Finite Group Databasebeta

← C3×#10615746 #14457664

Subgroups — C3×#10615746 #14457664

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#577C211yesmaximal, characteristic, complemented
2C3×#66171C211yesmaximal, characteristic, complemented
3C3×#66169C211yesmaximal, characteristic, complemented
4C3×#66103C211yesmaximal, characteristic, complemented
5C3×#65534C211yesmaximal, characteristic, complemented
6C3×#65530C211yesmaximal, characteristic, complemented
7C3×#65492C211yesmaximal, characteristic, complemented
8C3×#65491C211yesmaximal, characteristic, complemented
9C3×#65488C211yesmaximal, characteristic, complemented
10C3×#65487C211yesmaximal, characteristic, complemented
11C3×#65486C211yesmaximal, characteristic, complemented
12C3×#65466C211yesmaximal, characteristic, complemented
13C3×#65465C211yesmaximal, characteristic, complemented
14C3×#65434C211yesmaximal, characteristic, complemented
15C3×#65431C211yesmaximal, characteristic, complemented
16#10615746C311yesmaximal, characteristic, direct product factor, Hall
17C3×C5×2−1+4C2211yescharacteristic, complemented
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19C3×#4149C2211yescharacteristic
20C3×#4149C2211yescharacteristic, complemented
21C3×C5×#137—21no—
22C3×C5×#137C2211yescharacteristic, complemented
23C3×C5×AGL(1,ℤ/8)—21no—
24C3×C5×AGL(1,ℤ/8)C2211yescharacteristic, complemented
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×SD16—21no—
28C2×C3×C5×SD16C2211yescharacteristic, complemented
29C3×C5×#131C2211yescharacteristic, complemented
30C3×#4096—21no—
31C3×#4096—21no—
32C3×#4096C2211yescharacteristic
33C3×#4095—21no—
34C3×#4095—21no—
35C3×#4095C2211yescharacteristic
36C3×#4095C2211yescharacteristic, complemented
37C3×#4095C2211yescharacteristic, complemented
38C3×#4095C2211yescharacteristic, complemented
39C3×#4094C2211yescharacteristic, complemented
40C3×#4094C2211yescharacteristic, complemented
41C3×#4093C2211yescharacteristic, complemented
42C3×#4088—21no—
43C3×#4088C2211yescharacteristic, complemented
44C2×C3×#688—21no—
45C2×C3×#688C2211yescharacteristic, complemented
46C3×#4086C2211yescharacteristic, complemented
47C3×#4078—21no—
48C3×#4078C2211yescharacteristic
49C2×C3×#686—21no—
50C2×C3×#686C2211yescharacteristic, complemented
51C3×#4065—21no—
52C3×#4060—21no—
53C3×#4060—21no—
54C3×D5×D8—21no—
55C2×C3×D40C2211yescharacteristic, complemented
56C3×#4047C2211yescharacteristic, complemented
57C3×#3969C2211yescharacteristic, complemented
58C3×#3969C2211yescharacteristic, complemented
59C3×#3969C2211yescharacteristic, complemented
60C3×#3968C2211yescharacteristic, complemented
61C3×#3965C2211yescharacteristic, complemented
62C3×#3957C2211yescharacteristic, complemented
63C3×#3955C2211yescharacteristic, complemented
64C3×#3955C2211yescharacteristic, complemented
65C3×#3954C2211yescharacteristic, complemented
66C3×#3951C2211yescharacteristic, complemented
67C3×#3947C2211yescharacteristic, complemented
68C3×#3288—51nomaximal, Hall
69C5×#577C2×C311yescharacteristic, complemented
70#66171C2×C311yescharacteristic, complemented
71#66169C2×C311yescharacteristic, complemented
72#66103C2×C311yescharacteristic, complemented
73#65534C2×C311yescharacteristic, complemented
