Finite Group Databasebeta

← C3×#10612666 #14458096

Subgroups — C3×#10612666 #14458096

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×#66112C211yesmaximal, characteristic, complemented
2C3×#66109C211yesmaximal, characteristic, complemented
3C3×#66096C211yesmaximal, characteristic, complemented
4C3×#66085C211yesmaximal, characteristic, complemented
5C3×C5×#471C211yesmaximal, characteristic, complemented
6C3×#65494C211yesmaximal, characteristic, complemented
7C3×#65487C211yesmaximal, characteristic, complemented
8C3×#65464C211yesmaximal, characteristic, complemented
9C3×#65433C211yesmaximal, characteristic, complemented
10C3×#65187C211yesmaximal, characteristic, complemented
11C3×#65184C211yesmaximal, characteristic, complemented
12C3×#65043C211yesmaximal, characteristic, complemented
13C3×#65041C211yesmaximal, characteristic, complemented
14C3×#65037C211yesmaximal, characteristic, complemented
15C3×#65036C211yesmaximal, characteristic, complemented
16#10612666C311yesmaximal, characteristic, direct product factor, Hall
17C3×#4150C2211yescharacteristic
18C3×#4149C2211yescharacteristic, complemented
19C3×#4147C2211yescharacteristic
20C3×#4144C2211yescharacteristic, complemented
21C3×C5×#137C2211yescharacteristic, complemented
22C3×C5×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C3×C5×#131C2211yescharacteristic, complemented
25C3×#4096C2211yescharacteristic
26C3×#4090C2211yescharacteristic, complemented
27C3×#4088C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C3×#4086C2211yescharacteristic
30C2×C3×#687C2211yescharacteristic, complemented
31C3×#4078C2211yescharacteristic
32C3×#4065—21no—
33C3×#4064—21no—
34C3×#4062—21no—
35C3×#4061—21no—
36C3×#4061—21no—
37C3×#4060—21no—
38C3×#4060—21no—
39C3×D5×SD16—21no—
40C3×D5×SD16—21no—
41C3×D5×SD16—21no—
42C3×#4058—21no—
43C3×#4057—21no—
44C3×#4055—21no—
45C3×#4055C2211yescharacteristic, complemented
46C3×#4055C2211yescharacteristic, complemented
47C3×#4054—21no—
48C3×#4054C2211yescharacteristic
49C3×#4054C2211yescharacteristic
50C3×#4053C2211yescharacteristic, complemented
51C3×#4053C2211yescharacteristic, complemented
52C3×#4050—21no—
53C3×#4050C2211yescharacteristic
54C2×C3×#677—21no—
55C2×C3×#677C2211yescharacteristic, complemented
56C3×#4047C2211yescharacteristic, complemented
57C3×C5×#108C2211yescharacteristic, complemented
58C3×C5×#101C2211yescharacteristic, complemented
59C3×C5×#100C2211yescharacteristic, complemented
60C3×#3969C2211yescharacteristic, complemented
61C3×#3957C2211yescharacteristic, complemented
62C3×#3957C2211yescharacteristic, complemented
63C3×#3957C2211yescharacteristic, complemented
64C3×#3956C2211yescharacteristic, complemented
65C3×#3955C2211yescharacteristic, complemented
66C3×#3954C2211yescharacteristic, complemented
67C3×C8×Dic5C2211yescharacteristic, complemented
68C3×#3291—51nomaximal, Hall
69#66112C2×C311yescharacteristic, complemented
