Finite Group Databasebeta

← #14321916

Subgroups — #14321916

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
3D5×#897C211yesmaximal, characteristic
4C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C3×#65712C211yesmaximal, characteristic, complemented
6#11751932C212yesmaximal
7#11751931C212yesmaximal
8#11751855C211yesmaximal, characteristic
9#11751846C212yesmaximal, complemented
10#11751840C212yesmaximal, complemented
11#11751749C211yesmaximal, characteristic, complemented
12AGL(1,𝔽5)×C22⋊Q8—31nomaximal, Hall
13C22×D3×AGL(1,𝔽5)C2211yescharacteristic
14C22×D3×AGL(1,𝔽5)C2211yescharacteristic
15C2×C4×D3×D5C2211yescharacteristic
16C2×D5×Dic6C2211yescharacteristic
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)C2212yes—
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
22C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊AGL(1,𝔽5)C2212yes—
24C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
28C4×D3×AGL(1,𝔽5)—24no—
29ΓL(1,𝔽16)⋊Q8—24no—
30#91786C411yescharacteristic, complemented
31C5×#897C411yescharacteristic, complemented
32C3×D5×C4⋊C4C2211yescharacteristic
33D5×(C2×D3)⋊C4C2212yes—
34#91419C412yescomplemented
35#91417C412yescomplemented
36D5×C4⋊Dic3C2212yes—
37#91383C411yescharacteristic, complemented
38#91365C411yescharacteristic, complemented
39#91235C2212yes—
40C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#75965—51nomaximal, Hall
45C2×Q8×AGL(1,𝔽5)—31no—
46C22×C4×AGL(1,𝔽5)—31no—
47D5×C22⋊Q8—31no—
48(C2×AGL(1,𝔽5))⋊Q8—31no—
49#65765—31no—
50#65712D311yescharacteristic, complemented
51#65711—32no—
52C4⋊C4×AGL(1,𝔽5)—31no—
53C4⋊C4×AGL(1,𝔽5)—32no—
54#65699—32no—
55C22⋊C4×AGL(1,𝔽5)—32no—
56C22×D3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×ΓL(1,𝔽16)C2311yescharacteristic
59C22×ΓL(1,𝔽16)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2312yes—
61C22×C3×AGL(1,𝔽5)C2311yescharacteristic
62C22×C3×AGL(1,𝔽5)C2311yescharacteristic
63C2×D3×AGL(1,𝔽5)—22no—
64C2×D3×AGL(1,𝔽5)—22no—
65C2×D3×AGL(1,𝔽5)—22no—
66C2×D3×AGL(1,𝔽5)—22no—
67C2×D3×AGL(1,𝔽5)—22no—
68C2×D3×AGL(1,𝔽5)Q814yescomplemented
69C2×C4×D15C2×C411yescharacteristic
70C2×Dic30C2×C411yescharacteristic, complemented
71C2×C4×C5×D3C2×C411yescharacteristic
72C2×C5×Dic6C2×C411yescharacteristic, complemented
73C2×C3×C4×D5C2312yes—
74C2×C3×C4×D5C2311yescharacteristic
75C2×#1204C2×C412yescomplemented
76C2×#1200C2×C411yescharacteristic
77C2×D3×Dic5C2×C411yescharacteristic
78C2×D5×Dic3C2311yescharacteristic
79C2×D5×Dic3C2312yes—
80C4×D3×D5—22no—
81C4×D3×D5—22no—