74#65530C2×C311yescharacteristic, complemented
75#65492C2×C311yescharacteristic, complemented
76#65491C2×C311yescharacteristic, complemented
77#65488C2×C311yescharacteristic, complemented
78#65487C2×C311yescharacteristic, complemented
79#65486C2×C311yescharacteristic, complemented
80#65466C2×C311yescharacteristic, complemented
81#65465C2×C311yescharacteristic, complemented
82#65434C2×C311yescharacteristic, complemented
83#65431C2×C311yescharacteristic, complemented
84C3×C5×#41—21no—
85C3×C5×#41—21no—
86C3×C5×#41—21no—
87C3×C5×#41—21no—
88C3×C5×#41—41no—
89C3×C5×#41C2311yescharacteristic
90C3×C5×#41C2311yescharacteristic
91C3×C5×#41C2311yescharacteristic
92C2×C3×C5×Q8—21no—
93C2×C3×C5×Q8—21no—
94C2×C3×C5×Q8C2311yescharacteristic
95C2×C3×C5×D4—21no—
96C2×C3×C5×D4—21no—
97C2×C3×C5×D4—41no—
98C2×C3×C5×D4C2311yescharacteristic
99C2×C3×C22⋊D5—41no—
100C3×#713—21no—
101C3×#713—21no—
102C3×D4×D5—21no—
103C3×D4×D5—21no—
104C3×D4×D5—41no—
105C3×D4×D5—41no—
106C3×#709—21no—
107C3×#709—21no—
108C3×#709C2311yescharacteristic
109C2×C3×D20—21no—
110C2×C3×D20—21no—
111C2×C3×D20C2311yescharacteristic
112C2×C3×D20C2311yescharacteristic
113C3×C5×Q16—21no—
114C3×C5×Q16D411yescharacteristic, complemented
115C3×C5×SD16—21no—
116C3×C5×SD16—21no—
117C3×C5×SD16—21no—
118C3×C5×SD16—21no—
119C3×C5×SD16D411yescharacteristic, complemented
120C3×C5×SD16D411yescharacteristic, complemented
121C3×C5×D8—21no—
122C3×C5×D8D411yescharacteristic, complemented
123C3×C5×M16—21no—
124C3×C5×M16C2311yescharacteristic
125C2×C3×C5×C8—21no—
126C2×C3×C5×C8C2311yescharacteristic
127C3×#689—21no—
128C3×#689D411yescharacteristic, complemented
129C3×#688—21no—
130C3×#688—21no—
131C3×#688—21no—
132C3×#688—21no—
133C3×#688—21no—
134C3×#688—21no—
135C3×#688—21no—
136C3×#688D411yescharacteristic, complemented
137C3×#687—21no—
138C3×#687D411yescharacteristic, complemented
139C3×#686—21no—
140C3×#686—21no—
141C3×#686—21no—
142C3×#686—21no—
143C3×#686—21no—
144C3×#686—21no—
145C3×#686—21no—
146C3×#686D411yescharacteristic, complemented
147C3×#685—41no—
148C3×C4×Dic5C2311yescharacteristic
149C3×#681—21no—
150C3×#681—21no—
151C3×#681C2311yescharacteristic
152C3×#681C2311yescharacteristic
153C3×#681C2311yescharacteristic
154C2×C3×#168—21no—
155C2×C3×#168—21no—
156C2×C3×#168C2311yescharacteristic
157C3×D40—21no—
158C3×D40—21no—
159C3×#676—21no—
160C3×C8×D5—21no—
161C3×#577—51no—
162C3×#577D511yescharacteristic, complemented
163C3×#576—51no—
164C3×#576—51no—
165C3×#496—51no—
166C3×#472—51no—
167C3×#472—51no—
168C3×#471—51no—
169C3×#471—51no—
170C3×#455—51no—
171C3×#454—51no—
172C3×#453—51no—
173C3×#453—51no—
174C3×#444—51no—
175C3×#444—51no—
176C5×2−1+4C22×C311yescharacteristic, complemented
177C5×H(5,𝔽2)C22×C311yescharacteristic, complemented
178#4149C22×C311yescharacteristic
179#4149C22×C311yescharacteristic, complemented
180C5×#137—21no—
181C5×#137C22×C311yescharacteristic, complemented
182C5×AGL(1,ℤ/8)—21no—
183C5×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
184C5×#135—21no—
185C5×#135C22×C311yescharacteristic
186C2×C5×SD16—21no—
187C2×C5×SD16C22×C311yescharacteristic, complemented
188C5×#131C22×C311yescharacteristic, complemented
189#4096—21no—
190#4096—21no—
191#4096C22×C311yescharacteristic
