Finite Group Databasebeta

← #14329438

Subgroups — #14329438

Order 1920.

1104 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)⋊Q8C212yesmaximal
2D5×#888C211yesmaximal, characteristic
3C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
4C3×#65712C211yesmaximal, characteristic
5#11751861C211yesmaximal, characteristic
6C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
8#11751842C212yesmaximal
9AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic
10#11751835C212yesmaximal
11#11751747C212yesmaximal
12#10617388—31nomaximal, Hall
13C2×D5×Dic6C2212yes—
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2212yes—
16C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
18C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25ΓL(1,𝔽16)⋊Q8—28no—
26#91777C411yescharacteristic, complemented
27C5×#888C411yescharacteristic, complemented
28C3×D5×C4⋊C4C2211yescharacteristic
29#91470C411yescharacteristic, complemented
30#91469C411yescharacteristic, complemented
31D5×C4⋊Dic3C2211yescharacteristic
32D5×Dic3⋊C4C2212yes—
33C4×D5×Dic3C2211yescharacteristic
34#91329C412yescomplemented
35#91328C412yescomplemented
36#91235C2212yes—
37C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
38(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43#75986—51nomaximal, Hall
44C2×Q8×AGL(1,𝔽5)—32no—
45D5×C4⋊Q8—31no—
46(C2×AGL(1,𝔽5))⋊Q8—32no—
47#65712—31no—
48#65712D311yescharacteristic
49#65711—32no—
50#65711—32no—
51C4⋊C4×AGL(1,𝔽5)—31no—
52C4⋊C4×AGL(1,𝔽5)—31no—
53C4×C4⋊AGL(1,𝔽5)—31no—
54C4×C4⋊AGL(1,𝔽5)—31no—
55C22×ΓL(1,𝔽16)C2311yescharacteristic
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×C3×AGL(1,𝔽5)C2312yes—
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C2×Dic30C2×C412yes—
62C2×C5×Dic6C2×C412yes—
63C2×C3×C4×D5C2312yes—
64C2×C3×C4×D5C2311yescharacteristic
65C2×#1204C2×C412yes—
66C2×#1204C2×C412yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2312yes—
69C2×D5×Dic3C2311yescharacteristic
70D5×Dic6—24no—
71D5×Dic6—24no—
72C4⋊ΓL(1,𝔽16)Q814yescomplemented
73C4×ΓL(1,𝔽16)—24no—
74C4×ΓL(1,𝔽16)—22no—
75C3×C4⋊AGL(1,𝔽5)—24no—
76C3×C4⋊AGL(1,𝔽5)—22no—
77C3×C4×AGL(1,𝔽5)—22no—
78Dic3⋊AGL(1,𝔽5)—24no—
79Dic3⋊AGL(1,𝔽5)—22no—
80Dic3⋊AGL(1,𝔽5)D414yes—
81Dic3×AGL(1,𝔽5)—24no—
82Dic3×AGL(1,𝔽5)—24no—
83C3×C5×C4⋊C4C2×C411yescharacteristic
84C4⋊Dic15C2×C411yescharacteristic
85#6712C2×C412yes—
86C4×Dic15C2×C411yescharacteristic
87C5×C4⋊Dic3C2×C411yescharacteristic
88C5×Dic3⋊C4C2×C412yes—
89C4×C5×Dic3C2×C411yescharacteristic
90C3×C4⋊Dic5C2×C411yescharacteristic
91C3×#683C2×C412yes—
92Dic3⋊Dic5C2×C412yes—
93#6669C2×C412yes—
94#6668C2×C412yes—
95Dic3×Dic5C2×C411yescharacteristic
96Dic3×Dic5C2×C411yescharacteristic
97C2×#888—51no—
98C2×#887—52no—
99C3×#389—51no—
100#4978—52no—
101Dic3×C4⋊C4—51no—
102Dic3×C4⋊C4—51no—
103#4972—51no—
104C4×C4⋊Dic3—51no—
105C4×Dic3⋊C4—51no—
106#4652—52no—
107#4646—52no—
108C2×Q8×D5—32no—
109Q8×AGL(1,𝔽5)—68no—
