Finite Group Databasebeta

← #14415009

Subgroups — #14415009

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4053C211yesmaximal, characteristic, complemented
2#11754631C211yesmaximal, characteristic
3C2×D3×C8×D5C211yesmaximal, characteristic, complemented
4#11751228C211yesmaximal, characteristic, complemented
5C5×#5127C211yesmaximal, characteristic, complemented
6#11748485C211yesmaximal, characteristic, complemented
7#67×#168C211yesmaximal, characteristic, complemented
8#11748482C211yesmaximal, characteristic, complemented
9#11748101C211yesmaximal, characteristic, complemented
10#11747725C211yesmaximal, characteristic, complemented
11#11747711C211yesmaximal, characteristic, complemented
12#11747698C211yesmaximal, characteristic, complemented
13#11747694C211yesmaximal, characteristic, complemented
14#11747648C211yesmaximal, characteristic, complemented
15#11747646C211yesmaximal, characteristic, complemented
16#10611209—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C2×C3×C5×M16C2211yescharacteristic, complemented
20C4×#1220C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C4×C5×#67C2211yescharacteristic
23C2×C5×D3×C8C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic, complemented
25C3×#4053—24no—
26C2×C3×#676C2211yescharacteristic
27C2×C3×#676C2211yescharacteristic, complemented
28C2×C3×C8×D5C2211yescharacteristic
29C2×C3×C8×D5C2211yescharacteristic, complemented
30#91577C411yescharacteristic
31#91565C411yescharacteristic
32#91548C411yescharacteristic
33#91533C411yescharacteristic
34#91474C411yescharacteristic
35C4×#1202C2211yescharacteristic
36C4×#1201C2211yescharacteristic
37#91411C411yescharacteristic
38#91410C411yescharacteristic
39#91407C411yescharacteristic
40#91357C2211yescharacteristic
41C2×#6649C2211yescharacteristic
42C2×#6648C2211yescharacteristic
43C2×D3×#168C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45D3×C8×D5—24no—
46#91114C2211yescharacteristic, complemented
47#91104C2211yescharacteristic
48#91099C2211yescharacteristic, complemented
49#91098C2211yescharacteristic, complemented
50C5×#830C2211yescharacteristic, complemented
51C5×(C2×D3)⋊C8C2211yescharacteristic
52C5×#815C2211yescharacteristic, complemented
53C5×Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊#168C2211yescharacteristic, complemented
55#90983C2211yescharacteristic, complemented
56#90957C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90955C2211yescharacteristic, complemented
59#90955C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61Dic3×#168C2211yescharacteristic, complemented
62#83794—51nomaximal, Hall
63C2×#4053D311yescharacteristic, complemented
64C22×C8×D5—31no—
65#65881—31no—
66C5×#435—31no—
67#65416—31no—
68#65400—31no—
69D4×#168—31no—
70#65128—31no—
71#65123—31no—
72#65016—31no—
73#65015—31no—
74#65014—31no—
75#65014—31no—
76#64997—31no—
77#64995—31no—
78C22×D3×D5C2×C411yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C2×C4×D15C2311yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×C22⋊D5C2×C411yescharacteristic
85C2×C3×C22⋊D5C2×C411yescharacteristic
86C3×#709—22no—
87C3×#709—22no—
88C2×C3×D20C2×C411yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10C2×C411yescharacteristic
92C2×#1202C2×C411yescharacteristic
93C2×#1201C2×C411yescharacteristic
94C2×#1200C2×C411yescharacteristic
95C2×D3×Dic5C2×C411yescharacteristic
96C2×D5×Dic3C2×C411yescharacteristic
97C4×D3×D5—22no—
98C4×D3×D5—22no—
99C3×C5×M16—22no—
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102#6719C2×C411yescharacteristic
103#6714C2×C411yescharacteristic
104#6712C2×C411yescharacteristic
105C4×Dic15C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C8×D15—22no—
109C5×#217C2×C411yescharacteristic
110C5×(C2×D3)⋊C4C2×C411yescharacteristic