192#4095—21no—
193#4095—21no—
194#4095C22×C311yescharacteristic
195#4095C22×C311yescharacteristic, complemented
196#4095C22×C311yescharacteristic, complemented
197#4095C22×C311yescharacteristic, complemented
198#4094C22×C311yescharacteristic, complemented
199#4094C22×C311yescharacteristic, complemented
200#4093C22×C311yescharacteristic, complemented
201#4088—21no—
202#4088C22×C311yescharacteristic, complemented
203C2×#688—21no—
204C2×#688C22×C311yescharacteristic, complemented
205#4086C22×C311yescharacteristic, complemented
206#4078—21no—
207#4078C22×C311yescharacteristic
208C2×#686—21no—
209C2×#686C22×C311yescharacteristic, complemented
210#4065—21no—
211#4060—21no—
212#4060—21no—
213D5×D8—21no—
214C2×D40C22×C311yescharacteristic, complemented
215#4047C22×C311yescharacteristic, complemented
216#3969C22×C311yescharacteristic, complemented
217#3969C22×C311yescharacteristic, complemented
218#3969C22×C311yescharacteristic, complemented
219#3968C22×C311yescharacteristic, complemented
220#3965C22×C311yescharacteristic, complemented
221#3957C22×C311yescharacteristic, complemented
222#3955C22×C311yescharacteristic, complemented
223#3955C22×C311yescharacteristic, complemented
224#3954C22×C311yescharacteristic, complemented
225#3951C22×C311yescharacteristic, complemented
226#3947C22×C311yescharacteristic, complemented
227#3288—51noSylow
228C23×C3×C5—21no—
229C23×C3×C5—41no—
230C22×C3×D5—21no—
231C22×C3×D5—21no—
232C22×C3×D5—41no—
233C22×C3×D5—41no—
234C3×C5×Q8—21no—
235C3×C5×Q8—21no—
236C3×C5×Q8—41no—
237C3×C5×Q8C2×D411yescharacteristic
238C3×C5×Q8C2×D411yescharacteristic
239C3×C5×Q8C2×D411yescharacteristic
240C3×C5×D4—21no—
241C3×C5×D4—21no—
242C3×C5×D4—21no—
243C3×C5×D4—21no—
244C3×C5×D4—21no—
245C3×C5×D4—41no—
246C3×C5×D4—41no—
247C3×C5×D4—41no—
248C3×C5×D4C2×D411yescharacteristic
249C3×C5×D4C2×D411yescharacteristic
250C3×C5×D4C2×D411yescharacteristic
251C2×C3×C4×C5—21no—
252C2×C3×C4×C5—21no—
253C2×C3×C4×C5—21no—
254C2×C3×C4×C5—21no—
255C2×C3×C4×C5—41no—
256C2×C3×C4×C5—41no—
257C2×C3×C4×C5—41no—
258C2×C3×C4×C5C2411yescharacteristic
259C3×C22⋊D5—21no—
260C3×C22⋊D5—41no—
261C3×C22⋊D5—41no—
262C3×C22⋊D5—82no—
263C2×C3×Dic5—21no—
264C3×D20—21no—
265C3×D20—21no—
266C3×D20—21no—
267C3×D20—21no—
268C3×D20—41no—
269C3×D20—41no—
270C3×D20C2×D411yescharacteristic
271C3×C4×D5—21no—
272C3×C4×D5—41no—
273C3×C4×D5—41no—
274C3×Dic10C2×D411yescharacteristic
275C3×C5×C8—21no—
276C3×C5×C8C2×D411yescharacteristic
277C3×C5×C8C2×D411yescharacteristic
278C3×#168—21no—
279C3×#168—21no—
280C3×#168—21no—
281C3×#168C2×D411yescharacteristic
282C3×#168C2×D411yescharacteristic
283C3×2−1+4C2×D511yescharacteristic, complemented
284C3×H(5,𝔽2)—51no—
285C3×H(5,𝔽2)—51no—
286C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
287C3×#137—21no—
288C3×#137—51no—
289C3×#137—101no—
290C3×#137C2×D511yescharacteristic, complemented
291C3×AGL(1,ℤ/8)—21no—
292C3×AGL(1,ℤ/8)—51no—
293C3×AGL(1,ℤ/8)—51no—
294C3×AGL(1,ℤ/8)—51no—
295C3×AGL(1,ℤ/8)—51no—
296C3×AGL(1,ℤ/8)—51no—
297C3×AGL(1,ℤ/8)—101no—
298C3×AGL(1,ℤ/8)—101no—
299C3×AGL(1,ℤ/8)—101no—
300C3×AGL(1,ℤ/8)—101no—
301C3×AGL(1,ℤ/8)—101no—
302C3×AGL(1,ℤ/8)C2×D511yescharacteristic, complemented
303C3×#135—21no—
304C3×#135—51no—
