Finite Group Databasebeta

← #14327488

Subgroups — #14327488

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
1C2×#91923C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#67⋊C4C211yesmaximal, characteristic
4#11752359C211yesmaximal, characteristic, complemented
5C3×#65700C211yesmaximal, characteristic, complemented
6#11752055C211yesmaximal, characteristic
7#11752055C211yesmaximal, characteristic
8#11752028C211yesmaximal, characteristic, complemented
9#11751931C211yesmaximal, characteristic, complemented
10AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
12#11751854C211yesmaximal, characteristic, complemented
13#11751845C211yesmaximal, characteristic, complemented
14#11751835C211yesmaximal, characteristic, complemented
15#11751746C211yesmaximal, characteristic, complemented
16#10617179—31nomaximal, Hall
17C22×D3×AGL(1,𝔽5)C2211yescharacteristic
18C22×D3×AGL(1,𝔽5)C2211yescharacteristic
19C2×D5×#67C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C2×C4×D3×D5C2211yescharacteristic
22C2×#6763C2211yescharacteristic
23C2×#6763C2211yescharacteristic
24C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
25C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
26C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
29C2×C3×C4×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×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
35C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
36#91923—24no—
37C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
38C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
39D3×C4⋊AGL(1,𝔽5)—24no—
40#91770C411yescharacteristic, complemented
41C5×#67⋊C4C411yescharacteristic, complemented
42C3×D5×C22⋊C4C2211yescharacteristic
43#67⋊Dic5C411yescharacteristic, complemented
44#91556C411yescharacteristic, complemented
45D5×(C2×D3)⋊C4C2211yescharacteristic
46#91442C411yescharacteristic, complemented
47#91441C411yescharacteristic, complemented
48#91396C411yescharacteristic, complemented
49#91395C411yescharacteristic, complemented
50D5×Dic3⋊C4C2211yescharacteristic
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#75834—51nomaximal, Hall
63C2×#4130—31no—
64C22×C4⋊AGL(1,𝔽5)—31no—
65C4×D4×D5—31no—
66#65779—31no—
67#65779—31no—
68#65765—31no—
69#65765—31no—
70#65711—31no—
71#65711—31no—
72#65700—31no—
73#65700D311yescharacteristic, complemented
74C22⋊C4×AGL(1,𝔽5)—31no—
75C22⋊C4×AGL(1,𝔽5)—31no—
76#65689—31no—
77C4×C4⋊AGL(1,𝔽5)—31no—
78C23×C3×D5C2311yescharacteristic
79C22×D3×D5C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C22×C3×AGL(1,𝔽5)C2311yescharacteristic
86C22×C3×AGL(1,𝔽5)C2311yescharacteristic
87C22×C3×AGL(1,𝔽5)C2311yescharacteristic
88C2×D3×AGL(1,𝔽5)—22no—
89C2×D3×AGL(1,𝔽5)—22no—
90C2×D3×AGL(1,𝔽5)—22no—
91C2×D3×AGL(1,𝔽5)—22no—
92C2×D3×AGL(1,𝔽5)—41no—
93C2×D3×AGL(1,𝔽5)—41no—
94C2×#1220C2×C411yescharacteristic
95C22×Dic15C2×C411yescharacteristic, complemented
96C2×C4×D15C2×C411yescharacteristic
97C2×C5×#67C2×C411yescharacteristic
