Finite Group Databasebeta

← C2×C3×D5⋊#99 #14411892

Subgroups — C2×C3×D5⋊#99 #14411892

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C22×C3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
3C2×C3×#4011C212yesmaximal, complemented
4C3×D5⋊#99C218yesmaximal, direct product factor
5C2×C3×#3999C212yesmaximal, complemented
6C2×D5⋊#99C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×D5C411yescharacteristic, complemented
8C24×C3×D5C2211yescharacteristic
9C23×C3×AGL(1,𝔽5)—22no—
10C22×C3×C5×D4C411yescharacteristic, complemented
11C22×C3×C22⋊D5C411yescharacteristic, complemented
12C22×C3×C22⋊D5C2211yescharacteristic
13C2×C3×D4×D5—22no—
14C2×C3×D4×D5—22no—
15C2×C3×D4×D5—24no—
16C2×C3×D4×D5C414yescomplemented
17C2×C3×D4×D5C2214yes—
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C411yescharacteristic, complemented
20C2×C3×C22⋊AGL(1,𝔽5)—24no—
21C2×C3×C22⋊AGL(1,𝔽5)—22no—
22C2×C3×C22⋊AGL(1,𝔽5)C2214yescomplemented
23C2×C3×C22⋊AGL(1,𝔽5)C2218yescomplemented
24C3×#4011C2218yescomplemented
25C3×#3999C2218yescomplemented
26C22×C3×#99—51nomaximal, Hall
27C22×D4×D5C2×C311yescharacteristic
28C22×C22⋊AGL(1,𝔽5)C2×C312yescomplemented
29C2×#4011C2×C312yescomplemented
30D5⋊#99C2×C318yesdirect product factor
31C2×#3999C2×C312yescomplemented
32C24×C3×C5C2×C411yescharacteristic
33C24×C3×C5C2×C411yescharacteristic, complemented
34C23×C3×D5—22no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C23×C3×D5—44no—
38C23×C3×D5—44no—
39C23×C3×D5C2×C411yescharacteristic
40C23×C3×D5C2×C412yes—
41C23×C3×D5C2×C414yescomplemented
42C23×C3×D5C2×C411yescharacteristic, complemented
43C23×C3×D5D412yes—
44C23×C3×D5D414yes—
45C23×C3×D5D412yes—
46C23×C3×D5C2311yescharacteristic
47C23×C3×D5C2312yes—
48C22×C3×AGL(1,𝔽5)—24no—
49C22×C3×AGL(1,𝔽5)—28no—
50C22×C3×AGL(1,𝔽5)—48no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yescomplemented
54C22×C3×C4×C5C2×C411yescharacteristic, complemented
55C2×C3×C22⋊D5—22no—
56C2×C3×C22⋊D5—22no—
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5C2×C412yescomplemented
60C2×C3×C22⋊D5C2×C414yescomplemented
61C2×C3×C22⋊D5C2312yes—
62C22×C3×Dic5C2×C411yescharacteristic, complemented
63C3×D4×D5—28no—
64C3×D4×D5—28no—
65C3×D4×D5—28no—
66C3×D4×D5—28no—
67C2×C3×D20—22no—
68C2×C3×D20—22no—
69C2×C3×D20C2×C412yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5C2×C414yescomplemented
75C3×C22⋊AGL(1,𝔽5)—24no—
76C3×C22⋊AGL(1,𝔽5)—28no—
77C3×C22⋊AGL(1,𝔽5)C2318yescomplemented
78C23×C3×D4—51no—
79C22×C3×C22⋊C4—52no—
80C2×C3×#99—52no—
81C2×C3×#99—58no—
82C2×C3×#99—52no—
83C24×D5C3×C411yescharacteristic, complemented
