Finite Group Databasebeta

← C3×D5×#577 #14510016

Subgroups — C3×D5×#577 #14510016

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×2−1+4C211yesmaximal, characteristic, complemented
2C3×D5×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C3×C5×#577C211yesmaximal, characteristic, complemented
4C3×#66171C211yesmaximal, characteristic, complemented
5C3×#66170C211yesmaximal, characteristic, complemented
6C3×#66112C213yesmaximal, complemented
7C3×D5×#137C213yesmaximal, complemented
8C3×#66109C213yesmaximal, complemented
9C3×D5×AGL(1,ℤ/8)C213yesmaximal, complemented
10C3×#66104C213yesmaximal, complemented
11C3×D5×#135C213yesmaximal, complemented
12C3×#66096C213yesmaximal, complemented
13C2×C3×D5×SD16C213yesmaximal, complemented
14C3×#66085C211yesmaximal, characteristic, complemented
15C3×D5×#131C211yesmaximal, characteristic, complemented
16D5×#577C311yesmaximal, characteristic, direct product factor, Hall
17C3×C5×2−1+4C2211yescharacteristic, complemented
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19C3×#4150—23no—
20C3×#4150C2213yescomplemented
21C3×#4150C2211yescharacteristic, complemented
22C3×#4149—21no—
23C3×#4149C2213yescomplemented
24C3×#4149C2211yescharacteristic, complemented
25C3×D5×#41—21no—
26C3×D5×#41—23no—
27C3×D5×#41C2213yes—
28C3×D5×#41C2211yescharacteristic
29C3×D5×#41C2213yescomplemented
30C3×#4147—21no—
31C3×#4147C2213yescomplemented
32C2×C3×Q8×D5—21no—
33C2×C3×Q8×D5C2213yescomplemented
34C3×#4144—23no—
35C3×#4144C2213yescomplemented
36C2×C3×D4×D5—23no—
37C2×C3×D4×D5C2213yes—
38C3×C5×#137C2213yescomplemented
39C3×C5×AGL(1,ℤ/8)C2213yescomplemented
40C3×C5×#135C2213yescomplemented
41C2×C3×C5×SD16C2213yescomplemented
42C3×C5×#131C2211yescharacteristic, complemented
43C3×#4097C2213yescomplemented
44C3×#4096C2213yescomplemented
45C3×#4096C2213yescomplemented
46C3×#4095C2213yescomplemented
47C3×#4094C2211yescharacteristic, complemented
48C3×#4088C2213yescomplemented
49C2×C3×#688C2213yescomplemented
50C2×C3×#687C2213yescomplemented
51C3×#4078C2213yescomplemented
52C3×#4065C2213yescomplemented
53C3×#4064C2216yescomplemented
54C3×D5×Q16C2213yescomplemented
55C3×#4062C2213yescomplemented
56C3×#4062C2213yescomplemented
57C3×#4061C2216yescomplemented
58C3×#4060C2216yescomplemented
59C3×D5×SD16C2211yescharacteristic, complemented
60C3×D5×SD16C2213yescomplemented
61C3×D5×SD16C2216yescomplemented
62C3×D5×SD16C2216yescomplemented
63C3×D5×SD16C2216yescomplemented
64C3×#4058C2213yescomplemented
65C3×#4057C2216yescomplemented
66C3×D5×D8C2213yescomplemented
67C3×#4055C2213yescomplemented
68C3×#4054C2213yescomplemented
69C3×#4053C2213yescomplemented
70C3×D5×M16C2213yescomplemented
71C3×#4050C2213yescomplemented
72C2×C3×#677C2213yescomplemented
73C3×#4047C2213yescomplemented
74C2×C3×C8×D5C2213yescomplemented
75C2×C3×#577—51nomaximal, Hall
76D5×2−1+4C2×C311yescharacteristic, complemented
77D5×H(5,𝔽2)C2×C311yescharacteristic, complemented
78C5×#577C2×C311yescharacteristic, complemented
79#66171C2×C311yescharacteristic, complemented
80#66170C2×C311yescharacteristic, complemented
81#66112C2×C313yescomplemented
82D5×#137C2×C313yescomplemented
83#66109C2×C313yescomplemented
84D5×AGL(1,ℤ/8)C2×C313yescomplemented
85#66104C2×C313yescomplemented
86D5×#135C2×C313yescomplemented
87#66096C2×C313yescomplemented
88C2×D5×SD16C2×C313yescomplemented
89#66085C2×C311yescharacteristic, complemented
90D5×#131C2×C311yescharacteristic, complemented
91C23×C3×D5—23no—
92C3×C5×#41—21no—
93C3×C5×#41—23no—
94C3×C5×#41C2313yes—
95C3×C5×#41C2311yescharacteristic
96C3×C5×#41C2313yescomplemented
97C2×C3×C5×Q8—21no—
98C2×C3×C5×Q8C2313yescomplemented
99C2×C3×C5×D4—23no—
100C2×C3×C5×D4C2313yes—
101C2×C3×C22⋊D5—26no—
102C2×C3×C22⋊D5—23no—
103C3×#713—21no—
104C3×#713—23no—
105C3×#713D411yescharacteristic
