Finite Group Databasebeta

← C3×#10612079 #14454232

Subgroups — C3×#10612079 #14454232

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×#4058C211yesmaximal, characteristic, complemented
2C2×C3×#4057C211yesmaximal, characteristic, complemented
3C3×#66052C211yesmaximal, characteristic, complemented
4C3×#65888C211yesmaximal, characteristic, complemented
5C3×C5×#459C211yesmaximal, characteristic, complemented
6C3×#65447C211yesmaximal, characteristic, complemented
7C3×#65445C211yesmaximal, characteristic, complemented
8C3×#65363C211yesmaximal, characteristic, complemented
9C3×#65307C211yesmaximal, characteristic, complemented
10C3×#65134C211yesmaximal, characteristic, complemented
11C3×#65125C211yesmaximal, characteristic, complemented
12C3×#65072C211yesmaximal, characteristic, complemented
13C3×#65070C211yesmaximal, characteristic, complemented
14C3×#65069C211yesmaximal, characteristic, complemented
15C3×#65064C211yesmaximal, characteristic, complemented
16#10612079C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×#711C2211yescharacteristic, complemented
20C2×C3×D4×D5C2211yescharacteristic
21C2×C3×C5×D8C2211yescharacteristic
22C2×C3×C5×D8C2211yescharacteristic
23C3×C5×#127C2211yescharacteristic, complemented
24C3×C4×C5×D4C2211yescharacteristic
25C3×#4086—21no—
26C3×#4085—21no—
27C3×#4085—21no—
28C3×#4084C2211yescharacteristic
29C3×#4084C2211yescharacteristic, complemented
30C3×D4×Dic5—21no—
31C2×C3×#687C2211yescharacteristic
32C2×C3×#687C2211yescharacteristic, complemented
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic
36C3×#4076—21no—
37C2×C3×#685—21no—
38C3×#4058—24no—
39C3×#4057—24no—
40C2×C3×Dic20C2211yescharacteristic, complemented
41C2×C3×#677C2211yescharacteristic
42C2×C3×#676C2211yescharacteristic
43C2×C3×C8×D5C2211yescharacteristic, complemented
44C3×#4043C2211yescharacteristic
45C3×#4041C2211yescharacteristic
46C3×#4032—21no—
47C3×#4028—21no—
48C3×#4021C2211yescharacteristic
49C3×C4×D20C2211yescharacteristic
50C3×C4×Dic10C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54C3×#3964C2211yescharacteristic
55C3×#3953C2211yescharacteristic
56C3×#3952C2211yescharacteristic
57C3×#3952C2211yescharacteristic, complemented
58C3×#3948C2211yescharacteristic, complemented
59C3×#3942C2211yescharacteristic, complemented
60C3×#3939C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62C3×#3268—51nomaximal, Hall
63C2×#4058C2×C311yescharacteristic, complemented
64C2×#4057C2×C311yescharacteristic, complemented
65#66052C2×C311yescharacteristic, complemented
66#65888C2×C311yescharacteristic, complemented
67C5×#459C2×C311yescharacteristic, complemented
68#65447C2×C311yescharacteristic, complemented
69#65445C2×C311yescharacteristic, complemented
70#65363C2×C311yescharacteristic, complemented
71#65307C2×C311yescharacteristic, complemented
72#65134C2×C311yescharacteristic, complemented
73#65125C2×C311yescharacteristic, complemented
74#65072C2×C311yescharacteristic, complemented
75#65070C2×C311yescharacteristic, complemented
76#65069C2×C311yescharacteristic, complemented
77#65064C2×C311yescharacteristic, complemented
78C23×C3×D5—21no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5—21no—
