Finite Group Databasebeta

← #13028111

Subgroups — #13028111

Order 1280.

1486 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65711C212yesmaximal
2C2×#65688C211yesmaximal, characteristic
3C2×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4C4×D5×C4⋊C4C211yesmaximal, characteristic
5#10604344C212yesmaximal
6#10604198C211yesmaximal, characteristic
7#10604198C211yesmaximal, characteristic
8#10604198C211yesmaximal, characteristic
9#10604198C211yesmaximal, characteristic
10#10603802C212yesmaximal
11#10603801C212yesmaximal
12C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
14C22×C4⋊AGL(1,𝔽5)C2212yes—
15C22×C4⋊AGL(1,𝔽5)C2212yes—
16C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C22×C4×AGL(1,𝔽5)C2212yes—
19C2×D5×C4⋊C4C2211yescharacteristic
20C2×D5×C4⋊C4C2211yescharacteristic
21C2×C42×D5C2211yescharacteristic
22C2×C42×D5C2211yescharacteristic
23C2×C42×D5C2211yescharacteristic
24C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
25C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
26C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
27C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
28C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
29C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
30C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
31C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
32C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
33#65711—28no—
34#65688—24no—
35C4×C4⋊AGL(1,𝔽5)—24no—
36C4×C5×C4⋊C4C411yescharacteristic, complemented
37C4⋊C4×Dic5C411yescharacteristic, complemented
38C4⋊C4×Dic5C411yescharacteristic, complemented
39C4×C4⋊Dic5C411yescharacteristic, complemented
40C4×#683C411yescharacteristic, complemented
41C4×#683C411yescharacteristic, complemented
42D5×#95C2211yescharacteristic
43D5×#95C2211yescharacteristic
44#64938C411yescharacteristic, complemented
45#64938C411yescharacteristic, complemented
46#13884—51nomaximal, Sylow
47C23×AGL(1,𝔽5)C2312yes—
48C23×AGL(1,𝔽5)C2312yes—
49C23×AGL(1,𝔽5)C2312yes—
50C23×AGL(1,𝔽5)C2312yes—
51C22×C4×D5C2311yescharacteristic
52C22×C4×D5C2311yescharacteristic
53C22×C4×D5C2311yescharacteristic
54C22×C4×D5C2311yescharacteristic
55C22×C4×D5C2311yescharacteristic
56C22×C4×D5C2311yescharacteristic
57C22×C4×D5C2311yescharacteristic
58C2×C4⋊AGL(1,𝔽5)—22no—
59C2×C4⋊AGL(1,𝔽5)—22no—
60C2×C4⋊AGL(1,𝔽5)—22no—
61C2×C4⋊AGL(1,𝔽5)—22no—
62C2×C4⋊AGL(1,𝔽5)—24no—
63C2×C4⋊AGL(1,𝔽5)—24no—
64C2×C4⋊AGL(1,𝔽5)—22no—
65C2×C4⋊AGL(1,𝔽5)—24no—
66C2×C4⋊AGL(1,𝔽5)—24no—
67C2×C4⋊AGL(1,𝔽5)—22no—
68C2×C4⋊AGL(1,𝔽5)—22no—
69C2×C4⋊AGL(1,𝔽5)—22no—
70C2×C4⋊AGL(1,𝔽5)—22no—
71C2×C4⋊AGL(1,𝔽5)—22no—
72C2×C4⋊AGL(1,𝔽5)—42no—
73C2×C4⋊AGL(1,𝔽5)—42no—
74C2×C4⋊AGL(1,𝔽5)D414yes—
75C2×C4⋊AGL(1,𝔽5)Q814yes—
76C2×C4×AGL(1,𝔽5)—24no—
77C2×C4×AGL(1,𝔽5)—24no—
78C2×C4×AGL(1,𝔽5)—42no—
79C2×C5×C4⋊C4C2×C411yescharacteristic
80C2×C5×C4⋊C4C2×C411yescharacteristic
81C2×C42×C5C2×C411yescharacteristic
