Finite Group Databasebeta

← C2×C3×#65711 #14320360

Subgroups — C2×C3×#65711 #14320360

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×C3×C4×AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
5C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
6C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
7C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
8C3×#65711C218yesmaximal, direct product factor
9C2×#65711C311yesmaximal, characteristic, direct product factor, Hall
10C23×C3×AGL(1,𝔽5)C2211yescharacteristic
11C23×C3×AGL(1,𝔽5)C2211yescharacteristic
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C23×C3×AGL(1,𝔽5)C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)—24no—
18C2×C3×C4⋊AGL(1,𝔽5)C2214yes—
19C2×C3×C4×AGL(1,𝔽5)—24no—
20C2×C3×C4×AGL(1,𝔽5)C2214yes—
21C2×C3×C5×C4⋊C4C411yescharacteristic, complemented
22C2×C3×C4⋊Dic5C411yescharacteristic, complemented
23C2×C3×#683C411yescharacteristic, complemented
24C2×C3×#683C411yescharacteristic, complemented
25C3×D5×C4⋊C4C414yescomplemented
26C3×D5×C4⋊C4C2214yes—
27C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
28C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
29C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
30C3×(C2×AGL(1,𝔽5))⋊C4C2214yes—
31C2×C3×#387—51nomaximal, Hall
32C22×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic
33C22×C4×AGL(1,𝔽5)C2×C311yescharacteristic
34C2×D5×C4⋊C4C2×C311yescharacteristic
35C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
36C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
37C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
38C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
39#65711C2×C318yesdirect product factor
40C23×C3×D5C2311yescharacteristic
41C22×C3×AGL(1,𝔽5)—22no—
42C22×C3×AGL(1,𝔽5)—22no—
43C22×C3×AGL(1,𝔽5)—22no—
44C22×C3×AGL(1,𝔽5)—22no—
45C22×C3×AGL(1,𝔽5)—22no—
46C22×C3×AGL(1,𝔽5)—22no—
47C22×C3×AGL(1,𝔽5)—22no—
48C22×C3×AGL(1,𝔽5)—22no—
49C22×C3×AGL(1,𝔽5)—22no—
50C22×C3×AGL(1,𝔽5)—22no—
51C22×C3×AGL(1,𝔽5)D414yes—
52C22×C3×AGL(1,𝔽5)Q814yes—
53C22×C3×AGL(1,𝔽5)C2312yes—
54C22×C3×AGL(1,𝔽5)C2312yes—
55C22×C3×AGL(1,𝔽5)C2312yes—
56C22×C3×AGL(1,𝔽5)C2312yes—
57C22×C3×C4×C5C2×C411yescharacteristic
58C22×C3×C4×C5C2×C411yescharacteristic
59C22×C3×C4×C5C2×C411yescharacteristic
60C22×C3×Dic5C2×C411yescharacteristic
61C22×C3×Dic5C2×C411yescharacteristic
62C22×C3×Dic5C2×C411yescharacteristic
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5C2×C412yes—
70C2×C3×C4×D5C2×C412yes—
71C2×C3×C4×D5C2×C412yes—
72C2×C3×C4×D5C2312yes—
73C2×C3×C4×D5C2312yes—
74C2×C3×C4×D5C2312yes—
75C3×C4⋊AGL(1,𝔽5)—28no—
76C3×C4×AGL(1,𝔽5)—28no—
77C3×C5×C4⋊C4C2×C414yescomplemented
78C3×C4⋊Dic5C2×C414yescomplemented
79C3×#683C2×C414yescomplemented
80C3×#683C2×C414yescomplemented
81C22×C3×C4⋊C4—51no—
82C22×C3×C4⋊C4—51no—
83C22×C3×C42—51no—
84C3×#387—58no—
85C2×C3×#95—51no—
86C2×C3×#95—51no—
87C2×C3×#95—51no—
88C2×C3×#95—51no—
89C23×AGL(1,𝔽5)C22×C311yescharacteristic
90C23×AGL(1,𝔽5)C22×C311yescharacteristic
91C23×AGL(1,𝔽5)C22×C311yescharacteristic
92C23×AGL(1,𝔽5)C22×C311yescharacteristic
