Finite Group Databasebeta

← C3×D5⋊#413 #14412113

Subgroups — C3×D5⋊#413 #14412113

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×C3×D5⋊M16C212yesmaximal, complemented
3C3×D5⋊#101C212yesmaximal, complemented
4C3×D5⋊#100C212yesmaximal, complemented
5C3×#65777C214yesmaximal, complemented
6C3×#65761C214yesmaximal, complemented
7D5⋊#413C311yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C5×#41C411yescharacteristic
9C3×D5×#41—22no—
10C3×D5×#41—22no—
11C3×D5×#41—22no—
12C3×D5×#41—22no—
13C2×C3×#713C411yescharacteristic
14C2×C3×Q8×D5C2211yescharacteristic
15C2×C3×#711C411yescharacteristic
16C2×C3×#711C2212yes—
17C2×C3×D4×D5C412yes—
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×#709C411yescharacteristic
20C2×C3×#709C2212yes—
21C22×C3×C4×D5C412yes—
22C22×C3×C4×D5C2211yescharacteristic
23C2×C3×#704C2214yescomplemented
24C3×D5⋊M16—22no—
25C3×D5⋊M16—22no—
26C3×D5⋊M16C2214yes—
27C3×D5⋊M16C2214yescomplemented
28C2×C3×#700—22no—
29C2×C3×D5⋊C8—22no—
30C3×#4013C2218yescomplemented
31C3×#4005C2218yescomplemented
32C2×C3×#413—51nomaximal, Hall
33C2×D5×#41C2×C311yescharacteristic
34C2×D5⋊M16C2×C312yescomplemented
35D5⋊#101C2×C312yescomplemented
36D5⋊#100C2×C312yescomplemented
37#65777C2×C314yescomplemented
38#65761C2×C314yescomplemented
39C23×C3×D5C2×C412yes—
40C23×C3×D5C2×C411yescharacteristic
41C3×C5×#41—22no—
42C3×C5×#41—22no—
43C2×C3×C5×Q8C2×C411yescharacteristic
44C2×C3×C5×D4C2×C412yes—
45C2×C3×C5×D4C2×C411yescharacteristic
46C22×C3×C4×C5C2×C412yes—
47C22×C3×C4×C5C2×C411yescharacteristic
48C2×C3×C22⋊D5C2×C412yes—
49C2×C3×C22⋊D5C2×C412yes—
50C2×C3×C22⋊D5C2312yes—
51C22×C3×Dic5C2×C412yes—
52C22×C3×Dic5C2311yescharacteristic
53C3×#713—22no—
54C3×#713—22no—
55C3×Q8×D5—22no—
56C3×Q8×D5—22no—
57C3×#711—24no—
58C3×#711—24no—
59C3×#711—22no—
60C3×#711—22no—
61C3×D4×D5—24no—
62C3×D4×D5—24no—
63C3×D4×D5—22no—
64C3×D4×D5—22no—
65C3×#709—22no—
66C3×#709—22no—
67C3×#709—24no—
68C3×#709—24no—
69C2×C3×D20C2×C411yescharacteristic
70C2×C3×D20C2×C412yes—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2×C412yes—
76C2×C3×C4×D5C2×C412yes—
77C2×C3×C4×D5C2×C412yes—
78C2×C3×C4×D5C2×C411yescharacteristic
79C2×C3×C4×D5C2×C411yescharacteristic
80C2×C3×C4×D5D412yes—
81C2×C3×C4×D5D412yes—
82C2×C3×C4×D5D412yes—
83C2×C3×C4×D5D412yes—
84C2×C3×C4×D5C2311yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×Dic10C2×C411yescharacteristic
87C2×C3×Dic10C2312yes—
88C3×#704—24no—
89C3×#704C2318yes—
90C2×C3×#170—24no—
91C3×#700—24no—
92C3×#700—24no—
93C3×D5⋊C8—24no—
94C3×D5⋊C8—24no—
95C22×C3×#41—51no—
96C22×C3×M16—52no—
97C3×#413—54no—
98C3×#413—54no—
99C2×C3×#101—52no—
100C2×C3×#100—52no—
101C2×C5×#41C3×C411yescharacteristic
102D5×#41—22no—
103D5×#41—22no—
