Finite Group Databasebeta

← #14319792

Subgroups — #14319792

Order 1920.

1256 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic
3D5×#887C211yesmaximal, characteristic
4C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
5C3×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic
6C4×Dic3⋊AGL(1,𝔽5)C212yesmaximal
7Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
8#11751833C212yesmaximal
9#11751832C212yesmaximal
10AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal
11#11751748C211yesmaximal, characteristic
12#10617208—31nomaximal, Hall
13C2×D5×Dic6C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2212yes—
16C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
18C2×C3×C4×AGL(1,𝔽5)C2212yes—
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3×AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25ΓL(1,𝔽16)⋊Q8C418yescomplemented
26AGL(1,𝔽5)×Dic6C418yescomplemented
27#91776C411yescharacteristic, complemented
28C5×#887C411yescharacteristic, complemented
29C3×D5×C4⋊C4C2211yescharacteristic
30D5×Dic3⋊C4C2212yes—
31C4×D5×Dic3C2211yescharacteristic
32C4×D5×Dic3C2212yes—
33#91344C411yescharacteristic, complemented
34#91340C411yescharacteristic, complemented
35#91325C412yescomplemented
36#91324C412yescomplemented
37#91235C2212yes—
38C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73616—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C2×Q8×AGL(1,𝔽5)—31no—
47C4×Q8×D5—31no—
48C4⋊C4×AGL(1,𝔽5)—31no—
49C4⋊C4×AGL(1,𝔽5)—32no—
50C4⋊C4×AGL(1,𝔽5)—32no—
51C4⋊C4×AGL(1,𝔽5)D311yescharacteristic
52C4×C4⋊AGL(1,𝔽5)—31no—
53C4×C4⋊AGL(1,𝔽5)—32no—
54#65686—32no—
55#65686—31no—
56C22×ΓL(1,𝔽16)C2312yes—
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C2×Dic30C2×C411yescharacteristic
63C2×C5×Dic6C2×C411yescharacteristic
64C2×C3×C4×D5C2312yes—
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1204C2×C412yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2312yes—
70D5×Dic6C2×C414yes—
71D5×Dic6C2×C414yes—
72C4⋊ΓL(1,𝔽16)C2×C414yes—
73C4×ΓL(1,𝔽16)—42no—
74C4×ΓL(1,𝔽16)C2×C414yes—
75C3×C4⋊AGL(1,𝔽5)C2×C414yes—
76C3×C4×AGL(1,𝔽5)—42no—
77C3×C4×AGL(1,𝔽5)C2×C414yes—
78Dic3⋊AGL(1,𝔽5)C2×C418yes—
79Dic3⋊AGL(1,𝔽5)C2×C418yes—
80Dic3×AGL(1,𝔽5)—42no—
81Dic3×AGL(1,𝔽5)C2×C418yes—
82Dic3×AGL(1,𝔽5)C2×C418yes—
83C3×C5×C4⋊C4C2×C411yescharacteristic
84#6712C2×C412yes—
85C4×Dic15C2×C412yes—
86C4×Dic15C2×C411yescharacteristic
87C5×Dic3⋊C4C2×C412yes—
88C4×C5×Dic3C2×C412yes—
89C4×C5×Dic3C2×C411yescharacteristic
90C3×C4⋊Dic5C2×C411yescharacteristic
91C3×#683C2×C412yes—
92Dic3⋊Dic5C2×C412yes—
93#6669C2×C412yes—
94Dic3×Dic5C2×C411yescharacteristic
95Dic3×Dic5C2×C412yes—
96Dic3×Dic5C2×C411yescharacteristic
97Dic3×Dic5C2×C412yes—
98C2×#887—51no—
99C2×#887—51no—
100C2×C4×Dic6—51no—
101C3×C4×C4⋊C4—51no—
102Dic3×C4⋊C4—51no—
103Dic3×C4⋊C4—51no—
104#4932—51no—
105C4×Dic3⋊C4—52no—
106C4×Dic3⋊C4—52no—
107#4649—52no—
108#4648—52no—
109C2×Q8×D5—31no—
110Q8×AGL(1,𝔽5)—38no—
111Q8×AGL(1,𝔽5)—38no—
112C2×C4⋊AGL(1,𝔽5)—32no—