106C3×#713C2313yes—
107C3×#713C2313yescomplemented
108C3×Q8×D5—21no—
109C3×Q8×D5—23no—
110C3×Q8×D5—23no—
111C3×Q8×D5—23no—
112C3×Q8×D5D411yescharacteristic
113C3×Q8×D5C2313yes—
114C3×Q8×D5C2311yescharacteristic
115C3×Q8×D5C2316yescomplemented
116C3×#711—23no—
117C3×#711—26no—
118C3×#711—23no—
119C3×#711—23no—
120C3×#711—23no—
121C3×#711D413yes—
122C3×#711C2313yes—
123C3×#711C2313yescomplemented
124C3×D4×D5—23no—
125C3×D4×D5—23no—
126C3×D4×D5—23no—
127C3×D4×D5—26no—
128C3×D4×D5—23no—
129C3×D4×D5—23no—
130C3×D4×D5—23no—
131C3×D4×D5D413yes—
132C3×D4×D5C2313yes—
133C3×D4×D5C2316yes—
134C3×D4×D5C2311yescharacteristic
135C3×#709—26no—
136C3×#709—23no—
137C3×#709—23no—
138C3×#709—23no—
139C3×#709—23no—
140C3×#709C2313yes—
141C3×#709C2313yes—
142C3×#709C2313yescomplemented
143C2×C3×D20—23no—
144C2×C3×D20C2313yes—
145C2×C3×C4×D5—23no—
146C2×C3×C4×D5—23no—
147C2×C3×C4×D5—23no—
148C2×C3×C4×D5C2313yes—
149C2×C3×Dic10—23no—
150C2×C3×Dic10—23no—
151C2×C3×Dic10C2313yescomplemented
152C3×C5×Q16C2313yescomplemented
153C3×C5×SD16C2313yescomplemented
154C3×C5×SD16C2316yescomplemented
155C3×C5×SD16C2311yescharacteristic, complemented
156C3×C5×D8C2313yescomplemented
157C3×C5×M16C2313yescomplemented
158C2×C3×C5×C8C2313yescomplemented
159C3×#689C2313yescomplemented
160C3×#689C2313yescomplemented
161C3×#688C2313yescomplemented
162C3×#688C2316yescomplemented
163C3×#688C2311yescharacteristic, complemented
164C3×#687C2316yescomplemented
165C3×#687C2313yescomplemented
166C3×#687C2311yescharacteristic, complemented
167C3×#686C2313yescomplemented
168C3×#686C2313yescomplemented
169C3×#681C2313yescomplemented
170C2×C3×#168C2313yescomplemented
171C3×Dic20C2313yescomplemented
172C3×D40C2313yescomplemented
173C3×#677C2313yescomplemented
174C3×#677C2316yescomplemented
175C3×#677C2311yescharacteristic, complemented
176C3×#676C2316yescomplemented
177C3×C8×D5C2311yescharacteristic
178C3×C8×D5C2313yes—
179C3×C8×D5C2313yescomplemented
180C3×C8×D5C2313yescomplemented
181C2×C3×2−1+4—51no—
182C2×C3×H(5,𝔽2)—51no—
183C3×#577—51no—
184C3×#577—51no—
185C3×#577—53no—
186C3×#577—53no—
187C3×#577—53no—
188C3×#577—53no—
189C3×#577—51no—
190C3×#577D511yescharacteristic, direct product factor
191C2×C3×#137—53no—
192C2×C3×AGL(1,ℤ/8)—53no—
193C2×C3×#135—53no—
194C22×C3×SD16—53no—
195C2×C3×#131—51no—
196C5×2−1+4C22×C311yescharacteristic, complemented
197C5×H(5,𝔽2)C22×C311yescharacteristic, complemented
198#4150—23no—
199#4150C22×C313yescomplemented
200#4150C22×C311yescharacteristic, complemented
201#4149—21no—
202#4149C22×C313yescomplemented
203#4149C22×C311yescharacteristic, complemented
204D5×#41—21no—
205D5×#41—23no—
206D5×#41C22×C313yes—
207D5×#41C22×C311yescharacteristic
208D5×#41C22×C313yescomplemented
209#4147—21no—
210#4147C22×C313yescomplemented
211C2×Q8×D5—21no—
212C2×Q8×D5C22×C313yescomplemented
213#4144—23no—
214#4144C22×C313yescomplemented
215C2×D4×D5—23no—
216C2×D4×D5C22×C313yes—
217C5×#137C22×C313yescomplemented
218C5×AGL(1,ℤ/8)C22×C313yescomplemented
219C5×#135C22×C313yescomplemented
220C2×C5×SD16C22×C313yescomplemented
221C5×#131C22×C311yescharacteristic, complemented
222#4097C22×C313yescomplemented
223#4096C22×C313yescomplemented
224#4096C22×C313yescomplemented
225#4095C22×C313yescomplemented
226#4094C22×C311yescharacteristic, complemented
227#4088C22×C313yescomplemented
228C2×#688C22×C313yescomplemented
229C2×#687C22×C313yescomplemented
230#4078C22×C313yescomplemented
231#4065C22×C313yescomplemented
232#4064C22×C316yescomplemented
233D5×Q16C22×C313yescomplemented
234#4062C22×C313yescomplemented
235#4062C22×C313yescomplemented
236#4061C22×C316yescomplemented
237#4060C22×C316yescomplemented
238D5×SD16C22×C313yescomplemented
239D5×SD16C22×C316yescomplemented
240D5×SD16C22×C311yescharacteristic, complemented
