Finite Group Databasebeta

← #72260362

Subgroups — #72260362

Order 9600.

7492 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72260289C211yesmaximal, characteristic, complemented
2#72260285C212yesmaximal, complemented
3#72260284C214yesmaximal, complemented
4#72260282C214yesmaximal, complemented
5#72260278C214yesmaximal, complemented
6#72260276C211yesmaximal, characteristic
7#72260273C412yescomplemented
8#72260272C418yescomplemented
9#72260270C414yescomplemented
10C5×#92095C412yescomplemented
11D4×#10597182C214yesmaximal, complemented
12#72259540C214yesmaximal, complemented
13#72231041C2218yescomplemented
14#72231036C2218yescomplemented
15C2×#72224585C214yesmaximal, complemented
16#72231004C2214yescomplemented
17#72230992C2214yescomplemented
18D4×C3⋊#1044C2214yescomplemented
19D4×C3⋊#1044C2214yescomplemented
20#72230973C2214yescomplemented
21#72230959C2214yescomplemented
22#72230956C2214yes—
23#72230748C2218yescomplemented
24#72230748C2218yescomplemented
25D4×D15⋊D5C2214yes—
26#72230588C212yesmaximal, complemented
27#72230585C2214yescomplemented
28C4×#10597182C2214yescomplemented
29#72230553C2212yescomplemented
30#72230553C2212yescomplemented
31#72230539C2212yescomplemented
32#72230539C2212yescomplemented
33C2×#11925354C2214yescomplemented
34C2×#11925356C2214yescomplemented
35C2×#11925540C2214yescomplemented
36C2×#11925355C2214yescomplemented
37C2×#11925664C2214yes—
38C22×#10597182C2214yescomplemented
39C2×C3×D4×#1043C211yesmaximal, characteristic, complemented
40C2×C3×C22⋊#1043C2212yescomplemented
41C3×D4×#1043C2214yescomplemented
42C3×D4×#1043C2214yescomplemented
43#72229444C2212yescomplemented
44#72229438C2212yes—
45C23×C3×#1043C2212yescomplemented
46C2×C3×C4⋊#1043C2211yescharacteristic, complemented
47C2×C3×D4×C5⋊D5C2211yescharacteristic
48C2×C3×C4×#1043C2211yescharacteristic, complemented
49#72224585C2214yescomplemented
50#72224585C2218yescomplemented
51#72224585C2218yescomplemented
52#72224585C2218yescomplemented
53#72224585C2214yescomplemented
54#72213412—31nomaximal, Hall
55AGL(1,𝔽5)×#1004—52nomaximal
56#13107821—31no—
57#13107767—31no—
58C2×D4×#1043D311yescharacteristic, complemented
59#13107590—34no—
60C2×#11717375—34no—
61#13107570—34no—
62#13107569—34no—
63#13107568—34no—
64D4×D5⋊AGL(1,𝔽5)—34no—
65#13107562—32no—
66#13107559—32no—
67C23×C3×C5⋊D5C2312yes—
68C22×D15⋊D5C2314yes—
69C22×C3⋊#1044C2314yes—
70C22×C3⋊#1044C2314yes—
71C22×C3×#1043—44no—
72C22×C3×#1043C2311yescharacteristic
73C22×C3×#1043C2314yes—
74C22×C3×#1043C2311yescharacteristic
75C22×C3×#1043C2312yes—
76C22×C3×#1043C2314yes—
77C2×#10597182—48no—
78C2×#10597182C2314yes—
79C2×#10597182C2318yes—
80C2×#10597182C2314yes—
81C2×C3×C52×D4C2×C411yescharacteristic, complemented
82C2×C5×#1220C2×C418yescomplemented
83C5×#6819C2×C418yescomplemented
84C5×D4×D15C2×C418yescomplemented
85C5×#6817C2×C414yescomplemented
86C2×C3×C22⋊(C5⋊D5)C2×C412yescomplemented
87C3×D4×C5⋊D5C2×C414yescomplemented
88C3×D4×C5⋊D5C2314yes—
89C2×C3×C4⋊(C5⋊D5)C2×C411yescharacteristic, complemented
90C2×C3×C4×C5⋊D5C2311yescharacteristic
91#11925664C2×C418yescomplemented
92#11925664C2×C418yescomplemented
93#11925664C2318yes—
94#11925664C2314yes—
95#11925663C2×C4116yescomplemented
96C2×#10597127C2×C418yescomplemented
97C2×#10597126C2314yes—
98#11925658C2×C4116yescomplemented
99#11925657C2×C414yescomplemented
100#11925655C2312yes—
101#11925654C2×C418yescomplemented
102C4×D15⋊D5C2314yes—
103#11925652C2×C418yescomplemented
104#11925651C2×C414yescomplemented
105#11925650C2312yes—
106#11925648C2×C414yescomplemented
107#11925540C2314yes—
108#11925540C2318yes—
109C4⋊(C3⋊#1044)C2312yes—
110C4⋊(C3⋊#1044)C2312yes—
111C4×C3⋊#1044C2314yes—
112C3×C22⋊#1043C2318yes—
113C3×C4⋊#1043C2314yes—
114C3×C4×#1043C2312yes—
115C3×C4×#1043C2312yes—
116#11925356C2318yes—
117#11925356C2314yes—
118#11925356C2314yes—
119#11925355C2318yes—
120#11925355C2314yes—
121#11925355C2314yes—
122#11925354C2318yes—
123#11925354C2314yes—
124#11925354C2314yes—
125D5×#1004—52no—
126#11756987—52no—
127C2×C3×D4×AGL(1,𝔽5)—52no—
128C2×C3×D4×AGL(1,𝔽5)—102no—
129#11756871—58no—
130C2×AGL(1,𝔽5)×#67—58no—
131#11756846—58no—
132#11756845—58no—
133AGL(1,𝔽5)×#237—58no—
134D3×D4×AGL(1,𝔽5)—58no—
135#11756836—54no—
136AGL(1,𝔽5)×#235—54no—
137C23×#1043C2×D312yescomplemented
138C22×D5⋊AGL(1,𝔽5)—34no—
139C2×D4×C5⋊D5C2×D311yescharacteristic
140C5×#4144—32no—
141#11717495—34no—
142C2×#87886—34no—
143#11717479—38no—