84C24×D5C22×C311yescharacteristic
85C23×AGL(1,𝔽5)—22no—
86C22×C5×D4C3×C411yescharacteristic, complemented
87C22×C22⋊D5C3×C411yescharacteristic, complemented
88C22×C22⋊D5C22×C311yescharacteristic
89C2×D4×D5—22no—
90C2×D4×D5—22no—
91C2×D4×D5—24no—
92C2×D4×D5C3×C414yescomplemented
93C2×D4×D5C22×C314yes—
94C22×D20C22×C311yescharacteristic
95C22×C4×D5C3×C411yescharacteristic, complemented
96C2×C22⋊AGL(1,𝔽5)—24no—
97C2×C22⋊AGL(1,𝔽5)—22no—
98C2×C22⋊AGL(1,𝔽5)C22×C314yescomplemented
99C2×C22⋊AGL(1,𝔽5)C22×C318yescomplemented
100#4011C22×C318yescomplemented
101#3999C22×C318yescomplemented
102C22×#99—51noSylow
103C23×C3×C5—21no—
104C23×C3×C5—21no—
105C23×C3×C5—42no—
106C23×C3×C5—42no—
107C23×C3×C5C22⋊C412yes—
108C23×C3×C5C22⋊C412yes—
109C23×C3×C5C22×C411yescharacteristic
110C23×C3×C5C22×C412yes—
111C23×C3×C5C22×C412yescomplemented
112C22×C3×D5—28no—
113C22×C3×D5—24no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—44no—
119C22×C3×D5—48no—
120C22×C3×D5—44no—
121C22×C3×D5—44no—
122C22×C3×D5—42no—
123C22×C3×D5—44no—
124C22×C3×D5—48no—
125C22×C3×D5—48no—
126C22×C3×D5—44no—
127C22×C3×D5—42no—
128C22×C3×D5C22⋊C411yescharacteristic
129C22×C3×D5C22⋊C412yes—
130C22×C3×D5C22⋊C414yes—
131C22×C3×D5C22⋊C414yes—
132C22×C3×D5C22⋊C411yescharacteristic
133C22×C3×D5C22×C412yes—
134C22×C3×D5C22×C411yescharacteristic
135C22×C3×D5C22×C412yescomplemented
136C22×C3×D5C2×D412yes—
137C22×C3×D5C2×D414yes—
138C22×C3×D5C2×D412yes—
139C22×C3×D5C2×D414yes—
140C22×C3×D5C2411yescharacteristic
141C2×C3×AGL(1,𝔽5)—28no—
142C2×C3×AGL(1,𝔽5)—48no—
143C2×C3×AGL(1,𝔽5)—416no—
144C3×C5×D4—28no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C22×C412yescomplemented
148C3×C22⋊D5—28no—
149C3×C22⋊D5—24no—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5C22×C412yescomplemented
154C3×D20—24no—
155C3×D20—24no—
156C3×C4×D5—24no—
157C3×C4×D5—24no—
158C25×C3—51no—
159C25×C3—51no—
160C22×C3×D4—51no—
161C22×C3×D4—51no—
162C22×C3×D4—54no—
163C22×C3×D4—54no—
164C22×C3×D4—51no—
165C22×C3×D4—102no—
166C22×C3×D4—104no—
167C22×C3×D4—102no—
168C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
169C23×C3×C4—51no—
170C23×C3×C4—102no—
171C2×C3×C22⋊C4—54no—
172C2×C3×C22⋊C4—58no—
173C2×C3×C22⋊C4—104no—
174C2×C3×C22⋊C4—102no—
175C3×#99—58no—
176C3×#99—58no—
177C24×C5C2×C3×C411yescharacteristic
178C24×C5C2×C3×C411yescharacteristic, complemented
179C23×D5—22no—
180C23×D5—21no—
181C23×D5—21no—
182C23×D5—44no—
183C23×D5—44no—
184C23×D5C2×C3×C411yescharacteristic
185C23×D5C2×C3×C412yes—
186C23×D5C2×C3×C414yescomplemented
187C23×D5C2×C3×C411yescharacteristic, complemented
188C23×D5C3×D412yes—
