Finite Group Databasebeta

← #14327486

Subgroups — #14327486

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×#91923C211yesmaximal, characteristic, complemented
3D4×D5×Dic3C211yesmaximal, characteristic
4#11752438C211yesmaximal, characteristic
5C3×#65779C211yesmaximal, characteristic
6#11752028C211yesmaximal, characteristic, complemented
7#11752028C211yesmaximal, characteristic, complemented
8#11752021C211yesmaximal, characteristic, complemented
9#11752018C211yesmaximal, characteristic, complemented
10#11752017C211yesmaximal, characteristic, complemented
11AGL(1,𝔽5)×#217C211yesmaximal, characteristic, complemented
12#11751840C211yesmaximal, characteristic, complemented
13#11751839C211yesmaximal, characteristic, complemented
14#11751834C211yesmaximal, characteristic, complemented
15#11751746C211yesmaximal, characteristic, complemented
16#10617179—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C23×C3×AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×D4×D5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×#6763C2211yescharacteristic
23C2×#6763C2211yescharacteristic
24C2×#6763C2211yescharacteristic
25C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×Dic3⋊AGL(1,𝔽5)—24no—
29C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
30C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
31C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
32C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
34C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
35#91923—24no—
36C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
37C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
38C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
39C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
40D4×Dic15C411yescharacteristic, complemented
41C5×D4×Dic3C411yescharacteristic, complemented
42#91559C411yescharacteristic, complemented
43#91559C411yescharacteristic, complemented
44Dic3×C22⋊D5C411yescharacteristic, complemented
45Dic3×C22⋊D5C411yescharacteristic, complemented
46D5×#217C2211yescharacteristic
47D5×#217C2211yescharacteristic
48#91434C411yescharacteristic, complemented
49Dic3×D20C411yescharacteristic, complemented
50D5×C4⋊Dic3C2211yescharacteristic
51C4×D5×Dic3C2211yescharacteristic
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
55C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
56(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
57(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
58(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
59(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
60(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
61(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
62#74673—51nomaximal, Hall
63C2×#4130—31no—
64C22×C4⋊AGL(1,𝔽5)—31no—
65C4×D4×D5—31no—
66#65779—31no—
67#65779D311yescharacteristic
68#65765—31no—
69#65765—31no—
70#65711—31no—
71#65711—31no—
72#65700—31no—
73#65700—31no—
74C22⋊C4×AGL(1,𝔽5)—31no—
75C22⋊C4×AGL(1,𝔽5)—31no—
76#65689—31no—
77C4×C4⋊AGL(1,𝔽5)—31no—
78C23×C3×D5C2311yescharacteristic
79C23×C3×D5C2311yescharacteristic
80C22×ΓL(1,𝔽16)—22no—
81C22×ΓL(1,𝔽16)—22no—
82C22×ΓL(1,𝔽16)—41no—
