Finite Group Databasebeta

← C3×#10615745 #14458093

Subgroups — C3×#10615745 #14458093

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 912 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×#66170C211yesmaximal, characteristic, complemented
4C3×#66104C211yesmaximal, characteristic, complemented
5C3×#65535C211yesmaximal, characteristic, complemented
6C3×#65530C211yesmaximal, characteristic, complemented
7C3×#65494C211yesmaximal, characteristic, complemented
8C3×#65492C211yesmaximal, characteristic, complemented
9C3×#65489C211yesmaximal, characteristic, complemented
10C3×#65487C211yesmaximal, characteristic, complemented
11C3×#65485C211yesmaximal, characteristic, complemented
12C3×#65466C211yesmaximal, characteristic, complemented
13C3×#65464C211yesmaximal, characteristic, complemented
14C3×#65433C211yesmaximal, characteristic, complemented
15C3×#65430C211yesmaximal, characteristic, complemented
16#10615745C311yesmaximal, characteristic, direct product factor, Hall
17C3×C5×2−1+4C2211yescharacteristic
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19C3×#4150C2211yescharacteristic
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
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×SD16—21no—
28C2×C3×C5×SD16C2211yescharacteristic, complemented
29C3×C5×#131C2211yescharacteristic, complemented
30C3×#4097—21no—
31C3×#4097C2211yescharacteristic, complemented
32C3×#4097C2211yescharacteristic, complemented
33C3×#4096—21no—
34C3×#4096—21no—
35C3×#4096C2211yescharacteristic
36C3×#4095—21no—
37C3×#4095C2211yescharacteristic
38C3×#4095C2211yescharacteristic
39C3×#4094C2211yescharacteristic, complemented
40C3×#4094C2211yescharacteristic, complemented
41C3×#4090C2211yescharacteristic, complemented
42C3×#4088—21no—
43C3×#4088C2211yescharacteristic, complemented
44C2×C3×#688—21no—
45C2×C3×#688C2211yescharacteristic, complemented
46C3×#4086C2211yescharacteristic
47C2×C3×#687—21no—
48C2×C3×#687C2211yescharacteristic, complemented
49C3×#4078—21no—
50C3×#4078C2211yescharacteristic
51C3×#4064—21no—
52C3×#4062—21no—
53C3×D5×SD16—21no—
54C3×#4057—21no—
55C2×C3×#677C2211yescharacteristic, complemented
56C3×#4047C2211yescharacteristic, complemented
57C3×#3969C2211yescharacteristic, complemented
58C3×#3969C2211yescharacteristic, complemented
59C3×#3969C2211yescharacteristic, complemented
60C3×#3968C2211yescharacteristic, complemented
61C3×#3965C2211yescharacteristic, complemented
62C3×#3957C2211yescharacteristic, complemented
63C3×#3956C2211yescharacteristic, complemented
64C3×#3955C2211yescharacteristic, complemented
65C3×#3954C2211yescharacteristic, complemented
66C3×#3951C2211yescharacteristic, complemented
67C3×C8×Dic5C2211yescharacteristic, complemented
68C3×#3291—51nomaximal, Hall
69C5×#577C2×C311yescharacteristic, complemented
70#66171C2×C311yescharacteristic, complemented
71#66170C2×C311yescharacteristic, complemented
72#66104C2×C311yescharacteristic, complemented
73#65535C2×C311yescharacteristic, complemented
74#65530C2×C311yescharacteristic, complemented
