Finite Group Databasebeta

← #72260215

Subgroups — #72260215

Order 5760.

9042 conjugacy classes of subgroups.

The subgroup lattice has 1690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72230301C212yesmaximal, complemented
2#72230290C212yesmaximal, complemented
3#72230282C218yesmaximal, complemented
4D4×ΓL(1,𝔽16)⋊D3C218yesmaximal, complemented
5#72230108C214yesmaximal, complemented
6C3×#11756987C212yesmaximal, complemented
7C2×#13088746C214yesmaximal, complemented
8C2×D4×D5×C3⋊D3C211yesmaximal, characteristic
9D3×#66258—32nomaximal
10C23×D5×C3⋊D3C2212yes—
11C22×ΓL(1,𝔽16)⋊D3C2218yescomplemented
12C2×D4×C3⋊D15C411yescharacteristic, complemented
13C2×C5×D4×C3⋊D3C411yescharacteristic, complemented
14C2×C32×D4×D5C2211yescharacteristic
15C2×#10624173C412yescomplemented
16C2×C3⋊D3×C22⋊D5C412yescomplemented
17C2×D5×#638C2212yes—
18D4×D5×C3⋊D3C414yescomplemented
19D4×D5×C3⋊D3C414yescomplemented
20D4×D5×C3⋊D3C2214yes—
21D4×D5×C3⋊D3C2214yes—
22C2×#10624160C411yescharacteristic, complemented
23C2×C3⋊D3×D20C411yescharacteristic, complemented
24C2×D5×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C4×D5×C3⋊D3C2211yescharacteristic
26C2×C3×#6763C2218yescomplemented
27C3×D4×ΓL(1,𝔽16)C22116yescomplemented
28C3×#91989C2214yescomplemented
29#13088746C2214yes—
30#13088746C2218yescomplemented
31#13088746C2218yescomplemented
32#13088746C2218yescomplemented
33#13088745C22132yescomplemented
34C2×#10623978C2218yescomplemented
35#13088735C2214yescomplemented
36#13088733C2214yescomplemented
37#13088732C22116yescomplemented
38C4×ΓL(1,𝔽16)⋊D3C2214yescomplemented
39#13088724C2214yescomplemented
40#13088723C2214yescomplemented
41#11900012—51nomaximal, Hall
42C2×D3×D4×D5—32no—
43C2×D3×D4×D5—61no—
44#11756987D312yescomplemented
45C3×#66258—32no—
46#11756871—38no—
47C2×D3×C22⋊AGL(1,𝔽5)—38no—
48#11756845—316no—
49D3×D4×AGL(1,𝔽5)—316no—
50#11756837—34no—
51D3×#4130—34no—
52C23×C3⋊D15C2×C412yescomplemented
53C23×C5×C3⋊D3C2×C412yescomplemented
54C23×C32×D5C2312yes—
55C22×D5×C3⋊D3—48no—
56C22×D5×C3⋊D3C2×C412yescomplemented
57C22×D5×C3⋊D3C2×C414yescomplemented
58C22×D5×C3⋊D3C2×C412yescomplemented
59C22×D5×C3⋊D3C2×C414yescomplemented
60C22×D5×C3⋊D3C2314yes—
61C22×D5×C3⋊D3C2311yescharacteristic
62C22×D5×C3⋊D3C2312yes—
63C22×D5×C3⋊D3C2314yes—
64C22×C3×ΓL(1,𝔽16)C23116yescomplemented
65C2×ΓL(1,𝔽16)⋊D3—416no—
66C2×ΓL(1,𝔽16)⋊D3C2318yes—
67C2×ΓL(1,𝔽16)⋊D3C23116yescomplemented
68C2×C32×C5×D4C2×C411yescharacteristic, complemented
69C2×#67184C2×C412yescomplemented
70D4×C3⋊D15C2×C414yescomplemented
71D4×C3⋊D15C2×C414yescomplemented
72C2×C4⋊(C3⋊D15)C2×C411yescharacteristic, complemented
73C2×C4×C3⋊D15C2×C411yescharacteristic, complemented
74C2×C5×#638C2×C412yescomplemented
75C5×D4×C3⋊D3C2×C414yescomplemented
76C5×D4×C3⋊D3C2×C414yescomplemented
77C2×C5×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
78C2×C4×C5×C3⋊D3C2×C411yescharacteristic, complemented
79C2×C32×C22⋊D5C2×C412yescomplemented
80C32×D4×D5C2×C414yescomplemented
81C32×D4×D5C2314yes—
82C2×C32×D20C2×C411yescharacteristic, complemented
83C2×C32×C4×D5C2311yescharacteristic
84#10624173C2×C418yescomplemented
85#10624173C2×C418yescomplemented
86C3⋊D3×C22⋊D5C2×C418yescomplemented
87C3⋊D3×C22⋊D5C2×C418yescomplemented
88D5×#638C2×C418yescomplemented
89D5×#638C2318yes—
90C2×#67140C2×C412yescomplemented
91C2×#67139C2×C412yescomplemented
92C2×#67138C2×C412yescomplemented
93C2×#67137C2×C411yescharacteristic, complemented
94C2×C3⋊D3×Dic5C2×C411yescharacteristic, complemented
95C2×D5×C3⋊Dic3C2311yescharacteristic
96#10624160C2×C414yescomplemented
97#10624160C2×C414yescomplemented
98C3⋊D3×D20C2×C414yescomplemented
99C3⋊D3×D20C2×C414yescomplemented
100D5×C4⋊(C3⋊D3)C2×C414yescomplemented
101D5×C4⋊(C3⋊D3)C2314yes—
102C4×D5×C3⋊D3C2×C412yescomplemented
103C4×D5×C3⋊D3C2×C412yescomplemented
104C4×D5×C3⋊D3C2312yes—
105C4×D5×C3⋊D3C2312yes—
106C3×#6763C2318yes—
107C3×#6763C23116yescomplemented
108C3×C4⋊ΓL(1,𝔽16)C2318yescomplemented
109C3×C4×ΓL(1,𝔽16)C2318yescomplemented
110#10623979C2318yescomplemented
111#10623978C2318yes—
112#10623978C23116yescomplemented
113ΓL(1,𝔽16)⋊Dic3C2318yescomplemented
114C2×#66258—91noHall
115C22×D4×C3⋊D3—51no—
116C3×#5798—52no—
117#10595510—54no—
118C2×#63974—54no—
119#10595223—58no—
120D4×#624—58no—
121#10594996—52no—
122#10594969—52no—
123C23×D3×D5—34no—
124C23×D3×D5—62no—
125C22×D3×AGL(1,𝔽5)—316no—
126C2×D4×D15—32no—
127C2×D4×D15—61no—
128C2×C5×D3×D4—32no—
129C2×C5×D3×D4—61no—
130C2×C3×D4×D5—21no—
131C2×C3×D4×D5C2×D312yes—
132C2×#6790—34no—
133C2×#6790—62no—
134C2×D3×C22⋊D5—34no—
135C2×D3×C22⋊D5—62no—
136C2×D5×#67—34no—
137C2×D5×#67—62no—
138D3×D4×D5—38no—
139D3×D4×D5—38no—
140D3×D4×D5—38no—
141D3×D4×D5—38no—
142D3×D4×D5—64no—
143D3×D4×D5—64no—
144D3×D4×D5—64no—
145D3×D4×D5—64no—
146C2×#6777—32no—
147C2×#6777—61no—
148C2×D3×D20—32no—
149C2×D3×D20—61no—
150C2×D5×D12—32no—
151C2×D5×D12—61no—
152C2×C4×D3×D5—32no—
153C2×C4×D3×D5—61no—
154C2×#6763C2×D318yescomplemented
155D4×ΓL(1,𝔽16)C2×D3116yescomplemented
156#91989C2×D314yescomplemented
157C2×C3×C22⋊AGL(1,𝔽5)—38no—
158C3×D4×AGL(1,𝔽5)—316no—
159C3×#4130—34no—
160#67⋊AGL(1,𝔽5)—332no—
161D3×C22⋊AGL(1,𝔽5)—38no—
162D3×C22⋊AGL(1,𝔽5)—316no—
163D3×C22⋊AGL(1,𝔽5)—316no—
164D3×C22⋊AGL(1,𝔽5)—316no—
165AGL(1,𝔽5)×#67—332no—
