Finite Group Databasebeta

← #14321074

Subgroups — #14321074

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#887C211yesmaximal, characteristic
2#11752370C211yesmaximal, characteristic
3C3×#65711C211yesmaximal, characteristic
4#11751844C211yesmaximal, characteristic
5Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
6#11751842C211yesmaximal, characteristic
7#11751842C211yesmaximal, characteristic
8#11751837C211yesmaximal, characteristic
9#11751834C211yesmaximal, characteristic
10#11751834C211yesmaximal, characteristic
11#11751832C211yesmaximal, characteristic
12#11751832C211yesmaximal, characteristic
13C4×Dic3×AGL(1,𝔽5)C211yesmaximal, characteristic
14#11751747C211yesmaximal, characteristic
15#11751745C211yesmaximal, characteristic
16#10617209—31nomaximal, Hall
17C2×D5×Dic6C2211yescharacteristic
18C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
21C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
23C2×Dic3⋊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×Dic3×AGL(1,𝔽5)C2211yescharacteristic
29C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
30C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
31C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
32#91776C411yescharacteristic, complemented
33C5×#887C411yescharacteristic, complemented
34C3×D5×C4⋊C4C2211yescharacteristic
35D5×Dic3⋊C4C2211yescharacteristic
36D5×Dic3⋊C4C2211yescharacteristic
37C4×D5×Dic3C2211yescharacteristic
38C4×D5×Dic3C2211yescharacteristic
39C4×D5×Dic3C2211yescharacteristic
40#91344C411yescharacteristic, complemented
41#91340C411yescharacteristic, complemented
42#91325C411yescharacteristic, complemented
43#91325C411yescharacteristic, complemented
44#91324C411yescharacteristic, complemented
45#91324C411yescharacteristic, complemented
46#91235C2211yescharacteristic
47#91235C2211yescharacteristic
48#91235C2211yescharacteristic
49#91235C2211yescharacteristic
50C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
51C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
52C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
53C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
54(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
55(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
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#74938—51nomaximal, Hall
61C4×Q8×D5—31no—
62(C2×AGL(1,𝔽5))⋊Q8—31no—
63(C2×AGL(1,𝔽5))⋊Q8—31no—
64#65712—31no—
65#65712—31no—
66#65711—31no—
67#65711—31no—
68#65711—31no—
69#65711D311yescharacteristic
70C4×C4⋊AGL(1,𝔽5)—31no—
71C4×C4⋊AGL(1,𝔽5)—31no—
72C4×C4⋊AGL(1,𝔽5)—31no—
73#65686—31no—
74#65686—31no—
75C42×AGL(1,𝔽5)—31no—
