Finite Group Databasebeta

← C151×#15315 #50320240

Subgroups — C151×#15315 #50320240

Order 38656.

2922 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic, complemented
2C2×#396×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C211yesmaximal, characteristic, complemented
5C2×#392×C151C211yesmaximal, characteristic, complemented
6C2×#392×C151C211yesmaximal, characteristic, complemented
7C2×#390×C151C211yesmaximal, characteristic, complemented
8C2×#390×C151C211yesmaximal, characteristic, complemented
9C2×#386×C151C211yesmaximal, characteristic, complemented
10C2×#385×C151C211yesmaximal, characteristic, complemented
11#1439×C151C211yesmaximal, characteristic, complemented
12#1439×C151C211yesmaximal, characteristic, complemented
13#1438×C151C211yesmaximal, characteristic, complemented
14#1438×C151C211yesmaximal, characteristic, complemented
15#1436×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C23×D4×C151C2211yescharacteristic
20C23×D4×C151C2211yescharacteristic
21C23×D4×C151C2211yescharacteristic
22C24×C4×C151C2211yescharacteristic
23C2×#121×C151—24no—
24C2×#121×C151—24no—
25C2×#121×C151—24no—
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29C22×C4⋊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
42C22×C22⋊C4×C151C2211yescharacteristic
43C22×C22⋊C4×C151C2211yescharacteristic
44C22×C22⋊C4×C151C2211yescharacteristic
45C22×C42×C151C2211yescharacteristic
46#396×C151—24no—
47#394×C151—24no—
48#392×C151—24no—
49#392×C151—24no—
50#392×C151—24no—
51#390×C151—24no—
52#390×C151—24no—
53#386×C151—24no—
54#385×C151—24no—
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C2×#95×C151C2211yescharacteristic
58C2×#95×C151C2211yescharacteristic
59C2×#95×C151C2211yescharacteristic
60C2×#95×C151C2211yescharacteristic
61C2×#95×C151C2211yescharacteristic
62C2×#95×C151C2211yescharacteristic
63C25×C151C2311yescharacteristic
64C25×C151C2311yescharacteristic
65C25×C151C2311yescharacteristic
66C25×C151C2311yescharacteristic
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—22no—
92C22×D4×C151—22no—
93C22×D4×C151—22no—
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×C151—41no—
106C22×D4×C151—41no—
107C22×D4×C151—41no—
108C22×D4×C151D414yescomplemented
109C23×C4×C151—22no—
110C23×C4×C151—22no—
111C23×C4×C151—22no—
112C23×C4×C151—22no—
113C23×C4×C151—22no—
114C23×C4×C151—41no—
115C23×C4×C151—41no—
116C23×C4×C151C2311yescharacteristic
117C23×C4×C151C2311yescharacteristic
118C23×C4×C151C2311yescharacteristic
119C23×C4×C151C2311yescharacteristic
120C23×C4×C151C2311yescharacteristic
121C23×C4×C151C2311yescharacteristic
122C23×C4×C151C2311yescharacteristic
123C23×C4×C151C2311yescharacteristic
124C23×C4×C151C2311yescharacteristic
125C23×C4×C151C2311yescharacteristic
126C23×C4×C151C2311yescharacteristic
127#121×C151—232no—
128C2×C4⋊C4×C151—22no—
129C2×C4⋊C4×C151—22no—
130C2×C4⋊C4×C151—22no—
131C2×C4⋊C4×C151—22no—
132C2×C4⋊C4×C151—22no—
133C2×C4⋊C4×C151—22no—
134C2×C4⋊C4×C151—22no—
135C2×C4⋊C4×C151—22no—
136C2×C4⋊C4×C151—22no—
137C2×C4⋊C4×C151—41no—
138C2×C4⋊C4×C151—41no—
139C2×C4⋊C4×C151D414yescomplemented
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—22no—
