Finite Group Databasebeta

← #72230128

Subgroups — #72230128

Order 2880.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3804C211yesmaximal, characteristic
2#13088745C211yesmaximal, characteristic, complemented
3#67⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4C2×Dic3×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5#13088690C211yesmaximal, characteristic, complemented
6C3×#67⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
7C3×#91923C211yesmaximal, characteristic, complemented
8#13088420C211yesmaximal, characteristic, complemented
9#13088419C211yesmaximal, characteristic, complemented
10#13088417C211yesmaximal, characteristic, complemented
11#13088414C211yesmaximal, characteristic, complemented
12#13088409C211yesmaximal, characteristic, complemented
13#13088408C211yesmaximal, characteristic, complemented
14AGL(1,𝔽5)×#624C211yesmaximal, characteristic, complemented
15D3×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
16AGL(1,𝔽5)×#237—31nomaximal
17#11756835—31nomaximal
18C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
19C22×C3×ΓL(1,𝔽16)C2211yescharacteristic
20C2×ΓL(1,𝔽16)⋊D3C2211yescharacteristic
21C2×D3×ΓL(1,𝔽16)C2211yescharacteristic
22C2×C3⋊D3×AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×D3×AGL(1,𝔽5)C2211yescharacteristic
24#10624230C411yescharacteristic, complemented
25#10624210C411yescharacteristic, complemented
26#10624207C411yescharacteristic, complemented
27C5×#3804C411yescharacteristic, complemented
28D5×#638C2211yescharacteristic
29C3×D5×#67C2211yescharacteristic
30C2×C3×D5×Dic3C2211yescharacteristic
31C3×#6763C2211yescharacteristic
32C32×C22⋊AGL(1,𝔽5)C2211yescharacteristic
33#10624044C411yescharacteristic, complemented
34#10624043C411yescharacteristic, complemented
35#10624042C411yescharacteristic, complemented
36#10624041C411yescharacteristic, complemented
37D5×#627C2211yescharacteristic
38D5×#626C2211yescharacteristic
39D5×#624C2211yescharacteristic
40D3×D5×Dic3C2211yescharacteristic
41#10623979C2211yescharacteristic
42#10623978C2211yescharacteristic
43ΓL(1,𝔽16)⋊Dic3C2211yescharacteristic
44Dic3⋊ΓL(1,𝔽16)C2211yescharacteristic
45(C2×D3)⋊ΓL(1,𝔽16)C2211yescharacteristic
46Dic3×ΓL(1,𝔽16)C2211yescharacteristic
47Dic3×ΓL(1,𝔽16)C2211yescharacteristic
48Dic3×ΓL(1,𝔽16)C2211yescharacteristic
49Dic3×ΓL(1,𝔽16)C2211yescharacteristic
50Dic3×ΓL(1,𝔽16)C2211yescharacteristic
51#10623965C2211yescharacteristic
52(C2×AGL(1,𝔽5))⋊(C3⋊D3)C2211yescharacteristic
53AGL(1,𝔽5)×C3⋊Dic3C2211yescharacteristic
54C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
55C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
56C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
57C3×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
58C3×Dic3×AGL(1,𝔽5)C2211yescharacteristic
59C3×Dic3×AGL(1,𝔽5)C2211yescharacteristic
60C3×Dic3×AGL(1,𝔽5)C2211yescharacteristic
61#10594048—51nomaximal, Hall
62D5×#237—31no—
63D5×#235—31no—
64D4×ΓL(1,𝔽16)—31no—
65C2×C4×ΓL(1,𝔽16)—31no—
66C3×D4×AGL(1,𝔽5)—31no—
67C3×#4130—31no—
68#67⋊AGL(1,𝔽5)—31no—
69#67⋊AGL(1,𝔽5)—31no—
70#67⋊AGL(1,𝔽5)—31no—
71#67⋊AGL(1,𝔽5)—31no—
72#67⋊AGL(1,𝔽5)—31no—
73#67⋊AGL(1,𝔽5)—61no—
74#67⋊AGL(1,𝔽5)D311yescharacteristic, complemented
75AGL(1,𝔽5)×#67—31no—
76AGL(1,𝔽5)×#67—31no—
77#91923—31no—
78#91923D311yescharacteristic, complemented
79C2×Dic3×AGL(1,𝔽5)—31no—
80C2×Dic3×AGL(1,𝔽5)—31no—
81#91921—31no—
82#91921—31no—
83C4×D3×AGL(1,𝔽5)—31no—
84C4×D3×AGL(1,𝔽5)—31no—
85C4×D3×AGL(1,𝔽5)—31no—
86#91909—31no—
87#91909—31no—
88ΓL(1,𝔽16)⋊Q8—31no—
89ΓL(1,𝔽16)⋊Q8—31no—
90ΓL(1,𝔽16)⋊Q8—31no—
91#91907—31no—
92AGL(1,𝔽5)×Dic6—31no—
93C22×C32×D5C2311yescharacteristic
94C2×D5×C3⋊D3C2311yescharacteristic
95C2×C3×D3×D5C2311yescharacteristic
96C2×C3⋊ΓL(1,𝔽16)—22no—
97C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
98C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
99C2×C3×ΓL(1,𝔽16)—22no—
100C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
101C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