166C2×(C2×D3)⋊AGL(1,𝔽5)—316no—
167#91923—38no—
168#91921—316no—
169D3×C4⋊AGL(1,𝔽5)—38no—
170AGL(1,𝔽5)×D12—316no—
171C4×D3×AGL(1,𝔽5)—38no—
172#91909—38no—
173#91907—38no—
174D3×#518—152no—
175C23×C32×C5C22×C412yescomplemented
176C22×C3⋊D15—44no—
177C22×C3⋊D15C22×C411yescharacteristic
178C22×C3⋊D15C22×C414yes—
179C22×C3⋊D15C22×C412yescomplemented
180C22×C3⋊D15C22×C414yescomplemented
181C22×C5×C3⋊D3—44no—
182C22×C5×C3⋊D3C22×C411yescharacteristic
183C22×C5×C3⋊D3C22×C414yes—
184C22×C5×C3⋊D3C22×C412yescomplemented
185C22×C5×C3⋊D3C22×C414yescomplemented
186C22×C32×D5—44no—
187C22×C32×D5C22×C412yescomplemented
188C22×C32×D5C22×C414yescomplemented
189C22×C32×D5C2411yescharacteristic
190C22×C32×D5C2414yes—
191C2×D5×C3⋊D3—24no—
192C2×D5×C3⋊D3—216no—
193C2×D5×C3⋊D3—48no—
194C2×D5×C3⋊D3—44no—
195C2×D5×C3⋊D3—48no—
196C2×D5×C3⋊D3—44no—
197C2×D5×C3⋊D3—48no—
198C2×D5×C3⋊D3—44no—
199C2×D5×C3⋊D3C22×C411yescharacteristic
200C2×D5×C3⋊D3C22×C411yescharacteristic
201C2×D5×C3⋊D3C22×C414yes—
202C2×D5×C3⋊D3C22×C414yes—
203C2×D5×C3⋊D3C22×C414yescomplemented
204C2×D5×C3⋊D3C22×C414yescomplemented
205C2×D5×C3⋊D3C22×C414yescomplemented
206C2×D5×C3⋊D3C2414yes—
207C2×D5×C3⋊D3C2411yescharacteristic
208C2×D5×C3⋊D3C2411yescharacteristic
209C2×C3×ΓL(1,𝔽16)—416no—
210C2×C3×ΓL(1,𝔽16)C24116yes—
211ΓL(1,𝔽16)⋊D3—216no—
212ΓL(1,𝔽16)⋊D3—416no—
213C32×C5×D4C22×C414yescomplemented
214C2×C32×C4×C5C22×C411yescharacteristic, complemented
215#67184C22×C418yescomplemented
216C2×C3⋊Dic15C22×C411yescharacteristic, complemented
217C4⋊(C3⋊D15)C22×C414yescomplemented
218C4×C3⋊D15C22×C412yes—
219C4×C3⋊D15C22×C412yescomplemented
220C5×#638C22×C418yescomplemented
221C2×C5×C3⋊Dic3C22×C411yescharacteristic, complemented
222C5×C4⋊(C3⋊D3)C22×C414yescomplemented
223C4×C5×C3⋊D3C22×C412yes—
224C4×C5×C3⋊D3C22×C412yescomplemented
225C32×C22⋊D5C22×C418yescomplemented
226C2×C32×Dic5C22×C411yescharacteristic, complemented
227C32×D20C22×C414yescomplemented
228C32×C4×D5C22×C412yescomplemented
229C32×C4×D5C2412yes—
230#67140C22×C418yescomplemented
231#67139C22×C418yescomplemented
232#67138C22×C418yescomplemented
233#67137C22×C412yes—
234#67137C22×C412yescomplemented
235C3⋊D3×Dic5C22×C412yes—
236C3⋊D3×Dic5C22×C412yescomplemented
237D5×C3⋊Dic3C22×C412yescomplemented
238D5×C3⋊Dic3C2412yes—
239C22×D4×D5—91no—
240C22×C22⋊AGL(1,𝔽5)—94no—
241#66258—32no—
242#66258—92no—
243#66258—98no—
244#66258—94no—
245C2×D4×AGL(1,𝔽5)—98no—
246C2×#4130—92no—
247C24×C3⋊D3—52no—
248C22×C32×D4—51no—
249C22×#638—52no—
250C2×D4×C3⋊D3—51no—
251C2×D4×C3⋊D3—52no—
252C2×D4×C3⋊D3—54no—
253C2×D4×C3⋊D3—54no—
254C2×D4×C3⋊D3—54no—
255C2×D4×C3⋊D3—54no—
256C2×D4×C3⋊D3—51no—
257C2×D4×C3⋊D3—51no—
258C2×D4×C3⋊D3—52no—
259C2×D4×C3⋊D3AGL(1,𝔽5)11yescharacteristic, complemented
260C22×C4⋊(C3⋊D3)—51no—
261C22×C4×C3⋊D3—51no—
262C22×#624—58no—
263C2×C3×#217—58no—
264C3×D4×Dic3—516no—
265C3×#926—54no—
266#63974—58no—
267#63974—58no—
268#63974—54no—
269#63974—58no—
270C2×#3722—58no—
271#63957—54no—
272#63952—532no—
273#63900—54no—
274#63894—516no—
275C4×#624—54no—
276#63874—54no—
277#63849—54no—
278C23×D15—34no—
279C23×D15—62no—
280C23×C5×D3—34no—
281C23×C5×D3—62no—
282C23×C3×D5—22no—
283C23×C3×D5C22×D314yes—
284C22×D3×D5—32no—
285C22×D3×D5—38no—
286C22×D3×D5—34no—
287C22×D3×D5—34no—
288C22×D3×D5—38no—
289C22×D3×D5—38no—
290C22×D3×D5—38no—
291C22×D3×D5—34no—
292C22×D3×D5—61no—
293C22×D3×D5—62no—
294C22×D3×D5—62no—
295C22×D3×D5—64no—
296C22×D3×D5—64no—
297C22×D3×D5—62no—
298C22×D3×D5—64no—
299C22×D3×D5—64no—
300C22×D3×D5—1216no—
301C22×D3×D5—1216no—
302C22×ΓL(1,𝔽16)C22×D3116yescomplemented
303C22×C3×AGL(1,𝔽5)—316no—
304C2×D3×AGL(1,𝔽5)—316no—
305C2×D3×AGL(1,𝔽5)—332no—
306C2×D3×AGL(1,𝔽5)—1232no—
307C2×C3×C5×D4—21no—
308C2×C3×C5×D4C4×D312yescomplemented
309C2×#1220—34no—
310C2×#1220—62no—
311D4×D15—38no—
312D4×D15—38no—
313D4×D15—64no—
314D4×D15—64no—
315C2×D60—32no—
316C2×D60—61no—
317C2×C4×D15—32no—
318C2×C4×D15—61no—
319C2×C5×#67—34no—
320C2×C5×#67—62no—
321C5×D3×D4—38no—
322C5×D3×D4—38no—
323C5×D3×D4—64no—
324C5×D3×D4—64no—
325C2×C5×D12—32no—
326C2×C5×D12—61no—
327C2×C4×C5×D3—32no—
328C2×C4×C5×D3—61no—
329C2×C3×C22⋊D5—22no—
330C2×C3×C22⋊D5C4×D314yescomplemented
331C3×D4×D5—24no—
332C3×D4×D5—24no—
333C3×D4×D5C4×D318yescomplemented
334C3×D4×D5C22×D318yes—
335C2×C3×D20—21no—
336C2×C3×D20C4×D312yescomplemented
337C2×C3×C4×D5—21no—
338C2×C3×C4×D5C22×D312yes—
339#6790—316no—
340#6790—316no—
341#6790—68no—
342#6790—68no—
343D3×C22⋊D5—316no—
344D3×C22⋊D5—316no—
345D3×C22⋊D5—68no—
346D3×C22⋊D5—68no—
347D5×#67—316no—
348D5×#67—316no—
349D5×#67—68no—
350D5×#67—68no—
351C2×#1203—34no—
352C2×#1203—62no—
353C2×#1202—34no—
354C2×#1202—62no—
355C2×#1201—34no—
356C2×#1201—62no—
357C2×#1200—32no—
358C2×#1200—61no—
359C2×D3×Dic5—32no—
360C2×D3×Dic5—61no—
361C2×D5×Dic3—32no—
362C2×D5×Dic3—61no—
363#6777—38no—
364#6777—38no—
365#6777—64no—
366#6777—64no—
367D3×D20—38no—
368D3×D20—38no—
369D3×D20—64no—
370D3×D20—64no—
371D5×D12—38no—
372D5×D12—38no—
373D5×D12—64no—
374D5×D12—64no—
375C4×D3×D5—34no—
376C4×D3×D5—34no—
377C4×D3×D5—34no—
378C4×D3×D5—34no—
379C4×D3×D5—62no—
380C4×D3×D5—62no—
381C4×D3×D5—62no—
382C4×D3×D5—62no—
383#6763C22×D318yes—
384#6763C22×D3116yescomplemented
385C4⋊ΓL(1,𝔽16)C22×D318yescomplemented