104D5×#41—22no—
105D5×#41—22no—
106C2×#713C3×C411yescharacteristic
107C2×Q8×D5C22×C311yescharacteristic
108C2×#711C3×C411yescharacteristic
109C2×#711C22×C312yes—
110C2×D4×D5C3×C412yes—
111C2×D4×D5C22×C311yescharacteristic
112C2×#709C3×C411yescharacteristic
113C2×#709C22×C312yes—
114C22×C4×D5C3×C412yes—
115C22×C4×D5C22×C311yescharacteristic
116C2×#704C22×C314yescomplemented
117D5⋊M16—22no—
118D5⋊M16—22no—
119D5⋊M16C22×C314yes—
120D5⋊M16C22×C314yescomplemented
121C2×#700—22no—
122C2×D5⋊C8—22no—
123#4013C22×C318yescomplemented
124#4005C22×C318yescomplemented
125C2×#413—51noSylow
126C23×C3×C5C22×C412yes—
127C23×C3×C5C22×C411yescharacteristic
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5—42no—
131C22×C3×D5—44no—
132C22×C3×D5C22⋊C412yes—
133C22×C3×D5C22⋊C412yes—
134C22×C3×D5C22×C411yescharacteristic
135C22×C3×D5C22×C412yes—
136C22×C3×D5C22×C411yescharacteristic
137C3×C5×Q8—22no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22⋊C412yes—
143C2×C3×C4×C5C22⋊C412yes—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C22×C411yescharacteristic
146C2×C3×C4×C5C22×C411yescharacteristic
147C3×C22⋊D5—24no—
148C3×C22⋊D5—24no—
149C3×C22⋊D5—24no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5C22×C412yes—
153C2×C3×Dic5C22×C411yescharacteristic
154C2×C3×Dic5C2×D412yes—
155C2×C3×Dic5C2×D412yes—
156C2×C3×Dic5C2411yescharacteristic
157C3×D20—24no—
158C3×D20—22no—
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5—22no—
163C3×C4×D5—22no—
164C3×C4×D5—22no—
165C3×C4×D5C22⋊C411yescharacteristic
166C3×C4×D5C22⋊C411yescharacteristic
167C3×C4×D5C22⋊C411yescharacteristic
168C3×C4×D5C22⋊C411yescharacteristic
169C3×C4×D5C22⋊C412yes—
170C3×C4×D5C22⋊C412yes—
171C3×C4×D5C2×D412yes—
172C3×C4×D5C2×D412yes—
173C3×C4×D5C2×D412yes—
174C3×C4×D5C2×D412yes—
175C3×Dic10—22no—
176C3×Dic10—24no—
177C3×#170—28no—
178C2×C3×#41—51no—
179C2×C3×#41—51no—
180C2×C3×#41—52no—
181C2×C3×#41—52no—
182C2×C3×#41—51no—
183C2×C3×#41—102no—
184C2×C3×#41—102no—
185C2×C3×#41—102no—
186C2×C3×#41—102no—
187C2×C3×#41AGL(1,𝔽5)11yescharacteristic
188C22×C3×Q8—51no—
189C22×C3×D4—52no—
190C22×C3×D4—51no—
191C23×C3×C4—51no—
192C23×C3×C4—52no—
193C2×C3×M16—54no—
194C2×C3×M16—54no—
195C2×C3×M16—54no—
196C2×C3×M16—102no—
197C2×C3×M16—102no—
198C2×C3×M16—102no—
199C22×C3×C8—102no—
200C3×#101—58no—
201C3×#100—58no—
202C23×D5C2×C3×C412yes—
203C23×D5C2×C3×C411yescharacteristic
204C5×#41—22no—
205C5×#41—22no—
206C2×C5×Q8C2×C3×C411yescharacteristic
207C2×C5×D4C2×C3×C412yes—
208C2×C5×D4C2×C3×C411yescharacteristic
209C22×C4×C5C2×C3×C412yes—
210C22×C4×C5C2×C3×C411yescharacteristic
211C2×C22⋊D5C2×C3×C412yes—
212C2×C22⋊D5C2×C3×C412yes—
213C2×C22⋊D5C23×C312yes—
214C22×Dic5C2×C3×C412yes—