110C2×C4⋊AGL(1,𝔽5)—31no—
111C2×C4⋊AGL(1,𝔽5)—31no—
112C2×C4⋊AGL(1,𝔽5)—31no—
113C2×C4⋊AGL(1,𝔽5)—32no—
114C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
115C2×C4⋊AGL(1,𝔽5)C2×D312yes—
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)C2×D311yescharacteristic
121C5×C4⋊Q8—31no—
122#4090—32no—
123D5×C4⋊C4—32no—
124D5×C4⋊C4—31no—
125D5×C4⋊C4C2×D311yescharacteristic
126#4034—31no—
127#4034—31no—
128#4034—32no—
129C42×D5—31no—
130#4015—31no—
131(C2×AGL(1,𝔽5))⋊C4—31no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
133(C2×AGL(1,𝔽5))⋊C4—31no—
134(C2×AGL(1,𝔽5))⋊C4—32no—
135(C2×AGL(1,𝔽5))⋊C4—32no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
138#2365—151noSylow
139C22×C3×D5C2411yescharacteristic
140C2×ΓL(1,𝔽16)—22no—
141C2×ΓL(1,𝔽16)—21no—
142C2×ΓL(1,𝔽16)—21no—
143C2×ΓL(1,𝔽16)—22no—
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)—21no—
146C2×ΓL(1,𝔽16)—21no—
147C2×ΓL(1,𝔽16)C2×D412yes—
148C2×ΓL(1,𝔽16)C2×Q814yes—
149C2×C3×AGL(1,𝔽5)—21no—
150C2×C3×AGL(1,𝔽5)—21no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—21no—
153C2×C3×AGL(1,𝔽5)—21no—
154C2×C3×AGL(1,𝔽5)—22no—
155C2×C3×AGL(1,𝔽5)—22no—
156C2×C3×AGL(1,𝔽5)—21no—
157C2×C3×AGL(1,𝔽5)C2×D412yes—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C22×C411yescharacteristic
160C2×Dic15C22×C411yescharacteristic
161C2×Dic15C22×C412yes—
162C2×Dic15C22×C411yescharacteristic
163Dic30—24no—
164C2×C5×Dic3C22×C411yescharacteristic
165C2×C5×Dic3C22×C412yes—
166C2×C5×Dic3C22×C411yescharacteristic
167C5×Dic6—24no—
168C2×C3×Dic5C22×C412yes—
169C2×C3×Dic5C22×C411yescharacteristic
170C3×C4×D5—22no—
171C3×C4×D5—22no—
172C3×C4×D5C2×Q812yes—
173C3×C4×D5#4112yes—
174#1204—24no—
175#1204—24no—
176D5×Dic3—22no—
177D5×Dic3—22no—
178D5×Dic3—21no—
179D5×Dic3—21no—
180D5×Dic3C2×D412yes—
181D5×Dic3#4112yes—
182C22×Dic6—52no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C4⋊C4—51no—
185C2×C3×C4⋊C4—52no—
186C2×C3×C42—51no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—51no—
189C2×Dic3⋊C4—51no—
190C2×Dic3⋊C4—52no—
191C2×Dic3⋊C4—51no—
192C2×Dic3⋊C4—52no—
193C2×C4×Dic3—51no—
194C2×C4×Dic3—52no—
195C2×C4×Dic3—52no—
196C2×C4×Dic3—52no—
197C2×C4×Dic3—51no—
198#888—52no—
199#888—51no—
200#888—51no—
201#888—52no—
202#888—51no—
203#888AGL(1,𝔽5)11yescharacteristic, complemented
204#887—108no—
205C3×#95—52no—
206C3⋊#95—52no—
207C3⋊#95—52no—
208C3⋊#95—51no—
209C3⋊#95—52no—
210C3⋊#95—51no—
211C3⋊#95—52no—
212C22×AGL(1,𝔽5)—31no—
213C22×AGL(1,𝔽5)—32no—
214C22×AGL(1,𝔽5)—31no—
215C22×AGL(1,𝔽5)C22×D312yes—
216C22×AGL(1,𝔽5)C22×D311yescharacteristic
217C22×AGL(1,𝔽5)C22×D311yescharacteristic
218C2×C5×Q8—32no—
219Q8×D5—64no—
220Q8×D5—64no—
221C2×C4×D5—31no—
222C2×C4×D5—32no—
223C2×C4×D5—31no—
224C2×C4×D5C22×D312yes—
225C2×C4×D5C22×D311yescharacteristic
226C2×Dic10—32no—
227C2×Dic10—32no—
228C2×Dic10—32no—
229C4⋊AGL(1,𝔽5)—24no—
230C4⋊AGL(1,𝔽5)—22no—
231C4⋊AGL(1,𝔽5)—34no—
232C4⋊AGL(1,𝔽5)—34no—
233C4⋊AGL(1,𝔽5)—62no—
