Finite Group Databasebeta

← C2×C3×D5⋊#104 #14412804

Subgroups — C2×C3×D5⋊#104 #14412804

Order 1920.

1712 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C22×C3×C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
4C3×D5⋊#104C218yesmaximal, direct product factor
5C2×C3×#4010C212yesmaximal, complemented
6C2×C3×#4008C212yesmaximal, complemented
7C2×D5⋊#104C311yesmaximal, characteristic, direct product factor, Hall
8C23×C3×AGL(1,𝔽5)—21no—
9C2×C3×C5×#41C411yescharacteristic, complemented
10C3×D5×#41—22no—
11C3×D5×#41—22no—
12C3×D5×#41C414yescomplemented
13C3×D5×#41C2214yes—
14C2×C3×#713C2211yescharacteristic
15C2×C3×Q8×D5C411yescharacteristic, complemented
16C2×C3×#711—21no—
17C2×C3×#711C2211yescharacteristic
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C411yescharacteristic, complemented
20C2×C3×#709—21no—
21C2×C3×#709C411yescharacteristic, complemented
22C22×C3×C4×D5—21no—
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×#704—21no—
25C2×C3×C4×AGL(1,𝔽5)—21no—
26C2×C3×C4×AGL(1,𝔽5)—22no—
27C2×C3×C4×AGL(1,𝔽5)C2212yescomplemented
28C2×C3×C4×AGL(1,𝔽5)C2214yescomplemented
29C3×D5⋊M16—22no—
30C3×D5⋊M16C2214yescomplemented
31C2×C3×#700C2212yescomplemented
32C2×C3×D5⋊C8—21no—
33C3×#4010C2218yescomplemented
34C3×#4008C2218yescomplemented
35C22×C3×#104—51nomaximal, Hall
36C2×D5×#41C2×C311yescharacteristic
37C22×C4×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
38C2×D5⋊M16C2×C311yescharacteristic, complemented
39D5⋊#104C2×C318yesdirect product factor
40C2×#4010C2×C312yescomplemented
41C2×#4008C2×C312yescomplemented
42C23×C3×D5—21no—
43C23×C3×D5D411yescharacteristic
44C22×C3×AGL(1,𝔽5)—28no—
45C22×C3×AGL(1,𝔽5)—22no—
46C22×C3×AGL(1,𝔽5)—24no—
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—21no—
60C3×#713—21no—
61C3×#713C2×C412yescomplemented
62C3×#713C2312yes—
63C3×Q8×D5—22no—
64C3×Q8×D5C2×C414yescomplemented
65C3×#711—24no—
66C3×#711—24no—
67C3×#711—21no—
68C3×#711—21no—
69C3×#711C2×C412yescomplemented
70C3×#711C2312yes—
71C3×D4×D5—24no—
72C3×D4×D5—24no—
73C3×D4×D5—22no—
74C3×D4×D5C2×C414yescomplemented
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
96C3×#704—24no—
97C2×C3×#170—22no—
98C3×C4×AGL(1,𝔽5)—24no—
99C3×C4×AGL(1,𝔽5)—22no—
100C3×C4×AGL(1,𝔽5)C2314yescomplemented
101C3×#700—22no—
102C3×#700C2314yescomplemented
103C3×D5⋊C8—24no—
104C22×C3×#41—51no—
105C22×C3×M16—51no—
106C22×C3×C42—51no—
107C2×C3×#104—52no—
108C2×C3×#104—52no—
109C2×C3×#104—58no—
110C23×AGL(1,𝔽5)—21no—
111C2×C5×#41C3×C411yescharacteristic, complemented
112D5×#41—22no—
113D5×#41—22no—
114D5×#41C3×C414yescomplemented
115D5×#41C22×C314yes—
116C2×#713C22×C311yescharacteristic
117C2×Q8×D5C3×C411yescharacteristic, complemented
118C2×#711—21no—
119C2×#711C22×C311yescharacteristic
120C2×D4×D5—21no—
121C2×D4×D5C3×C411yescharacteristic, complemented
