Finite Group Databasebeta

← C2×C3×#65779 #14320290

Subgroups — C2×C3×#65779 #14320290

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C22×C3×D4×D5C211yesmaximal, characteristic
3C22×C3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C22×C3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
5C3×#65779C218yesmaximal, direct product factor
6C2×C3×(C2×AGL(1,𝔽5))⋊C4C212yesmaximal, complemented
7C2×#65779C311yesmaximal, characteristic, direct product factor, Hall
8C24×C3×D5C2211yescharacteristic
9C24×C3×D5C2211yescharacteristic
10C23×C3×AGL(1,𝔽5)—24no—
11C23×C3×AGL(1,𝔽5)—28no—
12C23×C3×AGL(1,𝔽5)C2212yes—
13C23×C3×AGL(1,𝔽5)C2212yes—
14C23×C3×AGL(1,𝔽5)C2214yescomplemented
15C22×C3×C5×D4C411yescharacteristic, complemented
16C22×C3×C22⋊D5C411yescharacteristic, complemented
17C22×C3×C22⋊D5C411yescharacteristic, complemented
18C2×C3×D4×D5—24no—
19C2×C3×D4×D5—24no—
20C2×C3×D4×D5C414yescomplemented
21C2×C3×D4×D5C2214yes—
22C22×C3×D20C411yescharacteristic, complemented
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×C22⋊AGL(1,𝔽5)—24no—
25C2×C3×C22⋊AGL(1,𝔽5)—28no—
26C2×C3×C22⋊AGL(1,𝔽5)C2214yescomplemented
27C2×C3×C22⋊AGL(1,𝔽5)C2218yescomplemented
28C3×(C2×AGL(1,𝔽5))⋊C4C2218yescomplemented
29C2×C3×#386—51nomaximal, Hall
30C24×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
31C22×D4×D5C2×C311yescharacteristic
32C22×C22⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
33C22×C22⋊AGL(1,𝔽5)C2×C312yescomplemented
34#65779C2×C318yesdirect product factor
35C2×(C2×AGL(1,𝔽5))⋊C4C2×C312yescomplemented
36C24×C3×C5C2×C411yescharacteristic
37C24×C3×C5C2×C411yescharacteristic, complemented
38C23×C3×D5—24no—
39C23×C3×D5—24no—
40C23×C3×D5—24no—
41C23×C3×D5—22no—
42C23×C3×D5—22no—
43C23×C3×D5—24no—
44C23×C3×D5C2×C411yescharacteristic
45C23×C3×D5C2×C412yes—
46C23×C3×D5C2×C412yescomplemented
47C23×C3×D5C2×C411yescharacteristic, complemented
48C23×C3×D5D414yes—
49C23×C3×D5D414yes—
50C23×C3×D5C2312yes—
51C23×C3×D5C2312yes—
52C23×C3×D5C2311yescharacteristic
53C22×C3×AGL(1,𝔽5)—232no—
54C22×C3×AGL(1,𝔽5)—24no—
55C22×C3×AGL(1,𝔽5)—24no—
56C22×C3×AGL(1,𝔽5)—28no—
57C22×C3×AGL(1,𝔽5)—216no—
58C22×C3×AGL(1,𝔽5)—24no—
59C22×C3×AGL(1,𝔽5)—24no—
60C22×C3×AGL(1,𝔽5)—24no—
61C22×C3×AGL(1,𝔽5)D418yescomplemented
62C22×C3×AGL(1,𝔽5)C2314yes—
63C22×C3×AGL(1,𝔽5)C2314yes—
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2×C414yescomplemented
66C22×C3×C4×C5C2×C411yescharacteristic, complemented
67C2×C3×C22⋊D5—24no—
68C2×C3×C22⋊D5—24no—
69C2×C3×C22⋊D5C2×C414yescomplemented
70C2×C3×C22⋊D5C2×C414yescomplemented
