Finite Group Databasebeta

← C151×#23115 #50328040

Subgroups — C151×#23115 #50328040

Order 38656.

762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3035×C151C211yesmaximal, characteristic
2#2935×C151C211yesmaximal, characteristic, complemented
3#2925×C151C211yesmaximal, characteristic, complemented
4#1975×C151C211yesmaximal, characteristic, complemented
5#1974×C151C211yesmaximal, characteristic, complemented
6#1963×C151C211yesmaximal, characteristic, complemented
7#1950×C151C211yesmaximal, characteristic, complemented
8#1929×C151C211yesmaximal, characteristic, complemented
9#1929×C151C211yesmaximal, characteristic, complemented
10#1876×C151C211yesmaximal, characteristic, complemented
11#1876×C151C211yesmaximal, characteristic, complemented
12#1768×C151C211yesmaximal, characteristic, complemented
13#1765×C151C211yesmaximal, characteristic, complemented
14#1764×C151C211yesmaximal, characteristic, complemented
15#1759×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151C2211yescharacteristic
17C2×#135×C151C2211yescharacteristic
18C2×#131×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic
20#532×C151C2211yescharacteristic
21C4×#41×C151C2211yescharacteristic
22#464×C151C411yescharacteristic, complemented
23#464×C151C411yescharacteristic, complemented
24#463×C151C411yescharacteristic, complemented
25#463×C151C411yescharacteristic, complemented
26#462×C151C411yescharacteristic, complemented
27#461×C151C411yescharacteristic, complemented
28#460×C151C411yescharacteristic, complemented
29#459×C151C411yescharacteristic, complemented
30#436×C151—21no—
31#435×C151—21no—
32#435×C151—21no—
33C8×D4×C151—21no—
34#433×C151—21no—
35#433×C151—21no—
36#432×C151—21no—
37#431×C151—21no—
38C2×#108×C151C2211yescharacteristic
39C2×#108×C151C2211yescharacteristic
40#423×C151C2211yescharacteristic
41C2×C4⋊C8×C151C2211yescharacteristic
42C2×C4⋊C8×C151C2211yescharacteristic
43C2×#104×C151C2211yescharacteristic
44C2×#104×C151C2211yescharacteristic
45C2×#104×C151C2211yescharacteristic
46C2×#104×C151C2211yescharacteristic
47C2×#104×C151C2211yescharacteristic
48C2×#104×C151C2211yescharacteristic
49#416×C151C2211yescharacteristic
50#416×C151C2211yescharacteristic
51#408×C151C2211yescharacteristic
52#408×C151C2211yescharacteristic
53#408×C151C2211yescharacteristic
54#408×C151C2211yescharacteristic
55#405×C151C2211yescharacteristic
56#405×C151C2211yescharacteristic
57C4×M16×C151C2211yescharacteristic
58C2×#97×C151C2211yescharacteristic
59C2×C4×C8×C151C2211yescharacteristic
60#376×C151C2211yescharacteristic
61#341×C151C2211yescharacteristic
62#341×C151C2211yescharacteristic
63#339×C151C2211yescharacteristic
64#339×C151C2211yescharacteristic
65#336×C151C2211yescharacteristic
66#336×C151C2211yescharacteristic
67C2×#41×C151C2311yescharacteristic
68C2×#41×C151C2311yescharacteristic
69C2×#41×C151C2311yescharacteristic
70#135×C151—41no—
71#135×C151—41no—
72#135×C151—41no—
73#135×C151—41no—
74C2×Q16×C151C2×C411yescharacteristic
75C2×Q16×C151C2×C411yescharacteristic
76C2×SD16×C151C2×C411yescharacteristic
77C2×SD16×C151C2×C411yescharacteristic
78C2×SD16×C151C2×C411yescharacteristic
79C2×SD16×C151C2×C411yescharacteristic
80C2×D8×C151C2×C411yescharacteristic
81C2×D8×C151C2×C411yescharacteristic
82#131×C151—22no—
83#131×C151—22no—
84#131×C151—41no—
85#131×C151—41no—
86C2×M16×C151—21no—
87C2×M16×C151—21no—
88C2×M16×C151C2311yescharacteristic
89C2×M16×C151C2311yescharacteristic
90C2×M16×C151C2311yescharacteristic
91C2×M16×C151C2311yescharacteristic
92C22×C8×C151—21no—
93C22×C8×C151—21no—
94C22×C8×C151C2311yescharacteristic
95C22×C8×C151C2311yescharacteristic
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98C4⋊Q8×C151C2×C411yescharacteristic
99#127×C151C2×C411yescharacteristic