82C2×C42×C5C2×C411yescharacteristic
83C2×C42×C5C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×C4⋊Dic5C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×#683C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2×C411yescharacteristic
94C2×C4×Dic5C2×C411yescharacteristic
95C2×C4×Dic5C2×C411yescharacteristic
96C2×C4×Dic5C2×C411yescharacteristic
97C2×C4×Dic5C2×C411yescharacteristic
98C2×C4×Dic5C2×C411yescharacteristic
99D5×C4⋊C4—22no—
100D5×C4⋊C4—22no—
101D5×C4⋊C4D414yes—
102D5×C4⋊C4Q814yes—
103C42×D5—22no—
104C42×D5—22no—
105C42×D5—22no—
106C42×D5—22no—
107C42×D5—22no—
108C42×D5—22no—
109(C2×AGL(1,𝔽5))⋊C4—24no—
110(C2×AGL(1,𝔽5))⋊C4—24no—
111(C2×AGL(1,𝔽5))⋊C4—24no—
112(C2×AGL(1,𝔽5))⋊C4—24no—
113(C2×AGL(1,𝔽5))⋊C4—24no—
114(C2×AGL(1,𝔽5))⋊C4—24no—
115(C2×AGL(1,𝔽5))⋊C4—42no—
116(C2×AGL(1,𝔽5))⋊C4—42no—
117(C2×AGL(1,𝔽5))⋊C4—42no—
118C5×#95C2×C411yescharacteristic
119C5×#95C2×C411yescharacteristic
120#3963C2×C411yescharacteristic
121#3963C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126C2×#387—52no—
127C2×#384—51no—
128C2×C4×C4⋊C4—51no—
129C2×C4×C4⋊C4—51no—
130#1442—52no—
131#1441—52no—
132#1436—52no—
133C4⋊#95—51no—
134C4⋊#95—51no—
135C4⋊#95—51no—
136C4⋊#95—51no—
137C23×D5C2411yescharacteristic
138C22×AGL(1,𝔽5)—22no—
139C22×AGL(1,𝔽5)—22no—
140C22×AGL(1,𝔽5)—22no—
141C22×AGL(1,𝔽5)—22no—
142C22×AGL(1,𝔽5)—22no—
143C22×AGL(1,𝔽5)—22no—
144C22×AGL(1,𝔽5)—22no—
145C22×AGL(1,𝔽5)—22no—
146C22×AGL(1,𝔽5)—22no—
147C22×AGL(1,𝔽5)—22no—
148C22×AGL(1,𝔽5)—22no—
149C22×AGL(1,𝔽5)—22no—
150C22×AGL(1,𝔽5)—22no—
151C22×AGL(1,𝔽5)—22no—
152C22×AGL(1,𝔽5)—22no—
153C22×AGL(1,𝔽5)—22no—
154C22×AGL(1,𝔽5)—22no—
155C22×AGL(1,𝔽5)—22no—
156C22×AGL(1,𝔽5)—22no—
157C22×AGL(1,𝔽5)—22no—
158C22×AGL(1,𝔽5)—22no—
159C22×AGL(1,𝔽5)—22no—
160C22×AGL(1,𝔽5)—22no—
161C22×AGL(1,𝔽5)—22no—
162C22×AGL(1,𝔽5)—22no—
163C22×AGL(1,𝔽5)—22no—
164C22×AGL(1,𝔽5)C2×D414yes—
165C22×AGL(1,𝔽5)C2×Q814yes—
166C22×C4×C5C22×C411yescharacteristic
167C22×C4×C5C22×C411yescharacteristic
168C22×C4×C5C22×C411yescharacteristic
169C22×C4×C5C22×C411yescharacteristic
170C22×C4×C5C22×C411yescharacteristic
171C22×C4×C5C22×C411yescharacteristic
172C22×C4×C5C22×C411yescharacteristic
173C22×Dic5C22×C411yescharacteristic
174C22×Dic5C22×C411yescharacteristic
175C22×Dic5C22×C411yescharacteristic
176C22×Dic5C22×C411yescharacteristic
177C22×Dic5C22×C411yescharacteristic
178C22×Dic5C22×C411yescharacteristic
179C22×Dic5C22×C411yescharacteristic
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—21no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—21no—
187C2×C4×D5—21no—
188C2×C4×D5—21no—
189C2×C4×D5—21no—
190C2×C4×D5—21no—
191C2×C4×D5—21no—
192C2×C4×D5—21no—
193C2×C4×D5—21no—
194C2×C4×D5—21no—
195C2×C4×D5—21no—
196C2×C4×D5—21no—
197C2×C4×D5—21no—
198C2×C4×D5—21no—
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5—21no—
207C2×C4×D5—21no—
208C2×C4×D5C2×D412yes—
209C2×C4×D5C2×D412yes—