163C2×C22⋊C4×C151—22no—
164C2×C22⋊C4×C151—22no—
165C2×C22⋊C4×C151—22no—
166C2×C22⋊C4×C151—22no—
167C2×C22⋊C4×C151—22no—
168C2×C22⋊C4×C151—22no—
169C2×C22⋊C4×C151—22no—
170C2×C22⋊C4×C151—22no—
171C2×C22⋊C4×C151—22no—
172C2×C22⋊C4×C151—22no—
173C2×C22⋊C4×C151—41no—
174C2×C22⋊C4×C151—41no—
175C2×C22⋊C4×C151—41no—
176C2×C22⋊C4×C151—41no—
177C2×C22⋊C4×C151—41no—
178C2×C22⋊C4×C151—41no—
179C2×C22⋊C4×C151—41no—
180C2×C22⋊C4×C151—41no—
181C2×C22⋊C4×C151—41no—
182C2×C22⋊C4×C151—41no—
183C2×C22⋊C4×C151D414yescomplemented
184C2×C22⋊C4×C151D414yescomplemented
185C2×C42×C151—22no—
186C2×C42×C151—22no—
187C2×C42×C151—41no—
188#95×C151—22no—
189#95×C151—22no—
190#95×C151—22no—
191#95×C151—22no—
192#95×C151—22no—
193#95×C151—41no—
194#95×C151D414yescomplemented
195#95×C151D414yescomplemented
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×C151—21no—
243C24×C151—21no—
244C24×C151—21no—
245C24×C151—21no—
246C24×C151—21no—
247C24×C151—21no—
248C24×C151—21no—
249C24×C151—21no—
250C24×C151C2×D412yes—
251C24×C151C2×D412yes—
252C24×C151C2×D412yes—
253C24×C151C2×D412yes—
254C24×C151#4112yes—
255C24×C151#4112yes—
256C24×C151C2411yescharacteristic
257C2×D4×C151—28no—
258C2×D4×C151—28no—
259C2×D4×C151—28no—
260C2×D4×C151—28no—
261C2×D4×C151—28no—
262C2×D4×C151—28no—
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—
293C2×D4×C151—44no—
294C2×D4×C151—44no—
295C2×D4×C151—44no—
296C2×D4×C151—44no—
297C2×D4×C151—44no—
298C2×D4×C151—44no—
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—28no—
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—21no—
361C22×C4×C151—21no—
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×C151C2×D412yes—
369C22×C4×C151C2×D412yes—
370C22×C4×C151C2×D412yes—
371C22×C4×C151C2×D412yes—
372C22×C4×C151C2×D412yes—
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—
383C4⋊C4×C151—28no—
384C4⋊C4×C151—44no—
385C4⋊C4×C151—44no—
386C4⋊C4×C151—44no—
387C22⋊C4×C151—28no—
388C22⋊C4×C151—28no—
389C22⋊C4×C151—28no—
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—
399C22⋊C4×C151—44no—
400C22⋊C4×C151—44no—
401C22⋊C4×C151—44no—
402C42×C151—44no—
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—41no—
443C23×C151—41no—
444C23×C151—41no—
445C23×C151—41no—
446C23×C151—41no—
447C23×C151—41no—
448C23×C151—41no—
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—41no—
538C23×C151—41no—
539C23×C151—41no—
540C23×C151—41no—
541C23×C151—41no—
542C23×C151#12114yes—
543C23×C151C22×D411yescharacteristic
544C23×C151C22×D411yescharacteristic
545C23×C151C22×D411yescharacteristic
546C23×C151C22×D411yescharacteristic
547C23×C151C22×D411yescharacteristic
548C23×C151C22×D411yescharacteristic
549C23×C151C2×#4111yescharacteristic
550C23×C151C2×#4111yescharacteristic
551C23×C151C2×#4111yescharacteristic
552C23×C151H(5,𝔽2)11yescharacteristic
553C23×C151H(5,𝔽2)11yescharacteristic
554C23×C151H(5,𝔽2)11yescharacteristic
555C23×C151H(5,𝔽2)11yescharacteristic
556C23×C151H(5,𝔽2)11yescharacteristic
557C23×C1512−1+411yescharacteristic
558D4×C151—416no—
559D4×C151—416no—
560D4×C151—416no—
561D4×C151—416no—
562D4×C151—416no—
563D4×C151—416no—