71C22×C3×Dic5C2×C411yescharacteristic, complemented
72C3×D4×D5—216no—
73C3×D4×D5—28no—
74C3×D4×D5—28no—
75C2×C3×D20—24no—
76C2×C3×D20C2×C414yescomplemented
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5C2×C412yescomplemented
80C2×C3×C4×D5C2312yes—
81C3×C22⋊AGL(1,𝔽5)—28no—
82C3×C22⋊AGL(1,𝔽5)—216no—
83C23×C3×D4—51no—
84C24×C3×C4—51no—
85C22×C3×C22⋊C4—51no—
86C22×C3×C22⋊C4—52no—
87C3×#386—58no—
88C2×C3×#95—52no—
89C24×D5C22×C311yescharacteristic
90C24×D5C22×C311yescharacteristic
91C23×AGL(1,𝔽5)—24no—
92C23×AGL(1,𝔽5)—28no—
93C23×AGL(1,𝔽5)C22×C312yes—
94C23×AGL(1,𝔽5)C22×C312yes—
95C23×AGL(1,𝔽5)C22×C314yescomplemented
96C22×C5×D4C3×C411yescharacteristic, complemented
97C22×C22⋊D5C3×C411yescharacteristic, complemented
98C22×C22⋊D5C3×C411yescharacteristic, complemented
99C2×D4×D5—24no—
100C2×D4×D5—24no—
101C2×D4×D5C3×C414yescomplemented
102C2×D4×D5C22×C314yes—
103C22×D20C3×C411yescharacteristic, complemented
104C22×C4×D5C22×C311yescharacteristic
105C2×C22⋊AGL(1,𝔽5)—24no—
106C2×C22⋊AGL(1,𝔽5)—28no—
107C2×C22⋊AGL(1,𝔽5)C22×C314yescomplemented
108C2×C22⋊AGL(1,𝔽5)C22×C318yescomplemented
109(C2×AGL(1,𝔽5))⋊C4C22×C318yescomplemented
110C2×#386—51noSylow
111C23×C3×C5—24no—
112C23×C3×C5—22no—
113C23×C3×C5—24no—
114C23×C3×C5C22⋊C414yescomplemented
115C23×C3×C5C22×C412yes—
116C23×C3×C5C22×C411yescharacteristic
117C23×C3×C5C22×C412yescomplemented
118C22×C3×D5—24no—
119C22×C3×D5—28no—
120C22×C3×D5—28no—
121C22×C3×D5—216no—
122C22×C3×D5—28no—
123C22×C3×D5—24no—
124C22×C3×D5—24no—
125C22×C3×D5—22no—
126C22×C3×D5—24no—
127C22×C3×D5—24no—
128C22×C3×D5—28no—
129C22×C3×D5—24no—
130C22×C3×D5—22no—
131C22×C3×D5—22no—
132C22×C3×D5—24no—
133C22×C3×D5—44no—
134C22×C3×D5—48no—
135C22×C3×D5—44no—
136C22×C3×D5C22⋊C418yescomplemented
137C22×C3×D5C22⋊C414yescomplemented
138C22×C3×D5C22×C412yes—
139C22×C3×D5C22×C411yescharacteristic
140C22×C3×D5C22×C412yescomplemented
141C22×C3×D5C2×D414yes—
142C22×C3×D5C2×D414yes—
143C22×C3×D5C2×D412yes—
144C22×C3×D5C2×D412yes—
145C22×C3×D5C2×D414yes—
146C22×C3×D5#4114yes—
147C22×C3×D5C2411yescharacteristic
148C2×C3×AGL(1,𝔽5)—232no—
149C2×C3×AGL(1,𝔽5)—216no—
150C2×C3×AGL(1,𝔽5)—24no—
151C2×C3×AGL(1,𝔽5)—24no—
152C2×C3×AGL(1,𝔽5)—24no—
153C2×C3×AGL(1,𝔽5)—24no—
154C2×C3×AGL(1,𝔽5)—24no—
155C2×C3×AGL(1,𝔽5)—48no—
156C2×C3×AGL(1,𝔽5)C2×D418yescomplemented
157C3×C5×D4—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5C22×C412yescomplemented
160C3×C22⋊D5—28no—
161C3×C22⋊D5—28no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5C22×C412yescomplemented
164C3×D20—28no—
165C3×C4×D5—24no—