189C23×D5C3×D414yes—
190C23×D5C3×D412yes—
191C23×D5C23×C311yescharacteristic
192C23×D5C23×C312yes—
193C22×AGL(1,𝔽5)—24no—
194C22×AGL(1,𝔽5)—28no—
195C22×AGL(1,𝔽5)—48no—
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4C2×C3×C414yescomplemented
199C22×C4×C5C2×C3×C411yescharacteristic, complemented
200C2×C22⋊D5—22no—
201C2×C22⋊D5—22no—
202C2×C22⋊D5—22no—
203C2×C22⋊D5—22no—
204C2×C22⋊D5C2×C3×C412yescomplemented
205C2×C22⋊D5C2×C3×C414yescomplemented
206C2×C22⋊D5C23×C312yes—
207C22×Dic5C2×C3×C411yescharacteristic, complemented
208D4×D5—28no—
209D4×D5—28no—
210D4×D5—28no—
211D4×D5—28no—
212C2×D20—22no—
213C2×D20—22no—
214C2×D20C2×C3×C412yescomplemented
215C2×D20C23×C312yes—
216C2×C4×D5—21no—
217C2×C4×D5—22no—
218C2×C4×D5—21no—
219C2×C4×D5C2×C3×C414yescomplemented
220C22⋊AGL(1,𝔽5)—24no—
221C22⋊AGL(1,𝔽5)—28no—
222C22⋊AGL(1,𝔽5)C23×C318yescomplemented
223C23×D4—51no—
224C22×C22⋊C4—52no—
225C2×#99—52no—
226C2×#99—52no—
227C2×#99—58no—
228C22×C3×C5—22no—
229C22×C3×C5—24no—
230C22×C3×C5—22no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—42no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5C2×C22⋊C411yescharacteristic
237C22×C3×C5C2×C22⋊C414yes—
238C22×C3×C5C2×C22⋊C411yescharacteristic
239C22×C3×C5C23×C411yescharacteristic
240C2×C3×D5—24no—
241C2×C3×D5—22no—
242C2×C3×D5—28no—
243C2×C3×D5—24no—
244C2×C3×D5—24no—
245C2×C3×D5—28no—
246C2×C3×D5—22no—
247C2×C3×D5—44no—
248C2×C3×D5—41no—
249C2×C3×D5—44no—
250C2×C3×D5—42no—
251C2×C3×D5—41no—
252C2×C3×D5—48no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—48no—
256C2×C3×D5—42no—
257C2×C3×D5#9914yescomplemented
258C2×C3×D5C2×C22⋊C412yes—
259C2×C3×D5C2×C22⋊C412yes—
260C2×C3×D5C2×C22⋊C412yes—
261C2×C3×D5C22×D412yes—
262C3×AGL(1,𝔽5)—48no—
263C3×C4×C5—22no—
264C3×Dic5—22no—
265C24×C3—52no—
266C24×C3—51no—
267C24×C3—54no—
268C24×C3—52no—
269C24×C3—52no—
270C24×C3—51no—
271C24×C3—52no—
272C24×C3—51no—
273C24×C3—54no—
274C24×C3—102no—
275C24×C3—101no—
276C24×C3—101no—
277C24×C3—204no—
278C24×C3—204no—
279C24×C3C2×AGL(1,𝔽5)11yescharacteristic
280C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—54no—
284C2×C3×D4—52no—
285C2×C3×D4—52no—
286C2×C3×D4—52no—
287C2×C3×D4—52no—
288C2×C3×D4—102no—
289C2×C3×D4—102no—
290C2×C3×D4—108no—
291C2×C3×D4—108no—
292C2×C3×D4—108no—
293C2×C3×D4—108no—
294C2×C3×D4—102no—
295C2×C3×D4—102no—
296C2×C3×D4—102no—
297C2×C3×D4—102no—
298C2×C3×D4C2×AGL(1,𝔽5)14yescomplemented
299C22×C3×C4—51no—
300C22×C3×C4—54no—
301C22×C3×C4—102no—
302C22×C3×C4—101no—
303C22×C3×C4—101no—
304C22×C3×C4—108no—
305C22×C3×C4—104no—
306C22×C3×C4—208no—
