Finite Group Databasebeta

← #14326775

Subgroups — #14326775

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D5×C4⋊C4C211yesmaximal, characteristic
2#11752370C211yesmaximal, characteristic, complemented
3C3×#65711C211yesmaximal, characteristic, complemented
4#11751855C211yesmaximal, characteristic
5#11751854C211yesmaximal, characteristic
6#11751854C211yesmaximal, characteristic
7#11751848C211yesmaximal, characteristic
8#11751848C211yesmaximal, characteristic
9C4×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
10#11751844C211yesmaximal, characteristic, complemented
11#11751840C211yesmaximal, characteristic, complemented
12#11751839C211yesmaximal, characteristic, complemented
13#11751837C211yesmaximal, characteristic, complemented
14#11751833C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10617104—31nomaximal, Hall
17C2×C4×D3×D5C2211yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
21C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
22C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
25C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
29C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
30C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
31C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
32C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
34C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
35C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
36C4⋊C4×D15C411yescharacteristic, complemented
37C5×D3×C4⋊C4C411yescharacteristic, complemented
38C3×D5×C4⋊C4C2211yescharacteristic
39#91437C411yescharacteristic, complemented
40D3×C4⋊Dic5C411yescharacteristic, complemented
41D5×C4⋊Dic3C2211yescharacteristic
42#91404C411yescharacteristic, complemented
43#91404C411yescharacteristic, complemented
44D3×#683C411yescharacteristic, complemented
45D3×#683C411yescharacteristic, complemented
46D5×Dic3⋊C4C2211yescharacteristic
47D5×Dic3⋊C4C2211yescharacteristic
48#91235C2211yescharacteristic
49#91235C2211yescharacteristic
50#91235C2211yescharacteristic
51#91235C2211yescharacteristic
52C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
53C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
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#74962—51nomaximal, Hall
61C2×D5×C4⋊C4—31no—
62#65765—31no—
63#65765—31no—
64#65765—31no—
65C4×C22⋊AGL(1,𝔽5)—31no—
66C4×C22⋊AGL(1,𝔽5)—31no—
67C4×C22⋊AGL(1,𝔽5)—31no—
68#65712—31no—
69#65712—31no—
70#65711—31no—
71#65711—31no—
72#65711—31no—
73#65711D311yescharacteristic, complemented
74C4⋊C4×AGL(1,𝔽5)—31no—
75C4⋊C4×AGL(1,𝔽5)—31no—
76C22×D3×D5C2311yescharacteristic
77C22×ΓL(1,𝔽16)C2311yescharacteristic
78C22×ΓL(1,𝔽16)C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×C3×AGL(1,𝔽5)C2311yescharacteristic
82C22×C3×AGL(1,𝔽5)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C2×C4×D15C2×C411yescharacteristic
86C2×C4×D15C2×C411yescharacteristic
87C2×C4×D15C2×C411yescharacteristic
88C2×C4×C5×D3C2×C411yescharacteristic