305C3×#135—101no—
306C3×#135—101no—
307C3×#135—101no—
308C3×#135C2×D511yescharacteristic
309C2×C3×SD16—21no—
310C2×C3×SD16—51no—
311C2×C3×SD16—101no—
312C2×C3×SD16C2×D511yescharacteristic, complemented
313C2×C3×D8—51no—
314C2×C3×D8—51no—
315C2×C3×D8—101no—
316C2×C3×D8—101no—
317C3×#131—51no—
318C3×#131—51no—
319C3×#131—51no—
320C3×#131C2×D511yescharacteristic, complemented
321C3×#127—51no—
322C3×#124—51no—
323C3×#108—51no—
324C3×#108—51no—
325C3×#104—51no—
326C3×#104—51no—
327C3×#104—51no—
328C3×#104—51no—
329C3×#101—51no—
330C3×#100—51no—
331C3×#100—51no—
332C3×#100—51no—
333C3×#97—51no—
334C5×#41—21no—
335C5×#41—21no—
336C5×#41—21no—
337C5×#41—21no—
338C5×#41—41no—
339C5×#41C23×C311yescharacteristic
340C5×#41C23×C311yescharacteristic
341C5×#41C23×C311yescharacteristic
342C2×C5×Q8—21no—
343C2×C5×Q8—21no—
344C2×C5×Q8C23×C311yescharacteristic
345C2×C5×D4—21no—
346C2×C5×D4—21no—
347C2×C5×D4—41no—
348C2×C5×D4C23×C311yescharacteristic
349C2×C22⋊D5—41no—
350#713—21no—
351#713—21no—
352D4×D5—21no—
353D4×D5—21no—
354D4×D5—41no—
355D4×D5—41no—
356#709—21no—
357#709—21no—
358#709C23×C311yescharacteristic
359C2×D20—21no—
360C2×D20—21no—
361C2×D20C23×C311yescharacteristic
362C2×D20C23×C311yescharacteristic
363C5×Q16—21no—
364C5×Q16C3×D411yescharacteristic, complemented
365C5×SD16—21no—
366C5×SD16—21no—
367C5×SD16—21no—
368C5×SD16—21no—
369C5×SD16C3×D411yescharacteristic, complemented
370C5×SD16C3×D411yescharacteristic, complemented
371C5×D8—21no—
372C5×D8C3×D411yescharacteristic, complemented
373C5×M16—21no—
374C5×M16C23×C311yescharacteristic
375C2×C5×C8—21no—
376C2×C5×C8C23×C311yescharacteristic
377#689—21no—
378#689C3×D411yescharacteristic, complemented
379#688—21no—
380#688—21no—
381#688—21no—
382#688—21no—
383#688—21no—
384#688—21no—
385#688—21no—
386#688C3×D411yescharacteristic, complemented
387#687—21no—
388#687C3×D411yescharacteristic, complemented
389#686—21no—
390#686—21no—
391#686—21no—
392#686—21no—
393#686—21no—
394#686—21no—
395#686—21no—
396#686C3×D411yescharacteristic, complemented
397#685—41no—
398C4×Dic5C23×C311yescharacteristic
399#681—21no—
400#681—21no—
401#681C23×C311yescharacteristic
402#681C23×C311yescharacteristic
403#681C23×C311yescharacteristic
404C2×#168—21no—
405C2×#168—21no—
406C2×#168C23×C311yescharacteristic
407D40—21no—
408D40—21no—
409#676—21no—
410C8×D5—21no—
411#577—51no—
412#577C3×D511yescharacteristic, complemented
413#576—51no—
414#576—51no—
415#496—51no—
416#472—51no—
417#472—51no—
418#471—51no—
419#471—51no—
420#455—51no—
421#454—51no—
422#453—51no—
423#453—51no—
424#444—51no—
425#444—51no—
426C22×C3×C5—21no—
427C22×C3×C5—21no—
428C22×C3×C5—21no—
429C22×C3×C5—41no—
430C22×C3×C5—81no—
431C22×C3×C5—161no—
432C22×C3×C5H(5,𝔽2)11yescharacteristic
433C2×C3×D5—21no—
434C2×C3×D5—41no—
435C2×C3×D5—41no—
436C2×C3×D5—81no—
437C2×C3×D5—81no—
438C2×C3×D5—161no—
439C2×C3×D5—161no—
440C3×C4×C5—21no—
441C3×C4×C5—21no—
442C3×C4×C5—21no—
443C3×C4×C5—41no—
444C3×C4×C5C22×D411yescharacteristic
445C3×C4×C5C22×D411yescharacteristic
446C3×Dic5—21no—
447C3×Dic5—41no—
448C3×#41—21no—
449C3×#41—21no—
450C3×#41—21no—
451C3×#41—21no—
452C3×#41—41no—
453C3×#41—51no—
454C3×#41—101no—
455C3×#41—101no—
456C3×#41—101no—
457C3×#41—101no—