75#65494C2×C311yescharacteristic, complemented
76#65492C2×C311yescharacteristic, complemented
77#65489C2×C311yescharacteristic, complemented
78#65487C2×C311yescharacteristic, complemented
79#65485C2×C311yescharacteristic, complemented
80#65466C2×C311yescharacteristic, complemented
81#65464C2×C311yescharacteristic, complemented
82#65433C2×C311yescharacteristic, complemented
83#65430C2×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×Q8×D5—21no—
102C3×#711—21no—
103C3×#711—41no—
104C3×D4×D5—21no—
105C3×D4×D5—41no—
106C3×#709—21no—
107C3×#709—21no—
108C3×#709C2311yescharacteristic
109C2×C3×D20—21no—
110C2×C3×D20C2311yescharacteristic
111C2×C3×Dic10—21no—
112C2×C3×Dic10C2311yescharacteristic
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×#689—21no—
129C3×#689—21no—
130C3×#689D411yescharacteristic, complemented
131C3×#688—21no—
132C3×#688—21no—
133C3×#688—21no—
134C3×#688—21no—
135C3×#688—21no—
136C3×#688D411yescharacteristic, complemented
137C3×#687—21no—
138C3×#687—21no—
139C3×#687—21no—
140C3×#687—21no—
141C3×#687—21no—
142C3×#687D411yescharacteristic, complemented
143C3×#686—21no—
144C3×#686—21no—
145C3×#686—21no—
146C3×#686D411yescharacteristic, complemented
147C3×#683—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×#677—21no—
158C3×#677—21no—
159C3×#676—21no—
160C3×C8×D5—21no—
161C3×#577—51no—
162C3×#577—51no—
163C3×#577—51no—
164C3×#577D511yescharacteristic, complemented
165C3×#492—51no—
166C3×#471—51no—
167C3×#471—51no—
168C3×#471—51no—
169C3×#471—51no—
170C3×#456—51no—
171C3×#456—51no—
172C3×#453—51no—
173C3×#453—51no—
174C3×#443—51no—
175C3×#443—51no—
176C5×2−1+4C22×C311yescharacteristic
177C5×H(5,𝔽2)C22×C311yescharacteristic, complemented
178#4150C22×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
184C5×#135—21no—
185C5×#135C22×C311yescharacteristic
186C2×C5×SD16—21no—
187C2×C5×SD16C22×C311yescharacteristic, complemented
188C5×#131C22×C311yescharacteristic, complemented
189#4097—21no—
190#4097C22×C311yescharacteristic, complemented
191#4097C22×C311yescharacteristic, complemented
192#4096—21no—
193#4096—21no—
194#4096C22×C311yescharacteristic
195#4095—21no—
196#4095C22×C311yescharacteristic
197#4095C22×C311yescharacteristic
198#4094C22×C311yescharacteristic, complemented
199#4094C22×C311yescharacteristic, complemented
200#4090C22×C311yescharacteristic, complemented
201#4088—21no—
202#4088C22×C311yescharacteristic, complemented
203C2×#688—21no—
204C2×#688C22×C311yescharacteristic, complemented
205#4086C22×C311yescharacteristic
206C2×#687—21no—
207C2×#687C22×C311yescharacteristic, complemented
208#4078—21no—
209#4078C22×C311yescharacteristic
210#4064—21no—
211#4062—21no—
212D5×SD16—21no—
213#4057—21no—
214C2×#677C22×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#3956C22×C311yescharacteristic, complemented
223#3955C22×C311yescharacteristic, complemented
224#3954C22×C311yescharacteristic, complemented
225#3951C22×C311yescharacteristic, complemented
226C8×Dic5C22×C311yescharacteristic, complemented
227#3291—51noSylow
228C23×C3×C5—21no—