98C22×C5×Dic3C2×C411yescharacteristic, complemented
99C2×C4×C5×D3C2×C411yescharacteristic
100C2×C3×C4×D5C2311yescharacteristic
101C2×C3×C4×D5C2311yescharacteristic
102D5×#67—22no—
103D5×#67—22no—
104C2×#1202C2×C411yescharacteristic
105C2×#1201C2×C411yescharacteristic
106C2×#1200C2×C411yescharacteristic
107C2×D3×Dic5C2×C411yescharacteristic
108C2×D5×Dic3—22no—
109C2×D5×Dic3—22no—
110C2×D5×Dic3C2×C411yescharacteristic, complemented
111C2×D5×Dic3C2×C411yescharacteristic, complemented
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2311yescharacteristic
114C2×D5×Dic3C2311yescharacteristic
115C4×D3×D5—22no—
116C4×D3×D5—22no—
117#6763—22no—
118#6763—41no—
119C4⋊ΓL(1,𝔽16)—22no—
120C4×ΓL(1,𝔽16)—41no—
121C3×C22⋊AGL(1,𝔽5)—22no—
122C3×C22⋊AGL(1,𝔽5)—41no—
123C3×C4⋊AGL(1,𝔽5)—22no—
124C3×C4×AGL(1,𝔽5)—41no—
125Dic3⋊AGL(1,𝔽5)—22no—
126Dic3⋊AGL(1,𝔽5)—22no—
127Dic3⋊AGL(1,𝔽5)—22no—
128Dic3⋊AGL(1,𝔽5)D414yescomplemented
129(C2×D3)⋊AGL(1,𝔽5)—22no—
130(C2×D3)⋊AGL(1,𝔽5)—22no—
131Dic3×AGL(1,𝔽5)—22no—
132Dic3×AGL(1,𝔽5)—22no—
133C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
134#6714C2×C411yescharacteristic
135#6712C2×C411yescharacteristic, complemented
136C4×Dic15C2×C411yescharacteristic, complemented
137C5×(C2×D3)⋊C4C2×C411yescharacteristic
138C5×Dic3⋊C4C2×C411yescharacteristic, complemented
139C4×C5×Dic3C2×C411yescharacteristic, complemented
140C3×C22⋊Dic5C2×C411yescharacteristic, complemented
141C3×#685C2×C411yescharacteristic, complemented
142C3×#685C2×C411yescharacteristic, complemented
143Dic3⋊Dic5C2×C411yescharacteristic, complemented
144#6669C2×C411yescharacteristic, complemented
145#6667C2×C411yescharacteristic
146(C2×D3)⋊Dic5C2×C411yescharacteristic
147Dic3×Dic5C2×C411yescharacteristic, complemented
148Dic3×Dic5C2×C411yescharacteristic, complemented
149C2×D3×C4⋊C4—51no—
150C2×#67⋊C4—51no—
151C2×#877—51no—
152C3×#388—51no—
153#4978—51no—
154#4956—51no—
155#4956—51no—
156#4951—51no—
157#4942—51no—
158C4×(C2×D3)⋊C4—51no—
159C4×Dic3⋊C4—51no—
160#4667—51no—
161#4666—51no—
162#4655—51no—
163#4650—51no—
164C23×AGL(1,𝔽5)—31no—
165C23×AGL(1,𝔽5)—31no—
166C2×D4×D5—31no—
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)—31no—
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)—64no—
182C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
183C2×C4×AGL(1,𝔽5)—31no—
184C2×C4×AGL(1,𝔽5)—31no—
185C2×C4×AGL(1,𝔽5)—31no—
186C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
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
211C22×D15C22×C411yescharacteristic
212C22×C5×D3C22×C411yescharacteristic
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×D5C22×C411yescharacteristic
220C22×C3×D5C2411yescharacteristic
221C2×D3×D5—21no—
222C2×D3×D5—21no—
223C2×D3×D5—21no—
224C2×D3×D5—21no—
225C2×D3×D5#4112yes—
226C2×D3×D5#4112yes—
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)C2×D412yes—
239C2×C3×AGL(1,𝔽5)—21no—
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)C2×D412yes—
251D3×AGL(1,𝔽5)—44no—
252D3×AGL(1,𝔽5)—44no—
