Finite Group Databasebeta

← C151×#23236 #50328161

Subgroups — C151×#23236 #50328161

Order 38656.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3135×C151C211yesmaximal, characteristic
2#2962×C151C211yesmaximal, characteristic, complemented
3#2935×C151C211yesmaximal, characteristic
4#1986×C151C211yesmaximal, characteristic, complemented
5#1980×C151C211yesmaximal, characteristic
6#1938×C151C211yesmaximal, characteristic, complemented
7#1937×C151C211yesmaximal, characteristic, complemented
8#1929×C151C211yesmaximal, characteristic, complemented
9#1929×C151C211yesmaximal, characteristic, complemented
10#1866×C151C211yesmaximal, characteristic, complemented
11#1866×C151C211yesmaximal, characteristic, complemented
12#1778×C151C211yesmaximal, characteristic, complemented
13#1771×C151C211yesmaximal, characteristic, complemented
14#1765×C151C211yesmaximal, characteristic, complemented
15#1764×C151C211yesmaximal, characteristic, complemented
16C2×#131×C151C2211yescharacteristic
17C2×#131×C151C2211yescharacteristic
18#533×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20#491×C151C411yescharacteristic, complemented
21#491×C151C411yescharacteristic, complemented
22#490×C151C411yescharacteristic, complemented
23#490×C151C411yescharacteristic, complemented
24#489×C151C411yescharacteristic, complemented
25#489×C151C411yescharacteristic, complemented
26#489×C151C411yescharacteristic, complemented
27#489×C151C411yescharacteristic, complemented
28#446×C151—21no—
29#446×C151—21no—
30#446×C151—21no—
31C8×Q8×C151—21no—
32#436×C151—21no—
33#435×C151—21no—
34#435×C151—21no—
35C8×D4×C151—21no—
36C2×#108×C151C2211yescharacteristic
37C2×#108×C151C2211yescharacteristic
38#424×C151C2211yescharacteristic
39#424×C151C2211yescharacteristic
40C2×C4⋊C8×C151C2211yescharacteristic
41C2×#104×C151C2211yescharacteristic
42C2×#104×C151C2211yescharacteristic
43C2×#104×C151C2211yescharacteristic
44C2×#104×C151C2211yescharacteristic
45#416×C151C2211yescharacteristic
46#416×C151C2211yescharacteristic
47#416×C151C2211yescharacteristic
48#416×C151C2211yescharacteristic
49#408×C151C2211yescharacteristic
50#408×C151C2211yescharacteristic
51#405×C151C2211yescharacteristic
52#405×C151C2211yescharacteristic
53C4×M16×C151C2211yescharacteristic
54C4×M16×C151C2211yescharacteristic
55C2×#97×C151C2211yescharacteristic
56C2×#97×C151C2211yescharacteristic
57C2×C4×C8×C151C2211yescharacteristic
58C4×C4⋊C4×C151C2211yescharacteristic
59#341×C151C2211yescharacteristic
60#341×C151C2211yescharacteristic
61#339×C151C2211yescharacteristic
62#339×C151C2211yescharacteristic
63#339×C151C2211yescharacteristic
64#339×C151C2211yescharacteristic
65#336×C151C2211yescharacteristic
66#336×C151C2211yescharacteristic
67C2×#41×C151C2311yescharacteristic
68C2×#41×C151C2311yescharacteristic
69#131×C151—22no—
70#131×C151—22no—
71#131×C151—41no—
72#131×C151—41no—
73C2×M16×C151—21no—
74C2×M16×C151—21no—
75C2×M16×C151C2311yescharacteristic
76C2×M16×C151C2311yescharacteristic
77C2×M16×C151C2311yescharacteristic
78C2×M16×C151C2311yescharacteristic
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C4⋊Q8×C151C2×C411yescharacteristic
86C4⋊Q8×C151C2×C411yescharacteristic
87C4⋊Q8×C151C2×C411yescharacteristic
88#127×C151C2×C411yescharacteristic
89#125×C151C2×C411yescharacteristic
90#125×C151C2×C411yescharacteristic
91#124×C151C2×C411yescharacteristic
92#124×C151C2×C411yescharacteristic