229C23×C3×C5—41no—
230C22×C3×D5—21no—
231C22×C3×D5—41no—
232C3×C5×Q8—21no—
233C3×C5×Q8—21no—
234C3×C5×Q8—41no—
235C3×C5×Q8C2×D411yescharacteristic
236C3×C5×Q8C2×D411yescharacteristic
237C3×C5×Q8C2×D411yescharacteristic
238C3×C5×D4—21no—
239C3×C5×D4—21no—
240C3×C5×D4—21no—
241C3×C5×D4—21no—
242C3×C5×D4—21no—
243C3×C5×D4—41no—
244C3×C5×D4—41no—
245C3×C5×D4—41no—
246C3×C5×D4C2×D411yescharacteristic
247C3×C5×D4C2×D411yescharacteristic
248C3×C5×D4C2×D411yescharacteristic
249C2×C3×C4×C5—21no—
250C2×C3×C4×C5—21no—
251C2×C3×C4×C5—21no—
252C2×C3×C4×C5—21no—
253C2×C3×C4×C5—41no—
254C2×C3×C4×C5—41no—
255C2×C3×C4×C5—41no—
256C2×C3×C4×C5C2411yescharacteristic
257C3×C22⋊D5—21no—
258C3×C22⋊D5—41no—
259C3×C22⋊D5—41no—
260C3×C22⋊D5—82no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—41no—
264C3×D20—21no—
265C3×D20—21no—
266C3×D20—41no—
267C3×D20C2×D411yescharacteristic
268C3×C4×D5—21no—
269C3×C4×D5—41no—
270C3×C4×D5—41no—
271C3×Dic10—21no—
272C3×Dic10—21no—
273C3×Dic10—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+4—51no—
284C3×2−1+4C2×D511yescharacteristic
285C3×H(5,𝔽2)—51no—
286C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
287C3×#137—21no—
288C3×#137—51no—
289C3×#137—51no—
290C3×#137—51no—
291C3×#137—101no—
292C3×#137—101no—
293C3×#137—101no—
294C3×#137C2×D511yescharacteristic, complemented
295C3×AGL(1,ℤ/8)—21no—
296C3×AGL(1,ℤ/8)—51no—
297C3×AGL(1,ℤ/8)—51no—
298C3×AGL(1,ℤ/8)—51no—
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
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—51no—
312C2×C3×SD16—51no—
313C2×C3×SD16—101no—
314C2×C3×SD16—101no—
315C2×C3×SD16—101no—
316C2×C3×SD16C2×D511yescharacteristic, complemented
317C3×#131—51no—
318C3×#131—51no—
319C3×#131—51no—
320C3×#131C2×D511yescharacteristic, complemented
321C3×C4⋊Q8—51no—
322C3×#127—51no—
323C3×#108—51no—
324C3×#108—51no—
325C3×#104—51no—
326C3×#104—51no—
327C3×#104—51no—
328C3×#104—51no—
329C3×#101—51no—
330C3×#101—51no—
331C3×#100—51no—
332C3×#100—51no—
333C3×C4×C8—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—
351Q8×D5—21no—
352#711—21no—
353#711—41no—
354D4×D5—21no—
355D4×D5—41no—
356#709—21no—
357#709—21no—
358#709C23×C311yescharacteristic
359C2×D20—21no—
360C2×D20C23×C311yescharacteristic
361C2×Dic10—21no—
362C2×Dic10C23×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#689—21no—
379#689—21no—
380#689C3×D411yescharacteristic, complemented
381#688—21no—
382#688—21no—
383#688—21no—
384#688—21no—
385#688—21no—
386#688C3×D411yescharacteristic, complemented
387#687—21no—
388#687—21no—
389#687—21no—
390#687—21no—
391#687—21no—
392#687C3×D411yescharacteristic, complemented
393#686—21no—
394#686—21no—
395#686—21no—
396#686C3×D411yescharacteristic, complemented
397#683—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
407#677—21no—
408#677—21no—
409#676—21no—
410C8×D5—21no—
411#577—51no—
412#577—51no—
413#577—51no—
414#577C3×D511yescharacteristic, complemented
415#492—51no—
416#471—51no—
417#471—51no—
418#471—51no—
419#471—51no—
420#456—51no—
421#456—51no—
422#453—51no—