215C22×Dic5C23×C311yescharacteristic
216#713—22no—
217#713—22no—
218Q8×D5—22no—
219Q8×D5—22no—
220#711—24no—
221#711—24no—
222#711—22no—
223#711—22no—
224D4×D5—24no—
225D4×D5—24no—
226D4×D5—22no—
227D4×D5—22no—
228#709—22no—
229#709—22no—
230#709—24no—
231#709—24no—
232C2×D20C2×C3×C411yescharacteristic
233C2×D20C2×C3×C412yes—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—22no—
238C2×C4×D5C2×C3×C412yes—
239C2×C4×D5C2×C3×C412yes—
240C2×C4×D5C2×C3×C412yes—
241C2×C4×D5C2×C3×C411yescharacteristic
242C2×C4×D5C2×C3×C411yescharacteristic
243C2×C4×D5C3×D412yes—
244C2×C4×D5C3×D412yes—
245C2×C4×D5C3×D412yes—
246C2×C4×D5C3×D412yes—
247C2×C4×D5C23×C311yescharacteristic
248C2×C4×D5C23×C311yescharacteristic
249C2×Dic10C2×C3×C411yescharacteristic
250C2×Dic10C23×C312yes—
251#704—24no—
252#704C23×C318yes—
253C2×#170—24no—
254#700—24no—
255#700—24no—
256D5⋊C8—24no—
257D5⋊C8—24no—
258C22×#41—51no—
259C22×M16—52no—
260#413—54no—
261#413—54no—
262C2×#101—52no—
263C2×#100—52no—
264C22×C3×C5—22no—
265C22×C3×C5—41no—
266C22×C3×C5—42no—
267C22×C3×C5C2×C22⋊C412yes—
268C22×C3×C5C23×C411yescharacteristic
269C2×C3×D5—22no—
270C2×C3×D5—24no—
271C2×C3×D5—22no—
272C2×C3×D5—42no—
273C2×C3×D5—41no—
274C2×C3×D5—44no—
275C2×C3×D5—44no—
276C2×C3×D5—42no—
277C2×C3×D5C2×C22⋊C411yescharacteristic
278C2×C3×D5C2×C22⋊C412yes—
279C2×C3×D5C2×C22⋊C411yescharacteristic
280C3×C4×C5—22no—
281C3×C4×C5C2×C22⋊C412yes—
282C3×C4×C5C2×C22⋊C411yescharacteristic
283C3×C4×C5C2×C22⋊C411yescharacteristic
284C3×Dic5—22no—
285C3×Dic5C2×C22⋊C411yescharacteristic
286C3×Dic5C2×C22⋊C411yescharacteristic
287C3×Dic5C22×D412yes—
288C24×C3—51no—
289C24×C3—52no—
290C3×#41—22no—
291C3×#41—22no—
292C3×#41—104no—
293C3×#41—104no—
294C3×#41—104no—
295C3×#41—104no—
296C3×#41—102no—
297C3×#41—102no—
298C3×#41—102no—
299C3×#41—102no—
300C3×#41—102no—
301C3×#41—102no—
302C2×C3×Q8—52no—
303C2×C3×Q8—51no—
304C2×C3×Q8—102no—
305C2×C3×Q8—102no—
306C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
307C2×C3×D4—52no—
308C2×C3×D4—52no—
309C2×C3×D4—52no—
310C2×C3×D4—52no—
311C2×C3×D4—51no—
312C2×C3×D4—102no—
313C2×C3×D4—102no—
314C2×C3×D4—104no—
315C2×C3×D4—104no—
316C2×C3×D4C2×AGL(1,𝔽5)12yes—
317C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
318C22×C3×C4—51no—
319C22×C3×C4—52no—
320C22×C3×C4—52no—
321C22×C3×C4—52no—
322C22×C3×C4—52no—
323C22×C3×C4—51no—
324C22×C3×C4—51no—
325C22×C3×C4—51no—
326C22×C3×C4—51no—
327C22×C3×C4—52no—
328C22×C3×C4—52no—
329C22×C3×C4—52no—
330C22×C3×C4—52no—
331C22×C3×C4—102no—
332C22×C3×C4—102no—
333C22×C3×C4—102no—
334C22×C3×C4—102no—
335C22×C3×C4C2×AGL(1,𝔽5)12yes—
336C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
337C3×M16—58no—
338C3×M16—104no—
339C3×M16—104no—
340C3×M16—104no—