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101#117×C151C2311yescharacteristic
102#117×C151C2311yescharacteristic
103C2×C4⋊C4×C151—21no—
104C2×C42×C151C2311yescharacteristic
105C2×C42×C151C2311yescharacteristic
106C2×C42×C151C2311yescharacteristic
107#108×C151—22no—
108#108×C151—22no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151D411yescharacteristic
114C4⋊C8×C151D411yescharacteristic
115C4⋊C8×C151D411yescharacteristic
116C4⋊C8×C151D411yescharacteristic
117#104×C151—22no—
118#104×C151—22no—
119#104×C151—41no—
120#104×C151—41no—
121#103×C151C2×C411yescharacteristic
122#103×C151C2×C411yescharacteristic
123#103×C151C2×C411yescharacteristic
124#103×C151C2×C411yescharacteristic
125#103×C151C2×C411yescharacteristic
126#103×C151C2×C411yescharacteristic
127#103×C151C2×C411yescharacteristic
128#103×C151C2×C411yescharacteristic
129#102×C151C2×C411yescharacteristic
130#102×C151C2×C411yescharacteristic
131#102×C151C2×C411yescharacteristic
132#102×C151C2×C411yescharacteristic
133#102×C151C2×C411yescharacteristic
134#102×C151C2×C411yescharacteristic
135#102×C151C2×C411yescharacteristic
136#102×C151C2×C411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C22⋊C8×C151—21no—
141#97×C151—21no—
142#97×C151—21no—
143#97×C151—21no—
144#97×C151—21no—
145#97×C151—41no—
146#97×C151C2×C411yescharacteristic
147#97×C151C2×C411yescharacteristic
148#97×C151C2×C411yescharacteristic
149#97×C151C2×C411yescharacteristic
150C4×C8×C151—21no—
151C4×C8×C151—21no—
152C4×C8×C151—21no—
153C4×C8×C151—21no—
154C4×C8×C151—41no—
155#95×C151—21no—
156#41×C151—21no—
157#41×C151—21no—
158#41×C151—21no—
159#41×C151—21no—
160#41×C151—21no—
161#41×C151—21no—
162#41×C151—21no—
163#41×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151C22×C411yescharacteristic
167C2×Q8×C151C22×C411yescharacteristic
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151C22×C411yescharacteristic
173C2×D4×C151C22×C411yescharacteristic
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151#4111yescharacteristic
179C22×C4×C151#4111yescharacteristic
180C22×C4×C151C2411yescharacteristic
181M16×C151—21no—
182M16×C151—21no—
183M16×C151—21no—
184M16×C151—21no—
185M16×C151—21no—
186M16×C151—21no—
187M16×C151—42no—
188M16×C151—42no—
189M16×C151#4112yes—
190M16×C151#4112yes—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—42no—
204C2×C8×C151—42no—
205C2×C8×C151C22×C411yescharacteristic
206C2×C8×C151C22×C411yescharacteristic
207C2×C8×C151C22×C411yescharacteristic
208C2×C8×C151C22×C411yescharacteristic
209C2×C8×C151C2×D411yescharacteristic
210C2×C8×C151C2×D411yescharacteristic
211C2×C8×C151C2×D411yescharacteristic
212C2×C8×C151C2×D411yescharacteristic
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—42no—
222C4⋊C4×C151C22×C411yescharacteristic
223C4⋊C4×C151C22×C411yescharacteristic
224C4⋊C4×C151C22×C411yescharacteristic
225C4⋊C4×C151C22×C411yescharacteristic
226C22⋊C4×C151—21no—
227C22⋊C4×C151—21no—
228C22⋊C4×C151—21no—
229C22⋊C4×C151—21no—
230C22⋊C4×C151—21no—
231C22⋊C4×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151C22×C411yescharacteristic
239C42×C151C22×C411yescharacteristic
240C42×C151C2×D411yescharacteristic
241C42×C151C2×D411yescharacteristic
242C23×C151—21no—
243C23×C151—21no—
244C23×C151C2×#4111yescharacteristic
245Q8×C151—21no—
246Q8×C151—21no—
247Q8×C151—21no—
248Q8×C151—21no—
249Q8×C151—42no—
250Q8×C151—81no—
251D4×C151—21no—
252D4×C151—21no—
253D4×C151—21no—
254D4×C151—21no—
255D4×C151—42no—
256D4×C151—41no—