144#11717477—34no—
145D4×D52—34no—
146#11717473—32no—
147#11717471—32no—
148C2×C22⋊#1044—34no—
149D4×#1044—34no—
150D4×#1044—34no—
151#11717451—32no—
152C2×C22⋊#1043C2×D312yescomplemented
153D4×#1043C2×D314yescomplemented
154D4×#1043C2×D314yescomplemented
155C2×C4⋊#1043C2×D311yescharacteristic, complemented
156C2×C4×#1043C2×D311yescharacteristic, complemented
157#11717377—38no—
158#11717377—38no—
159D5⋊(C22⋊AGL(1,𝔽5))—38no—
160#11717375—34no—
161#11717375—34no—
162#11717375—38no—
163#11717375—38no—
164#11717375—38no—
165C2×#87832—34no—
166C2×#87831—34no—
167#11717367—38no—
168C2×#87830—34no—
169#11717365—34no—
170D5⋊(C4⋊AGL(1,𝔽5))—34no—
171#11717363—32no—
172#11717363—32no—
173C4×D5⋊AGL(1,𝔽5)—34no—
174#11717356—34no—
175#11717355—34no—
176#11717354—34no—
177#11717353—32no—
178#11717353—32no—
179AGL(1,𝔽5)×H(5,𝔽2)—152no—
180C23×C3×C52C22×C412yescomplemented
181C22×C5×D15C22×C418yescomplemented
182C22×C3×C5⋊D5—42no—
183C22×C3×C5⋊D5—42no—
184C22×C3×C5⋊D5C22×C414yescomplemented
185C22×C3×C5⋊D5C22×C412yescomplemented
186C22×C3×C5⋊D5C2414yes—
187C22×C3×C5⋊D5C2411yescharacteristic
188C2×D15⋊D5—44no—
189C2×D15⋊D5—44no—
190C2×D15⋊D5C22×C418yescomplemented
191C2×D15⋊D5C2414yes—
192C2×C3⋊#1044—44no—
193C2×C3⋊#1044—44no—
194C2×C3⋊#1044C2414yes—
195C2×C3⋊#1044C2414yes—
196C2×C3×#1043—22no—
197C2×C3×#1043—28no—
198C2×C3×#1043—44no—
199C2×C3×#1043—42no—
200C2×C3×#1043—41no—
201C2×C3×#1043C2412yes—
202C2×C3×#1043C2414yes—
203C2×C3×#1043C2411yescharacteristic
204C2×C3×#1043C2411yescharacteristic
205#10597182—28no—
206#10597182—48no—
207#10597182—44no—
208C3×C52×D4C22×C414yescomplemented
209C2×C3×C4×C52C22×C411yescharacteristic, complemented
210C5×#1220C22×C418yescomplemented
211C5×#1220C22×C4116yescomplemented
212C2×C5×Dic15C22×C418yescomplemented
213C5×D60C22×C414yescomplemented
214C4×C5×D15C22×C418yescomplemented
215C5×Dic30C22×C414yescomplemented
216C3×C22⋊(C5⋊D5)C22×C418yescomplemented
217C2×C3×#1039C22×C411yescharacteristic, complemented
218C3×C4⋊(C5⋊D5)C22×C414yescomplemented
219C3×C4×C5⋊D5C22×C412yescomplemented
220C3×C4×C5⋊D5C2412yes—
221#10597129C22×C414yescomplemented
222#10597128C22×C414yescomplemented
223#10597127C22×C418yescomplemented
224#10597127C22×C4116yescomplemented
225#10597126C22×C418yescomplemented
226#10597126C2414yes—
227#10597125C22×C418yescomplemented
228C23×C3×AGL(1,𝔽5)—54no—
229C23×C3×AGL(1,𝔽5)—104no—
230C22×D3×AGL(1,𝔽5)—58no—
231#92095AGL(1,𝔽5)12yescomplemented
232C5×#1004—52no—
233C2×C3×D4×D5—52no—
234C2×C3×D4×D5—102no—
235#92049—58no—
236C2×D5×#67—58no—
237#92026—58no—
238#92025—58no—
239D5×#237—58no—
240D3×D4×D5—58no—
241#92017—54no—
242D5×#235—54no—
243C2×#6763—58no—
244D4×ΓL(1,𝔽16)—58no—
245D4×ΓL(1,𝔽16)—58no—
246#91989—54no—
247C2×C3×C22⋊AGL(1,𝔽5)—54no—
248C2×C3×C22⋊AGL(1,𝔽5)—104no—
249C3×D4×AGL(1,𝔽5)—58no—
250C3×D4×AGL(1,𝔽5)—58no—
251C3×D4×AGL(1,𝔽5)—108no—
252C3×D4×AGL(1,𝔽5)—108no—
253C2×C3×C4⋊AGL(1,𝔽5)—52no—
254C2×C3×C4⋊AGL(1,𝔽5)—102no—
255C2×C3×C4×AGL(1,𝔽5)—52no—
256C2×C3×C4×AGL(1,𝔽5)—102no—
257#67⋊AGL(1,𝔽5)—516no—
258#67⋊AGL(1,𝔽5)—516no—
259D3×C22⋊AGL(1,𝔽5)—516no—
260AGL(1,𝔽5)×#67—58no—
261AGL(1,𝔽5)×#67—58no—
262AGL(1,𝔽5)×#67—516no—
263AGL(1,𝔽5)×#67—516no—
264AGL(1,𝔽5)×#67—516no—
265C2×Dic3⋊AGL(1,𝔽5)—58no—
266C2×(C2×D3)⋊AGL(1,𝔽5)—58no—
267#91923—516no—
268C2×Dic3×AGL(1,𝔽5)—58no—
269#91921—58no—
270D3×C4⋊AGL(1,𝔽5)—58no—
271AGL(1,𝔽5)×D12—54no—
272AGL(1,𝔽5)×D12—54no—
273C4×D3×AGL(1,𝔽5)—58no—
274#91909—58no—
275ΓL(1,𝔽16)⋊Q8—58no—
276#91907—58no—
277AGL(1,𝔽5)×Dic6—54no—
278AGL(1,𝔽5)×Dic6—54no—
279C23×C5⋊D5C22×D312yes—
280C22×D52—34no—
281C22×#1044—34no—
282C22×#1044—34no—
283C22×#1043—44no—
284C22×#1043C22×D311yescharacteristic
285C22×#1043C22×D314yes—
286C22×#1043C22×D311yescharacteristic
287C22×#1043C22×D312yes—
288C22×#1043C22×D314yes—
289C2×D5⋊AGL(1,𝔽5)—34no—
290C2×D5⋊AGL(1,𝔽5)—34no—
291C2×D5⋊AGL(1,𝔽5)—38no—
292C2×D5⋊AGL(1,𝔽5)—128no—
293C2×C52×D4C4×D311yescharacteristic, complemented
294C2×C22⋊(C5⋊D5)C4×D312yescomplemented
295D4×C5⋊D5C4×D314yescomplemented
296D4×C5⋊D5C22×D314yes—
297C2×C4⋊(C5⋊D5)C4×D311yescharacteristic, complemented
298C2×C4×C5⋊D5C22×D311yescharacteristic
299C2×C5×C22⋊D5—38no—
300C5×#711—38no—
301C5×D4×D5—38no—
302C5×#709—34no—
303#87886—38no—
304#87886—38no—
305#87886—38no—
306#87886—34no—
307D5×C22⋊D5—316no—
308C2×#6038—38no—
309C2×#6036—34no—
310#87880—34no—
311#87879—316no—
312#87877—32no—
313D5×D20—38no—
314C4×D52—34no—
315#87874—38no—
316#87873—34no—