70#66109C2×C311yescharacteristic, complemented
71#66096C2×C311yescharacteristic, complemented
72#66085C2×C311yescharacteristic, complemented
73C5×#471C2×C311yescharacteristic, complemented
74#65494C2×C311yescharacteristic, complemented
75#65487C2×C311yescharacteristic, complemented
76#65464C2×C311yescharacteristic, complemented
77#65433C2×C311yescharacteristic, complemented
78#65187C2×C311yescharacteristic, complemented
79#65184C2×C311yescharacteristic, complemented
80#65043C2×C311yescharacteristic, complemented
81#65041C2×C311yescharacteristic, complemented
82#65037C2×C311yescharacteristic, complemented
83#65036C2×C311yescharacteristic, complemented
84C3×C5×#41C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C22⋊D5—41no—
88C2×C3×C22⋊D5—41no—
89C3×#713—21no—
90C3×#713—21no—
91C3×#713—21no—
92C3×Q8×D5—21no—
93C3×Q8×D5—21no—
94C3×Q8×D5—21no—
95C3×#711—21no—
96C3×#711—21no—
97C3×#711—21no—
98C3×#711—41no—
99C3×D4×D5—21no—
100C3×D4×D5—21no—
101C3×D4×D5—21no—
102C3×D4×D5—41no—
103C3×#709—21no—
104C3×#709—21no—
105C3×#709—41no—
106C3×#709C2311yescharacteristic
107C3×#709C2311yescharacteristic
108C3×#709C2311yescharacteristic
109C2×C3×D20—21no—
110C2×C3×D20C2311yescharacteristic
111C2×C3×Dic10—21no—
112C2×C3×Dic10C2311yescharacteristic
113C3×C5×Q16—21no—
114C3×C5×SD16—21no—
115C3×C5×SD16—21no—
116C3×C5×SD16—21no—
117C3×C5×SD16—21no—
118C3×C5×D8—21no—
119C3×C5×M16—21no—
120C3×C5×M16C2311yescharacteristic
121C3×C5×M16C2311yescharacteristic
122C3×C5×M16C2311yescharacteristic
123C2×C3×C5×C8—21no—
124C2×C3×C5×C8C2311yescharacteristic
125C3×#689—21no—
126C3×#689D411yescharacteristic, complemented
127C3×#688—21no—
128C3×#688—21no—
129C3×#688—21no—
130C3×#688D411yescharacteristic, complemented
131C3×#687—21no—
132C3×#687—21no—
133C3×#687—21no—
134C3×#687D411yescharacteristic, complemented
135C3×#686—21no—
136C3×#686D411yescharacteristic, complemented
137C3×#683—41no—
138C3×C4×Dic5C2311yescharacteristic
139C3×#681C2311yescharacteristic
140C2×C3×#168C2311yescharacteristic
141C3×Dic20—21no—
142C3×Dic20—21no—
143C3×Dic20D411yescharacteristic, complemented
144C3×D40—21no—
145C3×D40—21no—
146C3×D40D411yescharacteristic, complemented
147C3×#677—21no—
148C3×#677—21no—
149C3×#677—21no—
150C3×#677—21no—
151C3×#677—21no—
152C3×#677—21no—
153C3×#677D411yescharacteristic, complemented
154C3×#677D411yescharacteristic, complemented
155C3×#676—21no—
156C3×#676—21no—
157C3×#676—21no—
158C3×C8×D5—21no—
159C3×C8×D5—21no—
160C3×C8×D5—21no—
161C3×#577—51no—
162C3×#577—51no—
163C3×#577—51no—
164C3×#577—51no—
165C3×#492—51no—
166C3×#471—51no—
167C3×#471—51no—
168C3×#471—51no—
169C3×#471D511yescharacteristic, complemented
170C3×#456—51no—
171C3×#456—51no—
172C3×#453—51no—
173C3×#453—51no—
174C3×#443—51no—
175C3×#443—51no—
176#4150C22×C311yescharacteristic
177#4149C22×C311yescharacteristic, complemented
178#4147C22×C311yescharacteristic
179#4144C22×C311yescharacteristic, complemented