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×ΓL(1,𝔽16)C2311yescharacteristic
85C22×ΓL(1,𝔽16)C2311yescharacteristic
86C22×ΓL(1,𝔽16)C2311yescharacteristic
87C22×C3×AGL(1,𝔽5)—22no—
88C22×C3×AGL(1,𝔽5)—22no—
89C22×C3×AGL(1,𝔽5)—41no—
90C22×C3×AGL(1,𝔽5)C2311yescharacteristic
91C22×C3×AGL(1,𝔽5)C2311yescharacteristic
92C22×C3×AGL(1,𝔽5)C2311yescharacteristic
93C22×C3×AGL(1,𝔽5)C2311yescharacteristic
94C2×C3×C5×D4C2×C411yescharacteristic
95C22×Dic15C2×C411yescharacteristic
96C22×Dic15C2×C411yescharacteristic, complemented
97C22×C5×Dic3C2×C411yescharacteristic
98C22×C5×Dic3C2×C411yescharacteristic, complemented
99C2×C3×C22⋊D5C2×C411yescharacteristic
100C2×C3×C22⋊D5C2×C411yescharacteristic
101C3×D4×D5—22no—
102C3×D4×D5—22no—
103C2×C3×D20C2×C411yescharacteristic
104C2×C3×C4×D5C2311yescharacteristic
105C2×D5×Dic3—22no—
106C2×D5×Dic3—22no—
107C2×D5×Dic3—22no—
108C2×D5×Dic3—22no—
109C2×D5×Dic3C2×C411yescharacteristic
110C2×D5×Dic3C2×C411yescharacteristic
111C2×D5×Dic3C2×C411yescharacteristic, complemented
112C2×D5×Dic3C2×C411yescharacteristic, complemented
113C2×D5×Dic3C2311yescharacteristic
114C2×D5×Dic3C2311yescharacteristic
115C2×D5×Dic3C2311yescharacteristic
116C2×D5×Dic3C2311yescharacteristic
117#6763—22no—
118#6763—22no—
119#6763—41no—
120C3×C22⋊AGL(1,𝔽5)—22no—
121C3×C22⋊AGL(1,𝔽5)—22no—
122C3×C22⋊AGL(1,𝔽5)—41no—
123Dic3⋊AGL(1,𝔽5)—22no—
124Dic3⋊AGL(1,𝔽5)—22no—
125Dic3⋊AGL(1,𝔽5)—22no—
126Dic3⋊AGL(1,𝔽5)—22no—
127Dic3⋊AGL(1,𝔽5)—22no—
128Dic3⋊AGL(1,𝔽5)D414yescomplemented
129Dic3×AGL(1,𝔽5)—22no—
130Dic3×AGL(1,𝔽5)—22no—
131Dic3×AGL(1,𝔽5)—41no—
132Dic3×AGL(1,𝔽5)—41no—
133#6719C2×C411yescharacteristic
134#6719C2×C411yescharacteristic, complemented
135C4⋊Dic15C2×C411yescharacteristic, complemented
136C4×Dic15C2×C411yescharacteristic, complemented
137C5×#217C2×C411yescharacteristic
138C5×#217C2×C411yescharacteristic, complemented
139C5×C4⋊Dic3C2×C411yescharacteristic, complemented
140C4×C5×Dic3C2×C411yescharacteristic, complemented
141#6668C2×C411yescharacteristic, complemented
142#6668C2×C411yescharacteristic, complemented
143#6665C2×C411yescharacteristic
144#6665C2×C411yescharacteristic
145#6665C2×C411yescharacteristic, complemented
146#6665C2×C411yescharacteristic, complemented
147Dic3×Dic5C2×C411yescharacteristic, complemented
148Dic3×Dic5C2×C411yescharacteristic, complemented
149C2×D4×Dic3—51no—
150C22×Dic3⋊C4—51no—
151C2×#877—51no—
152C3×#386—51no—
153#5220—51no—
154C4×#217—51no—
155#4945—51no—
156#4944—51no—
157#4942—51no—
158#4942—51no—
159Dic3×C22⋊C4—51no—
160#4654—51no—
161#4653—51no—
162#4650—51no—
163#4649—51no—
164C23×AGL(1,𝔽5)—31no—
165C23×AGL(1,𝔽5)C2×D311yescharacteristic
166C2×D4×D5C2×D311yescharacteristic
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C2×C22⋊AGL(1,𝔽5)—31no—
170C2×C22⋊AGL(1,𝔽5)—31no—
171C2×C22⋊AGL(1,𝔽5)—31no—
172C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
173C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
174C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
175#4130—64no—
176C2×C4⋊AGL(1,𝔽5)—31no—
177C2×C4⋊AGL(1,𝔽5)—31no—
178C2×C4⋊AGL(1,𝔽5)—31no—
179C2×C4⋊AGL(1,𝔽5)—31no—
180C2×C4⋊AGL(1,𝔽5)—31no—
181C2×C4⋊AGL(1,𝔽5)—31no—