91C22×C3×Dic5—21no—
92C22×C3×Dic5—21no—
93C22×C3×Dic5—21no—
94C3×#711—22no—
95C3×#711—22no—
96C3×#711—22no—
97C3×#711—41no—
98C3×#711—41no—
99C3×#711—41no—
100C3×D4×D5—22no—
101C3×D4×D5—41no—
102C2×C3×D20—21no—
103C2×C3×D20D411yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×C3×C4×D5C2311yescharacteristic
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×Dic10C2311yescharacteristic
108C2×C3×Dic10C2311yescharacteristic
109C3×C5×D8—22no—
110C3×C5×D8—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113C3×C5×C4⋊C4C2311yescharacteristic
114C3×C5×C22⋊C4—21no—
115C3×C42×C5C2311yescharacteristic
116C3×C22⋊Dic5—21no—
117C3×C22⋊Dic5—21no—
118C3×#687—22no—
119C3×#687—41no—
120C3×#687D414yescomplemented
121C3×#686—22no—
122C3×#686—41no—
123C3×#685—21no—
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×#685D411yescharacteristic
129C3×C4⋊Dic5—21no—
130C3×C4⋊Dic5D411yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×C4×Dic5—21no—
134C2×C3×#168C2311yescharacteristic
135C2×C3×#168C2311yescharacteristic
136C3×Dic20—22no—
137C3×#677—22no—
138C3×#676—22no—
139C3×C8×D5—22no—
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×#459D511yescharacteristic, complemented
149C3×#452—51no—
150C3×#449—51no—
151C3×#449—51no—
152C3×#447—51no—
153C3×#440—51no—
154C3×#435—51no—
155C2×#711C22×C311yescharacteristic
156C2×#711C22×C311yescharacteristic
157C2×#711C22×C311yescharacteristic, complemented
158C2×D4×D5C22×C311yescharacteristic
159C2×C5×D8C22×C311yescharacteristic
160C2×C5×D8C22×C311yescharacteristic
161C5×#127C22×C311yescharacteristic, complemented
162C4×C5×D4C22×C311yescharacteristic
163#4086—21no—
164#4085—21no—
165#4085—21no—
166#4084C22×C311yescharacteristic
167#4084C22×C311yescharacteristic, complemented
168D4×Dic5—21no—
169C2×#687C22×C311yescharacteristic
170C2×#687C22×C311yescharacteristic, complemented
171C2×#687C22×C311yescharacteristic, complemented
172C2×#686C22×C311yescharacteristic
173C2×#686C22×C311yescharacteristic
174#4076—21no—
175C2×#685—21no—
176#4058—24no—
177#4057—24no—
178C2×Dic20C22×C311yescharacteristic, complemented
179C2×#677C22×C311yescharacteristic
180C2×#676C22×C311yescharacteristic
181C2×C8×D5C22×C311yescharacteristic, complemented
182#4043C22×C311yescharacteristic
183#4041C22×C311yescharacteristic
184#4032—21no—
185#4028—21no—
186#4021C22×C311yescharacteristic
187C4×D20C22×C311yescharacteristic
188C4×Dic10C22×C311yescharacteristic, complemented
189C5×C4⋊C8C22×C311yescharacteristic, complemented
190C5×#102C22×C311yescharacteristic, complemented
191C5×#102C22×C311yescharacteristic, complemented
192#3964C22×C311yescharacteristic
193#3953C22×C311yescharacteristic
194#3952C22×C311yescharacteristic
195#3952C22×C311yescharacteristic, complemented
196#3948C22×C311yescharacteristic, complemented
197#3942C22×C311yescharacteristic, complemented
198#3939C22×C311yescharacteristic, complemented
199#3935C22×C311yescharacteristic, complemented
200#3268—51noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
208C22×C3×D5C2×D411yescharacteristic
209C22×C3×D5C2×D411yescharacteristic