76C22×ΓL(1,𝔽16)C2311yescharacteristic
77C22×ΓL(1,𝔽16)C2311yescharacteristic
78C22×ΓL(1,𝔽16)C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×C3×AGL(1,𝔽5)C2311yescharacteristic
81C22×C3×AGL(1,𝔽5)C2311yescharacteristic
82C22×C3×AGL(1,𝔽5)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C2×Dic30C2×C411yescharacteristic
85C2×C5×Dic6C2×C411yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×#1204C2×C411yescharacteristic
90C2×#1204C2×C411yescharacteristic
91C2×D5×Dic3C2311yescharacteristic
92C2×D5×Dic3C2311yescharacteristic
93C2×D5×Dic3C2311yescharacteristic
94C2×D5×Dic3C2311yescharacteristic
95D5×Dic6—22no—
96D5×Dic6—22no—
97C4⋊ΓL(1,𝔽16)—22no—
98C4×ΓL(1,𝔽16)—22no—
99C3×C4⋊AGL(1,𝔽5)—22no—
100C3×C4×AGL(1,𝔽5)—22no—
101Dic3⋊AGL(1,𝔽5)—22no—
102Dic3⋊AGL(1,𝔽5)—22no—
103Dic3⋊AGL(1,𝔽5)—22no—
104Dic3⋊AGL(1,𝔽5)—22no—
105Dic3×AGL(1,𝔽5)—22no—
106Dic3×AGL(1,𝔽5)—22no—
107Dic3×AGL(1,𝔽5)—22no—
108Dic3×AGL(1,𝔽5)—22no—
109Dic3×AGL(1,𝔽5)—22no—
110Dic3×AGL(1,𝔽5)Q814yescomplemented
111C3×C5×C4⋊C4C2×C411yescharacteristic
112#6712C2×C411yescharacteristic
113#6712C2×C411yescharacteristic
114C4×Dic15C2×C411yescharacteristic
115C4×Dic15C2×C411yescharacteristic
116C4×Dic15C2×C411yescharacteristic
117C5×Dic3⋊C4C2×C411yescharacteristic
118C5×Dic3⋊C4C2×C411yescharacteristic
119C4×C5×Dic3C2×C411yescharacteristic
120C4×C5×Dic3C2×C411yescharacteristic
121C4×C5×Dic3C2×C411yescharacteristic
122C3×C4⋊Dic5C2×C411yescharacteristic
123C3×#683C2×C411yescharacteristic
124C3×#683C2×C411yescharacteristic
125Dic3⋊Dic5C2×C411yescharacteristic
126Dic3⋊Dic5C2×C411yescharacteristic
127#6669C2×C411yescharacteristic
128#6669C2×C411yescharacteristic
129Dic3×Dic5C2×C411yescharacteristic
130Dic3×Dic5C2×C411yescharacteristic
131Dic3×Dic5C2×C411yescharacteristic
132Dic3×Dic5C2×C411yescharacteristic
133Dic3×Dic5C2×C411yescharacteristic
134Dic3×Dic5C2×C411yescharacteristic
135C2×#887—51no—
136C3×#387—51no—
137#4980—51no—
138#4976—51no—
139Dic3×C4⋊C4—51no—
140#4933—51no—
141C42×Dic3—51no—
142#4652—51no—
143#4649—51no—
144#4649—51no—
145#4648—51no—
146#4648—51no—
147#4647—51no—
148#4646—51no—
149#4646—51no—
150C2×Q8×D5—31no—
151C2×C4⋊AGL(1,𝔽5)—31no—
152C2×C4⋊AGL(1,𝔽5)—31no—
153C2×C4⋊AGL(1,𝔽5)—31no—
154C2×C4⋊AGL(1,𝔽5)—31no—
155C2×C4⋊AGL(1,𝔽5)—31no—
156C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
157C2×C4×AGL(1,𝔽5)—31no—
158C2×C4×AGL(1,𝔽5)—31no—
159C2×C4×AGL(1,𝔽5)—31no—
160C2×C4×AGL(1,𝔽5)—31no—
161C2×C4×AGL(1,𝔽5)—31no—
162C2×C4×AGL(1,𝔽5)—31no—
163C2×C4×AGL(1,𝔽5)—31no—
164C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
165C4×C5×Q8—31no—
166Q8×Dic5—31no—
167D5×C4⋊C4—31no—
168D5×C4⋊C4—31no—