458C3×#41C22×D511yescharacteristic
459C3×#41C22×D511yescharacteristic
460C3×#41C22×D511yescharacteristic
461C2×C3×Q8—21no—
462C2×C3×Q8—21no—
463C2×C3×Q8C22×D511yescharacteristic
464C2×C3×D4—21no—
465C2×C3×D4—21no—
466C2×C3×D4—41no—
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×D4—201no—
474C2×C3×D4—201no—
475C2×C3×D4—201no—
476C2×C3×D4C22×D511yescharacteristic
477C3×Q16—21no—
478C3×Q16—51no—
479C3×Q16—101no—
480C3×Q16C22⋊D511yescharacteristic, complemented
481C3×SD16—21no—
482C3×SD16—21no—
483C3×SD16—21no—
484C3×SD16—21no—
485C3×SD16—51no—
486C3×SD16—51no—
487C3×SD16—101no—
488C3×SD16—101no—
489C3×SD16—101no—
490C3×SD16—101no—
491C3×SD16—101no—
492C3×SD16—101no—
493C3×SD16—101no—
494C3×SD16—101no—
495C3×SD16C22⋊D511yescharacteristic, complemented
496C3×SD16C22⋊D511yescharacteristic, complemented
497C3×D8—21no—
498C3×D8—51no—
499C3×D8—101no—
500C3×D8—101no—
501C3×D8—101no—
502C3×D8—101no—
503C3×D8—101no—
504C3×D8—101no—
505C3×D8—101no—
506C3×D8—101no—
507C3×D8—101no—
508C3×D8C22⋊D511yescharacteristic, complemented
509C3×M16—21no—
510C3×M16—51no—
511C3×M16—51no—
512C3×M16—51no—
513C3×M16—101no—
514C3×M16—101no—
515C3×M16—101no—
516C3×M16C22×D511yescharacteristic
517C2×C3×C8—21no—
518C2×C3×C8—51no—
519C2×C3×C8—101no—
520C2×C3×C8—101no—
521C2×C3×C8—101no—
522C2×C3×C8C22×D511yescharacteristic
523C3×C22⋊C4—201no—
524C3×C42—51no—
525C23×C5—21no—
526C23×C5—41no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—41no—
530C22×D5—41no—
531C5×Q8—21no—
532C5×Q8—21no—
533C5×Q8—41no—
534C5×Q8C2×C3×D411yescharacteristic
535C5×Q8C2×C3×D411yescharacteristic
536C5×Q8C2×C3×D411yescharacteristic
537C5×D4—21no—
538C5×D4—21no—
539C5×D4—21no—
540C5×D4—21no—
541C5×D4—21no—
542C5×D4—41no—
543C5×D4—41no—
544C5×D4—41no—
545C5×D4C2×C3×D411yescharacteristic
546C5×D4C2×C3×D411yescharacteristic
547C5×D4C2×C3×D411yescharacteristic
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—41no—
553C2×C4×C5—41no—
554C2×C4×C5—41no—
555C2×C4×C5C24×C311yescharacteristic
556C22⋊D5—21no—
557C22⋊D5—41no—
558C22⋊D5—41no—
559C22⋊D5—82no—
560C2×Dic5—21no—
561D20—21no—
562D20—21no—
563D20—21no—
564D20—21no—
565D20—41no—
566D20—41no—
567D20C2×C3×D411yescharacteristic
568C4×D5—21no—
569C4×D5—41no—
570C4×D5—41no—
571Dic10C2×C3×D411yescharacteristic
572C5×C8—21no—
573C5×C8C2×C3×D411yescharacteristic
574C5×C8C2×C3×D411yescharacteristic
575#168—21no—
576#168—21no—
577#168—21no—
578#168C2×C3×D411yescharacteristic
579#168C2×C3×D411yescharacteristic
5802−1+4C2×C3×D511yescharacteristic, complemented
581H(5,𝔽2)—51no—
582H(5,𝔽2)—51no—
583H(5,𝔽2)C2×C3×D511yescharacteristic, complemented
584#137—21no—
585#137—51no—
586#137—101no—
587#137C2×C3×D511yescharacteristic, complemented
588AGL(1,ℤ/8)—21no—
589AGL(1,ℤ/8)—51no—
590AGL(1,ℤ/8)—51no—
591AGL(1,ℤ/8)—51no—
592AGL(1,ℤ/8)—51no—
593AGL(1,ℤ/8)—51no—
594AGL(1,ℤ/8)—101no—
595AGL(1,ℤ/8)—101no—
596AGL(1,ℤ/8)—101no—
597AGL(1,ℤ/8)—101no—
598AGL(1,ℤ/8)—101no—
599AGL(1,ℤ/8)C2×C3×D511yescharacteristic, complemented
600#135—21no—
601#135—51no—
602#135—101no—
603#135—101no—
604#135—101no—
605#135C2×C3×D511yescharacteristic
606C2×SD16—21no—
607C2×SD16—51no—
608C2×SD16—101no—
609C2×SD16C2×C3×D511yescharacteristic, complemented
610C2×D8—51no—
