Finite Group Databasebeta

← C2×#11752452 #14412486

Subgroups — C2×#11752452 #14412486

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C22×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×D5⋊#208C211yesmaximal, characteristic, complemented
4#11752452C218yesmaximal, direct product factor
5C2×#91238C212yesmaximal, complemented
6C2×#91236C212yesmaximal, complemented
7C2×#65793—31nomaximal, Hall
8C23×ΓL(1,𝔽16)—21no—
9C2×C3×C5×#41C411yescharacteristic, complemented
10C3×D5×#41—22no—
11C3×D5×#41—22no—
12C3×D5×#41C414yescomplemented
13C3×D5×#41C2214yes—
14C2×C3×#713C411yescharacteristic, complemented
15C2×C3×Q8×D5C2211yescharacteristic
16C2×C3×#711—21no—
17C2×C3×#711C411yescharacteristic, complemented
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C2×C3×#709—21no—
21C2×C3×#709C411yescharacteristic, complemented
22C22×C3×C4×D5—21no—
23C22×C3×C4×D5C2211yescharacteristic
24C2×#6762—21no—
25C2×C4⋊ΓL(1,𝔽16)—22no—
26C2×C4⋊ΓL(1,𝔽16)—21no—
27C2×C4⋊ΓL(1,𝔽16)C2212yes—
28C2×C4⋊ΓL(1,𝔽16)C2214yescomplemented
29D5⋊#208—22no—
30D5⋊#208C2214yescomplemented
31C2×#6758—21no—
32C2×D5⋊(C3⋊C8)C2212yes—
33#91238C2218yescomplemented
34#91236C2218yescomplemented
35C2×#5232—51nomaximal, Hall
36C2×D5×#41D311yescharacteristic
37C22×C4⋊AGL(1,𝔽5)—31no—
38C2×D5⋊M16—31no—
39#65793—38no—
40C2×#4009—32no—
41C2×#4007—32no—
42C23×C3×D5—21no—
43C23×C3×D5D411yescharacteristic
44C22×ΓL(1,𝔽16)—22no—
45C22×ΓL(1,𝔽16)—24no—
46C22×ΓL(1,𝔽16)—44no—
47C3×C5×#41—22no—
48C3×C5×#41C2×C414yescomplemented
49C2×C3×C5×Q8C2×C411yescharacteristic, complemented
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4C2×C411yescharacteristic, complemented
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2×C411yescharacteristic
54C2×C3×C22⋊D5—21no—
55C2×C3×C22⋊D5—21no—
56C2×C3×C22⋊D5—21no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5D411yescharacteristic
59C3×#713—22no—
60C3×#713C2×C414yescomplemented
61C3×Q8×D5—21no—
62C3×Q8×D5—21no—
63C3×Q8×D5C2×C412yescomplemented
64C3×Q8×D5C2312yes—
65C3×#711—24no—
66C3×#711—24no—
67C3×#711—22no—
68C3×#711C2×C414yescomplemented
69C3×D4×D5—24no—
70C3×D4×D5—24no—
71C3×D4×D5—21no—
72C3×D4×D5—21no—
73C3×D4×D5C2×C412yescomplemented
74C3×D4×D5C2312yes—
75C3×#709—22no—
76C3×#709—24no—
77C3×#709—24no—
78C3×#709C2×C414yescomplemented
79C2×C3×D20—21no—
80C2×C3×D20C2×C411yescharacteristic, complemented
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—24no—
85C2×C3×C4×D5—24no—
86C2×C3×C4×D5C2×C411yescharacteristic
87C2×C3×C4×D5C2×C412yes—
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D412yes—
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5D412yes—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×C4×D5C2312yes—
94C2×C3×Dic10—21no—
95C2×C3×Dic10C2×C411yescharacteristic, complemented
96#6762—24no—
