Finite Group Databasebeta

← #14319701

Subgroups — #14319701

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×#91923C211yesmaximal, characteristic
3D5×#877C211yesmaximal, characteristic
4C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
5C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic
6#11752021C211yesmaximal, characteristic
7AGL(1,𝔽5)×#217C211yesmaximal, characteristic
8C4×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
9#11751834C212yesmaximal, complemented
10#11751833C212yesmaximal, complemented
11AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal, complemented
12#10617127—31nomaximal, Hall
13C23×ΓL(1,𝔽16)C2211yescharacteristic
14C23×C3×AGL(1,𝔽5)C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×#6763C2211yescharacteristic
17C2×C4×ΓL(1,𝔽16)C2212yes—
18C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4×AGL(1,𝔽5)C2212yes—
20C2×Dic3⋊AGL(1,𝔽5)C418yescomplemented
21C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2212yes—
26#91923C418yescomplemented
27C2×Dic3×AGL(1,𝔽5)C2212yes—
28C2×Dic3×AGL(1,𝔽5)C2212yes—
29C2×Dic3×AGL(1,𝔽5)C2212yes—
30#91766C411yescharacteristic, complemented
31C5×#877C411yescharacteristic, complemented
32C3×D5×C22⋊C4C2211yescharacteristic
33D5×#217C2211yescharacteristic
34#91532C411yescharacteristic, complemented
35#91529C411yescharacteristic, complemented
36#91394C412yescomplemented
37#91393C412yescomplemented
38D5×Dic3⋊C4C2212yes—
39C4×D5×Dic3C2212yes—
40#91235C2212yes—
41C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73435—51nomaximal, Hall
45C2×#4130—31no—
46C22×C4⋊AGL(1,𝔽5)—31no—
47D5×#117—31no—
48C4⋊C4×AGL(1,𝔽5)—32no—
49C4⋊C4×AGL(1,𝔽5)—32no—
50C22⋊C4×AGL(1,𝔽5)—31no—
51C22⋊C4×AGL(1,𝔽5)—31no—
52C22⋊C4×AGL(1,𝔽5)—31no—
53C22⋊C4×AGL(1,𝔽5)D311yescharacteristic
54C4×C4⋊AGL(1,𝔽5)—32no—
55C4×C4⋊AGL(1,𝔽5)—32no—
56C23×C3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)—42no—
58C22×ΓL(1,𝔽16)C2×C414yes—
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×ΓL(1,𝔽16)C2312yes—
61C22×ΓL(1,𝔽16)C2311yescharacteristic
62C22×C3×AGL(1,𝔽5)—42no—
63C22×C3×AGL(1,𝔽5)C2×C414yes—
64C22×C3×AGL(1,𝔽5)C2311yescharacteristic
65C22×C3×AGL(1,𝔽5)C2312yes—
66C22×C3×AGL(1,𝔽5)C2311yescharacteristic
67C22×Dic15C2×C411yescharacteristic
68C22×C5×Dic3C2×C411yescharacteristic
69C2×C3×C4×D5C2312yes—
70C2×D5×Dic3C2×C411yescharacteristic
71C2×D5×Dic3C2×C411yescharacteristic
72C2×D5×Dic3C2×C414yes—
73C2×D5×Dic3C2×C414yes—
74C2×D5×Dic3C2312yes—
75C2×D5×Dic3C2311yescharacteristic
76C2×D5×Dic3C2311yescharacteristic
77#6763C2×C414yes—
78C4×ΓL(1,𝔽16)—42no—
79C3×C22⋊AGL(1,𝔽5)C2×C414yes—
80C3×C4×AGL(1,𝔽5)—42no—
81Dic3⋊AGL(1,𝔽5)C2×C414yes—
82Dic3⋊AGL(1,𝔽5)C2×C414yes—
83Dic3⋊AGL(1,𝔽5)C2×C414yes—
84Dic3⋊AGL(1,𝔽5)C2×C414yes—
