Finite Group Databasebeta

← AGL(1,𝔽5)×#67⋊C4 #14319603

Subgroups — AGL(1,𝔽5)×#67⋊C4 #14319603

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×#67C211yesmaximal, characteristic
3C22×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
5D5×#67⋊C4C211yesmaximal, characteristic
6C22⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
7C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751931C211yesmaximal, characteristic, complemented
10AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11751848C211yesmaximal, characteristic, complemented
12#11751834C211yesmaximal, characteristic, complemented
13#11751833C211yesmaximal, characteristic, complemented
14AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C4×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
16C4×D4×AGL(1,𝔽5)—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C23×C3×AGL(1,𝔽5)C2211yescharacteristic
19C22×D3×AGL(1,𝔽5)C2211yescharacteristic
20C22×D3×AGL(1,𝔽5)C2211yescharacteristic
21C2×D5×#67C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×C4×D3×D5C2211yescharacteristic
24C2×#6763C2211yescharacteristic
25C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
26C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
27C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
29C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
30#67⋊AGL(1,𝔽5)C418yescomplemented
31AGL(1,𝔽5)×#67C418yescomplemented
32C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
34C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
35C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
36C2×Dic3×AGL(1,𝔽5)—24no—
37C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
38C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
39C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
40C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
41C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
42C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
43C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
44C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
45C4×D3×AGL(1,𝔽5)—24no—
46#91770C411yescharacteristic, complemented
47C5×#67⋊C4C411yescharacteristic, complemented
48C3×D5×C22⋊C4C2211yescharacteristic
49#67⋊Dic5C411yescharacteristic, complemented
50#91556C411yescharacteristic, complemented
51D5×(C2×D3)⋊C4C2211yescharacteristic
52#91442C411yescharacteristic, complemented
53#91441C411yescharacteristic, complemented
54#91396C411yescharacteristic, complemented
55#91395C411yescharacteristic, complemented
56D5×Dic3⋊C4C2211yescharacteristic
57C4×D5×Dic3C2211yescharacteristic
58#91235C2211yescharacteristic
59#91235C2211yescharacteristic
60C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
61C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
62(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
63(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
64C4×#67⋊C4—51nomaximal, Hall
65C2×D4×AGL(1,𝔽5)—31no—
66C2×D4×AGL(1,𝔽5)—31no—
67C22×C4×AGL(1,𝔽5)—31no—
68C22×C4×AGL(1,𝔽5)—31no—
69C4×D4×D5—31no—
70C4×C22⋊AGL(1,𝔽5)—31no—
71C4×C22⋊AGL(1,𝔽5)—31no—
72C4⋊C4×AGL(1,𝔽5)—31no—
73C4⋊C4×AGL(1,𝔽5)—31no—
74C22⋊C4×AGL(1,𝔽5)—31no—
75C22⋊C4×AGL(1,𝔽5)—31no—
76C22⋊C4×AGL(1,𝔽5)—31no—
77C22⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
78C4×C4⋊AGL(1,𝔽5)—31no—
79C42×AGL(1,𝔽5)—31no—
80C23×C3×D5C2311yescharacteristic
81C22×D3×D5C2311yescharacteristic
82C22×ΓL(1,𝔽16)—22no—
83C22×ΓL(1,𝔽16)—22no—
84C22×ΓL(1,𝔽16)C2×C414yescomplemented
85C22×ΓL(1,𝔽16)C2311yescharacteristic
86C22×ΓL(1,𝔽16)C2311yescharacteristic
87C22×ΓL(1,𝔽16)C2311yescharacteristic
88C22×ΓL(1,𝔽16)C2311yescharacteristic
89C22×C3×AGL(1,𝔽5)—22no—
90C22×C3×AGL(1,𝔽5)—22no—
91C22×C3×AGL(1,𝔽5)C2×C414yescomplemented