122C2×#709—21no—
123C2×#709C3×C411yescharacteristic, complemented
124C22×C4×D5—21no—
125C22×C4×D5C22×C311yescharacteristic
126C2×#704—21no—
127C2×C4×AGL(1,𝔽5)—21no—
128C2×C4×AGL(1,𝔽5)—22no—
129C2×C4×AGL(1,𝔽5)C22×C314yescomplemented
130C2×C4×AGL(1,𝔽5)C22×C312yescomplemented
131D5⋊M16—22no—
132D5⋊M16C22×C314yescomplemented
133C2×#700C22×C312yescomplemented
134C2×D5⋊C8—21no—
135#4010C22×C318yescomplemented
136#4008C22×C318yescomplemented
137C22×#104—51noSylow
138C23×C3×C5—21no—
139C23×C3×C5C22⋊C411yescharacteristic
140C22×C3×D5—24no—
141C22×C3×D5—21no—
142C22×C3×D5—24no—
143C22×C3×D5—44no—
144C22×C3×D5C22⋊C412yes—
145C22×C3×D5C22⋊C411yescharacteristic
146C22×C3×D5C2×D411yescharacteristic
147C22×C3×D5C2×D412yes—
148C2×C3×AGL(1,𝔽5)—28no—
149C2×C3×AGL(1,𝔽5)—216no—
150C2×C3×AGL(1,𝔽5)—24no—
151C3×C5×Q8—21no—
152C3×C5×Q8C22×C412yescomplemented
153C3×C5×D4—24no—
154C3×C5×D4—21no—
155C3×C5×D4C22×C412yescomplemented
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—24no—
158C2×C3×C4×C5C22⋊C412yes—
159C2×C3×C4×C5C22⋊C411yescharacteristic
160C2×C3×C4×C5C22×C411yescharacteristic
161C2×C3×C4×C5C22×C412yes—
162C3×C22⋊D5—24no—
163C3×C22⋊D5—22no—
164C3×C22⋊D5—22no—
165C3×C22⋊D5—24no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C22⋊C411yescharacteristic
170C2×C3×Dic5C22⋊C412yes—
171C2×C3×Dic5C2×D411yescharacteristic
172C2×C3×Dic5C2×D412yes—
173C3×D20—22no—
174C3×D20—22no—
175C3×D20—21no—
176C3×D20C22×C412yescomplemented
177C3×C4×D5—24no—
178C3×C4×D5—24no—
179C3×C4×D5—22no—
180C3×C4×D5—22no—
181C3×C4×D5C22⋊C412yes—
182C3×C4×D5C22⋊C412yes—
183C3×C4×D5C22⋊C412yes—
184C3×C4×D5C22×C412yes—
185C3×C4×D5C22×C411yescharacteristic
186C3×C4×D5C2×D412yes—
187C3×C4×D5C2×D411yescharacteristic
188C3×C4×D5C2×D412yes—
189C3×C4×D5C2×D411yescharacteristic
190C3×C4×D5C2411yescharacteristic
191C3×Dic10—21no—
192C3×Dic10—24no—
193C3×Dic10C22×C412yescomplemented
194C3×#170—24no—
195C2×C3×#41—54no—
196C2×C3×#41—54no—
197C2×C3×#41—51no—
198C2×C3×#41—51no—
199C2×C3×#41—51no—
200C2×C3×#41—101no—
201C2×C3×#41—101no—
202C2×C3×#41—102no—
203C2×C3×#41—102no—
204C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
205C22×C3×Q8—51no—
206C22×C3×D4—51no—
207C22×C3×D4—101no—
208C23×C3×C4—51no—
209C23×C3×C4—101no—
210C23×C3×C4—101no—
211C2×C3×M16—52no—
212C2×C3×M16—54no—
213C2×C3×M16—102no—
214C2×C3×M16—101no—
215C22×C3×C8—101no—
216C2×C3×C42—52no—
217C2×C3×C42—54no—
218C2×C3×C42—102no—
219C2×C3×C42—101no—
220C3×#104—58no—
221C3×#104—58no—
222C23×D5—21no—
223C23×D5C3×D411yescharacteristic
224C22×AGL(1,𝔽5)—28no—
225C22×AGL(1,𝔽5)—22no—
226C22×AGL(1,𝔽5)—24no—
227C5×#41—22no—
228C5×#41C2×C3×C414yescomplemented
229C2×C5×Q8C2×C3×C411yescharacteristic, complemented
230C2×C5×D4—21no—
231C2×C5×D4C2×C3×C411yescharacteristic, complemented
232C22×C4×C5—21no—