180C5×#137C22×C311yescharacteristic, complemented
181C5×AGL(1,ℤ/8)C22×C311yescharacteristic
182C2×C5×SD16C22×C311yescharacteristic, complemented
183C5×#131C22×C311yescharacteristic, complemented
184#4096C22×C311yescharacteristic
185#4090C22×C311yescharacteristic, complemented
186#4088C22×C311yescharacteristic, complemented
187C2×#688C22×C311yescharacteristic, complemented
188#4086C22×C311yescharacteristic
189C2×#687C22×C311yescharacteristic, complemented
190#4078C22×C311yescharacteristic
191#4065—21no—
192#4064—21no—
193#4062—21no—
194#4061—21no—
195#4061—21no—
196#4060—21no—
197#4060—21no—
198D5×SD16—21no—
199D5×SD16—21no—
200D5×SD16—21no—
201#4058—21no—
202#4057—21no—
203#4055—21no—
204#4055C22×C311yescharacteristic, complemented
205#4055C22×C311yescharacteristic, complemented
206#4054—21no—
207#4054C22×C311yescharacteristic
208#4054C22×C311yescharacteristic
209#4053C22×C311yescharacteristic, complemented
210#4053C22×C311yescharacteristic, complemented
211#4050—21no—
212#4050C22×C311yescharacteristic
213C2×#677—21no—
214C2×#677C22×C311yescharacteristic, complemented
215#4047C22×C311yescharacteristic, complemented
216C5×#108C22×C311yescharacteristic, complemented
217C5×#101C22×C311yescharacteristic, complemented
218C5×#100C22×C311yescharacteristic, complemented
219#3969C22×C311yescharacteristic, complemented
220#3957C22×C311yescharacteristic, complemented
221#3957C22×C311yescharacteristic, complemented
222#3957C22×C311yescharacteristic, complemented
223#3956C22×C311yescharacteristic, complemented
224#3955C22×C311yescharacteristic, complemented
225#3954C22×C311yescharacteristic, complemented
226C8×Dic5C22×C311yescharacteristic, complemented
227#3291—51noSylow
228C23×C3×C5—21no—
229C22×C3×D5—21no—
230C22×C3×D5—41no—
231C22×C3×D5—41no—
232C3×C5×Q8—21no—
233C3×C5×Q8—21no—
234C3×C5×Q8C2×D411yescharacteristic
235C3×C5×D4—21no—
236C3×C5×D4—21no—
237C3×C5×D4—21no—
238C3×C5×D4C2×D411yescharacteristic
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5C2411yescharacteristic
242C3×C22⋊D5—21no—
243C3×C22⋊D5—21no—
244C3×C22⋊D5—21no—
245C3×C22⋊D5—41no—
246C3×C22⋊D5—41no—
247C3×C22⋊D5—41no—
248C3×C22⋊D5—41no—
249C3×C22⋊D5—82no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—41no—
253C2×C3×Dic5—41no—
254C3×D20—21no—
255C3×D20—21no—
256C3×D20—41no—
257C3×D20—41no—
258C3×D20C2×D411yescharacteristic
259C3×D20C2×D411yescharacteristic
260C3×D20C2×D411yescharacteristic
261C3×C4×D5—21no—
262C3×C4×D5—21no—
263C3×C4×D5—21no—
264C3×C4×D5—41no—
265C3×C4×D5—41no—
266C3×C4×D5—41no—
267C3×C4×D5—41no—
268C3×Dic10—21no—
269C3×Dic10—21no—
270C3×Dic10—41no—
271C3×Dic10—41no—
272C3×Dic10C2×D411yescharacteristic
273C3×Dic10C2×D411yescharacteristic
274C3×Dic10C2×D411yescharacteristic
275C3×C5×C8—21no—
276C3×C5×C8—21no—
277C3×C5×C8—21no—
278C3×C5×C8C2×D411yescharacteristic
279C3×C5×C8C2×D411yescharacteristic
280C3×#168—21no—
281C3×#168C2×D411yescharacteristic
282C3×#168C2×D411yescharacteristic