317#87872—32no—
318#87871—34no—
319C22⋊#1044—38no—
320C22⋊#1044—34no—
321C4⋊#1044—32no—
322C4⋊#1044—32no—
323C4×#1044—34no—
324C22⋊#1043C22×D318yes—
325C4⋊#1043C22×D314yes—
326C4×#1043C22×D312yes—
327C4×#1043C22×D312yes—
328#87832—34no—
329#87832—38no—
330#87832—34no—
331#87831—34no—
332#87831—38no—
333#87831—34no—
334#87830—34no—
335#87830—38no—
336#87830—34no—
337C4×#1004—251noHall
338D5×H(5,𝔽2)—152no—
339#66266—154no—
340#66266—158no—
341#41×AGL(1,𝔽5)—154no—
342#41×AGL(1,𝔽5)—158no—
343#66258—158no—
344#66258—158no—
345#66258—152no—
346C2×D4×AGL(1,𝔽5)—52no—
347C2×D4×AGL(1,𝔽5)—102no—
348C2×D4×AGL(1,𝔽5)—158no—
349C2×D4×AGL(1,𝔽5)—158no—
350C22×C3×C52—42no—
351C22×C3×C52C23×C411yescharacteristic
352C22×C3×C52C23×C414yes—
353C2×C5×D15—48no—
354C2×C5×D15C23×C418yes—
355C2×C3×C5⋊D5—21no—
356C2×C3×C5⋊D5—24no—
357C2×C3×C5⋊D5—21no—
358C2×C3×C5⋊D5—24no—
359C2×C3×C5⋊D5—44no—
360C2×C3×C5⋊D5—42no—
361C2×C3×C5⋊D5C23×C414yes—
362C2×C3×C5⋊D5C23×C411yescharacteristic
363C2×C3×C5⋊D5C2511yescharacteristic
364D15⋊D5—24no—
365D15⋊D5—24no—
366D15⋊D5—48no—
367C3⋊#1044—24no—
368C3⋊#1044—24no—
369C3×#1043—21no—
370C3×#1043—24no—
371C3×#1043—22no—
372C3×#1043H(5,𝔽2)12yescomplemented
373C3×C4×C52C23×C412yes—
374C5×Dic15C23×C418yes—
375C3×#1039C23×C412yes—
376C23×C3×D5—54no—
377C23×C3×D5—104no—
378C22×D3×D5—58no—
379C22×ΓL(1,𝔽16)—58no—
380C22×ΓL(1,𝔽16)—58no—
381C22×C3×AGL(1,𝔽5)—58no—
382C22×C3×AGL(1,𝔽5)—52no—
383C22×C3×AGL(1,𝔽5)—58no—
384C22×C3×AGL(1,𝔽5)—52no—
385C22×C3×AGL(1,𝔽5)—54no—
386C22×C3×AGL(1,𝔽5)—102no—
387C22×C3×AGL(1,𝔽5)—102no—
388C22×C3×AGL(1,𝔽5)—104no—
389C22×C3×AGL(1,𝔽5)—108no—
390C22×C3×AGL(1,𝔽5)—108no—
391C22×C3×AGL(1,𝔽5)—208no—
392C22×C3×AGL(1,𝔽5)—2016no—
393C2×D3×AGL(1,𝔽5)—58no—
394C2×D3×AGL(1,𝔽5)—58no—
395C2×D3×AGL(1,𝔽5)—516no—
396C2×D3×AGL(1,𝔽5)—2016no—
397C2×C3×C5×D4—22no—
398C2×C3×C5×D4C2×AGL(1,𝔽5)12yescomplemented
399C2×#1220C2×AGL(1,𝔽5)18yescomplemented
400#6819C2×AGL(1,𝔽5)18yescomplemented
401D4×D15C2×AGL(1,𝔽5)18yescomplemented
402#6817C2×AGL(1,𝔽5)14yescomplemented
403C2×C5×#67—58no—
404C5×#237—58no—
405C5×D3×D4—58no—
406C5×#235—54no—
407C2×C3×C22⋊D5—54no—
408C2×C3×C22⋊D5—104no—
409C3×D4×D5—58no—
410C3×D4×D5—58no—
411C3×D4×D5—108no—
412C3×D4×D5—108no—
413C2×C3×D20—52no—
414C2×C3×D20—102no—
415C2×C3×C4×D5—52no—
416C2×C3×C4×D5—102no—
417#6790—516no—
418D3×C22⋊D5—516no—
419D5×#67—58no—
420D5×#67—516no—
421D5×#67—516no—
422D5×#67—516no—
423C2×#1202—58no—
424C2×#1201—58no—
425#6782—58no—
426#6780—516no—
427#6779—516no—
428C2×D5×Dic3—58no—
429#6777—58no—
430D3×D20—58no—
431D5×D12—54no—
432C4×D3×D5—58no—
433#6773—54no—
434#6772—54no—
435#6771—58no—
436#6766—58no—
437#6765—58no—
438D5×Dic6—54no—
439#6763—516no—
440#6763—58no—
441C4⋊ΓL(1,𝔽16)—54no—
442C4⋊ΓL(1,𝔽16)—54no—
443C4×ΓL(1,𝔽16)—58no—
444C3×C22⋊AGL(1,𝔽5)—516no—
445C3×C22⋊AGL(1,𝔽5)—1016no—
446C3×C4⋊AGL(1,𝔽5)—58no—
447C3×C4⋊AGL(1,𝔽5)—108no—
448C3×C4×AGL(1,𝔽5)—54no—
449C3×C4×AGL(1,𝔽5)—54no—
450C3×C4×AGL(1,𝔽5)—104no—
451C3×C4×AGL(1,𝔽5)—104no—
452Dic3⋊AGL(1,𝔽5)—58no—
453Dic3⋊AGL(1,𝔽5)—58no—
454Dic3⋊AGL(1,𝔽5)—516no—
455(C2×D3)⋊AGL(1,𝔽5)—516no—
456(C2×D3)⋊AGL(1,𝔽5)—58no—
457(C2×D3)⋊AGL(1,𝔽5)—58no—
458Dic3×AGL(1,𝔽5)—58no—
459Dic3×AGL(1,𝔽5)—58no—
460Dic3×AGL(1,𝔽5)—516no—
461C23×C52C2×C4×D312yescomplemented
462C22×C5⋊D5—42no—
463C22×C5⋊D5—42no—
464C22×C5⋊D5C2×C4×D314yescomplemented
465C22×C5⋊D5C2×C4×D312yescomplemented
466C22×C5⋊D5C23×D314yes—
467C22×C5⋊D5C23×D311yescharacteristic
468C22×C5×D5—38no—
469C2×D52—34no—
470C2×D52—38no—
471C2×D52—124no—
472C2×D52—124no—
473C2×#1044—34no—
474C2×#1044—34no—
475C2×#1044—124no—
476C2×#1044—124no—
477C2×#1043—22no—
478C2×#1043—28no—
479C2×#1043—44no—
480C2×#1043—42no—
481C2×#1043—41no—
482C2×#1043C23×D312yes—
483C2×#1043C23×D314yes—
484C2×#1043C23×D311yescharacteristic
485C2×#1043C23×D311yescharacteristic
486D5⋊AGL(1,𝔽5)—68no—
487D5⋊AGL(1,𝔽5)—124no—
488D5⋊AGL(1,𝔽5)—128no—
489C52×D4C2×C4×D314yescomplemented
490C2×C4×C52C2×C4×D311yescharacteristic, complemented
491C22⋊(C5⋊D5)C2×C4×D318yescomplemented
492C2×#1039C2×C4×D311yescharacteristic, complemented
493C4⋊(C5⋊D5)C2×C4×D314yescomplemented
494C4×C5⋊D5C2×C4×D312yescomplemented
495C4×C5⋊D5C23×D312yes—
496C5×C22⋊D5—316no—
497C5×C22⋊D5—38no—
498C2×C5×Dic5—38no—
499C5×D20—34no—
500C4×C5×D5—38no—
501C5×Dic10—34no—
502#6039—34no—
503#6038—38no—
504#6038—316no—
505#6037—34no—
506#6036—38no—
507#6036—34no—
508D5×Dic5—38no—
509C2×#1004—251no—
510C2×C3×C4×D4—251no—
511#5798—251no—