169D5×C4⋊C4C2×D311yescharacteristic
170#4033—31no—
171#4033—31no—
172#4033—31no—
173C42×D5—31no—
174C42×D5—31no—
175C42×D5—31no—
176C4×Dic10—31no—
177C4×Dic10—31no—
178C4×Dic10—31no—
179(C2×AGL(1,𝔽5))⋊C4—31no—
180(C2×AGL(1,𝔽5))⋊C4—31no—
181(C2×AGL(1,𝔽5))⋊C4—31no—
182(C2×AGL(1,𝔽5))⋊C4—31no—
183(C2×AGL(1,𝔽5))⋊C4—31no—
184(C2×AGL(1,𝔽5))⋊C4—31no—
185(C2×AGL(1,𝔽5))⋊C4—31no—
186(C2×AGL(1,𝔽5))⋊C4—31no—
187(C2×AGL(1,𝔽5))⋊C4—31no—
188(C2×AGL(1,𝔽5))⋊C4—31no—
189(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
190(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
191(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
192(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
193#2295—151noSylow
194C22×C3×D5C2411yescharacteristic
195C2×ΓL(1,𝔽16)—21no—
196C2×ΓL(1,𝔽16)—21no—
197C2×ΓL(1,𝔽16)—21no—
198C2×ΓL(1,𝔽16)—21no—
199C2×ΓL(1,𝔽16)—21no—
200C2×ΓL(1,𝔽16)—21no—
201C2×ΓL(1,𝔽16)—21no—
202C2×ΓL(1,𝔽16)—21no—
203C2×ΓL(1,𝔽16)—21no—
204C2×ΓL(1,𝔽16)—21no—
205C2×ΓL(1,𝔽16)C2×Q812yes—
206C2×ΓL(1,𝔽16)#4112yes—
207C2×C3×AGL(1,𝔽5)—21no—
208C2×C3×AGL(1,𝔽5)—21no—
209C2×C3×AGL(1,𝔽5)—21no—
210C2×C3×AGL(1,𝔽5)—21no—
211C2×C3×AGL(1,𝔽5)—21no—
212C2×C3×AGL(1,𝔽5)—21no—
213C2×C3×AGL(1,𝔽5)—21no—
214C2×C3×AGL(1,𝔽5)—21no—
215C2×C3×AGL(1,𝔽5)—21no—
216C2×C3×AGL(1,𝔽5)—21no—
217C2×C3×AGL(1,𝔽5)C2×Q812yes—
218C2×C3×AGL(1,𝔽5)#4112yes—
219C2×C3×C4×C5C22×C411yescharacteristic
220C2×C3×C4×C5C22×C411yescharacteristic
221C2×C3×C4×C5C22×C411yescharacteristic
222C2×Dic15C22×C411yescharacteristic
223C2×Dic15C22×C411yescharacteristic
224C2×Dic15C22×C411yescharacteristic
225C2×Dic15C22×C411yescharacteristic
226Dic30—22no—
227C2×C5×Dic3C22×C411yescharacteristic
228C2×C5×Dic3C22×C411yescharacteristic
229C2×C5×Dic3C22×C411yescharacteristic
230C2×C5×Dic3C22×C411yescharacteristic
231C5×Dic6—22no—
232C2×C3×Dic5C22×C411yescharacteristic
233C2×C3×Dic5C22×C411yescharacteristic
234C2×C3×Dic5C22×C411yescharacteristic
235C3×C4×D5—21no—
236C3×C4×D5—21no—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239C3×C4×D5—21no—
240C3×C4×D5—21no—
241#1204—22no—
242#1204—22no—
243D5×Dic3—21no—
244D5×Dic3—21no—
245D5×Dic3—21no—
246D5×Dic3—21no—
247D5×Dic3C2×Q812yes—
248D5×Dic3#4112yes—
249D5×Dic3#4112yes—
250D5×Dic3#4112yes—
251C22×Dic6—51no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C4⋊C4—51no—
254C2×C3×C42—51no—
255C2×C4⋊Dic3—51no—
256C2×Dic3⋊C4—51no—
257C2×Dic3⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×C4×Dic3—51no—
263C2×C4×Dic3—51no—
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266C2×C4×Dic3—51no—
267C2×C4×Dic3—51no—
268C2×C4×Dic3—51no—
269C2×C4×Dic3—51no—
270C2×C4×Dic3—51no—
271C2×C4×Dic3—51no—
272#887—51no—