210C2×C4×D5C2×D412yes—
211C2×C4×D5C2×D412yes—
212C2×C4×D5C2×Q812yes—
213C2×C4×D5C2×Q812yes—
214C2×C4×D5C2×Q812yes—
215C2×C4×D5C2×Q812yes—
216C2×C4×D5#4112yes—
217C2×C4×D5#4112yes—
218C2×C4×D5#4112yes—
219C2×C4×D5#4112yes—
220C2×C4×D5#4112yes—
221C2×C4×D5#4112yes—
222C4⋊AGL(1,𝔽5)—28no—
223C4⋊AGL(1,𝔽5)—28no—
224C4⋊AGL(1,𝔽5)—48no—
225C4⋊AGL(1,𝔽5)—48no—
226C4⋊AGL(1,𝔽5)—44no—
227C4⋊AGL(1,𝔽5)—44no—
228C4×AGL(1,𝔽5)—48no—
229C5×C4⋊C4—22no—
230C5×C4⋊C4C4⋊C414yescomplemented
231C42×C5—22no—
232C42×C5—22no—
233C42×C5—22no—
234C4⋊Dic5—22no—
235C4⋊Dic5C4⋊C414yescomplemented
236#683—22no—
237#683—22no—
238#683C4⋊C414yescomplemented
239#683C4⋊C414yescomplemented
240C4×Dic5—22no—
241C4×Dic5—22no—
242C4×Dic5—22no—
243C4×Dic5—22no—
244C4×Dic5—22no—
245C4×Dic5—22no—
246C4×Dic5—22no—
247C4×Dic5—22no—
248C4×Dic5—22no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—51no—
251C22×C4⋊C4—51no—
252C22×C4⋊C4—51no—
253C22×C4⋊C4—51no—
254C22×C4⋊C4—51no—
255C22×C4⋊C4—52no—
256C22×C4⋊C4—52no—
257C22×C42—51no—
258C22×C42—51no—
259C22×C42—51no—
260C22×C42—52no—
261#387—108no—
262#384—104no—
263C4×C4⋊C4—51no—
264C4×C4⋊C4—51no—
265C4×C4⋊C4—51no—
266C4×C4⋊C4—51no—
267C4×C4⋊C4—51no—
268C4×C4⋊C4—51no—
269C4×C4⋊C4—51no—
270C4×C4⋊C4—104no—
271C4×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
272C2×#95—51no—
273C2×#95—51no—
274C2×#95—52no—
275C2×#95—52no—
276C2×#95—52no—
277C2×#95—52no—
278C2×#95—52no—
279C2×#95—52no—
280C2×#95—52no—
281C2×#95—52no—
282C2×#95—52no—
283C23×C5C23×C411yescharacteristic
284C22×D5C22×D411yescharacteristic
285C22×D5C22×D411yescharacteristic
286C22×D5C22×Q811yescharacteristic
287C22×D5C22×Q811yescharacteristic
288C22×D5C2×#4111yescharacteristic
289C22×D5C2×#4111yescharacteristic
290C22×D5C2×#4111yescharacteristic
291C22×D5C2×#4111yescharacteristic
292C22×D5C2×#4111yescharacteristic
293C22×D5C2×#4111yescharacteristic
294C22×D5H(5,𝔽2)11yescharacteristic
295C22×D5H(5,𝔽2)11yescharacteristic
296C22×D52−1+411yescharacteristic
297C22×D52−1+411yescharacteristic
298C2×AGL(1,𝔽5)—24no—
299C2×AGL(1,𝔽5)—24no—
300C2×AGL(1,𝔽5)—24no—
301C2×AGL(1,𝔽5)—24no—
302C2×AGL(1,𝔽5)—24no—
303C2×AGL(1,𝔽5)—24no—
304C2×AGL(1,𝔽5)—42no—
305C2×AGL(1,𝔽5)—42no—
306C2×AGL(1,𝔽5)—42no—
307C2×AGL(1,𝔽5)—42no—
308C2×AGL(1,𝔽5)—42no—
309C2×AGL(1,𝔽5)—42no—
310C2×AGL(1,𝔽5)—42no—
311C2×AGL(1,𝔽5)—42no—
312C2×AGL(1,𝔽5)—42no—
313C2×AGL(1,𝔽5)—42no—
314C2×AGL(1,𝔽5)—42no—
315C2×AGL(1,𝔽5)—42no—
316C2×AGL(1,𝔽5)—42no—
317C2×AGL(1,𝔽5)—42no—
318C2×AGL(1,𝔽5)—42no—
319C2×AGL(1,𝔽5)—42no—
320C2×AGL(1,𝔽5)—42no—
321C2×AGL(1,𝔽5)—42no—
322C2×AGL(1,𝔽5)—42no—
323C2×AGL(1,𝔽5)—42no—
324C2×AGL(1,𝔽5)—42no—
325C2×AGL(1,𝔽5)—42no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5C2×C4⋊C412yes—
341C2×C4×C5C2×C4⋊C412yes—
342C2×C4×C5C2×C4⋊C412yes—
343C2×C4×C5#11712yes—
344C2×C4×C5#11712yes—
345C2×C4×C5C4×D412yes—
346C2×C4×C5C4×Q812yes—
347C2×Dic5—21no—
348C2×Dic5—21no—
349C2×Dic5—21no—