166C3×C4×D5—22no—
167C3×C4×D5—22no—
168C25×C3—51no—
169C25×C3—51no—
170C22×C3×D4—51no—
171C22×C3×D4—51no—
172C22×C3×D4—54no—
173C22×C3×D4—54no—
174C22×C3×D4—51no—
175C22×C3×D4—104no—
176C22×C3×D4—104no—
177C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
178C23×C3×C4—52no—
179C23×C3×C4—51no—
180C23×C3×C4—54no—
181C23×C3×C4—52no—
182C23×C3×C4—108no—
183C23×C3×C4—104no—
184C2×C3×C22⋊C4—58no—
185C2×C3×C22⋊C4—54no—
186C2×C3×C22⋊C4—108no—
187C2×C3×C22⋊C4—104no—
188C3×#95—58no—
189C24×C5C2×C3×C411yescharacteristic
190C24×C5C2×C3×C411yescharacteristic, complemented
191C23×D5—24no—
192C23×D5—24no—
193C23×D5—24no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—24no—
197C23×D5C2×C3×C411yescharacteristic
198C23×D5C2×C3×C412yes—
199C23×D5C2×C3×C412yescomplemented
200C23×D5C2×C3×C411yescharacteristic, complemented
201C23×D5C3×D414yes—
202C23×D5C3×D414yes—
203C23×D5C23×C312yes—
204C23×D5C23×C312yes—
205C23×D5C23×C311yescharacteristic
206C22×AGL(1,𝔽5)—232no—
207C22×AGL(1,𝔽5)—24no—
208C22×AGL(1,𝔽5)—24no—
209C22×AGL(1,𝔽5)—28no—
210C22×AGL(1,𝔽5)—216no—
211C22×AGL(1,𝔽5)—24no—
212C22×AGL(1,𝔽5)—24no—
213C22×AGL(1,𝔽5)—24no—
214C22×AGL(1,𝔽5)C3×D418yescomplemented
215C22×AGL(1,𝔽5)C23×C314yes—
216C22×AGL(1,𝔽5)C23×C314yes—
217C2×C5×D4—24no—
218C2×C5×D4C2×C3×C414yescomplemented
219C22×C4×C5C2×C3×C411yescharacteristic, complemented
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5C2×C3×C414yescomplemented
223C2×C22⋊D5C2×C3×C414yescomplemented
224C22×Dic5C2×C3×C411yescharacteristic, complemented
225D4×D5—216no—
226D4×D5—28no—
227D4×D5—28no—
228C2×D20—24no—
229C2×D20C2×C3×C414yescomplemented
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5C2×C3×C412yescomplemented
233C2×C4×D5C23×C312yes—
234C22⋊AGL(1,𝔽5)—28no—
235C22⋊AGL(1,𝔽5)—216no—
236C23×D4—51no—
237C24×C4—51no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4—51no—
240#386—58no—
241C2×#95—52no—
242C22×C3×C5—24no—
243C22×C3×C5—28no—
244C22×C3×C5—22no—
245C22×C3×C5—24no—
246C22×C3×C5—44no—
247C22×C3×C5C2×C22⋊C412yes—
248C22×C3×C5C2×C22⋊C414yescomplemented
249C22×C3×C5C4×D414yes—
250C22×C3×C5C23×C411yescharacteristic
251C2×C3×D5—24no—
252C2×C3×D5—28no—
253C2×C3×D5—24no—
254C2×C3×D5—28no—
255C2×C3×D5—24no—
256C2×C3×D5—216no—
257C2×C3×D5—22no—
258C2×C3×D5—24no—
259C2×C3×D5—44no—
260C2×C3×D5—42no—
261C2×C3×D5—44no—
262C2×C3×D5—42no—
263C2×C3×D5—48no—
264C2×C3×D5C2×C22⋊C412yes—
265C2×C3×D5C2×C22⋊C414yescomplemented
266C2×C3×D5C4×D414yes—
267C2×C3×D5#12014yes—
268C2×C3×D5#12118yes—
269C2×C3×D5#12314yes—
270C2×C3×D5C22×D412yes—
271C2×C3×D5C22×D411yescharacteristic