82D5×Dic6—22no—
83D5×Dic6—22no—
84C4⋊ΓL(1,𝔽16)—22no—
85C4×ΓL(1,𝔽16)—24no—
86C4×ΓL(1,𝔽16)D414yes—
87C3×C4⋊AGL(1,𝔽5)—24no—
88C3×C4⋊AGL(1,𝔽5)—22no—
89C3×C4×AGL(1,𝔽5)—22no—
90Dic3⋊AGL(1,𝔽5)—24no—
91(C2×D3)⋊AGL(1,𝔽5)—24no—
92Dic3×AGL(1,𝔽5)—24no—
93Dic3×AGL(1,𝔽5)—22no—
94Dic3×AGL(1,𝔽5)—22no—
95C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
96#6714C2×C412yes—
97C4⋊Dic15C2×C412yescomplemented
98C5×(C2×D3)⋊C4C2×C412yes—
99C5×C4⋊Dic3C2×C412yescomplemented
100C3×C4⋊Dic5C2×C411yescharacteristic, complemented
101C3×#683C2×C412yescomplemented
102#6668C2×C412yescomplemented
103#6668C2×C412yescomplemented
104#6667C2×C412yes—
105(C2×D3)⋊Dic5C2×C412yes—
106C2×#897—51no—
107C2×#887—51no—
108C2×C42×D3—51no—
109C3×#389—51no—
110#4989—52no—
111#4987—51no—
112Dic3×C4⋊C4—52no—
113Dic3×C4⋊C4—51no—
114#4929—51no—
115#4666—52no—
116#4654—52no—
117C23×AGL(1,𝔽5)—31no—
118C23×AGL(1,𝔽5)—31no—
119C2×Q8×D5—31no—
120C22×C4×D5—31no—
121C2×C22⋊AGL(1,𝔽5)—32no—
122Q8×AGL(1,𝔽5)—64no—
123C2×C4⋊AGL(1,𝔽5)—32no—
124C2×C4⋊AGL(1,𝔽5)—31no—
125C2×C4⋊AGL(1,𝔽5)C2×D312yes—
126C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
127C2×C4×AGL(1,𝔽5)—31no—
128C2×C4×AGL(1,𝔽5)—32no—
129C2×C4×AGL(1,𝔽5)—31no—
130C2×C4×AGL(1,𝔽5)—31no—
131C2×C4×AGL(1,𝔽5)—32no—
132C2×C4×AGL(1,𝔽5)—64no—
133C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
134C5×C22⋊Q8—31no—
135#4092—31no—
136#4070—31no—
137#4043—31no—
138#4042—32no—
139D5×C4⋊C4—32no—
140D5×C4⋊C4C2×D311yescharacteristic
141D5×C22⋊C4—32no—
142#4024—32no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4—32no—
145(C2×AGL(1,𝔽5))⋊C4—32no—
146(C2×AGL(1,𝔽5))⋊C4—32no—
147(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
148C4×C22⋊Q8—151noSylow
149C22×D15C22×C411yescharacteristic
150C22×C5×D3C22×C411yescharacteristic
151C22×C3×D5C2411yescharacteristic
152C2×D3×D5—21no—
153C2×D3×D5—21no—
154C2×D3×D5—21no—
155C2×D3×D5—21no—
156C2×D3×D5C2×Q812yes—
157C2×D3×D5#4112yes—
158C2×ΓL(1,𝔽16)—21no—
159C2×ΓL(1,𝔽16)—21no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)C2×D412yes—
164C2×ΓL(1,𝔽16)C2×D412yes—
165C2×ΓL(1,𝔽16)C2×Q812yes—
166C2×ΓL(1,𝔽16)#4112yes—
167C2×C3×AGL(1,𝔽5)—21no—
168C2×C3×AGL(1,𝔽5)—21no—
169C2×C3×AGL(1,𝔽5)—21no—
170C2×C3×AGL(1,𝔽5)—21no—
171C2×C3×AGL(1,𝔽5)—22no—
172C2×C3×AGL(1,𝔽5)—22no—
173C2×C3×AGL(1,𝔽5)—22no—
174C2×C3×AGL(1,𝔽5)C2×Q812yes—
175C2×C3×AGL(1,𝔽5)#4112yes—
176D3×AGL(1,𝔽5)—28no—
177D3×AGL(1,𝔽5)—28no—
178C2×C3×C4×C5C22×C412yes—
179C2×C3×C4×C5C22×C411yescharacteristic
180C2×Dic15C22×C412yes—
181C2×Dic15C22×C411yescharacteristic
