Finite Group Databasebeta

← #14329877

Subgroups — #14329877

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#888C211yesmaximal, characteristic
2C4⋊C4×ΓL(1,𝔽16)C211yesmaximal, characteristic
3C3×#65712C211yesmaximal, characteristic
4#11751861C211yesmaximal, characteristic
5C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
6Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7#11751842C212yesmaximal
8AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic
9#11751837C212yesmaximal
10#11751833C212yesmaximal
11#11751752C212yesmaximal
12#10617389—31nomaximal, Hall
13C2×D5×Dic6C2212yes—
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
16C2×C4×ΓL(1,𝔽16)C2212yes—
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)C2211yescharacteristic
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25#91777C411yescharacteristic, complemented
26C5×#888C411yescharacteristic, complemented
27C3×D5×C4⋊C4C2211yescharacteristic
28#91470C411yescharacteristic, complemented
29#91469C411yescharacteristic, complemented
30D5×C4⋊Dic3C2211yescharacteristic
31D5×Dic3⋊C4C2212yes—
32C4×D5×Dic3C2211yescharacteristic
33#91329C412yescomplemented
34#91328C412yescomplemented
35#91235C2212yes—
36C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42#75987—51nomaximal, Hall
43D5×C4⋊Q8—31no—
44(C2×AGL(1,𝔽5))⋊Q8—32no—
45(C2×AGL(1,𝔽5))⋊Q8—32no—
46#65712—32no—
47#65712—31no—
48#65712D311yescharacteristic
49C4⋊C4×AGL(1,𝔽5)—31no—
50C4⋊C4×AGL(1,𝔽5)—32no—
51C4⋊C4×AGL(1,𝔽5)—31no—
52C4×C4⋊AGL(1,𝔽5)—31no—
53C4×C4⋊AGL(1,𝔽5)—31no—
54C22×ΓL(1,𝔽16)C2311yescharacteristic
55C22×ΓL(1,𝔽16)C2312yes—
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×C3×AGL(1,𝔽5)C2312yes—
58C22×C3×AGL(1,𝔽5)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C2×Dic30C2×C412yes—
61C2×C5×Dic6C2×C412yes—
62C2×C3×C4×D5C2312yes—
63C2×C3×C4×D5C2311yescharacteristic
64C2×#1204C2×C412yes—
65C2×#1204C2×C412yes—
66C2×D5×Dic3C2312yes—
67C2×D5×Dic3C2311yescharacteristic
68C2×D5×Dic3C2311yescharacteristic
69D5×Dic6—42no—
70D5×Dic6—42no—
71C4⋊ΓL(1,𝔽16)Q814yescomplemented
72C4×ΓL(1,𝔽16)—22no—
73C4×ΓL(1,𝔽16)—42no—
74C3×C4⋊AGL(1,𝔽5)—22no—
75C3×C4⋊AGL(1,𝔽5)—42no—
76C3×C4×AGL(1,𝔽5)—22no—
77Dic3⋊AGL(1,𝔽5)—22no—
78Dic3⋊AGL(1,𝔽5)—42no—
79Dic3⋊AGL(1,𝔽5)Q814yescomplemented
80Dic3×AGL(1,𝔽5)—24no—
81Dic3×AGL(1,𝔽5)—42no—
82C3×C5×C4⋊C4C2×C411yescharacteristic
83C4⋊Dic15C2×C411yescharacteristic
84#6712C2×C412yes—
85C4×Dic15C2×C411yescharacteristic
86C5×C4⋊Dic3C2×C411yescharacteristic
87C5×Dic3⋊C4C2×C412yes—
88C4×C5×Dic3C2×C411yescharacteristic
89C3×C4⋊Dic5C2×C411yescharacteristic
90C3×#683C2×C412yes—
91Dic3⋊Dic5C2×C412yes—
92#6669C2×C412yes—
93#6668C2×C412yes—
94Dic3×Dic5C2×C411yescharacteristic
95Dic3×Dic5C2×C411yescharacteristic
96C2×#888—51no—
97C3×#389—51no—
98#4976—52no—
99Dic3×C4⋊C4—51no—
100Dic3×C4⋊C4—51no—
101#4973—52no—
102#4972—51no—
103C4×C4⋊Dic3—51no—
104C4×Dic3⋊C4—51no—
105#4649—52no—
106#4646—52no—
107C2×Q8×D5—32no—