85Dic3⋊AGL(1,𝔽5)C2×C418yescomplemented
86Dic3×AGL(1,𝔽5)—42no—
87Dic3×AGL(1,𝔽5)—42no—
88Dic3×AGL(1,𝔽5)C2×C418yescomplemented
89C3×C5×C22⋊C4C2×C411yescharacteristic
90#6719C2×C411yescharacteristic
91#6712C2×C412yescomplemented
92C4×Dic15C2×C412yescomplemented
93C5×#217C2×C411yescharacteristic
94C5×Dic3⋊C4C2×C412yescomplemented
95C4×C5×Dic3C2×C412yescomplemented
96C3×C22⋊Dic5C2×C411yescharacteristic
97C3×#685C2×C412yes—
98Dic3⋊Dic5C2×C412yescomplemented
99#6669C2×C412yescomplemented
100#6665C2×C412yes—
101Dic3×Dic5C2×C412yescomplemented
102Dic3×Dic5C2×C412yescomplemented
103C22×Dic3⋊C4—51no—
104C2×#877—51no—
105C2×#877—51no—
106C3×C4×C22⋊C4—51no—
107C4×#217—51no—
108Dic3×C22⋊C4—51no—
109Dic3×C22⋊C4—51no—
110C4×Dic3⋊C4—52no—
111C4×Dic3⋊C4—52no—
112#4649—52no—
113#4649—52no—
114C23×AGL(1,𝔽5)—31no—
115C23×AGL(1,𝔽5)C2×D311yescharacteristic
116C22×C4×D5—31no—
117C2×C22⋊AGL(1,𝔽5)—31no—
118C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
119#4130—38no—
120C2×C4⋊AGL(1,𝔽5)—38no—
121C2×C4⋊AGL(1,𝔽5)—31no—
122C2×C4⋊AGL(1,𝔽5)—31no—
123C2×C4⋊AGL(1,𝔽5)—32no—
124C2×C4⋊AGL(1,𝔽5)—31no—
125C2×C4⋊AGL(1,𝔽5)—31no—
126C2×C4×AGL(1,𝔽5)—32no—
127C2×C4×AGL(1,𝔽5)—32no—
128C2×C4×AGL(1,𝔽5)—32no—
129C2×C4×AGL(1,𝔽5)—32no—
130C2×C4×AGL(1,𝔽5)C2×D312yes—
131C5×#117—31no—
132#4072—31no—
133#4038—32no—
134D5×C4⋊C4—32no—
135D5×C22⋊C4—31no—
136D5×C22⋊C4C2×D311yescharacteristic
137#4023—31no—
138#4023—31no—
139#4018—32no—
140C42×D5—32no—
141(C2×AGL(1,𝔽5))⋊C4—32no—
142(C2×AGL(1,𝔽5))⋊C4—32no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
145#2274—151noSylow
146C23×C3×C5C22×C411yescharacteristic
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5C22×C411yescharacteristic
150C22×C3×D5C22×C412yes—
151C22×C3×D5C22×C412yes—
152C22×C3×D5C2411yescharacteristic
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—22no—
156C2×ΓL(1,𝔽16)—22no—
157C2×ΓL(1,𝔽16)—44no—
158C2×ΓL(1,𝔽16)C22×C414yes—
159C2×ΓL(1,𝔽16)C22×C412yes—
160C2×ΓL(1,𝔽16)C22×C412yes—
161C2×C3×AGL(1,𝔽5)—22no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—44no—
166C2×C3×AGL(1,𝔽5)C22×C414yes—
167C2×C3×AGL(1,𝔽5)C22×C412yes—
168C2×C3×AGL(1,𝔽5)C22×C412yes—
169C2×C3×C4×C5C22×C412yes—
170C2×Dic15C4214yescomplemented
171C2×Dic15C22×C412yes—
172C2×Dic15C22×C411yescharacteristic
173C2×Dic15C22×C411yescharacteristic
174C2×C5×Dic3C4214yescomplemented
175C2×C5×Dic3C22×C412yes—
176C2×C5×Dic3C22×C411yescharacteristic
177C2×C5×Dic3C22×C411yescharacteristic
178C2×C3×Dic5C22×C412yes—
179C3×C4×D5—22no—
180C3×C4×D5—22no—
181D5×Dic3—22no—
182D5×Dic3—22no—
183D5×Dic3C4214yescomplemented
184D5×Dic3C4214yescomplemented
185D5×Dic3C22×C412yes—
186D5×Dic3C22×C412yes—
187D5×Dic3C22×C412yes—
188D5×Dic3C22×C412yes—
189C23×C3×C4—51no—
