Finite Group Databasebeta

← C151×#15273 #50320198

Subgroups — C151×#15273 #50320198

Order 38656.

2946 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic, complemented
2C2×#392×C151C211yesmaximal, characteristic, complemented
3C2×#392×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C211yesmaximal, characteristic, complemented
5C2×#386×C151C211yesmaximal, characteristic, complemented
6C2×#386×C151C211yesmaximal, characteristic, complemented
7C2×#386×C151C211yesmaximal, characteristic, complemented
8C2×#386×C151C211yesmaximal, characteristic, complemented
9#1442×C151C211yesmaximal, characteristic, complemented
10#1440×C151C211yesmaximal, characteristic, complemented
11#1440×C151C211yesmaximal, characteristic, complemented
12#1439×C151C211yesmaximal, characteristic, complemented
13#1438×C151C211yesmaximal, characteristic, complemented
14#1438×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C23×D4×C151C2211yescharacteristic
20C23×D4×C151C2211yescharacteristic
21C23×D4×C151C2211yescharacteristic
22C24×C4×C151C2211yescharacteristic
23C24×C4×C151C2211yescharacteristic
24C2×#121×C151—24no—
25C2×#121×C151—24no—
26C2×#121×C151—24no—
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2211yescharacteristic
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic
37C22×C22⋊C4×C151C2211yescharacteristic
38C22×C22⋊C4×C151C2211yescharacteristic
39C22×C22⋊C4×C151C2211yescharacteristic
40C22×C22⋊C4×C151C2211yescharacteristic
41C22×C22⋊C4×C151C2211yescharacteristic
42#392×C151—24no—
43#392×C151—24no—
44#392×C151—24no—
45#386×C151—24no—
46#386×C151—24no—
47#386×C151—24no—
48#386×C151—24no—
49C2×#95×C151C2211yescharacteristic
50C2×#95×C151C2211yescharacteristic
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C2×#95×C151C2211yescharacteristic
58C2×#95×C151C2211yescharacteristic
59C2×#95×C151C2211yescharacteristic
60C2×#95×C151C2211yescharacteristic
61C25×C151C2311yescharacteristic
62C25×C151C2311yescharacteristic
63C25×C151C2311yescharacteristic
64C25×C151C2311yescharacteristic
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—22no—
74C22×D4×C151—22no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—22no—
79C22×D4×C151—22no—
80C22×D4×C151—22no—
81C22×D4×C151—22no—
82C22×D4×C151—22no—
83C22×D4×C151—22no—
84C22×D4×C151—22no—
85C22×D4×C151—22no—
86C22×D4×C151—22no—
87C22×D4×C151—22no—
88C22×D4×C151—22no—
89C22×D4×C151—22no—
90C22×D4×C151—22no—
91C22×D4×C151—41no—
92C22×D4×C151—41no—
93C22×D4×C151—41no—
94C22×D4×C151—41no—
95C22×D4×C151—41no—
96C22×D4×C151—41no—
97C22×D4×C151—41no—
98C22×D4×C151—41no—
99C22×D4×C151—41no—
100C22×D4×C151—41no—
101C22×D4×C151—41no—
102C22×D4×C151—41no—
103C22×D4×C151—41no—
104C22×D4×C151—41no—
105C22×D4×C151D414yescomplemented
106C22×D4×C151D414yescomplemented
107C23×C4×C151—22no—
108C23×C4×C151—22no—
109C23×C4×C151—22no—
110C23×C4×C151—22no—
111C23×C4×C151—22no—
112C23×C4×C151—22no—
113C23×C4×C151—22no—
114C23×C4×C151—22no—
115C23×C4×C151—41no—
116C23×C4×C151—41no—
117C23×C4×C151—41no—
118C23×C4×C151—41no—
119C23×C4×C151—41no—
120C23×C4×C151—41no—
121C23×C4×C151C2311yescharacteristic
122C23×C4×C151C2311yescharacteristic
123C23×C4×C151C2311yescharacteristic
124C23×C4×C151C2311yescharacteristic
125C23×C4×C151C2311yescharacteristic
126C23×C4×C151C2311yescharacteristic
127C23×C4×C151C2311yescharacteristic
128C23×C4×C151C2311yescharacteristic
129C23×C4×C151C2311yescharacteristic
130C23×C4×C151C2311yescharacteristic
131C23×C4×C151C2311yescharacteristic
132#121×C151—232no—
133C2×C4⋊C4×C151—22no—