182C2×C4⋊AGL(1,𝔽5)—64no—
183C2×C4×AGL(1,𝔽5)—31no—
184C2×C4×AGL(1,𝔽5)—31no—
185C2×C4×AGL(1,𝔽5)—31no—
186C2×C4×AGL(1,𝔽5)—31no—
187C4×C5×D4—31no—
188D4×Dic5—31no—
189C4×C22⋊D5—31no—
190C4×C22⋊D5—31no—
191#4039—31no—
192D5×C4⋊C4—31no—
193#4027—31no—
194#4027—31no—
195D5×C22⋊C4—31no—
196D5×C22⋊C4—31no—
197C4×D20—31no—
198C42×D5—31no—
199(C2×AGL(1,𝔽5))⋊C4—31no—
200(C2×AGL(1,𝔽5))⋊C4—31no—
201(C2×AGL(1,𝔽5))⋊C4—31no—
202(C2×AGL(1,𝔽5))⋊C4—31no—
203(C2×AGL(1,𝔽5))⋊C4—31no—
204(C2×AGL(1,𝔽5))⋊C4—31no—
205(C2×AGL(1,𝔽5))⋊C4—31no—
206(C2×AGL(1,𝔽5))⋊C4—31no—
207(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
208(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
209#2352—151noSylow
210C23×C3×C5C22×C411yescharacteristic
211C23×C3×C5C22×C411yescharacteristic
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5C22×C411yescharacteristic
223C22×C3×D5C22×C411yescharacteristic
224C22×C3×D5#4112yes—
225C22×C3×D5#4112yes—
226C22×C3×D5C2411yescharacteristic
227C2×ΓL(1,𝔽16)—21no—
228C2×ΓL(1,𝔽16)—21no—
229C2×ΓL(1,𝔽16)—21no—
230C2×ΓL(1,𝔽16)—21no—
231C2×ΓL(1,𝔽16)—21no—
232C2×ΓL(1,𝔽16)—21no—
233C2×ΓL(1,𝔽16)—21no—
234C2×ΓL(1,𝔽16)—21no—
235C2×ΓL(1,𝔽16)—21no—
236C2×ΓL(1,𝔽16)—21no—
237C2×ΓL(1,𝔽16)—21no—
238C2×ΓL(1,𝔽16)—44no—
239C2×ΓL(1,𝔽16)C2×D412yes—
240C2×C3×AGL(1,𝔽5)—21no—
241C2×C3×AGL(1,𝔽5)—21no—
242C2×C3×AGL(1,𝔽5)—21no—
243C2×C3×AGL(1,𝔽5)—21no—
244C2×C3×AGL(1,𝔽5)—21no—
245C2×C3×AGL(1,𝔽5)—21no—
246C2×C3×AGL(1,𝔽5)—21no—
247C2×C3×AGL(1,𝔽5)—21no—
248C2×C3×AGL(1,𝔽5)—21no—
249C2×C3×AGL(1,𝔽5)—21no—
250C2×C3×AGL(1,𝔽5)—21no—
251C2×C3×AGL(1,𝔽5)—44no—
252C2×C3×AGL(1,𝔽5)C2×D412yes—
253C3×C5×D4—22no—
254C2×C3×C4×C5C22×C411yescharacteristic
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C22×C411yescharacteristic
258C2×Dic15C22×C411yescharacteristic
259C2×Dic15C22×C411yescharacteristic
260C2×Dic15C22×C411yescharacteristic
261C2×C5×Dic3—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3C22×C411yescharacteristic
264C2×C5×Dic3C22×C411yescharacteristic
265C2×C5×Dic3C22×C411yescharacteristic
266C2×C5×Dic3C22×C411yescharacteristic
267C3×C22⋊D5—22no—
268C3×C22⋊D5—22no—
269C2×C3×Dic5C22×C411yescharacteristic
270C3×D20—22no—
271C3×C4×D5—21no—
272C3×C4×D5—21no—
273D5×Dic3—21no—
274D5×Dic3—21no—
275D5×Dic3—21no—
276D5×Dic3—21no—
277D5×Dic3—21no—
278D5×Dic3—21no—
279D5×Dic3—22no—
280D5×Dic3—22no—
281D5×Dic3—22no—
282D5×Dic3—22no—
283D5×Dic3C2×D412yes—
284D5×Dic3#4112yes—
285C22×C3×D4—51no—
286C23×C3×C4—51no—
287C23×Dic3—51no—
288C23×Dic3—51no—
289C23×Dic3—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×#217—51no—
294C2×#217—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×#217—51no—
298D4×Dic3—51no—
299D4×Dic3—51no—
300D4×Dic3—51no—
301D4×Dic3—51no—
302D4×Dic3—51no—
303D4×Dic3—51no—
304D4×Dic3—51no—
305D4×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
306C2×C4⋊Dic3—51no—
307C2×Dic3⋊C4—51no—
308C2×Dic3⋊C4—51no—
309C2×Dic3⋊C4—51no—
310C2×Dic3⋊C4—51no—
311C2×Dic3⋊C4—51no—
312C2×Dic3⋊C4—51no—
313C2×Dic3⋊C4—104no—
314C2×C4×Dic3—51no—
315C2×C4×Dic3—51no—
316C2×C4×Dic3—51no—
317C2×C4×Dic3—51no—
318C2×C4×Dic3—51no—
319#877—104no—
320C3×#95—51no—
321C3×#95—51no—
322C3⋊#95—51no—
323C3⋊#95—51no—
324C3⋊#95—51no—