241D5×SD16C22×C316yescomplemented
242D5×SD16C22×C316yescomplemented
243#4058C22×C313yescomplemented
244#4057C22×C316yescomplemented
245D5×D8C22×C313yescomplemented
246#4055C22×C313yescomplemented
247#4054C22×C313yescomplemented
248#4053C22×C313yescomplemented
249D5×M16C22×C313yescomplemented
250#4050C22×C313yescomplemented
251C2×#677C22×C313yescomplemented
252#4047C22×C313yescomplemented
253C2×C8×D5C22×C313yescomplemented
254C2×#577—51noSylow
255C23×C3×C5—23no—
256C22×C3×D5—23no—
257C22×C3×D5—21no—
258C22×C3×D5—23no—
259C22×C3×D5—26no—
260C22×C3×D5—86no—
261C22×C3×D5C2×D413yes—
262C3×C5×Q8—23no—
263C3×C5×Q8C2×D411yescharacteristic
264C3×C5×Q8C2413yes—
265C3×C5×Q8C2411yescharacteristic
266C3×C5×D4—23no—
267C3×C5×D4—23no—
268C3×C5×D4—23no—
269C3×C5×D4C2×D413yes—
270C3×C5×D4C2411yescharacteristic
271C3×C5×D4C2413yes—
272C2×C3×C4×C5—23no—
273C2×C3×C4×C5—23no—
274C2×C3×C4×C5—23no—
275C2×C3×C4×C5C2413yes—
276C3×C22⋊D5—23no—
277C3×C22⋊D5—23no—
278C3×C22⋊D5—23no—
279C3×C22⋊D5—23no—
280C3×C22⋊D5—21no—
281C3×C22⋊D5—23no—
282C3×C22⋊D5—26no—
283C3×C22⋊D5C2×D416yes—
284C2×C3×Dic5—23no—
285C2×C3×Dic5—23no—
286C2×C3×Dic5—23no—
287C2×C3×Dic5C2×D413yes—
288C3×D20—23no—
289C3×D20—23no—
290C3×D20—23no—
291C3×D20C2×D413yes—
292C3×D20C2413yes—
293C3×D20C2411yescharacteristic
294C3×C4×D5—21no—
295C3×C4×D5—23no—
296C3×C4×D5—26no—
297C3×C4×D5—23no—
298C3×C4×D5—23no—
299C3×C4×D5—23no—
300C3×C4×D5—23no—
301C3×C4×D5C2×D413yes—
302C3×C4×D5C2×D413yes—
303C3×C4×D5C2411yescharacteristic
304C3×C4×D5C2413yes—
305C3×Dic10—23no—
306C3×Dic10—23no—
307C3×Dic10—26no—
308C3×Dic10—21no—
309C3×Dic10C2×D413yes—
310C3×Dic10C2413yes—
311C3×Dic10C2411yescharacteristic
312C3×C5×C8C2411yescharacteristic
313C3×C5×C8C2413yes—
314C3×#168C2411yescharacteristic
315C3×#168C2413yes—
316C3×2−1+4—51no—
317C3×2−1+4—53no—
318C3×2−1+4—53no—
319C3×2−1+4—101no—
320C3×2−1+4—103no—
321C3×2−1+4C2×D511yescharacteristic, complemented
322C3×H(5,𝔽2)—53no—
323C3×H(5,𝔽2)—51no—
324C3×H(5,𝔽2)—53no—
325C3×H(5,𝔽2)—103no—
326C3×H(5,𝔽2)—101no—
327C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
328C2×C3×#41—51no—
329C2×C3×#41—53no—
330C2×C3×#41—53no—
331C2×C3×#41—103no—
332C2×C3×#41—101no—
333C22×C3×Q8—53no—
334C22×C3×Q8—101no—
335C22×C3×D4—53no—
336C22×C3×D4—103no—
337C3×#137—53no—
338C3×#137—53no—
339C3×#137—56no—
340C3×#137—56no—
341C3×#137—53no—
342C3×#137C2×D513yescomplemented
343C3×AGL(1,ℤ/8)—53no—
344C3×AGL(1,ℤ/8)—53no—
345C3×AGL(1,ℤ/8)—56no—
346C3×AGL(1,ℤ/8)—56no—
347C3×AGL(1,ℤ/8)—53no—
348C3×AGL(1,ℤ/8)C2×D513yescomplemented
349C3×#135—53no—
350C3×#135—53no—
351C3×#135—53no—
352C3×#135—53no—
353C3×#135—53no—
354C3×#135—53no—
355C3×#135—53no—
356C3×#135C2×D513yescomplemented
357C2×C3×Q16—53no—
358C2×C3×SD16—53no—
359C2×C3×SD16—53no—
360C2×C3×SD16—53no—
361C2×C3×SD16—56no—
362C2×C3×SD16—56no—
363C2×C3×SD16—56no—
364C2×C3×SD16—51no—
365C2×C3×SD16—53no—
366C2×C3×SD16C2×D513yescomplemented
367C2×C3×D8—53no—
368C3×#131—51no—
369C3×#131—53no—
370C3×#131—53no—
371C3×#131C2×D511yescharacteristic, complemented
372C2×C3×M16—53no—
373C22×C3×C8—53no—
374C23×D5—23no—
375C5×#41—21no—
376C5×#41—23no—
377C5×#41C23×C313yes—
378C5×#41C23×C311yescharacteristic
379C5×#41C23×C313yescomplemented
380C2×C5×Q8—21no—
381C2×C5×Q8C23×C313yescomplemented
382C2×C5×D4—23no—
383C2×C5×D4C23×C313yes—
384C2×C22⋊D5—26no—
385C2×C22⋊D5—23no—
386#713—21no—
387#713—23no—
388#713C3×D411yescharacteristic
389#713C23×C313yes—
390#713C23×C313yescomplemented
391Q8×D5—21no—
392Q8×D5—23no—
393Q8×D5—23no—
394Q8×D5—23no—
395Q8×D5C3×D411yescharacteristic
396Q8×D5C23×C313yes—
397Q8×D5C23×C311yescharacteristic
398Q8×D5C23×C316yescomplemented
399#711—23no—
400#711—26no—
401#711—23no—
402#711—23no—
403#711—23no—
404#711C3×D413yes—
405#711C23×C313yes—
406#711C23×C313yescomplemented
407D4×D5—23no—
408D4×D5—23no—