190C23×Dic3—51no—
191C23×Dic3—51no—
192C2×C3×C22⋊C4—51no—
193C2×C3×C22⋊C4—51no—
194C2×C3×C42—52no—
195C2×#217—51no—
196C2×#217—51no—
197C2×Dic3⋊C4—58no—
198C2×Dic3⋊C4—51no—
199C2×Dic3⋊C4—51no—
200C2×Dic3⋊C4—52no—
201C2×Dic3⋊C4—51no—
202C2×Dic3⋊C4—51no—
203C2×Dic3⋊C4—52no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—52no—
206C2×C4×Dic3—52no—
207C2×C4×Dic3—52no—
208C2×C4×Dic3—52no—
209#877—58no—
210#877—51no—
211#877—51no—
212#877—51no—
213#877—52no—
214#877—52no—
215#877AGL(1,𝔽5)11yescharacteristic, complemented
216C3×#95—52no—
217C3⋊#95—52no—
218C3⋊#95—52no—
219C3⋊#95—52no—
220C23×D5C22×D311yescharacteristic
221C22×AGL(1,𝔽5)—32no—
222C22×AGL(1,𝔽5)—31no—
223C22×AGL(1,𝔽5)—31no—
224C22×AGL(1,𝔽5)—34no—
225C22×AGL(1,𝔽5)—42no—
226C22×AGL(1,𝔽5)—122no—
227C22×AGL(1,𝔽5)C4×D314yes—
228C22×AGL(1,𝔽5)C22×D312yes—
229C22×AGL(1,𝔽5)C22×D311yescharacteristic
230C22×AGL(1,𝔽5)C22×D311yescharacteristic
231C22×C4×C5—31no—
232C22×Dic5—31no—
233C2×C4×D5—34no—
234C2×C4×D5—34no—
235C2×C4×D5—31no—
236C2×C4×D5—31no—
237C2×C4×D5—31no—
238C2×C4×D5—31no—
239C2×C4×D5—32no—
240C2×C4×D5C22×D312yes—
241C22⋊AGL(1,𝔽5)—34no—
242C22⋊AGL(1,𝔽5)C4×D314yes—
243C4⋊AGL(1,𝔽5)—34no—
244C4⋊AGL(1,𝔽5)—34no—
245C4⋊AGL(1,𝔽5)—34no—
246C4⋊AGL(1,𝔽5)—34no—
247C4⋊AGL(1,𝔽5)—38no—
248C4×AGL(1,𝔽5)—38no—
249C4×AGL(1,𝔽5)—42no—
250C4×AGL(1,𝔽5)—122no—
251C4×AGL(1,𝔽5)—122no—
252C4×AGL(1,𝔽5)—122no—
253C5×C4⋊C4—32no—
254C5×C22⋊C4—31no—
255C5×C22⋊C4C4×D311yescharacteristic
256C42×C5—32no—
257C22⋊Dic5—31no—
258C22⋊Dic5C4×D311yescharacteristic
259#685—32no—
260#685C4×D312yes—
261C4⋊Dic5—32no—
262#683—32no—
263#683—32no—
264C4×Dic5—32no—
265C4×Dic5—32no—
266C4×Dic5—32no—
267C2×#117—151no—
268C2×#117—151no—
269C22×C4⋊C4—151no—
270C4×C4⋊C4—152no—
271C4×C4⋊C4—152no—
272C4×C4⋊C4—152no—
273C4×C4⋊C4—152no—
274C4×C22⋊C4—51no—
275C4×C22⋊C4—151no—
276C4×C22⋊C4—151no—
277C4×C22⋊C4—151no—
278C22×C3×C5—22no—
279C22×C3×C5C2×C4212yes—
280C22×C3×C5C23×C411yescharacteristic
281C2×C3×D5—22no—
282C2×C3×D5—22no—
283C2×C3×D5—22no—
284C2×C3×D5—24no—
285C2×C3×D5C2×C4212yes—
286C2×C3×D5C23×C411yescharacteristic
287C2×C3×D5C23×C411yescharacteristic
288C2×C3×D5H(5,𝔽2)12yes—
289C2×C3×D52−1+412yes—
290ΓL(1,𝔽16)—22no—
291ΓL(1,𝔽16)—22no—
292ΓL(1,𝔽16)—24no—
293C3×AGL(1,𝔽5)—22no—
294C3×AGL(1,𝔽5)—22no—
295C3×AGL(1,𝔽5)—24no—
296C3×C4×C5—22no—
297Dic15—22no—
298Dic15C2×C4212yes—
299Dic15C2×C4212yes—
300C3×Dic5—22no—
301C5×Dic3—22no—
302C5×Dic3C2×C4212yes—
303C5×Dic3C2×C4212yes—
304C24×C3—51no—
305C22×C3×C4—51no—
306C22×C3×C4—52no—
307C22×C3×C4—51no—
308C22×C3×C4—54no—
309C22×C3×C4—52no—
310C22×C3×C4—202no—
311C22×Dic3—51no—
312C22×Dic3—54no—
313C22×Dic3—54no—
314C22×Dic3—51no—
315C22×Dic3—51no—
316C22×Dic3—51no—
317C22×Dic3—51no—