210C3×C5×D4—21no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C3×C5×D4—21no—
214C3×C5×D4—21no—
215C3×C5×D4—42no—
216C3×C5×D4—81no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—81no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223C3×C22⋊D5—42no—
224C3×C22⋊D5—42no—
225C3×C22⋊D5—42no—
226C3×C22⋊D5—42no—
227C3×C22⋊D5—81no—
228C3×C22⋊D5—81no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—42no—
233C2×C3×Dic5—42no—
234C2×C3×Dic5—42no—
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—41no—
240C3×D20—81no—
241C3×C4×D5—21no—
242C3×C4×D5—21no—
243C3×C4×D5—21no—
244C3×C4×D5—21no—
245C3×Dic10—21no—
246C3×Dic10—21no—
247C3×Dic10—21no—
248C3×Dic10C2×D412yes—
249C3×C5×C8—21no—
250C3×C5×C8—21no—
251C3×#168—21no—
252C3×#168C2×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×D8C2×D511yescharacteristic
267C2×C3×D8C2×D511yescharacteristic
268C2×C3×M16—51no—
269C22×C3×C8—51no—
270C3×#127—101no—
271C3×#127C2×D511yescharacteristic, complemented
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×#102C2×D511yescharacteristic, complemented
294C3×#102C2×D511yescharacteristic, complemented
295C3×C22⋊C8—51no—
296C3×C22⋊C8—51no—
297C3×#97—51no—
298C23×D5—21no—
299C2×C5×D4—21no—
300C2×C5×D4—21no—
301C2×C5×D4C23×C311yescharacteristic
302C2×C5×D4C23×C311yescharacteristic
303C2×C5×D4C23×C311yescharacteristic
304C22×C4×C5—21no—
305C2×C22⋊D5—21no—
306C2×C22⋊D5—21no—
307C2×C22⋊D5—21no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—21no—
311C22×Dic5—21no—
312C22×Dic5—21no—
313C22×Dic5—21no—
314#711—22no—
315#711—22no—
316#711—22no—
317#711—41no—
318#711—41no—
319#711—41no—
320D4×D5—22no—
321D4×D5—41no—
322C2×D20—21no—
323C2×D20C3×D411yescharacteristic
324C2×D20C23×C311yescharacteristic
325C2×C4×D5C23×C311yescharacteristic
326C2×C4×D5C23×C311yescharacteristic
327C2×Dic10C23×C311yescharacteristic
328C2×Dic10C23×C311yescharacteristic
329C5×D8—22no—
330C5×D8—22no—
331C2×C5×C8C23×C311yescharacteristic
332C2×C5×C8C23×C311yescharacteristic
333C5×C4⋊C4C23×C311yescharacteristic
334C5×C22⋊C4—21no—
335C42×C5C23×C311yescharacteristic
336C22⋊Dic5—21no—
337C22⋊Dic5—21no—
338#687—22no—
339#687—41no—
340#687C3×D414yescomplemented
341#686—22no—
342#686—41no—
343#685—21no—
344#685—21no—
345#685—21no—
346#685—21no—
347#685C3×D411yescharacteristic
348#685C3×D411yescharacteristic
349C4⋊Dic5—21no—
350C4⋊Dic5C3×D411yescharacteristic
351C4⋊Dic5C23×C311yescharacteristic
352#683—21no—
353C4×Dic5—21no—
354C2×#168C23×C311yescharacteristic
355C2×#168C23×C311yescharacteristic
356Dic20—22no—
357#677—22no—
358#676—22no—
359C8×D5—22no—
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#459C3×D511yescharacteristic, complemented
369#452—51no—
370#449—51no—
371#449—51no—
372#447—51no—
373#440—51no—
374#435—51no—
375C22×C3×C5—22no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5C22×D411yescharacteristic
385C2×C3×D5—21no—
386C2×C3×D5—21no—
387C2×C3×D5—21no—
388C2×C3×D5—21no—
389C2×C3×D5—21no—
390C2×C3×D5—21no—
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—41no—
398C3×C4×C5C22×D411yescharacteristic
399C3×C4×C5H(5,𝔽2)11yescharacteristic
400C3×Dic5—22no—
401C3×Dic5—21no—
402C3×Dic5—21no—
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—21no—