283C3×2−1+4—51no—
284C3×2−1+4—51no—
285C3×H(5,𝔽2)—51no—
286C3×H(5,𝔽2)—51no—
287C3×#137—51no—
288C3×#137—51no—
289C3×#137—51no—
290C3×#137—101no—
291C3×#137—101no—
292C3×#137—101no—
293C3×#137—101no—
294C3×#137C2×D511yescharacteristic, complemented
295C3×AGL(1,ℤ/8)—51no—
296C3×AGL(1,ℤ/8)—51no—
297C3×AGL(1,ℤ/8)—51no—
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
303C3×#135—51no—
304C3×#135—51no—
305C3×#135—101no—
306C3×#135—101no—
307C3×#135—101no—
308C3×#135—101no—
309C2×C3×SD16—51no—
310C2×C3×SD16—51no—
311C2×C3×SD16—51no—
312C2×C3×SD16—101no—
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×#108C2×D511yescharacteristic, complemented
325C3×#104—51no—
326C3×#104—51no—
327C3×#104—51no—
328C3×#104—51no—
329C3×#101—51no—
330C3×#101C2×D511yescharacteristic, complemented
331C3×#100—51no—
332C3×#100C2×D511yescharacteristic, complemented
333C3×C4×C8—51no—
334C5×#41C23×C311yescharacteristic
335C2×C5×Q8C23×C311yescharacteristic
336C2×C5×D4C23×C311yescharacteristic
337C2×C22⋊D5—41no—
338C2×C22⋊D5—41no—
339#713—21no—
340#713—21no—
341#713—21no—
342Q8×D5—21no—
343Q8×D5—21no—
344Q8×D5—21no—
345#711—21no—
346#711—21no—
347#711—21no—
348#711—41no—
349D4×D5—21no—
350D4×D5—21no—
351D4×D5—21no—
352D4×D5—41no—
353#709—21no—
354#709—21no—
355#709—41no—
356#709C23×C311yescharacteristic
357#709C23×C311yescharacteristic
358#709C23×C311yescharacteristic
359C2×D20—21no—
360C2×D20C23×C311yescharacteristic
361C2×Dic10—21no—
362C2×Dic10C23×C311yescharacteristic
363C5×Q16—21no—
364C5×SD16—21no—
365C5×SD16—21no—
366C5×SD16—21no—
367C5×SD16—21no—
368C5×D8—21no—
369C5×M16—21no—
370C5×M16C23×C311yescharacteristic
371C5×M16C23×C311yescharacteristic
372C5×M16C23×C311yescharacteristic
373C2×C5×C8—21no—
374C2×C5×C8C23×C311yescharacteristic
375#689—21no—
376#689C3×D411yescharacteristic, complemented
377#688—21no—
378#688—21no—
379#688—21no—
380#688C3×D411yescharacteristic, complemented
381#687—21no—
382#687—21no—
383#687—21no—
384#687C3×D411yescharacteristic, complemented
385#686—21no—
386#686C3×D411yescharacteristic, complemented
387#683—41no—
388C4×Dic5C23×C311yescharacteristic
389#681C23×C311yescharacteristic
390C2×#168C23×C311yescharacteristic
391Dic20—21no—
392Dic20—21no—
393Dic20C3×D411yescharacteristic, complemented
394D40—21no—
395D40—21no—
396D40C3×D411yescharacteristic, complemented
397#677—21no—
398#677—21no—
399#677—21no—
400#677—21no—
401#677—21no—
402#677—21no—
403#677C3×D411yescharacteristic, complemented
404#677C3×D411yescharacteristic, complemented
405#676—21no—
406#676—21no—
407#676—21no—
408C8×D5—21no—
409C8×D5—21no—
410C8×D5—21no—
411#577—51no—
412#577—51no—
413#577—51no—
414#577—51no—
415#492—51no—
416#471—51no—
417#471—51no—
418#471—51no—
419#471C3×D511yescharacteristic, complemented
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—41no—
428C22×C3×C5—81no—
429C22×C3×C5H(5,𝔽2)11yescharacteristic
430C2×C3×D5—21no—
431C2×C3×D5—21no—