97C2×C3⋊#170—22no—
98C4⋊ΓL(1,𝔽16)—22no—
99C4⋊ΓL(1,𝔽16)—24no—
100C4⋊ΓL(1,𝔽16)C2314yes—
101#6758—24no—
102D5⋊(C3⋊C8)—22no—
103D5⋊(C3⋊C8)C2314yes—
104C22×C3×#41—51no—
105C22×C4⋊Dic3—51no—
106C22×#208—51no—
107#5232—58no—
108C2×#835—52no—
109C2×#832—52no—
110C23×AGL(1,𝔽5)—61no—
111C2×C5×#41Dic311yescharacteristic, complemented
112D5×#41—22no—
113D5×#41—22no—
114D5×#41Dic314yescomplemented
115D5×#41C2×D314yes—
116C2×#713Dic311yescharacteristic, complemented
117C2×Q8×D5C2×D311yescharacteristic
118C2×#711—21no—
119C2×#711Dic311yescharacteristic, complemented
120C2×D4×D5—21no—
121C2×D4×D5C2×D311yescharacteristic
122C2×#709—21no—
123C2×#709Dic311yescharacteristic, complemented
124C22×C4×D5—21no—
125C22×C4×D5C2×D311yescharacteristic
126C2×#704—61no—
127C2×C4⋊AGL(1,𝔽5)—34no—
128C2×C4⋊AGL(1,𝔽5)—32no—
129C2×C4⋊AGL(1,𝔽5)—61no—
130C2×C4⋊AGL(1,𝔽5)—62no—
131D5⋊M16—34no—
132D5⋊M16—62no—
133C2×#700—61no—
134C2×D5⋊C8—32no—
135#4009—38no—
136#4007—38no—
137C2×#417—151noSylow
138C23×C3×C5—21no—
139C23×C3×C5C22⋊C411yescharacteristic
140C22×C3×D5—22no—
141C22×C3×D5—22no—
142C22×C3×D5—21no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—42no—
146C22×C3×D5—42no—
147C22×C3×D5C22⋊C411yescharacteristic
148C22×C3×D5C22⋊C412yes—
149C22×C3×D5C2×D412yes—
150C22×C3×D5C2×D411yescharacteristic
151C2×ΓL(1,𝔽16)—24no—
152C2×ΓL(1,𝔽16)—48no—
153C2×ΓL(1,𝔽16)—44no—
154C3×C5×Q8—21no—
155C3×C5×Q8C22×C412yescomplemented
156C3×C5×D4—24no—
157C3×C5×D4—21no—
158C3×C5×D4C22×C412yescomplemented
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—24no—
161C2×C3×C4×C5C22⋊C411yescharacteristic
162C2×C3×C4×C5C22⋊C412yes—
163C2×C3×C4×C5C22×C411yescharacteristic
164C2×C3×C4×C5C22×C412yes—
165C3×C22⋊D5—24no—
166C3×C22⋊D5—24no—
167C3×C22⋊D5—22no—
168C3×C22⋊D5—22no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—24no—
171C2×C3×Dic5C22⋊C411yescharacteristic
172C2×C3×Dic5C22⋊C412yes—
173C2×C3×Dic5C2×D411yescharacteristic
174C2×C3×Dic5C2×D412yes—
175C3×D20—24no—
176C3×D20—21no—
177C3×D20C22×C412yescomplemented
178C3×C4×D5—22no—
179C3×C4×D5—22no—
180C3×C4×D5—24no—
181C3×C4×D5—24no—
182C3×C4×D5C22⋊C412yes—
183C3×C4×D5C22⋊C412yes—
184C3×C4×D5C22⋊C412yes—
185C3×C4×D5C22×C411yescharacteristic
186C3×C4×D5C22×C412yes—
187C3×C4×D5C2×D412yes—
188C3×C4×D5C2×D411yescharacteristic
189C3×C4×D5C2×D411yescharacteristic
190C3×C4×D5C2×D412yes—
191C3×C4×D5C2411yescharacteristic
192C3×Dic10—21no—
193C3×Dic10—22no—
194C3×Dic10—22no—
195C3×Dic10C22×C412yescomplemented
196C3⋊#170—24no—
197C2×C3×#41—54no—
198C2×C3×#41—54no—
199C2×C3×#41—51no—
200C2×C3×#41—51no—
201C2×C3×#41—51no—
202C2×C3×#41—101no—
203C2×C3×#41—101no—
204C2×C3×#41—102no—
205C2×C3×#41—102no—
206C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
207C22×C3×Q8—51no—
208C22×C3×D4—51no—
209C22×C3×D4—101no—
210C23×C3×C4—51no—