113C2×C4⋊AGL(1,𝔽5)—32no—
114C2×C4⋊AGL(1,𝔽5)—31no—
115C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
116C2×C4×AGL(1,𝔽5)—32no—
117C2×C4×AGL(1,𝔽5)—32no—
118C2×C4×AGL(1,𝔽5)—31no—
119C2×C4×AGL(1,𝔽5)—32no—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)C2×D312yes—
122C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
123C4×C5×Q8—31no—
124Q8×Dic5—31no—
125D5×C4⋊C4—32no—
126D5×C4⋊C4C2×D311yescharacteristic
127#4033—31no—
128#4033—32no—
129C42×D5—32no—
130C42×D5—31no—
131C4×Dic10—31no—
132C4×Dic10—32no—
133(C2×AGL(1,𝔽5))⋊C4—31no—
134(C2×AGL(1,𝔽5))⋊C4—32no—
135(C2×AGL(1,𝔽5))⋊C4—31no—
136(C2×AGL(1,𝔽5))⋊C4—31no—
137(C2×AGL(1,𝔽5))⋊C4—31no—
138(C2×AGL(1,𝔽5))⋊C4—32no—
139(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
140#2276—151noSylow
141C22×C3×D5C2411yescharacteristic
142C2×ΓL(1,𝔽16)—22no—
143C2×ΓL(1,𝔽16)—21no—
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)—21no—
146C2×ΓL(1,𝔽16)—22no—
147C2×ΓL(1,𝔽16)—21no—
148C2×ΓL(1,𝔽16)C22×C412yes—
149C2×ΓL(1,𝔽16)C22×C414yes—
150C2×ΓL(1,𝔽16)C22×C412yes—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—21no—
153C2×C3×AGL(1,𝔽5)—21no—
154C2×C3×AGL(1,𝔽5)—21no—
155C2×C3×AGL(1,𝔽5)—21no—
156C2×C3×AGL(1,𝔽5)—22no—
157C2×C3×AGL(1,𝔽5)C22×C412yes—
158C2×C3×AGL(1,𝔽5)C22×C414yes—
159C2×C3×AGL(1,𝔽5)C22×C412yes—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C22×C411yescharacteristic
162C2×Dic15C22×C411yescharacteristic
163C2×Dic15C22×C411yescharacteristic
164C2×Dic15C22×C412yes—
165Dic30C4214yescomplemented
166C2×C5×Dic3C22×C411yescharacteristic
167C2×C5×Dic3C22×C411yescharacteristic
168C2×C5×Dic3C22×C412yes—
169C5×Dic6C4214yescomplemented
170C2×C3×Dic5C22×C412yes—
171C2×C3×Dic5C22×C411yescharacteristic
172C3×C4×D5—22no—
173C3×C4×D5—22no—
174C3×C4×D5C22×C412yes—
175C3×C4×D5C22×C412yes—
176#1204C4218yescomplemented
177D5×Dic3—21no—
178D5×Dic3—21no—
179D5×Dic3—21no—
180D5×Dic3—21no—
181D5×Dic3C22×C414yes—
182D5×Dic3C22×C414yes—
183C22×Dic6—51no—
184C2×C3×C4⋊C4—51no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C42—51no—
187C2×C3×C42—52no—
188C2×C4⋊Dic3—51no—
189C2×Dic3⋊C4—52no—
190C2×Dic3⋊C4—52no—
191C2×Dic3⋊C4—52no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—52no—
194C2×C4×Dic3—51no—
195C2×C4×Dic3—52no—
196C2×C4×Dic3—51no—
197C2×C4×Dic3—52no—
198C2×C4×Dic3—52no—
199#887—58no—
200#887—51no—
201#887—51no—
202#887—52no—
203#887—52no—
204#887—51no—
205#887AGL(1,𝔽5)11yescharacteristic, complemented
206C4×Dic6—58no—
207C3×#95—52no—
208C3⋊#95—51no—
209C3⋊#95—52no—
210C3⋊#95—51no—
211C3⋊#95—51no—
212C3⋊#95—51no—
213C3⋊#95—52no—
214C22×AGL(1,𝔽5)—32no—
215C22×AGL(1,𝔽5)—31no—
216C22×AGL(1,𝔽5)—31no—
217C22×AGL(1,𝔽5)C22×D312yes—
218C22×AGL(1,𝔽5)C22×D311yescharacteristic
219C22×AGL(1,𝔽5)C22×D311yescharacteristic
220C2×C5×Q8—31no—
221Q8×D5—34no—
222Q8×D5—34no—
223C2×C4×D5—32no—
224C2×C4×D5—31no—
225C2×C4×D5—31no—
226C2×C4×D5C22×D312yes—
227C2×C4×D5C22×D311yescharacteristic
228C2×Dic10—31no—
229C2×Dic10—32no—
230C4⋊AGL(1,𝔽5)—38no—
231C4⋊AGL(1,𝔽5)—38no—