409D4×D5—23no—
410D4×D5—26no—
411D4×D5—23no—
412D4×D5—23no—
413D4×D5—23no—
414D4×D5C3×D413yes—
415D4×D5C23×C313yes—
416D4×D5C23×C316yes—
417D4×D5C23×C311yescharacteristic
418#709—26no—
419#709—23no—
420#709—23no—
421#709—23no—
422#709—23no—
423#709C23×C313yes—
424#709C23×C313yes—
425#709C23×C313yescomplemented
426C2×D20—23no—
427C2×D20C23×C313yes—
428C2×C4×D5—23no—
429C2×C4×D5—23no—
430C2×C4×D5—23no—
431C2×C4×D5C23×C313yes—
432C2×Dic10—23no—
433C2×Dic10—23no—
434C2×Dic10C23×C313yescomplemented
435C5×Q16C23×C313yescomplemented
436C5×SD16C23×C313yescomplemented
437C5×SD16C23×C316yescomplemented
438C5×SD16C23×C311yescharacteristic, complemented
439C5×D8C23×C313yescomplemented
440C5×M16C23×C313yescomplemented
441C2×C5×C8C23×C313yescomplemented
442#689C23×C313yescomplemented
443#689C23×C313yescomplemented
444#688C23×C311yescharacteristic, complemented
445#688C23×C313yescomplemented
446#688C23×C316yescomplemented
447#687C23×C311yescharacteristic, complemented
448#687C23×C313yescomplemented
449#687C23×C316yescomplemented
450#686C23×C313yescomplemented
451#686C23×C313yescomplemented
452#681C23×C313yescomplemented
453C2×#168C23×C313yescomplemented
454Dic20C23×C313yescomplemented
455D40C23×C313yescomplemented
456#677C23×C313yescomplemented
457#677C23×C316yescomplemented
458#677C23×C311yescharacteristic, complemented
459#676C23×C316yescomplemented
460C8×D5C23×C311yescharacteristic
461C8×D5C23×C313yes—
462C8×D5C23×C313yescomplemented
463C8×D5C23×C313yescomplemented
464C2×2−1+4—51no—
465C2×H(5,𝔽2)—51no—
466#577—51no—
467#577—51no—
468#577—53no—
469#577—53no—
470#577—53no—
471#577—53no—
472#577—51no—
473#577C3×D511yescharacteristic, direct product factor
474C2×#137—53no—
475C2×AGL(1,ℤ/8)—53no—
476C2×#135—53no—
477C22×SD16—53no—
478C2×#131—51no—
479C22×C3×C5—21no—
480C22×C3×C5—23no—
481C22×C3×C5—83no—
482C22×C3×C5C22×D413yes—
483C2×C3×D5—26no—
484C2×C3×D5—21no—
485C2×C3×D5—23no—
486C2×C3×D5—42no—
487C2×C3×D5—46no—
488C2×C3×D5—86no—
489C2×C3×D5—83no—
490C2×C3×D5C22×D413yes—
491C2×C3×D5C22×D411yescharacteristic
492C3×C4×C5—23no—
493C3×C4×C5—21no—
494C3×C4×C5C22×D413yes—
495C3×C4×C5C2511yescharacteristic
496C3×Dic5—23no—
497C3×Dic5—21no—
498C3×Dic5C22×D411yescharacteristic
499C3×Dic5C22×D413yes—
500C24×C3—103no—
501C3×#41—21no—
502C3×#41—23no—
503C3×#41—51no—
504C3×#41—53no—
505C3×#41—53no—
506C3×#41—53no—
507C3×#41—53no—
508C3×#41—53no—
509C3×#41—53no—
510C3×#41—53no—
511C3×#41—53no—
512C3×#41—103no—
513C3×#41—103no—
514C3×#41—106no—
515C3×#41—103no—
516C3×#41—103no—
517C3×#41—103no—
518C3×#41—103no—
519C3×#41—106no—
520C3×#41—103no—
521C3×#41—103no—
522C3×#41—101no—
523C3×#41—103no—
524C3×#41C22×D513yes—
525C3×#41C22×D511yescharacteristic
526C3×#41C22×D513yescomplemented
527C2×C3×Q8—21no—
528C2×C3×Q8—51no—
529C2×C3×Q8—53no—
530C2×C3×Q8—51no—
531C2×C3×Q8—56no—
532C2×C3×Q8—53no—
533C2×C3×Q8—103no—
534C2×C3×Q8—103no—
535C2×C3×Q8—103no—
536C2×C3×Q8—103no—
537C2×C3×Q8—103no—
538C2×C3×Q8—101no—
539C2×C3×Q8C22×D513yescomplemented
540C2×C3×D4—23no—
541C2×C3×D4—53no—
542C2×C3×D4—51no—
543C2×C3×D4—53no—
544C2×C3×D4—56no—
545C2×C3×D4—53no—
546C2×C3×D4—103no—
547C2×C3×D4—103no—
548C2×C3×D4—103no—
549C2×C3×D4—103no—
550C2×C3×D4—106no—
551C2×C3×D4—103no—
552C2×C3×D4—103no—
553C2×C3×D4—103no—
554C2×C3×D4—106no—
555C2×C3×D4—103no—
556C2×C3×D4C22×D513yes—
557C22×C3×C4—53no—
558C22×C3×C4—103no—
559C22×C3×C4—103no—
560C22×C3×C4—103no—
561C3×Q16—53no—
562C3×Q16—53no—
563C3×Q16—53no—
564C3×Q16C22×D513yescomplemented
565C3×SD16—53no—
566C3×SD16—56no—
567C3×SD16—51no—
568C3×SD16—53no—
569C3×SD16—56no—
570C3×SD16—51no—
571C3×SD16—53no—
572C3×SD16—56no—
573C3×SD16—51no—
574C3×SD16C22×D513yescomplemented
575C3×SD16C22×D516yescomplemented
576C3×SD16C22×D511yescharacteristic, complemented
577C3×D8—53no—
578C3×D8—53no—