111C5×Dic3⋊C4C2×C411yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C5×D3×C8—22no—
116C2×C3×#168—22no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C3×#676—22no—
120C3×#676—22no—
121C3×C8×D5—22no—
122C3×C8×D5D414yescomplemented
123Dic3⋊Dic5C2×C411yescharacteristic
124#6669C2×C411yescharacteristic
125#6668C2×C411yescharacteristic
126#6668C2×C411yescharacteristic
127#6667C2×C411yescharacteristic
128(C2×D3)⋊Dic5C2×C411yescharacteristic
129#6665C2×C411yescharacteristic
130#6665C2×C411yescharacteristic
131#6665C2×C411yescharacteristic
132#6665C2×C411yescharacteristic
133#6649—22no—
134#6648—22no—
135D3×#168—22no—
136D5×C3⋊C8—22no—
137C2×C3×#131—51no—
138#5828—51no—
139C22×D3×C8—51no—
140#5234—51no—
141#5127—51no—
142#5127—51no—
143#5127—51no—
144#5127D511yescharacteristic, complemented
145#5126—51no—
146#5119—51no—
147C8×#67—51no—
148C8×#67—51no—
149C8×#67—51no—
150C8×#67—51no—
151#5101—51no—
152C2×#709C2×D311yescharacteristic
153C22×C4×D5—31no—
154C2×C5×M16C2×D311yescharacteristic, complemented
155C22×C5×C8—31no—
156C4×C5×D4—31no—
157#4085—31no—
158#4083—31no—
159C4×C22⋊D5—31no—
160C4×C22⋊D5—31no—
161C22×#168—31no—
162C22×#168C2×D311yescharacteristic, complemented
163#4053—24no—
164C2×#676—31no—
165C2×#676C2×D311yescharacteristic
166C2×#676C2×D311yescharacteristic, complemented
167C2×C8×D5—31no—
168C2×C8×D5—31no—
169C2×C8×D5—31no—
170C2×C8×D5—64no—
171C2×C8×D5C2×D311yescharacteristic
172C2×C8×D5C2×D311yescharacteristic, complemented
173#4042—31no—
174#4040—31no—
175#4030—31no—
176#4029—31no—
177#4028—31no—
178#4024—31no—
179C4×D20—31no—
180#4018—31no—
181C5×C4⋊C8—31no—
182C5×C22⋊C8—31no—
183C5×C22⋊C8—31no—
184C5×#97—31no—
185C22⋊#168—31no—
186C22⋊#168—31no—
187#3952—31no—
188#3952—31no—
189#3952—31no—
190#3952—31no—
191#3947—31no—
192#3946—31no—
193#3946—31no—
194C8×Dic5—31no—
195C4⋊#168—31no—
196C4×#168—31no—
197#2929—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C3×D5C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×D3×D5—22no—
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C22×C411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210#1220—22no—
211C2×Dic15C22×C411yescharacteristic
212C2×Dic15C22×C411yescharacteristic
213C2×Dic15C22×C411yescharacteristic
214C4×D15—21no—
215C4×D15—21no—
216C5×#67—22no—
217C2×C5×Dic3C22×C411yescharacteristic
218C2×C5×Dic3C22×C411yescharacteristic
219C2×C5×Dic3C22×C411yescharacteristic
220C4×C5×D3—21no—
221C4×C5×D3—21no—
222C3×C22⋊D5—22no—
223C3×C22⋊D5—22no—
224C2×C3×Dic5C22×C411yescharacteristic
225C2×C3×Dic5C22×C411yescharacteristic
226C3×D20—22no—
227C3×C4×D5—21no—
228C3×C4×D5—21no—
229C3×C4×D5C2×D412yes—
230C3×C4×D5#4112yes—
231C3×Dic10—22no—
232#1202—22no—
233#1201—22no—
234#1200—22no—
235D3×Dic5—22no—
236D5×Dic3—22no—
237C3×C5×C8—21no—
238C3×C5×C8C2×D412yes—
239C3⋊#168—21no—
240C3⋊#168—21no—
241C3×#168—21no—
242C3×#168C2×D412yes—
243C5×C3⋊C8—21no—
244C5×C3⋊C8—21no—
245C2×C3×#41—51no—
246C22×C4×D3—51no—
247C3×#131—104no—
248C2×C3×M16—51no—
249C2×C3×M16—51no—
250C2×C3×M16C2×D511yescharacteristic, complemented
251C22×C3×C8—51no—
252C22×C3×C8—51no—
253C22×C3×C8—51no—
254#946—51no—
255#946—51no—
256#938—51no—
257#938—51no—
258#937—51no—
259#937—51no—
260#935—51no—
261#935—51no—
262C4×#67—51no—
263C4×#67—51no—
264C4×#67—51no—
265C4×#67C2×D511yescharacteristic
266#926—51no—
267C2×#208—51no—
268C22×C3⋊C8—51no—
269C2×D3×C8—51no—
270C2×D3×C8—51no—
271C2×D3×C8—51no—
272C2×D3×C8—104no—
273C2×D3×C8C2×D511yescharacteristic
274#830—51no—
275#830—51no—
276#830—51no—
277#830C2×D511yescharacteristic, complemented
278(C2×D3)⋊C8—51no—
279(C2×D3)⋊C8—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8C2×D511yescharacteristic
282#815—51no—
283#815C2×D511yescharacteristic, complemented