432C2×C3×D5—21no—
433C2×C3×D5—41no—
434C2×C3×D5—81no—
435C2×C3×D5—161no—
436C2×C3×D5—161no—
437C3×C4×C5—21no—
438C3×C4×C5—41no—
439C3×C4×C5C22×D411yescharacteristic
440C3×C4×C5C22×D411yescharacteristic
441C3×Dic5—22no—
442C3×Dic5—21no—
443C3×Dic5—21no—
444C3×Dic5—21no—
445C3×Dic5—41no—
446C3×#41—51no—
447C3×#41—51no—
448C3×#41—51no—
449C3×#41—101no—
450C3×#41—101no—
451C3×#41—101no—
452C3×#41—101no—
453C3×#41—101no—
454C3×#41—101no—
455C3×#41—101no—
456C3×#41—101no—
457C3×#41—201no—
458C3×#41—201no—
459C3×#41C22×D511yescharacteristic
460C2×C3×Q8—51no—
461C2×C3×Q8—101no—
462C2×C3×Q8—101no—
463C2×C3×Q8—101no—
464C2×C3×Q8—101no—
465C2×C3×Q8C22×D511yescharacteristic
466C2×C3×D4—51no—
467C2×C3×D4—101no—
468C2×C3×D4—101no—
469C2×C3×D4—101no—
470C2×C3×D4—101no—
471C2×C3×D4—201no—
472C2×C3×D4—201no—
473C2×C3×D4—201no—
474C2×C3×D4C22×D511yescharacteristic
475C3×Q16—21no—
476C3×Q16—51no—
477C3×Q16—51no—
478C3×Q16—101no—
479C3×Q16—101no—
480C3×Q16—101no—
481C3×SD16—21no—
482C3×SD16—21no—
483C3×SD16—21no—
484C3×SD16—21no—
485C3×SD16—51no—
486C3×SD16—51no—
487C3×SD16—51no—
488C3×SD16—51no—
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×SD16—101no—
500C3×SD16—101no—
501C3×D8—21no—
502C3×D8—51no—
503C3×D8—51no—
504C3×D8—101no—
505C3×D8—101no—
506C3×D8—101no—
507C3×M16—21no—
508C3×M16—51no—
509C3×M16—101no—
510C3×M16—101no—
511C3×M16—101no—
512C3×M16C22×D511yescharacteristic
513C3×M16C22×D511yescharacteristic
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—
524C22×D5—21no—
525C22×D5—41no—
526C22×D5—41no—
527C5×Q8—21no—
528C5×Q8—21no—
529C5×Q8C2×C3×D411yescharacteristic
530C5×D4—21no—
531C5×D4—21no—
532C5×D4—21no—
533C5×D4C2×C3×D411yescharacteristic
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5C24×C311yescharacteristic
537C22⋊D5—21no—
538C22⋊D5—21no—
539C22⋊D5—21no—
540C22⋊D5—41no—
541C22⋊D5—41no—
542C22⋊D5—41no—
543C22⋊D5—41no—
544C22⋊D5—82no—
545C2×Dic5—21no—
546C2×Dic5—21no—
547C2×Dic5—41no—
548C2×Dic5—41no—
549D20—21no—
550D20—21no—
551D20—41no—
552D20—41no—
553D20C2×C3×D411yescharacteristic
554D20C2×C3×D411yescharacteristic
555D20C2×C3×D411yescharacteristic
556C4×D5—21no—
557C4×D5—21no—
558C4×D5—21no—
559C4×D5—41no—
560C4×D5—41no—
561C4×D5—41no—
562C4×D5—41no—
563Dic10—21no—
564Dic10—21no—
565Dic10—41no—
566Dic10—41no—
567Dic10C2×C3×D411yescharacteristic
568Dic10C2×C3×D411yescharacteristic
569Dic10C2×C3×D411yescharacteristic
570C5×C8—21no—
571C5×C8—21no—
572C5×C8—21no—
573C5×C8C2×C3×D411yescharacteristic
574C5×C8C2×C3×D411yescharacteristic
575#168—21no—
576#168C2×C3×D411yescharacteristic
577#168C2×C3×D411yescharacteristic
5782−1+4—51no—
5792−1+4—51no—
580H(5,𝔽2)—51no—
581H(5,𝔽2)—51no—
582#137—51no—
583#137—51no—
584#137—51no—
585#137—101no—
586#137—101no—
587#137—101no—
588#137—101no—
589#137C2×C3×D511yescharacteristic, complemented
590AGL(1,ℤ/8)—51no—
591AGL(1,ℤ/8)—51no—
592AGL(1,ℤ/8)—51no—
593AGL(1,ℤ/8)—101no—
594AGL(1,ℤ/8)—101no—