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—22no—
591C2×C4×C151—22no—
592C2×C4×C151—22no—
593C2×C4×C151—22no—
594C2×C4×C151—22no—
595C2×C4×C151—22no—
596C2×C4×C151—22no—
597C2×C4×C151—22no—
598C2×C4×C151—22no—
599C2×C4×C151—22no—
600C2×C4×C151—416no—
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—41no—
639C2×C4×C151#12014yes—
640C2×C4×C151#12114yescomplemented
641C2×C4×C151#12714yes—
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—81no—
679C22×C151—81no—
680C22×C151—81no—
681C22×C151—81no—
682C22×C151—81no—
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×C151—81no—
700C22×C151—81no—
701C22×C151—81no—
702C22×C151C2×#12011yescharacteristic
703C22×C151C2×#12111yescharacteristic
704C22×C151C2×#12111yescharacteristic
705C22×C151#52511yescharacteristic
706C22×C151#52511yescharacteristic
707C22×C151C2×#12711yescharacteristic
708C22×C151#53411yescharacteristic
709C22×C151#53511yescharacteristic
710C22×C151#53511yescharacteristic
711C22×C151#53711yescharacteristic
712C22×C151#53711yescharacteristic
713C22×C151#53711yescharacteristic
714C22×C151#53811yescharacteristic
715C22×C151#53811yescharacteristic
716C22×C151#53811yescharacteristic
717C22×C151D4211yescharacteristic
718C22×C151D4211yescharacteristic
719C22×C151D4211yescharacteristic
720C22×C151D4211yescharacteristic
721C22×C151D4211yescharacteristic
722C22×C151D4211yescharacteristic
723C22×C151D4211yescharacteristic
724C22×C151#54611yescharacteristic
725C22×C151#54611yescharacteristic
726C22×C151#54611yescharacteristic
727C22×C151#54611yescharacteristic
728C22×C151#54611yescharacteristic
729C22×C151#54711yescharacteristic
730C22×C151#54811yescharacteristic
731C22×C151#54811yescharacteristic
732C22×C151#55011yescharacteristic
733C22×C151#55011yescharacteristic
734C22×C151#55311yescharacteristic
735C22×C151#56011yescharacteristic
736C22×C151#56211yescharacteristic
737C4×C151—24no—
738C4×C151—24no—
739C4×C151—24no—
740C4×C151—42no—
741C4×C151—42no—
742C4×C151—42no—
743C4×C151—42no—
744C4×C151—42no—
745C4×C151—42no—
746C4×C151—81no—
747C4×C151—81no—
748C2×C151—44no—
749C2×C151—82no—
750C2×C151—82no—
751C2×C151—82no—
752C2×C151#240711yescharacteristic
753C2×C151#241011yescharacteristic
754C2×C151#241611yescharacteristic
755C2×C151#242411yescharacteristic
756C2×C151#242411yescharacteristic
757C2×C151#243311yescharacteristic
758C2×C151#245611yescharacteristic
759C2×C151#254011yescharacteristic
760C2×C151#254111yescharacteristic
761C2×C151#267511yescharacteristic
762C2×C151#267611yescharacteristic
763C2×C151#267611yescharacteristic
764C2×C151#267811yescharacteristic
765C2×C151#268211yescharacteristic
766C2×C151#271411yescharacteristic
767#15315C15111yesmaximal, characteristic, direct product factor, Sylow
768C151#1531511yescharacteristic, direct product factor, Sylow
769C22×#121C2×C15111yescharacteristic, complemented
770C2×#396C2×C15111yescharacteristic, complemented
771C2×#394C2×C15111yescharacteristic, complemented
772C2×#392C2×C15111yescharacteristic, complemented
773C2×#392C2×C15111yescharacteristic, complemented
774C2×#392C2×C15111yescharacteristic, complemented
775C2×#390C2×C15111yescharacteristic, complemented