272C2×C3×D5C22×D411yescharacteristic
273C2×C3×D5C2×#4112yes—
274C3×AGL(1,𝔽5)—28no—
275C3×AGL(1,𝔽5)—44no—
276C3×C4×C5—22no—
277C3×Dic5—22no—
278C24×C3—51no—
279C24×C3—54no—
280C24×C3—54no—
281C24×C3—52no—
282C24×C3—52no—
283C24×C3—51no—
284C24×C3—51no—
285C24×C3—52no—
286C24×C3—52no—
287C24×C3—104no—
288C24×C3—104no—
289C24×C3—104no—
290C24×C3—104no—
291C24×C3—102no—
292C24×C3—102no—
293C24×C3C2×AGL(1,𝔽5)11yescharacteristic
294C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
295C2×C3×D4—24no—
296C2×C3×D4—54no—
297C2×C3×D4—54no—
298C2×C3×D4—54no—
299C2×C3×D4—104no—
300C2×C3×D4—1016no—
301C2×C3×D4—108no—
302C2×C3×D4—108no—
303C2×C3×D4—104no—
304C2×C3×D4—104no—
305C2×C3×D4C2×AGL(1,𝔽5)14yescomplemented
306C22×C3×C4—54no—
307C22×C3×C4—58no—
308C22×C3×C4—51no—
309C22×C3×C4—52no—
310C22×C3×C4—52no—
311C22×C3×C4—54no—
312C22×C3×C4—102no—
313C22×C3×C4—102no—
314C22×C3×C4—1016no—
315C22×C3×C4—104no—
316C22×C3×C4—104no—
317C22×C3×C4—108no—
318C22×C3×C4—1032no—
319C22×C3×C4—104no—
320C22×C3×C4—104no—
321C22×C3×C4—104no—
322C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
323C3×C22⋊C4—1016no—
324C3×C22⋊C4—108no—
325C23×C5—24no—
326C23×C5—22no—
327C23×C5—24no—
328C23×C5C3×C22⋊C414yescomplemented
329C23×C5C22×C3×C412yes—
330C23×C5C22×C3×C411yescharacteristic
331C23×C5C22×C3×C412yescomplemented
332C22×D5—24no—
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—216no—
336C22×D5—28no—
337C22×D5—24no—
338C22×D5—24no—
339C22×D5—22no—
340C22×D5—24no—
341C22×D5—24no—
342C22×D5—28no—
343C22×D5—24no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—24no—
347C22×D5—44no—
348C22×D5—48no—
349C22×D5—44no—
350C22×D5C3×C22⋊C418yescomplemented
351C22×D5C3×C22⋊C414yescomplemented
352C22×D5C22×C3×C412yes—
353C22×D5C22×C3×C411yescharacteristic
354C22×D5C22×C3×C412yescomplemented
355C22×D5C2×C3×D414yes—
356C22×D5C2×C3×D414yes—
357C22×D5C2×C3×D412yes—
358C22×D5C2×C3×D412yes—
359C22×D5C2×C3×D414yes—
360C22×D5C3×#4114yes—
361C22×D5C24×C311yescharacteristic
362C2×AGL(1,𝔽5)—232no—
363C2×AGL(1,𝔽5)—216no—
364C2×AGL(1,𝔽5)—24no—
365C2×AGL(1,𝔽5)—24no—
366C2×AGL(1,𝔽5)—24no—
367C2×AGL(1,𝔽5)—24no—
368C2×AGL(1,𝔽5)—24no—
369C2×AGL(1,𝔽5)—48no—
370C2×AGL(1,𝔽5)C2×C3×D418yescomplemented
371C5×D4—28no—
372C2×C4×C5—22no—
373C2×C4×C5C22×C3×C412yescomplemented
374C22⋊D5—28no—
375C22⋊D5—28no—
376C2×Dic5—22no—
377C2×Dic5C22×C3×C412yescomplemented
378D20—28no—
379C4×D5—24no—
380C4×D5—22no—
381C4×D5—22no—
382C25—51no—
383C25—51no—
384C22×D4—51no—
385C22×D4—51no—
386C22×D4—54no—
387C22×D4—54no—
388C22×D4—51no—