595AGL(1,ℤ/8)—101no—
596AGL(1,ℤ/8)—101no—
597AGL(1,ℤ/8)C2×C3×D511yescharacteristic
598#135—51no—
599#135—51no—
600#135—101no—
601#135—101no—
602#135—101no—
603#135—101no—
604C2×SD16—51no—
605C2×SD16—51no—
606C2×SD16—51no—
607C2×SD16—101no—
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#108C2×C3×D511yescharacteristic, complemented
620#104—51no—
621#104—51no—
622#104—51no—
623#104—51no—
624#101—51no—
625#101C2×C3×D511yescharacteristic, complemented
626#100—51no—
627#100C2×C3×D511yescharacteristic, complemented
628C4×C8—51no—
629C2×C3×C5—21no—
630C2×C3×C5—41no—
631C2×C3×C5—81no—
632C2×C3×C5D4211yescharacteristic
633C3×D5—41no—
634C3×D5—41no—
635C3×D5—41no—
636C3×D5—81no—
637C23×C3—21no—
638C23×C3—101no—
639C23×C3—201no—
640C23×C3—201no—
641C3×Q8—21no—
642C3×Q8—21no—
643C3×Q8—51no—
644C3×Q8—51no—
645C3×Q8—51no—
646C3×Q8—101no—
647C3×Q8—101no—
648C3×Q8—201no—
649C3×Q8—201no—
650C3×Q8D4×D511yescharacteristic
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—51no—
655C3×D4—51no—
656C3×D4—51no—
657C3×D4—101no—
658C3×D4—101no—
659C3×D4—101no—
660C3×D4—101no—
661C3×D4—101no—
662C3×D4—201no—
663C3×D4—201no—
664C3×D4—201no—
665C3×D4—201no—
666C3×D4—201no—
667C3×D4—201no—
668C3×D4—402no—
669C3×D4D4×D511yescharacteristic
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—201no—
678C2×C3×C4—201no—
679C2×C3×C4—201no—
680C2×C3×C4—201no—
681C2×C3×C4—201no—
682C2×C3×C4—201no—
683C2×C3×C4C23×D511yescharacteristic
684C3×C8—21no—
685C3×C8—21no—
686C3×C8—21no—
687C3×C8—51no—
688C3×C8—51no—
689C3×C8—101no—
690C3×C8D4×D511yescharacteristic
691C3×C8D4×D511yescharacteristic
692C22×C5—21no—
693C22×C5—41no—
694C22×C5—81no—
695C22×C5C3×H(5,𝔽2)11yescharacteristic
696C2×D5—21no—
697C2×D5—21no—
698C2×D5—21no—
699C2×D5—41no—
700C2×D5—81no—
701C2×D5—161no—
702C2×D5—161no—
703C4×C5—21no—
704C4×C5—41no—
705C4×C5C22×C3×D411yescharacteristic
706C4×C5C22×C3×D411yescharacteristic
707Dic5—22no—
708Dic5—21no—
709Dic5—21no—
710Dic5—21no—
711Dic5—41no—
712#41—51no—
713#41—51no—
714#41—51no—
715#41—101no—
716#41—101no—
717#41—101no—
718#41—101no—
719#41—101no—
720#41—101no—
721#41—101no—
722#41—101no—
723#41—201no—
724#41—201no—
725#41C22×C3×D511yescharacteristic
726C2×Q8—51no—
727C2×Q8—101no—
728C2×Q8—101no—
729C2×Q8—101no—
730C2×Q8—101no—
731C2×Q8C22×C3×D511yescharacteristic
732C2×D4—51no—
733C2×D4—101no—
734C2×D4—101no—
735C2×D4—101no—
736C2×D4—101no—
737C2×D4—201no—
738C2×D4—201no—
739C2×D4—201no—
740C2×D4C22×C3×D511yescharacteristic
741Q16—21no—
742Q16—51no—
743Q16—51no—
744Q16—101no—
745Q16—101no—
746Q16—101no—
747SD16—21no—
748SD16—21no—
749SD16—21no—
750SD16—21no—
751SD16—51no—
752SD16—51no—
753SD16—51no—
754SD16—51no—
755SD16—101no—
756SD16—101no—
757SD16—101no—
758SD16—101no—
759SD16—101no—
760SD16—101no—
761SD16—101no—
762SD16—101no—
763SD16—101no—
764SD16—101no—
765SD16—101no—
766SD16—101no—
767D8—21no—
768D8—51no—
769D8—51no—
770D8—101no—
771D8—101no—
772D8—101no—
