Finite Group Databasebeta

← #14326770

Subgroups — #14326770

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic
3C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
4#11752028C211yesmaximal, characteristic
5#11752028C211yesmaximal, characteristic
6Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
7Dic3×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
8#11751845C212yesmaximal, complemented
9#11751844C212yesmaximal, complemented
10AGL(1,𝔽5)×Dic3⋊C4C212yesmaximal, complemented
11#11751745C212yesmaximal, complemented
12#10617104—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×#6763C2211yescharacteristic
17C2×#6763C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2212yes—
19C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
20C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3⋊AGL(1,𝔽5)C2212yes—
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C2×#6712C411yescharacteristic, complemented
27C2×C5×Dic3⋊C4C411yescharacteristic, complemented
28C2×Dic3⋊Dic5C411yescharacteristic, complemented
29C2×#6669C411yescharacteristic, complemented
30D5×Dic3⋊C4C411yescharacteristic, complemented
31D5×Dic3⋊C4C411yescharacteristic, complemented
32D5×Dic3⋊C4C411yescharacteristic, complemented
33D5×Dic3⋊C4C411yescharacteristic, complemented
34D5×Dic3⋊C4C2211yescharacteristic
35D5×Dic3⋊C4C2211yescharacteristic
36D5×Dic3⋊C4C2211yescharacteristic
37D5×Dic3⋊C4C2211yescharacteristic
38#91235C2212yes—
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73458—51nomaximal, Hall
45C2×D5×C4⋊C4—31no—
46#65765—31no—
47#65765—31no—
48#65765—31no—
49C4×C22⋊AGL(1,𝔽5)—31no—
50C4×C22⋊AGL(1,𝔽5)—31no—
51C4×C22⋊AGL(1,𝔽5)D311yescharacteristic
52#65712—32no—
53#65711—32no—
54#65711—32no—
55C4⋊C4×AGL(1,𝔽5)—32no—
56C23×C3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×ΓL(1,𝔽16)C2312yes—
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2312yes—
61C22×C3×C4×C5C2×C411yescharacteristic
62C22×Dic15C2×C411yescharacteristic
63C22×Dic15C2×C411yescharacteristic
64C22×C5×Dic3C2×C411yescharacteristic
65C22×C5×Dic3C2×C411yescharacteristic
66C22×C3×Dic5C2×C411yescharacteristic
67C2×C3×C4×D5—42no—
68C2×C3×C4×D5C2×C411yescharacteristic
69C2×C3×C4×D5C2×C411yescharacteristic
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×C4×D5C2311yescharacteristic
72C2×D5×Dic3—24no—
73C2×D5×Dic3—42no—
74C2×D5×Dic3C2×C411yescharacteristic
75C2×D5×Dic3C2×C411yescharacteristic
76C2×D5×Dic3C2×C411yescharacteristic
77C2×D5×Dic3C2×C411yescharacteristic
78C2×D5×Dic3C2311yescharacteristic
79C2×D5×Dic3C2311yescharacteristic
80C2×D5×Dic3C2311yescharacteristic
81C2×D5×Dic3C2311yescharacteristic
82#6763—22no—
83#6763—22no—
84C4⋊ΓL(1,𝔽16)—42no—
85C3×C22⋊AGL(1,𝔽5)—22no—
86C3×C22⋊AGL(1,𝔽5)Q814yes—
87C3×C4×AGL(1,𝔽5)—42no—
88Dic3⋊AGL(1,𝔽5)—24no—
89Dic3⋊AGL(1,𝔽5)—42no—