389C22×D4—104no—
390C22×D4—104no—
391C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
392C23×C4—52no—
393C23×C4—51no—
394C23×C4—52no—
395C23×C4—54no—
396C23×C4—108no—
397C23×C4—104no—
398C2×C22⋊C4—58no—
399C2×C22⋊C4—54no—
400C2×C22⋊C4—108no—
401C2×C22⋊C4—104no—
402#95—58no—
403C2×C3×C5—24no—
404C2×C3×C5—42no—
405C2×C3×C5#38614yescomplemented
406C2×C3×C5C22×C22⋊C411yescharacteristic
407C2×C3×C5C2×C4×D412yes—
408C3×D5—24no—
409C3×D5—42no—
410C3×D5#38614yescomplemented
411C3×D5C2×#12011yescharacteristic
412C3×D5C2×#12112yes—
413C3×D5C2×#12311yescharacteristic
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—22no—
417C23×C3—54no—
418C23×C3—54no—
419C23×C3—52no—
420C23×C3—52no—
421C23×C3—51no—
422C23×C3—51no—
423C23×C3—54no—
424C23×C3—58no—
425C23×C3—54no—
426C23×C3—54no—
427C23×C3—52no—
428C23×C3—52no—
429C23×C3—104no—
430C23×C3—108no—
431C23×C3—108no—
432C23×C3—104no—
433C23×C3—1016no—
434C23×C3—108no—
435C23×C3—104no—
436C23×C3—104no—
437C23×C3—102no—
438C23×C3—102no—
439C23×C3—108no—
440C23×C3—104no—
441C23×C3—104no—
442C23×C3—104no—
443C23×C3—102no—
444C23×C3—204no—
445C23×C3—208no—
446C23×C3—204no—
447C23×C3C22⋊AGL(1,𝔽5)14yescomplemented
448C23×C3C22×AGL(1,𝔽5)12yes—
449C23×C3C22×AGL(1,𝔽5)11yescharacteristic
450C23×C3C22×AGL(1,𝔽5)12yescomplemented
451C3×D4—28no—
452C3×D4—108no—
453C3×D4—108no—
454C3×D4—108no—
455C2×C3×C4—22no—
456C2×C3×C4—58no—
457C2×C3×C4—52no—
458C2×C3×C4—104no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4—104no—
462C2×C3×C4—104no—
463C2×C3×C4—1016no—
464C2×C3×C4—1032no—
465C2×C3×C4—102no—
466C2×C3×C4—104no—
467C2×C3×C4—104no—
468C2×C3×C4—104no—
469C2×C3×C4—208no—
470C2×C3×C4C22×AGL(1,𝔽5)12yescomplemented
471C22×C5—28no—
472C22×C5—24no—
473C22×C5—22no—
474C22×C5—24no—
475C22×C5—44no—
476C22×C5C2×C3×C22⋊C412yes—
477C22×C5C2×C3×C22⋊C414yescomplemented
478C22×C5C3×C4×D414yes—
479C22×C5C23×C3×C411yescharacteristic
480C2×D5—28no—
481C2×D5—24no—
482C2×D5—216no—
483C2×D5—24no—
484C2×D5—28no—
485C2×D5—24no—
486C2×D5—22no—
487C2×D5—24no—
488C2×D5—44no—
489C2×D5—48no—
490C2×D5—42no—
491C2×D5—44no—
492C2×D5—42no—
493C2×D5C2×C3×C22⋊C412yes—
494C2×D5C2×C3×C22⋊C414yescomplemented
495C2×D5C3×C4×D414yes—
496C2×D5C3×#12014yes—
497C2×D5C3×#12118yes—
498C2×D5C3×#12314yes—
499C2×D5C22×C3×D412yes—
500C2×D5C22×C3×D411yescharacteristic
501C2×D5C22×C3×D411yescharacteristic
502C2×D5C2×C3×#4112yes—
503AGL(1,𝔽5)—28no—
504AGL(1,𝔽5)—44no—
505C4×C5—22no—
506Dic5—22no—
507C24—51no—
508C24—54no—
509C24—54no—
510C24—52no—
511C24—52no—
512C24—51no—
513C24—51no—
514C24—52no—
515C24—52no—