325C3⋊#95—51no—
326C3⋊#95—51no—
327C3⋊#95—51no—
328C3⋊#95—51no—
329C3⋊#95—51no—
330C23×D5C22×D311yescharacteristic
331C23×D5C22×D311yescharacteristic
332C22×AGL(1,𝔽5)—22no—
333C22×AGL(1,𝔽5)—22no—
334C22×AGL(1,𝔽5)—31no—
335C22×AGL(1,𝔽5)—31no—
336C22×AGL(1,𝔽5)—31no—
337C22×AGL(1,𝔽5)—31no—
338C22×AGL(1,𝔽5)—41no—
339C22×AGL(1,𝔽5)—62no—
340C22×AGL(1,𝔽5)—62no—
341C22×AGL(1,𝔽5)—121no—
342C22×AGL(1,𝔽5)C22×D311yescharacteristic
343C22×AGL(1,𝔽5)C22×D311yescharacteristic
344C22×AGL(1,𝔽5)C22×D311yescharacteristic
345C22×AGL(1,𝔽5)C22×D311yescharacteristic
346C2×C5×D4C4×D311yescharacteristic
347C22×C4×C5—31no—
348C22×C4×C5—31no—
349C2×C22⋊D5C4×D311yescharacteristic
350C2×C22⋊D5C4×D311yescharacteristic
351C22×Dic5—31no—
352C22×Dic5—31no—
353D4×D5—22no—
354D4×D5—22no—
355C2×D20C4×D311yescharacteristic
356C2×C4×D5—31no—
357C2×C4×D5—31no—
358C2×C4×D5—31no—
359C2×C4×D5—31no—
360C2×C4×D5—31no—
361C2×C4×D5—31no—
362C2×C4×D5—31no—
363C2×C4×D5—31no—
364C2×C4×D5—62no—
365C2×C4×D5—62no—
366C2×C4×D5—62no—
367C2×C4×D5—62no—
368C2×C4×D5C22×D311yescharacteristic
369C22⋊AGL(1,𝔽5)—22no—
370C22⋊AGL(1,𝔽5)—22no—
371C22⋊AGL(1,𝔽5)—41no—
372C22⋊AGL(1,𝔽5)—62no—
373C22⋊AGL(1,𝔽5)—62no—
374C22⋊AGL(1,𝔽5)—121no—
375C4⋊AGL(1,𝔽5)—34no—
376C4⋊AGL(1,𝔽5)—62no—
377C4⋊AGL(1,𝔽5)—62no—
378C4⋊AGL(1,𝔽5)—62no—
379C4⋊AGL(1,𝔽5)—62no—
380C4⋊AGL(1,𝔽5)—62no—
381C4×AGL(1,𝔽5)—62no—
382C4×AGL(1,𝔽5)—62no—
383C4×AGL(1,𝔽5)—121no—
384C4×AGL(1,𝔽5)—121no—
385C5×C4⋊C4—31no—
386C5×C22⋊C4—31no—
387C5×C22⋊C4—31no—
388C42×C5—31no—
389C22⋊Dic5—31no—
390C22⋊Dic5—31no—
391#685—31no—
392#685—31no—
393#685—31no—
394#685—31no—
395C4⋊Dic5—31no—
396#683—31no—
397#683—31no—
398C4×Dic5—31no—
399C4×Dic5—31no—
400C4×Dic5—31no—
401C2×C4×D4—151no—
402C2×#117—151no—
403C22×C4⋊C4—151no—
404#388—151no—
405#388—151no—
406#387—151no—
407#387—151no—
408#386—51no—
409#386—151no—
410#382—151no—
411#380—151no—
412#380—151no—
413C4×C4⋊C4—151no—
414C4×C22⋊C4—151no—
415C4×C22⋊C4—151no—
416C22×C3×C5—21no—
417C22×C3×C5—21no—
418C22×C3×C5—21no—
419C22×C3×C5—21no—
420C22×C3×C5—21no—
421C22×C3×C5#11712yescomplemented
422C22×C3×C5C23×C411yescharacteristic
423C2×C3×D5—21no—
424C2×C3×D5—21no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—22no—
429C2×C3×D5—21no—
430C2×C3×D5—21no—
431C2×C3×D5—21no—
432C2×C3×D5—41no—
433C2×C3×D5—41no—
434C2×C3×D5—41no—
435C2×C3×D5—41no—
436C2×C3×D5#11712yescomplemented
437C2×C3×D5C22×D411yescharacteristic
438C2×C3×D5C2×#4111yescharacteristic
439C2×C3×D5C2×#4111yescharacteristic
440C2×C3×D5C2×#4111yescharacteristic
441C2×C3×D5H(5,𝔽2)11yescharacteristic
442C2×C3×D52−1+411yescharacteristic
443ΓL(1,𝔽16)—22no—
444ΓL(1,𝔽16)—41no—
445ΓL(1,𝔽16)—41no—
446ΓL(1,𝔽16)—41no—
447C3×AGL(1,𝔽5)—22no—
448C3×AGL(1,𝔽5)—41no—
449C3×AGL(1,𝔽5)—41no—
450C3×AGL(1,𝔽5)—41no—
451C3×C4×C5—21no—
452Dic15—21no—
453Dic15—21no—
454Dic15—21no—
455Dic15C4×D412yes—
456C3×Dic5—21no—
457C5×Dic3—21no—
458C5×Dic3—21no—
459C5×Dic3—21no—
460C5×Dic3C4×D412yes—
461C24×C3—51no—
462C24×C3—51no—
463C2×C3×D4—51no—
464C2×C3×D4—51no—
465C2×C3×D4—51no—
466C2×C3×D4—102no—
467C2×C3×D4—102no—
468C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—51no—
474C22×C3×C4—102no—
475C22×C3×C4—102no—
476C22×C3×C4—201no—