512C2×C4×#67—254no—
513#5546—254no—
514#5545—254no—
515C4×D3×D4—254no—
516C4×#237—254no—
517#5504—252no—
518#5486—254no—
519C4×#235—252no—
520C23×AGL(1,𝔽5)—54no—
521C23×AGL(1,𝔽5)—104no—
522C23×AGL(1,𝔽5)—158no—
523C5×H(5,𝔽2)—152no—
524#4149—154no—
525#4149—158no—
526D5×#41—154no—
527D5×#41—158no—
528#4144—32no—
529#4144—158no—
530#4144—158no—
531C2×D4×D5—52no—
532C2×D4×D5—102no—
533C2×D4×D5—158no—
534C2×D4×D5—158no—
535C2×C22⋊AGL(1,𝔽5)—54no—
536C2×C22⋊AGL(1,𝔽5)—104no—
537C2×C22⋊AGL(1,𝔽5)—1516no—
538C2×C22⋊AGL(1,𝔽5)—158no—
539C2×C22⋊AGL(1,𝔽5)—158no—
540Q8×AGL(1,𝔽5)—154no—
541Q8×AGL(1,𝔽5)—154no—
542Q8×AGL(1,𝔽5)—158no—
543D4×AGL(1,𝔽5)—58no—
544D4×AGL(1,𝔽5)—58no—
545D4×AGL(1,𝔽5)—108no—
546D4×AGL(1,𝔽5)—108no—
547D4×AGL(1,𝔽5)—154no—
548D4×AGL(1,𝔽5)—154no—
549D4×AGL(1,𝔽5)—158no—
550D4×AGL(1,𝔽5)—1516no—
551D4×AGL(1,𝔽5)—1516no—
552D4×AGL(1,𝔽5)—158no—
553D4×AGL(1,𝔽5)—158no—
554D4×AGL(1,𝔽5)—158no—
555D4×AGL(1,𝔽5)—1516no—
556D4×AGL(1,𝔽5)—1516no—
557D4×AGL(1,𝔽5)—1516no—
558D4×AGL(1,𝔽5)—158no—
559#4130—158no—
560#4130—158no—
561#4130—1516no—
562#4130—154no—
563C2×C4⋊AGL(1,𝔽5)—52no—
564C2×C4⋊AGL(1,𝔽5)—102no—
565C2×C4⋊AGL(1,𝔽5)—158no—
566C2×C4⋊AGL(1,𝔽5)—158no—
567C2×C4×AGL(1,𝔽5)—52no—
568C2×C4×AGL(1,𝔽5)—102no—
569C2×C4×AGL(1,𝔽5)—158no—
570C2×C4×AGL(1,𝔽5)—158no—
571C2×C3×C52—21no—
572C2×C3×C52—24no—
573C2×C3×C52C24×C411yescharacteristic
574C5×D15—28no—
575C3×C5⋊D5—21no—
576C3×C5⋊D5—24no—
577C3×C5⋊D5C2×H(5,𝔽2)11yescharacteristic
578C3×C5⋊D5#58511yescharacteristic
579C4×H(5,𝔽2)—751noSylow
580C23×C3×C5—24no—
581C23×C3×C5C22×AGL(1,𝔽5)14yescomplemented
582C22×D15C22×AGL(1,𝔽5)18yescomplemented
583C22×C5×D3—58no—
584C22×C3×D5—58no—
585C22×C3×D5—52no—
586C22×C3×D5—58no—
587C22×C3×D5—54no—
588C22×C3×D5—102no—
589C22×C3×D5—108no—
590C22×C3×D5—104no—
591C22×C3×D5—108no—
592C22×C3×D5—204no—
593C22×C3×D5—204no—
594C22×C3×D5—208no—
595C22×C3×D5—208no—
596C2×D3×D5—58no—
597C2×D3×D5—516no—
598C2×D3×D5—208no—
599C2×D3×D5—208no—
600C2×ΓL(1,𝔽16)—58no—
601C2×ΓL(1,𝔽16)—58no—
602C2×ΓL(1,𝔽16)—208no—
603C2×ΓL(1,𝔽16)—208no—
604C2×C3×AGL(1,𝔽5)—52no—
605C2×C3×AGL(1,𝔽5)—54no—
606C2×C3×AGL(1,𝔽5)—58no—
607C2×C3×AGL(1,𝔽5)—52no—
608C2×C3×AGL(1,𝔽5)—1016no—
609C2×C3×AGL(1,𝔽5)—104no—
610C2×C3×AGL(1,𝔽5)—102no—
611C2×C3×AGL(1,𝔽5)—102no—
612C2×C3×AGL(1,𝔽5)—108no—
613C2×C3×AGL(1,𝔽5)—104no—
614C2×C3×AGL(1,𝔽5)—108no—
615C2×C3×AGL(1,𝔽5)—202no—
616C2×C3×AGL(1,𝔽5)—204no—
617C2×C3×AGL(1,𝔽5)—208no—
618C2×C3×AGL(1,𝔽5)—2016no—
619C2×C3×AGL(1,𝔽5)—2016no—
620C2×C3×AGL(1,𝔽5)—204no—
621C2×C3×AGL(1,𝔽5)—208no—
622D3×AGL(1,𝔽5)—1016no—
623D3×AGL(1,𝔽5)—208no—
624D3×AGL(1,𝔽5)—2016no—
625C3×C5×D4—28no—
626C3×C5×D4C22×AGL(1,𝔽5)18yescomplemented
627C2×C3×C4×C5—22no—
628C2×C3×C4×C5C22×AGL(1,𝔽5)12yescomplemented
629#1220C22×AGL(1,𝔽5)116yescomplemented
630#1220C22×AGL(1,𝔽5)18yescomplemented
631C2×Dic15C22×AGL(1,𝔽5)18yescomplemented
632D60C22×AGL(1,𝔽5)14yescomplemented
633C4×D15C22×AGL(1,𝔽5)18yescomplemented
634Dic30C22×AGL(1,𝔽5)14yescomplemented
635C5×#67—516no—
636C5×#67—58no—
637C2×C5×Dic3—58no—
638C5×D12—54no—
639C4×C5×D3—58no—
640C5×Dic6—54no—
641C3×C22⋊D5—516no—
642C3×C22⋊D5—1016no—
643C2×C3×Dic5—52no—
644C2×C3×Dic5—102no—
645C3×D20—58no—
646C3×D20—108no—
647C3×C4×D5—54no—
648C3×C4×D5—54no—
649C3×C4×D5—104no—
650C3×C4×D5—104no—
651#1204—58no—
652#1203—58no—
653#1202—516no—
654#1202—58no—
655#1201—516no—
656#1201—58no—
657#1200—58no—
658D3×Dic5—58no—
659D5×Dic3—516no—
660D5×Dic3—58no—
661C22×C52—42no—
662C22×C52C22×C4×D314yes—
663C22×C52C22×C4×D311yescharacteristic
664C2×C5⋊D5—21no—
665C2×C5⋊D5—24no—
666C2×C5⋊D5—21no—
667C2×C5⋊D5—24no—
668C2×C5⋊D5—44no—
669C2×C5⋊D5—42no—
670C2×C5⋊D5C22×C4×D314yes—
671C2×C5⋊D5C22×C4×D311yescharacteristic
672C2×C5⋊D5C24×D311yescharacteristic
673C2×C5×D5—38no—
674C2×C5×D5—128no—
675D52—64no—
676D52—64no—
677D52—128no—
678#1044—64no—
679#1044—64no—
680#1043—21no—
681#1043—24no—
682#1043—22no—
683#1043#100412yescomplemented
684C4×C52C22×C4×D312yes—
685#1039C22×C4×D312yes—
686C5×Dic5—38no—
687C22×C3×D4—251no—
688C23×C3×C4—252no—
689C22×#67—254no—
690#1004—52no—
691#1004—252no—
692#1004—258no—
693#1004—254no—
694C2×#237—254no—
695C2×D3×D4—254no—
696C2×#235—252no—
697C22×C4×D3—254no—
698C3×C4×D4—254no—
699C3×C4×D4—254no—
700C2×C3×C4⋊C4—251no—
701C2×C3×C22⋊C4—252no—
702C2×C3×C42—251no—
703C2×#217—254no—
704D4×Dic3—254no—
705D4×Dic3—254no—
706C4×#67—254no—
707C4×#67—254no—
708C4×#67—258no—
709C4×#67—258no—
710C4×#67—258no—
711C2×(C2×D3)⋊C4—254no—