516C24—104no—
517C24—104no—
518C24—104no—
519C24—102no—
520C24—102no—
521C24—104no—
522C24C2×C3×AGL(1,𝔽5)11yescharacteristic
523C24C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
524C2×D4—24no—
525C2×D4—54no—
526C2×D4—54no—
527C2×D4—54no—
528C2×D4—104no—
529C2×D4—108no—
530C2×D4—108no—
531C2×D4—1016no—
532C2×D4—104no—
533C2×D4—104no—
534C2×D4C2×C3×AGL(1,𝔽5)14yescomplemented
535C22×C4—54no—
536C22×C4—58no—
537C22×C4—51no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—54no—
541C22×C4—102no—
542C22×C4—102no—
543C22×C4—1016no—
544C22×C4—104no—
545C22×C4—104no—
546C22×C4—108no—
547C22×C4—1032no—
548C22×C4—104no—
549C22×C4—104no—
550C22×C4—104no—
551C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
552C22⋊C4—1016no—
553C22⋊C4—108no—
554C3×C5C2×#38611yescharacteristic, complemented, Hall
555C22×C3—24no—
556C22×C3—28no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—44no—
560C22×C3—54no—
561C22×C3—52no—
562C22×C3—52no—
563C22×C3—52no—
564C22×C3—51no—
565C22×C3—51no—
566C22×C3—54no—
567C22×C3—58no—
568C22×C3—54no—
569C22×C3—54no—
570C22×C3—104no—
571C22×C3—108no—
572C22×C3—104no—
573C22×C3—1016no—
574C22×C3—104no—
575C22×C3—108no—
576C22×C3—104no—
577C22×C3—102no—
578C22×C3—202no—
579C22×C3—204no—
580C22×C3—202no—
581C22×C3—208no—
582C22×C3—204no—
583C22×C3D4×AGL(1,𝔽5)14yes—
584C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
585C22×C3C2×C22⋊AGL(1,𝔽5)14yescomplemented
586C22×C3C23×AGL(1,𝔽5)11yescharacteristic
587C3×C4—22no—
588C3×C4—108no—
589C3×C4—102no—
590C3×C4—204no—
591C2×C5—24no—
592C2×C5—42no—
593C2×C5C3×#38614yescomplemented
594C2×C5C22×C3×C22⋊C411yescharacteristic
595C2×C5C2×C3×C4×D412yes—
596D5—24no—
597D5—42no—
598D5C3×#38614yescomplemented
599D5C2×C3×#12011yescharacteristic
600D5C2×C3×#12112yes—
601D5C2×C3×#12311yescharacteristic
602C23—24no—
603C23—24no—
604C23—22no—
605C23—54no—
606C23—54no—
607C23—52no—
608C23—52no—
609C23—51no—
610C23—51no—
611C23—54no—
612C23—54no—
613C23—54no—
614C23—58no—
615C23—52no—
616C23—52no—
617C23—108no—
618C23—104no—
619C23—1016no—
620C23—108no—
621C23—104no—
622C23—108no—
623C23—104no—
624C23—102no—
625C23—102no—
626C23—104no—
627C23—104no—
628C23—108no—
629C23—104no—
630C23—104no—
631C23—102no—
632C23—204no—
633C23—208no—
634C23—204no—
635C23C3×C22⋊AGL(1,𝔽5)14yescomplemented
636C23C22×C3×AGL(1,𝔽5)12yes—
637C23C22×C3×AGL(1,𝔽5)11yescharacteristic
638C23C22×C3×AGL(1,𝔽5)12yescomplemented
639D4—28no—
640D4—108no—
641D4—108no—
642D4—108no—
643C2×C4—22no—
644C2×C4—58no—
645C2×C4—52no—
646C2×C4—102no—
647C2×C4—102no—
648C2×C4—104no—