253C2×C3×C4×C5C22×C411yescharacteristic
254C2×C3×C4×C5C22×C411yescharacteristic
255#1220—22no—
256C2×Dic15—22no—
257C2×Dic15C22×C411yescharacteristic
258C2×Dic15C22×C411yescharacteristic
259C2×Dic15C22×C411yescharacteristic
260C4×D15—22no—
261C5×#67—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3C22×C411yescharacteristic
264C2×C5×Dic3C22×C411yescharacteristic
265C2×C5×Dic3C22×C411yescharacteristic
266C4×C5×D3—22no—
267C2×C3×Dic5C22×C411yescharacteristic
268C2×C3×Dic5C22×C411yescharacteristic
269C3×C4×D5—21no—
270C3×C4×D5—21no—
271C3×C4×D5—21no—
272C3×C4×D5—21no—
273#1202—22no—
274#1201—22no—
275#1200—22no—
276D3×Dic5—22no—
277D5×Dic3—21no—
278D5×Dic3—21no—
279D5×Dic3—21no—
280D5×Dic3—21no—
281D5×Dic3—22no—
282D5×Dic3—22no—
283D5×Dic3C2×D412yes—
284D5×Dic3#4112yes—
285C22×#67—51no—
286C23×Dic3—51no—
287C22×C4×D3—51no—
288C22×C4×D3—51no—
289C22×C4×D3—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C42—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×C4⋊Dic3—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308C2×C4×Dic3—51no—
309C2×C4×Dic3—51no—
310D3×C4⋊C4—104no—
311#67⋊C4—51no—
312#67⋊C4—51no—
313#67⋊C4—51no—
314#67⋊C4—51no—
315#67⋊C4—51no—
316#67⋊C4—51no—
317#67⋊C4—51no—
318#67⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
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×D5—31no—
331C23×D5C22×D311yescharacteristic
332C22×AGL(1,𝔽5)—31no—
333C22×AGL(1,𝔽5)—31no—
334C22×AGL(1,𝔽5)—31no—
335C22×AGL(1,𝔽5)—31no—
336C22×AGL(1,𝔽5)—62no—
337C22×AGL(1,𝔽5)—62no—
338C22×AGL(1,𝔽5)—62no—
339C22×AGL(1,𝔽5)—62no—
340C22×AGL(1,𝔽5)—121no—
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×D4—31no—
347C22×C4×C5—31no—
348C22×C4×C5—31no—
349C2×C22⋊D5—31no—
350C2×C22⋊D5—31no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353D4×D5—62no—
354D4×D5—62no—
355C2×D20—31no—
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—62no—
364C2×C4×D5—62no—
365C2×C4×D5—62no—
366C2×C4×D5—62no—
367C2×C4×D5C22×D311yescharacteristic
368C2×C4×D5C22×D311yescharacteristic
369C22⋊AGL(1,𝔽5)—22no—
370C22⋊AGL(1,𝔽5)—41no—
371C22⋊AGL(1,𝔽5)—62no—
372C22⋊AGL(1,𝔽5)—62no—
373C22⋊AGL(1,𝔽5)—62no—
374C22⋊AGL(1,𝔽5)—121no—
375C4⋊AGL(1,𝔽5)—22no—
376C4⋊AGL(1,𝔽5)—34no—
377C4⋊AGL(1,𝔽5)—62no—
378C4⋊AGL(1,𝔽5)—62no—
379C4⋊AGL(1,𝔽5)—62no—
380C4⋊AGL(1,𝔽5)—62no—
381C4×AGL(1,𝔽5)—41no—
382C4×AGL(1,𝔽5)—62no—
383C4×AGL(1,𝔽5)—62no—
384C4×AGL(1,𝔽5)—121no—
385C5×C4⋊C4—31no—
386C5×C22⋊C4—31no—
387C5×C22⋊C4C4×D311yescharacteristic, complemented
388C42×C5—31no—
389C22⋊Dic5—31no—
390C22⋊Dic5C4×D311yescharacteristic, complemented
391#685—31no—
392#685—31no—
393#685C4×D311yescharacteristic, complemented
394#685C4×D311yescharacteristic, complemented
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—51no—
405#388—151no—
406#387—151no—
407#387—151no—
408#386—151no—
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×C5C23×C411yescharacteristic
420C2×D15—21no—
421C2×D15—21no—
422C2×D15#11712yescomplemented
423C2×C5×D3—21no—