102C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
103C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
104C2×C32×AGL(1,𝔽5)C2311yescharacteristic
105C2×C32×AGL(1,𝔽5)C2311yescharacteristic
106ΓL(1,𝔽16)⋊D3—22no—
107D3×ΓL(1,𝔽16)—22no—
108C3⋊D3×AGL(1,𝔽5)—22no—
109C3×D3×AGL(1,𝔽5)—22no—
110#67184C2×C411yescharacteristic, complemented
111C5×#638C2×C411yescharacteristic, complemented
112C3×#1220C2×C411yescharacteristic, complemented
113C2×C3×Dic15C2×C411yescharacteristic, complemented
114C3×C5×#67C2×C411yescharacteristic, complemented
115C2×C3×C5×Dic3C2×C411yescharacteristic, complemented
116#67158C2×C411yescharacteristic, complemented
117#67156C2×C411yescharacteristic, complemented
118#67155C2×C411yescharacteristic, complemented
119#67154C2×C411yescharacteristic, complemented
120#67153C2×C411yescharacteristic, complemented
121#67153C2×C411yescharacteristic, complemented
122#67152C2×C411yescharacteristic, complemented
123#67151C2×C411yescharacteristic, complemented
124#67149C2×C411yescharacteristic, complemented
125#67149C2×C411yescharacteristic, complemented
126D3×Dic15C2×C411yescharacteristic, complemented
127Dic3×D15C2×C411yescharacteristic, complemented
128C5×#627C2×C411yescharacteristic, complemented
129C5×#626C2×C411yescharacteristic, complemented
130C5×#624C2×C411yescharacteristic, complemented
131C5×D3×Dic3C2×C411yescharacteristic, complemented
132#67139C2×C411yescharacteristic, complemented
133#67138C2×C411yescharacteristic, complemented
134D5×C3⋊Dic3C2311yescharacteristic
135C3×#1202C2×C411yescharacteristic, complemented
136C3×#1201C2×C411yescharacteristic, complemented
137C3×D5×Dic3C2×C411yescharacteristic, complemented
138C3×D5×Dic3C2×C411yescharacteristic, complemented
139C3×D5×Dic3C2311yescharacteristic
140C3×D5×Dic3C2311yescharacteristic
141C3×D5×Dic3C2311yescharacteristic
142#41×AGL(1,𝔽5)—91noHall
143C2×#3804—51no—
144#64090—51no—
145C3×#67⋊C4—51no—
146C3×#877—51no—
147#67⋊Dic3—51no—
148C2×Dic32—51no—
149#63952—51no—
150#63904—51no—
151C4×#624—51no—
152#63881—51no—
153#63877—51no—
154C4×D3×Dic3—51no—
155#63838—51no—
156#63837—51no—
157#63836—51no—
158C22×ΓL(1,𝔽16)—31no—
159C22×ΓL(1,𝔽16)—31no—
160C22×ΓL(1,𝔽16)—31no—
161C22×ΓL(1,𝔽16)—61no—
162C22×ΓL(1,𝔽16)C2×D311yescharacteristic
163C22×C3×AGL(1,𝔽5)—31no—
164C22×C3×AGL(1,𝔽5)—31no—
165C2×D3×AGL(1,𝔽5)—31no—
166C2×D3×AGL(1,𝔽5)—31no—
167C2×D3×AGL(1,𝔽5)—31no—
168C2×D3×AGL(1,𝔽5)—31no—
169C2×D3×AGL(1,𝔽5)—31no—
170C2×D3×AGL(1,𝔽5)—61no—
171C2×D3×AGL(1,𝔽5)C2×D311yescharacteristic
172#6819—31no—
173#6817—31no—
174C5×#237—31no—
175C5×#235—31no—
176C3×D4×D5—31no—
177C2×C3×C4×D5—31no—
178D5×#67—31no—
179D5×#67—31no—
180D5×#67—31no—
181D5×#67—61no—
182D5×#67C2×D311yescharacteristic
183#6782—31no—
184#6782—31no—
185#6780—31no—
186#6780—31no—
187#6779—31no—
188#6779—31no—
189C2×D5×Dic3—31no—
190C2×D5×Dic3C2×D311yescharacteristic
191D5×D12—31no—
192C4×D3×D5—31no—
193C4×D3×D5—31no—
194C4×D3×D5—31no—
195#6773—31no—
196#6772—31no—
197#6771—31no—
198#6771—31no—
199#6766—31no—
200#6765—31no—
201D5×Dic6—31no—
202D5×Dic6—31no—
203#6763—31no—
204#6763C2×D311yescharacteristic
205C4⋊ΓL(1,𝔽16)—31no—
206C4×ΓL(1,𝔽16)—31no—
207C4×ΓL(1,𝔽16)—31no—
208C4×ΓL(1,𝔽16)—31no—
209C4×ΓL(1,𝔽16)—31no—
210C4×ΓL(1,𝔽16)—31no—
211C3×C22⋊AGL(1,𝔽5)—21no—
212C3×C22⋊AGL(1,𝔽5)—31no—
213C3×C22⋊AGL(1,𝔽5)—31no—
214C3×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
215C3×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
216C3×C4⋊AGL(1,𝔽5)—31no—
217C3×C4⋊AGL(1,𝔽5)—31no—
218C3×C4⋊AGL(1,𝔽5)—31no—
219C3×C4×AGL(1,𝔽5)—31no—
220C3×C4×AGL(1,𝔽5)—31no—
221C3×C4×AGL(1,𝔽5)—31no—
222Dic3⋊AGL(1,𝔽5)—31no—
223Dic3⋊AGL(1,𝔽5)—31no—
224Dic3⋊AGL(1,𝔽5)—31no—
225Dic3⋊AGL(1,𝔽5)—31no—
226Dic3⋊AGL(1,𝔽5)—31no—
227Dic3⋊AGL(1,𝔽5)—61no—
228Dic3⋊AGL(1,𝔽5)C2×D311yescharacteristic
229Dic3⋊AGL(1,𝔽5)C2×D311yescharacteristic
230Dic3⋊AGL(1,𝔽5)C2×D311yescharacteristic
231(C2×D3)⋊AGL(1,𝔽5)—31no—
232(C2×D3)⋊AGL(1,𝔽5)—31no—
233(C2×D3)⋊AGL(1,𝔽5)—31no—