415C2×C3×D4—21no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—101no—
419C2×C3×D4—101no—
420C2×C3×D4—102no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C2×C3×D4—101no—
424C2×C3×D4—101no—
425C2×C3×D4—101no—
426C2×C3×D4—201no—
427C2×C3×D4C22×D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—101no—
434C22×C3×C4—101no—
435C22×C3×C4—101no—
436C3×Q16—102no—
437C3×SD16—54no—
438C3×SD16—102no—
439C3×SD16—102no—
440C3×SD16—201no—
441C3×D8—22no—
442C3×D8—22no—
443C3×D8—102no—
444C3×D8—201no—
445C3×M16—102no—
446C2×C3×C8—51no—
447C2×C3×C8—51no—
448C2×C3×C8—102no—
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⋊C4C22×D511yescharacteristic
456C3×C22⋊C4—21no—
457C3×C22⋊C4—51no—
458C3×C22⋊C4—51no—
459C3×C22⋊C4—101no—
460C3×C22⋊C4—101no—
461C3×C22⋊C4—101no—
462C3×C22⋊C4—101no—
463C3×C22⋊C4—101no—
464C3×C22⋊C4—101no—
465C3×C42—101no—
466C3×C42C22×D511yescharacteristic
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C22×D5—21no—
471C22×D5—42no—
472C22×D5—42no—
473C22×D5—81no—
474C22×D5C2×C3×D411yescharacteristic
475C22×D5C2×C3×D411yescharacteristic
476C5×D4—21no—
477C5×D4—21no—
478C5×D4—21no—
479C5×D4—21no—
480C5×D4—21no—
481C5×D4—42no—
482C5×D4—81no—
483C5×D4C2×C3×D412yes—
484C2×C4×C5—21no—
485C2×C4×C5—81no—
486C2×C4×C5C2×C3×D411yescharacteristic
487C2×C4×C5C2×C3×D411yescharacteristic
488C2×C4×C5C24×C311yescharacteristic
489C22⋊D5—42no—
490C22⋊D5—42no—
491C22⋊D5—42no—
492C22⋊D5—42no—
493C22⋊D5—81no—
494C22⋊D5—81no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—42no—
499C2×Dic5—42no—
500C2×Dic5—42no—
501C2×Dic5C2×C3×D411yescharacteristic
502C2×Dic5C2×C3×D411yescharacteristic
503D20—21no—
504D20—21no—
505D20—41no—
506D20—81no—
507C4×D5—21no—
508C4×D5—21no—
509C4×D5—21no—
510C4×D5—21no—
511Dic10—21no—
512Dic10—21no—
513Dic10—21no—
514Dic10C2×C3×D412yes—
515C5×C8—21no—
516C5×C8—21no—
517#168—21no—
518#168C2×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×D8C2×C3×D511yescharacteristic
533C2×D8C2×C3×D511yescharacteristic
534C2×M16—51no—
535C22×C8—51no—
536#127—101no—
537#127C2×C3×D511yescharacteristic, complemented
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#102C2×C3×D511yescharacteristic, complemented
560#102C2×C3×D511yescharacteristic, complemented
561C22⋊C8—51no—
562C22⋊C8—51no—
563#97—51no—
564C2×C3×C5—42no—
565C2×C3×C5—81no—
566C2×C3×C5—81no—
567C2×C3×C5D4211yescharacteristic
568C2×C3×C5#57511yescharacteristic
569C2×C3×C5#57611yescharacteristic
570C3×D5—41no—
571C3×D5—41no—
572C3×D5—81no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—51no—
577C23×C3—51no—
578C23×C3—101no—
579C23×C3—202no—
580C23×C3—202no—
581C23×C3—401no—
582C3×Q8—52no—
583C3×Q8—101no—
584C3×Q8—101no—
585C3×Q8—101no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—42no—
592C3×D4—81no—
593C3×D4—101no—
594C3×D4—101no—
595C3×D4—201no—
596C3×D4—202no—
597C3×D4—202no—
598C3×D4—202no—
599C3×D4—202no—
600C3×D4—401no—
601C3×D4—401no—
602C3×D4—401no—
603C3×D4D4×D512yes—
604C2×C3×C4—21no—
605C2×C3×C4—51no—
606C2×C3×C4—51no—
607C2×C3×C4—81no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—202no—
616C2×C3×C4—202no—
617C2×C3×C4—202no—