341C2×C3×C8—104no—
342C2×C3×C8—104no—
343C2×C3×C8—104no—
344C23×C5C22×C3×C412yes—
345C23×C5C22×C3×C411yescharacteristic
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—42no—
349C22×D5—44no—
350C22×D5C3×C22⋊C412yes—
351C22×D5C3×C22⋊C412yes—
352C22×D5C22×C3×C411yescharacteristic
353C22×D5C22×C3×C412yes—
354C22×D5C22×C3×C411yescharacteristic
355C5×Q8—22no—
356C5×D4—24no—
357C5×D4—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5C3×C22⋊C412yes—
361C2×C4×C5C3×C22⋊C412yes—
362C2×C4×C5C22×C3×C412yes—
363C2×C4×C5C22×C3×C411yescharacteristic
364C2×C4×C5C22×C3×C411yescharacteristic
365C22⋊D5—24no—
366C22⋊D5—24no—
367C22⋊D5—24no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5C22×C3×C412yes—
371C2×Dic5C22×C3×C411yescharacteristic
372C2×Dic5C2×C3×D412yes—
373C2×Dic5C2×C3×D412yes—
374C2×Dic5C24×C311yescharacteristic
375D20—24no—
376D20—22no—
377C4×D5—22no—
378C4×D5—22no—
379C4×D5—22no—
380C4×D5—22no—
381C4×D5—22no—
382C4×D5—22no—
383C4×D5C3×C22⋊C411yescharacteristic
384C4×D5C3×C22⋊C411yescharacteristic
385C4×D5C3×C22⋊C411yescharacteristic
386C4×D5C3×C22⋊C411yescharacteristic
387C4×D5C3×C22⋊C412yes—
388C4×D5C3×C22⋊C412yes—
389C4×D5C2×C3×D412yes—
390C4×D5C2×C3×D412yes—
391C4×D5C2×C3×D412yes—
392C4×D5C2×C3×D412yes—
393Dic10—22no—
394Dic10—24no—
395#170—28no—
396C2×#41—51no—
397C2×#41—51no—
398C2×#41—52no—
399C2×#41—51no—
400C2×#41—52no—
401C2×#41—102no—
402C2×#41—102no—
403C2×#41—102no—
404C2×#41—102no—
405C2×#41C3×AGL(1,𝔽5)11yescharacteristic
406C22×Q8—51no—
407C22×D4—52no—
408C22×D4—51no—
409C23×C4—51no—
410C23×C4—52no—
411C2×M16—54no—
412C2×M16—54no—
413C2×M16—54no—
414C2×M16—102no—
415C2×M16—102no—
416C2×M16—102no—
417C22×C8—102no—
418#101—58no—
419#100—58no—
420C2×C3×C5—21no—
421C2×C3×C5—22no—
422C2×C3×C5—42no—
423C2×C3×C5C22×C22⋊C411yescharacteristic
424C3×D5—21no—
425C3×D5—22no—
426C3×D5—42no—
427C3×D5#41312yescomplemented
428C23×C3—52no—
429C23×C3—51no—
430C23×C3—52no—
431C23×C3—51no—
432C23×C3—52no—
433C23×C3—102no—
434C23×C3—102no—
435C23×C3—202no—
436C23×C3—204no—
437C23×C3C22×AGL(1,𝔽5)12yes—
438C23×C3C22×AGL(1,𝔽5)11yescharacteristic
439C3×Q8—22no—
440C3×Q8—104no—
441C3×Q8—102no—
442C3×D4—24no—
443C3×D4—22no—
444C3×D4—104no—
445C3×D4—104no—
446C3×D4—104no—
447C3×D4—104no—
448C3×D4—102no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—52no—
452C2×C3×C4—52no—
453C2×C3×C4—51no—
454C2×C3×C4—51no—
455C2×C3×C4—51no—
456C2×C3×C4—51no—
457C2×C3×C4—52no—
458C2×C3×C4—52no—
459C2×C3×C4—52no—
460C2×C3×C4—52no—
461C2×C3×C4—52no—
462C2×C3×C4—51no—
463C2×C3×C4—51no—
464C2×C3×C4—52no—
465C2×C3×C4—52no—
466C2×C3×C4—102no—
467C2×C3×C4—102no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—102no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