100#124×C151C2×C411yescharacteristic
101#124×C151C2×C411yescharacteristic
102#121×C151—21no—
103#121×C151—21no—
104C4×Q8×C151C2×C411yescharacteristic
105C4×Q8×C151C2×C411yescharacteristic
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151C2×C411yescharacteristic
111C4×D4×C151C2×C411yescharacteristic
112#117×C151—21no—
113#117×C151C2311yescharacteristic
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#108×C151—41no—
119#108×C151—41no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151C2×C411yescharacteristic
123C4⋊C8×C151C2×C411yescharacteristic
124C4⋊C8×C151C2×C411yescharacteristic
125C4⋊C8×C151C2×C411yescharacteristic
126C4⋊C8×C151D411yescharacteristic
127C4⋊C8×C151D411yescharacteristic
128C4⋊C8×C151D411yescharacteristic
129C4⋊C8×C151D411yescharacteristic
130#104×C151—22no—
131#104×C151—22no—
132#104×C151—22no—
133#104×C151—22no—
134#104×C151—41no—
135#104×C151—41no—
136#103×C151C2×C411yescharacteristic
137#103×C151C2×C411yescharacteristic
138#103×C151C2×C411yescharacteristic
139#103×C151C2×C411yescharacteristic
140#102×C151C2×C411yescharacteristic
141#102×C151C2×C411yescharacteristic
142#102×C151C2×C411yescharacteristic
143#102×C151C2×C411yescharacteristic
144C22⋊C8×C151—21no—
145C22⋊C8×C151—21no—
146C22⋊C8×C151—21no—
147C22⋊C8×C151—21no—
148C22⋊C8×C151—21no—
149C22⋊C8×C151—21no—
150C22⋊C8×C151—21no—
151C22⋊C8×C151—21no—
152#97×C151—21no—
153#97×C151—21no—
154#97×C151—21no—
155#97×C151—41no—
156C4×C8×C151—21no—
157C4×C8×C151—21no—
158C4×C8×C151—21no—
159C4×C8×C151—41no—
160#95×C151—21no—
161#95×C151—21no—
162#41×C151—21no—
163#41×C151—21no—
164#41×C151—21no—
165#41×C151—21no—
166#41×C151—21no—
167#41×C151—21no—
168#41×C151—21no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—21no—
173#41×C151—21no—
174C2×Q8×C151C22×C411yescharacteristic
175C2×Q8×C151C22×C411yescharacteristic
176C2×Q8×C151C22×C411yescharacteristic
177C2×D4×C151—21no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151C22×C411yescharacteristic
183C2×D4×C151C22×C411yescharacteristic
184C2×D4×C151C22×C411yescharacteristic
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151#4111yescharacteristic
193C22×C4×C151#4111yescharacteristic
194C22×C4×C151C2411yescharacteristic
195Q16×C151—41no—
196Q16×C151—41no—
197SD16×C151—41no—
198SD16×C151—41no—
199SD16×C151—41no—
200SD16×C151—41no—
201D8×C151—41no—
202D8×C151—41no—
203M16×C151—21no—
204M16×C151—21no—
205M16×C151—21no—
206M16×C151—21no—
207M16×C151—21no—
208M16×C151—21no—
209M16×C151—21no—
210M16×C151—42no—
211M16×C151—42no—
212M16×C151#4112yes—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—42no—
226C2×C8×C151—42no—
227C2×C8×C151C22×C411yescharacteristic
228C2×C8×C151C22×C411yescharacteristic
229C2×C8×C151C22×C411yescharacteristic
230C2×C8×C151C22×C411yescharacteristic
231C2×C8×C151C2×D411yescharacteristic
232C2×C8×C151C2×D411yescharacteristic
233C2×C8×C151C2×D411yescharacteristic
234C2×C8×C151C2×D411yescharacteristic
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—21no—
239C4⋊C4×C151C22×C411yescharacteristic
240C4⋊C4×C151C22×C411yescharacteristic
241C22⋊C4×C151—21no—
242C22⋊C4×C151—21no—
243C22⋊C4×C151—21no—
244C22⋊C4×C151—21no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—21no—
247C22⋊C4×C151—21no—
248C42×C151—21no—
249C42×C151—21no—
250C42×C151—21no—
251C42×C151—21no—
252C42×C151—21no—
253C42×C151—21no—
254C42×C151C22×C411yescharacteristic
255C42×C151C22×C411yescharacteristic
256C42×C151C2×D411yescharacteristic
257C42×C151C2×D411yescharacteristic
258C42×C151#4112yes—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151C2×#4111yescharacteristic
263Q8×C151—21no—
264Q8×C151—21no—
265Q8×C151—21no—
266Q8×C151—21no—
267Q8×C151—21no—
268Q8×C151—21no—
269D4×C151—21no—
270D4×C151—21no—