134C2×C4⋊C4×C151—22no—
135C2×C4⋊C4×C151—22no—
136C2×C22⋊C4×C151—22no—
137C2×C22⋊C4×C151—22no—
138C2×C22⋊C4×C151—22no—
139C2×C22⋊C4×C151—22no—
140C2×C22⋊C4×C151—22no—
141C2×C22⋊C4×C151—22no—
142C2×C22⋊C4×C151—22no—
143C2×C22⋊C4×C151—22no—
144C2×C22⋊C4×C151—22no—
145C2×C22⋊C4×C151—22no—
146C2×C22⋊C4×C151—22no—
147C2×C22⋊C4×C151—22no—
148C2×C22⋊C4×C151—22no—
149C2×C22⋊C4×C151—22no—
150C2×C22⋊C4×C151—22no—
151C2×C22⋊C4×C151—22no—
152C2×C22⋊C4×C151—22no—
153C2×C22⋊C4×C151—22no—
154C2×C22⋊C4×C151—22no—
155C2×C22⋊C4×C151—22no—
156C2×C22⋊C4×C151—22no—
157C2×C22⋊C4×C151—22no—
158C2×C22⋊C4×C151—22no—
159C2×C22⋊C4×C151—22no—
160C2×C22⋊C4×C151—22no—
161C2×C22⋊C4×C151—22no—
162C2×C22⋊C4×C151—41no—
163C2×C22⋊C4×C151—41no—
164C2×C22⋊C4×C151—41no—
165C2×C22⋊C4×C151—41no—
166C2×C22⋊C4×C151—41no—
167C2×C22⋊C4×C151—41no—
168C2×C22⋊C4×C151—41no—
169C2×C22⋊C4×C151—41no—
170C2×C22⋊C4×C151—41no—
171C2×C22⋊C4×C151—41no—
172C2×C22⋊C4×C151—41no—
173C2×C22⋊C4×C151—41no—
174C2×C22⋊C4×C151—41no—
175C2×C22⋊C4×C151—41no—
176C2×C22⋊C4×C151D414yescomplemented
177C2×C22⋊C4×C151D414yescomplemented
178#95×C151—22no—
179#95×C151—22no—
180#95×C151—22no—
181#95×C151—22no—
182#95×C151—22no—
183#95×C151—22no—
184#95×C151—22no—
185#95×C151—22no—
186#95×C151—22no—
187#95×C151—41no—
188#95×C151—41no—
189#95×C151D414yescomplemented
190C24×C151—21no—
191C24×C151—21no—
192C24×C151—21no—
193C24×C151—21no—
194C24×C151—21no—
195C24×C151—21no—
196C24×C151—21no—
197C24×C151—21no—
198C24×C151—21no—
199C24×C151—21no—
200C24×C151—21no—
201C24×C151—21no—
202C24×C151—21no—
203C24×C151—21no—
204C24×C151—21no—
205C24×C151—21no—
206C24×C151—21no—
207C24×C151—21no—
208C24×C151—21no—
209C24×C151—21no—
210C24×C151—21no—
211C24×C151—21no—
212C24×C151—21no—
213C24×C151—21no—
214C24×C151—21no—
215C24×C151—21no—
216C24×C151—21no—
217C24×C151—21no—
218C24×C151—21no—
219C24×C151—21no—
220C24×C151—21no—
221C24×C151—21no—
222C24×C151—21no—
223C24×C151—21no—
224C24×C151—21no—
225C24×C151—21no—
226C24×C151—21no—
227C24×C151—21no—
228C24×C151—21no—
229C24×C151—21no—
230C24×C151—21no—
231C24×C151—21no—
232C24×C151—21no—
233C24×C151—21no—
234C24×C151—21no—
235C24×C151—21no—
236C24×C151—21no—
237C24×C151—21no—
238C24×C151—21no—
239C24×C151—21no—
240C24×C151—21no—
241C24×C151—21no—
242C24×C151C2×D412yes—
243C24×C151C2×D412yes—
244C24×C151C2×D412yes—
245C24×C151C2×D412yes—
246C24×C151C2×D412yes—
247C24×C151C2×D412yes—
248C24×C151#4112yes—
249C24×C151#4112yes—
250C24×C151C2411yescharacteristic
251C2×D4×C151—28no—
252C2×D4×C151—28no—
253C2×D4×C151—28no—
254C2×D4×C151—28no—
255C2×D4×C151—28no—
256C2×D4×C151—28no—
257C2×D4×C151—28no—
258C2×D4×C151—44no—
259C2×D4×C151—44no—
260C2×D4×C151—44no—
261C2×D4×C151—44no—
262C2×D4×C151—44no—
263C2×D4×C151—44no—
264C2×D4×C151—44no—
265C2×D4×C151—44no—
266C2×D4×C151—44no—
267C2×D4×C151—44no—
268C2×D4×C151—44no—
269C2×D4×C151—44no—
270C2×D4×C151—44no—
271C2×D4×C151—44no—
272C2×D4×C151—44no—
273C2×D4×C151—44no—
274C2×D4×C151—44no—
275C2×D4×C151—44no—
276C2×D4×C151—44no—
277C2×D4×C151—44no—
278C2×D4×C151—44no—
279C2×D4×C151—44no—
280C2×D4×C151—44no—
281C2×D4×C151—44no—
282C2×D4×C151—44no—
283C2×D4×C151—44no—
284C2×D4×C151—44no—
285C2×D4×C151—44no—
286C2×D4×C151—44no—
287C2×D4×C151—44no—
288C2×D4×C151—44no—
289C2×D4×C151—44no—
290C2×D4×C151—44no—
291C2×D4×C151—44no—
292C2×D4×C151—44no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—28no—
298C22×C4×C151—21no—
299C22×C4×C151—21no—
300C22×C4×C151—21no—
301C22×C4×C151—21no—
302C22×C4×C151—21no—