776C2×#390C2×C15111yescharacteristic, complemented
777C2×#386C2×C15111yescharacteristic, complemented
778C2×#385C2×C15111yescharacteristic, complemented
779#1439C2×C15111yescharacteristic, complemented
780#1439C2×C15111yescharacteristic, complemented
781#1438C2×C15111yescharacteristic, complemented
782#1438C2×C15111yescharacteristic, complemented
783#1436C2×C15111yescharacteristic, complemented
784C23×D4C22×C15111yescharacteristic
785C23×D4C22×C15111yescharacteristic
786C23×D4C22×C15111yescharacteristic
787C23×D4C22×C15111yescharacteristic
788C23×D4C22×C15111yescharacteristic
789C23×D4C22×C15111yescharacteristic
790C24×C4C22×C15111yescharacteristic
791C2×#121—24no—
792C2×#121—24no—
793C2×#121—24no—
794C22×C4⋊C4C22×C15111yescharacteristic
795C22×C4⋊C4C22×C15111yescharacteristic
796C22×C4⋊C4C22×C15111yescharacteristic
797C22×C4⋊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
807C22×C22⋊C4C22×C15111yescharacteristic
808C22×C22⋊C4C22×C15111yescharacteristic
809C22×C22⋊C4C22×C15111yescharacteristic
810C22×C22⋊C4C22×C15111yescharacteristic
811C22×C22⋊C4C22×C15111yescharacteristic
812C22×C22⋊C4C22×C15111yescharacteristic
813C22×C42C22×C15111yescharacteristic
814#396—24no—
815#394—24no—
816#392—24no—
817#392—24no—
818#392—24no—
819#390—24no—
820#390—24no—
821#386—24no—
822#385—24no—
823C2×#95C22×C15111yescharacteristic
824C2×#95C22×C15111yescharacteristic
825C2×#95C22×C15111yescharacteristic
826C2×#95C22×C15111yescharacteristic
827C2×#95C22×C15111yescharacteristic
828C2×#95C22×C15111yescharacteristic
829C2×#95C22×C15111yescharacteristic
830C2×#95C22×C15111yescharacteristic
831C25C23×C15111yescharacteristic
832C25C23×C15111yescharacteristic
833C25C23×C15111yescharacteristic
834C25C23×C15111yescharacteristic
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—22no—
857C22×D4—22no—
858C22×D4—22no—
859C22×D4—22no—
860C22×D4—22no—
861C22×D4—22no—
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×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4—41no—
876C22×D4D4×C15114yescomplemented
877C23×C4—22no—
878C23×C4—22no—
879C23×C4—22no—
880C23×C4—22no—
881C23×C4—22no—
882C23×C4—41no—
883C23×C4—41no—
884C23×C4C23×C15111yescharacteristic
885C23×C4C23×C15111yescharacteristic
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
895#121—232no—
896C2×C4⋊C4—22no—
897C2×C4⋊C4—22no—
898C2×C4⋊C4—22no—
899C2×C4⋊C4—22no—
900C2×C4⋊C4—22no—
901C2×C4⋊C4—22no—
902C2×C4⋊C4—22no—
903C2×C4⋊C4—22no—
904C2×C4⋊C4—22no—
905C2×C4⋊C4—41no—
906C2×C4⋊C4—41no—
907C2×C4⋊C4D4×C15114yescomplemented
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—22no—
928C2×C22⋊C4—22no—
929C2×C22⋊C4—22no—
930C2×C22⋊C4—22no—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—22no—
934C2×C22⋊C4—22no—
935C2×C22⋊C4—22no—
936C2×C22⋊C4—22no—
937C2×C22⋊C4—22no—
938C2×C22⋊C4—22no—
939C2×C22⋊C4—22no—
940C2×C22⋊C4—22no—
941C2×C22⋊C4—41no—
942C2×C22⋊C4—41no—
943C2×C22⋊C4—41no—
944C2×C22⋊C4—41no—
945C2×C22⋊C4—41no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4—41no—
951C2×C22⋊C4D4×C15114yescomplemented
952C2×C22⋊C4D4×C15114yescomplemented
953C2×C42—22no—
954C2×C42—22no—
955C2×C42—41no—