649C2×C4—1016no—
650C2×C4—104no—
651C2×C4—104no—
652C2×C4—1032no—
653C2×C4—102no—
654C2×C4—104no—
655C2×C4—104no—
656C2×C4—104no—
657C2×C4—208no—
658C2×C4C22×C3×AGL(1,𝔽5)12yescomplemented
659C2×C3—24no—
660C2×C3—42no—
661C2×C3—51no—
662C2×C3—52no—
663C2×C3—51no—
664C2×C3—54no—
665C2×C3—104no—
666C2×C3—202no—
667C2×C3#6577914yesdirect product factor
668C2×C3C2×D4×AGL(1,𝔽5)12yes—
669C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
670C5C2×C3×#38611yescharacteristic, complemented, Sylow
671C22—28no—
672C22—24no—
673C22—24no—
674C22—22no—
675C22—44no—
676C22—54no—
677C22—58no—
678C22—54no—
679C22—52no—
680C22—52no—
681C22—54no—
682C22—51no—
683C22—51no—
684C22—52no—
685C22—54no—
686C22—104no—
687C22—108no—
688C22—1016no—
689C22—104no—
690C22—108no—
691C22—104no—
692C22—104no—
693C22—102no—
694C22—202no—
695C22—204no—
696C22—208no—
697C22—202no—
698C22—204no—
699C22C3×D4×AGL(1,𝔽5)14yes—
700C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
701C22C2×C3×C22⋊AGL(1,𝔽5)14yescomplemented
702C22C23×C3×AGL(1,𝔽5)11yescharacteristic
703C4—22no—
704C4—108no—
705C4—102no—
706C4—204no—
707C3C2×#6577911yescharacteristic, direct product factor, Sylow
708C2—24no—
709C2—42no—
710C2—51no—
711C2—52no—
712C2—54no—
713C2—51no—
714C2—104no—
715C2—202no—
716C2C3×#6577914yesdirect product factor
717C2C2×C3×D4×AGL(1,𝔽5)12yes—
718C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC23×C3×C5C22×C4
prime radicalC22×C3×D4×D5C2
cosocleC22×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C2×C3×#386
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
1. C24×C3×AGL(1,𝔽5)C2semidirect
3. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
4. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
5. C3×#65779C2direct (N × H)
6. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
7. C2×#65779C3direct (N × H)
14. C23×C3×AGL(1,𝔽5)C22semidirect
15. C22×C3×C5×D4C4semidirect
16. C22×C3×C22⋊D5C4semidirect
17. C22×C3×C22⋊D5C4semidirect
20. C2×C3×D4×D5C4semidirect
22. C22×C3×D20C4semidirect
26. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
27. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
28. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
30. C24×AGL(1,𝔽5)C2×C3semidirect
32. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
33. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
34. #65779C2×C3direct (N × H)
35. C2×(C2×AGL(1,𝔽5))⋊C4C2×C3semidirect
37. C24×C3×C5C2×C4semidirect
46. C23×C3×D5C2×C4semidirect
47. C23×C3×D5C2×C4semidirect
61. C22×C3×AGL(1,𝔽5)D4semidirect
65. C2×C3×C5×D4C2×C4semidirect