424C2×C5×D3—21no—
425C2×C5×D3#11712yescomplemented
426C2×C3×D5—21no—
427C2×C3×D5—21no—
428C2×C3×D5—21no—
429C2×C3×D5—41no—
430C2×C3×D5—41no—
431C2×C3×D5—41no—
432C2×C3×D5—41no—
433C2×C3×D5C22×D411yescharacteristic
434C2×C3×D5C2×#4111yescharacteristic
435C2×C3×D5C2×#4111yescharacteristic
436C2×C3×D5C2×#4111yescharacteristic
437C2×C3×D5H(5,𝔽2)11yescharacteristic
438C2×C3×D52−1+411yescharacteristic
439D3×D5—22no—
440D3×D5—22no—
441D3×D5—22no—
442D3×D5—22no—
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—
452C3×C4×C5—21no—
453Dic15—21no—
454Dic15—21no—
455Dic15C4×D412yes—
456C3×Dic5—21no—
457C3×Dic5—21no—
458C5×Dic3—21no—
459C5×Dic3—21no—
460C5×Dic3C4×D412yes—
461C24×C3—51no—
462C23×D3—51no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C2×#67—51no—
470C2×#67—51no—
471C2×#67—51no—
472C2×#67—102no—
473C2×#67—102no—
474C2×#67C2×AGL(1,𝔽5)11yescharacteristic
475C22×Dic3—51no—
476C22×Dic3—51no—
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—102no—
486C22×Dic3—102no—
487C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
488C2×C4×D3—51no—
489C2×C4×D3—51no—
490C2×C4×D3—51no—
491C2×C4×D3—102no—
492C2×C4×D3—102no—
493C2×C4×D3—102no—
494C2×C4×D3—102no—
495C2×C4×D3—102no—
496C2×C4×D3—102no—
497C2×C4×D3—201no—
498C2×C4×D3—201no—
499C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
500C3×C4⋊C4—102no—
501C3×C22⋊C4—51no—
502C3×C22⋊C4—51no—
503C3×C22⋊C4—51no—
504C3×C22⋊C4—102no—
505C3×C22⋊C4—201no—
506C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
507C3×C42—201no—
508#217—102no—
509#217—201no—
510(C2×D3)⋊C4—51no—
511(C2×D3)⋊C4—51no—
512(C2×D3)⋊C4—51no—
513(C2×D3)⋊C4—102no—
514(C2×D3)⋊C4—102no—
515(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
516C4⋊Dic3—102no—
517Dic3⋊C4—54no—
518Dic3⋊C4—51no—
519Dic3⋊C4—51no—
520Dic3⋊C4—51no—
521Dic3⋊C4—102no—
522Dic3⋊C4—102no—
523Dic3⋊C4—102no—
524Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
525C4×Dic3—51no—
526C4×Dic3—51no—
527C4×Dic3—51no—
528C4×Dic3—102no—
529C4×Dic3—102no—
530C4×Dic3—201no—
531C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
532C23×C5—31no—
533C23×C5C2×C4×D311yescharacteristic
534C22×D5—21no—
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—21no—
538C22×D5—21no—
539C22×D5—21no—
540C22×D5—31no—
541C22×D5—32no—
542C22×D5—32no—
543C22×D5—61no—
544C22×D5—61no—
545C22×D5—61no—
546C22×D5—61no—
547C22×D5C2×C4×D311yescharacteristic
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)—61no—
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)—124no—
573C2×AGL(1,𝔽5)—124no—
574C2×AGL(1,𝔽5)D3×D412yes—
575C5×D4—62no—
576C2×C4×C5—31no—
577C2×C4×C5—31no—
578C2×C4×C5—31no—
579C2×C4×C5—62no—
580C2×C4×C5—62no—
581C2×C4×C5C2×C4×D311yescharacteristic
582C2×C4×C5C2×C4×D311yescharacteristic
583C22⋊D5—62no—
584C22⋊D5—62no—
585C2×Dic5—31no—
586C2×Dic5—31no—
587C2×Dic5—31no—
588C2×Dic5—62no—
589C2×Dic5—62no—
590C2×Dic5C2×C4×D311yescharacteristic
591C2×Dic5C2×C4×D311yescharacteristic
592D20—62no—
593C4×D5—21no—
594C4×D5—21no—