182C4×D15—22no—
183Dic30—22no—
184C2×C5×Dic3C22×C412yes—
185C2×C5×Dic3C22×C411yescharacteristic
186C4×C5×D3—22no—
187C5×Dic6—22no—
188C2×C3×Dic5C22×C412yes—
189C2×C3×Dic5C22×C411yescharacteristic
190C3×C4×D5—22no—
191C3×C4×D5—22no—
192C3×C4×D5C2×D412yes—
193C3×C4×D5#4112yes—
194#1204—24no—
195#1200—22no—
196D3×Dic5—22no—
197D5×Dic3—21no—
198D5×Dic3—22no—
199D5×Dic3—22no—
200D5×Dic3—21no—
201C22×C4×D3—51no—
202C22×C4×D3—51no—
203C22×C4×D3—51no—
204C22×Dic6—51no—
205C2×C3×C4⋊C4—51no—
206C2×C3×C4⋊C4—52no—
207C2×C3×C4⋊C4—51no—
208C2×C3×C42—51no—
209C2×(C2×D3)⋊C4—52no—
210C2×(C2×D3)⋊C4—52no—
211C2×C4⋊Dic3—52no—
212C2×C4⋊Dic3—51no—
213C2×Dic3⋊C4—52no—
214C2×C4×Dic3—51no—
215C2×C4×Dic3—51no—
216C2×C4×Dic3—52no—
217C2×C4×Dic3—51no—
218C2×C4×Dic3—52no—
219#897—51no—
220#897—51no—
221#897—51no—
222#897—52no—
223#897—52no—
224#897AGL(1,𝔽5)11yescharacteristic, complemented
225#887—104no—
226C42×D3—104no—
227C3×#95—52no—
228C3⋊#95—52no—
229C3⋊#95—52no—
230C3⋊#95—52no—
231C3⋊#95—52no—
232C23×D5—31no—
233C22×AGL(1,𝔽5)—31no—
234C22×AGL(1,𝔽5)—31no—
235C22×AGL(1,𝔽5)—34no—
236C22×AGL(1,𝔽5)—32no—
237C22×AGL(1,𝔽5)—62no—
238C22×AGL(1,𝔽5)—62no—
239C22×AGL(1,𝔽5)—62no—
240C22×AGL(1,𝔽5)—62no—
241C22×AGL(1,𝔽5)—62no—
242C22×AGL(1,𝔽5)C22×D312yes—
243C22×AGL(1,𝔽5)C22×D311yescharacteristic
244C22×AGL(1,𝔽5)C22×D311yescharacteristic
245C2×C5×Q8—31no—
246C22×C4×C5—31no—
247C22×Dic5—31no—
248Q8×D5—62no—
249Q8×D5—62no—
250C2×C4×D5—31no—
251C2×C4×D5—32no—
252C2×C4×D5—31no—
253C2×C4×D5—31no—
254C2×C4×D5—62no—
255C2×C4×D5—62no—
256C2×C4×D5C22×D312yes—
257C2×C4×D5C22×D311yescharacteristic
258C2×Dic10—31no—
259C2×Dic10—32no—
260C22⋊AGL(1,𝔽5)—64no—
261C4⋊AGL(1,𝔽5)—24no—
262C4⋊AGL(1,𝔽5)—22no—
263C4⋊AGL(1,𝔽5)—64no—
264C4⋊AGL(1,𝔽5)—62no—
265C4×AGL(1,𝔽5)—22no—
266C4×AGL(1,𝔽5)—34no—
267C4×AGL(1,𝔽5)—64no—
268C4×AGL(1,𝔽5)—62no—
269C4×AGL(1,𝔽5)—62no—
270C4×AGL(1,𝔽5)—64no—
271C5×C4⋊C4—32no—
272C5×C4⋊C4C4×D311yescharacteristic, complemented
273C5×C22⋊C4—32no—
274C22⋊Dic5—32no—
275#685—32no—
276#685—32no—
277C4⋊Dic5—32no—
278C4⋊Dic5C4×D311yescharacteristic, complemented
279#683—32no—
280#683—32no—
281#683C4×D312yescomplemented
282C2×C22⋊Q8—151no—
283C2×C4×Q8—151no—
284C22×C42—151no—
285#391—151no—
286#389—51no—
287#387—152no—
288#385—152no—
289#380—151no—
290C4×C4⋊C4—152no—
291C4×C4⋊C4—151no—
292C4×C22⋊C4—152no—
293C22×C3×C5C23×C411yescharacteristic
294C2×D15—21no—
295C2×D15—21no—
296C2×D15C4×Q812yescomplemented
297C2×C5×D3—21no—
298C2×C5×D3—21no—
299C2×C5×D3C4×Q812yescomplemented