423#453—51no—
424#443—51no—
425#443—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—81no—
436C2×C3×D5—161no—
437C3×C4×C5—21no—
438C3×C4×C5—21no—
439C3×C4×C5—21no—
440C3×C4×C5—41no—
441C3×C4×C5C22×D411yescharacteristic
442C3×C4×C5C22×D411yescharacteristic
443C3×Dic5—22no—
444C3×Dic5—21no—
445C3×Dic5—41no—
446C3×#41—21no—
447C3×#41—21no—
448C3×#41—21no—
449C3×#41—21no—
450C3×#41—41no—
451C3×#41—51no—
452C3×#41—101no—
453C3×#41—101no—
454C3×#41—101no—
455C3×#41—101no—
456C3×#41—201no—
457C3×#41C22×D511yescharacteristic
458C3×#41C22×D511yescharacteristic
459C3×#41C22×D511yescharacteristic
460C2×C3×Q8—21no—
461C2×C3×Q8—21no—
462C2×C3×Q8—51no—
463C2×C3×Q8—101no—
464C2×C3×Q8—101no—
465C2×C3×Q8C22×D511yescharacteristic
466C2×C3×D4—21no—
467C2×C3×D4—21no—
468C2×C3×D4—41no—
469C2×C3×D4—51no—
470C2×C3×D4—101no—
471C2×C3×D4—101no—
472C2×C3×D4—201no—
473C2×C3×D4—201no—
474C2×C3×D4C22×D511yescharacteristic
475C3×Q16—21no—
476C3×Q16—51no—
477C3×Q16—101no—
478C3×Q16—101no—
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×SD16—101no—
496C3×SD16—101no—
497C3×SD16—101no—
498C3×SD16—101no—
499C3×SD16C22⋊D511yescharacteristic, complemented
500C3×SD16C22⋊D511yescharacteristic, complemented
501C3×D8—21no—
502C3×D8—51no—
503C3×D8—101no—
504C3×D8—101no—
505C3×D8—101no—
506C3×D8C22⋊D511yescharacteristic, complemented
507C3×M16—21no—
508C3×M16—51no—
509C3×M16—51no—
510C3×M16—51no—
511C3×M16—101no—
512C3×M16—101no—
513C3×M16—101no—
514C3×M16C22×D511yescharacteristic
515C2×C3×C8—21no—
516C2×C3×C8—51no—
517C2×C3×C8—101no—
518C2×C3×C8—101no—
519C2×C3×C8—101no—
520C2×C3×C8C22×D511yescharacteristic
521C3×C4⋊C4—201no—
522C3×C42—51no—
523C23×C5—21no—
524C23×C5—41no—
525C22×D5—21no—
526C22×D5—41no—
527C5×Q8—21no—
528C5×Q8—21no—
529C5×Q8—41no—
530C5×Q8C2×C3×D411yescharacteristic
531C5×Q8C2×C3×D411yescharacteristic
532C5×Q8C2×C3×D411yescharacteristic
533C5×D4—21no—
534C5×D4—21no—
535C5×D4—21no—
536C5×D4—21no—
537C5×D4—21no—
538C5×D4—41no—
539C5×D4—41no—
540C5×D4—41no—
541C5×D4C2×C3×D411yescharacteristic
542C5×D4C2×C3×D411yescharacteristic
543C5×D4C2×C3×D411yescharacteristic
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5C24×C311yescharacteristic
552C22⋊D5—21no—
553C22⋊D5—41no—
554C22⋊D5—41no—
555C22⋊D5—82no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—41no—
559D20—21no—
560D20—21no—
561D20—41no—
562D20C2×C3×D411yescharacteristic
563C4×D5—21no—
564C4×D5—41no—
565C4×D5—41no—
566Dic10—21no—
567Dic10—21no—
568Dic10—41no—
569Dic10C2×C3×D411yescharacteristic
570C5×C8—21no—
571C5×C8C2×C3×D411yescharacteristic
572C5×C8C2×C3×D411yescharacteristic
573#168—21no—
574#168—21no—
575#168—21no—
576#168C2×C3×D411yescharacteristic
577#168C2×C3×D411yescharacteristic
5782−1+4—51no—
5792−1+4C2×C3×D511yescharacteristic
580H(5,𝔽2)—51no—
581H(5,𝔽2)C2×C3×D511yescharacteristic, complemented
582#137—21no—
583#137—51no—
584#137—51no—
585#137—51no—
586#137—101no—
587#137—101no—
588#137—101no—
589#137C2×C3×D511yescharacteristic, complemented
590AGL(1,ℤ/8)—21no—
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)C2×C3×D511yescharacteristic