108C2×C4⋊AGL(1,𝔽5)—31no—
109C2×C4⋊AGL(1,𝔽5)—31no—
110C2×C4⋊AGL(1,𝔽5)—31no—
111C2×C4⋊AGL(1,𝔽5)—32no—
112C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
113C2×C4⋊AGL(1,𝔽5)C2×D312yes—
114C2×C4×AGL(1,𝔽5)—32no—
115C2×C4×AGL(1,𝔽5)—31no—
116C2×C4×AGL(1,𝔽5)—32no—
117C2×C4×AGL(1,𝔽5)—32no—
118C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
119C5×C4⋊Q8—31no—
120#4090—32no—
121D5×C4⋊C4—32no—
122D5×C4⋊C4—31no—
123D5×C4⋊C4C2×D311yescharacteristic
124#4034—31no—
125#4034—31no—
126#4034—32no—
127C42×D5—31no—
128#4015—31no—
129(C2×AGL(1,𝔽5))⋊C4—32no—
130(C2×AGL(1,𝔽5))⋊C4—31no—
131(C2×AGL(1,𝔽5))⋊C4—31no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
133(C2×AGL(1,𝔽5))⋊C4—32no—
134(C2×AGL(1,𝔽5))⋊C4—32no—
135(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
136#2369—151noSylow
137C22×C3×D5C2411yescharacteristic
138C2×ΓL(1,𝔽16)—22no—
139C2×ΓL(1,𝔽16)—21no—
140C2×ΓL(1,𝔽16)—22no—
141C2×ΓL(1,𝔽16)—21no—
142C2×ΓL(1,𝔽16)—21no—
143C2×ΓL(1,𝔽16)—21no—
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)C2×Q812yes—
146C2×ΓL(1,𝔽16)C2×Q814yes—
147C2×C3×AGL(1,𝔽5)—21no—
148C2×C3×AGL(1,𝔽5)—21no—
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—21no—
151C2×C3×AGL(1,𝔽5)—21no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—22no—
154C2×C3×AGL(1,𝔽5)—21no—
155C2×C3×AGL(1,𝔽5)C2×Q812yes—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C22×C411yescharacteristic
158C2×Dic15C22×C411yescharacteristic
159C2×Dic15C22×C412yes—
160C2×Dic15C22×C411yescharacteristic
161Dic30—42no—
162C2×C5×Dic3C22×C411yescharacteristic
163C2×C5×Dic3C22×C412yes—
164C2×C5×Dic3C22×C411yescharacteristic
165C5×Dic6—42no—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C411yescharacteristic
168C3×C4×D5—22no—
169C3×C4×D5—22no—
170C3×C4×D5C2×Q812yes—
171C3×C4×D5#4112yes—
172#1204—42no—
173#1204—42no—
174D5×Dic3—22no—
175D5×Dic3—22no—
176D5×Dic3—21no—
177D5×Dic3—21no—
178D5×Dic3C2×Q812yes—
179D5×Dic3#4112yes—
180C22×Dic6—52no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—51no—
183C2×C3×C4⋊C4—52no—
184C2×C3×C42—51no—
185C2×C4⋊Dic3—51no—
186C2×C4⋊Dic3—51no—
187C2×Dic3⋊C4—51no—
188C2×Dic3⋊C4—52no—
189C2×Dic3⋊C4—51no—
190C2×Dic3⋊C4—52no—
191C2×C4×Dic3—51no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—51no—
194C2×C4×Dic3—52no—
195C2×C4×Dic3—52no—
196#888—52no—
197#888—51no—
198#888—51no—
199#888—52no—
200#888—51no—
201#888AGL(1,𝔽5)11yescharacteristic, complemented
202C3×#95—52no—
203C3⋊#95—51no—
204C3⋊#95—52no—
205C3⋊#95—52no—
206C3⋊#95—51no—
207C3⋊#95—52no—
208C3⋊#95—52no—
209C22×AGL(1,𝔽5)—31no—
210C22×AGL(1,𝔽5)—32no—
211C22×AGL(1,𝔽5)—31no—
212C22×AGL(1,𝔽5)C22×D312yes—
213C22×AGL(1,𝔽5)C22×D311yescharacteristic
214C22×AGL(1,𝔽5)C22×D311yescharacteristic
215C2×C5×Q8—32no—
216Q8×D5—122no—
217Q8×D5—122no—
218C2×C4×D5—31no—
219C2×C4×D5—32no—
220C2×C4×D5—31no—
221C2×C4×D5C22×D312yes—
222C2×C4×D5C22×D311yescharacteristic
223C2×Dic10—32no—
224C2×Dic10—32no—
225C2×Dic10—32no—