90Dic3×AGL(1,𝔽5)—24no—
91Dic3×AGL(1,𝔽5)—42no—
92#6712C2×C411yescharacteristic
93#6712C2×C411yescharacteristic
94#6712C2×C411yescharacteristic
95#6712C2×C411yescharacteristic
96C5×Dic3⋊C4C2×C411yescharacteristic
97C5×Dic3⋊C4C2×C411yescharacteristic
98C5×Dic3⋊C4C2×C411yescharacteristic
99C5×Dic3⋊C4C2×C411yescharacteristic
100Dic3⋊Dic5C2×C411yescharacteristic
101Dic3⋊Dic5C2×C411yescharacteristic
102Dic3⋊Dic5C2×C411yescharacteristic
103Dic3⋊Dic5C2×C411yescharacteristic
104#6669C2×C411yescharacteristic
105#6669C2×C411yescharacteristic
106#6669C2×C411yescharacteristic
107#6669C2×C411yescharacteristic
108C22×Dic3⋊C4—51no—
109C3×C4×C22⋊C4—51no—
110#5212—51no—
111#4942—51no—
112#4942—51no—
113Dic3×C22⋊C4—51no—
114Dic3×C22⋊C4—51no—
115#4933—52no—
116C4×Dic3⋊C4—52no—
117#4655—52no—
118#4647—52no—
119C22×C4×D5—31no—
120C22×C4×D5—31no—
121C22×C4×D5C2×D311yescharacteristic
122C2×C22⋊AGL(1,𝔽5)—31no—
123C2×C22⋊AGL(1,𝔽5)—31no—
124C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
125C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
126C2×C4⋊AGL(1,𝔽5)—32no—
127C2×C4⋊AGL(1,𝔽5)—32no—
128C2×C4⋊AGL(1,𝔽5)—32no—
129C2×C4×AGL(1,𝔽5)—32no—
130C2×C4×AGL(1,𝔽5)—32no—
131C2×C4×AGL(1,𝔽5)C2×D312yes—
132C2×C5×C4⋊C4—31no—
133C2×C4⋊Dic5—31no—
134C2×#683—31no—
135C2×#683—31no—
136D5×C4⋊C4—31no—
137D5×C4⋊C4—31no—
138D5×C4⋊C4—31no—
139D5×C4⋊C4—31no—
140D5×C4⋊C4—31no—
141D5×C4⋊C4—31no—
142D5×C4⋊C4—31no—
143D5×C4⋊C4—31no—
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))⋊C4—32no—
148(C2×AGL(1,𝔽5))⋊C4—32no—
149(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
150#2345—151noSylow
151C23×C3×C5C22×C411yescharacteristic
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5C22×C411yescharacteristic
155C22×C3×D5C2×Q812yes—
156C22×C3×D5#4112yes—
157C22×C3×D5C2411yescharacteristic
158C2×ΓL(1,𝔽16)—22no—
159C2×ΓL(1,𝔽16)—22no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—22no—
164C2×C3×AGL(1,𝔽5)—22no—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—22no—
167C2×C3×AGL(1,𝔽5)—22no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)C2×Q814yes—
170C2×C3×C4×C5—41no—
171C2×C3×C4×C5C22×C411yescharacteristic
172C2×C3×C4×C5C22×C411yescharacteristic
173C2×Dic15—22no—
174C2×Dic15—41no—
175C2×Dic15C22×C411yescharacteristic
176C2×Dic15C22×C411yescharacteristic
177C2×Dic15C22×C411yescharacteristic
178C2×Dic15C22×C411yescharacteristic
179C2×C5×Dic3—22no—
180C2×C5×Dic3—41no—
181C2×C5×Dic3C22×C411yescharacteristic
182C2×C5×Dic3C22×C411yescharacteristic
183C2×C5×Dic3C22×C411yescharacteristic
184C2×C5×Dic3C22×C411yescharacteristic
185C2×C3×Dic5—41no—
186C2×C3×Dic5C22×C411yescharacteristic
187C2×C3×Dic5C22×C411yescharacteristic
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×C4×D5—41no—
191C3×C4×D5—41no—
192D5×Dic3—22no—
193D5×Dic3—22no—