233C22×C4×C5C2×C3×C411yescharacteristic
234C2×C22⋊D5—21no—
235C2×C22⋊D5—21no—
236C2×C22⋊D5—21no—
237C22×Dic5—21no—
238C22×Dic5C3×D411yescharacteristic
239#713—21no—
240#713—21no—
241#713C2×C3×C412yescomplemented
242#713C23×C312yes—
243Q8×D5—22no—
244Q8×D5C2×C3×C414yescomplemented
245#711—24no—
246#711—24no—
247#711—21no—
248#711—21no—
249#711C2×C3×C412yescomplemented
250#711C23×C312yes—
251D4×D5—24no—
252D4×D5—24no—
253D4×D5—22no—
254D4×D5C2×C3×C414yescomplemented
255#709—22no—
256#709—24no—
257#709—24no—
258#709C2×C3×C414yescomplemented
259C2×D20—21no—
260C2×D20C2×C3×C411yescharacteristic, complemented
261C2×C4×D5—21no—
262C2×C4×D5—21no—
263C2×C4×D5—21no—
264C2×C4×D5—24no—
265C2×C4×D5—24no—
266C2×C4×D5C2×C3×C411yescharacteristic
267C2×C4×D5C2×C3×C412yes—
268C2×C4×D5C3×D411yescharacteristic
269C2×C4×D5C3×D412yes—
270C2×C4×D5C3×D411yescharacteristic
271C2×C4×D5C3×D412yes—
272C2×C4×D5C23×C311yescharacteristic
273C2×C4×D5C23×C312yes—
274C2×Dic10—21no—
275C2×Dic10C2×C3×C411yescharacteristic, complemented
276#704—24no—
277C2×#170—22no—
278C4×AGL(1,𝔽5)—24no—
279C4×AGL(1,𝔽5)—22no—
280C4×AGL(1,𝔽5)C23×C314yescomplemented
281#700—22no—
282#700C23×C314yescomplemented
283D5⋊C8—24no—
284C22×#41—51no—
285C22×M16—51no—
286C22×C42—51no—
287C2×#104—58no—
288C2×#104—52no—
289C2×#104—52no—
290C22×C3×C5—22no—
291C22×C3×C5—22no—
292C22×C3×C5—42no—
293C22×C3×C5C2×C22⋊C412yes—
294C22×C3×C5C2×C22⋊C411yescharacteristic
295C2×C3×D5—22no—
296C2×C3×D5—24no—
297C2×C3×D5—24no—
298C2×C3×D5—22no—
299C2×C3×D5—42no—
300C2×C3×D5—48no—
301C2×C3×D5#10414yescomplemented
302C2×C3×D5C2×C22⋊C411yescharacteristic
303C2×C3×D5C2×C22⋊C412yes—
304C2×C3×D5C22×D411yescharacteristic
305C3×AGL(1,𝔽5)—28no—
306C3×C4×C5—22no—
307C3×C4×C5C2×C22⋊C411yescharacteristic
308C3×C4×C5C2×C22⋊C412yes—
309C3×C4×C5C23×C411yescharacteristic
310C3×Dic5—22no—
311C3×Dic5C2×C22⋊C412yes—
312C3×Dic5C2×C22⋊C411yescharacteristic
313C3×Dic5C22×D411yescharacteristic
314C24×C3—51no—
315C24×C3—101no—
316C3×#41—22no—
317C3×#41—52no—
318C3×#41—52no—
319C3×#41—52no—
320C3×#41—52no—
321C3×#41—54no—
322C3×#41—104no—
323C3×#41—104no—
324C3×#41—104no—
325C3×#41—104no—
326C3×#41—101no—
327C3×#41—101no—
328C3×#41—101no—
329C3×#41—101no—
330C3×#41—102no—
331C3×#41C2×AGL(1,𝔽5)14yescomplemented
332C2×C3×Q8—54no—
333C2×C3×Q8—51no—
334C2×C3×Q8—101no—
335C2×C3×Q8—102no—
336C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
337C2×C3×D4—21no—
338C2×C3×D4—54no—
339C2×C3×D4—51no—
340C2×C3×D4—101no—
341C2×C3×D4—102no—
342C2×C3×D4—101no—
343C2×C3×D4—104no—
344C2×C3×D4—104no—
345C2×C3×D4—101no—
346C2×C3×D4—101no—
347C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
348C22×C3×C4—21no—
349C22×C3×C4—51no—
350C22×C3×C4—52no—
351C22×C3×C4—52no—
352C22×C3×C4—51no—
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—52no—