595C4×D5—21no—
596C4×D5—21no—
597C4×D5—32no—
598C4×D5—32no—
599C4×D5—62no—
600C4×D5—62no—
601C4×D5—62no—
602C4×D5—62no—
603C4×D5—61no—
604C4×D5—61no—
605C4×D5—61no—
606C4×D5—61no—
607C22×D4—151no—
608C23×C4—151no—
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—51no—
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—51no—
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—41no—
653C2×C3×C5C2×#11711yescharacteristic
654C2×C3×C5C2×C4×D411yescharacteristic
655C2×C3×C5#52011yescharacteristic
656D15—22no—
657C3×D5—41no—
658C3×D5#54611yescharacteristic
659C3×D5#54811yescharacteristic
660C3×D5#55211yescharacteristic
661C3×D5#55311yescharacteristic
662C5×D3—22no—
663C23×C3—51no—
664C23×C3—51no—
665C23×C3—101no—
666C23×C3—101no—
667C23×C3—101no—
668C23×C3—101no—
669C23×C3—101no—
670C23×C3—101no—
671C23×C3C22×AGL(1,𝔽5)11yescharacteristic
672C22×D3—51no—
673C22×D3—52no—
674C22×D3—52no—
675C22×D3—101no—
676C22×D3—101no—
677C22×D3—101no—
678C22×D3—101no—
679C22×D3C22×AGL(1,𝔽5)11yescharacteristic
680C2×C3×C4—52no—
681C2×C3×C4—51no—
682C2×C3×C4—51no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
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×C4C22×AGL(1,𝔽5)11yescharacteristic
699C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
700#67—22no—
701#67—102no—
702#67—102no—
703#67—102no—
704C2×Dic3—22no—
705C2×Dic3—51no—
706C2×Dic3—52no—
707C2×Dic3—52no—
708C2×Dic3—52no—
709C2×Dic3—51no—
710C2×Dic3—51no—
711C2×Dic3—102no—
712C2×Dic3—101no—
713C2×Dic3—101no—
714C2×Dic3—101no—
715C2×Dic3—101no—
716C2×Dic3—102no—
717C2×Dic3—101no—
718C2×Dic3—101no—
719C2×Dic3—102no—
720C2×Dic3—101no—
721C2×Dic3—101no—
722C2×Dic3—101no—
723C2×Dic3—101no—
724C2×Dic3—101no—
725C2×Dic3—101no—
726C2×Dic3—101no—
727C2×Dic3—101no—
728C2×Dic3—101no—
729C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
730C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
731C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
732C4×D3—22no—
733C4×D3—102no—
734C4×D3—102no—
735C4×D3—102no—
736C4×D3—204no—
737C4×D3—204no—
738C22×C5—21no—
739C22×C5—21no—
740C22×C5—21no—
741C22×C5—32no—
742C22×C5—61no—
743C22×C5—61no—
744C22×C5C22×C4×D311yescharacteristic
745C2×D5—21no—
746C2×D5—21no—
747C2×D5—21no—
748C2×D5—32no—
749C2×D5—41no—
750C2×D5—41no—
751C2×D5—41no—
752C2×D5—41no—
753C2×D5—61no—
754C2×D5—61no—
755C2×D5—62no—
756C2×D5—62no—
757C2×D5—62no—
758C2×D5—62no—
759C2×D5C2×D3×D411yescharacteristic
760C2×D5#100411yescharacteristic
761C2×D5D3×#4111yescharacteristic
762C2×D5D3×#4111yescharacteristic
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—21no—
775C4×C5—32no—
776C4×C5—61no—
777C4×C5—61no—
778Dic5—21no—
779Dic5—21no—
780Dic5—32no—
781Dic5—61no—
782Dic5—61no—
783C24—51no—
784C24—151no—
785C2×D4—31no—
786C2×D4—151no—
787C2×D4—151no—
788C2×D4—151no—
789C2×D4—302no—
790C2×D4—302no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—51no—
794C22×C4—51no—
795C22×C4—51no—
796C22×C4—51no—
797C22×C4—51no—
798C22×C4—51no—