92C22×C3×AGL(1,𝔽5)C2311yescharacteristic
93C22×C3×AGL(1,𝔽5)C2311yescharacteristic
94C22×C3×AGL(1,𝔽5)C2311yescharacteristic
95C22×C3×AGL(1,𝔽5)C2311yescharacteristic
96C2×D3×AGL(1,𝔽5)—22no—
97C2×D3×AGL(1,𝔽5)—22no—
98C2×D3×AGL(1,𝔽5)—22no—
99C2×D3×AGL(1,𝔽5)—22no—
100C2×D3×AGL(1,𝔽5)C2×C414yescomplemented
101C2×D3×AGL(1,𝔽5)C2×C414yescomplemented
102C2×#1220C2×C411yescharacteristic
103C22×Dic15C2×C411yescharacteristic, complemented
104C2×C4×D15C2×C411yescharacteristic, complemented
105C2×C5×#67C2×C411yescharacteristic
106C22×C5×Dic3C2×C411yescharacteristic, complemented
107C2×C4×C5×D3C2×C411yescharacteristic, complemented
108C2×C3×C4×D5C2311yescharacteristic
109C2×C3×C4×D5C2311yescharacteristic
110D5×#67C2×C414yes—
111D5×#67C2×C414yes—
112C2×#1202C2×C411yescharacteristic
113C2×#1201C2×C411yescharacteristic
114C2×#1200C2×C411yescharacteristic, complemented
115C2×D3×Dic5C2×C411yescharacteristic, complemented
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3C2×C411yescharacteristic, complemented
119C2×D5×Dic3C2×C411yescharacteristic, complemented
120C2×D5×Dic3C2311yescharacteristic
121C2×D5×Dic3C2311yescharacteristic
122C2×D5×Dic3C2311yescharacteristic
123C4×D3×D5—22no—
124C4×D3×D5—22no—
125#6763C2×C414yescomplemented
126C4×ΓL(1,𝔽16)—22no—
127C4×ΓL(1,𝔽16)—22no—
128C3×C22⋊AGL(1,𝔽5)C2×C414yescomplemented
129C3×C4×AGL(1,𝔽5)—22no—
130C3×C4×AGL(1,𝔽5)—22no—
131Dic3⋊AGL(1,𝔽5)C2×C414yescomplemented
132Dic3⋊AGL(1,𝔽5)C2×C414yescomplemented
133(C2×D3)⋊AGL(1,𝔽5)C2×C414yescomplemented
134(C2×D3)⋊AGL(1,𝔽5)C2×C414yescomplemented
135Dic3×AGL(1,𝔽5)—22no—
136Dic3×AGL(1,𝔽5)—22no—
137Dic3×AGL(1,𝔽5)—22no—
138Dic3×AGL(1,𝔽5)—22no—
139Dic3×AGL(1,𝔽5)—22no—
140Dic3×AGL(1,𝔽5)C2×C414yescomplemented
141Dic3×AGL(1,𝔽5)C2×C414yescomplemented
142Dic3×AGL(1,𝔽5)D414yescomplemented
143C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
144#6714C2×C411yescharacteristic, complemented
145#6712C2×C411yescharacteristic, complemented
146C4×Dic15C2×C411yescharacteristic, complemented
147C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
148C5×Dic3⋊C4C2×C411yescharacteristic, complemented
149C4×C5×Dic3C2×C411yescharacteristic, complemented
150C3×C22⋊Dic5C2×C411yescharacteristic, complemented
151C3×#685C2×C411yescharacteristic, complemented
152C3×#685C2×C411yescharacteristic, complemented
153Dic3⋊Dic5C2×C411yescharacteristic, complemented
154#6669C2×C411yescharacteristic, complemented
155#6667C2×C411yescharacteristic, complemented
156(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
157Dic3×Dic5C2×C411yescharacteristic, complemented
158Dic3×Dic5C2×C411yescharacteristic, complemented
159C2×C4×#67—51no—
160C22×C4×Dic3—51no—
161C2×#67⋊C4—51no—
162C2×#67⋊C4—51no—
163C2×C42×D3—51no—
164C3×C4×C22⋊C4—51no—
165Dic3×C22⋊C4—51no—
166Dic3×C22⋊C4—51no—
167C4×(C2×D3)⋊C4—51no—
168C4×Dic3⋊C4—51no—
169C42×Dic3—51no—
170#4666—51no—
171#4666—51no—
172#4649—51no—
173#4649—51no—
174C23×AGL(1,𝔽5)—31no—
175C23×AGL(1,𝔽5)—31no—
176C23×AGL(1,𝔽5)—31no—
177C23×AGL(1,𝔽5)C2×D311yescharacteristic
178C2×D4×D5—31no—
179C22×C4×D5—31no—
180C22×C4×D5—31no—
181C2×C22⋊AGL(1,𝔽5)—31no—
182C2×C22⋊AGL(1,𝔽5)—31no—
183C2×C22⋊AGL(1,𝔽5)—31no—
184C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
185D4×AGL(1,𝔽5)—38no—
186D4×AGL(1,𝔽5)—38no—
187C2×C4⋊AGL(1,𝔽5)—31no—
188C2×C4⋊AGL(1,𝔽5)—31no—
189C2×C4×AGL(1,𝔽5)—31no—
190C2×C4×AGL(1,𝔽5)—31no—
191C2×C4×AGL(1,𝔽5)—31no—
192C2×C4×AGL(1,𝔽5)—31no—
193C2×C4×AGL(1,𝔽5)—31no—
194C2×C4×AGL(1,𝔽5)—31no—
195C2×C4×AGL(1,𝔽5)—31no—
196C2×C4×AGL(1,𝔽5)—31no—
197C2×C4×AGL(1,𝔽5)—31no—
198C2×C4×AGL(1,𝔽5)—31no—
199C2×C4×AGL(1,𝔽5)—64no—
200C2×C4×AGL(1,𝔽5)—64no—
201C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
202C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
203C4×C5×D4—31no—
204D4×Dic5—31no—