598#135—21no—
599#135—51no—
600#135—101no—
601#135—101no—
602#135—101no—
603#135C2×C3×D511yescharacteristic
604C2×SD16—21no—
605C2×SD16—51no—
606C2×SD16—51no—
607C2×SD16—51no—
608C2×SD16—101no—
609C2×SD16—101no—
610C2×SD16—101no—
611C2×SD16C2×C3×D511yescharacteristic, complemented
612#131—51no—
613#131—51no—
614#131—51no—
615#131C2×C3×D511yescharacteristic, complemented
616C4⋊Q8—51no—
617#127—51no—
618#108—51no—
619#108—51no—
620#104—51no—
621#104—51no—
622#104—51no—
623#104—51no—
624#101—51no—
625#101—51no—
626#100—51no—
627#100—51no—
628C4×C8—51no—
629C2×C3×C5—21no—
630C2×C3×C5—41no—
631C2×C3×C5—41no—
632C2×C3×C5—41no—
633C2×C3×C5—81no—
634C2×C3×C5D4211yescharacteristic
635C3×D5—41no—
636C3×D5—81no—
637C23×C3—21no—
638C23×C3—41no—
639C23×C3—101no—
640C23×C3—201no—
641C3×Q8—21no—
642C3×Q8—21no—
643C3×Q8—41no—
644C3×Q8—51no—
645C3×Q8—101no—
646C3×Q8—101no—
647C3×Q8—201no—
648C3×Q8D4×D511yescharacteristic
649C3×Q8C2×C22⋊D511yescharacteristic
650C3×Q8C2×C22⋊D511yescharacteristic
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—41no—
657C3×D4—41no—
658C3×D4—41no—
659C3×D4—51no—
660C3×D4—101no—
661C3×D4—101no—
662C3×D4—101no—
663C3×D4—201no—
664C3×D4—201no—
665C3×D4—201no—
666C3×D4—402no—
667C3×D4D4×D511yescharacteristic
668C3×D4C2×C22⋊D511yescharacteristic
669C3×D4C2×C22⋊D511yescharacteristic
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—201no—
681C2×C3×C4—201no—
682C2×C3×C4—201no—
683C2×C3×C4C23×D511yescharacteristic
684C3×C8—21no—
685C3×C8—51no—
686C3×C8—51no—
687C3×C8—101no—
688C3×C8—101no—
689C3×C8—101no—
690C3×C8C2×C22⋊D511yescharacteristic
691C3×C8C2×C22⋊D511yescharacteristic
692C22×C5—21no—
693C22×C5—21no—
694C22×C5—21no—
695C22×C5—41no—
696C22×C5—81no—
697C22×C5—161no—
698C22×C5C3×H(5,𝔽2)11yescharacteristic
699C2×D5—21no—
700C2×D5—41no—
701C2×D5—81no—
702C2×D5—161no—
703C4×C5—21no—
704C4×C5—21no—
705C4×C5—21no—
706C4×C5—41no—
707C4×C5C22×C3×D411yescharacteristic
708C4×C5C22×C3×D411yescharacteristic
709Dic5—22no—
710Dic5—21no—
711Dic5—41no—
712#41—21no—
713#41—21no—
714#41—21no—
715#41—21no—
716#41—41no—
717#41—51no—
718#41—101no—
719#41—101no—
720#41—101no—
721#41—101no—
722#41—201no—
723#41C22×C3×D511yescharacteristic
724#41C22×C3×D511yescharacteristic
725#41C22×C3×D511yescharacteristic
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—51no—
729C2×Q8—101no—
730C2×Q8—101no—
731C2×Q8C22×C3×D511yescharacteristic
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—41no—
735C2×D4—51no—
736C2×D4—101no—
737C2×D4—101no—
738C2×D4—201no—
739C2×D4—201no—
740C2×D4C22×C3×D511yescharacteristic
741Q16—21no—
742Q16—51no—
743Q16—101no—
744Q16—101no—
745Q16—101no—
746Q16C3×C22⋊D511yescharacteristic, complemented
747SD16—21no—
748SD16—21no—
749SD16—21no—
750SD16—21no—
751SD16—51no—
752SD16—51no—
753SD16—101no—
754SD16—101no—
755SD16—101no—
756SD16—101no—
757SD16—101no—
758SD16—101no—
759SD16—101no—
760SD16—101no—
761SD16—101no—
762SD16—101no—
763SD16—101no—
764SD16—101no—
765SD16C3×C22⋊D511yescharacteristic, complemented