234(C2×D3)⋊AGL(1,𝔽5)—31no—
235(C2×D3)⋊AGL(1,𝔽5)—31no—
236(C2×D3)⋊AGL(1,𝔽5)—61no—
237(C2×D3)⋊AGL(1,𝔽5)C2×D311yescharacteristic
238Dic3×AGL(1,𝔽5)—31no—
239Dic3×AGL(1,𝔽5)—31no—
240Dic3×AGL(1,𝔽5)—31no—
241Dic3×AGL(1,𝔽5)—31no—
242Dic3×AGL(1,𝔽5)—31no—
243Dic3×AGL(1,𝔽5)—31no—
244Dic3×AGL(1,𝔽5)—31no—
245Dic3×AGL(1,𝔽5)—31no—
246Dic3×AGL(1,𝔽5)—31no—
247Dic3×AGL(1,𝔽5)—61no—
248Dic3×AGL(1,𝔽5)C2×D311yescharacteristic
249Dic3×AGL(1,𝔽5)C2×D311yescharacteristic
250Dic3×AGL(1,𝔽5)C2×D311yescharacteristic
251C4×#237—151no—
252#5522—151no—
253C22×C32×C5C22×C411yescharacteristic
254C2×C3⋊D15C22×C411yescharacteristic
255C2×C5×C3⋊D3C22×C411yescharacteristic
256C2×C3×D15C22×C411yescharacteristic
257C2×C3×C5×D3C22×C411yescharacteristic
258C2×C32×D5—21no—
259C2×C32×D5—21no—
260C2×C32×D5C22×C411yescharacteristic
261C2×C32×D5C2411yescharacteristic
262D5×C3⋊D3—21no—
263D5×C3⋊D3—21no—
264C3×D3×D5—21no—
265C3×D3×D5—21no—
266C3⋊ΓL(1,𝔽16)—21no—
267C3⋊ΓL(1,𝔽16)#4112yescomplemented
268C3×ΓL(1,𝔽16)—21no—
269C3×ΓL(1,𝔽16)—21no—
270C3×ΓL(1,𝔽16)—21no—
271C3×ΓL(1,𝔽16)#4112yescomplemented
272C32×AGL(1,𝔽5)—21no—
273C32×AGL(1,𝔽5)—21no—
274C3⋊Dic15C22×C411yescharacteristic
275C5×C3⋊Dic3C22×C411yescharacteristic
276C3×Dic15C22×C411yescharacteristic
277C3×Dic15C22×C411yescharacteristic
278C3×Dic15C22×C411yescharacteristic
279C3×C5×Dic3C22×C411yescharacteristic
280C3×C5×Dic3C22×C411yescharacteristic
281C3×C5×Dic3C22×C411yescharacteristic
282D5×#41—91no—
283Q8×AGL(1,𝔽5)—91no—
284Q8×AGL(1,𝔽5)—91no—
285D4×AGL(1,𝔽5)—31no—
286D4×AGL(1,𝔽5)—91no—
287D4×AGL(1,𝔽5)—91no—
288D4×AGL(1,𝔽5)—91no—
289D4×AGL(1,𝔽5)—91no—
290D4×AGL(1,𝔽5)—91no—
291#4130—31no—
292#4130—91no—
293#4130—91no—
294C2×C4×AGL(1,𝔽5)—91no—
295C2×C4×AGL(1,𝔽5)—91no—
296C2×C4×AGL(1,𝔽5)—91no—
297C2×#638—51no—
298C22×C3⋊Dic3—51no—
299C2×C4×C3⋊D3—51no—
300C2×C3×#67—51no—
301C22×C3×Dic3—51no—
302C22×C3×Dic3—51no—
303C2×C3×C4×D3—51no—
304C2×#627—51no—
305C2×#626—51no—
306C2×#624—51no—
307C2×#624—51no—
308#3804—51no—
309#3804—51no—
310#3804—51no—
311#3804—51no—
312#3804—51no—
313#3804—51no—
314#3804—51no—
315#3804AGL(1,𝔽5)11yescharacteristic, complemented
316C2×D3×Dic3—51no—
317C2×D3×Dic3—51no—
318C32×C22⋊C4—51no—
319#3752—51no—
320#3750—51no—
321C4×C3⋊Dic3—51no—
322C3×#217—51no—
323C3×(C2×D3)⋊C4—51no—
324C3×Dic3⋊C4—51no—
325C3×Dic3⋊C4—51no—
326C3×Dic3⋊C4—51no—
327C3×C4×Dic3—51no—
328C3×C4×Dic3—51no—
329C3×C4×Dic3—51no—
330#3724—51no—
331Dic3⋊Dic3—51no—
332#3722—51no—
333(C2×D3)⋊Dic3—51no—
334Dic32—51no—
335Dic32—51no—
336Dic32—51no—
337Dic32—51no—
338Dic32—51no—
339Dic32—51no—
340C22×C3×D5—21no—
341C22×C3×D5—31no—
342C22×C3×D5C22×D311yescharacteristic
343C22×C3×D5C22×D311yescharacteristic
344C2×D3×D5—31no—
345C2×D3×D5—31no—
346C2×D3×D5—61no—
347C2×D3×D5C22×D311yescharacteristic
348C2×ΓL(1,𝔽16)—22no—
349C2×ΓL(1,𝔽16)—31no—
350C2×ΓL(1,𝔽16)—31no—
351C2×ΓL(1,𝔽16)—31no—
352C2×ΓL(1,𝔽16)—31no—
353C2×ΓL(1,𝔽16)—62no—
354C2×ΓL(1,𝔽16)—62no—
355C2×ΓL(1,𝔽16)—62no—
356C2×ΓL(1,𝔽16)—61no—
357C2×ΓL(1,𝔽16)—61no—
358C2×ΓL(1,𝔽16)—122no—
359C2×ΓL(1,𝔽16)C22×D311yescharacteristic
360C2×ΓL(1,𝔽16)C22×D311yescharacteristic
361C2×ΓL(1,𝔽16)C22×D311yescharacteristic
362C2×ΓL(1,𝔽16)C22×D311yescharacteristic
363C2×C3×AGL(1,𝔽5)—21no—
364C2×C3×AGL(1,𝔽5)—21no—
365C2×C3×AGL(1,𝔽5)—31no—
366C2×C3×AGL(1,𝔽5)—31no—
367C2×C3×AGL(1,𝔽5)—31no—
368C2×C3×AGL(1,𝔽5)—31no—
369C2×C3×AGL(1,𝔽5)—62no—
370C2×C3×AGL(1,𝔽5)—62no—
371C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
372C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
373C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
374C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
375D3×AGL(1,𝔽5)—22no—
376D3×AGL(1,𝔽5)—62no—
377D3×AGL(1,𝔽5)—62no—
378D3×AGL(1,𝔽5)—62no—
379D3×AGL(1,𝔽5)—62no—
380D3×AGL(1,𝔽5)—62no—
381D3×AGL(1,𝔽5)—122no—
382C3×C5×D4—31no—
383C2×C3×C4×C5—31no—
384#1220—31no—
385#1220—31no—
386#1220—31no—
387#1220—61no—
388#1220C4×D311yescharacteristic, complemented
389C2×Dic15—31no—
390C2×Dic15C4×D311yescharacteristic, complemented