303C22×C4×C151—21no—
304C22×C4×C151—21no—
305C22×C4×C151—21no—
306C22×C4×C151—21no—
307C22×C4×C151—21no—
308C22×C4×C151—21no—
309C22×C4×C151—21no—
310C22×C4×C151—21no—
311C22×C4×C151—21no—
312C22×C4×C151—21no—
313C22×C4×C151—21no—
314C22×C4×C151—21no—
315C22×C4×C151—21no—
316C22×C4×C151—21no—
317C22×C4×C151—21no—
318C22×C4×C151—21no—
319C22×C4×C151—21no—
320C22×C4×C151—21no—
321C22×C4×C151—21no—
322C22×C4×C151—21no—
323C22×C4×C151—21no—
324C22×C4×C151—21no—
325C22×C4×C151—21no—
326C22×C4×C151—21no—
327C22×C4×C151—21no—
328C22×C4×C151—21no—
329C22×C4×C151—21no—
330C22×C4×C151—21no—
331C22×C4×C151—21no—
332C22×C4×C151—21no—
333C22×C4×C151—21no—
334C22×C4×C151—21no—
335C22×C4×C151—21no—
336C22×C4×C151—21no—
337C22×C4×C151—21no—
338C22×C4×C151—21no—
339C22×C4×C151—21no—
340C22×C4×C151—21no—
341C22×C4×C151—21no—
342C22×C4×C151—21no—
343C22×C4×C151—21no—
344C22×C4×C151—21no—
345C22×C4×C151—21no—
346C22×C4×C151—21no—
347C22×C4×C151—21no—
348C22×C4×C151—21no—
349C22×C4×C151—21no—
350C22×C4×C151—21no—
351C22×C4×C151—21no—
352C22×C4×C151—21no—
353C22×C4×C151—21no—
354C22×C4×C151—21no—
355C22×C4×C151—21no—
356C22×C4×C151—21no—
357C22×C4×C151—21no—
358C22×C4×C151—21no—
359C22×C4×C151—21no—
360C22×C4×C151—44no—
361C22×C4×C151—44no—
362C22×C4×C151—44no—
363C22×C4×C151—44no—
364C22×C4×C151—44no—
365C22×C4×C151—44no—
366C22×C4×C151—44no—
367C22×C4×C151—44no—
368C22×C4×C151—44no—
369C22×C4×C151—44no—
370C22×C4×C151—44no—
371C22×C4×C151—44no—
372C22×C4×C151—44no—
373C22×C4×C151C2×D412yes—
374C22×C4×C151C2×D412yes—
375C22×C4×C151C2×D412yes—
376C22×C4×C151C2×D412yes—
377C22×C4×C151C2×D412yes—
378C22×C4×C151C2×D412yes—
379C22×C4×C151C2×D412yes—
380C22×C4×C151C2×D412yes—
381C22×C4×C151C2×D412yes—
382C22×C4×C151#4112yes—
383C22×C4×C151#4112yes—
384C4⋊C4×C151—28no—
385C22⋊C4×C151—28no—
386C22⋊C4×C151—28no—
387C22⋊C4×C151—44no—
388C22⋊C4×C151—44no—
389C22⋊C4×C151—44no—
390C22⋊C4×C151—44no—
391C22⋊C4×C151—44no—
392C22⋊C4×C151—44no—
393C22⋊C4×C151—44no—
394C22⋊C4×C151—44no—
395C22⋊C4×C151—44no—
396C22⋊C4×C151—44no—
397C22⋊C4×C151—44no—
398C22⋊C4×C151—44no—
399C23×C151—22no—
400C23×C151—22no—
401C23×C151—22no—
402C23×C151—22no—
403C23×C151—22no—
404C23×C151—22no—
405C23×C151—22no—
406C23×C151—22no—
407C23×C151—22no—
408C23×C151—22no—
409C23×C151—22no—
410C23×C151—22no—
411C23×C151—22no—
412C23×C151—22no—
413C23×C151—22no—
414C23×C151—22no—
415C23×C151—22no—
416C23×C151—22no—
417C23×C151—22no—
418C23×C151—22no—
419C23×C151—22no—
420C23×C151—22no—
421C23×C151—22no—
422C23×C151—22no—
423C23×C151—22no—
424C23×C151—22no—
425C23×C151—22no—
426C23×C151—22no—
427C23×C151—22no—
428C23×C151—22no—
429C23×C151—22no—
430C23×C151—22no—
431C23×C151—22no—
432C23×C151—22no—
433C23×C151—22no—
434C23×C151—22no—
435C23×C151—22no—
436C23×C151—22no—
437C23×C151—22no—
438C23×C151—22no—
439C23×C151—22no—
440C23×C151—22no—
441C23×C151—22no—
442C23×C151—22no—
443C23×C151—22no—
444C23×C151—22no—
445C23×C151—22no—
446C23×C151—22no—
447C23×C151—22no—
448C23×C151—22no—
449C23×C151—41no—
450C23×C151—41no—
451C23×C151—41no—
452C23×C151—41no—
453C23×C151—41no—
454C23×C151—41no—
455C23×C151—41no—
456C23×C151—41no—
457C23×C151—41no—
458C23×C151—41no—
459C23×C151—41no—
460C23×C151—41no—
461C23×C151—41no—
462C23×C151—41no—
463C23×C151—41no—
464C23×C151—41no—
465C23×C151—41no—
466C23×C151—41no—
467C23×C151—41no—
468C23×C151—41no—
469C23×C151—41no—
470C23×C151—41no—
471C23×C151—41no—
472C23×C151—41no—
473C23×C151—41no—
474C23×C151—41no—
475C23×C151—41no—
476C23×C151—41no—
477C23×C151—41no—