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8C2×D511yescharacteristic, complemented
288C8×Dic3—51no—
289C8×Dic3—51no—
290C23×D5—31no—
291C2×C5×D4—31no—
292C22×C4×C5—31no—
293C22×C4×C5C22×D311yescharacteristic
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5C4×D311yescharacteristic
297C2×C22⋊D5C4×D311yescharacteristic
298C22×Dic5—31no—
299#709—22no—
300#709—22no—
301C2×D20—31no—
302C2×D20C4×D311yescharacteristic
303C2×C4×D5—31no—
304C2×C4×D5—31no—
305C2×C4×D5—31no—
306C2×C4×D5—62no—
307C2×C4×D5—62no—
308C2×C4×D5C22×D311yescharacteristic
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10C4×D311yescharacteristic
311C5×M16—22no—
312C2×C5×C8—31no—
313C2×C5×C8—31no—
314C2×C5×C8—62no—
315C2×C5×C8C22×D311yescharacteristic
316C2×C5×C8C22×D311yescharacteristic
317C5×C4⋊C4—31no—
318C5×C22⋊C4—31no—
319C5×C22⋊C4—31no—
320C42×C5—31no—
321C22⋊Dic5—31no—
322C22⋊Dic5—31no—
323#685—31no—
324#685—31no—
325#685—31no—
326#685—31no—
327#685—31no—
328#685—31no—
329C4⋊Dic5—31no—
330#683—31no—
331#683—31no—
332#683—31no—
333#683—31no—
334C4×Dic5—31no—
335C2×#168—22no—
336C2×#168—31no—
337C2×#168—31no—
338C2×#168—62no—
339C2×#168C22×D311yescharacteristic
340C2×#168C22×D311yescharacteristic
341#676—22no—
342#676—22no—
343#676—62no—
344C8×D5—22no—
345C8×D5—62no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5#6714yescomplemented
349C2×#131—51no—
350C23×C8—151no—
351#525—151no—
352#435—31no—
353#435—151no—
354#435—151no—
355#435—151no—
356C8×D4—151no—
357C8×D4—151no—
358C8×D4—151no—
359C8×D4—151no—
360#424—151no—
361#408—151no—
362#407—151no—
363#405—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5C23×C411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15#13112yescomplemented
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3#13112yescomplemented
374C2×C3×D5—21no—
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5C4×D412yes—
380D3×D5—28no—
381C3×C4×C5—21no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—21no—
385Dic15—21no—
386Dic15—21no—
387C3×Dic5—21no—
388C3×Dic5C4×D412yes—
389C5×Dic3—21no—
390C5×Dic3—21no—
391C5×Dic3—21no—
392C23×D3—51no—
393C3×#41—102no—
394C3×#41—102no—
395C2×C3×Q8—51no—
396C2×C3×D4—51no—
397C2×C3×D4—51no—
398C2×C3×D4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4C22×D511yescharacteristic
402C2×#67—51no—
403C2×#67—51no—
404C2×#67—51no—
405C2×#67C4×D511yescharacteristic
406C22×Dic3—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—102no—
411C2×C4×D3—102no—
412C2×C4×D3C22×D511yescharacteristic
413C3×M16—22no—
414C3×M16—102no—
415C3×M16—102no—
416C2×C3×C8—51no—
417C2×C3×C8—54no—
418C2×C3×C8—51no—
419C2×C3×C8—102no—
420C2×C3×C8—102no—
421C2×C3×C8C22×D511yescharacteristic
422C2×C3×C8C22×D511yescharacteristic
423#217—51no—
424#217—51no—
425#217—51no—
426#217—51no—
427#217—51no—
428#217C4×D511yescharacteristic
429(C2×D3)⋊C4—51no—
430(C2×D3)⋊C4—51no—
431(C2×D3)⋊C4—51no—
432(C2×D3)⋊C4C4×D511yescharacteristic
433C4⋊Dic3—51no—
434C4⋊Dic3—51no—
435Dic3⋊C4—51no—
436Dic3⋊C4—51no—
437Dic3⋊C4—51no—
438Dic3⋊C4C4×D511yescharacteristic
439C4×Dic3—51no—
440C4×Dic3C22×D511yescharacteristic
441#208—102no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—102no—
445C2×C3⋊C8C22×D511yescharacteristic
446C2×C3⋊C8C22×D511yescharacteristic
447D3×C8—22no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—31no—
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—31no—
454C22×D5—62no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5C2×C4×D311yescharacteristic
458C22×D5C2×C4×D311yescharacteristic
459C5×D4—62no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—31no—
463C2×C4×C5—31no—
464C2×C4×C5—31no—
465C2×C4×C5—61no—
466C2×C4×C5—61no—
467C2×C4×C5C2×C4×D311yescharacteristic
468C2×C4×C5C23×D311yescharacteristic
469C22⋊D5—22no—
470C22⋊D5—22no—
471C22⋊D5—62no—