211C23×C3×C4—101no—
212C23×Dic3—101no—
213C2×C4⋊Dic3—52no—
214C2×C4⋊Dic3—54no—
215C2×C4⋊Dic3—101no—
216C2×C4⋊Dic3—102no—
217C2×#208—54no—
218C2×#208—101no—
219C2×#208—102no—
220C2×#208—101no—
221C22×C3⋊C8—52no—
222#835—58no—
223#832—58no—
224C23×D5—21no—
225C23×D5#6711yescharacteristic
226C22×AGL(1,𝔽5)—64no—
227C22×AGL(1,𝔽5)—62no—
228C22×AGL(1,𝔽5)—124no—
229C5×#41—22no—
230C5×#41C2×Dic314yescomplemented
231C2×C5×Q8C2×Dic311yescharacteristic, complemented
232C2×C5×D4—21no—
233C2×C5×D4C2×Dic311yescharacteristic, complemented
234C22×C4×C5—21no—
235C22×C4×C5C2×Dic311yescharacteristic
236C2×C22⋊D5—21no—
237C2×C22⋊D5—21no—
238C2×C22⋊D5—21no—
239C22×Dic5—21no—
240C22×Dic5#6711yescharacteristic
241#713—22no—
242#713C2×Dic314yescomplemented
243Q8×D5—21no—
244Q8×D5—21no—
245Q8×D5C2×Dic312yescomplemented
246Q8×D5C22×D312yes—
247#711—24no—
248#711—24no—
249#711—22no—
250#711C2×Dic314yescomplemented
251D4×D5—24no—
252D4×D5—24no—
253D4×D5—21no—
254D4×D5—21no—
255D4×D5C2×Dic312yescomplemented
256D4×D5C22×D312yes—
257#709—22no—
258#709—24no—
259#709—24no—
260#709C2×Dic314yescomplemented
261C2×D20—21no—
262C2×D20C2×Dic311yescharacteristic, complemented
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5—21no—
266C2×C4×D5—24no—
267C2×C4×D5—24no—
268C2×C4×D5C2×Dic311yescharacteristic
269C2×C4×D5C2×Dic312yes—
270C2×C4×D5#6711yescharacteristic
271C2×C4×D5#6712yes—
272C2×C4×D5#6711yescharacteristic
273C2×C4×D5#6712yes—
274C2×C4×D5C22×D311yescharacteristic
275C2×C4×D5C22×D312yes—
276C2×Dic10—21no—
277C2×Dic10C2×Dic311yescharacteristic, complemented
278#704—64no—
279C2×#170—62no—
280C4⋊AGL(1,𝔽5)—34no—
281C4⋊AGL(1,𝔽5)—64no—
282C4⋊AGL(1,𝔽5)—62no—
283#700—64no—
284D5⋊C8—34no—
285D5⋊C8—62no—
286C22×#41—51no—
287C22×M16—151no—
288C22×C4⋊C4—151no—
289#417—158no—
290C2×#103—152no—
291C2×#102—152no—
292C22×C3×C5—22no—
293C22×C3×C5—22no—
294C22×C3×C5—42no—
295C22×C3×C5C2×C22⋊C412yes—
296C22×C3×C5C2×C22⋊C411yescharacteristic
297C2×C3×D5—22no—
298C2×C3×D5—22no—
299C2×C3×D5—22no—
300C2×C3×D5—24no—
301C2×C3×D5—22no—
302C2×C3×D5—42no—
303C2×C3×D5—42no—
304C2×C3×D5—42no—
305C2×C3×D5—44no—
306C2×C3×D5C2×C22⋊C412yes—
307C2×C3×D5C2×C22⋊C411yescharacteristic
308C2×C3×D5AGL(1,ℤ/8)12yes—
309C2×C3×D5#13712yes—
310C2×C3×D5C22×D411yescharacteristic
311ΓL(1,𝔽16)—44no—
312C3×C4×C5—22no—
313C3×C4×C5C2×C22⋊C411yescharacteristic
314C3×C4×C5C2×C22⋊C412yes—
315C3×C4×C5C23×C411yescharacteristic
316C3×Dic5—22no—
317C3×Dic5C2×C22⋊C411yescharacteristic
318C3×Dic5C2×C22⋊C412yes—
319C3×Dic5C22×D411yescharacteristic
320C24×C3—51no—
321C24×C3—101no—
322C3×#41—22no—
323C3×#41—54no—
324C3×#41—54no—
325C3×#41—54no—
326C3×#41—104no—
327C3×#41—104no—
328C3×#41—104no—
329C3×#41—104no—
330C3×#41—102no—
331C3×#41—102no—
332C3×#41—102no—
333C3×#41C2×AGL(1,𝔽5)14yescomplemented