478C23×C151—41no—
479C23×C151—41no—
480C23×C151—41no—
481C23×C151—41no—
482C23×C151—41no—
483C23×C151—41no—
484C23×C151—41no—
485C23×C151—41no—
486C23×C151—41no—
487C23×C151—41no—
488C23×C151—41no—
489C23×C151—41no—
490C23×C151—41no—
491C23×C151—41no—
492C23×C151—41no—
493C23×C151—41no—
494C23×C151—41no—
495C23×C151—41no—
496C23×C151—41no—
497C23×C151—41no—
498C23×C151—41no—
499C23×C151—41no—
500C23×C151—41no—
501C23×C151—41no—
502C23×C151—41no—
503C23×C151—41no—
504C23×C151—41no—
505C23×C151—41no—
506C23×C151—41no—
507C23×C151—41no—
508C23×C151—41no—
509C23×C151—41no—
510C23×C151—41no—
511C23×C151—41no—
512C23×C151—41no—
513C23×C151—41no—
514C23×C151—41no—
515C23×C151—41no—
516C23×C151—41no—
517C23×C151—41no—
518C23×C151—41no—
519C23×C151—41no—
520C23×C151—41no—
521C23×C151—41no—
522C23×C151—41no—
523C23×C151—41no—
524C23×C151—41no—
525C23×C151—41no—
526C23×C151—41no—
527C23×C151—41no—
528C23×C151—41no—
529C23×C151—41no—
530C23×C151—41no—
531C23×C151—41no—
532C23×C151—41no—
533C23×C151—41no—
534C23×C151—41no—
535C23×C151—41no—
536C23×C151—41no—
537C23×C151#12014yes—
538C23×C151#12114yes—
539C23×C151C22×D411yescharacteristic
540C23×C151C22×D411yescharacteristic
541C23×C151C22×D411yescharacteristic
542C23×C151C22×D411yescharacteristic
543C23×C151C22×D411yescharacteristic
544C23×C151C2×#4111yescharacteristic
545C23×C151C2×#4111yescharacteristic
546C23×C151C2×#4111yescharacteristic
547C23×C151C2×#4111yescharacteristic
548C23×C151H(5,𝔽2)11yescharacteristic
549C23×C151H(5,𝔽2)11yescharacteristic
550C23×C151H(5,𝔽2)11yescharacteristic
551C23×C151H(5,𝔽2)11yescharacteristic
552C23×C151H(5,𝔽2)11yescharacteristic
553C23×C151H(5,𝔽2)11yescharacteristic
554D4×C151—416no—
555D4×C151—416no—
556D4×C151—416no—
557D4×C151—416no—
558D4×C151—416no—
559D4×C151—416no—
560C2×C4×C151—22no—
561C2×C4×C151—22no—
562C2×C4×C151—22no—
563C2×C4×C151—22no—
564C2×C4×C151—22no—
565C2×C4×C151—22no—
566C2×C4×C151—22no—
567C2×C4×C151—22no—
568C2×C4×C151—22no—
569C2×C4×C151—22no—
570C2×C4×C151—22no—
571C2×C4×C151—22no—
572C2×C4×C151—22no—
573C2×C4×C151—22no—
574C2×C4×C151—22no—
575C2×C4×C151—22no—
576C2×C4×C151—22no—
577C2×C4×C151—22no—
578C2×C4×C151—22no—
579C2×C4×C151—22no—
580C2×C4×C151—22no—
581C2×C4×C151—22no—
582C2×C4×C151—22no—
583C2×C4×C151—22no—
584C2×C4×C151—22no—
585C2×C4×C151—22no—
586C2×C4×C151—22no—
587C2×C4×C151—22no—
588C2×C4×C151—22no—
589C2×C4×C151—22no—
590C2×C4×C151—416no—
591C2×C4×C151—416no—
592C2×C4×C151—41no—
593C2×C4×C151—41no—
594C2×C4×C151—41no—
595C2×C4×C151—41no—
596C2×C4×C151—41no—
597C2×C4×C151—41no—
598C2×C4×C151—41no—
599C2×C4×C151—41no—
600C2×C4×C151—41no—
601C2×C4×C151—41no—
602C2×C4×C151—41no—
603C2×C4×C151—41no—
604C2×C4×C151—41no—
605C2×C4×C151—41no—
606C2×C4×C151—41no—
607C2×C4×C151—41no—
608C2×C4×C151—41no—
609C2×C4×C151—41no—
610C2×C4×C151—41no—
611C2×C4×C151—41no—
612C2×C4×C151—41no—
613C2×C4×C151—41no—
614C2×C4×C151—41no—
615C2×C4×C151—41no—
616C2×C4×C151—41no—
617C2×C4×C151—41no—
618C2×C4×C151—41no—
619C2×C4×C151—41no—
620C2×C4×C151—41no—
621C2×C4×C151—41no—
622C2×C4×C151—41no—
623C2×C4×C151—41no—
624C2×C4×C151—41no—
625C2×C4×C151—41no—
626C2×C4×C151—41no—
627C2×C4×C151—41no—
628C2×C4×C151—41no—
629C2×C4×C151—41no—
630C2×C4×C151—41no—
631C2×C4×C151—41no—
632C2×C4×C151—41no—
633C2×C4×C151—41no—
634C2×C4×C151—41no—
635C2×C4×C151—41no—
636C2×C4×C151—41no—
637C2×C4×C151—41no—
638C2×C4×C151#12114yes—
639C22×C151—24no—
640C22×C151—24no—
641C22×C151—24no—
642C22×C151—24no—
643C22×C151—24no—
644C22×C151—24no—