234C4⋊AGL(1,𝔽5)—64no—
235C4×AGL(1,𝔽5)—22no—
236C4×AGL(1,𝔽5)—64no—
237C4×AGL(1,𝔽5)—64no—
238C4×AGL(1,𝔽5)—64no—
239C4×AGL(1,𝔽5)—62no—
240C5×C4⋊C4—32no—
241C5×C4⋊C4—31no—
242C5×C4⋊C4C4×D311yescharacteristic
243C42×C5—31no—
244C4⋊Dic5—31no—
245C4⋊Dic5—32no—
246C4⋊Dic5C4×D311yescharacteristic
247#683—32no—
248#683—32no—
249#683—32no—
250#683C4×D312yes—
251C4×Dic5—31no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254C2×C4⋊Q8—151no—
255C2×C4×Q8—152no—
256#391—152no—
257#389—51no—
258#389—151no—
259#387—152no—
260#387—152no—
261C4×C4⋊C4—151no—
262C4×C4⋊C4—151no—
263C4×C4⋊C4—151no—
264C4×C4⋊C4—151no—
265C22×C3×C5C23×C411yescharacteristic
266C2×C3×D5C22×D411yescharacteristic
267C2×C3×D5C22×Q811yescharacteristic
268C2×C3×D5C2×#4111yescharacteristic
269C2×C3×D5C2×#4111yescharacteristic
270C2×C3×D52−1+411yescharacteristic
271C2×C3×D52−1+411yescharacteristic
272ΓL(1,𝔽16)—22no—
273ΓL(1,𝔽16)—24no—
274ΓL(1,𝔽16)—41no—
275C3×AGL(1,𝔽5)—22no—
276C3×AGL(1,𝔽5)—42no—
277C3×AGL(1,𝔽5)—41no—
278C3×C4×C5—22no—
279C3×C4×C5C4×Q812yescomplemented
280Dic15—22no—
281Dic15—21no—
282Dic15C4×D412yes—
283C3×Dic5—22no—
284C3×Dic5C4×Q812yescomplemented
285C5×Dic3—22no—
286C5×Dic3—21no—
287C5×Dic3C4×D412yes—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4—52no—
291C22×C3×C4—51no—
292C22×C3×C4—52no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—52no—
298C22×Dic3—51no—
299C2×Dic6—52no—
300C2×Dic6—52no—
301C2×Dic6—52no—
302C2×Dic6—104no—
303C2×Dic6—104no—
304C2×Dic6C2×AGL(1,𝔽5)12yes—
305C3×C4⋊C4—52no—
306C3×C4⋊C4—51no—
307C3×C4⋊C4—104no—
308C3×C4⋊C4—102no—
309C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
310C3×C42—102no—
311C4⋊Dic3—54no—
312C4⋊Dic3—51no—
313C4⋊Dic3—52no—
314C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
315Dic3⋊C4—54no—
316Dic3⋊C4—52no—
317Dic3⋊C4—52no—
318Dic3⋊C4—52no—
319Dic3⋊C4—104no—
320Dic3⋊C4—102no—
321Dic3⋊C4C2×AGL(1,𝔽5)12yes—
322C4×Dic3—51no—
323C4×Dic3—51no—
324C4×Dic3—51no—
325C4×Dic3—104no—
326C4×Dic3—104no—
327C4×Dic3—104no—
328C4×Dic3—102no—
329C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
330C22×D5C23×D311yescharacteristic
331C2×AGL(1,𝔽5)—21no—
332C2×AGL(1,𝔽5)—21no—
333C2×AGL(1,𝔽5)—22no—
334C2×AGL(1,𝔽5)—21no—
335C2×AGL(1,𝔽5)—22no—
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)—62no—
342C2×AGL(1,𝔽5)—61no—
343C2×AGL(1,𝔽5)—62no—
344C2×AGL(1,𝔽5)—61no—
345C2×AGL(1,𝔽5)—61no—
346C2×AGL(1,𝔽5)—61no—
347C2×AGL(1,𝔽5)—61no—
348C2×AGL(1,𝔽5)D3×D412yes—
349C5×Q8—64no—
350C2×C4×C5—31no—
351C2×C4×C5—31no—
352C2×C4×C5—32no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5C2×C4×D311yescharacteristic
355C2×Dic5—31no—
356C2×Dic5—31no—
357C2×Dic5—32no—
358C2×Dic5C2×C4×D312yes—
359C2×Dic5C2×C4×D311yescharacteristic
360C4×D5—22no—
361C4×D5—22no—
362C4×D5—32no—
363C4×D5—32no—
364C4×D5—62no—
365C4×D5—61no—
366C4×D5—62no—
367C4×D5—61no—
368C4×D5#23712yes—
369C4×D5D3×Q812yes—
370Dic10—64no—
371Dic10—64no—