773M16—21no—
774M16—51no—
775M16—101no—
776M16—101no—
777M16—101no—
778M16C22×C3×D511yescharacteristic
779M16C22×C3×D511yescharacteristic
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—41no—
792C22×C3—81no—
793C22×C3—101no—
794C22×C3—101no—
795C22×C3—101no—
796C22×C3—201no—
797C22×C3—401no—
798C22×C3—801no—
799C22×C3—801no—
800C22×C3#414911yescharacteristic
801C3×C4—21no—
802C3×C4—41no—
803C3×C4—102no—
804C3×C4—101no—
805C3×C4—101no—
806C3×C4—101no—
807C3×C4—201no—
808C3×C4C2×D4×D511yescharacteristic
809C3×C4C2×D4×D511yescharacteristic
810C2×C5—21no—
811C2×C5—41no—
812C2×C5—81no—
813C2×C5C3×D4211yescharacteristic
814D5—41no—
815D5—41no—
816D5—41no—
817D5—81no—
818C23—21no—
819C23—101no—
820C23—201no—
821C23—201no—
822Q8—21no—
823Q8—21no—
824Q8—51no—
825Q8—51no—
826Q8—51no—
827Q8—101no—
828Q8—101no—
829Q8—201no—
830Q8—201no—
831Q8C3×D4×D511yescharacteristic
832D4—21no—
833D4—21no—
834D4—21no—
835D4—51no—
836D4—51no—
837D4—51no—
838D4—101no—
839D4—101no—
840D4—101no—
841D4—101no—
842D4—101no—
843D4—201no—
844D4—201no—
845D4—201no—
846D4—201no—
847D4—201no—
848D4—201no—
849D4—402no—
850D4C3×D4×D511yescharacteristic
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—201no—
859C2×C4—201no—
860C2×C4—201no—
861C2×C4—201no—
862C2×C4—201no—
863C2×C4—201no—
864C2×C4C23×C3×D511yescharacteristic
865C8—21no—
866C8—21no—
867C8—21no—
868C8—51no—
869C8—51no—
870C8—101no—
871C8C3×D4×D511yescharacteristic
872C8C3×D4×D511yescharacteristic
873C2×C3—21no—
874C2×C3—41no—
875C2×C3—81no—
876C2×C3—201no—
877C2×C3—201no—
878C2×C3—201no—
879C2×C3—401no—
880C2×C3#6594311yescharacteristic
881C5C3×#329111yescharacteristic, complemented, Sylow
882C22—21no—
883C22—41no—
884C22—81no—
885C22—101no—
886C22—101no—
887C22—101no—
888C22—201no—
889C22—401no—
890C22—801no—
891C22—801no—
892C22C3×#414911yescharacteristic
893C4—21no—
894C4—41no—
895C4—102no—
896C4—101no—
897C4—101no—
898C4—101no—
899C4—201no—
900C4C2×C3×D4×D511yescharacteristic
901C4C2×C3×D4×D511yescharacteristic
902C3#1061266611yescharacteristic, direct product factor, Sylow
903C2—21no—
904C2—41no—
905C2—81no—
906C2—201no—
907C2—201no—
908C2—201no—
909C2—401no—
910C2C3×#6594311yescharacteristic
subgroupG/H
centerC2×C3#65943
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#471C2
socleC2×C3×C5D42
hypercenterC3×#471D5
hypocenterC5C3×#3291
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#471

Complements

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

NH ≅ G/Ntype
1. C3×#66112C2semidirect
2. C3×#66109C2semidirect
3. C3×#66096C2semidirect
4. C3×#66085C2semidirect
5. C3×C5×#471C2semidirect
6. C3×#65494C2semidirect
7. C3×#65487C2semidirect
8. C3×#65464C2semidirect
9. C3×#65433C2semidirect
10. C3×#65187C2semidirect
11. C3×#65184C2semidirect
12. C3×#65043C2semidirect
13. C3×#65041C2semidirect
14. C3×#65037C2semidirect
15. C3×#65036C2semidirect
16. #10612666C3direct (N × H)
18. C3×#4149C22semidirect