205C4×C22⋊D5—31no—
206C4×C22⋊D5—31no—
207#4039—31no—
208D5×C4⋊C4—31no—
209#4027—31no—
210#4027—31no—
211D5×C22⋊C4—31no—
212D5×C22⋊C4C2×D311yescharacteristic
213C4×D20—31no—
214C42×D5—31no—
215(C2×AGL(1,𝔽5))⋊C4—31no—
216(C2×AGL(1,𝔽5))⋊C4—31no—
217(C2×AGL(1,𝔽5))⋊C4—31no—
218(C2×AGL(1,𝔽5))⋊C4—31no—
219(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
220(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
221C42×D4—151noSylow
222C23×C3×C5C22×C411yescharacteristic
223C22×D15C22×C411yescharacteristic
224C22×C5×D3C22×C411yescharacteristic
225C22×C3×D5—21no—
226C22×C3×D5—21no—
227C22×C3×D5—21no—
228C22×C3×D5—21no—
229C22×C3×D5C22×C411yescharacteristic
230C22×C3×D5C22×C412yes—
231C22×C3×D5C22×C412yes—
232C22×C3×D5C2411yescharacteristic
233C2×D3×D5—21no—
234C2×D3×D5—21no—
235C2×D3×D5—21no—
236C2×D3×D5—21no—
237C2×D3×D5C22×C412yes—
238C2×D3×D5C22×C412yes—
239C2×ΓL(1,𝔽16)—21no—
240C2×ΓL(1,𝔽16)—21no—
241C2×ΓL(1,𝔽16)—21no—
242C2×ΓL(1,𝔽16)—21no—
243C2×ΓL(1,𝔽16)—21no—
244C2×ΓL(1,𝔽16)—21no—
245C2×ΓL(1,𝔽16)—28no—
246C2×ΓL(1,𝔽16)C22×C412yes—
247C2×ΓL(1,𝔽16)C22×C412yes—
248C2×ΓL(1,𝔽16)C22×C412yes—
249C2×ΓL(1,𝔽16)C22×C412yes—
250C2×ΓL(1,𝔽16)C2×D412yes—
251C2×ΓL(1,𝔽16)#4112yes—
252C2×C3×AGL(1,𝔽5)—21no—
253C2×C3×AGL(1,𝔽5)—21no—
254C2×C3×AGL(1,𝔽5)—21no—
255C2×C3×AGL(1,𝔽5)—21no—
256C2×C3×AGL(1,𝔽5)—21no—
257C2×C3×AGL(1,𝔽5)—21no—
258C2×C3×AGL(1,𝔽5)—28no—
259C2×C3×AGL(1,𝔽5)C22×C412yes—
260C2×C3×AGL(1,𝔽5)C22×C412yes—
261C2×C3×AGL(1,𝔽5)C22×C412yes—
262C2×C3×AGL(1,𝔽5)C22×C412yes—
263C2×C3×AGL(1,𝔽5)C2×D412yes—
264C2×C3×AGL(1,𝔽5)#4112yes—
265D3×AGL(1,𝔽5)—28no—
266D3×AGL(1,𝔽5)—28no—
267C2×C3×C4×C5C22×C411yescharacteristic
268C2×C3×C4×C5C22×C411yescharacteristic
269#1220C4214yescomplemented
270C2×Dic15—22no—
271C2×Dic15C22×C411yescharacteristic
272C2×Dic15C22×C411yescharacteristic
273C2×Dic15C22×C411yescharacteristic
274C4×D15—22no—
275C5×#67C4214yescomplemented
276C2×C5×Dic3—22no—
277C2×C5×Dic3C22×C411yescharacteristic
278C2×C5×Dic3C22×C411yescharacteristic
279C2×C5×Dic3C22×C411yescharacteristic
280C4×C5×D3—22no—
281C2×C3×Dic5C22×C411yescharacteristic
282C2×C3×Dic5C22×C411yescharacteristic
283C3×C4×D5—21no—
284C3×C4×D5—21no—
285C3×C4×D5—21no—
286C3×C4×D5—21no—
287#1202C4214yescomplemented
288#1201C4214yescomplemented
289#1200—22no—
290D3×Dic5—22no—
291D5×Dic3—21no—
292D5×Dic3—21no—
293D5×Dic3—22no—
294D5×Dic3—22no—
295D5×Dic3C22×C412yes—
296D5×Dic3C22×C412yes—
297D5×Dic3C2×D412yes—
298D5×Dic3#4112yes—
299C23×C3×C4—51no—
300C22×#67—51no—
301C23×Dic3—51no—
302C23×Dic3—51no—
303C22×C4×D3—51no—
304C22×C4×D3—51no—
305C22×C4×D3—51no—
306C2×C3×C22⋊C4—51no—
307C2×C3×C22⋊C4—51no—
308C2×C3×C42—51no—
309C2×C3×C42—51no—
310C2×#217—51no—
311C4×#67—58no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×C4×Dic3—51no—
319C2×C4×Dic3—51no—
320C2×C4×Dic3—51no—
321C2×C4×Dic3—51no—
322C2×C4×Dic3—51no—
323C2×C4×Dic3—51no—
324C2×C4×Dic3—51no—
325C2×C4×Dic3—51no—
326C2×C4×Dic3—51no—
327C2×C4×Dic3—51no—
328C2×C4×Dic3—51no—
329C2×C4×Dic3—104no—
330#67⋊C4—58no—
331#67⋊C4—51no—
332#67⋊C4—51no—
333#67⋊C4—51no—
334#67⋊C4—51no—
335#67⋊C4—51no—
336#67⋊C4—51no—
337#67⋊C4—51no—
338#67⋊C4AGL(1,𝔽5)11yescharacteristic, direct product factor
339C42×D3—104no—
340C3×#95—51no—
341C3×#95—51no—
342C3⋊#95—51no—
343C3⋊#95—51no—
344C3⋊#95—51no—
345C3⋊#95—51no—
346C23×D5—31no—
347C23×D5C22×D311yescharacteristic
348C22×AGL(1,𝔽5)—22no—
349C22×AGL(1,𝔽5)—22no—
350C22×AGL(1,𝔽5)—31no—
351C22×AGL(1,𝔽5)—34no—
352C22×AGL(1,𝔽5)—31no—
353C22×AGL(1,𝔽5)—31no—
354C22×AGL(1,𝔽5)—31no—
355C22×AGL(1,𝔽5)—34no—
356C22×AGL(1,𝔽5)—34no—
357C22×AGL(1,𝔽5)—62no—
358C22×AGL(1,𝔽5)—62no—
359C22×AGL(1,𝔽5)—62no—
360C22×AGL(1,𝔽5)—62no—
361C22×AGL(1,𝔽5)—62no—
362C22×AGL(1,𝔽5)—62no—
363C22×AGL(1,𝔽5)C4×D314yescomplemented