257D4×C151—41no—
258D4×C151—41no—
259D4×C151—41no—
260D4×C151—81no—
261C2×C4×C151—22no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151C4×D411yescharacteristic
280C2×C4×C151C4×D411yescharacteristic
281C2×C4×C151C4×D411yescharacteristic
282C2×C4×C151C4×D411yescharacteristic
283C2×C4×C151C23×C411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151C2×#4111yescharacteristic
287C2×C4×C151H(5,𝔽2)11yescharacteristic
288C2×C4×C1512−1+411yescharacteristic
289C8×C151—21no—
290C8×C151—21no—
291C8×C151—21no—
292C8×C151—21no—
293C8×C151—21no—
294C8×C151—21no—
295C8×C151—21no—
296C8×C151—21no—
297C8×C151—22no—
298C8×C151—22no—
299C8×C151—41no—
300C8×C151—41no—
301C22×C151—21no—
302C22×C151—21no—
303C22×C151—41no—
304C22×C151—41no—
305C22×C151—41no—
306C22×C151—41no—
307C22×C151—41no—
308C22×C151—41no—
309C22×C151C2×C4×D411yescharacteristic
310C22×C151#55611yescharacteristic
311C22×C151#55911yescharacteristic
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—21no—
315C4×C151—21no—
316C4×C151—42no—
317C4×C151—41no—
318C4×C151—41no—
319C4×C151—41no—
320C4×C151—41no—
321C4×C151—41no—
322C4×C151—41no—
323C4×C151—81no—
324C4×C151C4×#4111yescharacteristic
325C4×C151#52011yescharacteristic
326C4×C151#54611yescharacteristic
327C4×C151#54811yescharacteristic
328C2×C151—21no—
329C2×C151—21no—
330C2×C151—81no—
331C2×C151—81no—
332C2×C151#236711yescharacteristic
333C2×C151#295511yescharacteristic
334C2×C151#295611yescharacteristic
335#23236C15111yesmaximal, characteristic, direct product factor, Sylow
336C151#2323611yescharacteristic, direct product factor, Sylow
337#3135C2×C15111yescharacteristic
338#2962C2×C15111yescharacteristic, complemented
339#2935C2×C15111yescharacteristic
340#1986C2×C15111yescharacteristic, complemented
341#1980C2×C15111yescharacteristic
342#1938C2×C15111yescharacteristic, complemented
343#1937C2×C15111yescharacteristic, complemented
344#1929C2×C15111yescharacteristic, complemented
345#1929C2×C15111yescharacteristic, complemented
346#1866C2×C15111yescharacteristic, complemented
347#1866C2×C15111yescharacteristic, complemented
348#1778C2×C15111yescharacteristic, complemented
349#1771C2×C15111yescharacteristic, complemented
350#1765C2×C15111yescharacteristic, complemented
351#1764C2×C15111yescharacteristic, complemented
352C2×#131C22×C15111yescharacteristic
353C2×#131C22×C15111yescharacteristic
354#533C22×C15111yescharacteristic
355#532C22×C15111yescharacteristic
356#491C4×C15111yescharacteristic, complemented
357#491C4×C15111yescharacteristic, complemented
358#490C4×C15111yescharacteristic, complemented
359#490C4×C15111yescharacteristic, complemented
360#489C4×C15111yescharacteristic, complemented
361#489C4×C15111yescharacteristic, complemented
362#489C4×C15111yescharacteristic, complemented
363#489C4×C15111yescharacteristic, complemented
364#446—21no—
365#446—21no—
366#446—21no—
367C8×Q8—21no—
368#436—21no—
369#435—21no—
370#435—21no—
371C8×D4—21no—
372C2×#108C22×C15111yescharacteristic
373C2×#108C22×C15111yescharacteristic
374#424C22×C15111yescharacteristic
375#424C22×C15111yescharacteristic
376C2×C4⋊C8C22×C15111yescharacteristic
377C2×#104C22×C15111yescharacteristic
378C2×#104C22×C15111yescharacteristic
379C2×#104C22×C15111yescharacteristic
380C2×#104C22×C15111yescharacteristic
381#416C22×C15111yescharacteristic
382#416C22×C15111yescharacteristic
383#416C22×C15111yescharacteristic
384#416C22×C15111yescharacteristic
385#408C22×C15111yescharacteristic