334C2×C3×Q8—52no—
335C2×C3×Q8—52no—
336C2×C3×Q8—51no—
337C2×C3×Q8—101no—
338C2×C3×Q8—101no—
339C2×C3×Q8—101no—
340C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
341C2×C3×D4—21no—
342C2×C3×D4—52no—
343C2×C3×D4—52no—
344C2×C3×D4—51no—
345C2×C3×D4—101no—
346C2×C3×D4—101no—
347C2×C3×D4—101no—
348C2×C3×D4—101no—
349C2×C3×D4—104no—
350C2×C3×D4—104no—
351C2×C3×D4—101no—
352C2×C3×D4—101no—
353C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
354C22×C3×C4—21no—
355C22×C3×C4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—52no—
358C22×C3×C4—51no—
359C22×C3×C4—52no—
360C22×C3×C4—51no—
361C22×C3×C4—52no—
362C22×C3×C4—51no—
363C22×C3×C4—52no—
364C22×C3×C4—101no—
365C22×C3×C4—104no—
366C22×C3×C4—104no—
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
371C22×Dic3—102no—
372C22×Dic3—104no—
373C22×Dic3—204no—
374C4⋊Dic3—54no—
375C4⋊Dic3—104no—
376C4⋊Dic3—102no—
377#208—104no—
378#208—104no—
379C2×C3⋊C8—54no—
380C2×C3⋊C8—102no—
381C2×C3⋊C8—102no—
382C23×C5—21no—
383C23×C5#21711yescharacteristic
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—21no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5#21711yescharacteristic
392C22×D5#21712yes—
393C22×D5C2×#6712yes—
394C22×D5C2×#6711yescharacteristic
395C2×AGL(1,𝔽5)—64no—
396C2×AGL(1,𝔽5)—128no—
397C2×AGL(1,𝔽5)—124no—
398C5×Q8—21no—
399C5×Q8C22×Dic312yescomplemented
400C5×D4—24no—
401C5×D4—21no—
402C5×D4C22×Dic312yescomplemented
403C2×C4×C5—21no—
404C2×C4×C5—24no—
405C2×C4×C5#21711yescharacteristic
406C2×C4×C5#21712yes—
407C2×C4×C5C22×Dic311yescharacteristic
408C2×C4×C5C22×Dic312yes—
409C22⋊D5—24no—
410C22⋊D5—24no—
411C22⋊D5—22no—
412C22⋊D5—22no—
413C2×Dic5—21no—
414C2×Dic5—24no—
415C2×Dic5#21711yescharacteristic
416C2×Dic5#21712yes—
417C2×Dic5C2×#6711yescharacteristic
418C2×Dic5C2×#6712yes—
419D20—24no—
420D20—21no—
421D20C22×Dic312yescomplemented
422C4×D5—22no—
423C4×D5—22no—
424C4×D5—24no—
425C4×D5—24no—
426C4×D5#21712yes—
427C4×D5#21712yes—
428C4×D5#21712yes—
429C4×D5C22×Dic311yescharacteristic
430C4×D5C22×Dic312yes—
431C4×D5C2×#6712yes—
432C4×D5C2×#6711yescharacteristic
433C4×D5C2×#6711yescharacteristic
434C4×D5C2×#6712yes—
435C4×D5C23×D311yescharacteristic
436Dic10—21no—
437Dic10—22no—
438Dic10—22no—
439Dic10C22×Dic312yescomplemented
440#170—64no—
441C2×#41—54no—
442C2×#41—54no—
443C2×#41—51no—
444C2×#41—51no—
445C2×#41—51no—
446C2×#41—101no—
447C2×#41—101no—
448C2×#41—102no—
449C2×#41—102no—
450C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
451C22×Q8—51no—
452C22×D4—51no—
453C22×D4—101no—
454C23×C4—51no—
455C23×C4—101no—
456C23×C4—301no—
457C2×M16—154no—
458C2×M16—301no—
459C2×M16—302no—
460C2×M16—301no—
461C22×C8—152no—
462C2×C4⋊C4—152no—
463C2×C4⋊C4—154no—
464C2×C4⋊C4—301no—
465C2×C4⋊C4—302no—
466#103—158no—
467#102—158no—
468C2×C3×C5—22no—