364C22×AGL(1,𝔽5)C22×D311yescharacteristic
365C22×AGL(1,𝔽5)C22×D311yescharacteristic
366C22×AGL(1,𝔽5)C22×D311yescharacteristic
367C22×AGL(1,𝔽5)C22×D311yescharacteristic
368C2×C5×D4—31no—
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C2×C22⋊D5—31no—
372C2×C22⋊D5—31no—
373C22×Dic5—31no—
374C22×Dic5—31no—
375D4×D5—34no—
376D4×D5—34no—
377C2×D20—31no—
378C2×C4×D5—31no—
379C2×C4×D5—31no—
380C2×C4×D5—31no—
381C2×C4×D5—31no—
382C2×C4×D5—31no—
383C2×C4×D5—31no—
384C2×C4×D5—31no—
385C2×C4×D5—62no—
386C2×C4×D5—62no—
387C2×C4×D5—62no—
388C2×C4×D5—62no—
389C2×C4×D5C22×D311yescharacteristic
390C2×C4×D5C22×D311yescharacteristic
391C22⋊AGL(1,𝔽5)—34no—
392C22⋊AGL(1,𝔽5)—34no—
393C22⋊AGL(1,𝔽5)—34no—
394C22⋊AGL(1,𝔽5)C4×D314yescomplemented
395C4⋊AGL(1,𝔽5)—34no—
396C4⋊AGL(1,𝔽5)—34no—
397C4×AGL(1,𝔽5)—22no—
398C4×AGL(1,𝔽5)—22no—
399C4×AGL(1,𝔽5)—34no—
400C4×AGL(1,𝔽5)—34no—
401C4×AGL(1,𝔽5)—34no—
402C4×AGL(1,𝔽5)—62no—
403C4×AGL(1,𝔽5)—62no—
404C4×AGL(1,𝔽5)—62no—
405C4×AGL(1,𝔽5)—62no—
406C4×AGL(1,𝔽5)—62no—
407C4×AGL(1,𝔽5)—62no—
408C4×AGL(1,𝔽5)—62no—
409C5×C4⋊C4—31no—
410C5×C22⋊C4—31no—
411C5×C22⋊C4C4×D311yescharacteristic, complemented
412C42×C5—31no—
413C22⋊Dic5—31no—
414C22⋊Dic5C4×D311yescharacteristic, complemented
415#685—31no—
416#685—31no—
417#685C4×D311yescharacteristic, complemented
418#685C4×D311yescharacteristic, complemented
419C4⋊Dic5—31no—
420#683—31no—
421#683—31no—
422C4×Dic5—31no—
423C4×Dic5—31no—
424C4×Dic5—31no—
425C2×C4×D4—151no—
426C2×C4×D4—151no—
427C2×C4×D4—151no—
428C22×C42—151no—
429C22×C42—151no—
430C4×C4⋊C4—151no—
431C4×C4⋊C4—151no—
432C4×C4⋊C4—151no—
433C4×C22⋊C4—51no—
434C4×C22⋊C4—151no—
435C4×C22⋊C4—151no—
436C4×C22⋊C4—151no—
437C4×C22⋊C4—151no—
438C4×C22⋊C4—151no—
439C43—151no—
440C22×C3×C5—21no—
441C22×C3×C5—21no—
442C22×C3×C5C2×C4212yescomplemented
443C22×C3×C5C23×C411yescharacteristic
444C2×D15—21no—
445C2×D15—21no—
446C2×D15C2×C4212yescomplemented
447C2×C5×D3—21no—
448C2×C5×D3—21no—
449C2×C5×D3C2×C4212yescomplemented
450C2×C3×D5—21no—
451C2×C3×D5—21no—
452C2×C3×D5—22no—
453C2×C3×D5—22no—
454C2×C3×D5—22no—
455C2×C3×D5—22no—
456C2×C3×D5C2×C4212yescomplemented
457C2×C3×D5C23×C411yescharacteristic
458C2×C3×D5C23×C411yescharacteristic
459C2×C3×D5C22×D411yescharacteristic
460C2×C3×D5C2×#4111yescharacteristic
461C2×C3×D5C2×#4111yescharacteristic
462C2×C3×D5C2×#4111yescharacteristic
463D3×D5—22no—
464D3×D5—22no—
465D3×D5—22no—
466D3×D5—22no—
467ΓL(1,𝔽16)—22no—
468ΓL(1,𝔽16)—22no—
469ΓL(1,𝔽16)—22no—
470ΓL(1,𝔽16)C4×D414yescomplemented
471C3×AGL(1,𝔽5)—22no—
472C3×AGL(1,𝔽5)—22no—
473C3×AGL(1,𝔽5)—22no—
474C3×AGL(1,𝔽5)C4×D414yescomplemented
475C3×C4×C5—21no—
476C3×C4×C5—21no—
477Dic15—21no—
478Dic15C2×C4212yescomplemented
479Dic15C4×D412yescomplemented
480C3×Dic5—21no—
481C3×Dic5—21no—
482C5×Dic3—21no—
483C5×Dic3C2×C4212yescomplemented
484C5×Dic3C4×D412yescomplemented
485C24×C3—51no—
486C23×D3—51no—
487C22×C3×C4—51no—
488C22×C3×C4—51no—
489C22×C3×C4—51no—
490C22×C3×C4—51no—
491C22×C3×C4—54no—
492C22×C3×C4—51no—
493C22×C3×C4—51no—
494C22×C3×C4—102no—
495C22×C3×C4—102no—
496C2×#67—51no—
497C2×#67—51no—
498C2×#67—54no—
499C2×#67—54no—
500C2×#67—51no—
501C2×#67C2×AGL(1,𝔽5)11yescharacteristic
502C22×Dic3—51no—
503C22×Dic3—51no—
504C22×Dic3—51no—
505C22×Dic3—51no—
506C22×Dic3—51no—
507C22×Dic3—51no—
508C22×Dic3—54no—
509C22×Dic3—51no—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—51no—
513C22×Dic3—102no—
514C22×Dic3—102no—
515C22×Dic3—102no—
516C22×Dic3—102no—
517C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
518C2×C4×D3—54no—
519C2×C4×D3—54no—
520C2×C4×D3—51no—
521C2×C4×D3—51no—
522C2×C4×D3—51no—
523C2×C4×D3—102no—
524C2×C4×D3—102no—
525C2×C4×D3—102no—
526C2×C4×D3—102no—
527C2×C4×D3—102no—
528C2×C4×D3—102no—