386C4×ΓL(1,𝔽16)C22×D318yescomplemented
387C3×C22⋊AGL(1,𝔽5)—38no—
388C3×C22⋊AGL(1,𝔽5)—316no—
389C3×C4⋊AGL(1,𝔽5)—38no—
390C3×C4×AGL(1,𝔽5)—38no—
391Dic3⋊AGL(1,𝔽5)—316no—
392(C2×D3)⋊AGL(1,𝔽5)—316no—
393(C2×D3)⋊AGL(1,𝔽5)—332no—
394Dic3×AGL(1,𝔽5)—316no—
395C22×D3×D4—152no—
396C22×D3×D4—301no—
397C3×#518—152no—
398#5798—52no—
399#5545—1516no—
400C4×D3×D4—1516no—
401#5521—154no—
402D3×#117—154no—
403#5486—158no—
404C2×D3×C22⋊C4—158no—
405C22×C32×C5—42no—
406C22×C32×C5C23×C411yescharacteristic
407C22×C32×C5C23×C414yes—
408C2×C3⋊D15—22no—
409C2×C3⋊D15—28no—
410C2×C3⋊D15—44no—
411C2×C3⋊D15—42no—
412C2×C3⋊D15C23×C411yescharacteristic
413C2×C3⋊D15C23×C414yes—
414C2×C3⋊D15C23×C411yescharacteristic
415C2×C5×C3⋊D3—22no—
416C2×C5×C3⋊D3—28no—
417C2×C5×C3⋊D3—44no—
418C2×C5×C3⋊D3—42no—
419C2×C5×C3⋊D3C23×C411yescharacteristic
420C2×C5×C3⋊D3C23×C414yes—
421C2×C5×C3⋊D3C23×C411yescharacteristic
422C2×C32×D5—22no—
423C2×C32×D5—28no—
424C2×C32×D5—44no—
425C2×C32×D5—42no—
426C2×C32×D5C23×C411yescharacteristic
427C2×C32×D5C23×C414yes—
428C2×C32×D5C2511yescharacteristic
429D5×C3⋊D3—22no—
430D5×C3⋊D3—28no—
431D5×C3⋊D3—22no—
432D5×C3⋊D3—28no—
433D5×C3⋊D3—22no—
434D5×C3⋊D3—28no—
435D5×C3⋊D3—44no—
436D5×C3⋊D3—44no—
437D5×C3⋊D3—44no—
438D5×C3⋊D3H(5,𝔽2)14yes—
439C3×ΓL(1,𝔽16)—216no—
440C32×C4×C5C23×C412yes—
441C3⋊Dic15C23×C412yes—
442C5×C3⋊Dic3C23×C412yes—
443C32×Dic5C23×C412yes—
444C24×D5—92no—
445C23×AGL(1,𝔽5)—98no—
446C22×C5×D4—91no—
447C22×C22⋊D5—92no—
448C2×D4×D5—92no—
449C2×D4×D5—91no—
450C2×D4×D5—92no—
451C2×D4×D5—94no—
452C2×D4×D5—94no—
453C2×D4×D5—94no—
454C2×D4×D5—94no—
455C2×D4×D5—91no—
456C2×D4×D5—91no—
457C2×D4×D5D3211yescharacteristic
458C22×D20—91no—
459C22×C4×D5—91no—
460C2×C22⋊AGL(1,𝔽5)—38no—
461C2×C22⋊AGL(1,𝔽5)—94no—
462C2×C22⋊AGL(1,𝔽5)—98no—
463C2×C22⋊AGL(1,𝔽5)—98no—
464C2×C22⋊AGL(1,𝔽5)—98no—
465C2×C22⋊AGL(1,𝔽5)—98no—
466D4×AGL(1,𝔽5)—316no—
467D4×AGL(1,𝔽5)—916no—
468D4×AGL(1,𝔽5)—932no—
469#4130—34no—
470#4130—94no—
471#4130—94no—
472#4130—94no—
473C2×C4⋊AGL(1,𝔽5)—94no—
474C2×C4×AGL(1,𝔽5)—94no—
475C24×C32—52no—
476C23×C3⋊D3—52no—
477C23×C3⋊D3—54no—
478C23×C3⋊D3—51no—
479C23×C3⋊D3—52no—
480C23×C3⋊D3—54no—
481C23×C3⋊D3—52no—
482C23×C3⋊D3—52no—
483C23×C3⋊D3—54no—
484C23×C3⋊D3—54no—
485C23×C3⋊D3—208no—
486C23×C3⋊D3C2×AGL(1,𝔽5)12yescomplemented
487C2×C32×D4—52no—
488C2×C32×D4—54no—
489C2×C32×D4—54no—
490C2×C32×D4—51no—
491C2×C32×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
492C22×C32×C4—51no—
493C2×#638—52no—
494C2×#638—52no—
495C2×#638—58no—
496C2×#638—58no—
497C2×#638—52no—
498C2×#638C2×AGL(1,𝔽5)12yescomplemented
499C22×C3⋊Dic3—51no—
500D4×C3⋊D3—58no—
501D4×C3⋊D3—58no—
502D4×C3⋊D3—54no—
503D4×C3⋊D3—54no—
504D4×C3⋊D3—58no—
505D4×C3⋊D3—58no—
506D4×C3⋊D3—54no—
507D4×C3⋊D3—54no—
508D4×C3⋊D3—54no—
509D4×C3⋊D3—54no—
510D4×C3⋊D3C2×AGL(1,𝔽5)14yescomplemented
511D4×C3⋊D3C2×AGL(1,𝔽5)14yescomplemented
512C2×C4⋊(C3⋊D3)—52no—
513C2×C4⋊(C3⋊D3)—51no—
514C2×C4⋊(C3⋊D3)—54no—
515C2×C4⋊(C3⋊D3)—54no—
516C2×C4⋊(C3⋊D3)C2×AGL(1,𝔽5)11yescharacteristic, complemented
517C2×C4×C3⋊D3—51no—
518C2×C4×C3⋊D3—51no—
519C2×C4×C3⋊D3—51no—
520C2×C4×C3⋊D3—52no—
521C2×C4×C3⋊D3—52no—
522C2×C4×C3⋊D3—52no—
523C2×C4×C3⋊D3—52no—
524C2×C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
525C22×C3×Dic3—516no—
526C2×#624—58no—
527C2×#624—516no—
528C2×#624—2016no—
529C3×#217—58no—
530C3×#217—516no—
531C3×C4⋊Dic3—58no—
532C3×C4×Dic3—58no—
533#3724—58no—
534#3722—58no—
535#3722—516no—
536Dic32—58no—
537C2×#518—451noSylow
538C23×C3×C5—22no—
539C23×C3×C5C2×C4×D314yescomplemented
540C22×D15—32no—
541C22×D15—38no—
542C22×D15—34no—
543C22×D15—38no—
544C22×D15—61no—
545C22×D15—62no—
546C22×D15—64no—
547C22×D15—64no—
548C22×D15—128no—
549C22×D15—128no—
550C22×C5×D3—32no—
551C22×C5×D3—38no—
552C22×C5×D3—34no—
553C22×C5×D3—38no—
554C22×C5×D3—61no—
555C22×C5×D3—62no—
556C22×C5×D3—64no—
557C22×C5×D3—64no—
558C22×C5×D3—128no—
559C22×C5×D3—128no—
560C22×C3×D5—21no—
561C22×C3×D5—24no—
562C22×C3×D5—22no—
563C22×C3×D5—24no—
564C22×C3×D5—48no—
565C22×C3×D5—48no—
566C22×C3×D5C2×C4×D314yescomplemented
567C22×C3×D5C2×C4×D318yescomplemented
568C22×C3×D5C23×D312yes—
569C22×C3×D5C23×D318yes—
570C2×D3×D5—32no—
571C2×D3×D5—32no—
572C2×D3×D5—32no—
573C2×D3×D5—38no—
574C2×D3×D5—38no—
575C2×D3×D5—32no—
576C2×D3×D5—38no—
577C2×D3×D5—38no—
578C2×D3×D5—38no—
579C2×D3×D5—38no—
580C2×D3×D5—632no—
581C2×D3×D5—68no—
582C2×D3×D5—61no—
583C2×D3×D5—61no—
584C2×D3×D5—61no—
585C2×D3×D5—61no—
586C2×D3×D5—68no—
587C2×D3×D5—64no—
588C2×D3×D5—64no—
589C2×D3×D5—64no—
590C2×D3×D5—64no—
591C2×D3×D5—64no—
592C2×D3×D5—64no—
593C2×D3×D5—128no—
594C2×D3×D5—1216no—
595C2×D3×D5—128no—
596C2×D3×D5—1216no—
597C2×D3×D5—128no—
598C2×D3×D5—1216no—
599C2×D3×D5—1216no—
600C2×D3×D5—1216no—
601C2×D3×D5—1216no—
602C2×D3×D5—1216no—
603C2×D3×D5—128no—
604C2×D3×D5—128no—
605C2×D3×D5—128no—
606C2×ΓL(1,𝔽16)—416no—
607C2×ΓL(1,𝔽16)C23×D3116yes—
608C2×C3×AGL(1,𝔽5)—316no—
609C2×C3×AGL(1,𝔽5)—1216no—
610D3×AGL(1,𝔽5)—632no—
611D3×AGL(1,𝔽5)—1232no—
612C3×C5×D4—24no—
613C3×C5×D4C2×C4×D318yescomplemented
614C2×C3×C4×C5—21no—
615C2×C3×C4×C5C2×C4×D312yescomplemented
616#1220—316no—
617#1220—68no—
618C2×Dic15—32no—
619C2×Dic15—61no—
620D60—38no—
621D60—64no—
622C4×D15—34no—
623C4×D15—34no—
624C4×D15—62no—
625C4×D15—62no—
626C5×#67—316no—
