Finite Group Databasebeta

← C151×#24569 #50329494

Subgroups — C151×#24569 #50329494

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2C2×#408×C151C211yesmaximal, characteristic
3#2616×C151C211yesmaximal, characteristic
4#2311×C151C211yesmaximal, characteristic
5#2077×C151C211yesmaximal, characteristic, complemented
6#2076×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1892×C151C211yesmaximal, characteristic, complemented
11#1872×C151C211yesmaximal, characteristic, complemented
12#1853×C151C211yesmaximal, characteristic, complemented
13#1825×C151C211yesmaximal, characteristic, complemented
14#1809×C151C211yesmaximal, characteristic, complemented
15#1807×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24#485×C151—24no—
25C2×#107×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33#408×C151—24no—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38#395×C151—21no—
39#394×C151—21no—
40#394×C151—21no—
41#394×C151—21no—
42#391×C151—21no—
43#390×C151—21no—
44#386×C151—21no—
45#386×C151—21no—
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#380×C151C2211yescharacteristic
49#380×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151D411yescharacteristic
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151D411yescharacteristic
70C22×D4×C151D411yescharacteristic
71C22×D4×C151D411yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C22×C8×C151—22no—
80C22×C8×C151—22no—
81C22×C8×C151—41no—
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—41no—
91C22⋊Q8×C151—41no—
92#117×C151—22no—
93#117×C151—22no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—41no—
99C2×C4⋊C4×C151—41no—
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C42×C151—21no—
119#107×C151—22no—
120#106×C151—22no—
121#106×C151—41no—
122#106×C151—41no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—41no—
126#103×C151—41no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151D414yes—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151C2×D411yescharacteristic
139C24×C151C2×D411yescharacteristic
140C24×C151C2×D411yescharacteristic
141#41×C151—44no—
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145C2×Q8×C151—22no—
146C2×Q8×C151—22no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—41no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—22no—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—41no—
161C2×D4×C151—41no—
162C2×D4×C151—41no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—42no—
186C22×C4×C151—81no—
187C22×C4×C151—81no—
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D412yes—
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151#4112yes—
193C22×C4×C151#4112yes—
194C22×C4×C151#4112yes—
195C22×C4×C151C2411yescharacteristic
196M16×C151—44no—
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—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—44no—
208C2×C8×C151C2×D412yes—
209C2×C8×C151C2×D412yes—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
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—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—42no—
225C4⋊C4×C151—42no—
226C4⋊C4×C151—42no—
227C4⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—81no—
233C22⋊C4×C151—81no—
234C22⋊C4×C151—81no—
235C22⋊C4×C151—81no—
236C22⋊C4×C151—81no—
237C22⋊C4×C151—81no—
238C22⋊C4×C151—81no—
239C42×C151—42no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151#12112yes—
260C23×C151#12312yes—
261C23×C151C22×D411yescharacteristic
262Q8×C151—44no—
263Q8×C151—41no—
264Q8×C151—41no—
265Q8×C151—41no—
266Q8×C151—41no—
267D4×C151—44no—
268D4×C151—44no—
269D4×C151—44no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—22no—
275C2×C4×C151—22no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—22no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—84no—
314C2×C4×C151#12112yes—
315C2×C4×C151#12312yes—
316C2×C4×C151C22×D411yescharacteristic
317C2×C4×C151C2×#4111yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C2×C4×C151C2×#4111yescharacteristic
320C2×C4×C151H(5,𝔽2)11yescharacteristic
321C2×C4×C151H(5,𝔽2)11yescharacteristic
322C8×C151—22no—
323C8×C151—22no—
324C8×C151—41no—
325C8×C151—41no—
326C22×C151—22no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—22no—
331C22×C151—22no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151C2×#12111yescharacteristic
348C22×C151C2×#12311yescharacteristic
349C22×C151#53411yescharacteristic
350C22×C151#57711yescharacteristic
351C22×C151#57711yescharacteristic
352C22×C151#57711yescharacteristic
353C22×C151#57811yescharacteristic
354C4×C151—22no—
355C4×C151—22no—
356C4×C151—41no—
357C4×C151—81no—
358C4×C151—81no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151—81no—
364C4×C151—81no—
365C4×C151#54611yescharacteristic
366C4×C151#54611yescharacteristic
367C4×C151#55111yescharacteristic
368C4×C151#55111yescharacteristic
369C2×C151—42no—
370C2×C151—42no—
371C2×C151—81no—
372C2×C151#241211yescharacteristic
373C2×C151#306011yescharacteristic
374C2×C151#306311yescharacteristic
375C2×C151#309711yescharacteristic
376C2×C151#309911yescharacteristic
377C2×C151#320011yescharacteristic
378C2×C151#320111yescharacteristic
379#24569C15111yesmaximal, characteristic, direct product factor, Sylow
380C151#2456911yescharacteristic, direct product factor, Sylow
381C2×#485C2×C15111yescharacteristic, complemented
382C2×#408C2×C15111yescharacteristic
383#2616C2×C15111yescharacteristic
384#2311C2×C15111yescharacteristic
385#2077C2×C15111yescharacteristic, complemented
386#2076C2×C15111yescharacteristic, complemented