356C22×C3×C4—51no—
357C22×C3×C4—52no—
358C22×C3×C4—101no—
359C22×C3×C4—104no—
360C22×C3×C4—104no—
361C22×C3×C4—101no—
362C22×C3×C4—101no—
363C22×C3×C4—104no—
364C22×C3×C4—102no—
365C22×C3×C4—108no—
366C22×C3×C4—101no—
367C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
368C3×M16—54no—
369C3×M16—102no—
370C3×M16—104no—
371C2×C3×C8—104no—
372C2×C3×C8—102no—
373C3×C42—54no—
374C3×C42—102no—
375C3×C42—104no—
376C23×C5—21no—
377C23×C5C3×C22⋊C411yescharacteristic
378C22×D5—24no—
379C22×D5—21no—
380C22×D5—24no—
381C22×D5—44no—
382C22×D5C3×C22⋊C412yes—
383C22×D5C3×C22⋊C411yescharacteristic
384C22×D5C2×C3×D411yescharacteristic
385C22×D5C2×C3×D412yes—
386C2×AGL(1,𝔽5)—28no—
387C2×AGL(1,𝔽5)—216no—
388C2×AGL(1,𝔽5)—24no—
389C5×Q8—21no—
390C5×Q8C22×C3×C412yescomplemented
391C5×D4—24no—
392C5×D4—21no—
393C5×D4C22×C3×C412yescomplemented
394C2×C4×C5—21no—
395C2×C4×C5—24no—
396C2×C4×C5C3×C22⋊C411yescharacteristic
397C2×C4×C5C3×C22⋊C412yes—
398C2×C4×C5C22×C3×C411yescharacteristic
399C2×C4×C5C22×C3×C412yes—
400C22⋊D5—24no—
401C22⋊D5—22no—
402C22⋊D5—22no—
403C22⋊D5—24no—
404C2×Dic5—21no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5C3×C22⋊C411yescharacteristic
408C2×Dic5C3×C22⋊C412yes—
409C2×Dic5C2×C3×D411yescharacteristic
410C2×Dic5C2×C3×D412yes—
411D20—22no—
412D20—22no—
413D20—21no—
414D20C22×C3×C412yescomplemented
415C4×D5—24no—
416C4×D5—24no—
417C4×D5—22no—
418C4×D5—22no—
419C4×D5C3×C22⋊C412yes—
420C4×D5C3×C22⋊C412yes—
421C4×D5C3×C22⋊C412yes—
422C4×D5C22×C3×C412yes—
423C4×D5C22×C3×C411yescharacteristic
424C4×D5C2×C3×D412yes—
425C4×D5C2×C3×D411yescharacteristic
426C4×D5C2×C3×D412yes—
427C4×D5C2×C3×D411yescharacteristic
428C4×D5C24×C311yescharacteristic
429Dic10—21no—
430Dic10—24no—
431Dic10C22×C3×C412yescomplemented
432#170—24no—
433C2×#41—54no—
434C2×#41—54no—
435C2×#41—51no—
436C2×#41—51no—
437C2×#41—51no—
438C2×#41—101no—
439C2×#41—101no—
440C2×#41—102no—
441C2×#41—102no—
442C2×#41C3×AGL(1,𝔽5)11yescharacteristic, complemented
443C22×Q8—51no—
444C22×D4—51no—
445C22×D4—101no—
446C23×C4—51no—
447C23×C4—101no—
448C23×C4—101no—
449C2×M16—52no—
450C2×M16—54no—
451C2×M16—102no—
452C2×M16—101no—
453C22×C8—101no—
454C2×C42—54no—
455C2×C42—52no—
456C2×C42—101no—
457C2×C42—102no—
458#104—58no—
459#104—58no—
460C2×C3×C5—22no—
461C2×C3×C5—42no—
462C2×C3×C5C2×#10412yescomplemented
463C2×C3×C5C22×C22⋊C411yescharacteristic
464C3×D5—21no—
465C3×D5—21no—
466C3×D5—42no—
467C3×D5C2×#10414yescomplemented
468C23×C3—21no—
469C23×C3—51no—
470C23×C3—52no—
471C23×C3—52no—
472C23×C3—51no—
473C23×C3—104no—
474C23×C3—104no—
475C23×C3—101no—
476C23×C3—204no—
477C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
478C3×Q8—21no—
479C3×Q8—52no—
480C3×Q8—104no—
481C3×Q8—101no—
482C3×Q8C22×AGL(1,𝔽5)12yescomplemented
483C3×D4—24no—
484C3×D4—21no—
485C3×D4—52no—