93C22×C4×D5C22×C311yescharacteristic
94C22×C4×D5C22×C311yescharacteristic
95C22×C4×D5C22×C311yescharacteristic
96C2×C4⋊AGL(1,𝔽5)—24no—
97C2×C4⋊AGL(1,𝔽5)C22×C314yes—
98C2×C4×AGL(1,𝔽5)—24no—
99C2×C4×AGL(1,𝔽5)C22×C314yes—
100C2×C5×C4⋊C4C3×C411yescharacteristic, complemented
101C2×C4⋊Dic5C3×C411yescharacteristic, complemented
102C2×#683C3×C411yescharacteristic, complemented
103C2×#683C3×C411yescharacteristic, complemented
104D5×C4⋊C4C3×C414yescomplemented
105D5×C4⋊C4C22×C314yes—
106(C2×AGL(1,𝔽5))⋊C4C22×C314yes—
107(C2×AGL(1,𝔽5))⋊C4C22×C314yes—
108(C2×AGL(1,𝔽5))⋊C4C22×C314yes—
109(C2×AGL(1,𝔽5))⋊C4C22×C314yes—
110C2×#387—51noSylow
111C23×C3×C5C22×C411yescharacteristic
112C22×C3×D5C22×C411yescharacteristic
113C22×C3×D5C2×D412yes—
114C22×C3×D5C2×Q812yes—
115C22×C3×D5#4112yes—
116C22×C3×D5#4112yes—
117C22×C3×D5#4112yes—
118C22×C3×D5#4112yes—
119C22×C3×D5C2411yescharacteristic
120C2×C3×AGL(1,𝔽5)—28no—
121C2×C3×AGL(1,𝔽5)—28no—
122C2×C3×AGL(1,𝔽5)—22no—
123C2×C3×AGL(1,𝔽5)—22no—
124C2×C3×AGL(1,𝔽5)—22no—
125C2×C3×AGL(1,𝔽5)—22no—
126C2×C3×AGL(1,𝔽5)—22no—
127C2×C3×AGL(1,𝔽5)—22no—
128C2×C3×AGL(1,𝔽5)—22no—
129C2×C3×AGL(1,𝔽5)—22no—
130C2×C3×AGL(1,𝔽5)—22no—
131C2×C3×AGL(1,𝔽5)—22no—
132C2×C3×AGL(1,𝔽5)—44no—
133C2×C3×AGL(1,𝔽5)—44no—
134C2×C3×AGL(1,𝔽5)C2×D414yes—
135C2×C3×AGL(1,𝔽5)C2×Q814yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C412yes—
147C2×C3×Dic5C22×C412yes—
148C3×C4×D5—24no—
149C3×C4×D5—24no—
150C3×C4×D5—24no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×C4×D5—22no—
155C3×C4×D5—22no—
156C3×C4×D5—22no—
157C23×C3×C4—51no—
158C23×C3×C4—51no—
159C23×C3×C4—51no—
160C23×C3×C4—51no—
161C23×C3×C4—51no—
162C23×C3×C4—51no—
163C23×C3×C4—51no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—51no—
167C2×C3×C4⋊C4—54no—
168C2×C3×C4⋊C4—54no—
169C2×C3×C4⋊C4—54no—
170C2×C3×C4⋊C4—104no—
171C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
172C2×C3×C42—54no—
173C2×C3×C42—104no—
174C3×#95—54no—
175C3×#95—54no—
176C3×#95—54no—
177C3×#95—54no—
178C23×D5C23×C311yescharacteristic
179C22×AGL(1,𝔽5)—22no—
180C22×AGL(1,𝔽5)—22no—
181C22×AGL(1,𝔽5)—22no—
182C22×AGL(1,𝔽5)—22no—
183C22×AGL(1,𝔽5)—22no—
184C22×AGL(1,𝔽5)—22no—
185C22×AGL(1,𝔽5)—22no—
186C22×AGL(1,𝔽5)—22no—
187C22×AGL(1,𝔽5)—22no—
188C22×AGL(1,𝔽5)—22no—
189C22×AGL(1,𝔽5)C3×D414yes—
190C22×AGL(1,𝔽5)C3×Q814yes—
191C22×AGL(1,𝔽5)C23×C312yes—
192C22×AGL(1,𝔽5)C23×C312yes—
193C22×AGL(1,𝔽5)C23×C312yes—
194C22×AGL(1,𝔽5)C23×C312yes—
195C22×C4×C5C2×C3×C411yescharacteristic
196C22×C4×C5C2×C3×C411yescharacteristic
197C22×C4×C5C2×C3×C411yescharacteristic
198C22×Dic5C2×C3×C411yescharacteristic
199C22×Dic5C2×C3×C411yescharacteristic
200C22×Dic5C2×C3×C411yescharacteristic
201C2×C4×D5—22no—
202C2×C4×D5—22no—
203C2×C4×D5—22no—
204C2×C4×D5—22no—
205C2×C4×D5—22no—
206C2×C4×D5—22no—
207C2×C4×D5C2×C3×C412yes—
208C2×C4×D5C2×C3×C412yes—
209C2×C4×D5C2×C3×C412yes—
210C2×C4×D5C23×C312yes—
211C2×C4×D5C23×C312yes—
212C2×C4×D5C23×C312yes—
213C4⋊AGL(1,𝔽5)—28no—
214C4×AGL(1,𝔽5)—28no—
215C5×C4⋊C4C2×C3×C414yescomplemented
216C4⋊Dic5C2×C3×C414yescomplemented
217#683C2×C3×C414yescomplemented
218#683C2×C3×C414yescomplemented