89C2×C4×C5×D3C2×C411yescharacteristic
90C2×C4×C5×D3C2×C411yescharacteristic
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94C2×#1200C2×C411yescharacteristic
95C2×#1200C2×C411yescharacteristic
96C2×#1200C2×C411yescharacteristic
97C2×D3×Dic5C2×C411yescharacteristic
98C2×D3×Dic5C2×C411yescharacteristic
99C2×D3×Dic5C2×C411yescharacteristic
100C2×D5×Dic3C2311yescharacteristic
101C2×D5×Dic3C2311yescharacteristic
102C2×D5×Dic3C2311yescharacteristic
103C4×D3×D5—22no—
104C4×D3×D5—22no—
105C4×D3×D5—41no—
106C4×D3×D5—41no—
107C4×D3×D5—41no—
108C4×D3×D5—41no—
109C4⋊ΓL(1,𝔽16)—41no—
110C4×ΓL(1,𝔽16)—41no—
111C3×C4⋊AGL(1,𝔽5)—41no—
112C3×C4×AGL(1,𝔽5)—41no—
113Dic3⋊AGL(1,𝔽5)—22no—
114Dic3⋊AGL(1,𝔽5)—22no—
115Dic3⋊AGL(1,𝔽5)—41no—
116Dic3⋊AGL(1,𝔽5)—41no—
117(C2×D3)⋊AGL(1,𝔽5)—22no—
118(C2×D3)⋊AGL(1,𝔽5)—22no—
119(C2×D3)⋊AGL(1,𝔽5)—22no—
120(C2×D3)⋊AGL(1,𝔽5)Q814yes—
121Dic3×AGL(1,𝔽5)—22no—
122Dic3×AGL(1,𝔽5)—22no—
123Dic3×AGL(1,𝔽5)—41no—
124Dic3×AGL(1,𝔽5)—41no—
125C3×C5×C4⋊C4C2×C411yescharacteristic
126C4⋊Dic15C2×C411yescharacteristic
127#6712C2×C411yescharacteristic
128#6712C2×C411yescharacteristic
129C5×C4⋊Dic3C2×C411yescharacteristic
130C5×Dic3⋊C4C2×C411yescharacteristic
131C5×Dic3⋊C4C2×C411yescharacteristic
132C3×C4⋊Dic5C2×C411yescharacteristic
133C3×#683C2×C411yescharacteristic
134C3×#683C2×C411yescharacteristic
135Dic3⋊Dic5C2×C411yescharacteristic
136Dic3⋊Dic5C2×C411yescharacteristic
137#6669C2×C411yescharacteristic
138#6669C2×C411yescharacteristic
139#6668C2×C411yescharacteristic
140#6668C2×C411yescharacteristic
141C2×D3×C4⋊C4—51no—
142C3×#387—51no—
143#4987—51no—
144#4980—51no—
145#4976—51no—
146C4×(C2×D3)⋊C4—51no—
147C4×Dic3⋊C4—51no—
148#4667—51no—
149#4667—51no—
150#4666—51no—
151#4666—51no—
152#4654—51no—
153#4653—51no—
154#4649—51no—
155#4647—51no—
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C22×C4×D5—31no—
159C2×C22⋊AGL(1,𝔽5)—31no—
160C2×C22⋊AGL(1,𝔽5)—31no—
161C2×C22⋊AGL(1,𝔽5)—31no—
162C2×C22⋊AGL(1,𝔽5)—31no—
163C2×C4⋊AGL(1,𝔽5)—31no—
164C2×C4⋊AGL(1,𝔽5)—31no—
165C2×C4⋊AGL(1,𝔽5)—31no—
166C2×C4⋊AGL(1,𝔽5)—31no—
167C2×C4⋊AGL(1,𝔽5)—31no—
168C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
169C2×C4×AGL(1,𝔽5)—31no—
170C2×C4×AGL(1,𝔽5)—31no—
171C2×C4×AGL(1,𝔽5)—31no—
172C2×C4×AGL(1,𝔽5)—31no—
173C2×C4×AGL(1,𝔽5)—31no—
174C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
175C2×C5×C4⋊C4—31no—
176C2×C4⋊Dic5—31no—
177C2×#683—31no—
178C2×#683—31no—
179D5×C4⋊C4—31no—
180D5×C4⋊C4—31no—
181D5×C4⋊C4—31no—
182D5×C4⋊C4—31no—
183D5×C4⋊C4—31no—
184D5×C4⋊C4—31no—
185D5×C4⋊C4—31no—
186D5×C4⋊C4C2×D311yescharacteristic
187(C2×AGL(1,𝔽5))⋊C4—31no—
188(C2×AGL(1,𝔽5))⋊C4—31no—
189(C2×AGL(1,𝔽5))⋊C4—31no—
190(C2×AGL(1,𝔽5))⋊C4—31no—
191(C2×AGL(1,𝔽5))⋊C4—31no—
192(C2×AGL(1,𝔽5))⋊C4—31no—
193(C2×AGL(1,𝔽5))⋊C4—31no—
194(C2×AGL(1,𝔽5))⋊C4—31no—
195(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
196(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
197(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