477C22×Dic3—51no—
478C22×Dic3—51no—
479C22×Dic3—51no—
480C22×Dic3—51no—
481C22×Dic3—51no—
482C22×Dic3—51no—
483C22×Dic3—51no—
484C22×Dic3—51no—
485C22×Dic3—51no—
486C22×Dic3—51no—
487C22×Dic3—51no—
488C22×Dic3—51no—
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3—102no—
492C22×Dic3—102no—
493C22×Dic3—102no—
494C22×Dic3—102no—
495C22×Dic3—102no—
496C22×Dic3—102no—
497C22×Dic3—201no—
498C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
499C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
500C3×C22⋊C4—102no—
501C3×C22⋊C4—102no—
502C3×C22⋊C4—201no—
503#217—51no—
504#217—51no—
505#217—51no—
506#217—51no—
507#217—51no—
508#217—51no—
509#217—102no—
510#217—102no—
511#217—201no—
512#217C2×AGL(1,𝔽5)11yescharacteristic
513#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
514C4⋊Dic3—51no—
515C4⋊Dic3—51no—
516C4⋊Dic3—51no—
517C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
518Dic3⋊C4—54no—
519Dic3⋊C4—102no—
520Dic3⋊C4—102no—
521Dic3⋊C4—102no—
522Dic3⋊C4—102no—
523Dic3⋊C4—102no—
524C4×Dic3—51no—
525C4×Dic3—51no—
526C4×Dic3—51no—
527C4×Dic3—102no—
528C4×Dic3—102no—
529C4×Dic3—201no—
530C4×Dic3—201no—
531C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
532C23×C5C2×C4×D311yescharacteristic
533C23×C5C2×C4×D311yescharacteristic
534C22×D5—21no—
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—21no—
540C22×D5—21no—
541C22×D5—21no—
542C22×D5—21no—
543C22×D5—21no—
544C22×D5C2×C4×D311yescharacteristic
545C22×D5C2×C4×D311yescharacteristic
546C22×D5#23712yes—
547C22×D5#23712yes—
548C22×D5C23×D311yescharacteristic
549C2×AGL(1,𝔽5)—21no—
550C2×AGL(1,𝔽5)—21no—
551C2×AGL(1,𝔽5)—21no—
552C2×AGL(1,𝔽5)—21no—
553C2×AGL(1,𝔽5)—21no—
554C2×AGL(1,𝔽5)—21no—
555C2×AGL(1,𝔽5)—21no—
556C2×AGL(1,𝔽5)—21no—
557C2×AGL(1,𝔽5)—21no—
558C2×AGL(1,𝔽5)—21no—
559C2×AGL(1,𝔽5)—21no—
560C2×AGL(1,𝔽5)—32no—
561C2×AGL(1,𝔽5)—44no—
562C2×AGL(1,𝔽5)—61no—
563C2×AGL(1,𝔽5)—61no—
564C2×AGL(1,𝔽5)—61no—
565C2×AGL(1,𝔽5)—61no—
566C2×AGL(1,𝔽5)—61no—
567C2×AGL(1,𝔽5)—61no—
568C2×AGL(1,𝔽5)—61no—
569C2×AGL(1,𝔽5)—61no—
570C2×AGL(1,𝔽5)—61no—
571C2×AGL(1,𝔽5)—61no—
572C2×AGL(1,𝔽5)—61no—
573C2×AGL(1,𝔽5)—124no—
574C2×AGL(1,𝔽5)D3×D412yes—
575C5×D4—22no—
576C2×C4×C5—31no—
577C2×C4×C5—31no—
578C2×C4×C5—31no—
579C2×C4×C5—31no—
580C2×C4×C5—62no—
581C2×C4×C5—62no—
582C2×C4×C5C2×C4×D311yescharacteristic
583C22⋊D5—22no—
584C22⋊D5—22no—
585C2×Dic5—31no—
586C2×Dic5—31no—
587C2×Dic5—31no—
588C2×Dic5—31no—
589C2×Dic5—62no—
590C2×Dic5—62no—
591C2×Dic5C2×C4×D311yescharacteristic
592D20—22no—
593C4×D5—21no—
594C4×D5—21no—
595C4×D5—32no—
596C4×D5—32no—
597C4×D5—62no—
598C4×D5—62no—
599C4×D5—62no—
600C4×D5—62no—
601C4×D5—61no—
602C4×D5—61no—
603C4×D5—61no—
604C4×D5—61no—
605C4×D5—61no—
606C4×D5—61no—
607C22×D4—51no—
608C23×C4—51no—
609C23×C4—151no—
610C23×C4—151no—
611C23×C4—151no—
612C4×D4—31no—
613C4×D4—151no—
614C4×D4—151no—
615C4×D4—151no—
616C4×D4—151no—
617C4×D4—151no—
618C4×D4—151no—
619C4×D4—151no—
620#117—304no—
621C2×C4⋊C4—151no—
622C2×C4⋊C4—151no—
623C2×C4⋊C4—151no—
624C2×C4⋊C4—151no—
625C2×C4⋊C4—151no—
626C2×C4⋊C4—151no—
627C2×C4⋊C4—151no—
628C2×C4⋊C4—304no—
629C2×C22⋊C4—51no—
630C2×C22⋊C4—51no—
631C2×C22⋊C4—51no—