627C5×#67—68no—
628C2×C5×Dic3—32no—
629C2×C5×Dic3—61no—
630C5×D12—38no—
631C5×D12—64no—
632C4×C5×D3—34no—
633C4×C5×D3—34no—
634C4×C5×D3—62no—
635C4×C5×D3—62no—
636C3×C22⋊D5—28no—
637C3×C22⋊D5C2×C4×D3116yescomplemented
638C2×C3×Dic5—21no—
639C2×C3×Dic5C2×C4×D312yescomplemented
640C3×D20—24no—
641C3×D20C2×C4×D318yescomplemented
642C3×C4×D5—22no—
643C3×C4×D5—22no—
644C3×C4×D5C2×C4×D314yescomplemented
645C3×C4×D5C23×D314yes—
646#1203—316no—
647#1203—68no—
648#1202—316no—
649#1202—68no—
650#1201—316no—
651#1201—68no—
652#1200—34no—
653#1200—34no—
654#1200—62no—
655#1200—62no—
656D3×Dic5—34no—
657D3×Dic5—34no—
658D3×Dic5—62no—
659D3×Dic5—62no—
660D5×Dic3—34no—
661D5×Dic3—34no—
662D5×Dic3—62no—
663D5×Dic3—62no—
664C24×D3—154no—
665C24×D3—302no—
666C22×C3×D4—52no—
667C22×C3×D4—101no—
668C22×#67—154no—
669C22×#67—302no—
670C2×D3×D4—32no—
671C2×D3×D4—61no—
672C2×D3×D4—152no—
673C2×D3×D4—152no—
674C2×D3×D4—158no—
675C2×D3×D4—158no—
676C2×D3×D4—158no—
677C2×D3×D4—158no—
678C2×D3×D4—154no—
679C2×D3×D4—154no—
680C2×D3×D4—152no—
681C2×D3×D4—301no—
682C2×D3×D4—301no—
683C2×D3×D4—304no—
684C2×D3×D4—304no—
685C2×D3×D4—304no—
686C2×D3×D4—304no—
687C2×D3×D4—302no—
688C2×D3×D4—301no—
689C2×D3×D4—302no—
690C22×D12—152no—
691C22×D12—301no—
692C22×C4×D3—152no—
693C22×C4×D3—1516no—
694C22×C4×D3—301no—
695C3×C4×D4—1516no—
696C3×#117—154no—
697C2×C3×C22⋊C4—158no—
698C2×#217—58no—
699D4×Dic3—516no—
700C4×#67—1532no—
701C2×(C2×D3)⋊C4—1516no—
702#926—54no—
703#893—1516no—
704#892—158no—
705D3×C4⋊C4—158no—
706#67⋊C4—1532no—
707D3×C22⋊C4—158no—
708D3×C22⋊C4—1516no—
709D3×C22⋊C4—1516no—
710D3×C22⋊C4—1516no—
711#877—158no—
712C4×D12—1516no—
713#872—158no—
714C42×D3—158no—
715C2×C32×C5—21no—
716C2×C32×C5—24no—
717C2×C32×C5C24×C411yescharacteristic
718C3⋊D15—21no—
719C3⋊D15—24no—
720C3⋊D15#51812yescomplemented
721C5×C3⋊D3—21no—
722C5×C3⋊D3—24no—
723C5×C3⋊D3#51812yescomplemented
724C32×D5—21no—
725C32×D5—24no—
726C32×D5C2×H(5,𝔽2)12yes—
727C24×C5—92no—
728C23×D5—92no—
729C23×D5—91no—
730C23×D5—94no—
731C23×D5—92no—
732C23×D5—94no—
733C23×D5—92no—
734C23×D5—92no—
735C23×D5—94no—
736C23×D5—94no—
737C23×D5—368no—
738C23×D5C2×D3212yes—
739C22×AGL(1,𝔽5)—316no—
740C22×AGL(1,𝔽5)—98no—
741C22×AGL(1,𝔽5)—916no—
742C22×AGL(1,𝔽5)—3616no—
743C2×C5×D4—92no—
744C2×C5×D4—94no—
745C2×C5×D4—94no—
746C2×C5×D4—91no—
747C2×C5×D4#62411yescharacteristic, complemented
748C22×C4×C5—91no—
749C2×C22⋊D5—92no—
750C2×C22⋊D5—92no—
751C2×C22⋊D5—98no—
752C2×C22⋊D5—98no—
753C2×C22⋊D5—92no—
754C2×C22⋊D5#62412yescomplemented
755C22×Dic5—91no—
756D4×D5—98no—
757D4×D5—98no—
758D4×D5—94no—
759D4×D5—94no—
760D4×D5—98no—
761D4×D5—98no—
762D4×D5—94no—
763D4×D5—94no—
764D4×D5—94no—
765D4×D5—94no—
766D4×D5#62414yescomplemented
767D4×D5C2×D3214yes—
768C2×D20—92no—
769C2×D20—91no—
770C2×D20—94no—
771C2×D20—94no—
772C2×D20#62411yescharacteristic, complemented
773C2×C4×D5—91no—
774C2×C4×D5—91no—
775C2×C4×D5—91no—
776C2×C4×D5—92no—
777C2×C4×D5—92no—
778C2×C4×D5—92no—
779C2×C4×D5—92no—
780C2×C4×D5C2×D3211yescharacteristic
781C22⋊AGL(1,𝔽5)—38no—
782C22⋊AGL(1,𝔽5)—316no—
783C22⋊AGL(1,𝔽5)—98no—
784C22⋊AGL(1,𝔽5)—916no—
785C4⋊AGL(1,𝔽5)—38no—
786C4⋊AGL(1,𝔽5)—98no—
787C4×AGL(1,𝔽5)—38no—
788C4×AGL(1,𝔽5)—98no—
789C23×C32—51no—
790C23×C32—54no—
791C23×C32—54no—
792C23×C32—52no—
793C23×C32—204no—
794C23×C32C22×AGL(1,𝔽5)12yescomplemented
795C22×C3⋊D3—44no—
796C22×C3⋊D3—51no—
797C22×C3⋊D3—51no—
798C22×C3⋊D3—54no—
799C22×C3⋊D3—52no—
800C22×C3⋊D3—54no—
801C22×C3⋊D3—51no—
802C22×C3⋊D3—51no—
803C22×C3⋊D3—51no—
804C22×C3⋊D3—54no—
805C22×C3⋊D3—54no—
806C22×C3⋊D3—54no—
807C22×C3⋊D3—54no—
808C22×C3⋊D3—54no—
809C22×C3⋊D3—54no—
810C22×C3⋊D3—104no—
811C22×C3⋊D3—1016no—
812C22×C3⋊D3—204no—
813C22×C3⋊D3—208no—
814C22×C3⋊D3—208no—
815C22×C3⋊D3—204no—
816C22×C3⋊D3—208no—
817C22×C3⋊D3—204no—
818C22×C3⋊D3—204no—
819C22×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
820C22×C3⋊D3C22×AGL(1,𝔽5)14yes—
821C22×C3⋊D3C22×AGL(1,𝔽5)12yescomplemented
822C22×C3⋊D3C22×AGL(1,𝔽5)14yescomplemented
823C32×D4—58no—
824C32×D4—54no—
825C32×D4C22×AGL(1,𝔽5)14yescomplemented
826C2×C32×C4—51no—
827C2×C32×C4—52no—
828C2×C32×C4—52no—
829C2×C32×C4C22×AGL(1,𝔽5)11yescharacteristic, complemented
830#638—58no—
831#638—58no—
832#638—58no—
833#638C22×AGL(1,𝔽5)18yescomplemented
834C2×C3⋊Dic3—51no—
835C2×C3⋊Dic3—52no—
836C2×C3⋊Dic3—52no—
837C2×C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic, complemented
838C4⋊(C3⋊D3)—58no—
839C4⋊(C3⋊D3)—54no—
840C4⋊(C3⋊D3)C22×AGL(1,𝔽5)14yescomplemented
841C4×C3⋊D3—52no—
842C4×C3⋊D3—52no—
843C4×C3⋊D3—52no—
844C4×C3⋊D3—52no—
845C4×C3⋊D3—52no—
846C4×C3⋊D3—52no—
847C4×C3⋊D3C22×AGL(1,𝔽5)12yes—
848C4×C3⋊D3C22×AGL(1,𝔽5)12yescomplemented
849C2×C3×Dic3—516no—
850C2×C3×Dic3—2016no—
851#624—1016no—
852#624—2016no—
853C23×D4—451no—
854#518—152no—
855#518—454no—
856#518—452no—
857#518—458no—
858C2×C4×D4—458no—
859C2×#117—452no—
860C22×C22⋊C4—454no—
861C22×C3×C5—21no—
862C22×C3×C5—24no—
863C22×C3×C5—44no—
864C22×C3×C5—44no—
865C22×C3×C5C22×C4×D312yes—
866C22×C3×C5C22×C4×D318yes—
867C2×D15—32no—
868C2×D15—32no—
869C2×D15—38no—
870C2×D15—61no—
871C2×D15—61no—
872C2×D15—64no—
873C2×D15—64no—
874C2×D15—616no—
875C2×D15—64no—
876C2×D15—128no—
877C2×D15—128no—
878C2×D15—124no—
879C2×D15—128no—