232C4⋊AGL(1,𝔽5)—34no—
233C4⋊AGL(1,𝔽5)C4×D314yes—
234C4×AGL(1,𝔽5)—38no—
235C4×AGL(1,𝔽5)—38no—
236C4×AGL(1,𝔽5)—34no—
237C4×AGL(1,𝔽5)—42no—
238C4×AGL(1,𝔽5)—122no—
239C4×AGL(1,𝔽5)—122no—
240C4×AGL(1,𝔽5)C4×D314yes—
241C5×C4⋊C4—32no—
242C5×C4⋊C4C4×D311yescharacteristic
243C42×C5—32no—
244C42×C5—31no—
245C4⋊Dic5—32no—
246C4⋊Dic5C4×D311yescharacteristic
247#683—32no—
248#683—32no—
249#683C4×D312yes—
250C4×Dic5—32no—
251C4×Dic5—31no—
252C4×Dic5—32no—
253C4×Dic5—31no—
254C4×Dic5—31no—
255C4×Dic5—32no—
256C2×C4×Q8—151no—
257C2×C4×Q8—151no—
258C2×C4×Q8—151no—
259C4×C4⋊C4—51no—
260C4×C4⋊C4—152no—
261C4×C4⋊C4—152no—
262C4×C4⋊C4—152no—
263C4×C4⋊C4—151no—
264C4×C4⋊C4—151no—
265#376—152no—
266#376—151no—
267C22×C3×C5C23×C411yescharacteristic
268C2×C3×D5C23×C411yescharacteristic
269C2×C3×D5C23×C411yescharacteristic
270C2×C3×D5H(5,𝔽2)11yescharacteristic
271C2×C3×D52−1+411yescharacteristic
272C2×C3×D52−1+411yescharacteristic
273C2×C3×D52−1+411yescharacteristic
274ΓL(1,𝔽16)—22no—
275ΓL(1,𝔽16)—24no—
276ΓL(1,𝔽16)—22no—
277C3×AGL(1,𝔽5)—22no—
278C3×AGL(1,𝔽5)—22no—
279C3×AGL(1,𝔽5)—24no—
280C3×C4×C5—22no—
281C3×C4×C5C2×C4212yes—
282Dic15—21no—
283Dic15—21no—
284Dic15C2×C4214yes—
285C3×Dic5—22no—
286C3×Dic5C2×C4212yes—
287C5×Dic3—21no—
288C5×Dic3—21no—
289C5×Dic3C2×C4214yes—
290C22×C3×C4—51no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×Dic3—52no—
296C22×Dic3—51no—
297C22×Dic3—51no—
298C22×Dic3—52no—
299C22×Dic3—51no—
300C22×Dic3—51no—
301C2×Dic6—51no—
302C2×Dic6—52no—
303C2×Dic6—54no—
304C2×Dic6—54no—
305C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
306C3×C4⋊C4—54no—
307C3×C4⋊C4—52no—
308C3×C4⋊C4—51no—
309C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
310C3×C42—54no—
311C3×C42—202no—
312C4⋊Dic3—54no—
313Dic3⋊C4—58no—
314Dic3⋊C4—58no—
315Dic3⋊C4—52no—
316Dic3⋊C4—52no—
317Dic3⋊C4—52no—
318Dic3⋊C4C2×AGL(1,𝔽5)12yes—
319C4×Dic3—58no—
320C4×Dic3—58no—
321C4×Dic3—54no—
322C4×Dic3—52no—
323C4×Dic3—51no—
324C4×Dic3—52no—
325C4×Dic3—51no—
326C4×Dic3—52no—
327C4×Dic3—51no—
328C4×Dic3—202no—
329C4×Dic3—202no—
330C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
331C4×Dic3C2×AGL(1,𝔽5)12yes—
332C22×D5C23×D311yescharacteristic
333C2×AGL(1,𝔽5)—21no—
334C2×AGL(1,𝔽5)—22no—
335C2×AGL(1,𝔽5)—21no—
336C2×AGL(1,𝔽5)—21no—
337C2×AGL(1,𝔽5)—21no—
338C2×AGL(1,𝔽5)—22no—
339C2×AGL(1,𝔽5)—32no—
340C2×AGL(1,𝔽5)—34no—
341C2×AGL(1,𝔽5)—32no—
342C2×AGL(1,𝔽5)—62no—
343C2×AGL(1,𝔽5)—61no—
344C2×AGL(1,𝔽5)—62no—
345C2×AGL(1,𝔽5)—61no—
346C2×AGL(1,𝔽5)—61no—
347C2×AGL(1,𝔽5)—61no—
348C2×AGL(1,𝔽5)C2×C4×D312yes—
349C2×AGL(1,𝔽5)C2×C4×D314yes—
350C2×AGL(1,𝔽5)C2×C4×D312yes—
351C5×Q8—34no—
352C2×C4×C5—32no—
353C2×C4×C5—31no—
354C2×C4×C5—31no—
355C2×C4×C5C2×C4×D312yes—
356C2×C4×C5C2×C4×D311yescharacteristic
357C2×Dic5—32no—
358C2×Dic5—31no—
359C2×Dic5—31no—
360C2×Dic5C2×C4×D312yes—
361C2×Dic5C2×C4×D311yescharacteristic
362C4×D5—22no—
363C4×D5—22no—
364C4×D5—34no—
365C4×D5—34no—
366C4×D5—61no—
367C4×D5—61no—
368C4×D5—61no—
369C4×D5—61no—