66. C22×C3×C4×C5C2×C4semidirect
69. C2×C3×C22⋊D5C2×C4semidirect
70. C2×C3×C22⋊D5C2×C4semidirect
71. C22×C3×Dic5C2×C4semidirect
76. C2×C3×D20C2×C4semidirect
79. C2×C3×C4×D5C2×C4semidirect
95. C23×AGL(1,𝔽5)C22×C3semidirect
96. C22×C5×D4C3×C4semidirect
97. C22×C22⋊D5C3×C4semidirect
98. C22×C22⋊D5C3×C4semidirect
101. C2×D4×D5C3×C4semidirect
103. C22×D20C3×C4semidirect
107. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
108. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
109. (C2×AGL(1,𝔽5))⋊C4C22×C3semidirect
114. C23×C3×C5C22⋊C4semidirect
117. C23×C3×C5C22×C4semidirect
136. C22×C3×D5C22⋊C4semidirect
137. C22×C3×D5C22⋊C4semidirect
140. C22×C3×D5C22×C4semidirect
156. C2×C3×AGL(1,𝔽5)C2×D4semidirect
159. C2×C3×C4×C5C22×C4semidirect
163. C2×C3×Dic5C22×C4semidirect
177. C22×C3×D4AGL(1,𝔽5)semidirect
190. C24×C5C2×C3×C4semidirect
199. C23×D5C2×C3×C4semidirect
200. C23×D5C2×C3×C4semidirect
214. C22×AGL(1,𝔽5)C3×D4semidirect
218. C2×C5×D4C2×C3×C4semidirect
219. C22×C4×C5C2×C3×C4semidirect
222. C2×C22⋊D5C2×C3×C4semidirect
223. C2×C22⋊D5C2×C3×C4semidirect
224. C22×Dic5C2×C3×C4semidirect
229. C2×D20C2×C3×C4semidirect
232. C2×C4×D5C2×C3×C4semidirect
248. C22×C3×C5C2×C22⋊C4semidirect
265. C2×C3×D5C2×C22⋊C4semidirect
294. C24×C3C2×AGL(1,𝔽5)semidirect
305. C2×C3×D4C2×AGL(1,𝔽5)semidirect
322. C22×C3×C4C2×AGL(1,𝔽5)semidirect
328. C23×C5C3×C22⋊C4semidirect
331. C23×C5C22×C3×C4semidirect
350. C22×D5C3×C22⋊C4semidirect
351. C22×D5C3×C22⋊C4semidirect
354. C22×D5C22×C3×C4semidirect
370. C2×AGL(1,𝔽5)C2×C3×D4semidirect
373. C2×C4×C5C22×C3×C4semidirect
377. C2×Dic5C22×C3×C4semidirect
391. C22×D4C3×AGL(1,𝔽5)semidirect
405. C2×C3×C5#386semidirect
410. C3×D5#386semidirect
447. C23×C3C22⋊AGL(1,𝔽5)semidirect
450. C23×C3C22×AGL(1,𝔽5)semidirect
470. C2×C3×C4C22×AGL(1,𝔽5)semidirect
477. C22×C5C2×C3×C22⋊C4semidirect
494. C2×D5C2×C3×C22⋊C4semidirect
523. C24C2×C3×AGL(1,𝔽5)semidirect
534. C2×D4C2×C3×AGL(1,𝔽5)semidirect
551. C22×C4C2×C3×AGL(1,𝔽5)semidirect
554. C3×C5C2×#386semidirect
585. C22×C3C2×C22⋊AGL(1,𝔽5)semidirect
593. C2×C5C3×#386semidirect
598. D5C3×#386semidirect
635. C23C3×C22⋊AGL(1,𝔽5)semidirect
638. C23C22×C3×AGL(1,𝔽5)semidirect
658. C2×C4C22×C3×AGL(1,𝔽5)semidirect
667. C2×C3#65779direct (N × H)
670. C5C2×C3×#386semidirect
701. C22C2×C3×C22⋊AGL(1,𝔽5)semidirect
707. C3C2×#65779direct (N × H)
716. C2C3×#65779direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×AGL(1,𝔽5)2
C22×C3×D4×D52
C22×C3×C22⋊AGL(1,𝔽5)2
C3×#657792
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×#657793
C2×C3×#3865