469C2×C3×C5—42no—
470C2×C3×C5#41712yescomplemented
471C2×C3×C5C22×C22⋊C411yescharacteristic
472C3×D5—22no—
473C3×D5—42no—
474C3×D5#41712yescomplemented
475C3×D5C2×AGL(1,ℤ/8)11yescharacteristic
476C3×D5C2×#13711yescharacteristic
477C23×C3—21no—
478C23×C3—51no—
479C23×C3—52no—
480C23×C3—51no—
481C23×C3—52no—
482C23×C3—102no—
483C23×C3—102no—
484C23×C3—102no—
485C23×C3—102no—
486C23×C3—101no—
487C23×C3—202no—
488C23×C3—202no—
489C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
490C3×Q8—21no—
491C3×Q8—52no—
492C3×Q8—102no—
493C3×Q8—102no—
494C3×Q8—101no—
495C3×Q8C22×AGL(1,𝔽5)12yescomplemented
496C3×D4—24no—
497C3×D4—21no—
498C3×D4—52no—
499C3×D4—104no—
500C3×D4—102no—
501C3×D4—102no—
502C3×D4—104no—
503C3×D4—104no—
504C3×D4—101no—
505C3×D4C22×AGL(1,𝔽5)12yescomplemented
506C2×C3×C4—21no—
507C2×C3×C4—24no—
508C2×C3×C4—51no—
509C2×C3×C4—52no—
510C2×C3×C4—51no—
511C2×C3×C4—52no—
512C2×C3×C4—52no—
513C2×C3×C4—52no—
514C2×C3×C4—52no—
515C2×C3×C4—51no—
516C2×C3×C4—52no—
517C2×C3×C4—52no—
518C2×C3×C4—51no—
519C2×C3×C4—51no—
520C2×C3×C4—52no—
521C2×C3×C4—51no—
522C2×C3×C4—104no—
523C2×C3×C4—102no—
524C2×C3×C4—102no—
525C2×C3×C4—104no—
526C2×C3×C4—101no—
527C2×C3×C4—104no—
528C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
529C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
530C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
531C2×C3×C4C22×AGL(1,𝔽5)12yes—
532C2×Dic3—104no—
533C2×Dic3—204no—
534C2×Dic3—208no—
535C3⋊C8—104no—
536C22×C5—22no—
537C22×C5—22no—
538C22×C5—42no—
539C22×C5C2×#21712yes—
540C22×C5C2×#21711yescharacteristic
541C2×D5—22no—
542C2×D5—24no—
543C2×D5—22no—
544C2×D5—22no—
545C2×D5—22no—
546C2×D5—42no—
547C2×D5—44no—
548C2×D5—42no—
549C2×D5—42no—
550C2×D5#94912yes—
551C2×D5#95112yes—
552C2×D5C2×#21712yes—
553C2×D5C2×#21711yescharacteristic
554C2×D5C22×#6711yescharacteristic
555AGL(1,𝔽5)—124no—
556C4×C5—22no—
557C4×C5C2×#21711yescharacteristic
558C4×C5C2×#21712yes—
559C4×C5C23×Dic311yescharacteristic
560Dic5—22no—
561Dic5C2×#21711yescharacteristic
562Dic5C2×#21712yes—
563Dic5C22×#6711yescharacteristic
564C24—51no—
565C24—101no—
566#41—22no—
567#41—54no—
568#41—54no—
569#41—54no—
570#41—104no—
571#41—104no—
572#41—104no—
573#41—104no—
574#41—102no—
575#41—102no—
576#41—102no—
577#41C2×ΓL(1,𝔽16)14yescomplemented
578C2×Q8—52no—
579C2×Q8—52no—
580C2×Q8—51no—
581C2×Q8—101no—
582C2×Q8—101no—
583C2×Q8—101no—
584C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic, complemented
585C2×D4—21no—
586C2×D4—52no—
587C2×D4—52no—
588C2×D4—51no—
589C2×D4—101no—
590C2×D4—101no—
591C2×D4—101no—
592C2×D4—101no—
593C2×D4—104no—
594C2×D4—104no—
595C2×D4—101no—
596C2×D4—101no—
597C2×D4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
598C22×C4—21no—
599C22×C4—51no—
600C22×C4—51no—
601C22×C4—52no—