766SD16C3×C22⋊D511yescharacteristic, complemented
767D8—21no—
768D8—51no—
769D8—101no—
770D8—101no—
771D8—101no—
772D8C3×C22⋊D511yescharacteristic, complemented
773M16—21no—
774M16—51no—
775M16—51no—
776M16—51no—
777M16—101no—
778M16—101no—
779M16—101no—
780M16C22×C3×D511yescharacteristic
781C2×C8—21no—
782C2×C8—51no—
783C2×C8—101no—
784C2×C8—101no—
785C2×C8—101no—
786C2×C8C22×C3×D511yescharacteristic
787C4⋊C4—201no—
788C42—51no—
789C3×C5#329111yescharacteristic, complemented, Hall
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—41no—
794C22×C3—81no—
795C22×C3—101no—
796C22×C3—161no—
797C22×C3—201no—
798C22×C3—401no—
799C22×C3—801no—
800C22×C3#414411yescharacteristic
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—41no—
805C3×C4—102no—
806C3×C4—101no—
807C3×C4—201no—
808C3×C4C2×D4×D511yescharacteristic
809C3×C4C22×C22⋊D511yescharacteristic
810C2×C5—21no—
811C2×C5—41no—
812C2×C5—41no—
813C2×C5—41no—
814C2×C5—81no—
815C2×C5C3×D4211yescharacteristic
816D5—41no—
817D5—81no—
818C23—21no—
819C23—41no—
820C23—101no—
821C23—201no—
822Q8—21no—
823Q8—21no—
824Q8—41no—
825Q8—51no—
826Q8—101no—
827Q8—101no—
828Q8—201no—
829Q8C3×D4×D511yescharacteristic
830Q8C2×C3×C22⋊D511yescharacteristic
831Q8C2×C3×C22⋊D511yescharacteristic
832D4—21no—
833D4—21no—
834D4—21no—
835D4—21no—
836D4—21no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—51no—
841D4—101no—
842D4—101no—
843D4—101no—
844D4—201no—
845D4—201no—
846D4—201no—
847D4—402no—
848D4C3×D4×D511yescharacteristic
849D4C2×C3×C22⋊D511yescharacteristic
850D4C2×C3×C22⋊D511yescharacteristic
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—201no—
862C2×C4—201no—
863C2×C4—201no—
864C2×C4C23×C3×D511yescharacteristic
865C8—21no—
866C8—51no—
867C8—51no—
868C8—101no—
869C8—101no—
870C8—101no—
871C8C2×C3×C22⋊D511yescharacteristic
872C8C2×C3×C22⋊D511yescharacteristic
873C2×C3—21no—
874C2×C3—41no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—81no—
878C2×C3—201no—
879C2×C3—401no—
880C2×C3D4×C22⋊D511yescharacteristic
881C5C3×#329111yescharacteristic, complemented, Sylow
882C22—21no—
883C22—21no—
884C22—21no—
885C22—41no—
886C22—81no—
887C22—101no—
888C22—161no—
889C22—201no—
890C22—401no—
891C22—801no—
892C22C3×#414411yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—41no—
897C4—102no—
898C4—101no—
899C4—201no—
900C4C2×C3×D4×D511yescharacteristic
901C4C22×C3×C22⋊D511yescharacteristic
902C3#1061574511yescharacteristic, direct product factor, Sylow
903C2—21no—
904C2—41no—
905C2—41no—
906C2—41no—
907C2—81no—
908C2—201no—
909C2—401no—
910C2C3×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×#3291
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×#66170C2semidirect
4. C3×#66104C2semidirect
5. C3×#65535C2semidirect
6. C3×#65530C2semidirect
7. C3×#65494C2semidirect
8. C3×#65492C2semidirect
9. C3×#65489C2semidirect
10. C3×#65487C2semidirect
11. C3×#65485C2semidirect
12. C3×#65466C2semidirect
13. C3×#65464C2semidirect
14. C3×#65433C2semidirect
15. C3×#65430C2semidirect
16. #10615745C3direct (N × H)
18. C3×C5×H(5,𝔽2)C22semidirect