219C22×C4⋊C4—51no—
220C22×C4⋊C4—51no—
221C22×C42—51no—
222#387—58no—
223C2×#95—51no—
224C2×#95—51no—
225C2×#95—51no—
226C2×#95—51no—
227C22×C3×C5#11712yes—
228C22×C3×C5C4×D412yes—
229C22×C3×C5C4×Q812yes—
230C22×C3×C5C23×C411yescharacteristic
231C2×C3×D5#11712yes—
232C2×C3×D5C4×D412yes—
233C2×C3×D5C4×Q812yes—
234C2×C3×D5C22⋊Q814yes—
235C2×C3×D5#12314yes—
236C2×C3×D5#12514yes—
237C2×C3×D5#12614yes—
238C2×C3×D5C22×D411yescharacteristic
239C2×C3×D5C22×Q811yescharacteristic
240C2×C3×D5C2×#4111yescharacteristic
241C2×C3×D5C2×#4111yescharacteristic
242C2×C3×D5C2×#4111yescharacteristic
243C2×C3×D5C2×#4111yescharacteristic
244C3×AGL(1,𝔽5)—24no—
245C3×AGL(1,𝔽5)—24no—
246C3×AGL(1,𝔽5)—42no—
247C3×AGL(1,𝔽5)—42no—
248C3×C4×C5—22no—
249C3×C4×C5—22no—
250C3×C4×C5—22no—
251C3×Dic5—22no—
252C3×Dic5—22no—
253C3×Dic5—22no—
254C24×C3—51no—
255C22×C3×C4—52no—
256C22×C3×C4—52no—
257C22×C3×C4—54no—
258C22×C3×C4—54no—
259C22×C3×C4—51no—
260C22×C3×C4—51no—
261C22×C3×C4—51no—
262C22×C3×C4—52no—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4—52no—
267C22×C3×C4—52no—
268C22×C3×C4—52no—
269C22×C3×C4—52no—
270C22×C3×C4—102no—
271C22×C3×C4—102no—
272C22×C3×C4—102no—
273C22×C3×C4—102no—
274C22×C3×C4—102no—
275C22×C3×C4—102no—
276C22×C3×C4—102no—
277C22×C3×C4—102no—
278C22×C3×C4—102no—
279C22×C3×C4—102no—
280C22×C3×C4—102no—
281C22×C3×C4—102no—
282C22×C3×C4—102no—
283C22×C3×C4—102no—
284C22×C3×C4—102no—
285C22×C3×C4—102no—
286C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
287C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
288C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
289C3×C4⋊C4—54no—
290C3×C4⋊C4—54no—
291C3×C4⋊C4—54no—
292C3×C4⋊C4—108no—
293C3×C4⋊C4C2×AGL(1,𝔽5)14yescomplemented
294C3×C42—108no—
295C23×C5C22×C3×C411yescharacteristic
296C22×D5C22×C3×C411yescharacteristic
297C22×D5C2×C3×D412yes—
298C22×D5C2×C3×Q812yes—
299C22×D5C3×#4112yes—
300C22×D5C3×#4112yes—
301C22×D5C3×#4112yes—
302C22×D5C3×#4112yes—
303C22×D5C24×C311yescharacteristic
304C2×AGL(1,𝔽5)—28no—
305C2×AGL(1,𝔽5)—28no—
306C2×AGL(1,𝔽5)—22no—
307C2×AGL(1,𝔽5)—22no—
308C2×AGL(1,𝔽5)—22no—
309C2×AGL(1,𝔽5)—22no—
310C2×AGL(1,𝔽5)—22no—
311C2×AGL(1,𝔽5)—22no—
312C2×AGL(1,𝔽5)—22no—
313C2×AGL(1,𝔽5)—22no—
314C2×AGL(1,𝔽5)—22no—
315C2×AGL(1,𝔽5)—22no—
316C2×AGL(1,𝔽5)—44no—
317C2×AGL(1,𝔽5)—44no—
318C2×AGL(1,𝔽5)C2×C3×D414yes—
319C2×AGL(1,𝔽5)C2×C3×Q814yes—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5C22×C3×C412yes—
324C2×C4×C5C22×C3×C412yes—
325C2×C4×C5C22×C3×C412yes—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5C22×C3×C412yes—
330C2×Dic5C22×C3×C412yes—
331C2×Dic5C22×C3×C412yes—
332C4×D5—24no—
333C4×D5—24no—
334C4×D5—24no—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—22no—
338C4×D5—22no—
339C4×D5—22no—
340C4×D5—22no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—51no—
345C23×C4—51no—
346C23×C4—51no—
347C23×C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—54no—
352C2×C4⋊C4—54no—
353C2×C4⋊C4—54no—
354C2×C4⋊C4—104no—
355C2×C4⋊C4C3×AGL(1,𝔽5)11yescharacteristic, complemented
356C2×C42—54no—
357C2×C42—104no—
358#95—54no—
359#95—54no—