632C2×C22⋊C4—151no—
633C2×C22⋊C4—151no—
634C2×C22⋊C4—151no—
635C2×C22⋊C4—151no—
636C2×C22⋊C4—151no—
637C2×C42—151no—
638C2×C42—151no—
639C2×C42—151no—
640C2×C42—151no—
641C2×C42—151no—
642#95—51no—
643#95—51no—
644#95—151no—
645#95—151no—
646#95—151no—
647#95—151no—
648#95—151no—
649#95—151no—
650#95—151no—
651#95—151no—
652C2×C3×C5—22no—
653C2×C3×C5—41no—
654C2×C3×C5C2×#11711yescharacteristic
655C2×C3×C5C2×C4×D411yescharacteristic
656C2×C3×C5#52011yescharacteristic
657C3×D5—22no—
658C3×D5—41no—
659C3×D5#54611yescharacteristic
660C3×D5#54811yescharacteristic
661C3×D5#55211yescharacteristic
662C3×D5#55311yescharacteristic
663C23×C3—51no—
664C23×C3—52no—
665C23×C3—52no—
666C23×C3—51no—
667C23×C3—51no—
668C23×C3—101no—
669C23×C3—101no—
670C23×C3—101no—
671C23×C3—101no—
672C23×C3—101no—
673C23×C3—101no—
674C23×C3—101no—
675C23×C3—101no—
676C23×C3—101no—
677C23×C3—101no—
678C23×C3C22×AGL(1,𝔽5)11yescharacteristic
679C23×C3C22×AGL(1,𝔽5)11yescharacteristic
680C3×D4—22no—
681C3×D4—102no—
682C3×D4—102no—
683C3×D4—102no—
684C2×C3×C4—52no—
685C2×C3×C4—51no—
686C2×C3×C4—101no—
687C2×C3×C4—101no—
688C2×C3×C4—101no—
689C2×C3×C4—101no—
690C2×C3×C4—101no—
691C2×C3×C4—101no—
692C2×C3×C4—101no—
693C2×C3×C4—101no—
694C2×C3×C4—101no—
695C2×C3×C4—101no—
696C2×C3×C4—101no—
697C2×C3×C4—101no—
698C2×C3×C4—101no—
699C2×C3×C4—204no—
700C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—51no—
704C2×Dic3—52no—
705C2×Dic3—52no—
706C2×Dic3—52no—
707C2×Dic3—51no—
708C2×Dic3—51no—
709C2×Dic3—51no—
710C2×Dic3—102no—
711C2×Dic3—102no—
712C2×Dic3—101no—
713C2×Dic3—101no—
714C2×Dic3—101no—
715C2×Dic3—101no—
716C2×Dic3—101no—
717C2×Dic3—101no—
718C2×Dic3—102no—
719C2×Dic3—102no—
720C2×Dic3—101no—
721C2×Dic3—101no—
722C2×Dic3—102no—
723C2×Dic3—102no—
724C2×Dic3—101no—
725C2×Dic3—101no—
726C2×Dic3—101no—
727C2×Dic3—101no—
728C2×Dic3—101no—
729C2×Dic3—101no—
730C2×Dic3—101no—
731C2×Dic3—101no—
732C2×Dic3—101no—
733C2×Dic3—204no—
734C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
735C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
736C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
737C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
738C22×C5—21no—
739C22×C5—21no—
740C22×C5—21no—
741C22×C5—21no—
742C22×C5—21no—
743C22×C5#87712yescomplemented
744C22×C5C22×C4×D311yescharacteristic
745C2×D5—21no—
746C2×D5—21no—
747C2×D5—22no—
748C2×D5—22no—
749C2×D5—22no—
750C2×D5—22no—
751C2×D5—21no—
752C2×D5—21no—
753C2×D5—21no—
754C2×D5—41no—
755C2×D5—41no—
756C2×D5—41no—
757C2×D5—41no—
758C2×D5#87712yescomplemented
759C2×D5C2×D3×D411yescharacteristic
760C2×D5C2×#23711yescharacteristic
761C2×D5C2×#23711yescharacteristic
762C2×D5#100411yescharacteristic
763C2×D5D3×#4111yescharacteristic
764C2×D5#101011yescharacteristic
765AGL(1,𝔽5)—22no—
766AGL(1,𝔽5)—41no—
767AGL(1,𝔽5)—41no—
768AGL(1,𝔽5)—41no—
769AGL(1,𝔽5)—62no—
770AGL(1,𝔽5)—121no—
771AGL(1,𝔽5)—121no—
772AGL(1,𝔽5)—121no—
773C4×C5—21no—
774C4×C5—32no—
775C4×C5—61no—
776C4×C5—61no—
777C4×C5—61no—
778Dic5—21no—
779Dic5—32no—
780Dic5—61no—
781Dic5—61no—
782Dic5—61no—
783C24—51no—
784C24—51no—
785C2×D4—51no—
786C2×D4—51no—
787C2×D4—51no—
788C2×D4—102no—
789C2×D4—102no—