645C22×C151—42no—
646C22×C151—42no—
647C22×C151—42no—
648C22×C151—42no—
649C22×C151—42no—
650C22×C151—42no—
651C22×C151—42no—
652C22×C151—42no—
653C22×C151—42no—
654C22×C151—42no—
655C22×C151—42no—
656C22×C151—42no—
657C22×C151—42no—
658C22×C151—42no—
659C22×C151—42no—
660C22×C151—42no—
661C22×C151—42no—
662C22×C151—42no—
663C22×C151—42no—
664C22×C151—42no—
665C22×C151—42no—
666C22×C151—42no—
667C22×C151—42no—
668C22×C151—42no—
669C22×C151—42no—
670C22×C151—42no—
671C22×C151—42no—
672C22×C151—42no—
673C22×C151—42no—
674C22×C151—42no—
675C22×C151—42no—
676C22×C151—42no—
677C22×C151—42no—
678C22×C151—42no—
679C22×C151—42no—
680C22×C151—42no—
681C22×C151—42no—
682C22×C151—42no—
683C22×C151—81no—
684C22×C151—81no—
685C22×C151—81no—
686C22×C151—81no—
687C22×C151—81no—
688C22×C151—81no—
689C22×C151—81no—
690C22×C151—81no—
691C22×C151—81no—
692C22×C151—81no—
693C22×C151—81no—
694C22×C151—81no—
695C22×C151—81no—
696C22×C151—81no—
697C22×C151—81no—
698C22×C151—81no—
699C22×C151C2×#12011yescharacteristic
700C22×C151C2×#12111yescharacteristic
701C22×C151C2×#12111yescharacteristic
702C22×C151#52511yescharacteristic
703C22×C151#52511yescharacteristic
704C22×C151#53211yescharacteristic
705C22×C151#53411yescharacteristic
706C22×C151#53411yescharacteristic
707C22×C151#53411yescharacteristic
708C22×C151#53511yescharacteristic
709C22×C151#53511yescharacteristic
710C22×C151#53811yescharacteristic
711C22×C151#53811yescharacteristic
712C22×C151#54011yescharacteristic
713C22×C151#54011yescharacteristic
714C22×C151D4211yescharacteristic
715C22×C151D4211yescharacteristic
716C22×C151D4211yescharacteristic
717C22×C151D4211yescharacteristic
718C22×C151D4211yescharacteristic
719C22×C151#54611yescharacteristic
720C22×C151#54611yescharacteristic
721C22×C151#54611yescharacteristic
722C22×C151#54611yescharacteristic
723C22×C151#54611yescharacteristic
724C22×C151#54611yescharacteristic
725C22×C151#54611yescharacteristic
726C22×C151#54611yescharacteristic
727C22×C151#54611yescharacteristic
728C22×C151#55011yescharacteristic
729C22×C151#55311yescharacteristic
730C22×C151#55311yescharacteristic
731C22×C151#55311yescharacteristic
732C22×C151#56011yescharacteristic
733C22×C151#56011yescharacteristic
734C4×C151—24no—
735C4×C151—42no—
736C4×C151—42no—
737C4×C151—42no—
738C4×C151—42no—
739C4×C151—42no—
740C4×C151—42no—
741C4×C151—42no—
742C4×C151—42no—
743C4×C151—81no—
744C4×C151—81no—
745C2×C151—44no—
746C2×C151—44no—
747C2×C151—82no—
748C2×C151—82no—
749C2×C151#240411yescharacteristic
750C2×C151#241011yescharacteristic
751C2×C151#241011yescharacteristic
752C2×C151#242411yescharacteristic
753C2×C151#242811yescharacteristic
754C2×C151#245611yescharacteristic
755C2×C151#246411yescharacteristic
756C2×C151#253511yescharacteristic
757C2×C151#254311yescharacteristic
758C2×C151#266811yescharacteristic
759C2×C151#266911yescharacteristic
760C2×C151#267311yescharacteristic
761C2×C151#268811yescharacteristic
762C2×C151#268811yescharacteristic
763C2×C151#270311yescharacteristic
764#15273C15111yesmaximal, characteristic, direct product factor, Sylow
765C151#1527311yescharacteristic, direct product factor, Sylow
766C22×#121C2×C15111yescharacteristic, complemented
767C2×#392C2×C15111yescharacteristic, complemented
768C2×#392C2×C15111yescharacteristic, complemented
769C2×#392C2×C15111yescharacteristic, complemented
770C2×#386C2×C15111yescharacteristic, complemented
771C2×#386C2×C15111yescharacteristic, complemented
772C2×#386C2×C15111yescharacteristic, complemented