529C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
530C3×C22⋊C4—54no—
531C3×C22⋊C4—51no—
532C3×C22⋊C4—51no—
533C3×C22⋊C4—51no—
534C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
535C3×C42—102no—
536C3×C42—102no—
537#217—54no—
538(C2×D3)⋊C4—54no—
539(C2×D3)⋊C4—54no—
540(C2×D3)⋊C4—51no—
541(C2×D3)⋊C4—51no—
542(C2×D3)⋊C4—51no—
543(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
544Dic3⋊C4—54no—
545Dic3⋊C4—54no—
546Dic3⋊C4—51no—
547Dic3⋊C4—51no—
548Dic3⋊C4—51no—
549Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
550C4×Dic3—54no—
551C4×Dic3—54no—
552C4×Dic3—54no—
553C4×Dic3—51no—
554C4×Dic3—51no—
555C4×Dic3—51no—
556C4×Dic3—102no—
557C4×Dic3—102no—
558C4×Dic3—102no—
559C4×Dic3—102no—
560C4×Dic3—102no—
561C4×Dic3—102no—
562C4×Dic3—102no—
563C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
564C23×C5—31no—
565C23×C5C2×C4×D311yescharacteristic
566C22×D5—21no—
567C22×D5—21no—
568C22×D5—21no—
569C22×D5—21no—
570C22×D5—31no—
571C22×D5—32no—
572C22×D5—32no—
573C22×D5—61no—
574C22×D5—61no—
575C22×D5—61no—
576C22×D5—61no—
577C22×D5C2×C4×D311yescharacteristic
578C22×D5C2×C4×D312yes—
579C22×D5C2×C4×D312yes—
580C22×D5C23×D311yescharacteristic
581C2×AGL(1,𝔽5)—21no—
582C2×AGL(1,𝔽5)—21no—
583C2×AGL(1,𝔽5)—21no—
584C2×AGL(1,𝔽5)—21no—
585C2×AGL(1,𝔽5)—21no—
586C2×AGL(1,𝔽5)—21no—
587C2×AGL(1,𝔽5)—28no—
588C2×AGL(1,𝔽5)—32no—
589C2×AGL(1,𝔽5)—32no—
590C2×AGL(1,𝔽5)—32no—
591C2×AGL(1,𝔽5)—32no—
592C2×AGL(1,𝔽5)—32no—
593C2×AGL(1,𝔽5)—32no—
594C2×AGL(1,𝔽5)—68no—
595C2×AGL(1,𝔽5)—68no—
596C2×AGL(1,𝔽5)—61no—
597C2×AGL(1,𝔽5)—61no—
598C2×AGL(1,𝔽5)—61no—
599C2×AGL(1,𝔽5)—61no—
600C2×AGL(1,𝔽5)—61no—
601C2×AGL(1,𝔽5)—61no—
602C2×AGL(1,𝔽5)—68no—
603C2×AGL(1,𝔽5)C2×C4×D312yes—
604C2×AGL(1,𝔽5)C2×C4×D312yes—
605C2×AGL(1,𝔽5)C2×C4×D312yes—
606C2×AGL(1,𝔽5)C2×C4×D312yes—
607C2×AGL(1,𝔽5)D3×D412yes—
608C2×AGL(1,𝔽5)#23712yes—
609C5×D4—34no—
610C2×C4×C5—31no—
611C2×C4×C5—31no—
612C2×C4×C5—31no—
613C2×C4×C5—62no—
614C2×C4×C5—62no—
615C2×C4×C5C2×C4×D311yescharacteristic
616C2×C4×C5C2×C4×D311yescharacteristic
617C22⋊D5—34no—
618C22⋊D5—34no—
619C2×Dic5—31no—
620C2×Dic5—31no—
621C2×Dic5—31no—
622C2×Dic5—62no—
623C2×Dic5—62no—
624C2×Dic5C2×C4×D311yescharacteristic
625C2×Dic5C2×C4×D311yescharacteristic
626D20—34no—
627C4×D5—21no—
628C4×D5—21no—
629C4×D5—21no—
630C4×D5—21no—
631C4×D5—32no—
632C4×D5—32no—
633C4×D5—32no—
634C4×D5—32no—
635C4×D5—62no—
636C4×D5—62no—
637C4×D5—62no—
638C4×D5—62no—
639C4×D5—61no—
640C4×D5—61no—
641C22×D4—151no—
642C23×C4—51no—
643C23×C4—151no—
644C23×C4—151no—
645C23×C4—151no—
646C23×C4—151no—
647C23×C4—151no—
648C4×D4—31no—
649C4×D4—151no—
650C4×D4—151no—
651C4×D4—151no—
652C4×D4—151no—
653C4×D4—151no—
654C4×D4—151no—
655C4×D4—158no—
656C4×D4—158no—
657C4×D4—151no—
658C2×C4⋊C4—151no—
659C2×C4⋊C4—151no—
660C2×C4⋊C4—151no—
661C2×C22⋊C4—51no—
662C2×C22⋊C4—51no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C42—51no—
668C2×C42—51no—
669C2×C42—151no—
670C2×C42—151no—
671C2×C42—151no—
672C2×C42—151no—
673C2×C42—151no—
674C2×C42—151no—
675C2×C42—151no—
676C2×C42—151no—
677C2×C42—151no—
678C2×C42—151no—
679C2×C42—151no—
680C2×C42—304no—
681C2×C42—304no—
682#95—51no—
683#95—51no—
684#95—151no—
685#95—151no—
686#95—151no—
687#95—151no—
688C2×C3×C5—22no—
689C2×C3×C5C22×C4211yescharacteristic
690C2×C3×C5C2×C4×D411yescharacteristic
691C2×C3×C5C4×#4111yescharacteristic
692D15—22no—
693C3×D5—22no—
694C3×D5C2×C4×D411yescharacteristic
695C3×D5C2×C4×D411yescharacteristic
696C3×D5C4×#4111yescharacteristic
697C3×D5C4×#4111yescharacteristic
698C5×D3—22no—
699C23×C3—51no—
700C23×C3—52no—
701C23×C3—52no—
702C23×C3—51no—
703C23×C3—101no—
704C23×C3—101no—
705C23×C3—101no—
706C23×C3—101no—
707C23×C3C22×AGL(1,𝔽5)11yescharacteristic
708C22×D3—51no—
709C22×D3—52no—
710C22×D3—52no—
711C22×D3—101no—