611C2×D8—51no—
612C2×D8—101no—
613C2×D8—101no—
614#131—51no—
615#131—51no—
616#131—51no—
617#131C2×C3×D511yescharacteristic, complemented
618#127—51no—
619#124—51no—
620#108—51no—
621#108—51no—
622#104—51no—
623#104—51no—
624#104—51no—
625#104—51no—
626#101—51no—
627#100—51no—
628#100—51no—
629#100—51no—
630#97—51no—
631C2×C3×C5—21no—
632C2×C3×C5—41no—
633C2×C3×C5—41no—
634C2×C3×C5—41no—
635C2×C3×C5—81no—
636C2×C3×C5D4211yescharacteristic
637C3×D5—41no—
638C3×D5—81no—
639C3×D5—81no—
640C23×C3—21no—
641C23×C3—41no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—201no—
645C23×C3—201no—
646C3×Q8—21no—
647C3×Q8—21no—
648C3×Q8—41no—
649C3×Q8—51no—
650C3×Q8D4×D511yescharacteristic
651C3×Q8C2×C22⋊D511yescharacteristic
652C3×Q8C2×C22⋊D511yescharacteristic
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—21no—
658C3×D4—41no—
659C3×D4—41no—
660C3×D4—41no—
661C3×D4—51no—
662C3×D4—101no—
663C3×D4—101no—
664C3×D4—101no—
665C3×D4—101no—
666C3×D4—101no—
667C3×D4—201no—
668C3×D4—201no—
669C3×D4—201no—
670C3×D4—201no—
671C3×D4—402no—
672C3×D4D4×D511yescharacteristic
673C3×D4C2×C22⋊D511yescharacteristic
674C3×D4C2×C22⋊D511yescharacteristic
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—201no—
685C2×C3×C4—201no—
686C2×C3×C4C23×D511yescharacteristic
687C3×C8—21no—
688C3×C8—51no—
689C3×C8—51no—
690C3×C8—101no—
691C3×C8—101no—
692C3×C8—101no—
693C3×C8C2×C22⋊D511yescharacteristic
694C3×C8C2×C22⋊D511yescharacteristic
695C22×C5—21no—
696C22×C5—21no—
697C22×C5—21no—
698C22×C5—41no—
699C22×C5—81no—
700C22×C5—161no—
701C22×C5C3×H(5,𝔽2)11yescharacteristic
702C2×D5—21no—
703C2×D5—41no—
704C2×D5—41no—
705C2×D5—81no—
706C2×D5—81no—
707C2×D5—161no—
708C2×D5—161no—
709C4×C5—21no—
710C4×C5—21no—
711C4×C5—21no—
712C4×C5—41no—
713C4×C5C22×C3×D411yescharacteristic
714C4×C5C22×C3×D411yescharacteristic
715Dic5—21no—
716Dic5—41no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—41no—
722#41—51no—
723#41—101no—
724#41—101no—
725#41—101no—
726#41—101no—
727#41C22×C3×D511yescharacteristic
728#41C22×C3×D511yescharacteristic
729#41C22×C3×D511yescharacteristic
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8C22×C3×D511yescharacteristic
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—51no—
737C2×D4—51no—
738C2×D4—101no—
739C2×D4—101no—
740C2×D4—101no—
741C2×D4—101no—
742C2×D4—201no—
743C2×D4—201no—
744C2×D4—201no—
745C2×D4C22×C3×D511yescharacteristic
746Q16—21no—
747Q16—51no—
748Q16—101no—
749Q16C3×C22⋊D511yescharacteristic, complemented
750SD16—21no—
751SD16—21no—
752SD16—21no—
753SD16—21no—
754SD16—51no—
755SD16—51no—
756SD16—101no—
757SD16—101no—
758SD16—101no—
759SD16—101no—
760SD16—101no—
761SD16—101no—
762SD16—101no—
763SD16—101no—
764SD16C3×C22⋊D511yescharacteristic, complemented
765SD16C3×C22⋊D511yescharacteristic, complemented
766D8—21no—
767D8—51no—
768D8—101no—
769D8—101no—
770D8—101no—
771D8—101no—
772D8—101no—
773D8—101no—
774D8—101no—
775D8—101no—
776D8—101no—
777D8C3×C22⋊D511yescharacteristic, complemented
778M16—21no—
779M16—51no—
780M16—51no—
781M16—51no—
782M16—101no—
783M16—101no—
784M16—101no—
785M16C22×C3×D511yescharacteristic
786C2×C8—21no—
787C2×C8—51no—
788C2×C8—101no—
789C2×C8—101no—
790C2×C8—101no—
791C2×C8C22×C3×D511yescharacteristic