712#926—252no—
713C2×Dic3⋊C4—254no—
714C2×C4×Dic3—254no—
715#893—254no—
716#892—254no—
717D3×C4⋊C4—254no—
718#887—254no—
719#67⋊C4—258no—
720#67⋊C4—258no—
721D3×C22⋊C4—258no—
722#877—258no—
723C4×D12—252no—
724C4×D12—252no—
725#872—254no—
726C42×D3—254no—
727C4×Dic6—252no—
728C4×Dic6—252no—
729C23×D5—54no—
730C23×D5—104no—
731C23×D5—158no—
732C22×AGL(1,𝔽5)—52no—
733C22×AGL(1,𝔽5)—58no—
734C22×AGL(1,𝔽5)—52no—
735C22×AGL(1,𝔽5)—54no—
736C22×AGL(1,𝔽5)—58no—
737C22×AGL(1,𝔽5)—102no—
738C22×AGL(1,𝔽5)—102no—
739C22×AGL(1,𝔽5)—104no—
740C22×AGL(1,𝔽5)—108no—
741C22×AGL(1,𝔽5)—108no—
742C22×AGL(1,𝔽5)—158no—
743C22×AGL(1,𝔽5)—158no—
744C22×AGL(1,𝔽5)—1516no—
745C22×AGL(1,𝔽5)—158no—
746C22×AGL(1,𝔽5)—158no—
747C22×AGL(1,𝔽5)—208no—
748C22×AGL(1,𝔽5)—2016no—
749C22×AGL(1,𝔽5)—6016no—
750C5×#41—158no—
751C5×#41—154no—
752C2×C5×D4—22no—
753C2×C5×D4—158no—
754C2×C5×D4—158no—
755C2×C5×D4D3×AGL(1,𝔽5)12yescomplemented
756C2×C22⋊D5—38no—
757C2×C22⋊D5—54no—
758C2×C22⋊D5—104no—
759C2×C22⋊D5—158no—
760C2×C22⋊D5—1516no—
761#713—158no—
762#713—154no—
763Q8×D5—154no—
764#711—38no—
765#711—154no—
766#711—1516no—
767#711—158no—
768D4×D5—38no—
769D4×D5—58no—
770D4×D5—58no—
771D4×D5—108no—
772D4×D5—108no—
773D4×D5—158no—
774D4×D5—154no—
775D4×D5—158no—
776D4×D5—1516no—
777D4×D5—1516no—
778D4×D5—1516no—
779D4×D5—1516no—
780#709—34no—
781#709—158no—
782#709—158no—
783#709—1516no—
784C2×D20—52no—
785C2×D20—102no—
786C2×D20—158no—
787C2×D20—158no—
788C2×C4×D5—52no—
789C2×C4×D5—102no—
790C2×C4×D5—158no—
791C2×C4×D5—158no—
792C22⋊AGL(1,𝔽5)—516no—
793C22⋊AGL(1,𝔽5)—1016no—
794C22⋊AGL(1,𝔽5)—158no—
795C22⋊AGL(1,𝔽5)—158no—
796C22⋊AGL(1,𝔽5)—1516no—
797C22⋊AGL(1,𝔽5)—1516no—
798C22⋊AGL(1,𝔽5)—158no—
799C4⋊AGL(1,𝔽5)—58no—
800C4⋊AGL(1,𝔽5)—108no—
801C4⋊AGL(1,𝔽5)—154no—
802C4⋊AGL(1,𝔽5)—154no—
803C4⋊AGL(1,𝔽5)—158no—
804C4⋊AGL(1,𝔽5)—1516no—
805C4⋊AGL(1,𝔽5)—158no—
806C4×AGL(1,𝔽5)—54no—
807C4×AGL(1,𝔽5)—54no—
808C4×AGL(1,𝔽5)—104no—
809C4×AGL(1,𝔽5)—104no—
810C4×AGL(1,𝔽5)—158no—
811C4×AGL(1,𝔽5)—158no—
812C4×AGL(1,𝔽5)—158no—
813C4×AGL(1,𝔽5)—1516no—
814C3×C52C4×H(5,𝔽2)11yescharacteristic, complemented, Hall
815C2×H(5,𝔽2)—751no—
816#520—752no—
817#520—754no—
818#518—754no—
819#518—754no—
820#518—751no—
821C4×#41—752no—
822C4×#41—754no—
823C2×C4×D4—251no—
824C2×C4×D4—754no—
825C2×C4×D4—754no—
826C22×C3×C5—22no—
827C22×C3×C5—28no—
828C22×C3×C5—44no—
829C22×C3×C5—48no—
830C22×C3×C5C23×AGL(1,𝔽5)12yes—
831C22×C3×C5C23×AGL(1,𝔽5)18yes—
832C2×D15—48no—
833C2×D15C23×AGL(1,𝔽5)18yes—
834C2×C5×D3—58no—
835C2×C5×D3—208no—
836C2×C3×D5—52no—
837C2×C3×D5—58no—
838C2×C3×D5—52no—
839C2×C3×D5—102no—
840C2×C3×D5—102no—
841C2×C3×D5—108no—
842C2×C3×D5—102no—
843C2×C3×D5—108no—
844C2×C3×D5—102no—
845C2×C3×D5—108no—
846C2×C3×D5—104no—
847C2×C3×D5—104no—
848C2×C3×D5—208no—
849C2×C3×D5—208no—
850C2×C3×D5—204no—
851C2×C3×D5—208no—
852C2×C3×D5—2016no—
853C2×C3×D5—208no—
854D3×D5—108no—
855D3×D5—108no—
856D3×D5—2016no—
857ΓL(1,𝔽16)—108no—
858ΓL(1,𝔽16)—108no—
859C3×AGL(1,𝔽5)—54no—
860C3×AGL(1,𝔽5)—104no—
861C3×AGL(1,𝔽5)—108no—
862C3×AGL(1,𝔽5)—104no—
863C3×AGL(1,𝔽5)—102no—
864C3×AGL(1,𝔽5)—104no—
865C3×AGL(1,𝔽5)—208no—
866C3×AGL(1,𝔽5)—204no—
867C3×C4×C5—24no—
868C3×C4×C5C23×AGL(1,𝔽5)14yes—
869Dic15C23×AGL(1,𝔽5)18yes—
870C3×Dic5—54no—
871C3×Dic5—104no—
872C5×Dic3—58no—
873C2×C52—21no—
874C2×C52—24no—
875C2×C52C23×C4×D311yescharacteristic
876C5⋊D5—21no—
877C5⋊D5—24no—
878C5⋊D5C2×#100411yescharacteristic
879C5⋊D5#596411yescharacteristic
880C5×D5—68no—
881C24×C3—252no—
882C23×D3—254no—
883C2×C3×D4—252no—
884C2×C3×D4—254no—
885C2×C3×D4—254no—
886C2×C3×D4—251no—
887C2×C3×D4D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
888C22×C3×C4—251no—
889C22×C3×C4—254no—
890C22×C3×C4—251no—
891C22×C3×C4—254no—
892C22×C3×C4—251no—
893C22×C3×C4—252no—
894C22×C3×C4—1004no—
895C2×#67—58no—
896C2×#67—258no—
897C2×#67—258no—
898C2×#67—254no—
899C2×#67—258no—
900C2×#67—258no—
901C22×Dic3—254no—
902C22×Dic3—254no—
903C22×Dic3—254no—
904#237—58no—
905#237—258no—
906#237—2516no—
907D3×D4—58no—
908D3×D4—258no—
909D3×D4—2516no—
910#235—54no—
911#235—254no—
912#235—254no—
913#235—254no—
914C2×D12—252no—
915C2×C4×D3—254no—
916C2×C4×D3—254no—
917C2×C4×D3—254no—
918C2×C4×D3—258no—
919C2×C4×D3—1008no—
920C2×Dic6—252no—
921C3×C4⋊C4—254no—
922C3×C22⋊C4—258no—
923C3×C42—252no—
924C3×C42—252no—
925#217—258no—
926#217—254no—
927(C2×D3)⋊C4—254no—
928(C2×D3)⋊C4—254no—
929(C2×D3)⋊C4—258no—
930C4⋊Dic3—252no—
931C4⋊Dic3—252no—