602C22×C4—52no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—52no—
606C22×C4—52no—
607C22×C4—51no—
608C22×C4—101no—
609C22×C4—104no—
610C22×C4—104no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—302no—
615C22×C4—304no—
616C22×C4—604no—
617C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
618M16—304no—
619M16—304no—
620C2×C8—154no—
621C2×C8—302no—
622C2×C8—302no—
623C4⋊C4—154no—
624C4⋊C4—304no—
625C4⋊C4—302no—
626C3×C5C2×#41711yescharacteristic, complemented, Hall
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—42no—
630C22×C3—52no—
631C22×C3—52no—
632C22×C3—51no—
633C22×C3—51no—
634C22×C3—52no—
635C22×C3—102no—
636C22×C3—102no—
637C22×C3—104no—
638C22×C3—102no—
639C22×C3—102no—
640C22×C3—202no—
641C22×C3—202no—
642C22×C3—204no—
643C22×C3—202no—
644C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
645C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
646C3×C4—22no—
647C3×C4—52no—
648C3×C4—51no—
649C3×C4—51no—
650C3×C4—102no—
651C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
652C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
653C3×C4C23×AGL(1,𝔽5)11yescharacteristic
654Dic3—204no—
655C2×C5—22no—
656C2×C5—42no—
657C2×C5#523212yescomplemented
658C2×C5C22×#21711yescharacteristic
659D5—22no—
660D5—42no—
661D5#523212yescomplemented
662D5C2×#94911yescharacteristic
663D5C2×#95111yescharacteristic
664C23—21no—
665C23—51no—
666C23—52no—
667C23—52no—
668C23—51no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—101no—
674C23—202no—
675C23—202no—
676C23#676311yescharacteristic
677Q8—21no—
678Q8—52no—
679Q8—102no—
680Q8—102no—
681Q8—101no—
682Q8C22×ΓL(1,𝔽16)12yescomplemented
683D4—24no—
684D4—21no—
685D4—52no—
686D4—104no—
687D4—102no—
688D4—102no—
689D4—104no—
690D4—104no—
691D4—101no—
692D4C22×ΓL(1,𝔽16)12yescomplemented
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—51no—
698C2×C4—51no—
699C2×C4—52no—
700C2×C4—51no—
701C2×C4—51no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—51no—
707C2×C4—51no—
708C2×C4—52no—
709C2×C4—104no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—104no—
713C2×C4—101no—
714C2×C4—104no—
715C2×C4—304no—
716C2×C4—604no—
717C2×C4—608no—
718C2×C4#676312yes—
719C2×C4#676311yescharacteristic
720C2×C4C22×ΓL(1,𝔽16)12yes—
721C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
722C8—304no—
723C2×C3—22no—
724C2×C3—42no—
725C2×C3—51no—
726C2×C3—51no—
727C2×C3—52no—
728C2×C3—102no—
729C2×C3—202no—
730C2×C3#6579312yescomplemented
731C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
732C5C2×#523211yescharacteristic, complemented, Sylow
733C22—22no—
734C22—22no—
735C22—42no—
736C22—52no—
737C22—52no—
738C22—51no—
739C22—51no—
740C22—52no—
741C22—102no—
742C22—104no—
743C22—102no—
744C22—102no—
745C22—102no—
746C22—202no—
747C22—204no—
748C22—202no—