271D4×C151—21no—
272D4×C151—21no—
273D4×C151—21no—
274D4×C151—21no—
275D4×C151—42no—
276D4×C151—41no—
277D4×C151—41no—
278D4×C151—41no—
279D4×C151—41no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—81no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—22no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—42no—
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—81no—
304C2×C4×C151C4×D411yescharacteristic
305C2×C4×C151C4×D411yescharacteristic
306C2×C4×C151C4×D411yescharacteristic
307C2×C4×C151C4×D411yescharacteristic
308C2×C4×C151C23×C411yescharacteristic
309C2×C4×C151C22×D411yescharacteristic
310C2×C4×C151C2×#4111yescharacteristic
311C2×C4×C151C2×#4111yescharacteristic
312C2×C4×C151H(5,𝔽2)11yescharacteristic
313C2×C4×C151H(5,𝔽2)11yescharacteristic
314C8×C151—21no—
315C8×C151—21no—
316C8×C151—21no—
317C8×C151—21no—
318C8×C151—21no—
319C8×C151—21no—
320C8×C151—21no—
321C8×C151—21no—
322C8×C151—22no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C22×C151—21no—
327C22×C151—21no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151C2×C4×D411yescharacteristic
338C22×C151#55311yescharacteristic
339C22×C151#55511yescharacteristic
340C4×C151—21no—
341C4×C151—21no—
342C4×C151—21no—
343C4×C151—21no—
344C4×C151—42no—
345C4×C151—41no—
346C4×C151—41no—
347C4×C151—41no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—81no—
351C4×C151C4×#4111yescharacteristic
352C4×C151#51811yescharacteristic
353C4×C151#54611yescharacteristic
354C4×C151#55011yescharacteristic
355C2×C151—21no—
356C2×C151—21no—
357C2×C151—81no—
358C2×C151—81no—
359C2×C151—81no—
360C2×C151#236311yescharacteristic
361C2×C151#295511yescharacteristic
362C2×C151#295711yescharacteristic
363#23115C15111yesmaximal, characteristic, direct product factor, Sylow
364C151#2311511yescharacteristic, direct product factor, Sylow
365#3035C2×C15111yescharacteristic
366#2935C2×C15111yescharacteristic, complemented
367#2925C2×C15111yescharacteristic, complemented
368#1975C2×C15111yescharacteristic, complemented
369#1974C2×C15111yescharacteristic, complemented
370#1963C2×C15111yescharacteristic, complemented
371#1950C2×C15111yescharacteristic, complemented
372#1929C2×C15111yescharacteristic, complemented
373#1929C2×C15111yescharacteristic, complemented
374#1876C2×C15111yescharacteristic, complemented
375#1876C2×C15111yescharacteristic, complemented
376#1768C2×C15111yescharacteristic, complemented
377#1765C2×C15111yescharacteristic, complemented
378#1764C2×C15111yescharacteristic, complemented
379#1759C2×C15111yescharacteristic, complemented
380C2×#135C22×C15111yescharacteristic
381C2×#135C22×C15111yescharacteristic
382C2×#131C22×C15111yescharacteristic
383C2×#131C22×C15111yescharacteristic
384#532C22×C15111yescharacteristic
385C4×#41C22×C15111yescharacteristic
386#464C4×C15111yescharacteristic, complemented
387#464C4×C15111yescharacteristic, complemented
388#463C4×C15111yescharacteristic, complemented
389#463C4×C15111yescharacteristic, complemented
390#462C4×C15111yescharacteristic, complemented
391#461C4×C15111yescharacteristic, complemented
392#460C4×C15111yescharacteristic, complemented
393#459C4×C15111yescharacteristic, complemented
394#436—21no—
395#435—21no—
396#435—21no—
397C8×D4—21no—
398#433—21no—
399#433—21no—
400#432—21no—
401#431—21no—
402C2×#108C22×C15111yescharacteristic
403C2×#108C22×C15111yescharacteristic
404#423C22×C15111yescharacteristic
405C2×C4⋊C8C22×C15111yescharacteristic
406C2×C4⋊C8C22×C15111yescharacteristic
407C2×#104C22×C15111yescharacteristic
408C2×#104C22×C15111yescharacteristic
409C2×#104C22×C15111yescharacteristic
410C2×#104C22×C15111yescharacteristic
411C2×#104C22×C15111yescharacteristic
412C2×#104C22×C15111yescharacteristic
413#416C22×C15111yescharacteristic