198(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
199#2345—151noSylow
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C2411yescharacteristic
203C2×D3×D5—21no—
204C2×D3×D5—21no—
205C2×D3×D5—21no—
206C2×D3×D5—21no—
207C2×D3×D5C2×Q812yes—
208C2×D3×D5#4112yes—
209C2×ΓL(1,𝔽16)—21no—
210C2×ΓL(1,𝔽16)—21no—
211C2×ΓL(1,𝔽16)—21no—
212C2×ΓL(1,𝔽16)—21no—
213C2×ΓL(1,𝔽16)—21no—
214C2×ΓL(1,𝔽16)—21no—
215C2×ΓL(1,𝔽16)—21no—
216C2×ΓL(1,𝔽16)—21no—
217C2×ΓL(1,𝔽16)—21no—
218C2×ΓL(1,𝔽16)—21no—
219C2×ΓL(1,𝔽16)—21no—
220C2×ΓL(1,𝔽16)C2×Q812yes—
221C2×C3×AGL(1,𝔽5)—21no—
222C2×C3×AGL(1,𝔽5)—21no—
223C2×C3×AGL(1,𝔽5)—21no—
224C2×C3×AGL(1,𝔽5)—21no—
225C2×C3×AGL(1,𝔽5)—21no—
226C2×C3×AGL(1,𝔽5)—21no—
227C2×C3×AGL(1,𝔽5)—21no—
228C2×C3×AGL(1,𝔽5)—21no—
229C2×C3×AGL(1,𝔽5)—21no—
230C2×C3×AGL(1,𝔽5)—21no—
231C2×C3×AGL(1,𝔽5)—21no—
232C2×C3×AGL(1,𝔽5)C2×Q812yes—
233C2×C3×C4×C5C22×C411yescharacteristic
234C2×C3×C4×C5C22×C411yescharacteristic
235C2×C3×C4×C5C22×C411yescharacteristic
236C2×Dic15C22×C411yescharacteristic
237C2×Dic15C22×C411yescharacteristic
238C2×Dic15C22×C411yescharacteristic
239C4×D15—22no—
240C4×D15—41no—
241C4×D15—41no—
242C2×C5×Dic3C22×C411yescharacteristic
243C2×C5×Dic3C22×C411yescharacteristic
244C2×C5×Dic3C22×C411yescharacteristic
245C4×C5×D3—22no—
246C4×C5×D3—41no—
247C4×C5×D3—41no—
248C2×C3×Dic5C22×C411yescharacteristic
249C2×C3×Dic5C22×C411yescharacteristic
250C2×C3×Dic5C22×C411yescharacteristic
251C3×C4×D5—21no—
252C3×C4×D5—21no—
253C3×C4×D5—21no—
254C3×C4×D5—21no—
255C3×C4×D5—21no—
256C3×C4×D5—21no—
257#1200—22no—
258#1200—41no—
259#1200—41no—
260D3×Dic5—22no—
261D3×Dic5—41no—
262D3×Dic5—41no—
263D5×Dic3—21no—
264D5×Dic3—21no—
265D5×Dic3—21no—
266D5×Dic3—21no—
267D5×Dic3#4112yes—
268D5×Dic3#4112yes—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4—51no—
274C2×C3×C42—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×C4⋊Dic3—51no—
280C2×C4⋊Dic3—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×C4×Dic3—51no—
288C2×C4×Dic3—51no—
289C2×C4×Dic3—51no—
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292D3×C4⋊C4—51no—
293D3×C4⋊C4—51no—
294D3×C4⋊C4—51no—
295D3×C4⋊C4—51no—
296D3×C4⋊C4—51no—
297D3×C4⋊C4—51no—
298D3×C4⋊C4—51no—
299D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
300C3×#95—51no—
301C3×#95—51no—
302C3×#95—51no—
303C3×#95—51no—
304C3⋊#95—51no—
305C3⋊#95—51no—
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C23×D5—31no—
313C22×AGL(1,𝔽5)—31no—
314C22×AGL(1,𝔽5)—31no—
315C22×AGL(1,𝔽5)—31no—
316C22×AGL(1,𝔽5)—31no—
317C22×AGL(1,𝔽5)C22×D311yescharacteristic
318C22×AGL(1,𝔽5)C22×D311yescharacteristic
319C22×AGL(1,𝔽5)C22×D311yescharacteristic
320C22×AGL(1,𝔽5)C22×D311yescharacteristic
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C2×C4×D5—31no—
328C2×C4×D5—31no—
329C2×C4×D5—31no—
330C2×C4×D5—31no—
331C2×C4×D5—31no—
332C2×C4×D5—31no—
333C2×C4×D5—31no—
334C2×C4×D5—31no—
335C2×C4×D5—31no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C2×C4×D5—121no—
341C2×C4×D5—121no—