387#2035C2×C15111yescharacteristic, complemented
388#2035C2×C15111yescharacteristic, complemented
389#1894C2×C15111yescharacteristic, complemented
390#1892C2×C15111yescharacteristic, complemented
391#1872C2×C15111yescharacteristic, complemented
392#1853C2×C15111yescharacteristic, complemented
393#1825C2×C15111yescharacteristic, complemented
394#1809C2×C15111yescharacteristic, complemented
395#1807C2×C15111yescharacteristic, complemented
396C22×#41C22×C15111yescharacteristic
397C22×M16C22×C15111yescharacteristic
398C23×C8C22×C15111yescharacteristic
399C2×C22⋊Q8C22×C15111yescharacteristic
400C2×C22⋊Q8C22×C15111yescharacteristic
401C2×C22⋊Q8C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403C22×C4⋊C4C22×C15111yescharacteristic
404#485—24no—
405C2×#107C22×C15111yescharacteristic
406C2×#106C22×C15111yescharacteristic
407C2×#106C22×C15111yescharacteristic
408C2×#106C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413#408—24no—
414C2×C22⋊C8C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418#395—21no—
419#394—21no—
420#394—21no—
421#394—21no—
422#391—21no—
423#390—21no—
424#386—21no—
425#386—21no—
426#380C22×C15111yescharacteristic
427#380C22×C15111yescharacteristic
428#380C22×C15111yescharacteristic
429#380C22×C15111yescharacteristic
430#380C22×C15111yescharacteristic
431#380C22×C15111yescharacteristic
432#380C22×C15111yescharacteristic
433#340C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#340C22×C15111yescharacteristic
436#340C22×C15111yescharacteristic
437#340C22×C15111yescharacteristic
438#340C22×C15111yescharacteristic
439#340C22×C15111yescharacteristic
440#340C22×C15111yescharacteristic
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8D4×C15111yescharacteristic
448C22×Q8C23×C15111yescharacteristic
449C22×D4D4×C15111yescharacteristic
450C22×D4D4×C15111yescharacteristic
451C22×D4D4×C15111yescharacteristic
452C23×C4—21no—
453C23×C4C23×C15111yescharacteristic
454C23×C4C23×C15111yescharacteristic
455C23×C4C23×C15111yescharacteristic
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—41no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—41no—
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—41no—
471C22⋊Q8—41no—
472#117—22no—
473#117—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C4⋊C4C23×C15111yescharacteristic
482C2×C4⋊C4C23×C15111yescharacteristic
483C2×C4⋊C4C23×C15111yescharacteristic
484C2×C4⋊C4C23×C15111yescharacteristic
485C2×C4⋊C4C23×C15111yescharacteristic
486C2×C4⋊C4C23×C15111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C42—21no—
499#107—22no—
500#106—22no—
501#106—41no—
502#106—41no—
503#103—22no—
504#103—22no—
505#103—41no—
506#103—41no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8D4×C15114yes—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518C24C2×D4×C15111yescharacteristic
519C24C2×D4×C15111yescharacteristic
520C24C2×D4×C15111yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—41no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15112yes—
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4#41×C15112yes—
573C22×C4#41×C15112yes—
574C22×C4#41×C15112yes—
575C22×C4C24×C15111yescharacteristic
576M16—44no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8C2×D4×C15112yes—
589C2×C8C2×D4×C15112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C22⋊C4—81no—
619C42—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23#121×C15112yes—
640C23#123×C15112yes—
641C23C22×D4×C15111yescharacteristic
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647D4—44no—
648D4—44no—
649D4—44no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4#121×C15112yes—
695C2×C4#123×C15112yes—
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4C2×#41×C15111yescharacteristic
699C2×C4C2×#41×C15111yescharacteristic
700C2×C4H(5,𝔽2)×C15111yescharacteristic
701C2×C4H(5,𝔽2)×C15111yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×#121×C15111yescharacteristic
728C22C2×#123×C15111yescharacteristic
729C22#534×C15111yescharacteristic
730C22#577×C15111yescharacteristic
731C22#577×C15111yescharacteristic
732C22#577×C15111yescharacteristic
733C22#578×C15111yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4#546×C15111yescharacteristic
746C4#546×C15111yescharacteristic
747C4#551×C15111yescharacteristic
748C4#551×C15111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2#2412×C15111yescharacteristic
753C2#3060×C15111yescharacteristic
754C2#3063×C15111yescharacteristic
755C2#3097×C15111yescharacteristic
756C2#3099×C15111yescharacteristic
757C2#3200×C15111yescharacteristic
758C2#3201×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C151C2semidirect
5. #2077×C151C2semidirect
6. #2076×C151C2semidirect
7. #2035×C151C2semidirect
8. #2035×C151C2semidirect
9. #1894×C151C2semidirect
10. #1892×C151C2semidirect
11. #1872×C151C2semidirect
12. #1853×C151C2semidirect
13. #1825×C151C2semidirect
14. #1809×C151C2semidirect
15. #1807×C151C2semidirect
379. #24569C151direct (N × H)
380. C151#24569direct (N × H)
381. C2×#485C2×C151semidirect
385. #2077C2×C151semidirect
386. #2076C2×C151semidirect
387. #2035C2×C151semidirect
388. #2035C2×C151semidirect
389. #1894C2×C151semidirect
390. #1892C2×C151semidirect
391. #1872C2×C151semidirect
392. #1853C2×C151semidirect
393. #1825C2×C151semidirect
394. #1809C2×C151semidirect
395. #1807C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#408×C1512
#2616×C1512
#2311×C1512
#2077×C1512
#2076×C1512
#2035×C1512
#1894×C1512
#1892×C1512
#1872×C1512
#1853×C1512
#1825×C1512
#1809×C1512
#1807×C1512
#24569151