194D5×Dic3—22no—
195D5×Dic3—22no—
196D5×Dic3—22no—
197D5×Dic3—41no—
198D5×Dic3—41no—
199D5×Dic3#4114yes—
200C23×C3×C4—51no—
201C23×Dic3—51no—
202C23×Dic3—51no—
203C2×C3×C22⋊C4—51no—
204C2×C3×C22⋊C4—51no—
205C2×C3×C42—52no—
206C2×#217—51no—
207C2×#217—51no—
208C2×C4⋊Dic3—52no—
209C2×Dic3⋊C4—51no—
210C2×Dic3⋊C4—51no—
211C2×Dic3⋊C4—51no—
212C2×Dic3⋊C4—51no—
213C2×Dic3⋊C4—51no—
214C2×Dic3⋊C4—51no—
215C2×Dic3⋊C4—51no—
216C2×Dic3⋊C4—51no—
217C2×Dic3⋊C4—51no—
218C2×Dic3⋊C4—51no—
219C2×Dic3⋊C4—51no—
220C2×Dic3⋊C4—52no—
221C2×Dic3⋊C4—52no—
222C2×Dic3⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
223C2×C4×Dic3—52no—
224C2×C4×Dic3—52no—
225C3×#95—52no—
226C3⋊#95—52no—
227C3⋊#95—52no—
228C3⋊#95—52no—
229C3⋊#95—52no—
230C3⋊#95—52no—
231C23×D5C22×D311yescharacteristic
232C22×AGL(1,𝔽5)—32no—
233C22×AGL(1,𝔽5)—32no—
234C22×AGL(1,𝔽5)C22×D312yes—
235C22×AGL(1,𝔽5)C22×D312yes—
236C22×C4×C5—31no—
237C22×C4×C5—31no—
238C22×C4×C5C4×D311yescharacteristic
239C22×Dic5—31no—
240C22×Dic5—31no—
241C22×Dic5C4×D311yescharacteristic
242C2×C4×D5—31no—
243C2×C4×D5—31no—
244C2×C4×D5—31no—
245C2×C4×D5—31no—
246C2×C4×D5—31no—
247C2×C4×D5—31no—
248C2×C4×D5—31no—
249C2×C4×D5—31no—
250C2×C4×D5—42no—
251C2×C4×D5—64no—
252C2×C4×D5—122no—
253C2×C4×D5C4×D311yescharacteristic
254C2×C4×D5C4×D311yescharacteristic
255C2×C4×D5C22×D311yescharacteristic
256C2×C4×D5C22×D311yescharacteristic
257C22⋊AGL(1,𝔽5)—22no—
258C22⋊AGL(1,𝔽5)—62no—
259C22⋊AGL(1,𝔽5)—62no—
260C22⋊AGL(1,𝔽5)Dic614yes—
261C4⋊AGL(1,𝔽5)—64no—
262C4⋊AGL(1,𝔽5)—122no—
263C4⋊AGL(1,𝔽5)—122no—
264C4×AGL(1,𝔽5)—42no—
265C4×AGL(1,𝔽5)—64no—
266C4×AGL(1,𝔽5)—122no—
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—31no—
271C4⋊Dic5—31no—
272C4⋊Dic5—31no—
273C4⋊Dic5—31no—
274C4⋊Dic5—31no—
275#683—31no—
276#683—31no—
277#683—31no—
278#683—31no—
279#683—31no—
280#683—31no—
281#683—31no—
282#683—31no—
283C22×C4⋊C4—151no—
284#389—152no—
285#387—152no—
286#387—152no—
287#380—151no—
288#380—151no—
289#380—151no—
290C4×C4⋊C4—152no—
291C4×C22⋊C4—51no—
292C4×C22⋊C4—151no—
293C4×C22⋊C4—151no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5C4×Q812yes—
297C22×C3×C5C23×C411yescharacteristic
298C2×C3×D5—21no—
299C2×C3×D5—21no—
300C2×C3×D5—24no—
301C2×C3×D5—24no—
302C2×C3×D5C4×Q812yes—
303C2×C3×D5C22×Q811yescharacteristic
304C2×C3×D5C2×#4111yescharacteristic
305C2×C3×D5C2×#4112yes—
306C2×C3×D5H(5,𝔽2)12yes—
307ΓL(1,𝔽16)—42no—
308ΓL(1,𝔽16)—42no—
309C3×AGL(1,𝔽5)—24no—
310C3×AGL(1,𝔽5)—42no—
311C3×C4×C5—21no—
312C3×C4×C5—21no—
313Dic15—21no—
314Dic15—21no—
315Dic15—21no—
316Dic15#11712yes—
317C3×Dic5—21no—
318C3×Dic5—21no—
319C5×Dic3—21no—
320C5×Dic3—21no—
321C5×Dic3—21no—
322C5×Dic3#11712yes—
323C24×C3—51no—
324C22×C3×C4—52no—
325C22×C3×C4—51no—
326C22×C3×C4—51no—
327C22×C3×C4—51no—
328C22×C3×C4—51no—
329C22×C3×C4—51no—
330C22×C3×C4—52no—