226C4⋊AGL(1,𝔽5)—22no—
227C4⋊AGL(1,𝔽5)—34no—
228C4⋊AGL(1,𝔽5)—34no—
229C4⋊AGL(1,𝔽5)—42no—
230C4⋊AGL(1,𝔽5)—62no—
231C4⋊AGL(1,𝔽5)—122no—
232C4×AGL(1,𝔽5)—22no—
233C4×AGL(1,𝔽5)—64no—
234C4×AGL(1,𝔽5)—62no—
235C4×AGL(1,𝔽5)—122no—
236C4×AGL(1,𝔽5)—122no—
237C5×C4⋊C4—32no—
238C5×C4⋊C4—31no—
239C5×C4⋊C4C4×D311yescharacteristic
240C42×C5—31no—
241C4⋊Dic5—31no—
242C4⋊Dic5—32no—
243C4⋊Dic5C4×D311yescharacteristic
244#683—32no—
245#683—32no—
246#683—32no—
247#683C4×D312yes—
248C4×Dic5—31no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C2×C4⋊Q8—151no—
252#391—152no—
253#391—152no—
254#389—51no—
255#389—151no—
256#389—152no—
257C4×C4⋊C4—152no—
258C4×C4⋊C4—151no—
259C4×C4⋊C4—151no—
260C4×C4⋊C4—151no—
261C4×C4⋊C4—151no—
262C22×C3×C5C23×C411yescharacteristic
263C2×C3×D5C22×Q811yescharacteristic
264C2×C3×D5C22×Q811yescharacteristic
265C2×C3×D5C2×#4111yescharacteristic
266C2×C3×D5C2×#4111yescharacteristic
267C2×C3×D5H(5,𝔽2)11yescharacteristic
268C2×C3×D5H(5,𝔽2)11yescharacteristic
269ΓL(1,𝔽16)—22no—
270ΓL(1,𝔽16)—24no—
271ΓL(1,𝔽16)—41no—
272C3×AGL(1,𝔽5)—22no—
273C3×AGL(1,𝔽5)—42no—
274C3×AGL(1,𝔽5)—41no—
275C3×C4×C5—22no—
276C3×C4×C5C4×Q812yes—
277Dic15—21no—
278Dic15—22no—
279Dic15C4×Q812yes—
280C3×Dic5—22no—
281C3×Dic5C4×Q812yes—
282C5×Dic3—21no—
283C5×Dic3—22no—
284C5×Dic3C4×Q812yes—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—52no—
288C22×C3×C4—51no—
289C22×C3×C4—52no—
290C22×Dic3—51no—
291C22×Dic3—51no—
292C22×Dic3—52no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C2×Dic6—52no—
297C2×Dic6—52no—
298C2×Dic6—52no—
299C2×Dic6—202no—
300C2×Dic6—202no—
301C2×Dic6C2×AGL(1,𝔽5)12yes—
302C3×C4⋊C4—52no—
303C3×C4⋊C4—51no—
304C3×C4⋊C4—102no—
305C3×C4⋊C4—202no—
306C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
307C3×C42—102no—
308C4⋊Dic3—54no—
309C4⋊Dic3—51no—
310C4⋊Dic3—52no—
311C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
312Dic3⋊C4—54no—
313Dic3⋊C4—52no—
314Dic3⋊C4—52no—
315Dic3⋊C4—52no—
316Dic3⋊C4—102no—
317Dic3⋊C4—202no—
318Dic3⋊C4C2×AGL(1,𝔽5)12yes—
319C4×Dic3—51no—
320C4×Dic3—51no—
321C4×Dic3—51no—
322C4×Dic3—104no—
323C4×Dic3—102no—
324C4×Dic3—202no—
325C4×Dic3—202no—
326C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
327C22×D5C23×D311yescharacteristic
328C2×AGL(1,𝔽5)—21no—
329C2×AGL(1,𝔽5)—21no—
330C2×AGL(1,𝔽5)—21no—
331C2×AGL(1,𝔽5)—22no—
332C2×AGL(1,𝔽5)—21no—
333C2×AGL(1,𝔽5)—22no—
334C2×AGL(1,𝔽5)—22no—
335C2×AGL(1,𝔽5)—21no—
336C2×AGL(1,𝔽5)—32no—
337C2×AGL(1,𝔽5)—34no—
338C2×AGL(1,𝔽5)—61no—
339C2×AGL(1,𝔽5)—62no—
340C2×AGL(1,𝔽5)—61no—
341C2×AGL(1,𝔽5)—62no—
342C2×AGL(1,𝔽5)—61no—
343C2×AGL(1,𝔽5)—61no—
344C2×AGL(1,𝔽5)—61no—
345C2×AGL(1,𝔽5)D3×Q812yes—
346C5×Q8—122no—
347C2×C4×C5—31no—
348C2×C4×C5—31no—
349C2×C4×C5—32no—
350C2×C4×C5C2×C4×D312yes—
351C2×C4×C5C2×C4×D311yescharacteristic
352C2×Dic5—31no—
353C2×Dic5—31no—
354C2×Dic5—32no—
355C2×Dic5C2×C4×D312yes—
356C2×Dic5C2×C4×D311yescharacteristic
357C4×D5—22no—
358C4×D5—22no—
359C4×D5—32no—
360C4×D5—32no—