932Dic3⋊C4—254no—
933Dic3⋊C4—254no—
934Dic3⋊C4—258no—
935C4×Dic3—254no—
936C4×Dic3—254no—
937C4×Dic3—258no—
938C4×Dic3—254no—
939C23×C5—24no—
940C23×C5—158no—
941C23×C5C2×D3×AGL(1,𝔽5)14yescomplemented
942C22×D5—38no—
943C22×D5—58no—
944C22×D5—52no—
945C22×D5—54no—
946C22×D5—58no—
947C22×D5—102no—
948C22×D5—104no—
949C22×D5—108no—
950C22×D5—108no—
951C22×D5—158no—
952C22×D5—1516no—
953C22×D5—204no—
954C22×D5—204no—
955C22×D5—208no—
956C22×D5—208no—
957C22×D5—608no—
958C22×D5—608no—
959C2×AGL(1,𝔽5)—52no—
960C2×AGL(1,𝔽5)—54no—
961C2×AGL(1,𝔽5)—52no—
962C2×AGL(1,𝔽5)—58no—
963C2×AGL(1,𝔽5)—102no—
964C2×AGL(1,𝔽5)—102no—
965C2×AGL(1,𝔽5)—104no—
966C2×AGL(1,𝔽5)—108no—
967C2×AGL(1,𝔽5)—104no—
968C2×AGL(1,𝔽5)—1016no—
969C2×AGL(1,𝔽5)—108no—
970C2×AGL(1,𝔽5)—158no—
971C2×AGL(1,𝔽5)—158no—
972C2×AGL(1,𝔽5)—2016no—
973C2×AGL(1,𝔽5)—202no—
974C2×AGL(1,𝔽5)—208no—
975C2×AGL(1,𝔽5)—204no—
976C2×AGL(1,𝔽5)—2016no—
977C2×AGL(1,𝔽5)—204no—
978C2×AGL(1,𝔽5)—208no—
979C2×AGL(1,𝔽5)—3016no—
980C2×AGL(1,𝔽5)—608no—
981C2×AGL(1,𝔽5)—6016no—
982C2×AGL(1,𝔽5)—608no—
983C2×AGL(1,𝔽5)—608no—
984C5×Q8—154no—
985C5×D4—28no—
986C5×D4—1516no—
987C5×D4—158no—
988C5×D4—154no—
989C5×D4C2×D3×AGL(1,𝔽5)18yescomplemented
990C2×C4×C5—22no—
991C2×C4×C5—158no—
992C2×C4×C5—158no—
993C2×C4×C5C2×D3×AGL(1,𝔽5)12yescomplemented
994C22⋊D5—38no—
995C22⋊D5—316no—
996C22⋊D5—516no—
997C22⋊D5—1016no—
998C22⋊D5—158no—
999C22⋊D5—1516no—
1000C22⋊D5—158no—
1001C2×Dic5—38no—
1002C2×Dic5—52no—
1003C2×Dic5—102no—
1004C2×Dic5—158no—
1005D20—34no—
1006D20—58no—
1007D20—108no—
1008D20—158no—
1009D20—1516no—
1010C4×D5—38no—
1011C4×D5—54no—
1012C4×D5—54no—
1013C4×D5—104no—
1014C4×D5—104no—
1015C4×D5—158no—
1016C4×D5—1516no—
1017C4×D5—158no—
1018Dic10—34no—
1019Dic10—158no—
1020H(5,𝔽2)—152no—
1021H(5,𝔽2)—754no—
1022H(5,𝔽2)—758no—
1023H(5,𝔽2)—752no—
1024C2×#41—752no—
1025C2×#41—754no—
1026C22×D4—251no—
1027C22×D4—754no—
1028C22×D4—754no—
1029C23×C4—252no—
1030C23×C4—754no—
1031C4×Q8—752no—
1032C4×Q8—752no—
1033C4×Q8—754no—
1034C4×D4—254no—
1035C4×D4—254no—
1036C4×D4—752no—
1037C4×D4—752no—
1038C4×D4—758no—
1039C4×D4—758no—
1040C4×D4—754no—
1041C4×D4—754no—
1042C4×D4—758no—
1043C4×D4—758no—
1044C4×D4—758no—
1045C4×D4—754no—
1046C4×D4—754no—
1047C4×D4—754no—
1048#117—754no—
1049#117—758no—
1050#117—754no—
1051#117—752no—
1052C2×C4⋊C4—251no—
1053C2×C4⋊C4—754no—
1054C2×C4⋊C4—754no—
1055C2×C22⋊C4—252no—
1056C2×C22⋊C4—758no—
1057C2×C22⋊C4—754no—
1058C2×C22⋊C4—754no—
1059C2×C42—251no—
1060C2×C42—754no—
1061C2×C42—754no—
1062C2×C3×C5—24no—
1063C2×C3×C5—22no—
1064C2×C3×C5—28no—
1065C2×C3×C5—22no—
1066C2×C3×C5—48no—
1067C2×C3×C5C24×AGL(1,𝔽5)12yes—
1068D15—28no—
1069C3×D5—52no—
1070C3×D5—52no—
1071C3×D5—102no—
1072C3×D5—102no—
1073C3×D5—104no—
1074C3×D5—108no—
1075C3×D5—102no—
1076C3×D5—208no—
1077C5×D3—108no—
1078C52C4×#100411yescharacteristic, complemented, Sylow
1079C23×C3—251no—
1080C23×C3—254no—
1081C23×C3—252no—
1082C23×C3—254no—
1083C23×C3—1002no—
1084C23×C3—1002no—
1085C23×C3C2×D5⋊AGL(1,𝔽5)12yescomplemented
1086C22×D3—58no—
1087C22×D3—254no—
1088C22×D3—258no—
1089C22×D3—1004no—
1090C22×D3—1004no—
1091C3×D4—258no—
1092C3×D4—254no—
1093C3×D4C2×D5⋊AGL(1,𝔽5)14yescomplemented
1094C2×C3×C4—251no—
1095C2×C3×C4—251no—
1096C2×C3×C4—252no—
1097C2×C3×C4—252no—
1098C2×C3×C4—252no—
1099C2×C3×C4—254no—
1100C2×C3×C4—251no—
1101C2×C3×C4—502no—
1102C2×C3×C4—508no—
1103C2×C3×C4—1001no—
1104C2×C3×C4—1004no—
1105C2×C3×C4—1002no—
1106C2×C3×C4C2×D5⋊AGL(1,𝔽5)11yescharacteristic, complemented
1107#67—58no—
1108#67—516no—
1109#67—258no—
1110#67—2516no—
1111C2×Dic3—58no—
1112C2×Dic3—254no—
1113C2×Dic3—258no—
1114C2×Dic3—254no—
1115C2×Dic3—254no—
1116C2×Dic3—1004no—
1117C2×Dic3—1004no—
1118D12—54no—
1119D12—254no—
1120C4×D3—58no—
1121C4×D3—258no—
1122C4×D3—508no—
1123C4×D3—1004no—
1124C4×D3—1008no—
1125Dic6—54no—
1126Dic6—254no—
1127C22×C5—22no—
1128C22×C5—28no—
1129C22×C5—44no—
1130C22×C5—48no—
1131C22×C5—158no—
1132C22×C5—608no—
1133C22×C5C22×D3×AGL(1,𝔽5)18yes—
1134C22×C5C22×D3×AGL(1,𝔽5)12yes—
1135C2×D5—38no—
1136C2×D5—52no—
1137C2×D5—52no—
1138C2×D5—58no—
1139C2×D5—102no—
1140C2×D5—102no—
1141C2×D5—108no—
1142C2×D5—102no—
1143C2×D5—108no—
1144C2×D5—102no—
1145C2×D5—108no—
1146C2×D5—104no—
1147C2×D5—104no—
1148C2×D5—128no—
1149C2×D5—208no—
1150C2×D5—208no—
1151C2×D5—208no—
1152C2×D5—204no—
1153C2×D5—2016no—
1154C2×D5—208no—
1155C2×D5—308no—
1156C2×D5—308no—
1157C2×D5—6016no—
1158AGL(1,𝔽5)—54no—
1159AGL(1,𝔽5)—104no—