300C2×C3×D5C22×D411yescharacteristic
301C2×C3×D5C22×Q811yescharacteristic
302C2×C3×D5C2×#4111yescharacteristic
303C2×C3×D5C2×#4111yescharacteristic
304C2×C3×D5C2×#4111yescharacteristic
305C2×C3×D5C2×#4111yescharacteristic
306D3×D5—22no—
307D3×D5—22no—
308D3×D5—22no—
309D3×D5—22no—
310ΓL(1,𝔽16)—22no—
311ΓL(1,𝔽16)—42no—
312ΓL(1,𝔽16)C22⋊Q814yescomplemented
313C3×AGL(1,𝔽5)—22no—
314C3×AGL(1,𝔽5)—22no—
315C3×AGL(1,𝔽5)—42no—
316C3×C4×C5—22no—
317C3×C4×C5C4×D412yes—
318Dic15—21no—
319Dic15—22no—
320C3×Dic5—22no—
321C3×Dic5C4×D412yes—
322C5×Dic3—21no—
323C5×Dic3—22no—
324C23×D3—51no—
325C22×C3×C4—51no—
326C22×C3×C4—51no—
327C22×C3×C4—51no—
328C22×C3×C4—52no—
329C22×C3×C4—52no—
330C22×Dic3—51no—
331C22×Dic3—51no—
332C22×Dic3—51no—
333C22×Dic3—52no—
334C22×Dic3—52no—
335C2×C4×D3—54no—
336C2×C4×D3—51no—
337C2×C4×D3—51no—
338C2×C4×D3—51no—
339C2×C4×D3—102no—
340C2×C4×D3—102no—
341C2×C4×D3—102no—
342C2×C4×D3—102no—
343C2×C4×D3—102no—
344C2×C4×D3—102no—
345C2×C4×D3—102no—
346C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
347C2×Dic6—51no—
348C2×Dic6—52no—
349C2×Dic6—102no—
350C2×Dic6—102no—
351C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
352C3×C4⋊C4—52no—
353C3×C4⋊C4—51no—
354C3×C4⋊C4—102no—
355C3×C4⋊C4—104no—
356C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
357C3×C42—102no—
358(C2×D3)⋊C4—52no—
359(C2×D3)⋊C4—52no—
360(C2×D3)⋊C4—52no—
361(C2×D3)⋊C4—104no—
362(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
363C4⋊Dic3—52no—
364C4⋊Dic3—52no—
365C4⋊Dic3—52no—
366C4⋊Dic3—102no—
367C4⋊Dic3C2×AGL(1,𝔽5)12yescomplemented
368Dic3⋊C4—104no—
369C4×Dic3—54no—
370C4×Dic3—102no—
371C4×Dic3—102no—
372C4×Dic3—104no—
373C4×Dic3—104no—
374C23×C5—31no—
375C22×D5—31no—
376C22×D5—32no—
377C22×D5—32no—
378C22×D5—61no—
379C22×D5—61no—
380C22×D5—61no—
381C22×D5—61no—
382C22×D5C23×D311yescharacteristic
383C2×AGL(1,𝔽5)—21no—
384C2×AGL(1,𝔽5)—21no—
385C2×AGL(1,𝔽5)—21no—
386C2×AGL(1,𝔽5)—21no—
387C2×AGL(1,𝔽5)—22no—
388C2×AGL(1,𝔽5)—22no—
389C2×AGL(1,𝔽5)—22no—
390C2×AGL(1,𝔽5)—32no—
391C2×AGL(1,𝔽5)—32no—
392C2×AGL(1,𝔽5)—32no—
393C2×AGL(1,𝔽5)—32no—
394C2×AGL(1,𝔽5)—68no—
395C2×AGL(1,𝔽5)—68no—
396C2×AGL(1,𝔽5)—61no—
397C2×AGL(1,𝔽5)—61no—
398C2×AGL(1,𝔽5)—62no—
399C2×AGL(1,𝔽5)—62no—
400C2×AGL(1,𝔽5)—62no—
401C2×AGL(1,𝔽5)#23712yes—
402C2×AGL(1,𝔽5)D3×Q812yes—
403C5×Q8—62no—
404C2×C4×C5—31no—
405C2×C4×C5—32no—
406C2×C4×C5—62no—
407C2×C4×C5C2×C4×D312yes—
408C2×C4×C5C2×C4×D311yescharacteristic
409C2×Dic5—31no—
410C2×Dic5—32no—
411C2×Dic5—62no—