361C4×D5—62no—
362C4×D5—61no—
363C4×D5—62no—
364C4×D5—61no—
365C4×D5#23712yes—
366C4×D5D3×Q812yes—
367Dic10—122no—
368Dic10—122no—
369Dic10—122no—
370C22×Q8—152no—
371C4⋊Q8—31no—
372C4⋊Q8—151no—
373C4⋊Q8—152no—
374C4⋊Q8—151no—
375C4⋊Q8—152no—
376C4⋊Q8—151no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—51no—
379C2×C4⋊C4—52no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—151no—
382C2×C4⋊C4—151no—
383C2×C4⋊C4—151no—
384C2×C4⋊C4—151no—
385C2×C4⋊C4—152no—
386C2×C42—51no—
387C2×C42—151no—
388C2×C42—151no—
389C2×C42—152no—
390C2×C42—152no—
391C2×C42—152no—
392#95—52no—
393#95—152no—
394#95—152no—
395#95—152no—
396#95—151no—
397#95—152no—
398#95—151no—
399C2×C3×C5C2×C4×Q811yescharacteristic
400C2×C3×C5C2×C4×Q811yescharacteristic
401C2×C3×C5#51811yescharacteristic
402C3×D5#55411yescharacteristic
403C3×D5#55411yescharacteristic
404C3×D5#55511yescharacteristic
405C3×D5Q8211yescharacteristic
406C23×C3—51no—
407C2×C3×C4—51no—
408C2×C3×C4—52no—
409C2×C3×C4—52no—
410C2×C3×C4—52no—
411C2×C3×C4—52no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—101no—
415C2×C3×C4—101no—
416C2×C3×C4—102no—
417C2×C3×C4—101no—
418C2×C3×C4—102no—
419C2×C3×C4—101no—
420C2×C3×C4—102no—
421C2×C3×C4—101no—
422C2×C3×C4C22×AGL(1,𝔽5)12yes—
423C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
424C2×Dic3—51no—
425C2×Dic3—52no—
426C2×Dic3—52no—
427C2×Dic3—52no—
428C2×Dic3—54no—
429C2×Dic3—51no—
430C2×Dic3—52no—
431C2×Dic3—102no—
432C2×Dic3—102no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435C2×Dic3—102no—
436C2×Dic3—101no—
437C2×Dic3—102no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3—101no—
441C2×Dic3—101no—
442C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
443C2×Dic3C22×AGL(1,𝔽5)12yes—
444C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
445Dic6—42no—
446Dic6—202no—
447Dic6—202no—
448Dic6—202no—
449C22×C5C22×C4×D311yescharacteristic
450C2×D5C2×#23711yescharacteristic
451C2×D5#100411yescharacteristic
452C2×D5C2×D3×Q811yescharacteristic
453C2×D5C2×D3×Q811yescharacteristic
454C2×D5D3×#4111yescharacteristic
455C2×D5#100911yescharacteristic
456AGL(1,𝔽5)—22no—
457AGL(1,𝔽5)—41no—
458AGL(1,𝔽5)—42no—
459AGL(1,𝔽5)—62no—
460AGL(1,𝔽5)—64no—
461AGL(1,𝔽5)—121no—
462C4×C5—22no—
463C4×C5—32no—
464C4×C5—61no—
465C4×C5—62no—
466C4×C5#88712yes—
467Dic5—22no—
468Dic5—32no—
469Dic5—61no—
470Dic5—62no—
471Dic5#88712yes—
472C2×Q8—32no—
473C2×Q8—152no—
474C2×Q8—152no—
475C2×Q8—152no—
476C2×Q8—602no—
477C2×Q8—602no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—52no—
481C22×C4—52no—
482C22×C4—51no—
483C22×C4—151no—
484C22×C4—151no—
485C22×C4—152no—
486C22×C4—151no—
487C22×C4—152no—
488C22×C4—151no—
489C4⋊C4—32no—
490C4⋊C4—31no—
491C4⋊C4—52no—
492C4⋊C4—51no—
493C4⋊C4—102no—
494C4⋊C4—152no—
495C4⋊C4—152no—
496C4⋊C4—152no—
497C4⋊C4—154no—
498C4⋊C4—154no—
499C4⋊C4—152no—
500C4⋊C4—151no—
501C4⋊C4—202no—
502C4⋊C4—302no—
503C4⋊C4—602no—