618C2×C3×C4D4×D511yescharacteristic
619C2×C3×C4D4×D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621C3×C8—21no—
622C3×C8—21no—
623C3×C8—52no—
624C3×C8—101no—
625C22×C5—22no—
626C22×C5—41no—
627C22×C5—41no—
628C22×C5—41no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5C22×C3×D411yescharacteristic
635C2×D5—21no—
636C2×D5—21no—
637C2×D5—21no—
638C2×D5—21no—
639C2×D5—21no—
640C2×D5—21no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—41no—
648C4×C5C22×C3×D411yescharacteristic
649C4×C5C3×H(5,𝔽2)11yescharacteristic
650Dic5—22no—
651Dic5—21no—
652Dic5—21no—
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—21no—
665C2×D4—21no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—101no—
669C2×D4—101no—
670C2×D4—102no—
671C2×D4—101no—
672C2×D4—101no—
673C2×D4—101no—
674C2×D4—101no—
675C2×D4—101no—
676C2×D4—201no—
677C2×D4C22×C3×D511yescharacteristic
678C2×D4C22×C3×D511yescharacteristic
679C2×D4C22×C3×D511yescharacteristic
680C22×C4—21no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686Q16—102no—
687SD16—54no—
688SD16—102no—
689SD16—102no—
690SD16—201no—
691D8—22no—
692D8—22no—
693D8—102no—
694D8—201no—
695M16—102no—
696C2×C8—51no—
697C2×C8—51no—
698C2×C8—102no—
699C2×C8C22×C3×D511yescharacteristic
700C2×C8C22×C3×D511yescharacteristic
701C4⋊C4—51no—
702C4⋊C4—51no—
703C4⋊C4—101no—
704C4⋊C4—101no—
705C4⋊C4C22×C3×D511yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—51no—
708C22⋊C4—51no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4—101no—
714C22⋊C4—101no—
715C42—101no—
716C42C22×C3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—22no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—101no—
728C22×C3—101no—
729C22×C3—101no—
730C22×C3—101no—
731C22×C3—101no—
732C22×C3—101no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—404no—
737C22×C3C2×D4×D511yescharacteristic
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—41no—
741C3×C4—101no—
742C3×C4—101no—
743C3×C4—102no—
744C3×C4—201no—
745C3×C4—201no—
746C3×C4C2×D4×D511yescharacteristic
747C3×C4#414911yescharacteristic
748C2×C5—42no—
749C2×C5—81no—
750C2×C5—81no—
751C2×C5C3×D4211yescharacteristic
752C2×C5C3×#57511yescharacteristic
753C2×C5C3×#57611yescharacteristic
754D5—41no—
755D5—41no—
756D5—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—51no—
761C23—51no—
762C23—101no—
763C23—202no—
764C23—202no—
765C23—401no—
766Q8—52no—
767Q8—101no—
768Q8—101no—
769Q8—101no—
770D4—21no—
771D4—21no—
772D4—21no—
773D4—21no—
774D4—21no—
775D4—42no—
776D4—81no—
777D4—101no—
778D4—101no—
779D4—201no—
780D4—202no—
781D4—202no—
782D4—202no—
783D4—202no—
784D4—401no—
785D4—401no—
786D4—401no—
787D4C3×D4×D512yes—
788C2×C4—21no—
789C2×C4—51no—
790C2×C4—51no—
791C2×C4—81no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—202no—
800C2×C4—202no—
801C2×C4—202no—
802C2×C4C3×D4×D511yescharacteristic
803C2×C4C3×D4×D511yescharacteristic
804C2×C4C23×C3×D511yescharacteristic
805C8—21no—
806C8—21no—
807C8—52no—
808C8—101no—
809C2×C3—42no—
810C2×C3—81no—
811C2×C3—81no—
812C2×C3—201no—
813C2×C3—201no—
814C2×C3—401no—
815C2×C3#6594311yescharacteristic
816C2×C3#6609111yescharacteristic
817C2×C3#6610711yescharacteristic