342C2×C4×D5C22×D311yescharacteristic
343C2×C4×D5C22×D311yescharacteristic
344C2×C4×D5C22×D311yescharacteristic
345C22⋊AGL(1,𝔽5)—34no—
346C22⋊AGL(1,𝔽5)—62no—
347C22⋊AGL(1,𝔽5)—62no—
348C22⋊AGL(1,𝔽5)—62no—
349C4⋊AGL(1,𝔽5)—41no—
350C4⋊AGL(1,𝔽5)—62no—
351C4⋊AGL(1,𝔽5)—62no—
352C4⋊AGL(1,𝔽5)—121no—
353C4⋊AGL(1,𝔽5)—121no—
354C4⋊AGL(1,𝔽5)—121no—
355C4×AGL(1,𝔽5)—41no—
356C4×AGL(1,𝔽5)—62no—
357C4×AGL(1,𝔽5)—62no—
358C4×AGL(1,𝔽5)—121no—
359C4×AGL(1,𝔽5)—121no—
360C4×AGL(1,𝔽5)—121no—
361C5×C4⋊C4—31no—
362C5×C4⋊C4—31no—
363C5×C4⋊C4—31no—
364C5×C4⋊C4C4×D311yescharacteristic
365C4⋊Dic5—31no—
366C4⋊Dic5—31no—
367C4⋊Dic5—31no—
368C4⋊Dic5C4×D311yescharacteristic
369#683—31no—
370#683—31no—
371#683—31no—
372#683—31no—
373#683—31no—
374#683—31no—
375#683C4×D311yescharacteristic
376#683C4×D311yescharacteristic
377C22×C4⋊C4—151no—
378#389—151no—
379#389—151no—
380#387—51no—
381#387—151no—
382#387—151no—
383#387—151no—
384#380—151no—
385#380—151no—
386#380—151no—
387C4×C4⋊C4—151no—
388C4×C4⋊C4—151no—
389C4×C22⋊C4—151no—
390C4×C22⋊C4—151no—
391C4×C22⋊C4—151no—
392C22×C3×C5C23×C411yescharacteristic
393C2×D15—21no—
394C2×D15—21no—
395C2×D15C4×Q812yes—
396C2×C5×D3—21no—
397C2×C5×D3—21no—
398C2×C5×D3C4×Q812yes—
399C2×C3×D5C22×Q811yescharacteristic
400C2×C3×D5C2×#4111yescharacteristic
401C2×C3×D5C2×#4111yescharacteristic
402C2×C3×D5C2×#4111yescharacteristic
403C2×C3×D5H(5,𝔽2)11yescharacteristic
404C2×C3×D5H(5,𝔽2)11yescharacteristic
405D3×D5—22no—
406D3×D5—22no—
407D3×D5—22no—
408D3×D5—22no—
409ΓL(1,𝔽16)—22no—
410ΓL(1,𝔽16)—41no—
411ΓL(1,𝔽16)—41no—
412ΓL(1,𝔽16)—41no—
413C3×AGL(1,𝔽5)—22no—
414C3×AGL(1,𝔽5)—41no—
415C3×AGL(1,𝔽5)—41no—
416C3×AGL(1,𝔽5)—41no—
417C3×C4×C5—21no—
418C3×C4×C5—21no—
419C3×C4×C5—21no—
420Dic15—21no—
421Dic15—21no—
422Dic15#11712yes—
423C3×Dic5—21no—
424C3×Dic5—21no—
425C3×Dic5—21no—
426C5×Dic3—21no—
427C5×Dic3—21no—
428C5×Dic3#11712yes—
429C23×D3—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3—51no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—51no—
444C2×C4×D3—51no—
445C2×C4×D3—51no—
446C2×C4×D3—51no—
447C2×C4×D3—51no—
448C2×C4×D3—51no—
449C2×C4×D3—51no—
450C2×C4×D3—51no—
451C2×C4×D3—51no—
452C2×C4×D3—51no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3—201no—
456C2×C4×D3—201no—
457C2×C4×D3—201no—
458C2×C4×D3—201no—
459C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
460C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
461C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
462C3×C4⋊C4—51no—
463C3×C4⋊C4—51no—
464C3×C4⋊C4—51no—
465C3×C4⋊C4—201no—
466C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
467C3×C42—201no—
468(C2×D3)⋊C4—54no—
469(C2×D3)⋊C4—102no—
470(C2×D3)⋊C4—102no—
471(C2×D3)⋊C4—102no—
472C4⋊Dic3—51no—
473C4⋊Dic3—51no—
474C4⋊Dic3—51no—
475C4⋊Dic3—201no—
476C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
477Dic3⋊C4—51no—
478Dic3⋊C4—51no—
479Dic3⋊C4—51no—
480Dic3⋊C4—51no—
481Dic3⋊C4—51no—
482Dic3⋊C4—51no—
483Dic3⋊C4—102no—
484Dic3⋊C4—102no—
485Dic3⋊C4—201no—