318C22×Dic3—52no—
319C22×Dic3—51no—
320C22×Dic3—51no—
321C22×Dic3—54no—
322C22×Dic3—52no—
323C22×Dic3—202no—
324C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
325C3×C22⋊C4—54no—
326C3×C22⋊C4—51no—
327C3×C22⋊C4—52no—
328C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
329C3×C42—202no—
330#217—54no—
331#217—51no—
332#217—52no—
333#217C2×AGL(1,𝔽5)11yescharacteristic
334Dic3⋊C4—54no—
335Dic3⋊C4—54no—
336Dic3⋊C4—54no—
337Dic3⋊C4—54no—
338Dic3⋊C4—58no—
339Dic3⋊C4—52no—
340Dic3⋊C4—52no—
341Dic3⋊C4—52no—
342Dic3⋊C4C2×AGL(1,𝔽5)12yescomplemented
343C4×Dic3—58no—
344C4×Dic3—52no—
345C4×Dic3—52no—
346C4×Dic3—52no—
347C4×Dic3—202no—
348C4×Dic3—202no—
349C4×Dic3—202no—
350C4×Dic3C2×AGL(1,𝔽5)12yescomplemented
351C23×C5C2×C4×D311yescharacteristic
352C22×D5—22no—
353C22×D5—22no—
354C22×D5C2×C4×D311yescharacteristic
355C22×D5C2×C4×D312yes—
356C22×D5C2×C4×D312yes—
357C22×D5C23×D311yescharacteristic
358C2×AGL(1,𝔽5)—22no—
359C2×AGL(1,𝔽5)—22no—
360C2×AGL(1,𝔽5)—22no—
361C2×AGL(1,𝔽5)—22no—
362C2×AGL(1,𝔽5)—34no—
363C2×AGL(1,𝔽5)—32no—
364C2×AGL(1,𝔽5)—32no—
365C2×AGL(1,𝔽5)—44no—
366C2×AGL(1,𝔽5)—62no—
367C2×AGL(1,𝔽5)—62no—
368C2×AGL(1,𝔽5)—62no—
369C2×AGL(1,𝔽5)—62no—
370C2×AGL(1,𝔽5)—124no—
371C2×AGL(1,𝔽5)C2×C4×D314yes—
372C2×AGL(1,𝔽5)C2×C4×D312yes—
373C2×AGL(1,𝔽5)C2×C4×D312yes—
374C2×C4×C5—34no—
375C2×C4×C5—31no—
376C2×C4×C5—31no—
377C2×C4×C5—32no—
378C2×C4×C5C2×C4×D312yes—
379C2×Dic5—34no—
380C2×Dic5—31no—
381C2×Dic5—31no—
382C2×Dic5—32no—
383C2×Dic5C2×C4×D312yes—
384C4×D5—22no—
385C4×D5—22no—
386C4×D5—34no—
387C4×D5—34no—
388C4×D5—32no—
389C4×D5—32no—
390C4×D5—32no—
391C4×D5—32no—
392C4×D5—62no—
393C4×D5—62no—
394C23×C4—51no—
395C23×C4—151no—
396C23×C4—151no—
397#117—31no—
398#117—152no—
399#117—151no—
400#117—152no—
401#117—151no—
402#117—158no—
403#117—151no—
404C2×C4⋊C4—152no—
405C2×C4⋊C4—151no—
406C2×C4⋊C4—151no—
407C2×C4⋊C4—151no—
408C2×C4⋊C4—151no—
409C2×C4⋊C4—158no—
410C2×C4⋊C4—152no—
411C2×C22⋊C4—51no—
412C2×C22⋊C4—51no—
413C2×C22⋊C4—151no—
414C2×C22⋊C4—151no—
415C2×C42—52no—
416C2×C42—152no—
417C2×C42—152no—
418C2×C42—152no—
419C2×C42—152no—
420C2×C42—152no—
421#95—52no—
422#95—152no—
423#95—152no—
424#95—152no—
425C2×C3×C5—22no—
426C2×C3×C5C22×C4211yescharacteristic
427C2×C3×C5#52012yes—
428C3×D5—22no—
429C3×D5#51811yescharacteristic
430C3×D5#51911yescharacteristic
431C3×D5#52012yes—
432C23×C3—51no—
433C23×C3—52no—
434C23×C3—52no—
435C23×C3—51no—
436C23×C3—102no—
437C23×C3—102no—
438C23×C3C22×AGL(1,𝔽5)11yescharacteristic
439C2×C3×C4—54no—
440C2×C3×C4—52no—
441C2×C3×C4—52no—
442C2×C3×C4—52no—
443C2×C3×C4—102no—
444C2×C3×C4—102no—
445C2×C3×C4—102no—
446C2×C3×C4—102no—
447C2×C3×C4—102no—
448C2×C3×C4—102no—
449C2×C3×C4—204no—
450C2×C3×C4C22×AGL(1,𝔽5)12yes—