412C2×Dic5C2×C4×D312yes—
413C2×Dic5C2×C4×D311yescharacteristic
414C4×D5—22no—
415C4×D5—22no—
416C4×D5—61no—
417C4×D5—62no—
418C4×D5—61no—
419C4×D5—62no—
420C4×D5—62no—
421C4×D5—62no—
422C4×D5D3×D412yes—
423C4×D5#23912yes—
424Dic10—62no—
425Dic10—64no—
426C22×Q8—151no—
427C23×C4—151no—
428C23×C4—151no—
429C23×C4—151no—
430C22⋊Q8—31no—
431C22⋊Q8—152no—
432C22⋊Q8—152no—
433C22⋊Q8—151no—
434C22⋊Q8—151no—
435C22⋊Q8—151no—
436C4×Q8—304no—
437C2×C4⋊C4—51no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—52no—
440C2×C4⋊C4—152no—
441C2×C4⋊C4—152no—
442C2×C4⋊C4—151no—
443C2×C22⋊C4—152no—
444C2×C22⋊C4—152no—
445C2×C42—51no—
446C2×C42—151no—
447C2×C42—152no—
448C2×C42—152no—
449C2×C42—151no—
450C2×C42—151no—
451C2×C42—304no—
452#95—52no—
453#95—152no—
454#95—152no—
455#95—152no—
456#95—152no—
457C2×C3×C5C2×C4×D411yescharacteristic
458C2×C3×C5C2×C4×Q811yescharacteristic
459C2×C3×C5C4×#4111yescharacteristic
460D15—22no—
461C3×D5C2×C22⋊Q811yescharacteristic
462C3×D5#52511yescharacteristic
463C3×D5#52911yescharacteristic
464C3×D5#53311yescharacteristic
465C5×D3—22no—
466C23×C3—51no—
467C22×D3—51no—
468C22×D3—52no—
469C22×D3—52no—
470C22×D3—101no—
471C22×D3—101no—
472C22×D3—101no—
473C22×D3—101no—
474C22×D3C22×AGL(1,𝔽5)11yescharacteristic
475C2×C3×C4—51no—
476C2×C3×C4—52no—
477C2×C3×C4—52no—
478C2×C3×C4—52no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—102no—
482C2×C3×C4—102no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—102no—
488C2×C3×C4—102no—
489C2×C3×C4—102no—
490C2×C3×C4C22×AGL(1,𝔽5)12yes—
491C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
492C2×Dic3—52no—
493C2×Dic3—52no—
494C2×Dic3—52no—
495C2×Dic3—52no—
496C2×Dic3—51no—
497C2×Dic3—52no—
498C2×Dic3—101no—
499C2×Dic3—102no—
500C2×Dic3—102no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—101no—
504C2×Dic3—102no—
505C2×Dic3—102no—
506C2×Dic3—102no—
507C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
508C2×Dic3C22×AGL(1,𝔽5)12yes—
509C4×D3—22no—
510C4×D3—102no—
511C4×D3—108no—
512C4×D3—102no—
513C4×D3—108no—
514C4×D3—102no—
515Dic6—22no—
516Dic6—104no—
517Dic6—102no—
518C22×C5—32no—
519C22×C5—61no—
520C22×C5—61no—
521C22×C5C22×C4×D311yescharacteristic
522C2×D5—32no—
523C2×D5—61no—
524C2×D5—61no—
525C2×D5—62no—
526C2×D5—62no—
527C2×D5—62no—
528C2×D5—62no—
529C2×D5C2×D3×D411yescharacteristic
530C2×D5C2×#23711yescharacteristic
531C2×D5C2×D3×Q811yescharacteristic
532C2×D5C2×#23911yescharacteristic
533C2×D5D3×#4111yescharacteristic
534C2×D5D3×#4111yescharacteristic
535AGL(1,𝔽5)—22no—