360#95—54no—
361#95—54no—
362C2×C3×C5#38714yescomplemented
363C2×C3×C5C2×#11711yescharacteristic
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5C2×C4×Q811yescharacteristic
366C3×D5#38714yescomplemented
367C3×D5C2×C22⋊Q811yescharacteristic
368C3×D5C2×#12311yescharacteristic
369C3×D5C2×#12511yescharacteristic
370C3×D5C2×#12611yescharacteristic
371C23×C3—52no—
372C23×C3—52no—
373C23×C3—52no—
374C23×C3—52no—
375C23×C3—52no—
376C23×C3—52no—
377C23×C3—51no—
378C23×C3—51no—
379C23×C3C22×AGL(1,𝔽5)11yescharacteristic
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—54no—
384C2×C3×C4—54no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—104no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—104no—
394C2×C3×C4—104no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4—108no—
399C2×C3×C4—108no—
400C2×C3×C4—102no—
401C2×C3×C4—102no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4—102no—
406C2×C3×C4—102no—
407C2×C3×C4—102no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—204no—
413C2×C3×C4—204no—
414C2×C3×C4C22×AGL(1,𝔽5)12yes—
415C2×C3×C4C22×AGL(1,𝔽5)12yes—
416C2×C3×C4C22×AGL(1,𝔽5)12yes—
417C22×C5C3×#11712yes—
418C22×C5C3×C4×D412yes—
419C22×C5C3×C4×Q812yes—
420C22×C5C23×C3×C411yescharacteristic
421C2×D5C3×#11712yes—
422C2×D5C3×C4×D412yes—
423C2×D5C3×C4×Q812yes—
424C2×D5C3×C22⋊Q814yes—
425C2×D5C3×#12314yes—
426C2×D5C3×#12514yes—
427C2×D5C3×#12614yes—
428C2×D5C22×C3×D411yescharacteristic
429C2×D5C22×C3×Q811yescharacteristic
430C2×D5C2×C3×#4111yescharacteristic
431C2×D5C2×C3×#4111yescharacteristic
432C2×D5C2×C3×#4111yescharacteristic
433C2×D5C2×C3×#4111yescharacteristic
434AGL(1,𝔽5)—24no—
435AGL(1,𝔽5)—24no—
436AGL(1,𝔽5)—42no—
437AGL(1,𝔽5)—42no—
438C4×C5—22no—
439C4×C5—22no—
440C4×C5—22no—
441Dic5—22no—
442Dic5—22no—
443Dic5—22no—
444C24—51no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—54no—
448C22×C4—54no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—52no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—52no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—52no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
477C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
478C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
479C4⋊C4—54no—
480C4⋊C4—54no—
481C4⋊C4—54no—
482C4⋊C4—108no—
483C4⋊C4C2×C3×AGL(1,𝔽5)14yescomplemented
484C42—108no—
485C3×C5C2×#38711yescharacteristic, complemented, Hall
486C22×C3—54no—
487C22×C3—54no—
488C22×C3—54no—
489C22×C3—54no—
490C22×C3—52no—
491C22×C3—51no—
492C22×C3—51no—
493C22×C3—52no—
494C22×C3—51no—
495C22×C3—51no—
496C22×C3—52no—
497C22×C3—51no—
498C22×C3—51no—
499C22×C3#413012yes—
500C22×C3D4×AGL(1,𝔽5)12yes—
501C22×C3Q8×AGL(1,𝔽5)12yes—
502C22×C3C23×AGL(1,𝔽5)11yescharacteristic
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—104no—
507C3×C4—104no—
508C3×C4—102no—
509C3×C4—102no—
510C3×C4—102no—
511C3×C4—202no—
512C3×C4—202no—
513C2×C5C3×#38714yescomplemented
514C2×C5C2×C3×#11711yescharacteristic
515C2×C5C2×C3×C4×D411yescharacteristic
516C2×C5C2×C3×C4×Q811yescharacteristic
517D5C3×#38714yescomplemented
518D5C2×C3×C22⋊Q811yescharacteristic
