51no—
273C3×#123—101no—
274C3×C22⋊Q8—51no—
275C3×#121—51no—
276C3×#121—51no—
277C3×#121—51no—
278C3×#121—101no—
279C3×#121—101no—
280C3×#121—101no—
281C3×#120—101no—
282C3×C4×Q8—51no—
283C3×C4×D4—51no—
284C3×C4×D4—101no—
285C3×C4×D4C2×D511yescharacteristic
286C2×C3×C22⋊C4—101no—
287C3×#107—51no—
288C3×C4⋊C8C2×D511yescharacteristic, complemented
289C3×#103—51no—
290C3×#103—51no—
291C3×#102—51no—
292C3×#102—51no—
293C3×#102—51no—
294C3×#102—51no—
295C3×C22⋊C8C2×D511yescharacteristic
296C3×C22⋊C8C2×D511yescharacteristic, complemented
297C3×#97C2×D511yescharacteristic, complemented
298C23×D5—21no—
299C2×C5×D4C3×D411yescharacteristic
300C22×C4×C5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C2×C22⋊D5—21no—
303C2×C22⋊D5—21no—
304C2×C22⋊D5—21no—
305C2×C22⋊D5—21no—
306C2×C22⋊D5—21no—
307C2×C22⋊D5—21no—
308#709—22no—
309#709—22no—
310#709—22no—
311#709—41no—
312#709—41no—
313#709—41no—
314C2×D20—22no—
315C2×D20—21no—
316C2×D20—21no—
317C2×D20—21no—
318C2×D20—41no—
319C2×D20C23×C311yescharacteristic
320C2×D20C23×C311yescharacteristic
321C2×D20C23×C311yescharacteristic
322C2×D20C23×C311yescharacteristic
323C2×C4×D5—21no—
324C2×C4×D5—21no—
325C2×C4×D5—21no—
326C2×C4×D5—21no—
327C2×Dic10C23×C311yescharacteristic
328C2×Dic10C23×C311yescharacteristic
329C5×M16—22no—
330C2×C5×C8—22no—
331C2×C5×C8C23×C311yescharacteristic
332C2×C5×C8C23×C311yescharacteristic
333C2×C5×C8C23×C311yescharacteristic
334C2×C5×C8C23×C311yescharacteristic
335C5×C4⋊C4C3×D411yescharacteristic
336C5×C22⋊C4C3×D411yescharacteristic
337C5×C22⋊C4C3×D411yescharacteristic
338C42×C5C23×C311yescharacteristic
339C22⋊Dic5—21no—
340#685—21no—
341#685—21no—
342#685—21no—
343#685—21no—
344#685—21no—
345#685—21no—
346C4⋊Dic5C23×C311yescharacteristic
347C4⋊Dic5C23×C311yescharacteristic
348#683—21no—
349#683—21no—
350C4×Dic5—21no—
351Dic20—22no—
352D40—22no—
353D40—22no—
354D40—22no—
355D40—41no—
356#677—22no—
357#677—22no—
358#677—41no—
359#677C3×D414yescomplemented
360C2×AGL(1,ℤ/8)—51no—
361C2×#135—51no—
362#550—51no—
363#546—51no—
364#496—51no—
365#468—51no—
366#466—51no—
367#464—51no—
368#459—51no—
369#452—51no—
370#449—51no—
371#449—51no—
372#447—51no—
373#440—51no—
374#435C3×D511yescharacteristic, complemented
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5C22×D411yescharacteristic
382C2×C3×D5—22no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—41no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—84no—
395C3×C4×C5—21no—
396C3×C4×C5—21no—
397C3×C4×C5—21no—
398C3×C4×C5—21no—
399C3×C4×C5C22×D411yescharacteristic
400C3×C4×C5H(5,𝔽2)11yescharacteristic
401C3×Dic5—22no—
402C3×Dic5—41no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C24×C3—101no—
406C3×#41—102no—
407C3×#41—102no—
408C3×#41—102no—
409C3×#41—201no—
410C3×#41—201no—
411C3×#41—201no—
412C2×C3×Q8—51no—
413C2×C3×Q8—51no—
414C2×C3×D4—51no—
415C2×C3×D4—51no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—102no—
419C2×C3×D4—101no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—101no—
427C2×C3×D4—101no—
428C2×C3×D4—201no—
429C2×C3×D4D2011yescharacteristic
430C22×C3×C4—101no—
431C22×C3×C4—101no—
432C22×C3×C4—101no—
433C22×C3×C4—101no—
434C22×C3×C4C22×D511yescharacteristic
435C22×C3×C4C22×D511yescharacteristic
436C3×Q16—102no—
437C3×SD16—54no—
438C3×SD16—102no—
439C3×SD16—102no—