712C22×D3—101no—
713C22×D3—101no—
714C22×D3—101no—
715C22×D3C22×AGL(1,𝔽5)11yescharacteristic
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—52no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—51no—
723C2×C3×C4—51no—
724C2×C3×C4—101no—
725C2×C3×C4—101no—
726C2×C3×C4—101no—
727C2×C3×C4—101no—
728C2×C3×C4—108no—
729C2×C3×C4—101no—
730C2×C3×C4—101no—
731C2×C3×C4—101no—
732C2×C3×C4—101no—
733C2×C3×C4—101no—
734C2×C3×C4—101no—
735C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
736C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
737#67—54no—
738#67—54no—
739#67—54no—
740#67C4×AGL(1,𝔽5)14yescomplemented
741C2×Dic3—22no—
742C2×Dic3—52no—
743C2×Dic3—52no—
744C2×Dic3—52no—
745C2×Dic3—51no—
746C2×Dic3—51no—
747C2×Dic3—52no—
748C2×Dic3—52no—
749C2×Dic3—52no—
750C2×Dic3—52no—
751C2×Dic3—52no—
752C2×Dic3—52no—
753C2×Dic3—52no—
754C2×Dic3—51no—
755C2×Dic3—102no—
756C2×Dic3—101no—
757C2×Dic3—101no—
758C2×Dic3—102no—
759C2×Dic3—108no—
760C2×Dic3—101no—
761C2×Dic3—101no—
762C2×Dic3—101no—
763C2×Dic3—101no—
764C2×Dic3—101no—
765C2×Dic3—101no—
766C2×Dic3—102no—
767C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
768C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
769C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
770C4×D3—22no—
771C4×D3—102no—
772C4×D3—102no—
773C4×D3—108no—
774C4×D3—108no—
775C4×D3—102no—
776C22×C5—21no—
777C22×C5—21no—
778C22×C5—32no—
779C22×C5—61no—
780C22×C5—61no—
781C22×C5C42×D312yescomplemented
782C22×C5C22×C4×D311yescharacteristic
783C2×D5—21no—
784C2×D5—21no—
785C2×D5—22no—
786C2×D5—22no—
787C2×D5—22no—
788C2×D5—22no—
789C2×D5—32no—
790C2×D5—61no—
791C2×D5—61no—
792C2×D5—62no—
793C2×D5—62no—
794C2×D5—62no—
795C2×D5—62no—
796C2×D5C42×D312yescomplemented
797C2×D5C22×C4×D311yescharacteristic
798C2×D5C22×C4×D311yescharacteristic
799C2×D5C2×D3×D411yescharacteristic
800C2×D5C2×#23711yescharacteristic
801C2×D5D3×#4111yescharacteristic
802C2×D5D3×#4111yescharacteristic
803AGL(1,𝔽5)—22no—
804AGL(1,𝔽5)—22no—
805AGL(1,𝔽5)—22no—
806AGL(1,𝔽5)—34no—
807AGL(1,𝔽5)—62no—
808AGL(1,𝔽5)—62no—
809AGL(1,𝔽5)—62no—
810AGL(1,𝔽5)#67⋊C414yesdirect product factor
811C4×C5—21no—
812C4×C5—21no—
813C4×C5—32no—
814C4×C5—32no—
815C4×C5—61no—
816Dic5—21no—
817Dic5—21no—
818Dic5—32no—
819Dic5—32no—
820Dic5—61no—
821C24—51no—
822C24—151no—
823C2×D4—31no—
824C2×D4—151no—
825C2×D4—154no—
826C2×D4—154no—
827C2×D4—151no—
828C2×D4—151no—
829C22×C4—31no—
830C22×C4—31no—
831C22×C4—51no—
832C22×C4—51no—
833C22×C4—51no—
834C22×C4—51no—
835C22×C4—54no—
836C22×C4—51no—
837C22×C4—51no—
838C22×C4—102no—
839C22×C4—102no—
840C22×C4—151no—
841C22×C4—151no—
842C22×C4—151no—
843C22×C4—151no—
844C22×C4—151no—
845C22×C4—151no—
846C22×C4—151no—
847C22×C4—154no—
848C22×C4—154no—
849C22×C4—151no—
850C22×C4—151no—
851C22×C4—151no—
852C22×C4—151no—
853C22×C4—154no—
854C22×C4—151no—
855C22×C4—151no—
856C22×C4—302no—
857C22×C4—302no—
858C22×C4—302no—
859C22×C4—302no—
860C22×C4—302no—
861C22×C4—302no—
862C22×C4—302no—
863C22×C4—302no—
864C22×C4—302no—
865C22×C4—302no—
866C4⋊C4—31no—
867C4⋊C4—151no—
868C4⋊C4—151no—
869C4⋊C4—154no—
870C4⋊C4—154no—
871C4⋊C4—151no—
872C22⋊C4—31no—
873C22⋊C4—54no—
874C22⋊C4—51no—
875C22⋊C4—51no—
876C22⋊C4—51no—
877C22⋊C4—151no—
878C22⋊C4—151no—
879C22⋊C4—154no—
880C22⋊C4—154no—
881C22⋊C4—154no—
882C22⋊C4—151no—
883C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
884C42—31no—
885C42—102no—
886C42—102no—
887C42—151no—
888C42—151no—
889C42—154no—
890C42—154no—
891C42—154no—
892C42—151no—
893C42—302no—
894C42—302no—
895C42—302no—
896C42—302no—
897C42—302no—
898C42—302no—
899C42—302no—
900C3×C5C42×D411yescharacteristic, complemented, Hall
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—51no—
904C22×C3—51no—