956#95—22no—
957#95—22no—
958#95—22no—
959#95—22no—
960#95—22no—
961#95—41no—
962#95D4×C15114yescomplemented
963#95D4×C15114yescomplemented
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—
1007C24—21no—
1008C24—21no—
1009C24—21no—
1010C24—21no—
1011C24—21no—
1012C24—21no—
1013C24—21no—
1014C24—21no—
1015C24—21no—
1016C24—21no—
1017C24—21no—
1018C24C2×D4×C15112yes—
1019C24C2×D4×C15112yes—
1020C24C2×D4×C15112yes—
1021C24C2×D4×C15112yes—
1022C24#41×C15112yes—
1023C24#41×C15112yes—
1024C24C24×C15111yescharacteristic
1025C2×D4—28no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—28no—
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—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
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—28no—
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—21no—
1126C22×C4—21no—
1127C22×C4—21no—
1128C22×C4—21no—
1129C22×C4—21no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4C2×D4×C15112yes—
1137C22×C4C2×D4×C15112yes—
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×C4C2×D4×C15112yes—
1148C22×C4C2×D4×C15112yes—
1149C22×C4C2×D4×C15112yes—
1150C22×C4#41×C15112yes—
1151C4⋊C4—28no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C42—44no—
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—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
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—41no—
1303C23—41no—
1304C23—41no—
1305C23—41no—
1306C23—41no—
1307C23—41no—
1308C23—41no—
1309C23—41no—
1310C23#121×C15114yes—
1311C23C22×D4×C15111yescharacteristic
1312C23C22×D4×C15111yescharacteristic
1313C23C22×D4×C15111yescharacteristic
1314C23C22×D4×C15111yescharacteristic
1315C23C22×D4×C15111yescharacteristic
1316C23C22×D4×C15111yescharacteristic
1317C23C2×#41×C15111yescharacteristic
1318C23C2×#41×C15111yescharacteristic
1319C23C2×#41×C15111yescharacteristic
1320C23H(5,𝔽2)×C15111yescharacteristic
1321C23H(5,𝔽2)×C15111yescharacteristic
1322C23H(5,𝔽2)×C15111yescharacteristic
1323C23H(5,𝔽2)×C15111yescharacteristic
1324C23H(5,𝔽2)×C15111yescharacteristic
1325C232−1+4×C15111yescharacteristic
1326D4—416no—
1327D4—416no—
1328D4—416no—
1329D4—416no—
1330D4—416no—
1331D4—416no—
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—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—416no—
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—41no—
1404C2×C4—41no—
1405C2×C4—41no—
1406C2×C4—41no—
1407C2×C4#120×C15114yes—
1408C2×C4#121×C15114yescomplemented
1409C2×C4#127×C15114yes—
1410C22—24no—
1411C22—24no—
1412C22—24no—
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—81no—
1447C22—81no—
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—
1464C22—81no—
1465C22—81no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22C2×#120×C15111yescharacteristic
1471C22C2×#121×C15111yescharacteristic
1472C22C2×#121×C15111yescharacteristic
1473C22#525×C15111yescharacteristic
1474C22#525×C15111yescharacteristic
1475C22C2×#127×C15111yescharacteristic
1476C22#534×C15111yescharacteristic
1477C22#535×C15111yescharacteristic
1478C22#535×C15111yescharacteristic
1479C22#537×C15111yescharacteristic