386#408C22×C15111yescharacteristic
387#405C22×C15111yescharacteristic
388#405C22×C15111yescharacteristic
389C4×M16C22×C15111yescharacteristic
390C4×M16C22×C15111yescharacteristic
391C2×#97C22×C15111yescharacteristic
392C2×#97C22×C15111yescharacteristic
393C2×C4×C8C22×C15111yescharacteristic
394C4×C4⋊C4C22×C15111yescharacteristic
395#341C22×C15111yescharacteristic
396#341C22×C15111yescharacteristic
397#339C22×C15111yescharacteristic
398#339C22×C15111yescharacteristic
399#339C22×C15111yescharacteristic
400#339C22×C15111yescharacteristic
401#336C22×C15111yescharacteristic
402#336C22×C15111yescharacteristic
403C2×#41C23×C15111yescharacteristic
404C2×#41C23×C15111yescharacteristic
405#131—22no—
406#131—22no—
407#131—41no—
408#131—41no—
409C2×M16—21no—
410C2×M16—21no—
411C2×M16C23×C15111yescharacteristic
412C2×M16C23×C15111yescharacteristic
413C2×M16C23×C15111yescharacteristic
414C2×M16C23×C15111yescharacteristic
415C22×C8—21no—
416C22×C8—21no—
417C22×C8C23×C15111yescharacteristic
418C22×C8C23×C15111yescharacteristic
419C22×C8C23×C15111yescharacteristic
420C22×C8C23×C15111yescharacteristic
421C4⋊Q8C2×C4×C15111yescharacteristic
422C4⋊Q8C2×C4×C15111yescharacteristic
423C4⋊Q8C2×C4×C15111yescharacteristic
424#127C2×C4×C15111yescharacteristic
425#125C2×C4×C15111yescharacteristic
426#125C2×C4×C15111yescharacteristic
427#124C2×C4×C15111yescharacteristic
428#124C2×C4×C15111yescharacteristic
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431#121—21no—
432#121—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×D4—21no—
436C4×D4—21no—
437#117C23×C15111yescharacteristic
438#117C23×C15111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C42C23×C15111yescharacteristic
441C2×C42C23×C15111yescharacteristic
442C2×C42C23×C15111yescharacteristic
443#108—22no—
444#108—22no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8D4×C15111yescharacteristic
450C4⋊C8D4×C15111yescharacteristic
451C4⋊C8D4×C15111yescharacteristic
452C4⋊C8D4×C15111yescharacteristic
453#104—22no—
454#104—22no—
455#104—41no—
456#104—41no—
457#103C2×C4×C15111yescharacteristic
458#103C2×C4×C15111yescharacteristic
459#103C2×C4×C15111yescharacteristic
460#103C2×C4×C15111yescharacteristic
461#103C2×C4×C15111yescharacteristic
462#103C2×C4×C15111yescharacteristic
463#103C2×C4×C15111yescharacteristic
464#103C2×C4×C15111yescharacteristic
465#102C2×C4×C15111yescharacteristic
466#102C2×C4×C15111yescharacteristic
467#102C2×C4×C15111yescharacteristic
468#102C2×C4×C15111yescharacteristic
469#102C2×C4×C15111yescharacteristic
470#102C2×C4×C15111yescharacteristic
471#102C2×C4×C15111yescharacteristic
472#102C2×C4×C15111yescharacteristic
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477#97—21no—
478#97—21no—
479#97—21no—
480#97—21no—
481#97—41no—
482#97C2×C4×C15111yescharacteristic
483#97C2×C4×C15111yescharacteristic
484#97C2×C4×C15111yescharacteristic
485#97C2×C4×C15111yescharacteristic
486C4×C8—21no—
487C4×C8—21no—
488C4×C8—21no—
489C4×C8—21no—
490C4×C8—41no—
491#95—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C22×C4×C15111yescharacteristic
503C2×Q8C22×C4×C15111yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C15111yescharacteristic
509C2×D4C22×C4×C15111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4#41×C15111yescharacteristic
515C22×C4#41×C15111yescharacteristic
516C22×C4C24×C15111yescharacteristic
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—42no—
524M16—42no—