391D60—31no—
392C4×D15—31no—
393C4×D15—31no—
394C4×D15—31no—
395Dic30—31no—
396Dic30—31no—
397C5×#67—31no—
398C5×#67—31no—
399C5×#67—31no—
400C5×#67—61no—
401C5×#67C4×D311yescharacteristic, complemented
402C2×C5×Dic3—31no—
403C2×C5×Dic3C4×D311yescharacteristic, complemented
404C5×D12—31no—
405C4×C5×D3—31no—
406C4×C5×D3—31no—
407C4×C5×D3—31no—
408C5×Dic6—31no—
409C5×Dic6—31no—
410C3×C22⋊D5—31no—
411C3×C22⋊D5—31no—
412C2×C3×Dic5—31no—
413C3×D20—31no—
414C3×C4×D5—31no—
415C3×C4×D5—31no—
416C3×C4×D5—31no—
417C3×C4×D5—31no—
418C3×C4×D5—31no—
419#1204—31no—
420#1204—31no—
421#1204—31no—
422#1204—31no—
423#1203—31no—
424#1203—31no—
425#1202—31no—
426#1202—31no—
427#1202—31no—
428#1202—61no—
429#1202C4×D311yescharacteristic, complemented
430#1201—31no—
431#1201—31no—
432#1201—31no—
433#1201—61no—
434#1201C4×D311yescharacteristic, complemented
435#1200—31no—
436#1200—31no—
437#1200—31no—
438D3×Dic5—31no—
439D3×Dic5—31no—
440D3×Dic5—31no—
441D5×Dic3—31no—
442D5×Dic3—31no—
443D5×Dic3—31no—
444D5×Dic3—31no—
445D5×Dic3—61no—
446D5×Dic3C4×D311yescharacteristic, complemented
447D5×Dic3C4×D311yescharacteristic, complemented
448D5×Dic3C22×D311yescharacteristic
449D5×Dic3C22×D311yescharacteristic
450D5×Dic3C22×D311yescharacteristic
451C2×#237—151no—
452C2×#235—151no—
453C3×C4×D4—151no—
454C3×#117—151no—
455D4×Dic3—151no—
456C4×#67—151no—
457C4×#67—151no—
458C2×C4×Dic3—151no—
459C2×C4×Dic3—151no—
460C2×C4×Dic3—151no—
461#893—151no—
462#893—151no—
463#892—151no—
464#887—151no—
465#887—151no—
466#887—151no—
467#67⋊C4—51no—
468#67⋊C4—151no—
469#67⋊C4—151no—
470#67⋊C4—151no—
471#67⋊C4—151no—
472#67⋊C4—151no—
473#67⋊C4—301no—
474#877—51no—
475#877—151no—
476#872—151no—
477#872—151no—
478C42×D3—151no—
479C42×D3—151no—
480C42×D3—151no—
481C4×Dic6—151no—
482C2×C32×C5—21no—
483C2×C32×C5C23×C411yescharacteristic
484C3⋊D15—21no—
485C5×C3⋊D3—21no—
486C3×D15—21no—
487C3×C5×D3—21no—
488C32×D5—21no—
489C32×D5C2×#4111yescharacteristic
490C32×D5C2×#4111yescharacteristic
491C22×AGL(1,𝔽5)—31no—
492C22×AGL(1,𝔽5)—31no—
493C22×AGL(1,𝔽5)—91no—
494C22×AGL(1,𝔽5)—91no—
495C22×AGL(1,𝔽5)—91no—
496C22×AGL(1,𝔽5)—91no—
497C5×#41—91no—
498#713—91no—
499Q8×D5—91no—
500#711—91no—
501#711—91no—
502#711—91no—
503D4×D5—31no—
504D4×D5—91no—
505D4×D5—91no—
506#709—91no—
507#709—91no—
508#709—91no—
509C2×C4×D5—31no—
510C2×C4×D5—91no—
511C2×C4×D5—91no—
512C22⋊AGL(1,𝔽5)—31no—
513C22⋊AGL(1,𝔽5)—31no—
514C22⋊AGL(1,𝔽5)—91no—
515C22⋊AGL(1,𝔽5)—91no—
516C22⋊AGL(1,𝔽5)—91no—
517C22⋊AGL(1,𝔽5)D3211yescharacteristic
518C4⋊AGL(1,𝔽5)—31no—
519C4⋊AGL(1,𝔽5)—31no—
520C4⋊AGL(1,𝔽5)—31no—
521C4⋊AGL(1,𝔽5)—91no—
522C4⋊AGL(1,𝔽5)—91no—
523C4⋊AGL(1,𝔽5)—91no—
524C4×AGL(1,𝔽5)—31no—
525C4×AGL(1,𝔽5)—31no—
526C4×AGL(1,𝔽5)—31no—
527C4×AGL(1,𝔽5)—91no—
528C4×AGL(1,𝔽5)—91no—
529C4×AGL(1,𝔽5)—91no—
530C4×AGL(1,𝔽5)—91no—
531C4×AGL(1,𝔽5)—91no—
532C4×AGL(1,𝔽5)—91no—
533C4×AGL(1,𝔽5)—91no—
534C23×C32—51no—
535C22×C3⋊D3—51no—
536C22×C3×D3—51no—
537C2×C32×C4—51no—
538C2×C32×C4—51no—
539#638—51no—
540#638—51no—
541#638—51no—
542#638C2×AGL(1,𝔽5)11yescharacteristic, complemented
543C2×C3⋊Dic3—51no—
544C2×C3⋊Dic3—51no—
545C2×C3⋊Dic3—51no—
546C2×C3⋊Dic3—102no—
547C4×C3⋊D3—102no—
548C3×#67—51no—
549C3×#67—51no—
550C3×#67—51no—
551C3×#67C2×AGL(1,𝔽5)11yescharacteristic, complemented
552C2×C3×Dic3—51no—
553C2×C3×Dic3—51no—
554C2×C3×Dic3—51no—
555C2×C3×Dic3—51no—
556C2×C3×Dic3—51no—
557C2×C3×Dic3—51no—
558C2×C3×Dic3—51no—
559C2×C3×Dic3—51no—
560C2×C3×Dic3—51no—
561C2×C3×Dic3—51no—
562C2×C3×Dic3—102no—
563C2×C3×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
564C3×C4×D3—102no—
565#627—51no—
566#627—51no—
567#627—51no—
568#627C2×AGL(1,𝔽5)11yescharacteristic, complemented
569#626—51no—
570#626—51no—
571#626—51no—
572#626C2×AGL(1,𝔽5)11yescharacteristic, complemented
573#624—51no—
574#624—51no—
575#624—51no—
576#624—102no—
577#624C2×AGL(1,𝔽5)11yescharacteristic, complemented
578D3×Dic3—51no—
579D3×Dic3—51no—
580D3×Dic3—51no—
581D3×Dic3—102no—