350C2×Dic5—21no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—21no—
357C2×Dic5—21no—
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—21no—
361C2×Dic5C2×C4⋊C412yes—
362C2×Dic5C2×C4⋊C412yes—
363C2×Dic5C2×C4⋊C412yes—
364C2×Dic5#11712yes—
365C2×Dic5#11712yes—
366C2×Dic5C4×D412yes—
367C2×Dic5C4×Q812yes—
368C4×D5—22no—
369C4×D5—22no—
370C4×D5—22no—
371C4×D5—22no—
372C4×D5—22no—
373C4×D5—22no—
374C4×D5—22no—
375C4×D5—22no—
376C4×D5—22no—
377C4×D5—22no—
378C4×D5—22no—
379C4×D5—22no—
380C4×D5—22no—
381C4×D5—22no—
382C4×D5—22no—
383C4×D5—22no—
384C4×D5—41no—
385C4×D5—41no—
386C4×D5—41no—
387C4×D5—41no—
388C4×D5—41no—
389C4×D5—41no—
390C4×D5—41no—
391C4×D5—41no—
392C4×D5C22⋊Q814yes—
393C4×D5#12314yes—
394C4×D5#12514yes—
395C4×D5#12614yes—
396C23×C4—51no—
397C23×C4—51no—
398C23×C4—51no—
399C23×C4—51no—
400C23×C4—51no—
401C23×C4—52no—
402C23×C4—52no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—52no—
406C23×C4—52no—
407C2×C4⋊C4—51no—
408C2×C4⋊C4—51no—
409C2×C4⋊C4—51no—
410C2×C4⋊C4—54no—
411C2×C4⋊C4—54no—
412C2×C4⋊C4—54no—
413C2×C4⋊C4—54no—
414C2×C4⋊C4—51no—
415C2×C4⋊C4—51no—
416C2×C4⋊C4—51no—
417C2×C4⋊C4—102no—
418C2×C4⋊C4—102no—
419C2×C4⋊C4—102no—
420C2×C4⋊C4—102no—
421C2×C4⋊C4—102no—
422C2×C4⋊C4—102no—
423C2×C4⋊C4—102no—
424C2×C4⋊C4—102no—
425C2×C4⋊C4—102no—
426C2×C4⋊C4—102no—
427C2×C4⋊C4—102no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—102no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—104no—
432C2×C4⋊C4—104no—
433C2×C4⋊C4—202no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
436C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
437C2×C42—51no—
438C2×C42—51no—
439C2×C42—51no—
440C2×C42—51no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—51no—
444C2×C42—51no—
445C2×C42—51no—
446C2×C42—102no—
447C2×C42—102no—
448C2×C42—102no—
449C2×C42—102no—
450C2×C42—102no—
451C2×C42—102no—
452C2×C42—104no—
453C2×C42—104no—
454C2×C42—202no—
455C2×C42C2×AGL(1,𝔽5)11yescharacteristic
456C2×C42C2×AGL(1,𝔽5)11yescharacteristic
457C2×C42C2×AGL(1,𝔽5)11yescharacteristic
458#95—51no—
459#95—51no—
460#95—51no—
461#95—51no—
462#95—51no—
463#95—51no—
464#95—104no—
465#95—104no—
466#95—104no—
467#95—104no—
468#95—104no—
469#95—104no—
470#95—202no—
471#95—202no—
472#95—202no—
473#95C2×AGL(1,𝔽5)11yescharacteristic
474#95C2×AGL(1,𝔽5)11yescharacteristic
475C22×C5C22×C4⋊C411yescharacteristic
476C22×C5C2×#11711yescharacteristic
477C22×C5C2×#11711yescharacteristic
478C22×C5C2×C4×D411yescharacteristic
479C22×C5C2×C4×Q811yescharacteristic
480C22×C5#52011yescharacteristic
481C22×C5#52011yescharacteristic
482C2×D5C2×C22⋊Q811yescharacteristic
483C2×D5C2×#12311yescharacteristic
484C2×D5C2×#12511yescharacteristic
485C2×D5C2×#12611yescharacteristic
486C2×D5#53211yescharacteristic
487C2×D5#53211yescharacteristic
488C2×D5#53311yescharacteristic
489C2×D5#53311yescharacteristic
490C2×D5#54011yescharacteristic
491C2×D5#54111yescharacteristic