790C2×D4D3×AGL(1,𝔽5)11yescharacteristic
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—51no—
794C22×C4—51no—
795C22×C4—51no—
796C22×C4—51no—
797C22×C4—51no—
798C22×C4—102no—
799C22×C4—102no—
800C22×C4—151no—
801C22×C4—151no—
802C22×C4—151no—
803C22×C4—151no—
804C22×C4—151no—
805C22×C4—151no—
806C22×C4—151no—
807C22×C4—151no—
808C22×C4—151no—
809C22×C4—151no—
810C22×C4—151no—
811C22×C4—151no—
812C22×C4—151no—
813C22×C4—151no—
814C22×C4—201no—
815C22×C4—302no—
816C22×C4—302no—
817C22×C4—302no—
818C22×C4—302no—
819C22×C4—302no—
820C22×C4—302no—
821C22×C4—601no—
822C4⋊C4—31no—
823C4⋊C4—151no—
824C4⋊C4—151no—
825C4⋊C4—154no—
826C4⋊C4—151no—
827C4⋊C4—302no—
828C4⋊C4—302no—
829C4⋊C4—302no—
830C4⋊C4—302no—
831C4⋊C4—302no—
832C22⋊C4—31no—
833C22⋊C4—31no—
834C22⋊C4—102no—
835C22⋊C4—102no—
836C22⋊C4—151no—
837C22⋊C4—151no—
838C22⋊C4—151no—
839C22⋊C4—151no—
840C22⋊C4—151no—
841C22⋊C4—151no—
842C22⋊C4—201no—
843C22⋊C4—302no—
844C22⋊C4—302no—
845C22⋊C4—601no—
846C42—31no—
847C42—151no—
848C42—151no—
849C42—151no—
850C42—302no—
851C42—302no—
852C42—601no—
853C42—601no—
854C3×C5#235211yescharacteristic, complemented, Hall
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—51no—
861C22×C3—51no—
862C22×C3—51no—
863C22×C3—51no—
864C22×C3—51no—
865C22×C3—51no—
866C22×C3—52no—
867C22×C3—102no—
868C22×C3—102no—
869C22×C3—102no—
870C22×C3—102no—
871C22×C3—101no—
872C22×C3—101no—
873C22×C3—101no—
874C22×C3—101no—
875C22×C3—101no—
876C22×C3—201no—
877C22×C3—201no—
878C22×C3—201no—
879C22×C3—201no—
880C22×C3#413012yescomplemented
881C22×C3C23×AGL(1,𝔽5)11yescharacteristic
882C3×C4—21no—
883C3×C4—102no—
884C3×C4—101no—
885C3×C4—201no—
886C3×C4—201no—
887C3×C4—201no—
888Dic3—21no—
889Dic3—21no—
890Dic3—21no—
891Dic3—52no—
892Dic3—102no—
893Dic3—101no—
894Dic3—101no—
895Dic3—101no—
896Dic3—201no—
897Dic3—201no—
898Dic3—201no—
899Dic3D4×AGL(1,𝔽5)12yes—
900C2×C5—22no—
901C2×C5—41no—
902C2×C5C2×#87711yescharacteristic
903C2×C5C4×D3×D411yescharacteristic
904C2×C5#554611yescharacteristic
905D5—22no—
906D5—41no—
907D5#559111yescharacteristic
908D5#559811yescharacteristic
909D5#560111yescharacteristic
910D5#565011yescharacteristic
911C23—51no—
912C23—52no—
913C23—52no—
914C23—51no—
915C23—51no—
916C23—101no—
917C23—101no—
918C23—101no—
919C23—101no—
920C23—101no—
921C23—101no—
922C23—101no—
923C23—101no—
924C23—101no—
925C23—101no—
926C23C2×D3×AGL(1,𝔽5)11yescharacteristic
927C23C2×D3×AGL(1,𝔽5)11yescharacteristic
928D4—22no—
929D4—102no—
930D4—102no—
931D4—102no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—52no—
937C2×C4—51no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—101no—
948C2×C4—101no—
949C2×C4—101no—
950C2×C4—101no—
951C2×C4—101no—
952C2×C4—101no—
953C2×C4—152no—
954C2×C4—152no—
955C2×C4—151no—
956C2×C4—152no—
957C2×C4—151no—
958C2×C4—151no—
959C2×C4—151no—
960C2×C4—204no—
961C2×C4—302no—
962C2×C4—302no—
963C2×C4—302no—
964C2×C4—302no—
965C2×C4—301no—
966C2×C4—301no—
967C2×C4—301no—
968C2×C4—301no—
969C2×C4—301no—
970C2×C4—301no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—301no—
974C2×C4—301no—
975C2×C4—301no—
976C2×C4—301no—
977C2×C4—301no—
978C2×C4—301no—
979C2×C4—301no—