582D3×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
583C4×#41—451noSylow
584C22×C3×C5—21no—
585C22×C3×C5—31no—
586C22×C3×C5C2×C4×D311yescharacteristic
587C22×C3×C5C2×C4×D311yescharacteristic
588C2×D15—31no—
589C2×D15—31no—
590C2×D15—61no—
591C2×D15C2×C4×D311yescharacteristic
592C2×C5×D3—31no—
593C2×C5×D3—31no—
594C2×C5×D3—61no—
595C2×C5×D3C2×C4×D311yescharacteristic
596C2×C3×D5—21no—
597C2×C3×D5—21no—
598C2×C3×D5—21no—
599C2×C3×D5—21no—
600C2×C3×D5—21no—
601C2×C3×D5—21no—
602C2×C3×D5—31no—
603C2×C3×D5—41no—
604C2×C3×D5—41no—
605C2×C3×D5—61no—
606C2×C3×D5—61no—
607C2×C3×D5C2×C4×D311yescharacteristic
608C2×C3×D5C2×C4×D311yescharacteristic
609C2×C3×D5C23×D311yescharacteristic
610C2×C3×D5C23×D311yescharacteristic
611D3×D5—21no—
612D3×D5—21no—
613D3×D5—61no—
614D3×D5—61no—
615D3×D5—61no—
616D3×D5—61no—
617D3×D5—121no—
618D3×D5—121no—
619ΓL(1,𝔽16)—21no—
620ΓL(1,𝔽16)—21no—
621ΓL(1,𝔽16)—21no—
622ΓL(1,𝔽16)—32no—
623ΓL(1,𝔽16)—32no—
624ΓL(1,𝔽16)—62no—
625ΓL(1,𝔽16)—61no—
626ΓL(1,𝔽16)—61no—
627ΓL(1,𝔽16)—121no—
628ΓL(1,𝔽16)#23712yescomplemented
629C3×AGL(1,𝔽5)—21no—
630C3×AGL(1,𝔽5)—21no—
631C3×AGL(1,𝔽5)—21no—
632C3×AGL(1,𝔽5)—21no—
633C3×AGL(1,𝔽5)—32no—
634C3×AGL(1,𝔽5)—41no—
635C3×AGL(1,𝔽5)—41no—
636C3×AGL(1,𝔽5)—61no—
637C3×AGL(1,𝔽5)—61no—
638C3×AGL(1,𝔽5)—61no—
639C3×C4×C5—31no—
640C3×C4×C5—31no—
641C3×C4×C5—31no—
642Dic15—31no—
643Dic15—31no—
644Dic15—61no—
645Dic15C2×C4×D311yescharacteristic
646Dic15C2×C4×D311yescharacteristic
647Dic15C2×C4×D311yescharacteristic
648C3×Dic5—31no—
649C3×Dic5—31no—
650C3×Dic5—31no—
651C5×Dic3—31no—
652C5×Dic3—31no—
653C5×Dic3—61no—
654C5×Dic3C2×C4×D311yescharacteristic
655C5×Dic3C2×C4×D311yescharacteristic
656C5×Dic3C2×C4×D311yescharacteristic
657C2×C3×D4—151no—
658C22×C3×C4—151no—
659C22×C3×C4—151no—
660C22×C3×C4—151no—
661C2×#67—51no—
662C2×#67—151no—
663C2×#67—151no—
664C2×#67—151no—
665C2×#67—301no—
666C22×Dic3—51no—
667C22×Dic3—51no—
668C22×Dic3—151no—
669C22×Dic3—151no—
670C22×Dic3—151no—
671C22×Dic3—151no—
672C22×Dic3—301no—
673#237—31no—
674#237—151no—
675#237—151no—
676#237—151no—
677#237—151no—
678#237—151no—
679#237—151no—
680#237—151no—
681#235—31no—
682#235—151no—
683#235—151no—
684#235—151no—
685#235—151no—
686#235—151no—
687#235—151no—
688#235—151no—
689C2×D12—151no—
690C2×C4×D3—51no—
691C2×C4×D3—151no—
692C2×C4×D3—151no—
693C2×C4×D3—151no—
694C2×C4×D3—151no—
695C2×C4×D3—151no—
696C2×C4×D3—151no—
697C2×C4×D3—151no—
698C2×C4×D3—151no—
699C2×C4×D3—301no—
700C2×Dic6—151no—
701C2×Dic6—151no—
702C3×C4⋊C4—151no—
703C3×C4⋊C4—151no—
704C3×C4⋊C4—151no—
705C3×C22⋊C4—51no—
706C3×C22⋊C4—51no—
707C3×C22⋊C4—101no—
708C3×C22⋊C4—151no—
709C3×C22⋊C4—151no—
710C3×C42—151no—
711C3×C42—151no—
712C3×C42—151no—
713#217—51no—
714#217—151no—
715(C2×D3)⋊C4—51no—
716(C2×D3)⋊C4—151no—
717(C2×D3)⋊C4—151no—
718(C2×D3)⋊C4—151no—
719(C2×D3)⋊C4—151no—
720(C2×D3)⋊C4—151no—
721(C2×D3)⋊C4—301no—
722C4⋊Dic3—151no—
723Dic3⋊C4—51no—
724Dic3⋊C4—51no—
725Dic3⋊C4—51no—
726Dic3⋊C4—151no—
727Dic3⋊C4—151no—
728Dic3⋊C4—151no—
729Dic3⋊C4—151no—
730Dic3⋊C4—151no—
731Dic3⋊C4—301no—
732C4×Dic3—51no—
733C4×Dic3—51no—
734C4×Dic3—51no—
735C4×Dic3—151no—
736C4×Dic3—151no—
737C4×Dic3—151no—
738C4×Dic3—151no—
739C4×Dic3—151no—
740C4×Dic3—151no—
741C4×Dic3—151no—
742C4×Dic3—151no—
743C4×Dic3—151no—
744C4×Dic3—151no—
745C4×Dic3—151no—
746C4×Dic3—151no—
747C4×Dic3—151no—
748C4×Dic3—151no—
749C4×Dic3—301no—
750C32×C5C4×#4111yescharacteristic, complemented, Hall
751C22×D5—31no—
752C22×D5—91no—
753C22×D5C2×D3211yescharacteristic
754C2×AGL(1,𝔽5)—31no—
755C2×AGL(1,𝔽5)—31no—
756C2×AGL(1,𝔽5)—31no—
757C2×AGL(1,𝔽5)—31no—
758C2×AGL(1,𝔽5)—62no—
759C2×AGL(1,𝔽5)—62no—
760C2×AGL(1,𝔽5)—91no—
761C2×AGL(1,𝔽5)—91no—
762C2×AGL(1,𝔽5)—182no—
763C2×AGL(1,𝔽5)—182no—
764C2×AGL(1,𝔽5)—182no—
765C2×AGL(1,𝔽5)—182no—
766C2×AGL(1,𝔽5)C2×D3211yescharacteristic
767C2×AGL(1,𝔽5)C2×D3211yescharacteristic
768C5×Q8—91no—
769C5×D4—31no—
770C5×D4—91no—
771C5×D4—91no—
772C2×C4×C5—31no—
773C2×C4×C5—91no—
774C2×C4×C5—91no—
775C22⋊D5—31no—