792C22⋊C4—201no—
793C42—51no—
794C3×C5#328811yescharacteristic, complemented, Hall
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—41no—
799C22×C3—81no—
800C22×C3—101no—
801C22×C3—161no—
802C22×C3—201no—
803C22×C3—201no—
804C22×C3—401no—
805C22×C3—401no—
806C22×C3—801no—
807C22×C3—801no—
808C22×C3#414411yescharacteristic
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—41no—
813C3×C4—101no—
814C3×C4—201no—
815C3×C4C2×D4×D511yescharacteristic
816C3×C4C22×C22⋊D511yescharacteristic
817C2×C5—21no—
818C2×C5—41no—
819C2×C5—41no—
820C2×C5—41no—
821C2×C5—81no—
822C2×C5C3×D4211yescharacteristic
823D5—41no—
824D5—81no—
825D5—81no—
826C23—21no—
827C23—41no—
828C23—101no—
829C23—101no—
830C23—201no—
831C23—201no—
832Q8—21no—
833Q8—21no—
834Q8—41no—
835Q8—51no—
836Q8C3×D4×D511yescharacteristic
837Q8C2×C3×C22⋊D511yescharacteristic
838Q8C2×C3×C22⋊D511yescharacteristic
839D4—21no—
840D4—21no—
841D4—21no—
842D4—21no—
843D4—21no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—51no—
848D4—101no—
849D4—101no—
850D4—101no—
851D4—101no—
852D4—101no—
853D4—201no—
854D4—201no—
855D4—201no—
856D4—201no—
857D4—402no—
858D4C3×D4×D511yescharacteristic
859D4C2×C3×C22⋊D511yescharacteristic
860D4C2×C3×C22⋊D511yescharacteristic
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—201no—
871C2×C4—201no—
872C2×C4C23×C3×D511yescharacteristic
873C8—21no—
874C8—51no—
875C8—51no—
876C8—101no—
877C8—101no—
878C8—101no—
879C8C2×C3×C22⋊D511yescharacteristic
880C8C2×C3×C22⋊D511yescharacteristic
881C2×C3—21no—
882C2×C3—41no—
883C2×C3—41no—
884C2×C3—41no—
885C2×C3—81no—
886C2×C3—201no—
887C2×C3—401no—
888C2×C3—401no—
889C2×C3D4×C22⋊D511yescharacteristic
890C5C3×#328811yescharacteristic, complemented, Sylow
891C22—21no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—81no—
896C22—101no—
897C22—161no—
898C22—201no—
899C22—201no—
900C22—401no—
901C22—401no—
902C22—801no—
903C22—801no—
904C22C3×#414411yescharacteristic
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—101no—
910C4—201no—
911C4C2×C3×D4×D511yescharacteristic
912C4C22×C3×C22⋊D511yescharacteristic
913C3#1061574611yescharacteristic, direct product factor, Sylow
914C2—21no—
915C2—41no—
916C2—41no—
917C2—41no—
918C2—81no—
919C2—201no—
920C2—401no—
921C2—401no—
922C2C3×D4×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C3D4×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#577C2
socleC2×C3×C5D42
hypercenterC3×#577D5
hypocenterC5C3×#3288
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#577

Complements

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

NH ≅ G/Ntype
1. C3×C5×#577C2semidirect
2. C3×#66171C2semidirect
3. C3×#66169C2semidirect
4. C3×#66103C2semidirect
5. C3×#65534C2semidirect
6. C3×#65530C2semidirect
7. C3×#65492C2semidirect
8. C3×#65491C2semidirect
9. C3×#65488C2semidirect
10. C3×#65487C2semidirect
11. C3×#65486C2semidirect
12. C3×#65466C2semidirect
13. C3×#65465C2semidirect
14. C3×#65434C2semidirect
15. C3×#65431C2semidirect
16. #10615746C3direct (N × H)
17. C3×C5×2−1+4C22semidirect
18. C3×C5×H(5,𝔽2)C22semidirect
20. C3×#4149C22semidirect
22. C3×C5×#137C22semidirect
24. C3×C5×AGL(1,ℤ/8)C22semidirect
28. C2×C3×C5×SD16C22semidirect
29. C3×C5×#131C22semidirect