307C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
308C3×C22⋊C4—58no—
309C3×C22⋊C4—108no—
310C3×C22⋊C4—104no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—42no—
314C23×C5—42no—
315C23×C5C3×C22⋊C412yes—
316C23×C5C3×C22⋊C412yes—
317C23×C5C22×C3×C411yescharacteristic
318C23×C5C22×C3×C412yes—
319C23×C5C22×C3×C412yescomplemented
320C22×D5—28no—
321C22×D5—24no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—24no—
325C22×D5—24no—
326C22×D5—44no—
327C22×D5—48no—
328C22×D5—44no—
329C22×D5—44no—
330C22×D5—42no—
331C22×D5—44no—
332C22×D5—48no—
333C22×D5—48no—
334C22×D5—44no—
335C22×D5—42no—
336C22×D5C3×C22⋊C411yescharacteristic
337C22×D5C3×C22⋊C412yes—
338C22×D5C3×C22⋊C414yes—
339C22×D5C3×C22⋊C414yes—
340C22×D5C3×C22⋊C411yescharacteristic
341C22×D5C22×C3×C412yes—
342C22×D5C22×C3×C411yescharacteristic
343C22×D5C22×C3×C412yescomplemented
344C22×D5C2×C3×D412yes—
345C22×D5C2×C3×D414yes—
346C22×D5C2×C3×D412yes—
347C22×D5C2×C3×D414yes—
348C22×D5C24×C311yescharacteristic
349C2×AGL(1,𝔽5)—28no—
350C2×AGL(1,𝔽5)—48no—
351C2×AGL(1,𝔽5)—416no—
352C5×D4—28no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5C22×C3×C412yescomplemented
356C22⋊D5—28no—
357C22⋊D5—24no—
358C22⋊D5—24no—
359C2×Dic5—21no—
360C2×Dic5—21no—
361C2×Dic5C22×C3×C412yescomplemented
362D20—24no—
363D20—24no—
364C4×D5—24no—
365C4×D5—24no—
366C25—51no—
367C25—51no—
368C22×D4—51no—
369C22×D4—51no—
370C22×D4—54no—
371C22×D4—54no—
372C22×D4—51no—
373C22×D4—102no—
374C22×D4—102no—
375C22×D4—104no—
376C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
377C23×C4—51no—
378C23×C4—102no—
379C2×C22⋊C4—54no—
380C2×C22⋊C4—58no—
381C2×C22⋊C4—104no—
382C2×C22⋊C4—102no—
383#99—58no—
384#99—58no—
385C2×C3×C5—21no—
386C2×C3×C5—21no—
387C2×C3×C5—24no—
388C2×C3×C5—42no—
389C2×C3×C5C2×#9912yescomplemented
390C2×C3×C5C22×C22⋊C411yescharacteristic
391C3×D5—22no—
392C3×D5—22no—
393C3×D5—22no—
394C3×D5—42no—
395C3×D5C2×#9914yescomplemented
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—51no—
401C23×C3—52no—
402C23×C3—54no—
403C23×C3—54no—
404C23×C3—51no—
405C23×C3—52no—
406C23×C3—52no—
407C23×C3—54no—
408C23×C3—54no—
409C23×C3—52no—
410C23×C3—51no—
411C23×C3—51no—
412C23×C3—52no—
413C23×C3—108no—
414C23×C3—104no—
415C23×C3—104no—
416C23×C3—104no—
417C23×C3—101no—
418C23×C3—101no—
419C23×C3—202no—
420C23×C3—204no—
421C23×C3—202no—
422C23×C3—204no—
423C23×C3—208no—
424C23×C3—204no—
425C23×C3—204no—
426C23×C3—208no—
427C23×C3—208no—
428C23×C3—204no—
429C23×C3C22⋊AGL(1,𝔽5)12yes—
430C23×C3C22⋊AGL(1,𝔽5)12yes—
431C23×C3C22×AGL(1,𝔽5)11yescharacteristic
432C23×C3C22×AGL(1,𝔽5)12yes—