331C22×C3×C4—202no—
332C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
333C22×Dic3—51no—
334C22×Dic3—51no—
335C22×Dic3—51no—
336C22×Dic3—51no—
337C22×Dic3—51no—
338C22×Dic3—51no—
339C22×Dic3—51no—
340C22×Dic3—51no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—52no—
344C22×Dic3—52no—
345C22×Dic3—104no—
346C22×Dic3—202no—
347C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
348C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
349C3×C22⋊C4—54no—
350C3×C22⋊C4—102no—
351C3×C42—202no—
352#217—102no—
353#217—102no—
354C4⋊Dic3—202no—
355Dic3⋊C4—51no—
356Dic3⋊C4—51no—
357Dic3⋊C4—51no—
358Dic3⋊C4—51no—
359Dic3⋊C4—51no—
360Dic3⋊C4—51no—
361Dic3⋊C4—51no—
362Dic3⋊C4—51no—
363Dic3⋊C4—51no—
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—51no—
367Dic3⋊C4—104no—
368Dic3⋊C4—202no—
369Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
370Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
371Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
372Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
373C4×Dic3—104no—
374C4×Dic3—202no—
375C23×C5C2×C4×D311yescharacteristic
376C22×D5—22no—
377C22×D5—22no—
378C22×D5C2×Dic612yes—
379C22×D5C2×C4×D311yescharacteristic
380C22×D5#23512yes—
381C22×D5C23×D311yescharacteristic
382C2×AGL(1,𝔽5)—22no—
383C2×AGL(1,𝔽5)—22no—
384C2×AGL(1,𝔽5)—22no—
385C2×AGL(1,𝔽5)—22no—
386C2×AGL(1,𝔽5)—22no—
387C2×AGL(1,𝔽5)—62no—
388C2×AGL(1,𝔽5)—62no—
389C2×AGL(1,𝔽5)—62no—
390C2×AGL(1,𝔽5)—62no—
391C2×AGL(1,𝔽5)—62no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)C2×Dic614yes—
394C2×C4×C5—31no—
395C2×C4×C5—31no—
396C2×C4×C5—31no—
397C2×C4×C5—31no—
398C2×C4×C5—41no—
399C2×C4×C5—62no—
400C2×C4×C5—121no—
401C2×C4×C5C2×C4×D311yescharacteristic
402C2×C4×C5C2×C4×D311yescharacteristic
403C2×Dic5—31no—
404C2×Dic5—31no—
405C2×Dic5—31no—
406C2×Dic5—31no—
407C2×Dic5—41no—
408C2×Dic5—62no—
409C2×Dic5—121no—
410C2×Dic5C2×C4×D311yescharacteristic
411C2×Dic5C2×C4×D311yescharacteristic
412C4×D5—22no—
413C4×D5—22no—
414C4×D5—34no—
415C4×D5—41no—
416C4×D5—41no—
417C4×D5—62no—
418C4×D5—62no—
419C4×D5—62no—
420C4×D5—62no—
421C4×D5—62no—
422C4×D5—121no—
423C4×D5—121no—
424C23×C4—51no—
425C23×C4—151no—
426C23×C4—151no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—151no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—151no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—152no—
440C2×C4⋊C4—152no—
441C2×C4⋊C4—152no—
442C2×C22⋊C4—51no—
443C2×C22⋊C4—51no—
444C2×C22⋊C4—151no—
445C2×C22⋊C4—151no—
446C2×C42—52no—
447C2×C42—152no—
448C2×C42—152no—
449#95—52no—
450#95—152no—
451#95—152no—
452#95—152no—
453#95—152no—
454#95—152no—
455C2×C3×C5—22no—
456C2×C3×C5C2×#11711yescharacteristic
457C2×C3×C5C2×C4×Q811yescharacteristic
458C2×C3×C5#51811yescharacteristic
459C3×D5—22no—
460C3×D5#55312yes—