36. C3×#4095C22semidirect
37. C3×#4095C22semidirect
38. C3×#4095C22semidirect
39. C3×#4094C22semidirect
40. C3×#4094C22semidirect
41. C3×#4093C22semidirect
43. C3×#4088C22semidirect
45. C2×C3×#688C22semidirect
46. C3×#4086C22semidirect
50. C2×C3×#686C22semidirect
55. C2×C3×D40C22semidirect
56. C3×#4047C22semidirect
57. C3×#3969C22semidirect
58. C3×#3969C22semidirect
59. C3×#3969C22semidirect
60. C3×#3968C22semidirect
61. C3×#3965C22semidirect
62. C3×#3957C22semidirect
63. C3×#3955C22semidirect
64. C3×#3955C22semidirect
65. C3×#3954C22semidirect
66. C3×#3951C22semidirect
67. C3×#3947C22semidirect
69. C5×#577C2×C3semidirect
70. #66171C2×C3semidirect
71. #66169C2×C3semidirect
72. #66103C2×C3semidirect
73. #65534C2×C3semidirect
74. #65530C2×C3semidirect
75. #65492C2×C3semidirect
76. #65491C2×C3semidirect
77. #65488C2×C3semidirect
78. #65487C2×C3semidirect
79. #65486C2×C3semidirect
80. #65466C2×C3semidirect
81. #65465C2×C3semidirect
82. #65434C2×C3semidirect
83. #65431C2×C3semidirect
114. C3×C5×Q16D4semidirect
119. C3×C5×SD16D4semidirect
120. C3×C5×SD16D4semidirect
122. C3×C5×D8D4semidirect
128. C3×#689D4semidirect
136. C3×#688D4semidirect
138. C3×#687D4semidirect
146. C3×#686D4semidirect
162. C3×#577D5semidirect
176. C5×2−1+4C22×C3semidirect
177. C5×H(5,𝔽2)C22×C3semidirect
179. #4149C22×C3semidirect
181. C5×#137C22×C3semidirect
183. C5×AGL(1,ℤ/8)C22×C3semidirect
187. C2×C5×SD16C22×C3semidirect
188. C5×#131C22×C3semidirect
195. #4095C22×C3semidirect
196. #4095C22×C3semidirect
197. #4095C22×C3semidirect
198. #4094C22×C3semidirect
199. #4094C22×C3semidirect
200. #4093C22×C3semidirect
202. #4088C22×C3semidirect
204. C2×#688C22×C3semidirect
205. #4086C22×C3semidirect
209. C2×#686C22×C3semidirect
214. C2×D40C22×C3semidirect
215. #4047C22×C3semidirect
216. #3969C22×C3semidirect
217. #3969C22×C3semidirect
218. #3969C22×C3semidirect
219. #3968C22×C3semidirect
220. #3965C22×C3semidirect
221. #3957C22×C3semidirect
222. #3955C22×C3semidirect
223. #3955C22×C3semidirect
224. #3954C22×C3semidirect
225. #3951C22×C3semidirect
226. #3947C22×C3semidirect
283. C3×2−1+4C2×D5semidirect
286. C3×H(5,𝔽2)C2×D5semidirect
290. C3×#137C2×D5semidirect
302. C3×AGL(1,ℤ/8)C2×D5semidirect
312. C2×C3×SD16C2×D5semidirect
320. C3×#131C2×D5semidirect
364. C5×Q16C3×D4semidirect
369. C5×SD16C3×D4semidirect
370. C5×SD16C3×D4semidirect
372. C5×D8C3×D4semidirect
378. #689C3×D4semidirect
386. #688C3×D4semidirect
388. #687C3×D4semidirect
396. #686C3×D4semidirect
412. #577C3×D5semidirect
480. C3×Q16C22⋊D5semidirect
495. C3×SD16C22⋊D5semidirect
496. C3×SD16C22⋊D5semidirect
508. C3×D8C22⋊D5semidirect
580. 2−1+4C2×C3×D5semidirect
583. H(5,𝔽2)C2×C3×D5semidirect
587. #137C2×C3×D5semidirect
599. AGL(1,ℤ/8)C2×C3×D5semidirect
609. C2×SD16C2×C3×D5semidirect
617. #131C2×C3×D5semidirect
749. Q16C3×C22⋊D5semidirect
764. SD16C3×C22⋊D5semidirect
765. SD16C3×C22⋊D5semidirect
777. D8C3×C22⋊D5semidirect
794. C3×C5#3288semidirect
890. C5C3×#3288semidirect
913. C3#10615746direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5772
C3×#661712
C3×#661692
C3×#661032
C3×#655342
C3×#655302
C3×#654922
C3×#654912
C3×#654882
C3×#654872
C3×#654862
C3×#654662
C3×#654652
C3×#654342
C3×#654312
#106157463
C3×#32885