776C22⋊D5—31no—
777C22⋊D5—91no—
778C22⋊D5—91no—
779C22⋊D5—91no—
780C22⋊D5—91no—
781C2×Dic5—31no—
782C2×Dic5—91no—
783C2×Dic5—91no—
784D20—31no—
785D20—91no—
786D20—91no—
787C4×D5—31no—
788C4×D5—31no—
789C4×D5—31no—
790C4×D5—31no—
791C4×D5—31no—
792C4×D5—91no—
793C4×D5—91no—
794C4×D5—91no—
795C4×D5—91no—
796C4×D5—91no—
797Dic10—91no—
798Dic10—91no—
799Dic10—91no—
800C22×C32—51no—
801C22×C32—51no—
802C22×C32—101no—
803C22×C32—101no—
804C22×C32C22×AGL(1,𝔽5)11yescharacteristic
805C2×C3⋊D3—51no—
806C2×C3⋊D3—101no—
807C2×C3⋊D3—101no—
808C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
809C2×C3×D3—51no—
810C2×C3×D3—101no—
811C2×C3×D3—101no—
812C2×C3×D3C22×AGL(1,𝔽5)11yescharacteristic
813C32×C4—101no—
814C32×C4—101no—
815C3⋊Dic3—52no—
816C3⋊Dic3—51no—
817C3⋊Dic3—101no—
818C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
819C3×Dic3—52no—
820C3×Dic3—51no—
821C3×Dic3—51no—
822C3×Dic3—51no—
823C3×Dic3—101no—
824C3×Dic3—101no—
825C3×Dic3—101no—
826C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
827C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
828C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
829C2×#41—451no—
830C4×Q8—451no—
831C4×Q8—451no—
832C4×D4—151no—
833C4×D4—451no—
834C4×D4—451no—
835C4×D4—451no—
836C4×D4—451no—
837C4×D4—451no—
838#117—151no—
839#117—451no—
840#117—451no—
841C2×C42—451no—
842C2×C42—451no—
843C2×C42—451no—
844C2×C3×C5—21no—
845C2×C3×C5—21no—
846C2×C3×C5—21no—
847C2×C3×C5—41no—
848C2×C3×C5—61no—
849C2×C3×C5C22×C4×D311yescharacteristic
850C2×C3×C5C22×C4×D311yescharacteristic
851D15—21no—
852D15—61no—
853D15—61no—
854D15—121no—
855C3×D5—21no—
856C3×D5—21no—
857C3×D5—21no—
858C3×D5—21no—
859C3×D5—41no—
860C3×D5—61no—
861C3×D5C2×#23711yescharacteristic
862C3×D5D3×#4111yescharacteristic
863C3×D5D3×#4111yescharacteristic
864C3×D5D3×#4111yescharacteristic
865C5×D3—21no—
866C5×D3—61no—
867C5×D3—61no—
868C5×D3—121no—
869C23×C3—51no—
870C23×C3—51no—
871C23×C3—101no—
872C23×C3—151no—
873C22×D3—51no—
874C22×D3—151no—
875C22×D3—151no—
876C22×D3—301no—
877C3×D4—31no—
878C3×D4—151no—
879C3×D4—151no—
880C3×D4—151no—
881C2×C3×C4—31no—
882C2×C3×C4—51no—
883C2×C3×C4—51no—
884C2×C3×C4—51no—
885C2×C3×C4—51no—
886C2×C3×C4—101no—
887C2×C3×C4—101no—
888C2×C3×C4—151no—
889C2×C3×C4—151no—
890C2×C3×C4—151no—
891C2×C3×C4—151no—
892C2×C3×C4—151no—
893C2×C3×C4—151no—
894C2×C3×C4—151no—
895C2×C3×C4—151no—
896C2×C3×C4—151no—
897C2×C3×C4—151no—
898C2×C3×C4—302no—
899C2×C3×C4—302no—
900#67—31no—
901#67—31no—
902#67—31no—
903#67—51no—
904#67—51no—
905#67—51no—
906#67—61no—
907#67—151no—
908#67—151no—
909#67—151no—
910#67—151no—
911#67—151no—
912#67—151no—
913#67—151no—
914#67—151no—
915#67—151no—
916#67—301no—
917#67—301no—
918#67—301no—
919#67D3×AGL(1,𝔽5)11yescharacteristic, complemented
920C2×Dic3—31no—
921C2×Dic3—51no—
922C2×Dic3—51no—
923C2×Dic3—51no—
924C2×Dic3—51no—
925C2×Dic3—51no—
926C2×Dic3—51no—
927C2×Dic3—51no—
928C2×Dic3—51no—
929C2×Dic3—51no—
930C2×Dic3—51no—
931C2×Dic3—102no—
932C2×Dic3—151no—
933C2×Dic3—151no—
934C2×Dic3—151no—
935C2×Dic3—151no—
936C2×Dic3—151no—
937C2×Dic3—151no—
938C2×Dic3—151no—
939C2×Dic3—151no—
940C2×Dic3—151no—
941C2×Dic3—301no—
942C2×Dic3—301no—
943C2×Dic3—301no—
944C2×Dic3—302no—
945C2×Dic3—302no—
946C2×Dic3—302no—
947C2×Dic3—602no—
948C2×Dic3D3×AGL(1,𝔽5)11yescharacteristic, complemented
949D12—31no—
950D12—151no—
951D12—151no—
952D12—151no—
953C4×D3—31no—
954C4×D3—31no—
955C4×D3—31no—
956C4×D3—102no—
957C4×D3—151no—
958C4×D3—151no—
959C4×D3—151no—
960C4×D3—151no—
961C4×D3—151no—
962C4×D3—151no—
963C4×D3—151no—
964C4×D3—151no—
965C4×D3—151no—
966C4×D3—302no—
967C4×D3—302no—
968C4×D3—302no—
969C4×D3—302no—
970C4×D3—302no—
971C4×D3—602no—
972Dic6—31no—
973Dic6—31no—
974Dic6—151no—
975Dic6—151no—
976Dic6—151no—
977Dic6—151no—
978Dic6—151no—
979Dic6—151no—
980C22×C5—31no—
981C22×C5—91no—
982C22×C5C4×D3211yescharacteristic
983C2×D5—21no—
984C2×D5—21no—
985C2×D5—31no—
986C2×D5—61no—
987C2×D5—61no—
988C2×D5—91no—