370C4×D5C2×C4×D312yes—
371C4×D5C2×C4×D312yes—
372Dic10—34no—
373Dic10—38no—
374C22×Q8—151no—
375C4×Q8—31no—
376C4×Q8—152no—
377C4×Q8—151no—
378C4×Q8—158no—
379C4×Q8—152no—
380C4×Q8—151no—
381C4×Q8—158no—
382C4×Q8—151no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—152no—
388C2×C4⋊C4—151no—
389C2×C42—51no—
390C2×C42—52no—
391C2×C42—151no—
392C2×C42—152no—
393C2×C42—151no—
394C2×C42—152no—
395C2×C42—152no—
396C2×C42—152no—
397C2×C42—152no—
398#95—52no—
399#95—151no—
400#95—151no—
401#95—152no—
402#95—151no—
403#95—151no—
404#95—152no—
405C2×C3×C5C22×C4211yescharacteristic
406C2×C3×C5#51911yescharacteristic
407C2×C3×C5#52011yescharacteristic
408C3×D5#51911yescharacteristic
409C3×D5#51911yescharacteristic
410C3×D5#52011yescharacteristic
411C3×D5#52011yescharacteristic
412C23×C3—51no—
413C2×C3×C4—51no—
414C2×C3×C4—52no—
415C2×C3×C4—52no—
416C2×C3×C4—52no—
417C2×C3×C4—54no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—102no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—101no—
426C2×C3×C4—102no—
427C2×C3×C4—101no—
428C2×C3×C4C22×AGL(1,𝔽5)12yes—
429C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
430C2×Dic3—52no—
431C2×Dic3—54no—
432C2×Dic3—54no—
433C2×Dic3—52no—
434C2×Dic3—52no—
435C2×Dic3—54no—
436C2×Dic3—51no—
437C2×Dic3—51no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3—101no—
441C2×Dic3—101no—
442C2×Dic3—102no—
443C2×Dic3—101no—
444C2×Dic3—101no—
445C2×Dic3—102no—
446C2×Dic3—101no—
447C2×Dic3—101no—
448C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
449C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
450C2×Dic3C22×AGL(1,𝔽5)12yes—
451Dic6—54no—
452Dic6—58no—
453Dic6C4×AGL(1,𝔽5)14yescomplemented
454C22×C5C22×C4×D311yescharacteristic
455C2×D5C22×C4×D311yescharacteristic
456C2×D5C22×C4×D311yescharacteristic
457C2×D5#100411yescharacteristic
458C2×D5#100711yescharacteristic
459C2×D5#101011yescharacteristic
460C2×D5#101011yescharacteristic
461AGL(1,𝔽5)—22no—
462AGL(1,𝔽5)—22no—
463AGL(1,𝔽5)—24no—
464AGL(1,𝔽5)—64no—
465AGL(1,𝔽5)—62no—
466AGL(1,𝔽5)—62no—
467C4×C5—22no—
468C4×C5—34no—
469C4×C5—61no—
470C4×C5—61no—
471C4×C5C42×D312yes—
472Dic5—22no—
473Dic5—34no—
474Dic5—61no—
475Dic5—61no—
476Dic5C42×D312yes—
477C2×Q8—31no—
478C2×Q8—152no—
479C2×Q8—154no—
480C2×Q8—154no—
481C2×Q8—151no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—52no—
485C22×C4—51no—
486C22×C4—52no—
487C22×C4—152no—
488C22×C4—151no—
489C22×C4—151no—
490C22×C4—151no—
491C22×C4—151no—
492C22×C4—152no—
493C4⋊C4—32no—
494C4⋊C4—54no—
495C4⋊C4—52no—
496C4⋊C4—51no—
497C4⋊C4—152no—
498C4⋊C4—152no—
499C4⋊C4—158no—
500C4⋊C4—158no—
501C4⋊C4—154no—
502C4⋊C4—152no—
503C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
504C42—32no—
505C42—31no—
506C42—54no—
507C42—152no—
508C42—151no—
509C42—152no—
510C42—151no—
511C42—154no—
512C42—158no—
513C42—158no—
514C42—152no—
515C42—151no—
516C42—202no—
517C42—602no—
518C42—602no—
519C3×C5#227611yescharacteristic, complemented, Hall
520C22×C3—51no—