504C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
505C42—31no—
506C42—102no—
507C42—151no—
508C42—151no—
509C42—151no—
510C42—302no—
511C42—304no—
512C42—602no—
513C42—602no—
514C3×C5#236911yescharacteristic, complemented, Hall
515C22×C3—51no—
516C22×C3—51no—
517C22×C3—51no—
518C22×C3—51no—
519C22×C3—51no—
520C22×C3—51no—
521C22×C3C23×AGL(1,𝔽5)11yescharacteristic
522C3×C4—22no—
523C3×C4—52no—
524C3×C4—102no—
525C3×C4—102no—
526C3×C4—202no—
527C3×C4—201no—
528C3×C4Q8×AGL(1,𝔽5)12yes—
529Dic3—21no—
530Dic3—22no—
531Dic3—52no—
532Dic3—104no—
533Dic3—102no—
534Dic3—101no—
535Dic3—102no—
536Dic3—201no—
537Dic3Q8×AGL(1,𝔽5)12yes—
538C2×C5C2×#88711yescharacteristic
539C2×C5#554511yescharacteristic
540C2×C5C4×D3×Q811yescharacteristic
541D5#561611yescharacteristic
542D5#563511yescharacteristic
543D5#569011yescharacteristic
544D5#572211yescharacteristic
545C23—51no—
546Q8—122no—
547Q8—602no—
548Q8—602no—
549Q8—602no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—32no—
553C2×C4—51no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—101no—
566C2×C4—102no—
567C2×C4—101no—
568C2×C4—152no—
569C2×C4—152no—
570C2×C4—151no—
571C2×C4—154no—
572C2×C4—152no—
573C2×C4—151no—
574C2×C4—152no—
575C2×C4—302no—
576C2×C4—302no—
577C2×C4—301no—
578C2×C4—301no—
579C2×C4—301no—
580C2×C4—302no—
581C2×C4—301no—
582C2×C4—302no—
583C2×C4—301no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4C2×D3×AGL(1,𝔽5)12yes—
587C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
588C2×C3—51no—
589C2×C3—51no—
590C2×C3—51no—
591C2×C3—51no—
592C2×C3#6625811yescharacteristic
593C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
594C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
595C5#7598711yescharacteristic, complemented, Sylow
596C22—51no—
597C22—51no—
598C22—51no—
599C22—51no—
600C22—51no—
601C22—51no—
602C22C22×D3×AGL(1,𝔽5)11yescharacteristic
603C4—22no—
604C4—32no—
605C4—52no—
606C4—61no—
607C4—62no—
608C4—102no—
609C4—102no—
610C4—152no—
611C4—201no—
612C4—202no—
613C4—302no—
614C4—304no—
615C4—301no—
616C4—302no—
617C4—601no—
618C4ΓL(1,𝔽16)⋊Q812yes—
619C3#1061738911yescharacteristic, complemented, Sylow
620C2—51no—
621C2—51no—
622C2—51no—
623C2—51no—
624C2C2×ΓL(1,𝔽16)⋊Q811yescharacteristic
625C2#1175684511yescharacteristic
626C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
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#2369
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
25. #91777C4semidirect
26. C5×#888C4semidirect
28. #91470C4semidirect
29. #91469C4semidirect
33. #91329C4semidirect
34. #91328C4semidirect
71. C4⋊ΓL(1,𝔽16)Q8semidirect
79. Dic3⋊AGL(1,𝔽5)Q8semidirect
201. #888AGL(1,𝔽5)semidirect
514. C3×C5#2369semidirect
595. C5#75987semidirect
619. C3#10617389semidirect

Maximal subgroups

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

subgroupindex
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
#117518372
#117518332
#117517522
#106173893
#759875