880C2×D15—124no—
881C2×C5×D3—32no—
882C2×C5×D3—32no—
883C2×C5×D3—38no—
884C2×C5×D3—61no—
885C2×C5×D3—61no—
886C2×C5×D3—64no—
887C2×C5×D3—64no—
888C2×C5×D3—616no—
889C2×C5×D3—64no—
890C2×C5×D3—128no—
891C2×C5×D3—128no—
892C2×C5×D3—124no—
893C2×C5×D3—128no—
894C2×C5×D3—124no—
895C2×C3×D5—24no—
896C2×C3×D5—216no—
897C2×C3×D5—24no—
898C2×C3×D5—21no—
899C2×C3×D5—24no—
900C2×C3×D5—21no—
901C2×C3×D5—48no—
902C2×C3×D5—48no—
903C2×C3×D5—44no—
904C2×C3×D5—48no—
905C2×C3×D5—44no—
906C2×C3×D5C22×C4×D312yes—
907C2×C3×D5C22×C4×D318yes—
908C2×C3×D5C24×D312yes—
909D3×D5—38no—
910D3×D5—64no—
911D3×D5—616no—
912D3×D5—64no—
913D3×D5—616no—
914D3×D5—64no—
915D3×D5—64no—
916D3×D5—64no—
917D3×D5—64no—
918D3×D5—616no—
919D3×D5—64no—
920D3×D5—128no—
921D3×D5—128no—
922D3×D5—128no—
923D3×D5—128no—
924D3×D5—128no—
925D3×D5—128no—
926D3×D5—128no—
927D3×D5—128no—
928D3×D5—128no—
929ΓL(1,𝔽16)—216no—
930C3×AGL(1,𝔽5)—616no—
931C3×C4×C5—22no—
932C3×C4×C5C22×C4×D314yes—
933Dic15—34no—
934Dic15—62no—
935C3×Dic5—22no—
936C3×Dic5C22×C4×D314yes—
937C5×Dic3—34no—
938C5×Dic3—62no—
939C24×C3—54no—
940C24×C3—102no—
941C23×D3—34no—
942C23×D3—62no—
943C23×D3—152no—
944C23×D3—158no—
945C23×D3—154no—
946C23×D3—158no—
947C23×D3—154no—
948C23×D3—158no—
949C23×D3—154no—
950C23×D3—158no—
951C23×D3—154no—
952C23×D3—301no—
953C23×D3—302no—
954C23×D3—304no—
955C23×D3—304no—
956C23×D3—302no—
957C23×D3—304no—
958C23×D3—302no—
959C23×D3—304no—
960C23×D3—302no—
961C23×D3—6016no—
962C23×D3—6016no—
963C2×C3×D4—21no—
964C2×C3×D4—54no—
965C2×C3×D4—58no—
966C2×C3×D4—58no—
967C2×C3×D4—52no—
968C2×C3×D4—101no—
969C2×C3×D4—104no—
970C2×C3×D4—104no—
971C2×C3×D4—102no—
972C2×C3×D4D3×AGL(1,𝔽5)12yescomplemented
973C22×C3×C4—52no—
974C22×C3×C4—101no—
975C22×C3×C4—1516no—
976C2×#67—34no—
977C2×#67—62no—
978C2×#67—154no—
979C2×#67—1516no—
980C2×#67—1516no—
981C2×#67—154no—
982C2×#67—154no—
983C2×#67—302no—
984C2×#67—308no—
985C2×#67—308no—
986C2×#67—302no—
987C2×#67—302no—
988C22×Dic3—516no—
989C22×Dic3—152no—
990C22×Dic3—301no—
991D3×D4—38no—
992D3×D4—38no—
993D3×D4—64no—
994D3×D4—64no—
995D3×D4—158no—
996D3×D4—158no—
997D3×D4—158no—
998D3×D4—158no—
999D3×D4—1516no—
1000D3×D4—1516no—
1001D3×D4—1516no—
1002D3×D4—1516no—
1003D3×D4—158no—
1004D3×D4—158no—
1005D3×D4—304no—
1006D3×D4—304no—
1007D3×D4—304no—
1008D3×D4—304no—
1009D3×D4—308no—
1010D3×D4—308no—
1011D3×D4—304no—
1012D3×D4—304no—
1013D3×D4—308no—
1014D3×D4—308no—
1015C2×D12—32no—
1016C2×D12—61no—
1017C2×D12—158no—
1018C2×D12—158no—
1019C2×D12—154no—
1020C2×D12—152no—
1021C2×D12—304no—
1022C2×D12—304no—
1023C2×D12—301no—
1024C2×D12—302no—
1025C2×C4×D3—32no—
1026C2×C4×D3—61no—
1027C2×C4×D3—154no—
1028C2×C4×D3—154no—
1029C2×C4×D3—154no—
1030C2×C4×D3—154no—
1031C2×C4×D3—152no—
1032C2×C4×D3—152no—
1033C2×C4×D3—152no—
1034C2×C4×D3—1516no—
1035C2×C4×D3—1532no—
1036C2×C4×D3—302no—
1037C2×C4×D3—302no—
1038C2×C4×D3—302no—
1039C2×C4×D3—302no—
1040C2×C4×D3—301no—
1041C2×C4×D3—301no—
1042C2×C4×D3—301no—
1043C2×C4×D3—6032no—
1044C3×C4⋊C4—158no—
1045C3×C22⋊C4—158no—
1046C3×C22⋊C4—1516no—
1047C3×C42—158no—
1048#217—58no—
1049#217—516no—
1050(C2×D3)⋊C4—1516no—
1051(C2×D3)⋊C4—1532no—
1052C4⋊Dic3—58no—
1053Dic3⋊C4—1516no—
1054C4×Dic3—58no—
1055C4×Dic3—1516no—
1056C32×C5C2×#51811yescharacteristic, complemented, Hall
1057C23×C5—91no—
1058C23×C5—94no—
1059C23×C5—94no—
1060C23×C5—92no—
1061C23×C5—364no—
1062C23×C5C2×#62412yescomplemented
1063C22×D5—44no—
1064C22×D5—91no—
1065C22×D5—91no—
1066C22×D5—94no—
1067C22×D5—92no—
1068C22×D5—94no—
1069C22×D5—91no—
1070C22×D5—91no—
1071C22×D5—94no—
1072C22×D5—94no—
1073C22×D5—91no—
1074C22×D5—94no—
1075C22×D5—94no—
1076C22×D5—94no—
1077C22×D5—94no—
1078C22×D5—184no—
1079C22×D5—1816no—
1080C22×D5—364no—
1081C22×D5—368no—
1082C22×D5—368no—
1083C22×D5—364no—
1084C22×D5—368no—
1085C22×D5—364no—
1086C22×D5—364no—
1087C22×D5C2×#62412yescomplemented
1088C22×D5C2×#62414yescomplemented
1089C22×D5C22×D3211yescharacteristic
1090C22×D5C22×D3214yes—
1091C2×AGL(1,𝔽5)—316no—
1092C2×AGL(1,𝔽5)—1216no—
1093C2×AGL(1,𝔽5)—1816no—
1094C2×AGL(1,𝔽5)—3616no—
1095C5×D4—98no—
1096C5×D4—94no—
1097C5×D4C2×#62414yescomplemented
1098C2×C4×C5—91no—
1099C2×C4×C5—92no—
1100C2×C4×C5—92no—
1101C2×C4×C5C2×#62411yescharacteristic, complemented
1102C22⋊D5—98no—
1103C22⋊D5—98no—
1104C22⋊D5—98no—
1105C22⋊D5C2×#62418yescomplemented
1106C2×Dic5—91no—
1107C2×Dic5—92no—
1108C2×Dic5—92no—
1109C2×Dic5C2×#62411yescharacteristic, complemented
1110D20—98no—
1111D20—94no—
1112D20C2×#62414yescomplemented
1113C4×D5—92no—
1114C4×D5—92no—
1115C4×D5—92no—
1116C4×D5—92no—
1117C4×D5—92no—
1118C4×D5—92no—
1119C4×D5C2×#62412yescomplemented
1120C4×D5C22×D3212yes—
1121C22×C32—42no—
1122C22×C32—51no—
1123C22×C32—51no—
1124C22×C32—54no—
1125C22×C32—102no—
1126C22×C32—108no—
1127C22×C32—202no—
1128C22×C32—204no—
1129C22×C32C23×AGL(1,𝔽5)11yescharacteristic
1130C22×C32C23×AGL(1,𝔽5)14yes—
1131C2×C3⋊D3—22no—
1132C2×C3⋊D3—28no—
1133C2×C3⋊D3—44no—
1134C2×C3⋊D3—42no—
1135C2×C3⋊D3—51no—
1136C2×C3⋊D3—54no—
1137C2×C3⋊D3—51no—
1138C2×C3⋊D3—54no—
1139C2×C3⋊D3—102no—
1140C2×C3⋊D3—102no—
1141C2×C3⋊D3—102no—
1142C2×C3⋊D3—102no—
1143C2×C3⋊D3—108no—
1144C2×C3⋊D3—108no—
1145C2×C3⋊D3—108no—
1146C2×C3⋊D3—108no—
1147C2×C3⋊D3—204no—
1148C2×C3⋊D3—204no—
1149C2×C3⋊D3—204no—