521C22×C3—51no—
522C22×C3—51no—
523C22×C3—51no—
524C22×C3—51no—
525C22×C3—51no—
526C22×C3C23×AGL(1,𝔽5)11yescharacteristic
527C3×C4—22no—
528C3×C4—52no—
529C3×C4—102no—
530C3×C4—104no—
531C3×C4—102no—
532C3×C4—102no—
533C3×C4C2×C4×AGL(1,𝔽5)12yes—
534Dic3—21no—
535Dic3—21no—
536Dic3—54no—
537Dic3—104no—
538Dic3—102no—
539Dic3—102no—
540Dic3—101no—
541Dic3—101no—
542Dic3C2×C4×AGL(1,𝔽5)14yes—
543C2×C5C2×C42×D311yescharacteristic
544C2×C5#554611yescharacteristic
545C2×C5#557211yescharacteristic
546D5#550411yescharacteristic
547D5#551611yescharacteristic
548D5#554611yescharacteristic
549D5#557211yescharacteristic
550C23—51no—
551Q8—34no—
552Q8—158no—
553Q8—154no—
554C2×C4—32no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—51no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—52no—
562C2×C4—54no—
563C2×C4—52no—
564C2×C4—102no—
565C2×C4—102no—
566C2×C4—101no—
567C2×C4—102no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—102no—
571C2×C4—101no—
572C2×C4—154no—
573C2×C4—154no—
574C2×C4—152no—
575C2×C4—152no—
576C2×C4—152no—
577C2×C4—154no—
578C2×C4—151no—
579C2×C4—151no—
580C2×C4—301no—
581C2×C4—301no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—301no—
585C2×C4—302no—
586C2×C4—301no—
587C2×C4—301no—
588C2×C4—301no—
589C2×C4—302no—
590C2×C4C2×D3×AGL(1,𝔽5)12yes—
591C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
592C2×C3—51no—
593C2×C3—51no—
594C2×C3—51no—
595C2×C3—51no—
596C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
597C2×C3#6626211yescharacteristic
598C2×C3#6626611yescharacteristic
599C5#7361611yescharacteristic, complemented, Sylow
600C22—51no—
601C22—51no—
602C22—51no—
603C22—51no—
604C22—51no—
605C22—51no—
606C22C22×D3×AGL(1,𝔽5)11yescharacteristic
607C4—22no—
608C4—34no—
609C4—52no—
610C4—61no—
611C4—61no—
612C4—104no—
613C4—102no—
614C4—102no—
615C4—102no—
616C4—154no—
617C4—302no—
618C4—304no—
619C4—302no—
620C4—301no—
621C4—301no—
622C4C4×D3×AGL(1,𝔽5)12yes—
623C3#1061720811yescharacteristic, complemented, Sylow
624C2—51no—
625C2—51no—
626C2—51no—
627C2—51no—
628C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
629C2#1175684611yescharacteristic
630C2#1175684711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2276
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
25. ΓL(1,𝔽16)⋊Q8C4semidirect
26. AGL(1,𝔽5)×Dic6C4semidirect
27. #91776C4semidirect
28. C5×#887C4semidirect
33. #91344C4semidirect
34. #91340C4semidirect
35. #91325C4semidirect
36. #91324C4semidirect
165. Dic30C42semidirect
169. C5×Dic6C42semidirect
176. #1204C42semidirect
205. #887AGL(1,𝔽5)semidirect
453. Dic6C4×AGL(1,𝔽5)semidirect
519. C3×C5#2276semidirect
599. C5#73616semidirect
623. C3#10617208semidirect

Maximal subgroups

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

subgroupindex
C2×ΓL(1,𝔽16)⋊Q82
C2×AGL(1,𝔽5)×Dic62
D5×#8872
C4⋊C4×ΓL(1,𝔽16)2
C3×C4⋊C4×AGL(1,𝔽5)2
C4×Dic3⋊AGL(1,𝔽5)2
Dic3×C4⋊AGL(1,𝔽5)2
#117518332
#117518322
AGL(1,𝔽5)×Dic3⋊C42
#117517482
#106172083
#736165