486Dic3⋊C4—201no—
487Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
488Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
489C4×Dic3—102no—
490C4×Dic3—102no—
491C4×Dic3—201no—
492C4×Dic3—201no—
493C4×Dic3—201no—
494C23×C5—31no—
495C22×D5—31no—
496C22×D5—32no—
497C22×D5—32no—
498C22×D5—61no—
499C22×D5—61no—
500C22×D5—61no—
501C22×D5—61no—
502C22×D5C23×D311yescharacteristic
503C2×AGL(1,𝔽5)—21no—
504C2×AGL(1,𝔽5)—21no—
505C2×AGL(1,𝔽5)—21no—
506C2×AGL(1,𝔽5)—21no—
507C2×AGL(1,𝔽5)—21no—
508C2×AGL(1,𝔽5)—21no—
509C2×AGL(1,𝔽5)—21no—
510C2×AGL(1,𝔽5)—21no—
511C2×AGL(1,𝔽5)—21no—
512C2×AGL(1,𝔽5)—21no—
513C2×AGL(1,𝔽5)—21no—
514C2×AGL(1,𝔽5)—32no—
515C2×AGL(1,𝔽5)—61no—
516C2×AGL(1,𝔽5)—61no—
517C2×AGL(1,𝔽5)—61no—
518C2×AGL(1,𝔽5)—61no—
519C2×AGL(1,𝔽5)—61no—
520C2×AGL(1,𝔽5)—61no—
521C2×AGL(1,𝔽5)—61no—
522C2×AGL(1,𝔽5)—61no—
523C2×AGL(1,𝔽5)—61no—
524C2×AGL(1,𝔽5)—61no—
525C2×AGL(1,𝔽5)—61no—
526C2×AGL(1,𝔽5)D3×Q812yes—
527C2×C4×C5—31no—
528C2×C4×C5—31no—
529C2×C4×C5—31no—
530C2×C4×C5—62no—
531C2×C4×C5—121no—
532C2×C4×C5—121no—
533C2×C4×C5C2×C4×D311yescharacteristic
534C2×C4×C5C2×C4×D311yescharacteristic
535C2×C4×C5C2×C4×D311yescharacteristic
536C2×Dic5—31no—
537C2×Dic5—31no—
538C2×Dic5—31no—
539C2×Dic5—62no—
540C2×Dic5—121no—
541C2×Dic5—121no—
542C2×Dic5C2×C4×D311yescharacteristic
543C2×Dic5C2×C4×D311yescharacteristic
544C2×Dic5C2×C4×D311yescharacteristic
545C4×D5—21no—
546C4×D5—21no—
547C4×D5—21no—
548C4×D5—21no—
549C4×D5—21no—
550C4×D5—21no—
551C4×D5—32no—
552C4×D5—32no—
553C4×D5—62no—
554C4×D5—62no—
555C4×D5—61no—
556C4×D5—61no—
557C4×D5—61no—
558C4×D5—61no—
559C4×D5—121no—
560C4×D5—121no—
561C4×D5—121no—
562C4×D5—121no—
563C23×C4—151no—
564C23×C4—151no—
565C23×C4—151no—
566C2×C4⋊C4—31no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C4⋊C4—151no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C4⋊C4—151no—
574C2×C4⋊C4—151no—
575C2×C4⋊C4—151no—
576C2×C4⋊C4—151no—
577C2×C4⋊C4—151no—
578C2×C4⋊C4—151no—
579C2×C4⋊C4—151no—
580C2×C4⋊C4—151no—
581C2×C4⋊C4—151no—
582C2×C4⋊C4—151no—
583C2×C4⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4—151no—
588C2×C42—51no—
589C2×C42—151no—
590C2×C42—151no—
591C2×C42—151no—
592C2×C42—151no—
593C2×C42—151no—
594#95—51no—
595#95—51no—
596#95—51no—
597#95—51no—
598#95—151no—
599#95—151no—
600#95—151no—
601#95—151no—
602#95—151no—
603#95—151no—
604#95—151no—
605#95—151no—
606C2×C3×C5C2×#11711yescharacteristic
607C2×C3×C5C2×C4×Q811yescharacteristic
608C2×C3×C5#51811yescharacteristic
609D15—22no—
610C3×D5#55311yescharacteristic
611C3×D5#55311yescharacteristic
612C3×D5#55411yescharacteristic
613C3×D5#55411yescharacteristic
614C5×D3—22no—
615C23×C3—51no—
616C22×D3—51no—
617C22×D3—52no—
618C22×D3—52no—
619C22×D3—101no—
620C22×D3—101no—
621C22×D3—101no—
622C22×D3—101no—
623C22×D3C22×AGL(1,𝔽5)11yescharacteristic
624C2×C3×C4—52no—
625C2×C3×C4—51no—
626C2×C3×C4—51no—
627C2×C3×C4—51no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
646C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