475C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
476C2×C3×C4C22×AGL(1,𝔽5)12yes—
477C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
478C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
479C3×C8—108no—
480C22×C5—22no—
481C22×C5—41no—
482C22×C5—42no—
483C22×C5C2×C3×C22⋊C412yes—
484C22×C5C23×C3×C411yescharacteristic
485C2×D5—22no—
486C2×D5—24no—
487C2×D5—22no—
488C2×D5—42no—
489C2×D5—41no—
490C2×D5—44no—
491C2×D5—44no—
492C2×D5—42no—
493C2×D5C2×C3×C22⋊C411yescharacteristic
494C2×D5C2×C3×C22⋊C412yes—
495C2×D5C2×C3×C22⋊C411yescharacteristic
496C4×C5—22no—
497C4×C5C2×C3×C22⋊C412yes—
498C4×C5C2×C3×C22⋊C411yescharacteristic
499C4×C5C2×C3×C22⋊C411yescharacteristic
500Dic5—22no—
501Dic5C2×C3×C22⋊C411yescharacteristic
502Dic5C2×C3×C22⋊C411yescharacteristic
503Dic5C22×C3×D412yes—
504C24—51no—
505C24—52no—
506#41—22no—
507#41—22no—
508#41—104no—
509#41—104no—
510#41—104no—
511#41—104no—
512#41—102no—
513#41—102no—
514#41—102no—
515#41—102no—
516#41—102no—
517#41—102no—
518C2×Q8—52no—
519C2×Q8—51no—
520C2×Q8—102no—
521C2×Q8—102no—
522C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
523C2×D4—52no—
524C2×D4—52no—
525C2×D4—52no—
526C2×D4—52no—
527C2×D4—51no—
528C2×D4—102no—
529C2×D4—102no—
530C2×D4—104no—
531C2×D4—104no—
532C2×D4C2×C3×AGL(1,𝔽5)12yes—
533C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
534C22×C4—51no—
535C22×C4—52no—
536C22×C4—52no—
537C22×C4—52no—
538C22×C4—52no—
539C22×C4—51no—
540C22×C4—51no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—52no—
544C22×C4—52no—
545C22×C4—52no—
546C22×C4—52no—
547C22×C4—102no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—102no—
551C22×C4C2×C3×AGL(1,𝔽5)12yes—
552C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
553M16—58no—
554M16—104no—
555M16—104no—
556M16—104no—
557C2×C8—104no—
558C2×C8—104no—
559C2×C8—104no—
560C3×C5C2×#41311yescharacteristic, complemented, Hall
561C22×C3—22no—
562C22×C3—41no—
563C22×C3—42no—
564C22×C3—51no—
565C22×C3—51no—
566C22×C3—52no—
567C22×C3—104no—
568C22×C3—102no—
569C22×C3—102no—
570C22×C3—201no—
571C22×C3—202no—
572C22×C3—202no—
573C22×C3—204no—
574C22×C3—204no—
575C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
576C22×C3C23×AGL(1,𝔽5)11yescharacteristic
577C3×C4—22no—
578C3×C4—51no—
579C3×C4—51no—
580C3×C4—52no—
581C3×C4—102no—
582C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
583C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
584C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
585C2×C5—21no—
586C2×C5—22no—
587C2×C5—42no—
588C2×C5C22×C3×C22⋊C411yescharacteristic
589D5—21no—
590D5—22no—
591D5—42no—
592D5C3×#41312yescomplemented
593C23—52no—
594C23—51no—
595C23—52no—
596C23—51no—
597C23—52no—