20. C3×#4149C22semidirect
22. C3×C5×#137C22semidirect
28. C2×C3×C5×SD16C22semidirect
29. C3×C5×#131C22semidirect
31. C3×#4097C22semidirect
32. C3×#4097C22semidirect
39. C3×#4094C22semidirect
40. C3×#4094C22semidirect
41. C3×#4090C22semidirect
43. C3×#4088C22semidirect
45. C2×C3×#688C22semidirect
48. C2×C3×#687C22semidirect
55. C2×C3×#677C22semidirect
56. C3×#4047C22semidirect
57. C3×#3969C22semidirect
58. C3×#3969C22semidirect
59. C3×#3969C22semidirect
60. C3×#3968C22semidirect
61. C3×#3965C22semidirect
62. C3×#3957C22semidirect
63. C3×#3956C22semidirect
64. C3×#3955C22semidirect
65. C3×#3954C22semidirect
66. C3×#3951C22semidirect
67. C3×C8×Dic5C22semidirect
69. C5×#577C2×C3semidirect
70. #66171C2×C3semidirect
71. #66170C2×C3semidirect
72. #66104C2×C3semidirect
73. #65535C2×C3semidirect
74. #65530C2×C3semidirect
75. #65494C2×C3semidirect
76. #65492C2×C3semidirect
77. #65489C2×C3semidirect
78. #65487C2×C3semidirect
79. #65485C2×C3semidirect
80. #65466C2×C3semidirect
81. #65464C2×C3semidirect
82. #65433C2×C3semidirect
83. #65430C2×C3semidirect
114. C3×C5×Q16D4semidirect
119. C3×C5×SD16D4semidirect
120. C3×C5×SD16D4semidirect
122. C3×C5×D8D4semidirect
130. C3×#689D4semidirect
136. C3×#688D4semidirect
142. C3×#687D4semidirect
146. C3×#686D4semidirect
164. C3×#577D5semidirect
177. C5×H(5,𝔽2)C22×C3semidirect
179. #4149C22×C3semidirect
181. C5×#137C22×C3semidirect
187. C2×C5×SD16C22×C3semidirect
188. C5×#131C22×C3semidirect
190. #4097C22×C3semidirect
191. #4097C22×C3semidirect
198. #4094C22×C3semidirect
199. #4094C22×C3semidirect
200. #4090C22×C3semidirect
202. #4088C22×C3semidirect
204. C2×#688C22×C3semidirect
207. C2×#687C22×C3semidirect
214. C2×#677C22×C3semidirect
215. #4047C22×C3semidirect
216. #3969C22×C3semidirect
217. #3969C22×C3semidirect
218. #3969C22×C3semidirect
219. #3968C22×C3semidirect
220. #3965C22×C3semidirect
221. #3957C22×C3semidirect
222. #3956C22×C3semidirect
223. #3955C22×C3semidirect
224. #3954C22×C3semidirect
225. #3951C22×C3semidirect
226. C8×Dic5C22×C3semidirect
286. C3×H(5,𝔽2)C2×D5semidirect
294. C3×#137C2×D5semidirect
316. C2×C3×SD16C2×D5semidirect
320. C3×#131C2×D5semidirect
364. C5×Q16C3×D4semidirect
369. C5×SD16C3×D4semidirect
370. C5×SD16C3×D4semidirect
372. C5×D8C3×D4semidirect
380. #689C3×D4semidirect
386. #688C3×D4semidirect
392. #687C3×D4semidirect
396. #686C3×D4semidirect
414. #577C3×D5semidirect
480. C3×Q16C22⋊D5semidirect
499. C3×SD16C22⋊D5semidirect
500. C3×SD16C22⋊D5semidirect
506. C3×D8C22⋊D5semidirect
581. H(5,𝔽2)C2×C3×D5semidirect
589. #137C2×C3×D5semidirect
611. C2×SD16C2×C3×D5semidirect
615. #131C2×C3×D5semidirect
746. Q16C3×C22⋊D5semidirect
765. SD16C3×C22⋊D5semidirect
766. SD16C3×C22⋊D5semidirect
772. D8C3×C22⋊D5semidirect
789. C3×C5#3291semidirect
881. C5C3×#3291semidirect
902. C3#10615745direct (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×#661702
C3×#661042
C3×#655352
C3×#655302
C3×#654942
C3×#654922
C3×#654892
C3×#654872
C3×#654852
C3×#654662
C3×#654642
C3×#654332
C3×#654302
#106157453
C3×#32915