647C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
648C2×Dic3—51no—
649C2×Dic3—52no—
650C2×Dic3—52no—
651C2×Dic3—52no—
652C2×Dic3—51no—
653C2×Dic3—51no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
670C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
671C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
672C4×D3—22no—
673C4×D3—41no—
674C4×D3—41no—
675C4×D3—102no—
676C4×D3—102no—
677C4×D3—102no—
678C4×D3—201no—
679C4×D3—201no—
680C4×D3—201no—
681C4×D3—201no—
682C4×D3—201no—
683C4×D3—201no—
684C22×C5—32no—
685C22×C5—61no—
686C22×C5—61no—
687C22×C5C22×C4×D311yescharacteristic
688C2×D5—32no—
689C2×D5—61no—
690C2×D5—61no—
691C2×D5—62no—
692C2×D5—62no—
693C2×D5—62no—
694C2×D5—62no—
695C2×D5#100411yescharacteristic
696C2×D5C2×D3×Q811yescharacteristic
697C2×D5D3×#4111yescharacteristic
698C2×D5D3×#4111yescharacteristic
699C2×D5D3×#4111yescharacteristic
700C2×D5#100911yescharacteristic
701AGL(1,𝔽5)—22no—
702AGL(1,𝔽5)—41no—
703AGL(1,𝔽5)—41no—
704AGL(1,𝔽5)—41no—
705AGL(1,𝔽5)—62no—
706AGL(1,𝔽5)—121no—
707AGL(1,𝔽5)—121no—
708AGL(1,𝔽5)—121no—
709C4×C5—21no—
710C4×C5—21no—
711C4×C5—21no—
712C4×C5—32no—
713C4×C5—61no—
714C4×C5—61no—
715Dic5—21no—
716Dic5—21no—
717Dic5—21no—
718Dic5—32no—
719Dic5—61no—
720Dic5—61no—
721C24—151no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—51no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—51no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—151no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—151no—
743C22×C4—151no—
744C22×C4—151no—
745C22×C4—151no—
746C22×C4—151no—
747C22×C4—151no—
748C22×C4—302no—
749C22×C4—302no—
750C22×C4—601no—
751C22×C4—601no—
752C22×C4—601no—
753C22×C4—601no—
754C4⋊C4—31no—
755C4⋊C4—31no—
756C4⋊C4—31no—
757C4⋊C4—51no—
758C4⋊C4—51no—
759C4⋊C4—51no—
760C4⋊C4—151no—
761C4⋊C4—151no—
762C4⋊C4—151no—
763C4⋊C4—151no—
764C4⋊C4—151no—
765C4⋊C4—151no—
766C4⋊C4—151no—
767C4⋊C4—151no—
768C4⋊C4—151no—
769C4⋊C4—201no—
770C4⋊C4—302no—
771C4⋊C4—302no—
772C4⋊C4—601no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
776C22⋊C4—154no—
777C22⋊C4—302no—
778C22⋊C4—302no—
779C22⋊C4—302no—
780C42—201no—
781C42—302no—
782C42—302no—
783C42—601no—
784C42—601no—
785C42—601no—
786C3×C5#234511yescharacteristic, complemented, Hall
787C22×C3—51no—
788C22×C3—51no—
789C22×C3—51no—
790C22×C3—51no—
791C22×C3—51no—
792C22×C3—51no—
793C22×C3C23×AGL(1,𝔽5)11yescharacteristic
794C2×D3—21no—
795C2×D3—21no—
796C2×D3—52no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—101no—
802C2×D3—101no—
803C2×D3Q8×AGL(1,𝔽5)12yes—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—21no—
807C3×C4—102no—
808C3×C4—101no—
809C3×C4—101no—
810C3×C4—101no—
811C3×C4—201no—
812C3×C4—201no—
813C3×C4—201no—
814Dic3—21no—
815Dic3—21no—
816Dic3—52no—
817Dic3—102no—
818Dic3—101no—
819Dic3—101no—
820Dic3—201no—
821Dic3—201no—
822Dic3—201no—
823Dic3#413012yes—
824C2×C5—62no—
825C2×C5D3×#11711yescharacteristic
826C2×C5#554511yescharacteristic