519D5C2×C3×#12311yescharacteristic
520D5C2×C3×#12511yescharacteristic
521D5C2×C3×#12611yescharacteristic
522C23—52no—
523C23—52no—
524C23—52no—
525C23—52no—
526C23—52no—
527C23—52no—
528C23—51no—
529C23—51no—
530C23C22×C3×AGL(1,𝔽5)11yescharacteristic
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—54no—
535C2×C4—54no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—104no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—104no—
547C2×C4—104no—
548C2×C4—102no—
549C2×C4—108no—
550C2×C4—108no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—204no—
564C2×C4—204no—
565C2×C4C22×C3×AGL(1,𝔽5)12yes—
566C2×C4C22×C3×AGL(1,𝔽5)12yes—
567C2×C4C22×C3×AGL(1,𝔽5)12yes—
568C2×C3—51no—
569C2×C3—51no—
570C2×C3—51no—
571C2×C3—51no—
572C2×C3—54no—
573C2×C3#6571114yesdirect product factor
574C2×C3C2×#413011yescharacteristic
575C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
576C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
577C5C2×C3×#38711yescharacteristic, complemented, Sylow
578C22—54no—
579C22—54no—
580C22—54no—
581C22—54no—
582C22—51no—
583C22—51no—
584C22—52no—
585C22—51no—
586C22—51no—
587C22—52no—
588C22—51no—
589C22—51no—
590C22—52no—
591C22C3×#413012yes—
592C22C3×D4×AGL(1,𝔽5)12yes—
593C22C3×Q8×AGL(1,𝔽5)12yes—
594C22C23×C3×AGL(1,𝔽5)11yescharacteristic
595C4—22no—
596C4—22no—
597C4—22no—
598C4—104no—
599C4—104no—
600C4—102no—
601C4—102no—
602C4—102no—
603C4—202no—
604C4—202no—
605C3C2×#6571111yescharacteristic, direct product factor, Sylow
606C2—51no—
607C2—51no—
608C2—51no—
609C2—54no—
610C2—51no—
611C2C3×#6571114yesdirect product factor
612C2C2×C3×#413011yescharacteristic
613C2C2×C3×D4×AGL(1,𝔽5)11yescharacteristic
614C2C2×C3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC22×D5C24×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×C3×#387
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×#65711C2direct (N × H)
9. C2×#65711C3direct (N × H)
21. C2×C3×C5×C4⋊C4C4semidirect
22. C2×C3×C4⋊Dic5C4semidirect
23. C2×C3×#683C4semidirect
24. C2×C3×#683C4semidirect
25. C3×D5×C4⋊C4C4semidirect
39. #65711C2×C3direct (N × H)
77. C3×C5×C4⋊C4C2×C4semidirect
78. C3×C4⋊Dic5C2×C4semidirect
79. C3×#683C2×C4semidirect
80. C3×#683C2×C4semidirect
100. C2×C5×C4⋊C4C3×C4semidirect
101. C2×C4⋊Dic5C3×C4semidirect
102. C2×#683C3×C4semidirect
103. C2×#683C3×C4semidirect
104. D5×C4⋊C4C3×C4semidirect
171. C2×C3×C4⋊C4AGL(1,𝔽5)semidirect
215. C5×C4⋊C4C2×C3×C4semidirect
216. C4⋊Dic5C2×C3×C4semidirect
217. #683C2×C3×C4semidirect
218. #683C2×C3×C4semidirect
293. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
355. C2×C4⋊C4C3×AGL(1,𝔽5)semidirect
362. C2×C3×C5#387semidirect
366. C3×D5#387semidirect
483. C4⋊C4C2×C3×AGL(1,𝔽5)semidirect
485. C3×C5C2×#387semidirect
513. C2×C5C3×#387semidirect
517. D5C3×#387semidirect
573. C2×C3#65711direct (N × H)
577. C5C2×C3×#387semidirect
605. C3C2×#65711direct (N × H)
611. C2C3×#65711direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊AGL(1,𝔽5)2
C22×C3×C4×AGL(1,𝔽5)2
C2×C3×D5×C4⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C3×#657112
C2×#657113
C2×C3×#3875