818C5C3×#326811yescharacteristic, complemented, Sylow
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—101no—
829C22—101no—
830C22—101no—
831C22—101no—
832C22—101no—
833C22—101no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C2×C3×D4×D511yescharacteristic
839C4—21no—
840C4—21no—
841C4—41no—
842C4—101no—
843C4—101no—
844C4—102no—
845C4—201no—
846C4—201no—
847C4C2×C3×D4×D511yescharacteristic
848C4C3×#414911yescharacteristic
849C3#1061207911yescharacteristic, direct product factor, Sylow
850C2—42no—
851C2—81no—
852C2—81no—
853C2—201no—
854C2—201no—
855C2—401no—
856C2C3×#6594311yescharacteristic
857C2C3×#6609111yescharacteristic
858C2C3×#6610711yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#459C2
socleC22×C3×C5C22×D4
hypercenterC3×#459D5
hypocenterC5C3×#3268
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4058C2semidirect
2. C2×C3×#4057C2semidirect
3. C3×#66052C2semidirect
4. C3×#65888C2semidirect
5. C3×C5×#459C2semidirect
6. C3×#65447C2semidirect
7. C3×#65445C2semidirect
8. C3×#65363C2semidirect
9. C3×#65307C2semidirect
10. C3×#65134C2semidirect
11. C3×#65125C2semidirect
12. C3×#65072C2semidirect
13. C3×#65070C2semidirect
14. C3×#65069C2semidirect
15. C3×#65064C2semidirect
16. #10612079C3direct (N × H)
19. C2×C3×#711C22semidirect
23. C3×C5×#127C22semidirect
29. C3×#4084C22semidirect
32. C2×C3×#687C22semidirect
33. C2×C3×#687C22semidirect
40. C2×C3×Dic20C22semidirect
43. C2×C3×C8×D5C22semidirect
50. C3×C4×Dic10C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
57. C3×#3952C22semidirect
58. C3×#3948C22semidirect
59. C3×#3942C22semidirect
60. C3×#3939C22semidirect
61. C3×#3935C22semidirect
63. C2×#4058C2×C3semidirect
64. C2×#4057C2×C3semidirect
65. #66052C2×C3semidirect
66. #65888C2×C3semidirect
67. C5×#459C2×C3semidirect
68. #65447C2×C3semidirect
69. #65445C2×C3semidirect
70. #65363C2×C3semidirect
71. #65307C2×C3semidirect
72. #65134C2×C3semidirect
73. #65125C2×C3semidirect
74. #65072C2×C3semidirect
75. #65070C2×C3semidirect
76. #65069C2×C3semidirect
77. #65064C2×C3semidirect
120. C3×#687D4semidirect
148. C3×#459D5semidirect
157. C2×#711C22×C3semidirect
161. C5×#127C22×C3semidirect
167. #4084C22×C3semidirect
170. C2×#687C22×C3semidirect
171. C2×#687C22×C3semidirect
178. C2×Dic20C22×C3semidirect
181. C2×C8×D5C22×C3semidirect
188. C4×Dic10C22×C3semidirect
189. C5×C4⋊C8C22×C3semidirect
190. C5×#102C22×C3semidirect
191. C5×#102C22×C3semidirect
195. #3952C22×C3semidirect
196. #3948C22×C3semidirect
197. #3942C22×C3semidirect
198. #3939C22×C3semidirect
199. #3935C22×C3semidirect
271. C3×#127C2×D5semidirect
288. C3×C4⋊C8C2×D5semidirect
293. C3×#102C2×D5semidirect
294. C3×#102C2×D5semidirect
340. #687C3×D4semidirect
368. #459C3×D5semidirect
537. #127C2×C3×D5semidirect
554. C4⋊C8C2×C3×D5semidirect
559. #102C2×C3×D5semidirect
560. #102C2×C3×D5semidirect
717. C3×C5#3268semidirect
818. C5C3×#3268semidirect
849. C3#10612079direct (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×#660522
C3×#658882
C3×C5×#4592
C3×#654472
C3×#654452
C3×#653632
C3×#653072
C3×#651342
C3×#651252
C3×#650722
C3×#650702
C3×#650692
C3×#650642
#106120793
C3×#32685