486C3×D4—102no—
487C3×D4—102no—
488C3×D4—104no—
489C3×D4—102no—
490C3×D4—102no—
491C3×D4—104no—
492C3×D4—101no—
493C3×D4C22×AGL(1,𝔽5)12yescomplemented
494C2×C3×C4—21no—
495C2×C3×C4—24no—
496C2×C3×C4—51no—
497C2×C3×C4—52no—
498C2×C3×C4—51no—
499C2×C3×C4—52no—
500C2×C3×C4—52no—
501C2×C3×C4—52no—
502C2×C3×C4—52no—
503C2×C3×C4—51no—
504C2×C3×C4—52no—
505C2×C3×C4—52no—
506C2×C3×C4—51no—
507C2×C3×C4—52no—
508C2×C3×C4—51no—
509C2×C3×C4—51no—
510C2×C3×C4—102no—
511C2×C3×C4—102no—
512C2×C3×C4—104no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—104no—
516C2×C3×C4—1016no—
517C2×C3×C4—108no—
518C2×C3×C4—101no—
519C2×C3×C4—104no—
520C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
521C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
522C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
523C2×C3×C4C22×AGL(1,𝔽5)12yes—
524C3×C8—104no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—42no—
528C22×C5C2×C3×C22⋊C412yes—
529C22×C5C2×C3×C22⋊C411yescharacteristic
530C2×D5—22no—
531C2×D5—24no—
532C2×D5—24no—
533C2×D5—22no—
534C2×D5—42no—
535C2×D5—48no—
536C2×D5C3×#10414yescomplemented
537C2×D5C2×C3×C22⋊C411yescharacteristic
538C2×D5C2×C3×C22⋊C412yes—
539C2×D5C22×C3×D411yescharacteristic
540AGL(1,𝔽5)—28no—
541C4×C5—22no—
542C4×C5C2×C3×C22⋊C411yescharacteristic
543C4×C5C2×C3×C22⋊C412yes—
544C4×C5C23×C3×C411yescharacteristic
545Dic5—22no—
546Dic5C2×C3×C22⋊C412yes—
547Dic5C2×C3×C22⋊C411yescharacteristic
548Dic5C22×C3×D411yescharacteristic
549C24—51no—
550C24—101no—
551#41—22no—
552#41—52no—
553#41—52no—
554#41—52no—
555#41—52no—
556#41—54no—
557#41—104no—
558#41—104no—
559#41—104no—
560#41—104no—
561#41—101no—
562#41—101no—
563#41—101no—
564#41—101no—
565#41—102no—
566#41C2×C3×AGL(1,𝔽5)14yescomplemented
567C2×Q8—54no—
568C2×Q8—51no—
569C2×Q8—101no—
570C2×Q8—102no—
571C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
572C2×D4—21no—
573C2×D4—54no—
574C2×D4—51no—
575C2×D4—101no—
576C2×D4—102no—
577C2×D4—101no—
578C2×D4—104no—
579C2×D4—104no—
580C2×D4—101no—
581C2×D4—101no—
582C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
583C22×C4—21no—
584C22×C4—51no—
585C22×C4—51no—
586C22×C4—52no—
587C22×C4—51no—
588C22×C4—52no—
589C22×C4—51no—
590C22×C4—52no—
591C22×C4—51no—
592C22×C4—52no—
593C22×C4—101no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—104no—
599C22×C4—102no—
600C22×C4—108no—
601C22×C4—101no—
602C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
603M16—54no—
604M16—102no—
605M16—104no—
606C2×C8—104no—
607C2×C8—102no—
608C42—54no—
609C42—102no—
610C42—104no—
611C3×C5C22×#10411yescharacteristic, complemented, Hall
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—42no—
615C22×C3—54no—
616C22×C3—52no—
617C22×C3—51no—
618C22×C3—51no—
619C22×C3—104no—
620C22×C3—104no—
621C22×C3—102no—
622C22×C3—102no—
623C22×C3—208no—