461C3×D5#55412yes—
462C23×C3—51no—
463C23×C3—52no—
464C23×C3—52no—
465C23×C3—51no—
466C23×C3—102no—
467C23×C3—102no—
468C23×C3C22×AGL(1,𝔽5)11yescharacteristic
469C2×C3×C4—41no—
470C2×C3×C4—54no—
471C2×C3×C4—51no—
472C2×C3×C4—51no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4—201no—
481C2×C3×C4—201no—
482C2×C3×C4—201no—
483C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
484C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
485C2×Dic3—22no—
486C2×Dic3—41no—
487C2×Dic3—51no—
488C2×Dic3—54no—
489C2×Dic3—51no—
490C2×Dic3—51no—
491C2×Dic3—51no—
492C2×Dic3—102no—
493C2×Dic3—102no—
494C2×Dic3—102no—
495C2×Dic3—102no—
496C2×Dic3—102no—
497C2×Dic3—102no—
498C2×Dic3—102no—
499C2×Dic3—102no—
500C2×Dic3—102no—
501C2×Dic3—102no—
502C2×Dic3—102no—
503C2×Dic3—102no—
504C2×Dic3—201no—
505C2×Dic3—201no—
506C2×Dic3—201no—
507C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
508C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
509C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
510C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
511C22×C5—21no—
512C22×C5—21no—
513C22×C5C4×Dic612yes—
514C22×C5C22×C4×D311yescharacteristic
515C2×D5—21no—
516C2×D5—21no—
517C2×D5—24no—
518C2×D5—24no—
519C2×D5C4×Dic612yes—
520C2×D5C22×Dic611yescharacteristic
521C2×D5C2×#23511yescharacteristic
522C2×D5#100412yes—
523C2×D5D3×#4112yes—
524AGL(1,𝔽5)—24no—
525AGL(1,𝔽5)—42no—
526AGL(1,𝔽5)—122no—
527AGL(1,𝔽5)—122no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—32no—
531C4×C5—61no—
532C4×C5—61no—
533C4×C5—61no—
534Dic5—21no—
535Dic5—21no—
536Dic5—32no—
537Dic5—61no—
538Dic5—61no—
539Dic5—61no—
540C24—51no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—52no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—52no—
550C22×C4—151no—
551C22×C4—151no—
552C22×C4—151no—
553C22×C4—151no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—152no—
561C22×C4—152no—
562C22×C4—202no—
563C22×C4—304no—
564C22×C4—602no—
565C22×C4D3×AGL(1,𝔽5)11yescharacteristic
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—151no—
571C4⋊C4—151no—
572C4⋊C4—151no—
573C4⋊C4—151no—
574C4⋊C4—151no—
575C4⋊C4—151no—
576C4⋊C4—151no—
577C4⋊C4—151no—
578C4⋊C4—151no—
579C4⋊C4—151no—
580C4⋊C4—151no—
581C4⋊C4—151no—
582C4⋊C4—304no—
583C4⋊C4—602no—
584C4⋊C4—602no—
585C22⋊C4—54no—
586C22⋊C4—102no—
587C22⋊C4—302no—
588C22⋊C4—302no—
589C42—202no—
590C42—304no—
591C42—602no—
592C3×C5#234511yescharacteristic, complemented, Hall
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—52no—
596C22×C3—52no—
597C22×C3—51no—
598C22×C3—51no—
599C22×C3—52no—
600C22×C3—104no—
601C22×C3—104no—
602C22×C3—101no—
603C22×C3—101no—
604C22×C3Q8×AGL(1,𝔽5)12yes—
605C22×C3C23×AGL(1,𝔽5)11yescharacteristic
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—104no—
609C3×C4—101no—