773C2×#386C2×C15111yescharacteristic, complemented
774#1442C2×C15111yescharacteristic, complemented
775#1440C2×C15111yescharacteristic, complemented
776#1440C2×C15111yescharacteristic, complemented
777#1439C2×C15111yescharacteristic, complemented
778#1438C2×C15111yescharacteristic, complemented
779#1438C2×C15111yescharacteristic, complemented
780C22⋊#95C2×C15111yescharacteristic, complemented
781C23×D4C22×C15111yescharacteristic
782C23×D4C22×C15111yescharacteristic
783C23×D4C22×C15111yescharacteristic
784C23×D4C22×C15111yescharacteristic
785C23×D4C22×C15111yescharacteristic
786C23×D4C22×C15111yescharacteristic
787C24×C4C22×C15111yescharacteristic
788C24×C4C22×C15111yescharacteristic
789C2×#121—24no—
790C2×#121—24no—
791C2×#121—24no—
792C22×C4⋊C4C22×C15111yescharacteristic
793C22×C22⋊C4C22×C15111yescharacteristic
794C22×C22⋊C4C22×C15111yescharacteristic
795C22×C22⋊C4C22×C15111yescharacteristic
796C22×C22⋊C4C22×C15111yescharacteristic
797C22×C22⋊C4C22×C15111yescharacteristic
798C22×C22⋊C4C22×C15111yescharacteristic
799C22×C22⋊C4C22×C15111yescharacteristic
800C22×C22⋊C4C22×C15111yescharacteristic
801C22×C22⋊C4C22×C15111yescharacteristic
802C22×C22⋊C4C22×C15111yescharacteristic
803C22×C22⋊C4C22×C15111yescharacteristic
804C22×C22⋊C4C22×C15111yescharacteristic
805C22×C22⋊C4C22×C15111yescharacteristic
806C22×C22⋊C4C22×C15111yescharacteristic
807#392—24no—
808#392—24no—
809#392—24no—
810#386—24no—
811#386—24no—
812#386—24no—
813#386—24no—
814C2×#95C22×C15111yescharacteristic
815C2×#95C22×C15111yescharacteristic
816C2×#95C22×C15111yescharacteristic
817C2×#95C22×C15111yescharacteristic
818C2×#95C22×C15111yescharacteristic
819C2×#95C22×C15111yescharacteristic
820C2×#95C22×C15111yescharacteristic
821C2×#95C22×C15111yescharacteristic
822C2×#95C22×C15111yescharacteristic
823C2×#95C22×C15111yescharacteristic
824C2×#95C22×C15111yescharacteristic
825C2×#95C22×C15111yescharacteristic
826C25C23×C15111yescharacteristic
827C25C23×C15111yescharacteristic
828C25C23×C15111yescharacteristic
829C25C23×C15111yescharacteristic
830C22×D4—22no—
831C22×D4—22no—
832C22×D4—22no—
833C22×D4—22no—
834C22×D4—22no—
835C22×D4—22no—
836C22×D4—22no—
837C22×D4—22no—
838C22×D4—22no—
839C22×D4—22no—
840C22×D4—22no—
841C22×D4—22no—
842C22×D4—22no—
843C22×D4—22no—
844C22×D4—22no—
845C22×D4—22no—
846C22×D4—22no—
847C22×D4—22no—
848C22×D4—22no—
849C22×D4—22no—
850C22×D4—22no—
851C22×D4—22no—
852C22×D4—22no—
853C22×D4—22no—
854C22×D4—22no—
855C22×D4—22no—
856C22×D4—41no—
857C22×D4—41no—
858C22×D4—41no—
859C22×D4—41no—
860C22×D4—41no—
861C22×D4—41no—
862C22×D4—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4—41no—
866C22×D4—41no—
867C22×D4—41no—
868C22×D4—41no—
869C22×D4—41no—
870C22×D4D4×C15114yescomplemented
871C22×D4D4×C15114yescomplemented
872C23×C4—22no—
873C23×C4—22no—
874C23×C4—22no—
875C23×C4—22no—
876C23×C4—22no—
877C23×C4—22no—
878C23×C4—22no—
879C23×C4—22no—
880C23×C4—41no—
881C23×C4—41no—
882C23×C4—41no—
883C23×C4—41no—
884C23×C4—41no—
885C23×C4—41no—
886C23×C4C23×C15111yescharacteristic
887C23×C4C23×C15111yescharacteristic
888C23×C4C23×C15111yescharacteristic
889C23×C4C23×C15111yescharacteristic
890C23×C4C23×C15111yescharacteristic
891C23×C4C23×C15111yescharacteristic
892C23×C4C23×C15111yescharacteristic
893C23×C4C23×C15111yescharacteristic
894C23×C4C23×C15111yescharacteristic
895C23×C4C23×C15111yescharacteristic
896C23×C4C23×C15111yescharacteristic
897#121—232no—
898C2×C4⋊C4—22no—
899C2×C4⋊C4—22no—
900C2×C4⋊C4—22no—
901C2×C22⋊C4—22no—
902C2×C22⋊C4—22no—