579C3×D8—53no—
580C3×D8C22×D513yescomplemented
581C3×M16—53no—
582C3×M16—56no—
583C3×M16C22×D513yescomplemented
584C2×C3×C8—53no—
585C2×C3×C8—51no—
586C2×C3×C8—53no—
587C2×C3×C8—53no—
588C2×C3×C8—53no—
589C2×C3×C8C22×D513yescomplemented
590C23×C5—23no—
591C22×D5—23no—
592C22×D5—21no—
593C22×D5—23no—
594C22×D5—26no—
595C22×D5—86no—
596C22×D5C2×C3×D413yes—
597C5×Q8—23no—
598C5×Q8C2×C3×D411yescharacteristic
599C5×Q8C24×C313yes—
600C5×Q8C24×C311yescharacteristic
601C5×D4—23no—
602C5×D4—23no—
603C5×D4—23no—
604C5×D4C2×C3×D413yes—
605C5×D4C24×C311yescharacteristic
606C5×D4C24×C313yes—
607C2×C4×C5—23no—
608C2×C4×C5—23no—
609C2×C4×C5—23no—
610C2×C4×C5C24×C313yes—
611C22⋊D5—23no—
612C22⋊D5—23no—
613C22⋊D5—23no—
614C22⋊D5—23no—
615C22⋊D5—21no—
616C22⋊D5—23no—
617C22⋊D5—26no—
618C22⋊D5C2×C3×D416yes—
619C2×Dic5—23no—
620C2×Dic5—23no—
621C2×Dic5—23no—
622C2×Dic5C2×C3×D413yes—
623D20—23no—
624D20—23no—
625D20—23no—
626D20C2×C3×D413yes—
627D20C24×C313yes—
628D20C24×C311yescharacteristic
629C4×D5—21no—
630C4×D5—23no—
631C4×D5—26no—
632C4×D5—23no—
633C4×D5—23no—
634C4×D5—23no—
635C4×D5—23no—
636C4×D5C2×C3×D413yes—
637C4×D5C2×C3×D413yes—
638C4×D5C24×C311yescharacteristic
639C4×D5C24×C313yes—
640Dic10—23no—
641Dic10—23no—
642Dic10—26no—
643Dic10—21no—
644Dic10C2×C3×D413yes—
645Dic10C24×C313yes—
646Dic10C24×C311yescharacteristic
647C5×C8C24×C311yescharacteristic
648C5×C8C24×C313yes—
649#168C24×C311yescharacteristic
650#168C24×C313yes—
6512−1+4—51no—
6522−1+4—53no—
6532−1+4—53no—
6542−1+4—101no—
6552−1+4—103no—
6562−1+4C2×C3×D511yescharacteristic, complemented
657H(5,𝔽2)—53no—
658H(5,𝔽2)—51no—
659H(5,𝔽2)—53no—
660H(5,𝔽2)—103no—
661H(5,𝔽2)—101no—
662H(5,𝔽2)C2×C3×D511yescharacteristic, complemented
663C2×#41—51no—
664C2×#41—53no—
665C2×#41—53no—
666C2×#41—103no—
667C2×#41—101no—
668C22×Q8—53no—
669C22×Q8—101no—
670C22×D4—53no—
671C22×D4—103no—
672#137—53no—
673#137—53no—
674#137—56no—
675#137—56no—
676#137—53no—
677#137C2×C3×D513yescomplemented
678AGL(1,ℤ/8)—53no—
679AGL(1,ℤ/8)—53no—
680AGL(1,ℤ/8)—56no—
681AGL(1,ℤ/8)—56no—
682AGL(1,ℤ/8)—53no—
683AGL(1,ℤ/8)C2×C3×D513yescomplemented
684#135—53no—
685#135—53no—
686#135—53no—
687#135—53no—
688#135—53no—
689#135—53no—
690#135—53no—
691#135C2×C3×D513yescomplemented
692C2×Q16—53no—
693C2×SD16—53no—
694C2×SD16—53no—
695C2×SD16—53no—
696C2×SD16—56no—
697C2×SD16—56no—
698C2×SD16—56no—
699C2×SD16—51no—
700C2×SD16—53no—
701C2×SD16C2×C3×D513yescomplemented
702C2×D8—53no—
703#131—51no—
704#131—53no—
705#131—53no—
706#131C2×C3×D511yescharacteristic, complemented
707C2×M16—53no—
708C22×C8—53no—
709C2×C3×C5—23no—
710C2×C3×C5—43no—
711C2×C3×C5—41no—
712C2×C3×C5C23×D411yescharacteristic
713C3×D5—23no—
714C3×D5—41no—
715C3×D5—43no—
716C3×D5#57712yesdirect product factor
717C23×C3—23no—
718C23×C3—53no—
719C23×C3—101no—
720C23×C3—103no—
721C23×C3—106no—
722C23×C3—103no—
723C23×C3—406no—
724C3×Q8—23no—
725C3×Q8—53no—
726C3×Q8—53no—
727C3×Q8—51no—
728C3×Q8—103no—
729C3×Q8—106no—
730C3×Q8—101no—
731C3×Q8—103no—
732C3×Q8D4×D511yescharacteristic
733C3×Q8C23×D513yes—
734C3×Q8C23×D511yescharacteristic
735C3×D4—23no—
736C3×D4—23no—
737C3×D4—23no—
738C3×D4—56no—
739C3×D4—53no—
740C3×D4—51no—
741C3×D4—53no—
742C3×D4—103no—
743C3×D4—103no—
744C3×D4—103no—
745C3×D4—106no—
746C3×D4—101no—
747C3×D4—103no—
748C3×D4—103no—
749C3×D4—103no—
750C3×D4—103no—
751C3×D4—103no—
752C3×D4D4×D513yes—
753C3×D4C23×D511yescharacteristic
754C3×D4C23×D513yes—
755C2×C3×C4—23no—
756C2×C3×C4—23no—
757C2×C3×C4—23no—
758C2×C3×C4—53no—
759C2×C3×C4—53no—
760C2×C3×C4—53no—
761C2×C3×C4—51no—
762C2×C3×C4—53no—
763C2×C3×C4—103no—
764C2×C3×C4—103no—
765C2×C3×C4—101no—
766C2×C3×C4—103no—
767C2×C3×C4—106no—
768C2×C3×C4—103no—
769C2×C3×C4—103no—
770C2×C3×C4—103no—
771C2×C3×C4—103no—
772C2×C3×C4—103no—
773C2×C3×C4C23×D513yes—