624C22×C3—202no—
625C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
626C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
627C3×C4—22no—
628C3×C4—51no—
629C3×C4—52no—
630C3×C4—51no—
631C3×C4—108no—
632C3×C4—102no—
633C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
634C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
635C3×C4C23×AGL(1,𝔽5)11yescharacteristic
636C2×C5—22no—
637C2×C5—42no—
638C2×C5C2×C3×#10412yescomplemented
639C2×C5C22×C3×C22⋊C411yescharacteristic
640D5—21no—
641D5—21no—
642D5—42no—
643D5C2×C3×#10414yescomplemented
644C23—21no—
645C23—51no—
646C23—52no—
647C23—51no—
648C23—52no—
649C23—104no—
650C23—104no—
651C23—101no—
652C23—204no—
653C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
654Q8—21no—
655Q8—52no—
656Q8—104no—
657Q8—101no—
658Q8C22×C3×AGL(1,𝔽5)12yescomplemented
659D4—24no—
660D4—21no—
661D4—52no—
662D4—102no—
663D4—102no—
664D4—104no—
665D4—102no—
666D4—102no—
667D4—104no—
668D4—101no—
669D4C22×C3×AGL(1,𝔽5)12yescomplemented
670C2×C4—21no—
671C2×C4—24no—
672C2×C4—51no—
673C2×C4—52no—
674C2×C4—51no—
675C2×C4—52no—
676C2×C4—51no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—51no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—51no—
684C2×C4—52no—
685C2×C4—51no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—104no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—104no—
692C2×C4—1016no—
693C2×C4—108no—
694C2×C4—101no—
695C2×C4—104no—
696C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
697C2×C4C3×C22⋊AGL(1,𝔽5)12yes—
698C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
699C2×C4C22×C3×AGL(1,𝔽5)12yes—
700C8—104no—
701C2×C3—22no—
702C2×C3—42no—
703C2×C3—54no—
704C2×C3—101no—
705C2×C3—101no—
706C2×C3—202no—
707C2×C3D5⋊#10412yesdirect product factor
708C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
709C5C22×C3×#10411yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—42no—
713C22—54no—
714C22—52no—
715C22—51no—
716C22—51no—
717C22—104no—
718C22—104no—
719C22—102no—
720C22—102no—
721C22—208no—
722C22—202no—
723C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
724C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
725C4—22no—
726C4—51no—
727C4—51no—
728C4—52no—
729C4—108no—
730C4—102no—
731C4C2×C3×C22⋊AGL(1,𝔽5)12yes—
732C4C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
733C4C23×C3×AGL(1,𝔽5)11yescharacteristic
734C3C2×D5⋊#10411yescharacteristic, direct product factor, Sylow
735C2—22no—
736C2—42no—
737C2—54no—
738C2—101no—
739C2—101no—
740C2—202no—
741C2C3×D5⋊#10412yesdirect product factor
742C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×#41C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC4×D5C24×C3
hypercenterC2×C3×#41AGL(1,𝔽5)
hypocenterC5C22×C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×AGL(1,𝔽5)C2semidirect