433C23×C3C22×AGL(1,𝔽5)12yescomplemented
434C3×D4—28no—
435C3×D4—104no—
436C3×D4—104no—
437C3×D4—104no—
438C3×D4—104no—
439C3×D4—108no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—52no—
443C2×C3×C4—104no—
444C2×C3×C4—104no—
445C2×C3×C4—101no—
446C2×C3×C4—101no—
447C2×C3×C4—108no—
448C2×C3×C4—2016no—
449C2×C3×C4—208no—
450C2×C3×C4C22×AGL(1,𝔽5)12yescomplemented
451C22×C5—22no—
452C22×C5—24no—
453C22×C5—22no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5C2×C3×C22⋊C411yescharacteristic
460C22×C5C2×C3×C22⋊C414yes—
461C22×C5C2×C3×C22⋊C411yescharacteristic
462C22×C5C23×C3×C411yescharacteristic
463C2×D5—24no—
464C2×D5—22no—
465C2×D5—28no—
466C2×D5—24no—
467C2×D5—24no—
468C2×D5—28no—
469C2×D5—22no—
470C2×D5—44no—
471C2×D5—41no—
472C2×D5—44no—
473C2×D5—42no—
474C2×D5—41no—
475C2×D5—48no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—48no—
479C2×D5—42no—
480C2×D5C3×#9914yescomplemented
481C2×D5C2×C3×C22⋊C412yes—
482C2×D5C2×C3×C22⋊C412yes—
483C2×D5C2×C3×C22⋊C412yes—
484C2×D5C22×C3×D412yes—
485AGL(1,𝔽5)—48no—
486C4×C5—22no—
487Dic5—22no—
488C24—52no—
489C24—51no—
490C24—54no—
491C24—52no—
492C24—52no—
493C24—51no—
494C24—52no—
495C24—51no—
496C24—54no—
497C24—101no—
498C24—102no—
499C24—101no—
500C24—204no—
501C24—204no—
502C24C2×C3×AGL(1,𝔽5)11yescharacteristic
503C24C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—54no—
507C2×D4—52no—
508C2×D4—52no—
509C2×D4—52no—
510C2×D4—52no—
511C2×D4—102no—
512C2×D4—102no—
513C2×D4—108no—
514C2×D4—108no—
515C2×D4—108no—
516C2×D4—108no—
517C2×D4—102no—
518C2×D4—102no—
519C2×D4—102no—
520C2×D4—102no—
521C2×D4C2×C3×AGL(1,𝔽5)14yescomplemented
522C22×C4—51no—
523C22×C4—54no—
524C22×C4—101no—
525C22×C4—102no—
526C22×C4—101no—
527C22×C4—108no—
528C22×C4—104no—
529C22×C4—208no—
530C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
531C22⋊C4—58no—
532C22⋊C4—108no—
533C22⋊C4—104no—
534C3×C5C22×#9911yescharacteristic, complemented, Hall
535C22×C3—22no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—52no—
544C22×C3—54no—
545C22×C3—52no—
546C22×C3—52no—
547C22×C3—52no—
548C22×C3—108no—
549C22×C3—108no—
550C22×C3—104no—
551C22×C3—104no—
552C22×C3—104no—
553C22×C3—102no—
554C22×C3—102no—
555C22×C3—202no—
556C22×C3—201no—
557C22×C3—201no—
558C22×C3—204no—
559C22×C3—204no—
560C22×C3—202no—
561C22×C3—202no—
562C22×C3—208no—
563C22×C3—208no—
564C22×C3—202no—
565C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
566C22×C3C2×C22⋊AGL(1,𝔽5)14yes—
567C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
568C22×C3C23×AGL(1,𝔽5)11yescharacteristic
569C3×C4—22no—
570C3×C4—102no—