989C2×D5—181no—
990C2×D5—181no—
991C2×D5C4×D3211yescharacteristic
992C2×D5C22×D3211yescharacteristic
993AGL(1,𝔽5)—21no—
994AGL(1,𝔽5)—21no—
995AGL(1,𝔽5)—32no—
996AGL(1,𝔽5)—61no—
997AGL(1,𝔽5)—61no—
998AGL(1,𝔽5)—61no—
999AGL(1,𝔽5)—92no—
1000AGL(1,𝔽5)—181no—
1001C4×C5—31no—
1002C4×C5—31no—
1003C4×C5—31no—
1004C4×C5—91no—
1005Dic5—31no—
1006Dic5—31no—
1007Dic5—31no—
1008Dic5—91no—
1009C2×C32—21no—
1010C2×C32—51no—
1011C2×C32—51no—
1012C2×C32—101no—
1013C2×C32C23×AGL(1,𝔽5)11yescharacteristic
1014C3⋊D3—21no—
1015C3⋊D3—101no—
1016C3×D3—21no—
1017C3×D3—101no—
1018#41—91no—
1019#41—451no—
1020#41—451no—
1021#41—451no—
1022#41—451no—
1023#41—451no—
1024#41—451no—
1025#41—451no—
1026C2×Q8—451no—
1027C2×D4—151no—
1028C2×D4—451no—
1029C2×D4—451no—
1030C22×C4—151no—
1031C22×C4—151no—
1032C22×C4—151no—
1033C22×C4—451no—
1034C22×C4—451no—
1035C22×C4—451no—
1036C22×C4—451no—
1037C22×C4—451no—
1038C22×C4—451no—
1039C4⋊C4—151no—
1040C4⋊C4—151no—
1041C4⋊C4—151no—
1042C4⋊C4—451no—
1043C4⋊C4—451no—
1044C4⋊C4—451no—
1045C22⋊C4—51no—
1046C22⋊C4—151no—
1047C22⋊C4—151no—
1048C22⋊C4—451no—
1049C22⋊C4—451no—
1050C22⋊C4—451no—
1051C42—151no—
1052C42—151no—
1053C42—151no—
1054C42—451no—
1055C42—451no—
1056C42—451no—
1057C42—451no—
1058C42—451no—
1059C42—451no—
1060C42—451no—
1061C3×C5—21no—
1062C3×C5#552211yescharacteristic, complemented
1063C3×C5C4×#23711yescharacteristic, complemented
1064C22×C3—21no—
1065C22×C3—31no—
1066C22×C3—51no—
1067C22×C3—51no—
1068C22×C3—51no—
1069C22×C3—51no—
1070C22×C3—101no—
1071C22×C3—101no—
1072C22×C3—101no—
1073C22×C3—101no—
1074C22×C3—101no—
1075C22×C3—101no—
1076C22×C3—151no—
1077C22×C3—201no—
1078C22×C3—201no—
1079C22×C3—301no—
1080C22×C3—301no—
1081C22×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
1082C22×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
1083C2×D3—31no—
1084C2×D3—31no—
1085C2×D3—51no—
1086C2×D3—61no—
1087C2×D3—101no—
1088C2×D3—101no—
1089C2×D3—151no—
1090C2×D3—151no—
1091C2×D3—301no—
1092C2×D3—301no—
1093C2×D3—301no—
1094C2×D3—301no—
1095C2×D3—301no—
1096C2×D3—601no—
1097C2×D3—601no—
1098C2×D3C2×D3×AGL(1,𝔽5)11yescharacteristic
1099C3×C4—31no—
1100C3×C4—31no—
1101C3×C4—31no—
1102C3×C4—101no—
1103C3×C4—101no—
1104C3×C4—101no—
1105C3×C4—101no—
1106C3×C4—152no—
1107C3×C4—151no—
1108C3×C4—151no—
1109C3×C4—151no—
1110C3×C4—201no—
1111C3×C4—201no—
1112C3×C4—301no—
1113C3×C4—301no—
1114C3×C4—301no—
1115Dic3—31no—
1116Dic3—31no—
1117Dic3—52no—
1118Dic3—51no—
1119Dic3—51no—
1120Dic3—51no—
1121Dic3—61no—
1122Dic3—101no—
1123Dic3—101no—
1124Dic3—101no—
1125Dic3—152no—
1126Dic3—152no—
1127Dic3—151no—
1128Dic3—151no—
1129Dic3—301no—
1130Dic3—302no—
1131Dic3—301no—
1132Dic3—301no—
1133Dic3—601no—
1134Dic3C2×D3×AGL(1,𝔽5)11yescharacteristic
1135Dic3C2×D3×AGL(1,𝔽5)11yescharacteristic
1136Dic3C2×D3×AGL(1,𝔽5)11yescharacteristic
1137C2×C5—21no—
1138C2×C5—61no—
1139C2×C5—181no—
1140C2×C5C2×C4×D3211yescharacteristic
1141D5—21no—
1142D5—61no—
1143D5—181no—
1144D5D3×#23711yescharacteristic
1145D5#6431211yescharacteristic
1146C32#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
1147C23—51no—
1148C23—151no—
1149C23—451no—
1150Q8—91no—
1151Q8—451no—
1152Q8—451no—
1153Q8—451no—
1154D4—31no—
1155D4—91no—
1156D4—91no—
1157D4—151no—
1158D4—151no—
1159D4—151no—
1160D4—451no—
1161D4—451no—
1162D4—451no—
1163D4—451no—
1164D4—451no—
1165D4—451no—
1166C2×C4—31no—
1167C2×C4—51no—
1168C2×C4—51no—
1169C2×C4—91no—
1170C2×C4—91no—
1171C2×C4—151no—
1172C2×C4—151no—
1173C2×C4—151no—
1174C2×C4—151no—
1175C2×C4—151no—
1176C2×C4—151no—
1177C2×C4—151no—
1178C2×C4—151no—
1179C2×C4—151no—
1180C2×C4—151no—
1181C2×C4—302no—
1182C2×C4—302no—
1183C2×C4—451no—
1184C2×C4—451no—
1185C2×C4—451no—
1186C2×C4—451no—
1187C2×C4—451no—
1188C2×C4—451no—
1189C2×C4—451no—
1190C2×C4—451no—
1191C2×C4—451no—
1192C2×C4—902no—
1193C2×C4—902no—
1194C2×C4—902no—
1195C2×C4—902no—
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—41no—
1200C2×C3—51no—
1201C2×C3—51no—
1202C2×C3—51no—