440C3×SD16—201no—
441C3×D8—102no—
442C3×D8—102no—
443C3×D8—102no—
444C3×D8—201no—
445C3×M16—22no—
446C2×C3×C8—22no—
447C2×C3×C8C22×D511yescharacteristic
448C2×C3×C8C22×D511yescharacteristic
449C2×C3×C8C22×D511yescharacteristic
450C2×C3×C8C22×D511yescharacteristic
451C3×C4⋊C4—51no—
452C3×C4⋊C4—51no—
453C3×C4⋊C4—101no—
454C3×C4⋊C4—101no—
455C3×C4⋊C4D2011yescharacteristic
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4D2011yescharacteristic
464C3×C22⋊C4D2011yescharacteristic
465C3×C42—101no—
466C3×C42C22×D511yescharacteristic
467C23×C5C2×C3×D411yescharacteristic
468C23×C5C2×C3×D411yescharacteristic
469C22×D5—21no—
470C22×D5—21no—
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—42no—
474C22×D5—42no—
475C22×D5—81no—
476C5×D4—41no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5C2×C3×D411yescharacteristic
482C2×C4×C5C2×C3×D411yescharacteristic
483C2×C4×C5C2×C3×D411yescharacteristic
484C2×C4×C5C2×C3×D411yescharacteristic
485C2×C4×C5C24×C311yescharacteristic
486C22⋊D5—42no—
487C22⋊D5—42no—
488C22⋊D5—42no—
489C22⋊D5—81no—
490C22⋊D5—81no—
491C22⋊D5—81no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496D20—21no—
497D20—21no—
498D20—21no—
499D20—21no—
500D20—21no—
501D20—21no—
502D20—21no—
503D20—42no—
504D20—42no—
505D20—81no—
506D20C2×C3×D412yes—
507C4×D5—42no—
508C4×D5—42no—
509C4×D5—42no—
510C4×D5—81no—
511Dic10—21no—
512Dic10—21no—
513Dic10—21no—
514Dic10C2×C3×D412yes—
515C5×C8—21no—
516C5×C8—21no—
517C5×C8—21no—
518C5×C8C2×C3×D412yes—
519C2×#41—51no—
520C2×#41—51no—
521C2×#41—51no—
522C22×D4—51no—
523AGL(1,ℤ/8)—104no—
524#135—104no—
525C2×Q16—51no—
526C2×SD16—51no—
527C2×SD16—51no—
528C2×SD16—51no—
529C2×SD16—51no—
530C2×D8—51no—
531C2×D8—51no—
532C2×D8—51no—
533C2×D8—51no—
534C2×M16C2×C3×D511yescharacteristic
535C22×C8C2×C3×D511yescharacteristic, complemented
536#127—51no—
537#127—101no—
538#124—51no—
539#123—101no—
540C22⋊Q8—51no—
541#121—51no—
542#121—51no—
543#121—51no—
544#121—101no—
545#121—101no—
546#121—101no—
547#120—101no—
548C4×Q8—51no—
549C4×D4—51no—
550C4×D4—101no—
551C4×D4C2×C3×D511yescharacteristic
552C2×C22⋊C4—101no—
553#107—51no—
554C4⋊C8C2×C3×D511yescharacteristic, complemented
555#103—51no—
556#103—51no—
557#102—51no—
558#102—51no—
559#102—51no—
560#102—51no—
561C22⋊C8C2×C3×D511yescharacteristic
562C22⋊C8C2×C3×D511yescharacteristic, complemented
563#97C2×C3×D511yescharacteristic, complemented
564C2×C3×C5—41no—
565C2×C3×C5—41no—
566C2×C3×C5D4211yescharacteristic
567C2×C3×C5#57511yescharacteristic
568C2×C3×C5#57611yescharacteristic
569C3×D5—42no—
570C3×D5—81no—
571C3×D5—81no—
572C3×D5—81no—
573C23×C3—101no—
574C23×C3—101no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—202no—
578C23×C3—202no—
579C23×C3—401no—
580C23×C3C2×D2011yescharacteristic
581C23×C3C2×D2011yescharacteristic
582C3×Q8—52no—
583C3×Q8—101no—
584C3×Q8—101no—
585C3×Q8—101no—
586C3×D4—41no—
587C3×D4—52no—
588C3×D4—101no—
589C3×D4—101no—
590C3×D4—101no—
591C3×D4—101no—
592C3×D4—101no—
593C3×D4—101no—
594C3×D4—101no—
595C3×D4—202no—
596C3×D4—202no—
597C3×D4—202no—
598C3×D4—202no—
599C3×D4—202no—
600C3×D4—401no—
601C3×D4—401no—
602C3×D4—401no—
603C3×D4—401no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—202no—
613C2×C3×C4—202no—
614C2×C3×C4—202no—
615C2×C3×C4—401no—
616C2×C3×C4C2×D2011yescharacteristic