3. C2×C3×D5⋊M16C2semidirect
4. C3×D5⋊#104C2direct (N × H)
5. C2×C3×#4010C2semidirect
6. C2×C3×#4008C2semidirect
7. C2×D5⋊#104C3direct (N × H)
9. C2×C3×C5×#41C4semidirect
12. C3×D5×#41C4semidirect
15. C2×C3×Q8×D5C4semidirect
19. C2×C3×D4×D5C4semidirect
21. C2×C3×#709C4semidirect
27. C2×C3×C4×AGL(1,𝔽5)C22semidirect
28. C2×C3×C4×AGL(1,𝔽5)C22semidirect
30. C3×D5⋊M16C22semidirect
31. C2×C3×#700C22semidirect
33. C3×#4010C22semidirect
34. C3×#4008C22semidirect
37. C22×C4×AGL(1,𝔽5)C2×C3semidirect
38. C2×D5⋊M16C2×C3semidirect
39. D5⋊#104C2×C3direct (N × H)
40. C2×#4010C2×C3semidirect
41. C2×#4008C2×C3semidirect
48. C3×C5×#41C2×C4semidirect
49. C2×C3×C5×Q8C2×C4semidirect
51. C2×C3×C5×D4C2×C4semidirect
61. C3×#713C2×C4semidirect
64. C3×Q8×D5C2×C4semidirect
69. C3×#711C2×C4semidirect
74. C3×D4×D5C2×C4semidirect
78. C3×#709C2×C4semidirect
80. C2×C3×D20C2×C4semidirect
95. C2×C3×Dic10C2×C4semidirect
100. C3×C4×AGL(1,𝔽5)C23semidirect
102. C3×#700C23semidirect
111. C2×C5×#41C3×C4semidirect
114. D5×#41C3×C4semidirect
117. C2×Q8×D5C3×C4semidirect
121. C2×D4×D5C3×C4semidirect
123. C2×#709C3×C4semidirect
129. C2×C4×AGL(1,𝔽5)C22×C3semidirect
130. C2×C4×AGL(1,𝔽5)C22×C3semidirect
132. D5⋊M16C22×C3semidirect
133. C2×#700C22×C3semidirect
135. #4010C22×C3semidirect
136. #4008C22×C3semidirect
152. C3×C5×Q8C22×C4semidirect
155. C3×C5×D4C22×C4semidirect
176. C3×D20C22×C4semidirect
193. C3×Dic10C22×C4semidirect
204. C2×C3×#41AGL(1,𝔽5)semidirect
228. C5×#41C2×C3×C4semidirect
229. C2×C5×Q8C2×C3×C4semidirect
231. C2×C5×D4C2×C3×C4semidirect
241. #713C2×C3×C4semidirect
244. Q8×D5C2×C3×C4semidirect
249. #711C2×C3×C4semidirect
254. D4×D5C2×C3×C4semidirect
258. #709C2×C3×C4semidirect
260. C2×D20C2×C3×C4semidirect
275. C2×Dic10C2×C3×C4semidirect
280. C4×AGL(1,𝔽5)C23×C3semidirect
282. #700C23×C3semidirect
301. C2×C3×D5#104semidirect
331. C3×#41C2×AGL(1,𝔽5)semidirect
336. C2×C3×Q8C2×AGL(1,𝔽5)semidirect
347. C2×C3×D4C2×AGL(1,𝔽5)semidirect
390. C5×Q8C22×C3×C4semidirect
393. C5×D4C22×C3×C4semidirect
414. D20C22×C3×C4semidirect
431. Dic10C22×C3×C4semidirect
442. C2×#41C3×AGL(1,𝔽5)semidirect
462. C2×C3×C5C2×#104semidirect
467. C3×D5C2×#104semidirect
482. C3×Q8C22×AGL(1,𝔽5)semidirect
493. C3×D4C22×AGL(1,𝔽5)semidirect
536. C2×D5C3×#104semidirect
566. #41C2×C3×AGL(1,𝔽5)semidirect
571. C2×Q8C2×C3×AGL(1,𝔽5)semidirect
582. C2×D4C2×C3×AGL(1,𝔽5)semidirect
611. C3×C5C22×#104semidirect
638. C2×C5C2×C3×#104semidirect
643. D5C2×C3×#104semidirect
658. Q8C22×C3×AGL(1,𝔽5)semidirect
669. D4C22×C3×AGL(1,𝔽5)semidirect
707. C2×C3D5⋊#104direct (N × H)
709. C5C22×C3×#104semidirect
734. C3C2×D5⋊#104direct (N × H)
741. C2C3×D5⋊#104direct (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×C3×C4×AGL(1,𝔽5)2
C2×C3×D5⋊M162
C3×D5⋊#1042
C2×C3×#40102
C2×C3×#40082
C2×D5⋊#1043
C22×C3×#1045