1150C2×C3⋊D3—204no—
1151C2×C3⋊D3—202no—
1152C2×C3⋊D3C23×AGL(1,𝔽5)11yescharacteristic
1153C2×C3⋊D3C23×AGL(1,𝔽5)14yes—
1154C2×C3⋊D3C23×AGL(1,𝔽5)11yescharacteristic
1155C32×C4—52no—
1156C32×C4C23×AGL(1,𝔽5)12yes—
1157C3⋊Dic3—52no—
1158C3⋊Dic3C23×AGL(1,𝔽5)12yes—
1159C3×Dic3—1016no—
1160C25—452no—
1161C22×D4—51no—
1162C22×D4—91no—
1163C22×D4—451no—
1164C22×D4—451no—
1165C22×D4—454no—
1166C22×D4—454no—
1167C22×D4—452no—
1168C22×D4—454no—
1169C22×D4—454no—
1170C22×D4—451no—
1171C22×D4—452no—
1172C22×D4—452no—
1173C22×D4—451no—
1174C23×C4—451no—
1175C23×C4—458no—
1176C4×D4—1516no—
1177C4×D4—4516no—
1178C4×D4—4532no—
1179#117—154no—
1180#117—454no—
1181#117—454no—
1182#117—454no—
1183C2×C4⋊C4—454no—
1184C2×C22⋊C4—158no—
1185C2×C22⋊C4—454no—
1186C2×C22⋊C4—458no—
1187C2×C22⋊C4—458no—
1188C2×C22⋊C4—458no—
1189C2×C22⋊C4—458no—
1190C2×C42—454no—
1191C2×C3×C5—22no—
1192C2×C3×C5—22no—
1193C2×C3×C5—28no—
1194C2×C3×C5—21no—
1195C2×C3×C5—44no—
1196C2×C3×C5C23×C4×D312yes—
1197D15—34no—
1198D15—62no—
1199D15—62no—
1200D15—62no—
1201D15—68no—
1202D15—124no—
1203C3×D5—22no—
1204C3×D5—22no—
1205C3×D5—28no—
1206C3×D5—22no—
1207C3×D5—44no—
1208C3×D5D3×H(5,𝔽2)14yes—
1209C5×D3—34no—
1210C5×D3—62no—
1211C5×D3—62no—
1212C5×D3—62no—
1213C5×D3—68no—
1214C5×D3—124no—
1215C23×C3—22no—
1216C23×C3—52no—
1217C23×C3—58no—
1218C23×C3—58no—
1219C23×C3—54no—
1220C23×C3—101no—
1221C23×C3—104no—
1222C23×C3—102no—
1223C23×C3—104no—
1224C23×C3—208no—
1225C23×C3—208no—
1226C23×C3C2×D3×AGL(1,𝔽5)14yescomplemented
1227C22×D3—32no—
1228C22×D3—38no—
1229C22×D3—34no—
1230C22×D3—38no—
1231C22×D3—61no—
1232C22×D3—64no—
1233C22×D3—62no—
1234C22×D3—64no—
1235C22×D3—128no—
1236C22×D3—128no—
1237C22×D3—152no—
1238C22×D3—152no—
1239C22×D3—158no—
1240C22×D3—152no—
1241C22×D3—152no—
1242C22×D3—158no—
1243C22×D3—158no—
1244C22×D3—158no—
1245C22×D3—158no—
1246C22×D3—158no—
1247C22×D3—152no—
1248C22×D3—158no—
1249C22×D3—154no—
1250C22×D3—158no—
1251C22×D3—301no—
1252C22×D3—301no—
1253C22×D3—301no—
1254C22×D3—301no—
1255C22×D3—304no—
1256C22×D3—304no—
1257C22×D3—304no—
1258C22×D3—304no—
1259C22×D3—304no—
1260C22×D3—304no—
1261C22×D3—301no—
1262C22×D3—302no—
1263C22×D3—304no—
1264C22×D3—304no—
1265C22×D3—3032no—
1266C22×D3—308no—
1267C22×D3—308no—
1268C22×D3—6016no—
1269C22×D3—608no—
1270C22×D3—6016no—
1271C22×D3—608no—
1272C22×D3—6016no—
1273C22×D3—608no—
1274C22×D3—608no—
1275C22×D3—6016no—
1276C22×D3—6016no—
1277C22×D3—6016no—
1278C22×D3—6016no—
1279C22×D3—608no—
1280C22×D3—608no—
1281C22×D3—608no—
1282C22×D3—608no—
1283C3×D4—24no—
1284C3×D4—516no—
1285C3×D4—58no—
1286C3×D4—104no—
1287C3×D4—108no—
1288C3×D4C2×D3×AGL(1,𝔽5)18yescomplemented
1289C2×C3×C4—21no—
1290C2×C3×C4—52no—
1291C2×C3×C4—54no—
1292C2×C3×C4—54no—
1293C2×C3×C4—102no—
1294C2×C3×C4—102no—
1295C2×C3×C4—101no—
1296C2×C3×C4—1516no—
1297C2×C3×C4—6016no—
1298C2×C3×C4C2×D3×AGL(1,𝔽5)12yescomplemented
1299#67—316no—
1300#67—68no—
1301#67—1516no—
1302#67—1516no—
1303#67—1516no—
1304#67—308no—
1305#67—308no—
1306#67—308no—
1307C2×Dic3—32no—
1308C2×Dic3—516no—
1309C2×Dic3—61no—
1310C2×Dic3—154no—
1311C2×Dic3—154no—
1312C2×Dic3—152no—
1313C2×Dic3—2016no—
1314C2×Dic3—302no—
1315C2×Dic3—302no—
1316C2×Dic3—301no—
1317D12—38no—
1318D12—64no—
1319D12—1516no—
1320D12—158no—
1321D12—304no—
1322D12—308no—
1323C4×D3—34no—
1324C4×D3—34no—
1325C4×D3—62no—
1326C4×D3—62no—
1327C4×D3—154no—
1328C4×D3—154no—
1329C4×D3—154no—
1330C4×D3—154no—
1331C4×D3—154no—
1332C4×D3—154no—
1333C4×D3—302no—
1334C4×D3—302no—
1335C4×D3—302no—
1336C4×D3—302no—
1337C4×D3—302no—
1338C4×D3—302no—
1339C4×D3—3032no—
1340C4×D3—6032no—
1341C22×C5—42no—
1342C22×C5—91no—
1343C22×C5—91no—
1344C22×C5—94no—
1345C22×C5—182no—
1346C22×C5—188no—
1347C22×C5—362no—
1348C22×C5—364no—
1349C22×C5C22×#62411yescharacteristic
1350C22×C5C22×#62414yes—
1351C2×D5—22no—
1352C2×D5—28no—
1353C2×D5—44no—
1354C2×D5—42no—
1355C2×D5—91no—
1356C2×D5—94no—
1357C2×D5—91no—
1358C2×D5—94no—
1359C2×D5—182no—
1360C2×D5—188no—
1361C2×D5—182no—
1362C2×D5—188no—
1363C2×D5—182no—
1364C2×D5—188no—
1365C2×D5—182no—
1366C2×D5—188no—
1367C2×D5—364no—
1368C2×D5—364no—
1369C2×D5—364no—
1370C2×D5—364no—
1371C2×D5—362no—
1372C2×D5C22×#62411yescharacteristic
1373C2×D5C22×#62414yes—
1374C2×D5C23×D3211yescharacteristic
1375AGL(1,𝔽5)—616no—
1376C4×C5—92no—
1377C4×C5C22×#62412yes—
1378Dic5—92no—
1379Dic5C22×#62412yes—
1380C2×C32—21no—
1381C2×C32—24no—
1382C2×C32—52no—
1383C2×C32—101no—
1384C2×C32—104no—
1385C2×C32C24×AGL(1,𝔽5)11yescharacteristic
1386C3⋊D3—21no—
1387C3⋊D3—24no—
1388C3⋊D3—52no—
1389C3⋊D3—101no—
1390C3⋊D3—104no—
1391C3⋊D3#6625812yescomplemented
1392C24—52no—
1393C24—92no—
1394C24—451no—
1395C24—454no—
1396C24—452no—
1397C24—454no—
1398C24—452no—
1399C24—454no—
1400C24—454no—
1401C24—452no—
1402C24—452no—
1403C24—1808no—
1404C2×D4—52no—
1405C2×D4—54no—
1406C2×D4—54no—
1407C2×D4—51no—
1408C2×D4—92no—
1409C2×D4—94no—
1410C2×D4—94no—
1411C2×D4—91no—
1412C2×D4—454no—
1413C2×D4—454no—
1414C2×D4—452no—
1415C2×D4—454no—
1416C2×D4—454no—
1417C2×D4—452no—
1418C2×D4—458no—
1419C2×D4—458no—
1420C2×D4—454no—
1421C2×D4—454no—
1422C2×D4—458no—
1423C2×D4—458no—
1424C2×D4—458no—
1425C2×D4—458no—
1426C2×D4—452no—
1427C2×D4—452no—
1428C2×D4—454no—
1429C2×D4—454no—
1430C2×D4—451no—