414#416C22×C15111yescharacteristic
415#408C22×C15111yescharacteristic
416#408C22×C15111yescharacteristic
417#408C22×C15111yescharacteristic
418#408C22×C15111yescharacteristic
419#405C22×C15111yescharacteristic
420#405C22×C15111yescharacteristic
421C4×M16C22×C15111yescharacteristic
422C2×#97C22×C15111yescharacteristic
423C2×C4×C8C22×C15111yescharacteristic
424#376C22×C15111yescharacteristic
425#341C22×C15111yescharacteristic
426#341C22×C15111yescharacteristic
427#339C22×C15111yescharacteristic
428#339C22×C15111yescharacteristic
429#336C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431C2×#41C23×C15111yescharacteristic
432C2×#41C23×C15111yescharacteristic
433C2×#41C23×C15111yescharacteristic
434#135—41no—
435#135—41no—
436#135—41no—
437#135—41no—
438C2×Q16C2×C4×C15111yescharacteristic
439C2×Q16C2×C4×C15111yescharacteristic
440C2×SD16C2×C4×C15111yescharacteristic
441C2×SD16C2×C4×C15111yescharacteristic
442C2×SD16C2×C4×C15111yescharacteristic
443C2×SD16C2×C4×C15111yescharacteristic
444C2×D8C2×C4×C15111yescharacteristic
445C2×D8C2×C4×C15111yescharacteristic
446#131—22no—
447#131—22no—
448#131—41no—
449#131—41no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16C23×C15111yescharacteristic
453C2×M16C23×C15111yescharacteristic
454C2×M16C23×C15111yescharacteristic
455C2×M16C23×C15111yescharacteristic
456C22×C8—21no—
457C22×C8—21no—
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460C22×C8C23×C15111yescharacteristic
461C22×C8C23×C15111yescharacteristic
462C4⋊Q8C2×C4×C15111yescharacteristic
463#127C2×C4×C15111yescharacteristic
464#124C2×C4×C15111yescharacteristic
465#124C2×C4×C15111yescharacteristic
466#121—21no—
467#121—21no—
468C4×Q8C2×C4×C15111yescharacteristic
469C4×Q8C2×C4×C15111yescharacteristic
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4C2×C4×C15111yescharacteristic
475C4×D4C2×C4×C15111yescharacteristic
476#117—21no—
477#117C23×C15111yescharacteristic
478C2×C42—21no—
479C2×C42C23×C15111yescharacteristic
480C2×C42C23×C15111yescharacteristic
481C2×C42C23×C15111yescharacteristic
482#108—41no—
483#108—41no—
484C4⋊C8—21no—
485C4⋊C8—21no—
486C4⋊C8C2×C4×C15111yescharacteristic
487C4⋊C8C2×C4×C15111yescharacteristic
488C4⋊C8C2×C4×C15111yescharacteristic
489C4⋊C8C2×C4×C15111yescharacteristic
490C4⋊C8D4×C15111yescharacteristic
491C4⋊C8D4×C15111yescharacteristic
492C4⋊C8D4×C15111yescharacteristic
493C4⋊C8D4×C15111yescharacteristic
494#104—22no—
495#104—22no—
496#104—22no—
497#104—22no—
498#104—41no—
499#104—41no—
500#103C2×C4×C15111yescharacteristic
501#103C2×C4×C15111yescharacteristic
502#103C2×C4×C15111yescharacteristic
503#103C2×C4×C15111yescharacteristic
504#102C2×C4×C15111yescharacteristic
505#102C2×C4×C15111yescharacteristic
506#102C2×C4×C15111yescharacteristic
507#102C2×C4×C15111yescharacteristic
508C22⋊C8—21no—
509C22⋊C8—21no—
510C22⋊C8—21no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516#97—21no—
517#97—21no—
518#97—21no—
519#97—41no—
520C4×C8—21no—
521C4×C8—21no—
522C4×C8—21no—
523C4×C8—41no—
524#95—21no—
525#95—21no—
526#41—21no—
527#41—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538C2×Q8C22×C4×C15111yescharacteristic
539C2×Q8C22×C4×C15111yescharacteristic
540C2×Q8C22×C4×C15111yescharacteristic
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4C22×C4×C15111yescharacteristic
547C2×D4C22×C4×C15111yescharacteristic
548C2×D4C22×C4×C15111yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4#41×C15111yescharacteristic
557C22×C4#41×C15111yescharacteristic
558C22×C4C24×C15111yescharacteristic
559Q16—41no—
560Q16—41no—
561SD16—41no—
562SD16—41no—
563SD16—41no—
564SD16—41no—
565D8—41no—
566D8—41no—
567M16—21no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—21no—
573M16—21no—
574M16—42no—
575M16—42no—