774C3×C8—51no—
775C3×C8—53no—
776C3×C8C23×D511yescharacteristic
777C3×C8C23×D513yes—
778C22×C5—21no—
779C22×C5—23no—
780C22×C5—83no—
781C22×C5C22×C3×D413yes—
782C2×D5—26no—
783C2×D5—21no—
784C2×D5—23no—
785C2×D5—42no—
786C2×D5—46no—
787C2×D5—86no—
788C2×D5—83no—
789C2×D5C22×C3×D413yes—
790C2×D5C22×C3×D411yescharacteristic
791C4×C5—23no—
792C4×C5—21no—
793C4×C5C22×C3×D413yes—
794C4×C5C25×C311yescharacteristic
795Dic5—23no—
796Dic5—21no—
797Dic5C22×C3×D411yescharacteristic
798Dic5C22×C3×D413yes—
799C24—103no—
800#41—21no—
801#41—23no—
802#41—51no—
803#41—53no—
804#41—53no—
805#41—53no—
806#41—53no—
807#41—53no—
808#41—53no—
809#41—53no—
810#41—53no—
811#41—103no—
812#41—103no—
813#41—106no—
814#41—103no—
815#41—103no—
816#41—103no—
817#41—103no—
818#41—106no—
819#41—103no—
820#41—103no—
821#41—101no—
822#41—103no—
823#41C22×C3×D513yes—
824#41C22×C3×D511yescharacteristic
825#41C22×C3×D513yescomplemented
826C2×Q8—21no—
827C2×Q8—51no—
828C2×Q8—53no—
829C2×Q8—56no—
830C2×Q8—51no—
831C2×Q8—53no—
832C2×Q8—103no—
833C2×Q8—103no—
834C2×Q8—103no—
835C2×Q8—103no—
836C2×Q8—103no—
837C2×Q8—101no—
838C2×Q8C22×C3×D513yescomplemented
839C2×D4—23no—
840C2×D4—53no—
841C2×D4—51no—
842C2×D4—53no—
843C2×D4—56no—
844C2×D4—53no—
845C2×D4—103no—
846C2×D4—103no—
847C2×D4—103no—
848C2×D4—103no—
849C2×D4—106no—
850C2×D4—103no—
851C2×D4—103no—
852C2×D4—103no—
853C2×D4—106no—
854C2×D4—103no—
855C2×D4C22×C3×D513yes—
856C22×C4—53no—
857C22×C4—103no—
858C22×C4—103no—
859C22×C4—103no—
860Q16—53no—
861Q16—53no—
862Q16—53no—
863Q16C22×C3×D513yescomplemented
864SD16—53no—
865SD16—56no—
866SD16—51no—
867SD16—53no—
868SD16—56no—
869SD16—51no—
870SD16—53no—
871SD16—56no—
872SD16—51no—
873SD16C22×C3×D513yescomplemented
874SD16C22×C3×D516yescomplemented
875SD16C22×C3×D511yescharacteristic, complemented
876D8—53no—
877D8—53no—
878D8—53no—
879D8C22×C3×D513yescomplemented
880M16—53no—
881M16—56no—
882M16C22×C3×D513yescomplemented
883C2×C8—53no—
884C2×C8—51no—
885C2×C8—53no—
886C2×C8—53no—
887C2×C8—53no—
888C2×C8C22×C3×D513yescomplemented
889C3×C5C2×#57711yescharacteristic, complemented, Hall
890C22×C3—21no—
891C22×C3—23no—
892C22×C3—51no—
893C22×C3—53no—
894C22×C3—83no—
895C22×C3—106no—
896C22×C3—101no—
897C22×C3—103no—
898C22×C3—202no—
899C22×C3—206no—
900C22×C3—403no—
901C22×C3—406no—
902C22×C3C2×D4×D513yes—
903C3×C4—21no—
904C3×C4—23no—
905C3×C4—51no—
906C3×C4—53no—
907C3×C4—101no—
908C3×C4—103no—
909C3×C4C2×D4×D513yes—
910C3×C4C24×D511yescharacteristic
911C2×C5—23no—
912C2×C5—43no—
913C2×C5—41no—
914C2×C5C23×C3×D411yescharacteristic
915D5—23no—
916D5—43no—
917D5—41no—
918D5C3×#57712yesdirect product factor
919C23—23no—
920C23—53no—
921C23—101no—
922C23—103no—
923C23—106no—
924C23—103no—
925C23—406no—
926Q8—23no—
927Q8—53no—
928Q8—53no—
929Q8—51no—
930Q8—103no—
931Q8—106no—
932Q8—101no—
933Q8—103no—
934Q8C3×D4×D511yescharacteristic
935Q8C23×C3×D513yes—
936Q8C23×C3×D511yescharacteristic
937D4—23no—
938D4—23no—
939D4—23no—
940D4—56no—
941D4—53no—
942D4—51no—
943D4—53no—
944D4—103no—
945D4—103no—
946D4—103no—
947D4—106no—
948D4—101no—
949D4—103no—
950D4—103no—
951D4—103no—
952D4—103no—
953D4—103no—
954D4C3×D4×D513yes—
955D4C23×C3×D511yescharacteristic
956D4C23×C3×D513yes—
957C2×C4—23no—
958C2×C4—23no—
959C2×C4—23no—
960C2×C4—53no—
961C2×C4—53no—
962C2×C4—53no—
963C2×C4—51no—
964C2×C4—53no—
965C2×C4—103no—
966C2×C4—103no—
967C2×C4—101no—
968C2×C4—103no—
969C2×C4—106no—
970C2×C4—103no—
971C2×C4—103no—
972C2×C4—103no—
973C2×C4—103no—
974C2×C4—103no—
975C2×C4C23×C3×D513yes—
976C8—51no—
977C8—53no—
978C8C23×C3×D511yescharacteristic
979C8C23×C3×D513yes—
980C2×C3—23no—
981C2×C3—43no—
982C2×C3—41no—
983C2×C3—52no—
984C2×C3—103no—
985C2×C3—203no—
986C2×C3—201no—
987C2×C3C22×D4×D511yescharacteristic
988C5C2×C3×#57711yescharacteristic, complemented, Sylow