492C2×D5#54211yescharacteristic
493C2×D5#54211yescharacteristic
494C2×D5D4211yescharacteristic
495C2×D5#54611yescharacteristic
496C2×D5#54711yescharacteristic
497C2×D5#54811yescharacteristic
498C2×D5D4×Q811yescharacteristic
499C2×D5D4×Q811yescharacteristic
500C2×D5#55011yescharacteristic
501C2×D5#55211yescharacteristic
502C2×D5#55311yescharacteristic
503C2×D5#55411yescharacteristic
504C2×D5#55411yescharacteristic
505C2×D5#55611yescharacteristic
506C2×D5#55711yescharacteristic
507C2×D5#55711yescharacteristic
508C2×D5Q8211yescharacteristic
509C2×D5#55911yescharacteristic
510AGL(1,𝔽5)—44no—
511AGL(1,𝔽5)—44no—
512AGL(1,𝔽5)—82no—
513AGL(1,𝔽5)—82no—
514C4×C5—22no—
515C4×C5—22no—
516C4×C5—22no—
517C4×C5—22no—
518C4×C5—41no—
519C4×C5—41no—
520C4×C5#38714yescomplemented
521Dic5—22no—
522Dic5—22no—
523Dic5—22no—
524Dic5—22no—
525Dic5—41no—
526Dic5—41no—
527Dic5#38714yescomplemented
528C24—51no—
529C22×C4—51no—
530C22×C4—52no—
531C22×C4—52no—
532C22×C4—52no—
533C22×C4—52no—
534C22×C4—52no—
535C22×C4—52no—
536C22×C4—51no—
537C22×C4—51no—
538C22×C4—51no—
539C22×C4—51no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—52no—
543C22×C4—52no—
544C22×C4—52no—
545C22×C4—52no—
546C22×C4—52no—
547C22×C4—52no—
548C22×C4—54no—
549C22×C4—54no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4C22×AGL(1,𝔽5)11yescharacteristic
607C22×C4C22×AGL(1,𝔽5)11yescharacteristic
608C22×C4C22×AGL(1,𝔽5)11yescharacteristic
609C22×C4C22×AGL(1,𝔽5)11yescharacteristic
610C22×C4C22×AGL(1,𝔽5)11yescharacteristic
611C22×C4C22×AGL(1,𝔽5)11yescharacteristic
612C22×C4C22×AGL(1,𝔽5)11yescharacteristic
613C4⋊C4—22no—
614C4⋊C4—54no—
615C4⋊C4—54no—
616C4⋊C4—54no—
617C4⋊C4—102no—
618C4⋊C4—102no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—102no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C4⋊C4—208no—
625C4⋊C4—208no—
626C4⋊C4C4⋊AGL(1,𝔽5)14yescomplemented
627C42—22no—
628C42—22no—
629C42—22no—
630C42—102no—
631C42—102no—
632C42—102no—
633C42—102no—
634C42—102no—
635C42—102no—
636C42—102no—
637C42—102no—
638C42—102no—
639C42—208no—
640C2×C5#228511yescharacteristic
641C2×C5C2×#38711yescharacteristic
642C2×C5#231411yescharacteristic
643C2×C5D4×C4⋊C411yescharacteristic
644C2×C5Q8×C4⋊C411yescharacteristic
645C2×C5#235211yescharacteristic
646C2×C5#235511yescharacteristic
647D5#244511yescharacteristic
648D5#244611yescharacteristic
649D5#245111yescharacteristic
650D5#245211yescharacteristic
651D5#250611yescharacteristic
652D5#250711yescharacteristic
653D5#251111yescharacteristic
654D5#251211yescharacteristic
655C23—51no—
656C23—51no—
657C23—51no—
658C23—51no—
659C23—51no—
660C23—51no—
661C23—51no—
662C23—51no—
663C23—51no—
664C23—51no—
665C23—51no—
666C23—51no—
667C23—51no—
668C23—51no—
669C23C23×AGL(1,𝔽5)11yescharacteristic
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—52no—
685C2×C4—52no—
686C2×C4—52no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—54no—