905C22×C3—51no—
906C22×C3—51no—
907C22×C3—51no—
908C22×C3—51no—
909C22×C3—52no—
910C22×C3—102no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—101no—
915C22×C3—101no—
916C22×C3C2×C4×AGL(1,𝔽5)12yescomplemented
917C22×C3C23×AGL(1,𝔽5)11yescharacteristic
918C2×D3—21no—
919C2×D3—21no—
920C2×D3—52no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—101no—
926C2×D3—101no—
927C2×D3C2×C4×AGL(1,𝔽5)12yescomplemented
928C3×C4—21no—
929C3×C4—21no—
930C3×C4—54no—
931C3×C4—102no—
932C3×C4—102no—
933C3×C4—102no—
934C3×C4—101no—
935C3×C4—101no—
936Dic3—21no—
937Dic3—54no—
938Dic3—52no—
939Dic3—52no—
940Dic3—102no—
941Dic3—102no—
942Dic3—102no—
943Dic3—101no—
944Dic3C2×C4×AGL(1,𝔽5)12yescomplemented
945Dic3D4×AGL(1,𝔽5)12yescomplemented
946C2×C5—22no—
947C2×C5—62no—
948C2×C5C2×C42×D311yescharacteristic
949C2×C5C4×#23711yescharacteristic
950C2×C5C4×D3×D411yescharacteristic
951D5—22no—
952D5—62no—
953D5C2×#67⋊C411yescharacteristic
954D5#552211yescharacteristic
955D5C4×#23711yescharacteristic
956D5C4×D3×D411yescharacteristic
957C23—31no—
958C23—51no—
959C23—52no—
960C23—52no—
961C23—51no—
962C23—101no—
963C23—101no—
964C23—101no—
965C23—101no—
966C23—152no—
967C23—152no—
968C23—151no—
969C23—301no—
970C23—301no—
971C23—301no—
972C23—301no—
973C23C2×D3×AGL(1,𝔽5)11yescharacteristic
974D4—34no—
975D4—154no—
976D4—154no—
977D4—154no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—52no—
982C2×C4—52no—
983C2×C4—52no—
984C2×C4—52no—
985C2×C4—52no—
986C2×C4—52no—
987C2×C4—51no—
988C2×C4—51no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—101no—
992C2×C4—101no—
993C2×C4—101no—
994C2×C4—101no—
995C2×C4—108no—
996C2×C4—101no—
997C2×C4—101no—
998C2×C4—101no—
999C2×C4—101no—
1000C2×C4—101no—
1001C2×C4—101no—
1002C2×C4—152no—
1003C2×C4—152no—
1004C2×C4—152no—
1005C2×C4—152no—
1006C2×C4—152no—
1007C2×C4—152no—
1008C2×C4—152no—
1009C2×C4—151no—
1010C2×C4—151no—
1011C2×C4—152no—
1012C2×C4—152no—
1013C2×C4—152no—
1014C2×C4—151no—
1015C2×C4—302no—
1016C2×C4—302no—
1017C2×C4—302no—
1018C2×C4—308no—
1019C2×C4—302no—
1020C2×C4—301no—
1021C2×C4—301no—
1022C2×C4—302no—
1023C2×C4—308no—
1024C2×C4—302no—
1025C2×C4—308no—
1026C2×C4—301no—
1027C2×C4—301no—
1028C2×C4—301no—
1029C2×C4—301no—
1030C2×C4—301no—
1031C2×C4—301no—
1032C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
1033C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
1034C2×C3—22no—
1035C2×C3—51no—
1036C2×C3—51no—
1037C2×C3—51no—
1038C2×C3—51no—
1039C2×C3—102no—
1040C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
1041C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
1042C2×C3#41×AGL(1,𝔽5)11yescharacteristic
1043D3—22no—
1044D3—102no—
1045C5C4×#67⋊C411yescharacteristic, complemented, Sylow
1046C22—21no—
1047C22—21no—
1048C22—32no—
1049C22—51no—
1050C22—51no—
1051C22—51no—
1052C22—51no—
1053C22—51no—
1054C22—51no—
1055C22—52no—
1056C22—61no—
1057C22—61no—
1058C22—102no—
1059C22—102no—
1060C22—102no—
1061C22—102no—
1062C22—101no—
1063C22—101no—
1064C22—152no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—302no—
1069C22—301no—
1070C22—301no—
1071C22C4×D3×AGL(1,𝔽5)12yescomplemented
1072C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1073C4—21no—
1074C4—21no—
1075C4—32no—
1076C4—32no—
1077C4—54no—
1078C4—61no—
1079C4—102no—
1080C4—102no—
1081C4—102no—
1082C4—101no—
1083C4—101no—
1084C4—154no—
1085C4—152no—
1086C4—152no—
1087C4—302no—
1088C4—302no—
1089C4—302no—
1090C4—301no—
1091C3C4×D4×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
1092C2—22no—
1093C2—51no—
1094C2—51no—
1095C2—51no—
1096C2—51no—
1097C2—62no—
1098C2—102no—
1099C2—302no—
1100C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
1101C2D3×D4×AGL(1,𝔽5)11yescharacteristic