372Dic10—64no—
373C22×Q8—152no—
374C4⋊Q8—31no—
375C4⋊Q8—151no—
376C4⋊Q8—152no—
377C4⋊Q8—151no—
378C4⋊Q8—152no—
379C4⋊Q8—151no—
380C4×Q8—308no—
381C2×C4⋊C4—51no—
382C2×C4⋊C4—52no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—151no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—151no—
387C2×C4⋊C4—151no—
388C2×C4⋊C4—152no—
389C2×C4⋊C4—151no—
390C2×C42—51no—
391C2×C42—151no—
392C2×C42—152no—
393C2×C42—152no—
394C2×C42—152no—
395C2×C42—151no—
396#95—52no—
397#95—151no—
398#95—151no—
399#95—152no—
400#95—152no—
401#95—152no—
402#95—152no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×C4×Q811yescharacteristic
405C2×C3×C5#51911yescharacteristic
406C3×D5#54711yescharacteristic
407C3×D5D4×Q811yescharacteristic
408C3×D5#55611yescharacteristic
409C3×D5#55711yescharacteristic
410C23×C3—51no—
411C2×C3×C4—51no—
412C2×C3×C4—52no—
413C2×C3×C4—52no—
414C2×C3×C4—52no—
415C2×C3×C4—52no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—102no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—102no—
424C2×C3×C4—101no—
425C2×C3×C4—102no—
426C2×C3×C4C22×AGL(1,𝔽5)12yes—
427C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
428C2×Dic3—51no—
429C2×Dic3—52no—
430C2×Dic3—52no—
431C2×Dic3—52no—
432C2×Dic3—54no—
433C2×Dic3—51no—
434C2×Dic3—52no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—101no—
438C2×Dic3—101no—
439C2×Dic3—102no—
440C2×Dic3—101no—
441C2×Dic3—102no—
442C2×Dic3—101no—
443C2×Dic3—101no—
444C2×Dic3—101no—
445C2×Dic3—101no—
446C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
447C2×Dic3C22×AGL(1,𝔽5)12yes—
448C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
449Dic6—24no—
450Dic6—104no—
451Dic6—104no—
452Dic6—104no—
453C22×C5C22×C4×D311yescharacteristic
454C2×D5C2×D3×D411yescharacteristic
455C2×D5C2×#23711yescharacteristic
456C2×D5C2×D3×Q811yescharacteristic
457C2×D5#100711yescharacteristic
458C2×D5D3×#4111yescharacteristic
459C2×D5#101011yescharacteristic
460AGL(1,𝔽5)—22no—
461AGL(1,𝔽5)—41no—
462AGL(1,𝔽5)—42no—
463AGL(1,𝔽5)—64no—
464AGL(1,𝔽5)—62no—
465AGL(1,𝔽5)—121no—
466C4×C5—22no—
467C4×C5—32no—
468C4×C5—62no—
469C4×C5—61no—
470C4×C5#88712yescomplemented
471Dic5—22no—
472Dic5—32no—
473Dic5—62no—
474Dic5—61no—
475Dic5#88712yescomplemented
476C2×Q8—32no—
477C2×Q8—152no—
478C2×Q8—152no—
479C2×Q8—152no—
480C2×Q8—304no—
481C2×Q8—304no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—52no—
485C22×C4—51no—
486C22×C4—52no—
487C22×C4—151no—
488C22×C4—151no—
489C22×C4—152no—
490C22×C4—152no—
491C22×C4—151no—
492C22×C4—151no—
493C4⋊C4—32no—
494C4⋊C4—31no—
495C4⋊C4—52no—
496C4⋊C4—51no—
497C4⋊C4—104no—
498C4⋊C4—102no—
499C4⋊C4—152no—
500C4⋊C4—152no—
501C4⋊C4—152no—
502C4⋊C4—154no—
503C4⋊C4—154no—
504C4⋊C4—152no—
505C4⋊C4—151no—
506C4⋊C4—304no—
507C4⋊C4—302no—
508C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
509C42—31no—
510C42—102no—
511C42—151no—
512C42—151no—
513C42—151no—
514C42—304no—