799C22×C4—151no—
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—302no—
813C22×C4—302no—
814C22×C4—302no—
815C22×C4—302no—
816C22×C4—302no—
817C22×C4—302no—
818C22×C4—302no—
819C22×C4—302no—
820C22×C4—601no—
821C22×C4—601no—
822C4⋊C4—31no—
823C4⋊C4—102no—
824C4⋊C4—151no—
825C4⋊C4—151no—
826C4⋊C4—154no—
827C4⋊C4—151no—
828C4⋊C4—302no—
829C4⋊C4—302no—
830C4⋊C4—302no—
831C4⋊C4—302no—
832C22⋊C4—31no—
833C22⋊C4—51no—
834C22⋊C4—51no—
835C22⋊C4—51no—
836C22⋊C4—102no—
837C22⋊C4—151no—
838C22⋊C4—151no—
839C22⋊C4—151no—
840C22⋊C4—201no—
841C22⋊C4—302no—
842C22⋊C4—302no—
843C22⋊C4—302no—
844C22⋊C4—601no—
845C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
846C42—31no—
847C42—151no—
848C42—151no—
849C42—151no—
850C42—201no—
851C42—302no—
852C42—302no—
853C42—601no—
854C3×C5#235211yescharacteristic, complemented, Hall
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—51no—
859C22×C3—51no—
860C22×C3—51no—
861C22×C3—51no—
862C22×C3—51no—
863C22×C3—51no—
864C22×C3—101no—
865C22×C3—101no—
866C22×C3—101no—
867C22×C3—201no—
868C22×C3—201no—
869C22×C3—201no—
870C22×C3—201no—
871C22×C3C23×AGL(1,𝔽5)11yescharacteristic
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—52no—
875C2×D3—102no—
876C2×D3—102no—
877C2×D3—102no—
878C2×D3—102no—
879C2×D3—101no—
880C2×D3—101no—
881C2×D3#413012yescomplemented
882C3×C4—21no—
883C3×C4—21no—
884C3×C4—102no—
885C3×C4—101no—
886C3×C4—101no—
887C3×C4—201no—
888C3×C4—201no—
889C3×C4—201no—
890Dic3—21no—
891Dic3—21no—
892Dic3—52no—
893Dic3—102no—
894Dic3—101no—
895Dic3—101no—
896Dic3—201no—
897Dic3—201no—
898Dic3—201no—
899Dic3D4×AGL(1,𝔽5)12yes—
900C2×C5—41no—
901C2×C5—62no—
902C2×C5D3×#11711yescharacteristic
903C2×C5C4×D3×D411yescharacteristic
904C2×C5#554611yescharacteristic
905D5—41no—
906D5—62no—
907D5#561011yescharacteristic
908D5#566111yescharacteristic
909D5#567711yescharacteristic
910D5#570811yescharacteristic
911C23—31no—
912C23—51no—
913C23—51no—
914C23—101no—
915C23—101no—
916C23—101no—
917C23—101no—
918C23—101no—
919C23—101no—
920C23—152no—
921C23—152no—
922C23—151no—
923C23—301no—
924C23—301no—
925C23—301no—
926C23—301no—
927C23C2×D3×AGL(1,𝔽5)11yescharacteristic
928D4—62no—
929D4—302no—
930D4—302no—
931D4—302no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—52no—
936C2×C4—51no—
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—101no—
954C2×C4—101no—
955C2×C4—152no—
956C2×C4—152no—
957C2×C4—151no—
958C2×C4—152no—
959C2×C4—151no—
960C2×C4—151no—
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—302no—
970C2×C4—302no—
971C2×C4—301no—
972C2×C4—301no—
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—604no—
983C2×C4—604no—
984C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
985C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
986C2×C3—41no—
987C2×C3—51no—
988C2×C3—51no—
989C2×C3—51no—
990C2×C3—51no—
991C2×C3—201no—
992C2×C3C2×#413011yescharacteristic
993C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
994C2×C3#6626611yescharacteristic