20. C3×#4144C22semidirect
21. C3×C5×#137C22semidirect
23. C2×C3×C5×SD16C22semidirect
24. C3×C5×#131C22semidirect
26. C3×#4090C22semidirect
27. C3×#4088C22semidirect
28. C2×C3×#688C22semidirect
30. C2×C3×#687C22semidirect
45. C3×#4055C22semidirect
46. C3×#4055C22semidirect
50. C3×#4053C22semidirect
51. C3×#4053C22semidirect
55. C2×C3×#677C22semidirect
56. C3×#4047C22semidirect
57. C3×C5×#108C22semidirect
58. C3×C5×#101C22semidirect
59. C3×C5×#100C22semidirect
60. C3×#3969C22semidirect
61. C3×#3957C22semidirect
62. C3×#3957C22semidirect
63. C3×#3957C22semidirect
64. C3×#3956C22semidirect
65. C3×#3955C22semidirect
66. C3×#3954C22semidirect
67. C3×C8×Dic5C22semidirect
69. #66112C2×C3semidirect
70. #66109C2×C3semidirect
71. #66096C2×C3semidirect
72. #66085C2×C3semidirect
73. C5×#471C2×C3semidirect
74. #65494C2×C3semidirect
75. #65487C2×C3semidirect
76. #65464C2×C3semidirect
77. #65433C2×C3semidirect
78. #65187C2×C3semidirect
79. #65184C2×C3semidirect
80. #65043C2×C3semidirect
81. #65041C2×C3semidirect
82. #65037C2×C3semidirect
83. #65036C2×C3semidirect
126. C3×#689D4semidirect
130. C3×#688D4semidirect
134. C3×#687D4semidirect
136. C3×#686D4semidirect
143. C3×Dic20D4semidirect
146. C3×D40D4semidirect
153. C3×#677D4semidirect
154. C3×#677D4semidirect
169. C3×#471D5semidirect
177. #4149C22×C3semidirect
179. #4144C22×C3semidirect
180. C5×#137C22×C3semidirect
182. C2×C5×SD16C22×C3semidirect
183. C5×#131C22×C3semidirect
185. #4090C22×C3semidirect
186. #4088C22×C3semidirect
187. C2×#688C22×C3semidirect
189. C2×#687C22×C3semidirect
204. #4055C22×C3semidirect
205. #4055C22×C3semidirect
209. #4053C22×C3semidirect
210. #4053C22×C3semidirect
214. C2×#677C22×C3semidirect
215. #4047C22×C3semidirect
216. C5×#108C22×C3semidirect
217. C5×#101C22×C3semidirect
218. C5×#100C22×C3semidirect
219. #3969C22×C3semidirect
220. #3957C22×C3semidirect
221. #3957C22×C3semidirect
222. #3957C22×C3semidirect
223. #3956C22×C3semidirect
224. #3955C22×C3semidirect
225. #3954C22×C3semidirect
226. C8×Dic5C22×C3semidirect
294. C3×#137C2×D5semidirect
316. C2×C3×SD16C2×D5semidirect
320. C3×#131C2×D5semidirect
324. C3×#108C2×D5semidirect
330. C3×#101C2×D5semidirect
332. C3×#100C2×D5semidirect
376. #689C3×D4semidirect
380. #688C3×D4semidirect
384. #687C3×D4semidirect
386. #686C3×D4semidirect
393. Dic20C3×D4semidirect
396. D40C3×D4semidirect
403. #677C3×D4semidirect
404. #677C3×D4semidirect
419. #471C3×D5semidirect
589. #137C2×C3×D5semidirect
611. C2×SD16C2×C3×D5semidirect
615. #131C2×C3×D5semidirect
619. #108C2×C3×D5semidirect
625. #101C2×C3×D5semidirect
627. #100C2×C3×D5semidirect
789. C3×C5#3291semidirect
881. C5C3×#3291semidirect
902. C3#10612666direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661122
C3×#661092
C3×#660962
C3×#660852
C3×C5×#4712
C3×#654942
C3×#654872
C3×#654642
C3×#654332
C3×#651872
C3×#651842
C3×#650432
C3×#650412
C3×#650372
C3×#650362
#106126663
C3×#32915