576M16#41×C15112yes—
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—21no—
588C2×C8—21no—
589C2×C8—42no—
590C2×C8—42no—
591C2×C8C22×C4×C15111yescharacteristic
592C2×C8C22×C4×C15111yescharacteristic
593C2×C8C22×C4×C15111yescharacteristic
594C2×C8C22×C4×C15111yescharacteristic
595C2×C8C2×D4×C15111yescharacteristic
596C2×C8C2×D4×C15111yescharacteristic
597C2×C8C2×D4×C15111yescharacteristic
598C2×C8C2×D4×C15111yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4C22×C4×C15111yescharacteristic
604C4⋊C4C22×C4×C15111yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C22×C4×C15111yescharacteristic
619C42C22×C4×C15111yescharacteristic
620C42C2×D4×C15111yescharacteristic
621C42C2×D4×C15111yescharacteristic
622C42#41×C15112yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23C2×#41×C15111yescharacteristic
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—21no—
633D4—21no—
634D4—21no—
635D4—21no—
636D4—21no—
637D4—21no—
638D4—21no—
639D4—42no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—81no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—81no—
668C2×C4C4×D4×C15111yescharacteristic
669C2×C4C4×D4×C15111yescharacteristic
670C2×C4C4×D4×C15111yescharacteristic
671C2×C4C4×D4×C15111yescharacteristic
672C2×C4C23×C4×C15111yescharacteristic
673C2×C4C22×D4×C15111yescharacteristic
674C2×C4C2×#41×C15111yescharacteristic
675C2×C4C2×#41×C15111yescharacteristic
676C2×C4H(5,𝔽2)×C15111yescharacteristic
677C2×C4H(5,𝔽2)×C15111yescharacteristic
678C8—21no—
679C8—21no—
680C8—21no—
681C8—21no—
682C8—21no—
683C8—21no—
684C8—21no—
685C8—21no—
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—21no—
691C22—21no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22C2×C4×D4×C15111yescharacteristic
702C22#553×C15111yescharacteristic
703C22#555×C15111yescharacteristic
704C4—21no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—81no—
715C4C4×#41×C15111yescharacteristic
716C4#518×C15111yescharacteristic
717C4#546×C15111yescharacteristic
718C4#550×C15111yescharacteristic
719C2—21no—
720C2—21no—
721C2—81no—
722C2—81no—
723C2—81no—
724C2#2363×C15111yescharacteristic
725C2#2955×C15111yescharacteristic
726C2#2957×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radical#3035×C151C2
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. #2935×C151C2semidirect
3. #2925×C151C2semidirect
4. #1975×C151C2semidirect
5. #1974×C151C2semidirect
6. #1963×C151C2semidirect
7. #1950×C151C2semidirect
8. #1929×C151C2semidirect
9. #1929×C151C2semidirect
10. #1876×C151C2semidirect
11. #1876×C151C2semidirect
12. #1768×C151C2semidirect
13. #1765×C151C2semidirect
14. #1764×C151C2semidirect
15. #1759×C151C2semidirect
22. #464×C151C4semidirect
23. #464×C151C4semidirect
24. #463×C151C4semidirect
25. #463×C151C4semidirect
26. #462×C151C4semidirect
27. #461×C151C4semidirect
28. #460×C151C4semidirect
29. #459×C151C4semidirect
363. #23115C151direct (N × H)
364. C151#23115direct (N × H)
366. #2935C2×C151semidirect
367. #2925C2×C151semidirect
368. #1975C2×C151semidirect
369. #1974C2×C151semidirect
370. #1963C2×C151semidirect
371. #1950C2×C151semidirect
372. #1929C2×C151semidirect
373. #1929C2×C151semidirect
374. #1876C2×C151semidirect
375. #1876C2×C151semidirect
376. #1768C2×C151semidirect
377. #1765C2×C151semidirect
378. #1764C2×C151semidirect
379. #1759C2×C151semidirect
386. #464C4×C151semidirect
387. #464C4×C151semidirect
388. #463C4×C151semidirect
389. #463C4×C151semidirect
390. #462C4×C151semidirect
391. #461C4×C151semidirect
392. #460C4×C151semidirect
393. #459C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3035×C1512
#2935×C1512
#2925×C1512
#1975×C1512
#1974×C1512
#1963×C1512
#1950×C1512
#1929×C1512
#1876×C1512
#1768×C1512
#1765×C1512
#1764×C1512
#1759×C1512
#23115151