571C3×C4—208no—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—24no—
575C2×C5—42no—
576C2×C5C2×C3×#9912yescomplemented
577C2×C5C22×C3×C22⋊C411yescharacteristic
578D5—22no—
579D5—22no—
580D5—22no—
581D5—42no—
582D5C2×C3×#9914yescomplemented
583C23—21no—
584C23—21no—
585C23—42no—
586C23—42no—
587C23—51no—
588C23—54no—
589C23—52no—
590C23—52no—
591C23—51no—
592C23—54no—
593C23—52no—
594C23—54no—
595C23—52no—
596C23—54no—
597C23—51no—
598C23—51no—
599C23—52no—
600C23—108no—
601C23—104no—
602C23—104no—
603C23—104no—
604C23—101no—
605C23—101no—
606C23—202no—
607C23—204no—
608C23—202no—
609C23—204no—
610C23—208no—
611C23—204no—
612C23—204no—
613C23—208no—
614C23—208no—
615C23—204no—
616C23C3×C22⋊AGL(1,𝔽5)12yes—
617C23C3×C22⋊AGL(1,𝔽5)12yes—
618C23C22×C3×AGL(1,𝔽5)11yescharacteristic
619C23C22×C3×AGL(1,𝔽5)12yes—
620C23C22×C3×AGL(1,𝔽5)12yescomplemented
621D4—28no—
622D4—104no—
623D4—104no—
624D4—104no—
625D4—104no—
626D4—108no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—52no—
630C2×C4—104no—
631C2×C4—104no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—108no—
635C2×C4—2016no—
636C2×C4—208no—
637C2×C4C22×C3×AGL(1,𝔽5)12yescomplemented
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—24no—
641C2×C3—42no—
642C2×C3—54no—
643C2×C3—102no—
644C2×C3—102no—
645C2×C3—102no—
646C2×C3—202no—
647C2×C3D5⋊#9912yesdirect product factor
648C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
649C5C22×C3×#9911yescharacteristic, complemented, Sylow
650C22—22no—
651C22—24no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—54no—
659C22—52no—
660C22—52no—
661C22—52no—
662C22—52no—
663C22—108no—
664C22—104no—
665C22—104no—
666C22—108no—
667C22—104no—
668C22—102no—
669C22—102no—
670C22—202no—
671C22—201no—
672C22—201no—
673C22—204no—
674C22—204no—
675C22—202no—
676C22—202no—
677C22—208no—
678C22—208no—
679C22—202no—
680C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
681C22C2×C3×C22⋊AGL(1,𝔽5)14yes—
682C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
683C22C23×C3×AGL(1,𝔽5)11yescharacteristic
684C4—22no—
685C4—102no—
686C4—208no—
687C3C2×D5⋊#9911yescharacteristic, direct product factor, Sylow
688C2—21no—
689C2—21no—
690C2—24no—
691C2—42no—
692C2—54no—
693C2—102no—
694C2—102no—
695C2—102no—
696C2—202no—
697C2C3×D5⋊#9912yesdirect product factor
698C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC22×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C22×C3×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
3. C2×C3×#4011C2semidirect
4. C3×D5⋊#99C2direct (N × H)
5. C2×C3×#3999C2semidirect
6. C2×D5⋊#99C3direct (N × H)