995D3—22no—
996D3—102no—
997C5#7583411yescharacteristic, complemented, Sylow
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—32no—
1002C22—51no—
1003C22—51no—
1004C22—51no—
1005C22—51no—
1006C22—51no—
1007C22—51no—
1008C22—61no—
1009C22—61no—
1010C22—101no—
1011C22—101no—
1012C22—101no—
1013C22—152no—
1014C22—201no—
1015C22—201no—
1016C22—201no—
1017C22—201no—
1018C22—302no—
1019C22—302no—
1020C22—302no—
1021C22—302no—
1022C22—301no—
1023C22—301no—
1024C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1025C4—21no—
1026C4—21no—
1027C4—32no—
1028C4—61no—
1029C4—61no—
1030C4—102no—
1031C4—101no—
1032C4—101no—
1033C4—152no—
1034C4—201no—
1035C4—201no—
1036C4—201no—
1037C4—302no—
1038C4—301no—
1039C4—301no—
1040C4—601no—
1041C4—601no—
1042C4—601no—
1043C3#1061717911yescharacteristic, complemented, Sylow
1044C2—41no—
1045C2—51no—
1046C2—51no—
1047C2—51no—
1048C2—51no—
1049C2—62no—
1050C2—201no—
1051C2—302no—
1052C2D3×#413011yescharacteristic
1053C2D3×D4×AGL(1,𝔽5)11yescharacteristic
1054C2#1175684611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91923C2semidirect
2. C2×D3×C4⋊AGL(1,𝔽5)C2semidirect
4. #11752359C2semidirect
5. C3×#65700C2semidirect
8. #11752028C2semidirect
9. #11751931C2semidirect
10. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
11. C4×Dic3⋊AGL(1,𝔽5)C2semidirect
12. #11751854C2semidirect
13. #11751845C2semidirect
14. #11751835C2semidirect
15. #11751746C2semidirect
40. #91770C4semidirect
41. C5×#67⋊C4C4semidirect
43. #67⋊Dic5C4semidirect
44. #91556C4semidirect
46. #91442C4semidirect
47. #91441C4semidirect
48. #91396C4semidirect
49. #91395C4semidirect
73. #65700D3semidirect
95. C22×Dic15C2×C4semidirect
98. C22×C5×Dic3C2×C4semidirect
110. C2×D5×Dic3C2×C4semidirect
111. C2×D5×Dic3C2×C4semidirect
128. Dic3⋊AGL(1,𝔽5)D4semidirect
133. C3×C5×C22⋊C4C2×C4semidirect
135. #6712C2×C4semidirect
136. C4×Dic15C2×C4semidirect
138. C5×Dic3⋊C4C2×C4semidirect
139. C4×C5×Dic3C2×C4semidirect
140. C3×C22⋊Dic5C2×C4semidirect
141. C3×#685C2×C4semidirect
142. C3×#685C2×C4semidirect
143. Dic3⋊Dic5C2×C4semidirect
144. #6669C2×C4semidirect
147. Dic3×Dic5C2×C4semidirect
148. Dic3×Dic5C2×C4semidirect
318. #67⋊C4AGL(1,𝔽5)semidirect
387. C5×C22⋊C4C4×D3semidirect
390. C22⋊Dic5C4×D3semidirect
393. #685C4×D3semidirect
394. #685C4×D3semidirect
422. C2×D15#117semidirect
425. C2×C5×D3#117semidirect
487. C22×Dic3C2×AGL(1,𝔽5)semidirect
506. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
524. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
531. C4×Dic3C2×AGL(1,𝔽5)semidirect
845. C22⋊C4D3×AGL(1,𝔽5)semidirect
854. C3×C5#2352semidirect
881. C2×D3#4130semidirect
997. C5#75834semidirect
1043. C3#10617179semidirect

Maximal subgroups

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

subgroupindex
C2×#919232
C2×D3×C4⋊AGL(1,𝔽5)2
D5×#67⋊C42
#117523592
C3×#657002
#117520552
#117520282
#117519312
AGL(1,𝔽5)×(C2×D3)⋊C42
C4×Dic3⋊AGL(1,𝔽5)2
#117518542
#117518452
#117518352
#117517462
#106171793
#758345