472C22⋊D5—62no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476C2×Dic5—62no—
477C2×Dic5C2×C4×D311yescharacteristic
478C2×Dic5C2×C4×D311yescharacteristic
479D20—22no—
480D20—62no—
481C4×D5—21no—
482C4×D5—21no—
483C4×D5—62no—
484C4×D5—61no—
485C4×D5—61no—
486C4×D5—62no—
487C4×D5#23512yes—
488C4×D5C2×#6712yes—
489Dic10—22no—
490C5×C8—21no—
491C5×C8—61no—
492C5×C8—61no—
493C5×C8C2×#6712yes—
494#168—21no—
495#168—61no—
496#168—61no—
497#168C2×#6712yes—
498C2×#41—51no—
499C23×C4—151no—
500#131—104no—
501C2×M16—51no—
502C2×M16—51no—
503C2×M16—151no—
504C2×M16D3×D511yescharacteristic, complemented
505C22×C8—31no—
506C22×C8—51no—
507C22×C8—51no—
508C22×C8—51no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—304no—
514#123—151no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—151no—
519#121—151no—
520#120—151no—
521#120—151no—
522C4×D4—31no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4—151no—
526#117—151no—
527C4⋊C8—31no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—31no—
532C22⋊C8—31no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C22⋊C8—151no—
539#97—31no—
540#97—151no—
541C4×C8—151no—
542C4×C8—151no—
543C2×C3×C5—41no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5C2×#13111yescharacteristic
546C2×C3×C5C2×#13111yescharacteristic
547D15—22no—
548C3×D5—22no—
549C3×D5—41no—
550C5×D3—22no—
551C23×C3—51no—
552C23×C3—51no—
553C23×C3C2×C4×D511yescharacteristic
554C22×D3—51no—
555C22×D3—102no—
556C22×D3—102no—
557C22×D3—102no—
558C22×D3C2×C4×D511yescharacteristic
559C3×Q8—102no—
560C3×D4—102no—
561C3×D4—102no—
562C3×D4—102no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—51no—
566C2×C3×C4—52no—
567C2×C3×C4—52no—
568C2×C3×C4—51no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4C2×C4×D511yescharacteristic
572C2×C3×C4C23×D511yescharacteristic
573#67—22no—
574#67—102no—
575#67—102no—
576#67—102no—
577C2×Dic3—51no—
578C2×Dic3—51no—
579C2×Dic3—51no—
580C2×Dic3—102no—
581C2×Dic3C2×C4×D511yescharacteristic
582C2×Dic3C2×C4×D511yescharacteristic
583C2×Dic3C2×C4×D511yescharacteristic
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—102no—
587C4×D3—102no—
588C4×D3—101no—
589C4×D3—101no—
590C3×C8—21no—
591C3×C8—52no—
592C3×C8—101no—
593C3×C8D4×D512yes—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—32no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5C22×C4×D311yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—32no—
611C2×D5—68no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5C4×#6712yes—
615C4×C5—21no—
616C4×C5—61no—
617C4×C5—61no—
618C4×C5—61no—
619C4×C5C2×#23511yescharacteristic
620C4×C5C22×#6711yescharacteristic
621Dic5—21no—
622Dic5—61no—
623Dic5—61no—
624Dic5—61no—
625Dic5C4×#6712yes—
626C24—151no—
627#41—102no—
628#41—102no—
629C2×Q8—51no—
630C2×D4—31no—
631C2×D4—51no—
632C2×D4—51no—
633C2×D4—51no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C22×C4—31no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—151no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—302no—
645C22×C4—302no—
646C22×C4C2×D3×D511yescharacteristic
647M16—22no—
648M16—102no—
649M16—102no—
650M16—302no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—51no—
654C2×C8—54no—
655C2×C8—51no—
656C2×C8—62no—
657C2×C8—102no—
658C2×C8—102no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8C2×D3×D511yescharacteristic
666C2×C8C2×D3×D511yescharacteristic
667C4⋊C4—31no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C22⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4—151no—
683C42—31no—
684C42—151no—
685C3×C5#292911yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—52no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3—101no—
693C22×C3—101no—
694C22×C3—101no—
695C22×C3C22×C4×D511yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—52no—