525M16#41×C15112yes—
526M16#41×C15112yes—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8C22×C4×C15111yescharacteristic
542C2×C8C22×C4×C15111yescharacteristic
543C2×C8C22×C4×C15111yescharacteristic
544C2×C8C22×C4×C15111yescharacteristic
545C2×C8C2×D4×C15111yescharacteristic
546C2×C8C2×D4×C15111yescharacteristic
547C2×C8C2×D4×C15111yescharacteristic
548C2×C8C2×D4×C15111yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4C22×C4×C15111yescharacteristic
559C4⋊C4C22×C4×C15111yescharacteristic
560C4⋊C4C22×C4×C15111yescharacteristic
561C4⋊C4C22×C4×C15111yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42C22×C4×C15111yescharacteristic
575C42C22×C4×C15111yescharacteristic
576C42C2×D4×C15111yescharacteristic
577C42C2×D4×C15111yescharacteristic
578C23—21no—
579C23—21no—
580C23C2×#41×C15111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—21no—
585Q8—42no—
586Q8—81no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—21no—
591D4—42no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—81no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4C4×D4×C15111yescharacteristic
616C2×C4C4×D4×C15111yescharacteristic
617C2×C4C4×D4×C15111yescharacteristic
618C2×C4C4×D4×C15111yescharacteristic
619C2×C4C23×C4×C15111yescharacteristic
620C2×C4C22×D4×C15111yescharacteristic
621C2×C4C2×#41×C15111yescharacteristic
622C2×C4C2×#41×C15111yescharacteristic
623C2×C4H(5,𝔽2)×C15111yescharacteristic
624C2×C42−1+4×C15111yescharacteristic
625C8—21no—
626C8—21no—
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×C4×D4×C15111yescharacteristic
646C22#556×C15111yescharacteristic
647C22#559×C15111yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4C4×#41×C15111yescharacteristic
661C4#520×C15111yescharacteristic
662C4#546×C15111yescharacteristic
663C4#548×C15111yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2#2367×C15111yescharacteristic
669C2#2955×C15111yescharacteristic
670C2#2956×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radical#532×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C4⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2962×C151C2semidirect
4. #1986×C151C2semidirect
6. #1938×C151C2semidirect
7. #1937×C151C2semidirect
8. #1929×C151C2semidirect
9. #1929×C151C2semidirect
10. #1866×C151C2semidirect
11. #1866×C151C2semidirect
12. #1778×C151C2semidirect
13. #1771×C151C2semidirect
14. #1765×C151C2semidirect
15. #1764×C151C2semidirect
20. #491×C151C4semidirect
21. #491×C151C4semidirect
22. #490×C151C4semidirect
23. #490×C151C4semidirect
24. #489×C151C4semidirect
25. #489×C151C4semidirect
26. #489×C151C4semidirect
27. #489×C151C4semidirect
335. #23236C151direct (N × H)
336. C151#23236direct (N × H)
338. #2962C2×C151semidirect
340. #1986C2×C151semidirect
342. #1938C2×C151semidirect
343. #1937C2×C151semidirect
344. #1929C2×C151semidirect
345. #1929C2×C151semidirect
346. #1866C2×C151semidirect
347. #1866C2×C151semidirect
348. #1778C2×C151semidirect
349. #1771C2×C151semidirect
350. #1765C2×C151semidirect
351. #1764C2×C151semidirect
356. #491C4×C151semidirect
357. #491C4×C151semidirect
358. #490C4×C151semidirect
359. #490C4×C151semidirect
360. #489C4×C151semidirect
361. #489C4×C151semidirect
362. #489C4×C151semidirect
363. #489C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3135×C1512
#2962×C1512
#2935×C1512
#1986×C1512
#1980×C1512
#1938×C1512
#1937×C1512
#1929×C1512
#1866×C1512
#1778×C1512
#1771×C1512
#1765×C1512
#1764×C1512
#23236151