1431C2×D4ΓL(1,𝔽16)⋊D311yescharacteristic, complemented
1432C22×C4—51no—
1433C22×C4—91no—
1434C22×C4—1516no—
1435C22×C4—452no—
1436C22×C4—452no—
1437C22×C4—451no—
1438C22×C4—452no—
1439C22×C4—452no—
1440C22×C4—451no—
1441C22×C4—451no—
1442C22×C4—458no—
1443C22×C4—4516no—
1444C22×C4—451no—
1445C22×C4—18016no—
1446C4⋊C4—158no—
1447C4⋊C4—458no—
1448C22⋊C4—158no—
1449C22⋊C4—1516no—
1450C22⋊C4—458no—
1451C22⋊C4—4516no—
1452C42—158no—
1453C42—458no—
1454C3×C5—21no—
1455C3×C5D3×#51812yescomplemented
1456C22×C3—21no—
1457C22×C3—24no—
1458C22×C3—44no—
1459C22×C3—44no—
1460C22×C3—52no—
1461C22×C3—52no—
1462C22×C3—58no—
1463C22×C3—101no—
1464C22×C3—101no—
1465C22×C3—104no—
1466C22×C3—1016no—
1467C22×C3—104no—
1468C22×C3—104no—
1469C22×C3—208no—
1470C22×C3—204no—
1471C22×C3—208no—
1472C22×C3—204no—
1473C22×C3—208no—
1474C22×C3C22×D3×AGL(1,𝔽5)12yes—
1475C22×C3C22×D3×AGL(1,𝔽5)18yes—
1476C2×D3—32no—
1477C2×D3—32no—
1478C2×D3—38no—
1479C2×D3—61no—
1480C2×D3—61no—
1481C2×D3—64no—
1482C2×D3—64no—
1483C2×D3—616no—
1484C2×D3—64no—
1485C2×D3—128no—
1486C2×D3—128no—
1487C2×D3—124no—
1488C2×D3—128no—
1489C2×D3—124no—
1490C2×D3—158no—
1491C2×D3—152no—
1492C2×D3—152no—
1493C2×D3—158no—
1494C2×D3—304no—
1495C2×D3—301no—
1496C2×D3—301no—
1497C2×D3—304no—
1498C2×D3—304no—
1499C2×D3—3016no—
1500C2×D3—304no—
1501C2×D3—3016no—
1502C2×D3—3016no—
1503C2×D3—304no—
1504C2×D3—304no—
1505C2×D3—304no—
1506C2×D3—304no—
1507C2×D3—304no—
1508C2×D3—3016no—
1509C2×D3—304no—
1510C2×D3—608no—
1511C2×D3—608no—
1512C2×D3—608no—
1513C2×D3—608no—
1514C2×D3—608no—
1515C2×D3—608no—
1516C2×D3—608no—
1517C2×D3—608no—
1518C2×D3—608no—
1519C2×D3—608no—
1520C2×D3—608no—
1521C2×D3—604no—
1522C2×D3—608no—
1523C2×D3—604no—
1524C3×C4—22no—
1525C3×C4—54no—
1526C3×C4—102no—
1527C3×C4—3016no—
1528C3×C4C22×D3×AGL(1,𝔽5)14yes—
1529Dic3—34no—
1530Dic3—62no—
1531Dic3—1016no—
1532Dic3—154no—
1533Dic3—302no—
1534C2×C5—21no—
1535C2×C5—24no—
1536C2×C5—92no—
1537C2×C5—181no—
1538C2×C5—184no—
1539C2×C5C23×#62411yescharacteristic
1540D5—21no—
1541D5—24no—
1542D5—92no—
1543D5—181no—
1544D5—184no—
1545D5#1059667512yes—
1546C32C2×#6625811yescharacteristic, complemented, Sylow
1547C23—51no—
1548C23—54no—
1549C23—54no—
1550C23—52no—
1551C23—91no—
1552C23—94no—
1553C23—94no—
1554C23—92no—
1555C23—204no—
1556C23—364no—
1557C23—451no—
1558C23—451no—
1559C23—454no—
1560C23—451no—
1561C23—451no—
1562C23—454no—
1563C23—454no—
1564C23—454no—
1565C23—454no—
1566C23—454no—
1567C23—451no—
1568C23—454no—
1569C23—454no—
1570C23—452no—
1571C23—9016no—
1572C23—904no—
1573C23—1804no—
1574C23—1808no—
1575C23—1804no—
1576C23—1804no—
1577C23—1808no—
1578C23—1804no—
1579C23—1808no—
1580C23C2×ΓL(1,𝔽16)⋊D312yescomplemented
1581D4—58no—
1582D4—54no—
1583D4—98no—
1584D4—94no—
1585D4—458no—
1586D4—458no—
1587D4—458no—
1588D4—458no—
1589D4—454no—
1590D4C2×ΓL(1,𝔽16)⋊D314yescomplemented
1591C2×C4—51no—
1592C2×C4—52no—
1593C2×C4—52no—
1594C2×C4—91no—
1595C2×C4—92no—
1596C2×C4—92no—
1597C2×C4—1516no—
1598C2×C4—452no—
1599C2×C4—452no—
1600C2×C4—452no—
1601C2×C4—452no—
1602C2×C4—452no—
1603C2×C4—452no—
1604C2×C4—451no—
1605C2×C4—452no—
1606C2×C4—452no—
1607C2×C4—6016no—
1608C2×C4—9016no—
1609C2×C4—18016no—
1610C2×C4C2×ΓL(1,𝔽16)⋊D311yescharacteristic, complemented
1611C2×C3—22no—
1612C2×C3—22no—
1613C2×C3—28no—
1614C2×C3—21no—
1615C2×C3—44no—
1616C2×C3—54no—
1617C2×C3—102no—
1618C2×C3—102no—
1619C2×C3—102no—
1620C2×C3—108no—
1621C2×C3—204no—
1622C2×C3C23×D3×AGL(1,𝔽5)12yes—
1623D3—34no—
1624D3—62no—
1625D3—62no—
1626D3—62no—
1627D3—68no—
1628D3—124no—
1629D3—154no—
1630D3—302no—
1631D3—302no—
1632D3—302no—
1633D3—308no—
1634D3—604no—
1635C5#1190001211yescharacteristic, complemented, Sylow
1636C22—42no—
1637C22—51no—
1638C22—51no—
1639C22—54no—
1640C22—91no—
1641C22—91no—
1642C22—94no—
1643C22—108no—
1644C22—102no—
1645C22—182no—
1646C22—188no—
1647C22—202no—
1648C22—204no—
1649C22—362no—
1650C22—364no—
1651C22—454no—
1652C22—451no—
1653C22—451no—
1654C22—454no—
1655C22—902no—
1656C22—908no—
1657C22—908no—
1658C22—902no—
1659C22—902no—
1660C22—908no—
1661C22—902no—
1662C22—908no—
1663C22—1802no—
1664C22—1804no—
1665C22—1804no—
1666C22—1804no—
1667C22—1804no—
1668C22C22×ΓL(1,𝔽16)⋊D311yescharacteristic
1669C22C22×ΓL(1,𝔽16)⋊D314yes—
1670C4—52no—
1671C4—92no—
1672C4—3016no—
1673C4—452no—
1674C4C22×ΓL(1,𝔽16)⋊D312yes—
1675C3—21no—
1676C3D3×#6625812yescomplemented
1677C2—21no—
1678C2—24no—
1679C2—52no—
1680C2—92no—
1681C2—101no—
1682C2—104no—
1683C2—181no—
1684C2—184no—
1685C2—452no—
1686C2—901no—
1687C2—904no—
1688C2C23×ΓL(1,𝔽16)⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C23×ΓL(1,𝔽16)⋊D3
commutator, socleC2×C32×C5C24×C4
FittingC2×C32×C5×D4C2×C4
prime radicalC2×D4×D5×C3⋊D3C2
cosocleC2×C32×D5C25
hypercenterC2×D4ΓL(1,𝔽16)⋊D3
hypocenterC32×C5C2×#518
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #72230301C2semidirect
2. #72230290C2semidirect
3. #72230282C2semidirect
4. D4×ΓL(1,𝔽16)⋊D3C2semidirect
5. #72230108C2semidirect
6. C3×#11756987C2semidirect
7. C2×#13088746C2semidirect
11. C22×ΓL(1,𝔽16)⋊D3C22semidirect
12. C2×D4×C3⋊D15C4semidirect
13. C2×C5×D4×C3⋊D3C4semidirect
15. C2×#10624173C4semidirect
16. C2×C3⋊D3×C22⋊D5C4semidirect
18. D4×D5×C3⋊D3C4semidirect
19. D4×D5×C3⋊D3C4semidirect
22. C2×#10624160C4semidirect