451C2×Dic3—54no—
452C2×Dic3—51no—
453C2×Dic3—51no—
454C2×Dic3—54no—
455C2×Dic3—54no—
456C2×Dic3—52no—
457C2×Dic3—52no—
458C2×Dic3—52no—
459C2×Dic3—52no—
460C2×Dic3—54no—
461C2×Dic3—52no—
462C2×Dic3—52no—
463C2×Dic3—52no—
464C2×Dic3—102no—
465C2×Dic3—102no—
466C2×Dic3—102no—
467C2×Dic3—102no—
468C2×Dic3—102no—
469C2×Dic3—102no—
470C2×Dic3—204no—
471C2×Dic3C4×AGL(1,𝔽5)14yescomplemented
472C2×Dic3C22×AGL(1,𝔽5)12yes—
473C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
474C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
475C22×C5—22no—
476C22×C5C42×D312yes—
477C22×C5C22×C4×D311yescharacteristic
478C2×D5—22no—
479C2×D5—22no—
480C2×D5—22no—
481C2×D5—24no—
482C2×D5C42×D312yes—
483C2×D5C22×C4×D311yescharacteristic
484C2×D5C22×C4×D311yescharacteristic
485C2×D5#100412yes—
486C2×D5#101012yes—
487AGL(1,𝔽5)—22no—
488AGL(1,𝔽5)—22no—
489AGL(1,𝔽5)—24no—
490AGL(1,𝔽5)—62no—
491AGL(1,𝔽5)—62no—
492AGL(1,𝔽5)—64no—
493C4×C5—22no—
494C4×C5—32no—
495C4×C5—32no—
496C4×C5—62no—
497Dic5—22no—
498Dic5—32no—
499Dic5—32no—
500Dic5—62no—
501C24—51no—
502C22×C4—31no—
503C22×C4—51no—
504C22×C4—52no—
505C22×C4—51no—
506C22×C4—54no—
507C22×C4—52no—
508C22×C4—151no—
509C22×C4—151no—
510C22×C4—154no—
511C22×C4—154no—
512C22×C4—151no—
513C22×C4—151no—
514C22×C4—152no—
515C22×C4—151no—
516C22×C4—152no—
517C22×C4—151no—
518C22×C4—151no—
519C22×C4—154no—
520C22×C4—202no—
521C22×C4—602no—
522C4⋊C4—32no—
523C4⋊C4—152no—
524C4⋊C4—152no—
525C4⋊C4—154no—
526C4⋊C4—154no—
527C4⋊C4—154no—
528C4⋊C4—154no—
529C4⋊C4—158no—
530C4⋊C4—152no—
531C22⋊C4—31no—
532C22⋊C4—54no—
533C22⋊C4—51no—
534C22⋊C4—52no—
535C22⋊C4—152no—
536C22⋊C4—154no—
537C22⋊C4—151no—
538C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
539C42—32no—
540C42—152no—
541C42—152no—
542C42—158no—
543C42—152no—
544C42—202no—
545C42—602no—
546C42—602no—
547C42—602no—
548C3×C5#227411yescharacteristic, complemented, Hall
549C22×C3—22no—
550C22×C3—51no—
551C22×C3—51no—
552C22×C3—52no—
553C22×C3—52no—
554C22×C3—52no—
555C22×C3—102no—
556C22×C3—104no—
557C22×C3—102no—
558C22×C3—102no—
559C22×C3C2×C4×AGL(1,𝔽5)12yes—
560C22×C3C23×AGL(1,𝔽5)11yescharacteristic
561C3×C4—22no—
562C3×C4—104no—
563C3×C4—102no—
564C3×C4—102no—
565C3×C4—102no—
566Dic3—22no—
567Dic3—52no—
568Dic3—52no—
569Dic3—104no—
570Dic3—102no—
571Dic3—102no—
572Dic3—102no—
573Dic3C2×C4×AGL(1,𝔽5)12yes—
574Dic3C2×C4×AGL(1,𝔽5)12yes—
575C2×C5—22no—
576C2×C5C2×C42×D311yescharacteristic
577C2×C5#554612yes—
578D5—22no—
579D5#548611yescharacteristic
580D5#551611yescharacteristic
581D5#554612yes—
582C23—51no—
583C23—52no—
584C23—52no—
585C23—51no—
586C23—102no—
587C23—102no—
588C23C2×D3×AGL(1,𝔽5)11yescharacteristic
589C2×C4—34no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—32no—