989C22—21no—
990C22—23no—
991C22—51no—
992C22—53no—
993C22—83no—
994C22—106no—
995C22—101no—
996C22—103no—
997C22—206no—
998C22—202no—
999C22—403no—
1000C22—406no—
1001C22C2×C3×D4×D513yes—
1002C4—21no—
1003C4—23no—
1004C4—51no—
1005C4—53no—
1006C4—101no—
1007C4—103no—
1008C4C2×C3×D4×D513yes—
1009C4C24×C3×D511yescharacteristic
1010C3D5×#57711yescharacteristic, direct product factor, Sylow
1011C2—23no—
1012C2—43no—
1013C2—41no—
1014C2—52no—
1015C2—103no—
1016C2—203no—
1017C2—201no—
1018C2C22×C3×D4×D511yescharacteristic
subgroupG/H
centerC2×C3C22×D4×D5
commutator, cosocleC4×C5C25×C3
FrattiniC4C24×C3×D5
FittingC3×C5×#577C2
socleC2×C3×C5C23×D4
hypercenterC3×#577D5
hypocenterC5C2×C3×#577
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#577

Complements

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

NH ≅ G/Ntype
1. C3×D5×2−1+4C2semidirect
2. C3×D5×H(5,𝔽2)C2semidirect
3. C3×C5×#577C2semidirect
4. C3×#66171C2semidirect
5. C3×#66170C2semidirect
6. C3×#66112C2semidirect
7. C3×D5×#137C2semidirect
8. C3×#66109C2semidirect
9. C3×D5×AGL(1,ℤ/8)C2semidirect
10. C3×#66104C2semidirect
11. C3×D5×#135C2semidirect
12. C3×#66096C2semidirect
13. C2×C3×D5×SD16C2semidirect
14. C3×#66085C2semidirect
15. C3×D5×#131C2semidirect
16. D5×#577C3direct (N × H)
17. C3×C5×2−1+4C22semidirect
18. C3×C5×H(5,𝔽2)C22semidirect
20. C3×#4150C22semidirect
21. C3×#4150C22semidirect
23. C3×#4149C22semidirect
24. C3×#4149C22semidirect
29. C3×D5×#41C22semidirect
31. C3×#4147C22semidirect
33. C2×C3×Q8×D5C22semidirect
35. C3×#4144C22semidirect
38. C3×C5×#137C22semidirect
39. C3×C5×AGL(1,ℤ/8)C22semidirect
40. C3×C5×#135C22semidirect
41. C2×C3×C5×SD16C22semidirect
42. C3×C5×#131C22semidirect
43. C3×#4097C22semidirect
44. C3×#4096C22semidirect
45. C3×#4096C22semidirect
46. C3×#4095C22semidirect
47. C3×#4094C22semidirect
48. C3×#4088C22semidirect
49. C2×C3×#688C22semidirect
50. C2×C3×#687C22semidirect
51. C3×#4078C22semidirect
52. C3×#4065C22semidirect
53. C3×#4064C22semidirect
54. C3×D5×Q16C22semidirect
55. C3×#4062C22semidirect
56. C3×#4062C22semidirect
57. C3×#4061C22semidirect
58. C3×#4060C22semidirect
59. C3×D5×SD16C22semidirect
60. C3×D5×SD16C22semidirect
61. C3×D5×SD16C22semidirect
62. C3×D5×SD16C22semidirect
63. C3×D5×SD16C22semidirect
64. C3×#4058C22semidirect
65. C3×#4057C22semidirect
66. C3×D5×D8C22semidirect
67. C3×#4055C22semidirect
68. C3×#4054C22semidirect
69. C3×#4053C22semidirect
70. C3×D5×M16C22semidirect
71. C3×#4050C22semidirect
72. C2×C3×#677C22semidirect
73. C3×#4047C22semidirect
74. C2×C3×C8×D5C22semidirect
76. D5×2−1+4C2×C3semidirect
77. D5×H(5,𝔽2)C2×C3semidirect
78. C5×#577C2×C3semidirect
79. #66171C2×C3semidirect
80. #66170C2×C3semidirect
81. #66112C2×C3semidirect
82. D5×#137C2×C3semidirect
83. #66109C2×C3semidirect
84. D5×AGL(1,ℤ/8)C2×C3semidirect
85. #66104C2×C3semidirect
86. D5×#135C2×C3semidirect
87. #66096C2×C3semidirect
88. C2×D5×SD16C2×C3semidirect
89. #66085C2×C3semidirect
90. D5×#131C2×C3semidirect
96. C3×C5×#41C23semidirect
98. C2×C3×C5×Q8C23semidirect
107. C3×#713C23semidirect
115. C3×Q8×D5C23semidirect
123. C3×#711C23semidirect
142. C3×#709C23semidirect
151. C2×C3×Dic10C23semidirect
152. C3×C5×Q16C23semidirect
153. C3×C5×SD16C23semidirect
154. C3×C5×SD16C23semidirect
155. C3×C5×SD16C23semidirect
156. C3×C5×D8C23semidirect
157. C3×C5×M16C23semidirect
158. C2×C3×C5×C8C23semidirect
159. C3×#689C23semidirect
160. C3×#689C23semidirect
161. C3×#688C23semidirect
162. C3×#688C23semidirect
163. C3×#688C23semidirect
164. C3×#687C23semidirect
165. C3×#687C23semidirect
166. C3×#687C23semidirect
167. C3×#686C23semidirect
168. C3×#686C23semidirect
169. C3×#681C23semidirect
170. C2×C3×#168C23semidirect
171. C3×Dic20C23semidirect
172. C3×D40C23semidirect
173. C3×#677C23semidirect