23. C2×C3⋊D3×D20C4semidirect
26. C2×C3×#6763C22semidirect
27. C3×D4×ΓL(1,𝔽16)C22semidirect
28. C3×#91989C22semidirect
30. #13088746C22semidirect
31. #13088746C22semidirect
32. #13088746C22semidirect
33. #13088745C22semidirect
34. C2×#10623978C22semidirect
35. #13088735C22semidirect
36. #13088733C22semidirect
37. #13088732C22semidirect
38. C4×ΓL(1,𝔽16)⋊D3C22semidirect
39. #13088724C22semidirect
40. #13088723C22semidirect
44. #11756987D3semidirect
52. C23×C3⋊D15C2×C4semidirect
53. C23×C5×C3⋊D3C2×C4semidirect
56. C22×D5×C3⋊D3C2×C4semidirect
57. C22×D5×C3⋊D3C2×C4semidirect
58. C22×D5×C3⋊D3C2×C4semidirect
59. C22×D5×C3⋊D3C2×C4semidirect
64. C22×C3×ΓL(1,𝔽16)C23semidirect
67. C2×ΓL(1,𝔽16)⋊D3C23semidirect
68. C2×C32×C5×D4C2×C4semidirect
69. C2×#67184C2×C4semidirect
70. D4×C3⋊D15C2×C4semidirect
71. D4×C3⋊D15C2×C4semidirect
72. C2×C4⋊(C3⋊D15)C2×C4semidirect
73. C2×C4×C3⋊D15C2×C4semidirect
74. C2×C5×#638C2×C4semidirect
75. C5×D4×C3⋊D3C2×C4semidirect
76. C5×D4×C3⋊D3C2×C4semidirect
77. C2×C5×C4⋊(C3⋊D3)C2×C4semidirect
78. C2×C4×C5×C3⋊D3C2×C4semidirect
79. C2×C32×C22⋊D5C2×C4semidirect
80. C32×D4×D5C2×C4semidirect
82. C2×C32×D20C2×C4semidirect
84. #10624173C2×C4semidirect
85. #10624173C2×C4semidirect
86. C3⋊D3×C22⋊D5C2×C4semidirect
87. C3⋊D3×C22⋊D5C2×C4semidirect
88. D5×#638C2×C4semidirect
90. C2×#67140C2×C4semidirect
91. C2×#67139C2×C4semidirect
92. C2×#67138C2×C4semidirect
93. C2×#67137C2×C4semidirect
94. C2×C3⋊D3×Dic5C2×C4semidirect
96. #10624160C2×C4semidirect
97. #10624160C2×C4semidirect
98. C3⋊D3×D20C2×C4semidirect
99. C3⋊D3×D20C2×C4semidirect
100. D5×C4⋊(C3⋊D3)C2×C4semidirect
102. C4×D5×C3⋊D3C2×C4semidirect
103. C4×D5×C3⋊D3C2×C4semidirect
107. C3×#6763C23semidirect
108. C3×C4⋊ΓL(1,𝔽16)C23semidirect
109. C3×C4×ΓL(1,𝔽16)C23semidirect
110. #10623979C23semidirect
112. #10623978C23semidirect
113. ΓL(1,𝔽16)⋊Dic3C23semidirect
154. C2×#6763C2×D3semidirect
155. D4×ΓL(1,𝔽16)C2×D3semidirect
156. #91989C2×D3semidirect
175. C23×C32×C5C22×C4semidirect
179. C22×C3⋊D15C22×C4semidirect
180. C22×C3⋊D15C22×C4semidirect
184. C22×C5×C3⋊D3C22×C4semidirect
185. C22×C5×C3⋊D3C22×C4semidirect
187. C22×C32×D5C22×C4semidirect
188. C22×C32×D5C22×C4semidirect
203. C2×D5×C3⋊D3C22×C4semidirect
204. C2×D5×C3⋊D3C22×C4semidirect
205. C2×D5×C3⋊D3C22×C4semidirect
213. C32×C5×D4C22×C4semidirect
214. C2×C32×C4×C5C22×C4semidirect
215. #67184C22×C4semidirect
216. C2×C3⋊Dic15C22×C4semidirect
217. C4⋊(C3⋊D15)C22×C4semidirect
219. C4×C3⋊D15C22×C4semidirect
220. C5×#638C22×C4semidirect
221. C2×C5×C3⋊Dic3C22×C4semidirect
222. C5×C4⋊(C3⋊D3)C22×C4semidirect
224. C4×C5×C3⋊D3C22×C4semidirect
225. C32×C22⋊D5C22×C4semidirect
226. C2×C32×Dic5C22×C4semidirect
227. C32×D20C22×C4semidirect
228. C32×C4×D5C22×C4semidirect
230. #67140C22×C4semidirect
231. #67139C22×C4semidirect
232. #67138C22×C4semidirect
234. #67137C22×C4semidirect
236. C3⋊D3×Dic5C22×C4semidirect
237. D5×C3⋊Dic3C22×C4semidirect
259. C2×D4×C3⋊D3AGL(1,𝔽5)semidirect
302. C22×ΓL(1,𝔽16)C22×D3semidirect
308. C2×C3×C5×D4C4×D3semidirect
330. C2×C3×C22⋊D5C4×D3semidirect
333. C3×D4×D5C4×D3semidirect
336. C2×C3×D20C4×D3semidirect
384. #6763C22×D3semidirect
385. C4⋊ΓL(1,𝔽16)C22×D3semidirect
386. C4×ΓL(1,𝔽16)C22×D3semidirect
486. C23×C3⋊D3C2×AGL(1,𝔽5)semidirect
491. C2×C32×D4C2×AGL(1,𝔽5)semidirect
498. C2×#638C2×AGL(1,𝔽5)semidirect
510. D4×C3⋊D3C2×AGL(1,𝔽5)semidirect
511. D4×C3⋊D3C2×AGL(1,𝔽5)semidirect
516. C2×C4⋊(C3⋊D3)C2×AGL(1,𝔽5)semidirect
524. C2×C4×C3⋊D3C2×AGL(1,𝔽5)semidirect
539. C23×C3×C5C2×C4×D3semidirect
566. C22×C3×D5C2×C4×D3semidirect
567. C22×C3×D5C2×C4×D3semidirect
613. C3×C5×D4C2×C4×D3semidirect
615. C2×C3×C4×C5C2×C4×D3semidirect
637. C3×C22⋊D5C2×C4×D3semidirect
639. C2×C3×Dic5C2×C4×D3semidirect
641. C3×D20C2×C4×D3semidirect
644. C3×C4×D5C2×C4×D3semidirect
720. C3⋊D15#518semidirect
723. C5×C3⋊D3#518semidirect
747. C2×C5×D4#624semidirect
754. C2×C22⋊D5#624semidirect
766. D4×D5#624semidirect
772. C2×D20#624semidirect
794. C23×C32C22×AGL(1,𝔽5)semidirect
821. C22×C3⋊D3C22×AGL(1,𝔽5)semidirect
822. C22×C3⋊D3C22×AGL(1,𝔽5)semidirect
825. C32×D4C22×AGL(1,𝔽5)semidirect
829. C2×C32×C4C22×AGL(1,𝔽5)semidirect
833. #638C22×AGL(1,𝔽5)semidirect
837. C2×C3⋊Dic3C22×AGL(1,𝔽5)semidirect
840. C4⋊(C3⋊D3)C22×AGL(1,𝔽5)semidirect
848. C4×C3⋊D3C22×AGL(1,𝔽5)semidirect
972. C2×C3×D4D3×AGL(1,𝔽5)semidirect
1056. C32×C5C2×#518semidirect
1062. C23×C5C2×#624semidirect
1087. C22×D5C2×#624semidirect
1088. C22×D5C2×#624semidirect
1097. C5×D4C2×#624semidirect
1101. C2×C4×C5C2×#624semidirect
1105. C22⋊D5C2×#624semidirect
1109. C2×Dic5C2×#624semidirect
1112. D20C2×#624semidirect
1119. C4×D5C2×#624semidirect
1226. C23×C3C2×D3×AGL(1,𝔽5)semidirect
1288. C3×D4C2×D3×AGL(1,𝔽5)semidirect
1298. C2×C3×C4C2×D3×AGL(1,𝔽5)semidirect
1391. C3⋊D3#66258semidirect
1431. C2×D4ΓL(1,𝔽16)⋊D3semidirect
1455. C3×C5D3×#518semidirect
1546. C32C2×#66258semidirect
1580. C23C2×ΓL(1,𝔽16)⋊D3semidirect
1590. D4C2×ΓL(1,𝔽16)⋊D3semidirect
1610. C2×C4C2×ΓL(1,𝔽16)⋊D3semidirect
1635. C5#11900012semidirect
1676. C3D3×#66258semidirect

Maximal subgroups

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

subgroupindex
#722303012
#722302902
#722302822
D4×ΓL(1,𝔽16)⋊D32
#722301082
C3×#117569872
C2×#130887462
C2×D4×D5×C3⋊D32
D3×#662583
#119000125