690C2×C4—54no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—52no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—101no—
712C2×C4—101no—
713C2×C4—101no—
714C2×C4—101no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—101no—
719C2×C4—104no—
720C2×C4—104no—
721C2×C4—104no—
722C2×C4—104no—
723C2×C4—104no—
724C2×C4—104no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—201no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—201no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—202no—
748C2×C4—202no—
749C2×C4—202no—
750C2×C4—202no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
762C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
763C2×C4C2×C4⋊AGL(1,𝔽5)12yes—
764C2×C4#413012yes—
765C2×C4#413012yes—
766C2×C4D4×AGL(1,𝔽5)12yes—
767C2×C4Q8×AGL(1,𝔽5)12yes—
768C5#1388411yescharacteristic, complemented, Sylow
769C22—51no—
770C22—51no—
771C22—51no—
772C22—51no—
773C22—51no—
774C22—51no—
775C22—51no—
776C22—51no—
777C22—51no—
778C22—51no—
779C22—51no—
780C22—51no—
781C22—51no—
782C22—51no—
783C22—51no—
784C22—51no—
785C22—51no—
786C22—51no—
787C22—51no—
788C22—51no—
789C22—51no—
790C22—51no—
791C22—51no—
792C22—51no—
793C22—51no—
794C22—51no—
795C22—51no—
796C22—51no—
797C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
798C22C2×#413011yescharacteristic
799C22C2×#413011yescharacteristic
800C22C2×D4×AGL(1,𝔽5)11yescharacteristic
801C22C2×Q8×AGL(1,𝔽5)11yescharacteristic
802C22#6626611yescharacteristic
803C22#6626611yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—54no—
811C4—102no—
812C4—102no—
813C4—102no—
814C4—102no—
815C4—204no—
816C4—204no—
817C4—201no—
818C4—201no—
819C4—402no—
820C4—402no—
821C4#6571114yescomplemented
822C2—51no—
823C2—51no—
824C2—51no—
825C2—51no—
826C2—51no—
827C2—51no—
828C2—51no—
829C2—51no—
830C2#1061704811yescharacteristic
831C2C2×#6571111yescharacteristic
832C2#1061713011yescharacteristic
833C2D4×C4⋊AGL(1,𝔽5)11yescharacteristic
834C2#1061717911yescharacteristic
835C2Q8×C4⋊AGL(1,𝔽5)11yescharacteristic
836C2#1061721311yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC4×C5×C4⋊C4C4
prime radical, cosocleC23×D5C24
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#13884
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C4×C5×C4⋊C4C4semidirect
37. C4⋊C4×Dic5C4semidirect
38. C4⋊C4×Dic5C4semidirect
39. C4×C4⋊Dic5C4semidirect
40. C4×#683C4semidirect
41. C4×#683C4semidirect
44. #64938C4semidirect
45. #64938C4semidirect
230. C5×C4⋊C4C4⋊C4semidirect
235. C4⋊Dic5C4⋊C4semidirect
238. #683C4⋊C4semidirect
239. #683C4⋊C4semidirect
271. C4×C4⋊C4AGL(1,𝔽5)semidirect
520. C4×C5#387semidirect
527. Dic5#387semidirect
626. C4⋊C4C4⋊AGL(1,𝔽5)semidirect
768. C5#13884semidirect
821. C4#65711semidirect

Maximal subgroups

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

subgroupindex
C2×#657112
C2×#656882
C2×C4×C4⋊AGL(1,𝔽5)2
C4×D5×C4⋊C42
#106043442
#106041982
#106038022
#106038012
#138845