7. C24×C3×D5C4semidirect
10. C22×C3×C5×D4C4semidirect
11. C22×C3×C22⋊D5C4semidirect
16. C2×C3×D4×D5C4semidirect
19. C22×C3×C4×D5C4semidirect
22. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
23. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
24. C3×#4011C22semidirect
25. C3×#3999C22semidirect
28. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
29. C2×#4011C2×C3semidirect
30. D5⋊#99C2×C3direct (N × H)
31. C2×#3999C2×C3semidirect
33. C24×C3×C5C2×C4semidirect
41. C23×C3×D5C2×C4semidirect
42. C23×C3×D5C2×C4semidirect
53. C2×C3×C5×D4C2×C4semidirect
54. C22×C3×C4×C5C2×C4semidirect
59. C2×C3×C22⋊D5C2×C4semidirect
60. C2×C3×C22⋊D5C2×C4semidirect
62. C22×C3×Dic5C2×C4semidirect
69. C2×C3×D20C2×C4semidirect
74. C2×C3×C4×D5C2×C4semidirect
77. C3×C22⋊AGL(1,𝔽5)C23semidirect
83. C24×D5C3×C4semidirect
86. C22×C5×D4C3×C4semidirect
87. C22×C22⋊D5C3×C4semidirect
92. C2×D4×D5C3×C4semidirect
95. C22×C4×D5C3×C4semidirect
98. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
99. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
100. #4011C22×C3semidirect
101. #3999C22×C3semidirect
111. C23×C3×C5C22×C4semidirect
135. C22×C3×D5C22×C4semidirect
147. C2×C3×C4×C5C22×C4semidirect
153. C2×C3×Dic5C22×C4semidirect
168. C22×C3×D4AGL(1,𝔽5)semidirect
178. C24×C5C2×C3×C4semidirect
186. C23×D5C2×C3×C4semidirect
187. C23×D5C2×C3×C4semidirect
198. C2×C5×D4C2×C3×C4semidirect
199. C22×C4×C5C2×C3×C4semidirect
204. C2×C22⋊D5C2×C3×C4semidirect
205. C2×C22⋊D5C2×C3×C4semidirect
207. C22×Dic5C2×C3×C4semidirect
214. C2×D20C2×C3×C4semidirect
219. C2×C4×D5C2×C3×C4semidirect
222. C22⋊AGL(1,𝔽5)C23×C3semidirect
257. C2×C3×D5#99semidirect
280. C24×C3C2×AGL(1,𝔽5)semidirect
298. C2×C3×D4C2×AGL(1,𝔽5)semidirect
307. C22×C3×C4C2×AGL(1,𝔽5)semidirect
319. C23×C5C22×C3×C4semidirect
343. C22×D5C22×C3×C4semidirect
355. C2×C4×C5C22×C3×C4semidirect
361. C2×Dic5C22×C3×C4semidirect
376. C22×D4C3×AGL(1,𝔽5)semidirect
389. C2×C3×C5C2×#99semidirect
395. C3×D5C2×#99semidirect
433. C23×C3C22×AGL(1,𝔽5)semidirect
450. C2×C3×C4C22×AGL(1,𝔽5)semidirect
480. C2×D5C3×#99semidirect
503. C24C2×C3×AGL(1,𝔽5)semidirect
521. C2×D4C2×C3×AGL(1,𝔽5)semidirect
530. C22×C4C2×C3×AGL(1,𝔽5)semidirect
534. C3×C5C22×#99semidirect
576. C2×C5C2×C3×#99semidirect
582. D5C2×C3×#99semidirect
620. C23C22×C3×AGL(1,𝔽5)semidirect
637. C2×C4C22×C3×AGL(1,𝔽5)semidirect
647. C2×C3D5⋊#99direct (N × H)
649. C5C22×C3×#99semidirect
687. C3C2×D5⋊#99direct (N × H)
697. C2C3×D5⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C22×C3×C22⋊AGL(1,𝔽5)2
C2×C3×#40112
C3×D5⋊#992
C2×C3×#39992
C2×D5⋊#993
C22×C3×#995