903C2×C22⋊C4—22no—
904C2×C22⋊C4—22no—
905C2×C22⋊C4—22no—
906C2×C22⋊C4—22no—
907C2×C22⋊C4—22no—
908C2×C22⋊C4—22no—
909C2×C22⋊C4—22no—
910C2×C22⋊C4—22no—
911C2×C22⋊C4—22no—
912C2×C22⋊C4—22no—
913C2×C22⋊C4—22no—
914C2×C22⋊C4—22no—
915C2×C22⋊C4—22no—
916C2×C22⋊C4—22no—
917C2×C22⋊C4—22no—
918C2×C22⋊C4—22no—
919C2×C22⋊C4—22no—
920C2×C22⋊C4—22no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—22no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—22no—
926C2×C22⋊C4—22no—
927C2×C22⋊C4—41no—
928C2×C22⋊C4—41no—
929C2×C22⋊C4—41no—
930C2×C22⋊C4—41no—
931C2×C22⋊C4—41no—
932C2×C22⋊C4—41no—
933C2×C22⋊C4—41no—
934C2×C22⋊C4—41no—
935C2×C22⋊C4—41no—
936C2×C22⋊C4—41no—
937C2×C22⋊C4—41no—
938C2×C22⋊C4—41no—
939C2×C22⋊C4—41no—
940C2×C22⋊C4—41no—
941C2×C22⋊C4D4×C15114yescomplemented
942C2×C22⋊C4D4×C15114yescomplemented
943#95—22no—
944#95—22no—
945#95—22no—
946#95—22no—
947#95—22no—
948#95—22no—
949#95—22no—
950#95—22no—
951#95—22no—
952#95—41no—
953#95—41no—
954#95D4×C15114yescomplemented
955C24—21no—
956C24—21no—
957C24—21no—
958C24—21no—
959C24—21no—
960C24—21no—
961C24—21no—
962C24—21no—
963C24—21no—
964C24—21no—
965C24—21no—
966C24—21no—
967C24—21no—
968C24—21no—
969C24—21no—
970C24—21no—
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24—21no—
989C24—21no—
990C24—21no—
991C24—21no—
992C24—21no—
993C24—21no—
994C24—21no—
995C24—21no—
996C24—21no—
997C24—21no—
998C24—21no—
999C24—21no—
1000C24—21no—
1001C24—21no—
1002C24—21no—
1003C24—21no—
1004C24—21no—
1005C24—21no—
1006C24—21no—
1007C24C2×D4×C15112yes—
1008C24C2×D4×C15112yes—
1009C24C2×D4×C15112yes—
1010C24C2×D4×C15112yes—
1011C24C2×D4×C15112yes—
1012C24C2×D4×C15112yes—
1013C24#41×C15112yes—
1014C24#41×C15112yes—
1015C24C24×C15111yescharacteristic
1016C2×D4—28no—
1017C2×D4—28no—
1018C2×D4—28no—
1019C2×D4—28no—
1020C2×D4—28no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—28no—
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—21no—
1083C22×C4—21no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4C2×D4×C15112yes—
1139C22×C4C2×D4×C15112yes—
1140C22×C4C2×D4×C15112yes—
1141C22×C4C2×D4×C15112yes—
1142C22×C4C2×D4×C15112yes—
1143C22×C4C2×D4×C15112yes—
1144C22×C4C2×D4×C15112yes—
1145C22×C4C2×D4×C15112yes—
1146C22×C4C2×D4×C15112yes—
1147C22×C4#41×C15112yes—
1148C22×C4#41×C15112yes—
1149C4⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—41no—
1281C23—41no—
1282C23—41no—
1283C23—41no—
1284C23—41no—
1285C23—41no—
1286C23—41no—
1287C23—41no—
1288C23—41no—
1289C23—41no—
1290C23—41no—
1291C23—41no—
1292C23—41no—
1293C23—41no—
1294C23—41no—
1295C23—41no—
1296C23—41no—
1297C23—41no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23#120×C15114yes—
1303C23#121×C15114yes—
1304C23C22×D4×C15111yescharacteristic
1305C23C22×D4×C15111yescharacteristic
1306C23C22×D4×C15111yescharacteristic
1307C23C22×D4×C15111yescharacteristic
1308C23C22×D4×C15111yescharacteristic
1309C23C2×#41×C15111yescharacteristic
1310C23C2×#41×C15111yescharacteristic
1311C23C2×#41×C15111yescharacteristic
1312C23C2×#41×C15111yescharacteristic
1313C23H(5,𝔽2)×C15111yescharacteristic
1314C23H(5,𝔽2)×C15111yescharacteristic
1315C23H(5,𝔽2)×C15111yescharacteristic
1316C23H(5,𝔽2)×C15111yescharacteristic
1317C23H(5,𝔽2)×C15111yescharacteristic
1318C23H(5,𝔽2)×C15111yescharacteristic
1319D4—416no—
1320D4—416no—
1321D4—416no—
1322D4—416no—
1323D4—416no—
1324D4—416no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—416no—
1356C2×C4—416no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4#121×C15114yes—
1404C22—24no—