980C2×C4—301no—
981C2×C4—301no—
982C2×C4—301no—
983C2×C4—301no—
984C2×C4—604no—
985C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
986C2×C3—22no—
987C2×C3—41no—
988C2×C3—51no—
989C2×C3—51no—
990C2×C3—51no—
991C2×C3—51no—
992C2×C3—102no—
993C2×C3—201no—
994C2×C3C2×#413011yescharacteristic
995C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
996C2×C3#6626611yescharacteristic
997C5#7467311yescharacteristic, complemented, Sylow
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—51no—
1004C22—51no—
1005C22—51no—
1006C22—51no—
1007C22—51no—
1008C22—51no—
1009C22—52no—
1010C22—102no—
1011C22—102no—
1012C22—102no—
1013C22—102no—
1014C22—101no—
1015C22—101no—
1016C22—101no—
1017C22—101no—
1018C22—101no—
1019C22—201no—
1020C22—201no—
1021C22—201no—
1022C22—201no—
1023C22#9192312yescomplemented
1024C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1025C4—21no—
1026C4—32no—
1027C4—61no—
1028C4—61no—
1029C4—61no—
1030C4—102no—
1031C4—101no—
1032C4—152no—
1033C4—201no—
1034C4—201no—
1035C4—201no—
1036C4—302no—
1037C4—301no—
1038C4—301no—
1039C4—301no—
1040C4—601no—
1041C4—601no—
1042C4—601no—
1043C3#1061717911yescharacteristic, complemented, Sylow
1044C2—22no—
1045C2—41no—
1046C2—51no—
1047C2—51no—
1048C2—51no—
1049C2—51no—
1050C2—102no—
1051C2—201no—
1052C2D3×D4×AGL(1,𝔽5)11yescharacteristic
1053C2#1175684611yescharacteristic
1054C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C3×D4×D5C22
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×Dic3⋊AGL(1,𝔽5)C2semidirect
2. C2×#91923C2semidirect
6. #11752028C2semidirect
7. #11752028C2semidirect
8. #11752021C2semidirect
9. #11752018C2semidirect
10. #11752017C2semidirect
11. AGL(1,𝔽5)×#217C2semidirect
12. #11751840C2semidirect
13. #11751839C2semidirect
14. #11751834C2semidirect
15. #11751746C2semidirect
40. D4×Dic15C4semidirect
41. C5×D4×Dic3C4semidirect
42. #91559C4semidirect
43. #91559C4semidirect
44. Dic3×C22⋊D5C4semidirect
45. Dic3×C22⋊D5C4semidirect
48. #91434C4semidirect
49. Dic3×D20C4semidirect
96. C22×Dic15C2×C4semidirect
98. C22×C5×Dic3C2×C4semidirect
111. C2×D5×Dic3C2×C4semidirect
112. C2×D5×Dic3C2×C4semidirect
128. Dic3⋊AGL(1,𝔽5)D4semidirect
134. #6719C2×C4semidirect
135. C4⋊Dic15C2×C4semidirect
136. C4×Dic15C2×C4semidirect
138. C5×#217C2×C4semidirect
139. C5×C4⋊Dic3C2×C4semidirect
140. C4×C5×Dic3C2×C4semidirect
141. #6668C2×C4semidirect
142. #6668C2×C4semidirect
145. #6665C2×C4semidirect
146. #6665C2×C4semidirect
147. Dic3×Dic5C2×C4semidirect
148. Dic3×Dic5C2×C4semidirect
305. D4×Dic3AGL(1,𝔽5)semidirect
421. C22×C3×C5#117semidirect
436. C2×C3×D5#117semidirect
499. C22×Dic3C2×AGL(1,𝔽5)semidirect
513. #217C2×AGL(1,𝔽5)semidirect
517. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
531. C4×Dic3C2×AGL(1,𝔽5)semidirect
743. C22×C5#877semidirect
758. C2×D5#877semidirect
854. C3×C5#2352semidirect
880. C22×C3#4130semidirect
997. C5#74673semidirect
1023. C22#91923semidirect
1043. C3#10617179semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊AGL(1,𝔽5)2
C2×#919232
D4×D5×Dic32
#117524382
C3×#657792
#117520282
#117520212
#117520182
#117520172
AGL(1,𝔽5)×#2172
#117518402
#117518392
#117518342
#117517462
#106171793
#746735