699C2×D3—108no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3#405312yescomplemented
703C3×C4—21no—
704C3×C4—52no—
705C3×C4—101no—
706C3×C4C2×D4×D511yescharacteristic
707C3×C4D5×#4111yescharacteristic
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—101no—
712Dic3—101no—
713Dic3—101no—
714C2×C5—41no—
715C2×C5—62no—
716C2×C5D3×#13111yescharacteristic
717C2×C5D3×#13111yescharacteristic
718C2×C5C2×C4×#6711yescharacteristic
719D5—22no—
720D5—41no—
721D5—62no—
722C23—31no—
723C23—51no—
724C23—51no—
725C23—151no—
726C23—302no—
727C23—302no—
728C23—302no—
729C23C4×D3×D511yescharacteristic
730Q8—102no—
731D4—62no—
732D4—102no—
733D4—102no—
734D4—102no—
735D4—302no—
736D4—302no—
737D4—302no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—51no—
744C2×C4—52no—
745C2×C4—52no—
746C2×C4—51no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—151no—
752C2×C4—151no—
753C2×C4—151no—
754C2×C4—302no—
755C2×C4—302no—
756C2×C4—302no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4C4×D3×D511yescharacteristic
760C2×C4C22×D3×D511yescharacteristic
761C8—21no—
762C8—52no—
763C8—61no—
764C8—61no—
765C8—101no—
766C8—301no—
767C8—301no—
768C8D5×#6712yes—
769C2×C3—41no—
770C2×C3—102no—
771C2×C3—201no—
772C2×C3C4×D4×D511yescharacteristic
773C2×C3C2×#405311yescharacteristic
774C2×C3D5×#13111yescharacteristic
775D3—22no—
776D3—102no—
777C5#8379411yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—32no—
782C22—52no—
783C22—61no—
784C22—61no—
785C22—101no—
786C22—101no—
787C22—101no—
788C22—101no—
789C22—101no—
790C22—152no—
791C22—308no—
792C22—301no—
793C22—301no—
794C22C2×C4×D3×D511yescharacteristic
795C4—21no—
796C4—52no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—101no—
801C4—301no—
802C4—301no—
803C4—301no—
804C4D5×#23511yescharacteristic
805C4C2×D5×#6711yescharacteristic
806C3#1061120911yescharacteristic, complemented, Sylow
807C2—41no—
808C2—62no—
809C2—102no—
810C2—201no—
811C2—302no—
812C2D3×#405311yescharacteristic
813C2#1175401711yescharacteristic
814C2C4×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×M16C22
prime radical#11754631C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2929
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4053C2semidirect
3. C2×D3×C8×D5C2semidirect
4. #11751228C2semidirect
5. C5×#5127C2semidirect
6. #11748485C2semidirect
7. #67×#168C2semidirect
8. #11748482C2semidirect
9. #11748101C2semidirect
10. #11747725C2semidirect
11. #11747711C2semidirect
12. #11747698C2semidirect
13. #11747694C2semidirect
14. #11747648C2semidirect
15. #11747646C2semidirect
19. C2×C3×C5×M16C22semidirect
24. C22×C3×#168C22semidirect
27. C2×C3×#676C22semidirect
29. C2×C3×C8×D5C22semidirect
46. #91114C22semidirect
48. #91099C22semidirect
49. #91098C22semidirect
50. C5×#830C22semidirect
52. C5×#815C22semidirect
53. C5×Dic3⋊C8C22semidirect
54. Dic3⋊#168C22semidirect
55. #90983C22semidirect
58. #90955C22semidirect
59. #90955C22semidirect
60. #90951C22semidirect
61. Dic3×#168C22semidirect
63. C2×#4053D3semidirect
122. C3×C8×D5D4semidirect
144. #5127D5semidirect
154. C2×C5×M16C2×D3semidirect
162. C22×#168C2×D3semidirect
166. C2×#676C2×D3semidirect
172. C2×C8×D5C2×D3semidirect
250. C2×C3×M16C2×D5semidirect
277. #830C2×D5semidirect
283. #815C2×D5semidirect
287. Dic3⋊C8C2×D5semidirect
348. C8×D5#67semidirect
370. C2×D15#131semidirect
373. C2×C5×D3#131semidirect
504. C2×M16D3×D5semidirect
685. C3×C5#2929semidirect
702. C2×D3#4053semidirect
777. C5#83794semidirect
806. C3#10611209semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40532
#117546312
C2×D3×C8×D52
#117512282
C5×#51272
#117484852
#67×#1682
#117484822
#117481012
#117477252
#117477112
#117476982
#117476942
#117476482
#117476462
#106112093
#837945