536AGL(1,𝔽5)—22no—
537AGL(1,𝔽5)—34no—
538AGL(1,𝔽5)—42no—
539AGL(1,𝔽5)—62no—
540AGL(1,𝔽5)—122no—
541C4×C5—22no—
542C4×C5—62no—
543C4×C5—61no—
544C4×C5#89312yes—
545Dic5—22no—
546Dic5—62no—
547Dic5—61no—
548Dic5#89312yes—
549C24—151no—
550C2×Q8—31no—
551C2×Q8—152no—
552C2×Q8—151no—
553C2×Q8—302no—
554C2×Q8—302no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—152no—
564C22×C4—151no—
565C22×C4—154no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—151no—
569C22×C4—152no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4—302no—
573C22×C4—302no—
574C22×C4—302no—
575C22×C4—302no—
576C22×C4—302no—
577C4⋊C4—32no—
578C4⋊C4—52no—
579C4⋊C4—51no—
580C4⋊C4—102no—
581C4⋊C4—104no—
582C4⋊C4—152no—
583C4⋊C4—152no—
584C4⋊C4—152no—
585C4⋊C4—302no—
586C4⋊C4—304no—
587C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
588C22⋊C4—32no—
589C22⋊C4—152no—
590C22⋊C4—152no—
591C22⋊C4—152no—
592C22⋊C4—304no—
593C42—102no—
594C42—154no—
595C42—302no—
596C42—302no—
597C42—304no—
598C42—304no—
599C3×C5C4×C22⋊Q811yescharacteristic, complemented, Hall
600C22×C3—51no—
601C22×C3—51no—
602C22×C3—51no—
603C22×C3—51no—
604C22×C3—51no—
605C22×C3—51no—
606C22×C3C23×AGL(1,𝔽5)11yescharacteristic
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—52no—
610C2×D3—102no—
611C2×D3—102no—
612C2×D3—102no—
613C2×D3—102no—
614C2×D3—101no—
615C2×D3—101no—
616C2×D3Q8×AGL(1,𝔽5)12yescomplemented
617C3×C4—22no—
618C3×C4—52no—
619C3×C4—102no—
620C3×C4—102no—
621C3×C4—102no—
622C3×C4—202no—
623C3×C4D4×AGL(1,𝔽5)12yes—
624Dic3—22no—
625Dic3—21no—
626Dic3—54no—
627Dic3—102no—
628Dic3—102no—
629Dic3—101no—
630Dic3—202no—
631C2×C5—62no—
632C2×C5C2×#89311yescharacteristic
633C2×C5C4×#23711yescharacteristic
634C2×C5C4×D3×Q811yescharacteristic
635D5—62no—
636D5#560611yescharacteristic
637D5D3×C22⋊Q811yescharacteristic
638D5#569111yescharacteristic
639D5#572811yescharacteristic
640C23—31no—
641C23—51no—
642C23—152no—
643C23—152no—
644C23—151no—
645C23—301no—
646C23—301no—
647C23—301no—
648C23—301no—
649Q8—62no—
650Q8—304no—
651Q8—302no—
652C2×C4—32no—
653C2×C4—31no—
654C2×C4—51no—
655C2×C4—52no—
656C2×C4—52no—
657C2×C4—52no—
658C2×C4—52no—
659C2×C4—52no—
660C2×C4—62no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—152no—
671C2×C4—152no—
672C2×C4—152no—
673C2×C4—152no—
674C2×C4—152no—
675C2×C4—151no—
676C2×C4—302no—
677C2×C4—302no—
678C2×C4—301no—
679C2×C4—302no—
680C2×C4—301no—
681C2×C4—302no—
682C2×C4—308no—
683C2×C4—308no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4—302no—