1405C22—24no—
1406C22—24no—
1407C22—24no—
1408C22—24no—
1409C22—24no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22—81no—
1461C22—81no—
1462C22—81no—
1463C22—81no—
1464C22C2×#120×C15111yescharacteristic
1465C22C2×#121×C15111yescharacteristic
1466C22C2×#121×C15111yescharacteristic
1467C22#525×C15111yescharacteristic
1468C22#525×C15111yescharacteristic
1469C22#532×C15111yescharacteristic
1470C22#534×C15111yescharacteristic
1471C22#534×C15111yescharacteristic
1472C22#534×C15111yescharacteristic
1473C22#535×C15111yescharacteristic
1474C22#535×C15111yescharacteristic
1475C22#538×C15111yescharacteristic
1476C22#538×C15111yescharacteristic
1477C22#540×C15111yescharacteristic
1478C22#540×C15111yescharacteristic
1479C22D42×C15111yescharacteristic
1480C22D42×C15111yescharacteristic
1481C22D42×C15111yescharacteristic
1482C22D42×C15111yescharacteristic
1483C22D42×C15111yescharacteristic
1484C22#546×C15111yescharacteristic
1485C22#546×C15111yescharacteristic
1486C22#546×C15111yescharacteristic
1487C22#546×C15111yescharacteristic
1488C22#546×C15111yescharacteristic
1489C22#546×C15111yescharacteristic
1490C22#546×C15111yescharacteristic
1491C22#546×C15111yescharacteristic
1492C22#546×C15111yescharacteristic
1493C22#550×C15111yescharacteristic
1494C22#553×C15111yescharacteristic
1495C22#553×C15111yescharacteristic
1496C22#553×C15111yescharacteristic
1497C22#560×C15111yescharacteristic
1498C22#560×C15111yescharacteristic
1499C4—24no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4—81no—
1509C4—81no—
1510C2—44no—
1511C2—44no—
1512C2—82no—
1513C2—82no—
1514C2#2404×C15111yescharacteristic
1515C2#2410×C15111yescharacteristic
1516C2#2410×C15111yescharacteristic
1517C2#2424×C15111yescharacteristic
1518C2#2428×C15111yescharacteristic
1519C2#2456×C15111yescharacteristic
1520C2#2464×C15111yescharacteristic
1521C2#2535×C15111yescharacteristic
1522C2#2543×C15111yescharacteristic
1523C2#2668×C15111yescharacteristic
1524C2#2669×C15111yescharacteristic
1525C2#2673×C15111yescharacteristic
1526C2#2688×C15111yescharacteristic
1527C2#2688×C15111yescharacteristic
1528C2#2703×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C151C2semidirect
2. C2×#392×C151C2semidirect
3. C2×#392×C151C2semidirect
4. C2×#392×C151C2semidirect
5. C2×#386×C151C2semidirect
6. C2×#386×C151C2semidirect
7. C2×#386×C151C2semidirect
8. C2×#386×C151C2semidirect
9. #1442×C151C2semidirect
10. #1440×C151C2semidirect
11. #1440×C151C2semidirect
12. #1439×C151C2semidirect
13. #1438×C151C2semidirect
14. #1438×C151C2semidirect
15. C22⋊#95×C151C2semidirect
105. C22×D4×C151D4semidirect
106. C22×D4×C151D4semidirect
176. C2×C22⋊C4×C151D4semidirect
177. C2×C22⋊C4×C151D4semidirect
189. #95×C151D4semidirect
764. #15273C151direct (N × H)
765. C151#15273direct (N × H)
766. C22×#121C2×C151semidirect
767. C2×#392C2×C151semidirect
768. C2×#392C2×C151semidirect
769. C2×#392C2×C151semidirect
770. C2×#386C2×C151semidirect
771. C2×#386C2×C151semidirect
772. C2×#386C2×C151semidirect
773. C2×#386C2×C151semidirect
774. #1442C2×C151semidirect
775. #1440C2×C151semidirect
776. #1440C2×C151semidirect
777. #1439C2×C151semidirect
778. #1438C2×C151semidirect
779. #1438C2×C151semidirect
780. C22⋊#95C2×C151semidirect
870. C22×D4D4×C151semidirect
871. C22×D4D4×C151semidirect
941. C2×C22⋊C4D4×C151semidirect
942. C2×C22⋊C4D4×C151semidirect
954. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1512
C2×#392×C1512
C2×#386×C1512
#1442×C1512
#1440×C1512
#1439×C1512
#1438×C1512
C22⋊#95×C1512
#15273151