1160AGL(1,𝔽5)—102no—
1161AGL(1,𝔽5)—108no—
1162AGL(1,𝔽5)—104no—
1163AGL(1,𝔽5)—104no—
1164AGL(1,𝔽5)—204no—
1165AGL(1,𝔽5)—208no—
1166AGL(1,𝔽5)—308no—
1167AGL(1,𝔽5)—308no—
1168C4×C5—24no—
1169C4×C5—158no—
1170C4×C5C22×D3×AGL(1,𝔽5)14yes—
1171Dic5—38no—
1172Dic5—54no—
1173Dic5—104no—
1174C24—252no—
1175C24—754no—
1176#41—158no—
1177#41—154no—
1178#41—754no—
1179#41—7516no—
1180#41—758no—
1181#41—754no—
1182#41—754no—
1183C2×Q8—752no—
1184C2×D4—158no—
1185C2×D4—158no—
1186C2×D4—252no—
1187C2×D4—254no—
1188C2×D4—254no—
1189C2×D4—251no—
1190C2×D4—758no—
1191C2×D4—758no—
1192C2×D4—752no—
1193C2×D4—758no—
1194C2×D4—754no—
1195C2×D4—758no—
1196C2×D4—758no—
1197C2×D4—7516no—
1198C2×D4#1059718211yescharacteristic, complemented
1199C22×C4—251no—
1200C22×C4—251no—
1201C22×C4—254no—
1202C22×C4—251no—
1203C22×C4—252no—
1204C22×C4—254no—
1205C22×C4—3008no—
1206C22×C4—754no—
1207C22×C4—754no—
1208C22×C4—754no—
1209C22×C4—758no—
1210C22×C4—754no—
1211C22×C4—754no—
1212C22×C4—754no—
1213C22×C4—1004no—
1214C4⋊C4—254no—
1215C4⋊C4—754no—
1216C4⋊C4—758no—
1217C4⋊C4—752no—
1218C4⋊C4—754no—
1219C4⋊C4—752no—
1220C22⋊C4—258no—
1221C22⋊C4—754no—
1222C22⋊C4—754no—
1223C22⋊C4—758no—
1224C22⋊C4—758no—
1225C22⋊C4—754no—
1226C42—252no—
1227C42—252no—
1228C42—754no—
1229C42—754no—
1230C42—754no—
1231C42—758no—
1232C3×C5—22no—
1233C3×C5AGL(1,𝔽5)×H(5,𝔽2)12yescomplemented
1234C22×C3—42no—
1235C22×C3—251no—
1236C22×C3—254no—
1237C22×C3—251no—
1238C22×C3—501no—
1239C22×C3—501no—
1240C22×C3—504no—
1241C22×C3—504no—
1242C22×C3—1004no—
1243C22×C3—1002no—
1244C22×C3C22×D5⋊AGL(1,𝔽5)14yes—
1245C22×C3C22×D5⋊AGL(1,𝔽5)11yescharacteristic
1246C2×D3—58no—
1247C2×D3—208no—
1248C2×D3—504no—
1249C2×D3—504no—
1250C2×D3—1008no—
1251C3×C4—252no—
1252C3×C4—252no—
1253C3×C4—501no—
1254C3×C4—504no—
1255C3×C4—502no—
1256C3×C4C22×D5⋊AGL(1,𝔽5)12yes—
1257Dic3—58no—
1258Dic3—504no—
1259Dic3—504no—
1260C2×C5—24no—
1261C2×C5—28no—
1262C2×C5—22no—
1263C2×C5—22no—
1264C2×C5—48no—
1265C2×C5—308no—
1266C2×C5C23×D3×AGL(1,𝔽5)12yes—
1267D5—52no—
1268D5—52no—
1269D5—68no—
1270D5—102no—
1271D5—102no—
1272D5—104no—
1273D5—102no—
1274D5—108no—
1275D5—208no—
1276C23—158no—
1277C23—254no—
1278C23—251no—
1279C23—254no—
1280C23—252no—
1281C23—3004no—
1282C23—3004no—
1283C23—758no—
1284C23—754no—
1285C23—1002no—
1286C23—1002no—
1287C23C2×#1059718212yescomplemented
1288Q8—154no—
1289Q8—754no—
1290D4—1516no—
1291D4—158no—
1292D4—154no—
1293D4—258no—
1294D4—254no—
1295D4—758no—
1296D4—7516no—
1297D4—754no—
1298D4C2×#1059718214yescomplemented
1299C2×C4—158no—
1300C2×C4—158no—
1301C2×C4—251no—
1302C2×C4—251no—
1303C2×C4—252no—
1304C2×C4—252no—
1305C2×C4—252no—
1306C2×C4—251no—
1307C2×C4—254no—
1308C2×C4—3008no—
1309C2×C4—3004no—
1310C2×C4—3004no—
1311C2×C4—3004no—
1312C2×C4—508no—
1313C2×C4—502no—
1314C2×C4—754no—
1315C2×C4—758no—
1316C2×C4—758no—
1317C2×C4—754no—
1318C2×C4—754no—
1319C2×C4—1002no—
1320C2×C4—1004no—
1321C2×C4—1001no—
1322C2×C4—1508no—
1323C2×C4C2×#1059718211yescharacteristic, complemented
1324C2×C3—24no—
1325C2×C3—21no—
1326C2×C3—251no—
1327C2×C3—251no—
1328C2×C3—504no—
1329C2×C3—501no—
1330C2×C3C23×D5⋊AGL(1,𝔽5)11yescharacteristic
1331D3—108no—
1332C5—22no—
1333C5AGL(1,𝔽5)×#100412yescomplemented
1334C22—42no—
1335C22—158no—
1336C22—251no—
1337C22—251no—
1338C22—254no—
1339C22—3008no—
1340C22—504no—
1341C22—504no—
1342C22—501no—
1343C22—501no—
1344C22—608no—
1345C22—1002no—
1346C22—1004no—
1347C22—1504no—
1348C22—1504no—
1349C22C22×#1059718214yes—
1350C22C22×#1059718211yescharacteristic
1351C4—158no—
1352C4—252no—
1353C4—252no—
1354C4—504no—
1355C4—502no—
1356C4—501no—
1357C4—1504no—
1358C4—1504no—
1359C4C22×#1059718212yes—
1360C3#7221341211yescharacteristic, complemented, Sylow
1361C2—21no—
1362C2—24no—
1363C2—251no—
1364C2—251no—
1365C2—308no—
1366C2—504no—
1367C2—501no—
1368C2C23×#1059718211yescharacteristic
subgroupG/H
center, FrattiniC2C23×#10597182
commutator, socleC2×C3×C52C24×C4
FittingC2×C3×C52×D4C2×C4
prime radical#72260276C2
cosocleC2×C3×C5⋊D5C25
hypercenterC2×D4#10597182
hypocenterC3×C52C4×H(5,𝔽2)
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #72260289C2semidirect
2. #72260285C2semidirect
3. #72260284C2semidirect
4. #72260282C2semidirect
5. #72260278C2semidirect
7. #72260273C4semidirect
8. #72260272C4semidirect
9. #72260270C4semidirect
10. C5×#92095C4semidirect
11. D4×#10597182C2semidirect
12. #72259540C2semidirect
13. #72231041C22semidirect