1102C2AGL(1,𝔽5)×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C22⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×Dic3×AGL(1,𝔽5)C2semidirect
4. C2×C4×D3×AGL(1,𝔽5)C2semidirect
6. C22⋊C4×ΓL(1,𝔽16)C2semidirect
7. C3×C22⋊C4×AGL(1,𝔽5)C2semidirect
8. Dic3×C22⋊AGL(1,𝔽5)C2semidirect
9. #11751931C2semidirect
10. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
11. #11751848C2semidirect
12. #11751834C2semidirect
13. #11751833C2semidirect
14. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
15. C4×Dic3×AGL(1,𝔽5)C2semidirect
30. #67⋊AGL(1,𝔽5)C4semidirect
31. AGL(1,𝔽5)×#67C4semidirect
46. #91770C4semidirect
47. C5×#67⋊C4C4semidirect
49. #67⋊Dic5C4semidirect
50. #91556C4semidirect
52. #91442C4semidirect
53. #91441C4semidirect
54. #91396C4semidirect
55. #91395C4semidirect
77. C22⋊C4×AGL(1,𝔽5)D3semidirect
84. C22×ΓL(1,𝔽16)C2×C4semidirect
91. C22×C3×AGL(1,𝔽5)C2×C4semidirect
100. C2×D3×AGL(1,𝔽5)C2×C4semidirect
101. C2×D3×AGL(1,𝔽5)C2×C4semidirect
103. C22×Dic15C2×C4semidirect
104. C2×C4×D15C2×C4semidirect
106. C22×C5×Dic3C2×C4semidirect
107. C2×C4×C5×D3C2×C4semidirect
114. C2×#1200C2×C4semidirect
115. C2×D3×Dic5C2×C4semidirect
118. C2×D5×Dic3C2×C4semidirect
119. C2×D5×Dic3C2×C4semidirect
125. #6763C2×C4semidirect
128. C3×C22⋊AGL(1,𝔽5)C2×C4semidirect
131. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
132. Dic3⋊AGL(1,𝔽5)C2×C4semidirect
133. (C2×D3)⋊AGL(1,𝔽5)C2×C4semidirect
134. (C2×D3)⋊AGL(1,𝔽5)C2×C4semidirect
140. Dic3×AGL(1,𝔽5)C2×C4semidirect
141. Dic3×AGL(1,𝔽5)C2×C4semidirect
142. Dic3×AGL(1,𝔽5)D4semidirect
143. C3×C5×C22⋊C4C2×C4semidirect
144. #6714C2×C4semidirect
145. #6712C2×C4semidirect
146. C4×Dic15C2×C4semidirect
147. C5×(C2×D3)⋊C4C2×C4semidirect
148. C5×Dic3⋊C4C2×C4semidirect
149. C4×C5×Dic3C2×C4semidirect
150. C3×C22⋊Dic5C2×C4semidirect
151. C3×#685C2×C4semidirect
152. C3×#685C2×C4semidirect
153. Dic3⋊Dic5C2×C4semidirect
154. #6669C2×C4semidirect
155. #6667C2×C4semidirect
156. (C2×D3)⋊Dic5C2×C4semidirect
157. Dic3×Dic5C2×C4semidirect
158. Dic3×Dic5C2×C4semidirect
269. #1220C42semidirect
275. C5×#67C42semidirect
287. #1202C42semidirect
288. #1201C42semidirect
338. #67⋊C4AGL(1,𝔽5)direct (N × H)
363. C22×AGL(1,𝔽5)C4×D3semidirect
394. C22⋊AGL(1,𝔽5)C4×D3semidirect
411. C5×C22⋊C4C4×D3semidirect
414. C22⋊Dic5C4×D3semidirect
417. #685C4×D3semidirect
418. #685C4×D3semidirect
442. C22×C3×C5C2×C42semidirect
446. C2×D15C2×C42semidirect
449. C2×C5×D3C2×C42semidirect
456. C2×C3×D5C2×C42semidirect
470. ΓL(1,𝔽16)C4×D4semidirect
474. C3×AGL(1,𝔽5)C4×D4semidirect
478. Dic15C2×C42semidirect
479. Dic15C4×D4semidirect
483. C5×Dic3C2×C42semidirect
484. C5×Dic3C4×D4semidirect
517. C22×Dic3C2×AGL(1,𝔽5)semidirect
529. C2×C4×D3C2×AGL(1,𝔽5)semidirect
534. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
543. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
549. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
563. C4×Dic3C2×AGL(1,𝔽5)semidirect
740. #67C4×AGL(1,𝔽5)semidirect
781. C22×C5C42×D3semidirect
796. C2×D5C42×D3semidirect
810. AGL(1,𝔽5)#67⋊C4direct (N × H)
883. C22⋊C4D3×AGL(1,𝔽5)semidirect
900. C3×C5C42×D4semidirect
916. C22×C3C2×C4×AGL(1,𝔽5)semidirect
927. C2×D3C2×C4×AGL(1,𝔽5)semidirect
944. Dic3C2×C4×AGL(1,𝔽5)semidirect
945. Dic3D4×AGL(1,𝔽5)semidirect
1045. C5C4×#67⋊C4semidirect
1071. C22C4×D3×AGL(1,𝔽5)semidirect
1091. C3C4×D4×AGL(1,𝔽5)semidirect

Maximal subgroups

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

subgroupindex
C2×#67⋊AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C22×Dic3×AGL(1,𝔽5)2
C2×C4×D3×AGL(1,𝔽5)2
D5×#67⋊C42
C22⋊C4×ΓL(1,𝔽16)2
C3×C22⋊C4×AGL(1,𝔽5)2
Dic3×C22⋊AGL(1,𝔽5)2
#117519312
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518482
#117518342
#117518332
AGL(1,𝔽5)×Dic3⋊C42
C4×Dic3×AGL(1,𝔽5)2
C4×D4×AGL(1,𝔽5)3
C4×#67⋊C45