610C3×C4—101no—
611C3×C4—202no—
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—52no—
616Dic3—101no—
617Dic3—101no—
618Dic3—101no—
619Dic3—202no—
620Dic3—202no—
621Dic3#413012yes—
622C2×C5—22no—
623C2×C5C2×C4×Dic611yescharacteristic
624C2×C5#548611yescharacteristic
625C2×C5D3×#11711yescharacteristic
626D5—22no—
627D5#553912yes—
628D5#554012yes—
629C23—51no—
630C23—52no—
631C23—52no—
632C23—51no—
633C23—102no—
634C23—102no—
635C23C2×D3×AGL(1,𝔽5)11yescharacteristic
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—41no—
641C2×C4—54no—
642C2×C4—51no—
643C2×C4—51no—
644C2×C4—62no—
645C2×C4—102no—
646C2×C4—102no—
647C2×C4—102no—
648C2×C4—102no—
649C2×C4—102no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—121no—
653C2×C4—154no—
654C2×C4—151no—
655C2×C4—151no—
656C2×C4—151no—
657C2×C4—151no—
658C2×C4—201no—
659C2×C4—201no—
660C2×C4—201no—
661C2×C4—302no—
662C2×C4—302no—
663C2×C4—302no—
664C2×C4—302no—
665C2×C4—302no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—302no—
669C2×C4—302no—
670C2×C4—302no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—601no—
674C2×C4—601no—
675C2×C4—601no—
676C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
677C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
678C2×C3—22no—
679C2×C3—52no—
680C2×C3—52no—
681C2×C3—102no—
682C2×C3C2×#413011yescharacteristic
683C2×C3#6625811yescharacteristic
684C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
685C5#7345811yescharacteristic, complemented, Sylow
686C22—21no—
687C22—21no—
688C22—51no—
689C22—51no—
690C22—52no—
691C22—52no—
692C22—52no—
693C22—104no—
694C22—104no—
695C22—101no—
696C22—101no—
697C22AGL(1,𝔽5)×Dic612yes—
698C22C22×D3×AGL(1,𝔽5)11yescharacteristic
699C4—21no—
700C4—21no—
701C4—32no—
702C4—61no—
703C4—61no—
704C4—61no—
705C4—104no—
706C4—101no—
707C4—101no—
708C4—152no—
709C4—202no—
710C4—301no—
711C4—301no—
712C4—301no—
713C4—602no—
714C4—602no—
715C3#1061710411yescharacteristic, complemented, Sylow
716C2—22no—
717C2—52no—
718C2—52no—
719C2—102no—
720C2C2×AGL(1,𝔽5)×Dic611yescharacteristic
721C2D3×#413011yescharacteristic
722C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #11751845C2semidirect
9. #11751844C2semidirect
10. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
11. #11751745C2semidirect
26. C2×#6712C4semidirect
27. C2×C5×Dic3⋊C4C4semidirect
28. C2×Dic3⋊Dic5C4semidirect
29. C2×#6669C4semidirect
30. D5×Dic3⋊C4C4semidirect
31. D5×Dic3⋊C4C4semidirect
32. D5×Dic3⋊C4C4semidirect
33. D5×Dic3⋊C4C4semidirect
222. C2×Dic3⋊C4AGL(1,𝔽5)semidirect
592. C3×C5#2345semidirect
685. C5#73458semidirect
715. C3#10617104semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
#117524242
C3×C4×C22⋊AGL(1,𝔽5)2
#117520282
Dic3×C22⋊AGL(1,𝔽5)2
#117518452
#117518442
AGL(1,𝔽5)×Dic3⋊C42
#117517452
#106171043
#734585