174. C3×#677C23semidirect
175. C3×#677C23semidirect
176. C3×#676C23semidirect
179. C3×C8×D5C23semidirect
180. C3×C8×D5C23semidirect
190. C3×#577D5direct (N × H)
196. C5×2−1+4C22×C3semidirect
197. C5×H(5,𝔽2)C22×C3semidirect
199. #4150C22×C3semidirect
200. #4150C22×C3semidirect
202. #4149C22×C3semidirect
203. #4149C22×C3semidirect
208. D5×#41C22×C3semidirect
210. #4147C22×C3semidirect
212. C2×Q8×D5C22×C3semidirect
214. #4144C22×C3semidirect
217. C5×#137C22×C3semidirect
218. C5×AGL(1,ℤ/8)C22×C3semidirect
219. C5×#135C22×C3semidirect
220. C2×C5×SD16C22×C3semidirect
221. C5×#131C22×C3semidirect
222. #4097C22×C3semidirect
223. #4096C22×C3semidirect
224. #4096C22×C3semidirect
225. #4095C22×C3semidirect
226. #4094C22×C3semidirect
227. #4088C22×C3semidirect
228. C2×#688C22×C3semidirect
229. C2×#687C22×C3semidirect
230. #4078C22×C3semidirect
231. #4065C22×C3semidirect
232. #4064C22×C3semidirect
233. D5×Q16C22×C3semidirect
234. #4062C22×C3semidirect
235. #4062C22×C3semidirect
236. #4061C22×C3semidirect
237. #4060C22×C3semidirect
238. D5×SD16C22×C3semidirect
239. D5×SD16C22×C3semidirect
240. D5×SD16C22×C3semidirect
241. D5×SD16C22×C3semidirect
242. D5×SD16C22×C3semidirect
243. #4058C22×C3semidirect
244. #4057C22×C3semidirect
245. D5×D8C22×C3semidirect
246. #4055C22×C3semidirect
247. #4054C22×C3semidirect
248. #4053C22×C3semidirect
249. D5×M16C22×C3semidirect
250. #4050C22×C3semidirect
251. C2×#677C22×C3semidirect
252. #4047C22×C3semidirect
253. C2×C8×D5C22×C3semidirect
321. C3×2−1+4C2×D5semidirect
327. C3×H(5,𝔽2)C2×D5semidirect
342. C3×#137C2×D5semidirect
348. C3×AGL(1,ℤ/8)C2×D5semidirect
356. C3×#135C2×D5semidirect
366. C2×C3×SD16C2×D5semidirect
371. C3×#131C2×D5semidirect
379. C5×#41C23×C3semidirect
381. C2×C5×Q8C23×C3semidirect
390. #713C23×C3semidirect
398. Q8×D5C23×C3semidirect
406. #711C23×C3semidirect
425. #709C23×C3semidirect
434. C2×Dic10C23×C3semidirect
435. C5×Q16C23×C3semidirect
436. C5×SD16C23×C3semidirect
437. C5×SD16C23×C3semidirect
438. C5×SD16C23×C3semidirect
439. C5×D8C23×C3semidirect
440. C5×M16C23×C3semidirect
441. C2×C5×C8C23×C3semidirect
442. #689C23×C3semidirect
443. #689C23×C3semidirect
444. #688C23×C3semidirect
445. #688C23×C3semidirect
446. #688C23×C3semidirect
447. #687C23×C3semidirect
448. #687C23×C3semidirect
449. #687C23×C3semidirect
450. #686C23×C3semidirect
451. #686C23×C3semidirect
452. #681C23×C3semidirect
453. C2×#168C23×C3semidirect
454. Dic20C23×C3semidirect
455. D40C23×C3semidirect
456. #677C23×C3semidirect
457. #677C23×C3semidirect
458. #677C23×C3semidirect
459. #676C23×C3semidirect
462. C8×D5C23×C3semidirect
463. C8×D5C23×C3semidirect
473. #577C3×D5direct (N × H)
526. C3×#41C22×D5semidirect
539. C2×C3×Q8C22×D5semidirect
564. C3×Q16C22×D5semidirect
574. C3×SD16C22×D5semidirect
575. C3×SD16C22×D5semidirect
576. C3×SD16C22×D5semidirect
580. C3×D8C22×D5semidirect
583. C3×M16C22×D5semidirect
589. C2×C3×C8C22×D5semidirect
656. 2−1+4C2×C3×D5semidirect
662. H(5,𝔽2)C2×C3×D5semidirect
677. #137C2×C3×D5semidirect
683. AGL(1,ℤ/8)C2×C3×D5semidirect
691. #135C2×C3×D5semidirect
701. C2×SD16C2×C3×D5semidirect
706. #131C2×C3×D5semidirect
716. C3×D5#577direct (N × H)
825. #41C22×C3×D5semidirect
838. C2×Q8C22×C3×D5semidirect
863. Q16C22×C3×D5semidirect
873. SD16C22×C3×D5semidirect
874. SD16C22×C3×D5semidirect
875. SD16C22×C3×D5semidirect
879. D8C22×C3×D5semidirect
882. M16C22×C3×D5semidirect
888. C2×C8C22×C3×D5semidirect
889. C3×C5C2×#577semidirect
918. D5C3×#577direct (N × H)
988. C5C2×C3×#577semidirect
1010. C3D5×#577direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×2−1+42
C3×D5×H(5,𝔽2)2
C3×C5×#5772
C3×#661712
C3×#661702
C3×#661122
C3×D5×#1372
C3×#661092
C3×D5×AGL(1,ℤ/8)2
C3×#661042
C3×D5×#1352
C3×#660962
C2×C3×D5×SD162
C3×#660852
C3×D5×#1312
D5×#5773
C2×C3×#5775