598C23—102no—
599C23—102no—
600C23—202no—
601C23—204no—
602C23C22×C3×AGL(1,𝔽5)12yes—
603C23C22×C3×AGL(1,𝔽5)11yescharacteristic
604Q8—22no—
605Q8—104no—
606Q8—102no—
607D4—24no—
608D4—22no—
609D4—104no—
610D4—104no—
611D4—104no—
612D4—104no—
613D4—102no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—52no—
617C2×C4—52no—
618C2×C4—51no—
619C2×C4—51no—
620C2×C4—52no—
621C2×C4—52no—
622C2×C4—52no—
623C2×C4—52no—
624C2×C4—51no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—51no—
628C2×C4—52no—
629C2×C4—52no—
630C2×C4—52no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
640C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
641C2×C4C22×C3×AGL(1,𝔽5)12yes—
642C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
643C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
644C8—108no—
645C2×C3—21no—
646C2×C3—22no—
647C2×C3—42no—
648C2×C3—52no—
649C2×C3—101no—
650C2×C3—102no—
651C2×C3—202no—
652C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
653C5C2×C3×#41311yescharacteristic, complemented, Sylow
654C22—22no—
655C22—41no—
656C22—42no—
657C22—51no—
658C22—51no—
659C22—52no—
660C22—102no—
661C22—104no—
662C22—102no—
663C22—201no—
664C22—202no—
665C22—202no—
666C22—204no—
667C22—204no—
668C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
669C22C23×C3×AGL(1,𝔽5)11yescharacteristic
670C4—22no—
671C4—52no—
672C4—51no—
673C4—51no—
674C4—102no—
675C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
676C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
677C4C2×C3×C22⋊AGL(1,𝔽5)12yes—
678C3D5⋊#41311yescharacteristic, direct product factor, Sylow
679C2—21no—
680C2—22no—
681C2—42no—
682C2—52no—
683C2—101no—
684C2—102no—
685C2—202no—
686C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC3×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC2×Dic5C24×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C2×C3×#413
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5⋊M16C2semidirect
3. C3×D5⋊#101C2semidirect
4. C3×D5⋊#100C2semidirect
5. C3×#65777C2semidirect
6. C3×#65761C2semidirect
7. D5⋊#413C3direct (N × H)
23. C2×C3×#704C22semidirect
27. C3×D5⋊M16C22semidirect
30. C3×#4013C22semidirect
31. C3×#4005C22semidirect
34. C2×D5⋊M16C2×C3semidirect
35. D5⋊#101C2×C3semidirect
36. D5⋊#100C2×C3semidirect
37. #65777C2×C3semidirect
38. #65761C2×C3semidirect
116. C2×#704C22×C3semidirect
120. D5⋊M16C22×C3semidirect
123. #4013C22×C3semidirect
124. #4005C22×C3semidirect
427. C3×D5#413semidirect
560. C3×C5C2×#413semidirect
592. D5C3×#413semidirect
653. C5C2×C3×#413semidirect
678. C3D5⋊#413direct (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
C2×C3×D5⋊M162
C3×D5⋊#1012
C3×D5⋊#1002
C3×#657772
C3×#657612
D5⋊#4133
C2×C3×#4135