1480C22#537×C15111yescharacteristic
1481C22#537×C15111yescharacteristic
1482C22#538×C15111yescharacteristic
1483C22#538×C15111yescharacteristic
1484C22#538×C15111yescharacteristic
1485C22D42×C15111yescharacteristic
1486C22D42×C15111yescharacteristic
1487C22D42×C15111yescharacteristic
1488C22D42×C15111yescharacteristic
1489C22D42×C15111yescharacteristic
1490C22D42×C15111yescharacteristic
1491C22D42×C15111yescharacteristic
1492C22#546×C15111yescharacteristic
1493C22#546×C15111yescharacteristic
1494C22#546×C15111yescharacteristic
1495C22#546×C15111yescharacteristic
1496C22#546×C15111yescharacteristic
1497C22#547×C15111yescharacteristic
1498C22#548×C15111yescharacteristic
1499C22#548×C15111yescharacteristic
1500C22#550×C15111yescharacteristic
1501C22#550×C15111yescharacteristic
1502C22#553×C15111yescharacteristic
1503C22#560×C15111yescharacteristic
1504C22#562×C15111yescharacteristic
1505C4—24no—
1506C4—24no—
1507C4—24no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—42no—
1512C4—42no—
1513C4—42no—
1514C4—81no—
1515C4—81no—
1516C2—44no—
1517C2—82no—
1518C2—82no—
1519C2—82no—
1520C2#2407×C15111yescharacteristic
1521C2#2410×C15111yescharacteristic
1522C2#2416×C15111yescharacteristic
1523C2#2424×C15111yescharacteristic
1524C2#2424×C15111yescharacteristic
1525C2#2433×C15111yescharacteristic
1526C2#2456×C15111yescharacteristic
1527C2#2540×C15111yescharacteristic
1528C2#2541×C15111yescharacteristic
1529C2#2675×C15111yescharacteristic
1530C2#2676×C15111yescharacteristic
1531C2#2676×C15111yescharacteristic
1532C2#2678×C15111yescharacteristic
1533C2#2682×C15111yescharacteristic
1534C2#2714×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×#396×C151C2semidirect
3. C2×#394×C151C2semidirect
4. C2×#392×C151C2semidirect
5. C2×#392×C151C2semidirect
6. C2×#392×C151C2semidirect
7. C2×#390×C151C2semidirect
8. C2×#390×C151C2semidirect
9. C2×#386×C151C2semidirect
10. C2×#385×C151C2semidirect
11. #1439×C151C2semidirect
12. #1439×C151C2semidirect
13. #1438×C151C2semidirect
14. #1438×C151C2semidirect
15. #1436×C151C2semidirect
108. C22×D4×C151D4semidirect
139. C2×C4⋊C4×C151D4semidirect
183. C2×C22⋊C4×C151D4semidirect
184. C2×C22⋊C4×C151D4semidirect
194. #95×C151D4semidirect
195. #95×C151D4semidirect
640. C2×C4×C151#121semidirect
767. #15315C151direct (N × H)
768. C151#15315direct (N × H)
769. C22×#121C2×C151semidirect
770. C2×#396C2×C151semidirect
771. C2×#394C2×C151semidirect
772. C2×#392C2×C151semidirect
773. C2×#392C2×C151semidirect
774. C2×#392C2×C151semidirect
775. C2×#390C2×C151semidirect
776. C2×#390C2×C151semidirect
777. C2×#386C2×C151semidirect
778. C2×#385C2×C151semidirect
779. #1439C2×C151semidirect
780. #1439C2×C151semidirect
781. #1438C2×C151semidirect
782. #1438C2×C151semidirect
783. #1436C2×C151semidirect
876. C22×D4D4×C151semidirect
907. C2×C4⋊C4D4×C151semidirect
951. C2×C22⋊C4D4×C151semidirect
952. C2×C22⋊C4D4×C151semidirect
962. #95D4×C151semidirect
963. #95D4×C151semidirect
1408. C2×C4#121×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×#396×C1512
C2×#394×C1512
C2×#392×C1512
C2×#390×C1512
C2×#386×C1512
C2×#385×C1512
#1439×C1512
#1438×C1512
#1436×C1512
#15315151