515C42—302no—
516C42—304no—
517C42—304no—
518C3×C5#236511yescharacteristic, complemented, Hall
519C22×C3—51no—
520C22×C3—51no—
521C22×C3—51no—
522C22×C3—51no—
523C22×C3—51no—
524C22×C3—51no—
525C22×C3C23×AGL(1,𝔽5)11yescharacteristic
526C3×C4—22no—
527C3×C4—52no—
528C3×C4—102no—
529C3×C4—102no—
530C3×C4—202no—
531C3×C4—201no—
532C3×C4Q8×AGL(1,𝔽5)12yescomplemented
533Dic3—22no—
534Dic3—21no—
535Dic3—52no—
536Dic3—104no—
537Dic3—102no—
538Dic3—102no—
539Dic3—101no—
540Dic3—201no—
541Dic3D4×AGL(1,𝔽5)12yes—
542C2×C5C2×#88711yescharacteristic
543C2×C5C4×D3×D411yescharacteristic
544C2×C5#557211yescharacteristic
545D5#561111yescharacteristic
546D5#564111yescharacteristic
547D5#568511yescharacteristic
548D5#572711yescharacteristic
549C23—51no—
550Q8—64no—
551Q8—304no—
552Q8—304no—
553Q8—304no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—32no—
557C2×C4—51no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—52no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—101no—
570C2×C4—102no—
571C2×C4—101no—
572C2×C4—152no—
573C2×C4—152no—
574C2×C4—151no—
575C2×C4—152no—
576C2×C4—154no—
577C2×C4—151no—
578C2×C4—152no—
579C2×C4—302no—
580C2×C4—302no—
581C2×C4—301no—
582C2×C4—301no—
583C2×C4—302no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4—302no—
587C2×C4—301no—
588C2×C4—301no—
589C2×C4—301no—
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×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
597C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
598C2×C3#6626211yescharacteristic
599C5#7598611yescharacteristic, complemented, Sylow
600C22—51no—
601C22—51no—
602C22—51no—
603C22—51no—
604C22—51no—
605C22—51no—
606C22C22×D3×AGL(1,𝔽5)11yescharacteristic
607C4—22no—
608C4—32no—
609C4—52no—
610C4—62no—
611C4—61no—
612C4—102no—
613C4—102no—
614C4—152no—
615C4—202no—
616C4—201no—
617C4—302no—
618C4—304no—
619C4—302no—
620C4—301no—
621C4—601no—
622C4ΓL(1,𝔽16)⋊Q812yescomplemented
623C3#1061738811yescharacteristic, complemented, Sylow
624C2—51no—
625C2—51no—
626C2—51no—
627C2—51no—
628C2C2×ΓL(1,𝔽16)⋊Q811yescharacteristic
629C2D3×D4×AGL(1,𝔽5)11yescharacteristic
630C2#1175684711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2365
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
26. #91777C4semidirect
27. C5×#888C4semidirect
29. #91470C4semidirect
30. #91469C4semidirect
34. #91329C4semidirect
35. #91328C4semidirect
72. C4⋊ΓL(1,𝔽16)Q8semidirect
203. #888AGL(1,𝔽5)semidirect
279. C3×C4×C5C4×Q8semidirect
284. C3×Dic5C4×Q8semidirect
470. C4×C5#887semidirect
475. Dic5#887semidirect
518. C3×C5#2365semidirect
532. C3×C4Q8×AGL(1,𝔽5)semidirect
599. C5#75986semidirect
622. C4ΓL(1,𝔽16)⋊Q8semidirect
623. C3#10617388semidirect

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
D5×#8882
C4⋊C4×ΓL(1,𝔽16)2
C3×#657122
#117518612
C4×Dic3⋊AGL(1,𝔽5)2
Dic3×C4⋊AGL(1,𝔽5)2
#117518422
AGL(1,𝔽5)×C4⋊Dic32
#117518352
#117517472
#106173883
#759865