14. #72231036C22semidirect
15. C2×#72224585C2semidirect
16. #72231004C22semidirect
17. #72230992C22semidirect
18. D4×C3⋊#1044C22semidirect
19. D4×C3⋊#1044C22semidirect
20. #72230973C22semidirect
21. #72230959C22semidirect
23. #72230748C22semidirect
24. #72230748C22semidirect
26. #72230588C2semidirect
27. #72230585C22semidirect
28. C4×#10597182C22semidirect
29. #72230553C22semidirect
30. #72230553C22semidirect
31. #72230539C22semidirect
32. #72230539C22semidirect
33. C2×#11925354C22semidirect
34. C2×#11925356C22semidirect
35. C2×#11925540C22semidirect
36. C2×#11925355C22semidirect
38. C22×#10597182C22semidirect
39. C2×C3×D4×#1043C2semidirect
40. C2×C3×C22⋊#1043C22semidirect
41. C3×D4×#1043C22semidirect
42. C3×D4×#1043C22semidirect
43. #72229444C22semidirect
45. C23×C3×#1043C22semidirect
46. C2×C3×C4⋊#1043C22semidirect
48. C2×C3×C4×#1043C22semidirect
49. #72224585C22semidirect
50. #72224585C22semidirect
51. #72224585C22semidirect
52. #72224585C22semidirect
53. #72224585C22semidirect
58. C2×D4×#1043D3semidirect
81. C2×C3×C52×D4C2×C4semidirect
82. C2×C5×#1220C2×C4semidirect
83. C5×#6819C2×C4semidirect
84. C5×D4×D15C2×C4semidirect
85. C5×#6817C2×C4semidirect
86. C2×C3×C22⋊(C5⋊D5)C2×C4semidirect
87. C3×D4×C5⋊D5C2×C4semidirect
89. C2×C3×C4⋊(C5⋊D5)C2×C4semidirect
91. #11925664C2×C4semidirect
92. #11925664C2×C4semidirect
95. #11925663C2×C4semidirect
96. C2×#10597127C2×C4semidirect
98. #11925658C2×C4semidirect
99. #11925657C2×C4semidirect
101. #11925654C2×C4semidirect
103. #11925652C2×C4semidirect
104. #11925651C2×C4semidirect
106. #11925648C2×C4semidirect
137. C23×#1043C2×D3semidirect
152. C2×C22⋊#1043C2×D3semidirect
153. D4×#1043C2×D3semidirect
154. D4×#1043C2×D3semidirect
155. C2×C4⋊#1043C2×D3semidirect
156. C2×C4×#1043C2×D3semidirect
180. C23×C3×C52C22×C4semidirect
181. C22×C5×D15C22×C4semidirect
184. C22×C3×C5⋊D5C22×C4semidirect
185. C22×C3×C5⋊D5C22×C4semidirect
190. C2×D15⋊D5C22×C4semidirect
208. C3×C52×D4C22×C4semidirect
209. C2×C3×C4×C52C22×C4semidirect
210. C5×#1220C22×C4semidirect
211. C5×#1220C22×C4semidirect
212. C2×C5×Dic15C22×C4semidirect
213. C5×D60C22×C4semidirect
214. C4×C5×D15C22×C4semidirect
215. C5×Dic30C22×C4semidirect
216. C3×C22⋊(C5⋊D5)C22×C4semidirect
217. C2×C3×#1039C22×C4semidirect
218. C3×C4⋊(C5⋊D5)C22×C4semidirect
219. C3×C4×C5⋊D5C22×C4semidirect
221. #10597129C22×C4semidirect
222. #10597128C22×C4semidirect
223. #10597127C22×C4semidirect
224. #10597127C22×C4semidirect
225. #10597126C22×C4semidirect
227. #10597125C22×C4semidirect
231. #92095AGL(1,𝔽5)semidirect
293. C2×C52×D4C4×D3semidirect
294. C2×C22⋊(C5⋊D5)C4×D3semidirect
295. D4×C5⋊D5C4×D3semidirect
297. C2×C4⋊(C5⋊D5)C4×D3semidirect
372. C3×#1043H(5,𝔽2)semidirect
398. C2×C3×C5×D4C2×AGL(1,𝔽5)semidirect
399. C2×#1220C2×AGL(1,𝔽5)semidirect
400. #6819C2×AGL(1,𝔽5)semidirect
401. D4×D15C2×AGL(1,𝔽5)semidirect
402. #6817C2×AGL(1,𝔽5)semidirect
461. C23×C52C2×C4×D3semidirect
464. C22×C5⋊D5C2×C4×D3semidirect
465. C22×C5⋊D5C2×C4×D3semidirect
489. C52×D4C2×C4×D3semidirect
490. C2×C4×C52C2×C4×D3semidirect
491. C22⋊(C5⋊D5)C2×C4×D3semidirect
492. C2×#1039C2×C4×D3semidirect
493. C4⋊(C5⋊D5)C2×C4×D3semidirect
494. C4×C5⋊D5C2×C4×D3semidirect
581. C23×C3×C5C22×AGL(1,𝔽5)semidirect
582. C22×D15C22×AGL(1,𝔽5)semidirect
626. C3×C5×D4C22×AGL(1,𝔽5)semidirect
628. C2×C3×C4×C5C22×AGL(1,𝔽5)semidirect
629. #1220C22×AGL(1,𝔽5)semidirect
630. #1220C22×AGL(1,𝔽5)semidirect
631. C2×Dic15C22×AGL(1,𝔽5)semidirect
632. D60C22×AGL(1,𝔽5)semidirect
633. C4×D15C22×AGL(1,𝔽5)semidirect
634. Dic30C22×AGL(1,𝔽5)semidirect
683. #1043#1004semidirect
755. C2×C5×D4D3×AGL(1,𝔽5)semidirect
814. C3×C52C4×H(5,𝔽2)semidirect
887. C2×C3×D4D5⋊AGL(1,𝔽5)semidirect
941. C23×C5C2×D3×AGL(1,𝔽5)semidirect
989. C5×D4C2×D3×AGL(1,𝔽5)semidirect
993. C2×C4×C5C2×D3×AGL(1,𝔽5)semidirect
1078. C52C4×#1004semidirect
1085. C23×C3C2×D5⋊AGL(1,𝔽5)semidirect
1093. C3×D4C2×D5⋊AGL(1,𝔽5)semidirect
1106. C2×C3×C4C2×D5⋊AGL(1,𝔽5)semidirect
1198. C2×D4#10597182semidirect
1233. C3×C5AGL(1,𝔽5)×H(5,𝔽2)semidirect
1287. C23C2×#10597182semidirect
1298. D4C2×#10597182semidirect
1323. C2×C4C2×#10597182semidirect
1333. C5AGL(1,𝔽5)×#1004semidirect
1360. C3#72213412semidirect

Maximal subgroups

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

subgroupindex
#722602892
#722602852
#722602842
#722602822
#722602782
#722602762
D4×#105971822
#722595402
C2×#722245852
#722305882
C2×C3×D4×#10432
#722134123
AGL(1,𝔽5)×#10045