617C2×C3×C4C2×D2011yescharacteristic
618C2×C3×C4C2×D2011yescharacteristic
619C2×C3×C4C2×D2011yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—21no—
622C3×C8—21no—
623C3×C8—21no—
624C3×C8D4×D512yes—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—21no—
628C22×C5—21no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5C22×C3×D411yescharacteristic
632C2×D5—22no—
633C2×D5—41no—
634C2×D5—41no—
635C2×D5—41no—
636C2×D5—41no—
637C2×D5—41no—
638C2×D5—41no—
639C2×D5—41no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—21no—
648C4×C5—21no—
649C4×C5C22×C3×D411yescharacteristic
650C4×C5C3×H(5,𝔽2)11yescharacteristic
651Dic5—22no—
652Dic5—41no—
653Dic5—41no—
654Dic5—41no—
655C24—101no—
656#41—102no—
657#41—102no—
658#41—102no—
659#41—201no—
660#41—201no—
661#41—201no—
662C2×Q8—51no—
663C2×Q8—51no—
664C2×D4—51no—
665C2×D4—51no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—102no—
669C2×D4—101no—
670C2×D4—101no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—101no—
677C2×D4—101no—
678C2×D4—201no—
679C2×D4C3×D2011yescharacteristic
680C22×C4—101no—
681C22×C4—101no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4C22×C3×D511yescharacteristic
685C22×C4C22×C3×D511yescharacteristic
686Q16—102no—
687SD16—54no—
688SD16—102no—
689SD16—102no—
690SD16—201no—
691D8—102no—
692D8—102no—
693D8—102no—
694D8—201no—
695M16—22no—
696C2×C8—22no—
697C2×C8C22×C3×D511yescharacteristic
698C2×C8C22×C3×D511yescharacteristic
699C2×C8C22×C3×D511yescharacteristic
700C2×C8C22×C3×D511yescharacteristic
701C4⋊C4—51no—
702C4⋊C4—51no—
703C4⋊C4—101no—
704C4⋊C4—101no—
705C4⋊C4C3×D2011yescharacteristic
706C22⋊C4—101no—
707C22⋊C4—101no—
708C22⋊C4—101no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4C3×D2011yescharacteristic
714C22⋊C4C3×D2011yescharacteristic
715C42—101no—
716C42C22×C3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—102no—
725C22×C3—201no—
726C22×C3—201no—
727C22×C3—201no—
728C22×C3—201no—
729C22×C3—201no—
730C22×C3—201no—
731C22×C3—201no—
732C22×C3—201no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—404no—
737C22×C3C22×D2011yescharacteristic
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—102no—
743C3×C4—201no—
744C3×C4—201no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414911yescharacteristic
748C2×C5—41no—
749C2×C5—41no—
750C2×C5C3×D4211yescharacteristic
751C2×C5C3×#57511yescharacteristic
752C2×C5C3×#57611yescharacteristic
753D5—42no—
754D5—81no—
755D5—81no—
756D5—81no—
757C23—101no—
758C23—101no—
759C23—101no—
760C23—101no—
761C23—202no—
762C23—202no—
763C23—401no—
764C23C2×C3×D2011yescharacteristic
765C23C2×C3×D2011yescharacteristic
766Q8—52no—
767Q8—101no—
768Q8—101no—
769Q8—101no—
770D4—41no—
771D4—52no—
772D4—101no—
773D4—101no—
774D4—101no—
775D4—101no—
776D4—101no—
777D4—101no—
778D4—101no—
779D4—202no—
780D4—202no—
781D4—202no—
782D4—202no—
783D4—202no—
784D4—401no—
785D4—401no—
786D4—401no—
787D4—401no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—202no—
797C2×C4—202no—
798C2×C4—202no—
799C2×C4—401no—
800C2×C4C2×C3×D2011yescharacteristic
801C2×C4C2×C3×D2011yescharacteristic
802C2×C4C2×C3×D2011yescharacteristic
803C2×C4C2×C3×D2011yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—21no—
806C8—21no—
807C8—21no—