827C2×C5C4×D3×Q811yescharacteristic
828D5—62no—
829D5#563611yescharacteristic
830D5#566111yescharacteristic
831D5#569011yescharacteristic
832D5#570911yescharacteristic
833C23—31no—
834C23—51no—
835C23—152no—
836C23—152no—
837C23—151no—
838C23—301no—
839C23—301no—
840C23—301no—
841C23—301no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—52no—
846C2×C4—51no—
847C2×C4—51no—
848C2×C4—51no—
849C2×C4—62no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—152no—
870C2×C4—152no—
871C2×C4—151no—
872C2×C4—152no—
873C2×C4—151no—
874C2×C4—151no—
875C2×C4—302no—
876C2×C4—302no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—302no—
882C2×C4—301no—
883C2×C4—301no—
884C2×C4—301no—
885C2×C4—301no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—601no—
894C2×C4—601no—
895C2×C4—601no—
896C2×C4—601no—
897C2×C4—601no—
898C2×C4—601no—
899C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
900C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
901C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
902C2×C3—51no—
903C2×C3—51no—
904C2×C3—51no—
905C2×C3—51no—
906C2×C3C2×#413011yescharacteristic
907C2×C3#6625811yescharacteristic
908C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
909D3—22no—
910D3—102no—
911C5#7496211yescharacteristic, complemented, Sylow
912C22—32no—
913C22—51no—
914C22—51no—
915C22—51no—
916C22—51no—
917C22—51no—
918C22—51no—
919C22—61no—
920C22—61no—
921C22—152no—
922C22—302no—
923C22—302no—
924C22—302no—
925C22—302no—
926C22—301no—
927C22—301no—
928C22C22×D3×AGL(1,𝔽5)11yescharacteristic
929C4—21no—
930C4—21no—
931C4—21no—
932C4—32no—
933C4—61no—
934C4—61no—
935C4—102no—
936C4—101no—
937C4—101no—
938C4—101no—
939C4—152no—
940C4—201no—
941C4—201no—
942C4—201no—
943C4—302no—
944C4—301no—
945C4—301no—
946C4—601no—
947C4—601no—
948C4—601no—
949C3#1061710411yescharacteristic, complemented, Sylow
950C2—51no—
951C2—51no—
952C2—51no—
953C2—51no—
954C2—62no—
955C2—302no—
956C2D3×#413011yescharacteristic
957C2#1175684511yescharacteristic
958C2D3×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×C5#2345
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. #11752370C2semidirect
3. C3×#65711C2semidirect
10. #11751844C2semidirect
11. #11751840C2semidirect
12. #11751839C2semidirect
13. #11751837C2semidirect
14. #11751833C2semidirect
15. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
36. C4⋊C4×D15C4semidirect
37. C5×D3×C4⋊C4C4semidirect
39. #91437C4semidirect
40. D3×C4⋊Dic5C4semidirect
42. #91404C4semidirect
43. #91404C4semidirect
44. D3×#683C4semidirect
45. D3×#683C4semidirect
73. #65711D3semidirect
299. D3×C4⋊C4AGL(1,𝔽5)semidirect
786. C3×C5#2345semidirect
911. C5#74962semidirect
949. C3#10617104semidirect

Maximal subgroups

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

subgroupindex
D3×D5×C4⋊C42
#117523702
C3×#657112
#117518552
#117518542
#117518482
C4×(C2×D3)⋊AGL(1,𝔽5)2
#117518442
#117518402
#117518392
#117518372
#117518332
AGL(1,𝔽5)×Dic3⋊C42
#106171043
#749625