687C2×C4—302no—
688C2×C4—302no—
689C2×C4—302no—
690C2×C4C2×D3×AGL(1,𝔽5)12yes—
691C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
692C2×C3—51no—
693C2×C3—51no—
694C2×C3—51no—
695C2×C3—51no—
696C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
697C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
698C2×C3#41×AGL(1,𝔽5)11yescharacteristic
699D3—22no—
700D3—102no—
701C5#7596511yescharacteristic, complemented, Sylow
702C22—32no—
703C22—51no—
704C22—51no—
705C22—51no—
706C22—51no—
707C22—51no—
708C22—51no—
709C22—61no—
710C22—61no—
711C22—152no—
712C22—302no—
713C22—302no—
714C22—302no—
715C22—302no—
716C22—301no—
717C22—301no—
718C22C22×D3×AGL(1,𝔽5)11yescharacteristic
719C4—22no—
720C4—52no—
721C4—61no—
722C4—62no—
723C4—102no—
724C4—102no—
725C4—102no—
726C4—154no—
727C4—202no—
728C4—302no—
729C4—301no—
730C4—302no—
731C4—602no—
732C4#9192112yes—
733C3AGL(1,𝔽5)×C22⋊Q811yescharacteristic, complemented, Sylow
734C2—51no—
735C2—51no—
736C2—51no—
737C2—51no—
738C2—62no—
739C2—302no—
740C2C2×#9192111yescharacteristic
741C2AGL(1,𝔽5)×#23711yescharacteristic
742C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×ΓL(1,𝔽16)⋊Q8C2semidirect
4. C4⋊C4×ΓL(1,𝔽16)C2semidirect
5. C3×#65712C2semidirect
9. #11751846C2semidirect
10. #11751840C2semidirect
11. #11751749C2semidirect
30. #91786C4semidirect
31. C5×#897C4semidirect
34. #91419C4semidirect
35. #91417C4semidirect
37. #91383C4semidirect
38. #91365C4semidirect
50. #65712D3semidirect
68. C2×D3×AGL(1,𝔽5)Q8semidirect
70. C2×Dic30C2×C4semidirect
72. C2×C5×Dic6C2×C4semidirect
75. C2×#1204C2×C4semidirect
95. C3×C5×C4⋊C4C2×C4semidirect
97. C4⋊Dic15C2×C4semidirect
99. C5×C4⋊Dic3C2×C4semidirect
100. C3×C4⋊Dic5C2×C4semidirect
101. C3×#683C2×C4semidirect
102. #6668C2×C4semidirect
103. #6668C2×C4semidirect
224. #897AGL(1,𝔽5)semidirect
272. C5×C4⋊C4C4×D3semidirect
278. C4⋊Dic5C4×D3semidirect
281. #683C4×D3semidirect
296. C2×D15C4×Q8semidirect
299. C2×C5×D3C4×Q8semidirect
312. ΓL(1,𝔽16)C22⋊Q8semidirect
351. C2×Dic6C2×AGL(1,𝔽5)semidirect
356. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
367. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
587. C4⋊C4D3×AGL(1,𝔽5)semidirect
599. C3×C5C4×C22⋊Q8semidirect
616. C2×D3Q8×AGL(1,𝔽5)semidirect
701. C5#75965semidirect
733. C3AGL(1,𝔽5)×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×AGL(1,𝔽5)2
C2×ΓL(1,𝔽16)⋊Q82
D5×#8972
C4⋊C4×ΓL(1,𝔽16)2
C3×#657122
#117519322
#117519312
#117518552
#117518462
#117518402
#117517492
AGL(1,𝔽5)×C22⋊Q83
#759655