808C8C3×D4×D512yes—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—202no—
812C2×C3—401no—
813C2×C3—401no—
814C2×C3—401no—
815C2×C3D4×D2011yescharacteristic
816C2×C3#6608211yescharacteristic
817C2×C3#6608611yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—102no—
826C22—201no—
827C22—201no—
828C22—201no—
829C22—201no—
830C22—201no—
831C22—201no—
832C22—201no—
833C22—201no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C22×C3×D2011yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—102no—
844C4—201no—
845C4—201no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414911yescharacteristic
849C3#1061122811yescharacteristic, direct product factor, Sylow
850C2—41no—
851C2—41no—
852C2—202no—
853C2—401no—
854C2—401no—
855C2—401no—
856C2C3×D4×D2011yescharacteristic
857C2C3×#6608211yescharacteristic
858C2C3×#6608611yescharacteristic
subgroupG/H
centerC22×C3C22×D20
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
hypercenterC3×#435D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4054C2semidirect
2. C2×C3×#4050C2semidirect
3. C3×#65887C2semidirect
4. C3×#65884C2semidirect
5. C3×C5×#435C2semidirect
6. C3×#65423C2semidirect
7. C3×#65404C2semidirect
8. C3×#65134C2semidirect
9. C3×#65132C2semidirect
10. C3×#65023C2semidirect
11. C3×#65023C2semidirect
12. C3×#65022C2semidirect
13. C3×#65021C2semidirect
14. C3×#65001C2semidirect
15. C3×#64999C2semidirect
16. #10611228C3direct (N × H)
19. C2×C3×#709C22semidirect
22. C22×C3×C5×C8C22semidirect
28. C3×#4076C22semidirect
31. C2×C3×Dic20C22semidirect
39. C2×C3×#677C22semidirect
40. C2×C3×#677C22semidirect
48. C3×#4020C22semidirect
50. C3×C4×Dic10C22semidirect
51. C3×C5×C4⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
57. C3×#3953C22semidirect
58. C3×#3953C22semidirect
59. C3×#3950C22semidirect
60. C3×#3948C22semidirect
61. C3×#3948C22semidirect
63. C2×#4054C2×C3semidirect
64. C2×#4050C2×C3semidirect
65. #65887C2×C3semidirect
66. #65884C2×C3semidirect
67. C5×#435C2×C3semidirect
68. #65423C2×C3semidirect
69. #65404C2×C3semidirect
70. #65134C2×C3semidirect
71. #65132C2×C3semidirect
72. #65023C2×C3semidirect
73. #65023C2×C3semidirect
74. #65022C2×C3semidirect
75. #65021C2×C3semidirect
76. #65001C2×C3semidirect
77. #64999C2×C3semidirect
139. C3×#677D4semidirect
154. C3×#435D5semidirect
157. C2×#709C22×C3semidirect
160. C22×C5×C8C22×C3semidirect
166. #4076C22×C3semidirect
169. C2×Dic20C22×C3semidirect
177. C2×#677C22×C3semidirect
178. C2×#677C22×C3semidirect
186. #4020C22×C3semidirect
188. C4×Dic10C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
191. C5×C22⋊C8C22×C3semidirect
192. C5×#97C22×C3semidirect
195. #3953C22×C3semidirect
196. #3953C22×C3semidirect
197. #3950C22×C3semidirect
198. #3948C22×C3semidirect
199. #3948C22×C3semidirect
269. C22×C3×C8C2×D5semidirect
288. C3×C4⋊C8C2×D5semidirect
296. C3×C22⋊C8C2×D5semidirect
297. C3×#97C2×D5semidirect
359. #677C3×D4semidirect
374. #435C3×D5semidirect
535. C22×C8C2×C3×D5semidirect
554. C4⋊C8C2×C3×D5semidirect
562. C22⋊C8C2×C3×D5semidirect
563. #97C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10611228direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C2×C3×#40502
C3×#658872
C3×#658842
C3×C5×#4352
C3×#654232
C3×#654042
C3×#651342
C3×#651322
C3×#650232
C3×#650222
C3×#650212
C3×#650012
C3×#649992
#106112283
C3×#32685