1203C2×C3—51no—
1204C2×C3—61no—
1205C2×C3—101no—
1206C2×C3—101no—
1207C2×C3—101no—
1208C2×C3—101no—
1209C2×C3—201no—
1210C2×C3—301no—
1211C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
1212C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
1213D3—21no—
1214D3—61no—
1215D3—61no—
1216D3—101no—
1217D3—121no—
1218D3—301no—
1219D3—301no—
1220D3—601no—
1221C5#1059404811yescharacteristic, complemented, Sylow
1222C22—31no—
1223C22—51no—
1224C22—51no—
1225C22—91no—
1226C22—101no—
1227C22—101no—
1228C22—151no—
1229C22—301no—
1230C22—301no—
1231C22—451no—
1232C22—901no—
1233C22—901no—
1234C22D32×AGL(1,𝔽5)11yescharacteristic
1235C4—31no—
1236C4—31no—
1237C4—31no—
1238C4—91no—
1239C4—101no—
1240C4—101no—
1241C4—152no—
1242C4—151no—
1243C4—151no—
1244C4—151no—
1245C4—301no—
1246C4—301no—
1247C4—301no—
1248C4—452no—
1249C4—451no—
1250C4—901no—
1251C3—21no—
1252C3#1175683511yescharacteristic, complemented
1253C3AGL(1,𝔽5)×#23711yescharacteristic, complemented
1254C2—21no—
1255C2—51no—
1256C2—51no—
1257C2—61no—
1258C2—101no—
1259C2—181no—
1260C2—301no—
1261C2—901no—
1262C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC22×C32×C5C22×C4
prime radicalD5×#3804C2
cosocleC2×C32×D5C24
hypercenterC22D32×AGL(1,𝔽5)
hypocenterC32×C5C4×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #13088745C2semidirect
3. #67⋊ΓL(1,𝔽16)C2semidirect
4. C2×Dic3×ΓL(1,𝔽16)C2semidirect
5. #13088690C2semidirect
6. C3×#67⋊AGL(1,𝔽5)C2semidirect
7. C3×#91923C2semidirect
8. #13088420C2semidirect
9. #13088419C2semidirect
10. #13088417C2semidirect
11. #13088414C2semidirect
12. #13088409C2semidirect
13. #13088408C2semidirect
14. AGL(1,𝔽5)×#624C2semidirect
15. D3×Dic3×AGL(1,𝔽5)C2semidirect
24. #10624230C4semidirect
25. #10624210C4semidirect
26. #10624207C4semidirect
27. C5×#3804C4semidirect
33. #10624044C4semidirect
34. #10624043C4semidirect
35. #10624042C4semidirect
36. #10624041C4semidirect
74. #67⋊AGL(1,𝔽5)D3semidirect
78. #91923D3semidirect
110. #67184C2×C4semidirect
111. C5×#638C2×C4semidirect
112. C3×#1220C2×C4semidirect
113. C2×C3×Dic15C2×C4semidirect
114. C3×C5×#67C2×C4semidirect
115. C2×C3×C5×Dic3C2×C4semidirect
116. #67158C2×C4semidirect
117. #67156C2×C4semidirect
118. #67155C2×C4semidirect
119. #67154C2×C4semidirect
120. #67153C2×C4semidirect
121. #67153C2×C4semidirect
122. #67152C2×C4semidirect
123. #67151C2×C4semidirect
124. #67149C2×C4semidirect
125. #67149C2×C4semidirect
126. D3×Dic15C2×C4semidirect
127. Dic3×D15C2×C4semidirect
128. C5×#627C2×C4semidirect
129. C5×#626C2×C4semidirect
130. C5×#624C2×C4semidirect
131. C5×D3×Dic3C2×C4semidirect
132. #67139C2×C4semidirect
133. #67138C2×C4semidirect
135. C3×#1202C2×C4semidirect
136. C3×#1201C2×C4semidirect
137. C3×D5×Dic3C2×C4semidirect
138. C3×D5×Dic3C2×C4semidirect
267. C3⋊ΓL(1,𝔽16)#41semidirect
271. C3×ΓL(1,𝔽16)#41semidirect
315. #3804AGL(1,𝔽5)semidirect
388. #1220C4×D3semidirect
390. C2×Dic15C4×D3semidirect
401. C5×#67C4×D3semidirect
403. C2×C5×Dic3C4×D3semidirect
429. #1202C4×D3semidirect
434. #1201C4×D3semidirect
446. D5×Dic3C4×D3semidirect
447. D5×Dic3C4×D3semidirect
542. #638C2×AGL(1,𝔽5)semidirect
551. C3×#67C2×AGL(1,𝔽5)semidirect
563. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
568. #627C2×AGL(1,𝔽5)semidirect
572. #626C2×AGL(1,𝔽5)semidirect
577. #624C2×AGL(1,𝔽5)semidirect
582. D3×Dic3C2×AGL(1,𝔽5)semidirect
628. ΓL(1,𝔽16)#237semidirect
750. C32×C5C4×#41semidirect
919. #67D3×AGL(1,𝔽5)semidirect
948. C2×Dic3D3×AGL(1,𝔽5)semidirect
1062. C3×C5#5522semidirect
1063. C3×C5C4×#237semidirect
1146. C32#41×AGL(1,𝔽5)semidirect
1221. C5#10594048semidirect
1252. C3#11756835semidirect
1253. C3AGL(1,𝔽5)×#237semidirect

Maximal subgroups

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

subgroupindex
D5×#38042
#130887452
#67⋊ΓL(1,𝔽16)2
C2×Dic3×ΓL(1,𝔽16)2
#130886902
C3×#67⋊AGL(1,𝔽5)2
C3×#919232
#130884202
#130884192
#130884172
#130884142
#130884092
#130884082
AGL(1,𝔽5)×#6242
D3×Dic3×AGL(1,𝔽5)2
AGL(1,𝔽5)×#2373
#117568353
#105940485