593C2×C4—54no—
594C2×C4—52no—
595C2×C4—52no—
596C2×C4—52no—
597C2×C4—102no—
598C2×C4—102no—
599C2×C4—102no—
600C2×C4—102no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—152no—
604C2×C4—152no—
605C2×C4—152no—
606C2×C4—152no—
607C2×C4—154no—
608C2×C4—154no—
609C2×C4—154no—
610C2×C4—151no—
611C2×C4—151no—
612C2×C4—154no—
613C2×C4—152no—
614C2×C4—152no—
615C2×C4—152no—
616C2×C4—204no—
617C2×C4—302no—
618C2×C4—302no—
619C2×C4—302no—
620C2×C4—302no—
621C2×C4—302no—
622C2×C4—302no—
623C2×C4—604no—
624C2×C4C2×D3×AGL(1,𝔽5)12yes—
625C2×C3—22no—
626C2×C3—51no—
627C2×C3—52no—
628C2×C3—51no—
629C2×C3—102no—
630C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
631C2×C3#6626612yes—
632C5#7343511yescharacteristic, complemented, Sylow
633C22—22no—
634C22—51no—
635C22—51no—
636C22—52no—
637C22—52no—
638C22—52no—
639C22—102no—
640C22—104no—
641C22—102no—
642C22—102no—
643C22C4×D3×AGL(1,𝔽5)12yes—
644C22C22×D3×AGL(1,𝔽5)11yescharacteristic
645C4—22no—
646C4—32no—
647C4—32no—
648C4—62no—
649C4—102no—
650C4—102no—
651C4—104no—
652C4—102no—
653C4—152no—
654C4—152no—
655C4—302no—
656C4—302no—
657C4—304no—
658C4—302no—
659C3#1061712711yescharacteristic, complemented, Sylow
660C2—22no—
661C2—51no—
662C2—52no—
663C2—51no—
664C2—102no—
665C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
666C2#1175684612yes—
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C22⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2274
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
9. #11751834C2semidirect
10. #11751833C2semidirect
11. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
20. C2×Dic3⋊AGL(1,𝔽5)C4semidirect
26. #91923C4semidirect
30. #91766C4semidirect
31. C5×#877C4semidirect
34. #91532C4semidirect
35. #91529C4semidirect
36. #91394C4semidirect
37. #91393C4semidirect
85. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
88. Dic3×AGL(1,𝔽5)C2×C4semidirect
91. #6712C2×C4semidirect
92. C4×Dic15C2×C4semidirect
94. C5×Dic3⋊C4C2×C4semidirect
95. C4×C5×Dic3C2×C4semidirect
98. Dic3⋊Dic5C2×C4semidirect
99. #6669C2×C4semidirect
101. Dic3×Dic5C2×C4semidirect
102. Dic3×Dic5C2×C4semidirect
170. C2×Dic15C42semidirect
174. C2×C5×Dic3C42semidirect
183. D5×Dic3C42semidirect
184. D5×Dic3C42semidirect
215. #877AGL(1,𝔽5)semidirect
342. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
350. C4×Dic3C2×AGL(1,𝔽5)semidirect
471. C2×Dic3C4×AGL(1,𝔽5)semidirect
548. C3×C5#2274semidirect
632. C5#73435semidirect
659. C3#10617127semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊AGL(1,𝔽5)2
C2×#919232
D5×#8772
C22⋊C4×ΓL(1,𝔽16)2
C3×C22⋊C4×AGL(1,𝔽5)2
#117520212
AGL(1,𝔽5)×#2172
C4×Dic3⋊AGL(1,𝔽5)2
#117518342
#117518332
AGL(1,𝔽5)×Dic3⋊C42
#106171273
#734355