749C22—202no—
750C22C2×#676312yes—
751C22C2×#676311yescharacteristic
752C4—22no—
753C4—51no—
754C4—52no—
755C4—51no—
756C4—102no—
757C4—604no—
758C4C2×#676312yes—
759C4C2×#676311yescharacteristic
760C4C23×ΓL(1,𝔽16)11yescharacteristic
761C3C2×#6579311yescharacteristic, complemented, Sylow
762C2—22no—
763C2—42no—
764C2—51no—
765C2—52no—
766C2—51no—
767C2—102no—
768C2—202no—
769C2#1175245212yesdirect product factor
770C2C22×#676311yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC2×C3×C5×#41C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC3×C4×D5C24
hypercenterC2×#41ΓL(1,𝔽16)
hypocenterC3×C5C2×#417
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊ΓL(1,𝔽16)C2semidirect
3. C2×D5⋊#208C2semidirect
4. #11752452C2direct (N × H)
5. C2×#91238C2semidirect
6. C2×#91236C2semidirect
9. C2×C3×C5×#41C4semidirect
12. C3×D5×#41C4semidirect
14. C2×C3×#713C4semidirect
17. C2×C3×#711C4semidirect
21. C2×C3×#709C4semidirect
28. C2×C4⋊ΓL(1,𝔽16)C22semidirect
30. D5⋊#208C22semidirect
33. #91238C22semidirect
34. #91236C22semidirect
48. C3×C5×#41C2×C4semidirect
49. C2×C3×C5×Q8C2×C4semidirect
51. C2×C3×C5×D4C2×C4semidirect
60. C3×#713C2×C4semidirect
63. C3×Q8×D5C2×C4semidirect
68. C3×#711C2×C4semidirect
73. C3×D4×D5C2×C4semidirect
78. C3×#709C2×C4semidirect
80. C2×C3×D20C2×C4semidirect
95. C2×C3×Dic10C2×C4semidirect
111. C2×C5×#41Dic3semidirect
114. D5×#41Dic3semidirect
116. C2×#713Dic3semidirect
119. C2×#711Dic3semidirect
123. C2×#709Dic3semidirect
155. C3×C5×Q8C22×C4semidirect
158. C3×C5×D4C22×C4semidirect
177. C3×D20C22×C4semidirect
195. C3×Dic10C22×C4semidirect
206. C2×C3×#41AGL(1,𝔽5)semidirect
230. C5×#41C2×Dic3semidirect
231. C2×C5×Q8C2×Dic3semidirect
233. C2×C5×D4C2×Dic3semidirect
242. #713C2×Dic3semidirect
245. Q8×D5C2×Dic3semidirect
250. #711C2×Dic3semidirect
255. D4×D5C2×Dic3semidirect
260. #709C2×Dic3semidirect
262. C2×D20C2×Dic3semidirect
277. C2×Dic10C2×Dic3semidirect
333. C3×#41C2×AGL(1,𝔽5)semidirect
340. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
353. C2×C3×D4C2×AGL(1,𝔽5)semidirect
399. C5×Q8C22×Dic3semidirect
402. C5×D4C22×Dic3semidirect
421. D20C22×Dic3semidirect
439. Dic10C22×Dic3semidirect
450. C2×#41ΓL(1,𝔽16)semidirect
470. C2×C3×C5#417semidirect
474. C3×D5#417semidirect
495. C3×Q8C22×AGL(1,𝔽5)semidirect
505. C3×D4C22×AGL(1,𝔽5)semidirect
577. #41C2×ΓL(1,𝔽16)semidirect
584. C2×Q8C2×ΓL(1,𝔽16)semidirect
597. C2×D4C2×ΓL(1,𝔽16)semidirect
626. C3×C5C2×#417semidirect
657. C2×C5#5232semidirect
661. D5#5232semidirect
682. Q8C22×ΓL(1,𝔽16)semidirect
692. D4C22×ΓL(1,𝔽16)semidirect
730. C2×C3#65793semidirect
732. C5C2×#5232semidirect
761. C3C2×#65793semidirect
769. C2#11752452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C22×C4⋊ΓL(1,𝔽16)2
C2×D5⋊#2082
#117524522
C2×#912382
C2×#912362
C2×#657933
C2×#52325