273#887—51no—
274#887—51no—
275#887—51no—
276#887—51no—
277#887—51no—
278#887—51no—
279#887AGL(1,𝔽5)11yescharacteristic, complemented
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C22×AGL(1,𝔽5)—31no—
295C22×AGL(1,𝔽5)—31no—
296C22×AGL(1,𝔽5)—31no—
297C22×AGL(1,𝔽5)—31no—
298C22×AGL(1,𝔽5)C22×D311yescharacteristic
299C22×AGL(1,𝔽5)C22×D311yescharacteristic
300C22×AGL(1,𝔽5)C22×D311yescharacteristic
301C22×AGL(1,𝔽5)C22×D311yescharacteristic
302C2×C5×Q8—31no—
303Q8×D5—62no—
304Q8×D5—62no—
305C2×C4×D5—31no—
306C2×C4×D5—31no—
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5C22×D311yescharacteristic
310C2×C4×D5C22×D311yescharacteristic
311C2×C4×D5C22×D311yescharacteristic
312C2×Dic10—31no—
313C2×Dic10—31no—
314C2×Dic10—31no—
315C4⋊AGL(1,𝔽5)—22no—
316C4⋊AGL(1,𝔽5)—62no—
317C4⋊AGL(1,𝔽5)—62no—
318C4⋊AGL(1,𝔽5)—62no—
319C4⋊AGL(1,𝔽5)—62no—
320C4⋊AGL(1,𝔽5)—62no—
321C4×AGL(1,𝔽5)—22no—
322C4×AGL(1,𝔽5)—34no—
323C4×AGL(1,𝔽5)—62no—
324C4×AGL(1,𝔽5)—62no—
325C4×AGL(1,𝔽5)—62no—
326C4×AGL(1,𝔽5)—62no—
327C4×AGL(1,𝔽5)—62no—
328C4×AGL(1,𝔽5)—62no—
329C5×C4⋊C4—31no—
330C5×C4⋊C4—31no—
331C5×C4⋊C4C4×D311yescharacteristic
332C42×C5—31no—
333C42×C5—31no—
334C42×C5—31no—
335C4⋊Dic5—31no—
336C4⋊Dic5—31no—
337C4⋊Dic5C4×D311yescharacteristic
338#683—31no—
339#683—31no—
340#683—31no—
341#683—31no—
342#683C4×D311yescharacteristic
343#683C4×D311yescharacteristic
344C4×Dic5—31no—
345C4×Dic5—31no—
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5—31no—
349C4×Dic5—31no—
350C4×Dic5—31no—
351C4×Dic5—31no—
352C4×Dic5—31no—
353C2×C4×Q8—151no—
354#391—151no—
355#391—151no—
356#389—151no—
357#389—151no—
358#387—51no—
359#387—151no—
360#387—151no—
361#387—151no—
362C4×C4⋊C4—151no—
363C4×C4⋊C4—151no—
364C4×C4⋊C4—151no—
365#376—151no—
366#376—151no—
367C43—151no—
368C22×C3×C5C23×C411yescharacteristic
369C2×C3×D5C22×Q811yescharacteristic
370C2×C3×D5C2×#4111yescharacteristic
371C2×C3×D5C2×#4111yescharacteristic
372C2×C3×D5C2×#4111yescharacteristic
373C2×C3×D5C2×#4111yescharacteristic
374C2×C3×D5C2×#4111yescharacteristic
375ΓL(1,𝔽16)—22no—
376ΓL(1,𝔽16)—22no—
377ΓL(1,𝔽16)—41no—
378ΓL(1,𝔽16)—41no—
379C3×AGL(1,𝔽5)—22no—
380C3×AGL(1,𝔽5)—22no—
381C3×AGL(1,𝔽5)—41no—
382C3×AGL(1,𝔽5)—41no—
383C3×C4×C5—21no—
384C3×C4×C5—21no—
385C3×C4×C5—21no—
386Dic15—21no—
387Dic15—21no—
388Dic15#11712yes—
389Dic15C4×Q812yes—
390C3×Dic5—21no—
391C3×Dic5—21no—
392C3×Dic5—21no—
393C5×Dic3—21no—
394C5×Dic3—21no—
395C5×Dic3#11712yes—
396C5×Dic3C4×Q812yes—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×C3×C4—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3—51no—
407C22×Dic3—51no—
408C22×Dic3—51no—
409C22×Dic3—51no—
410C22×Dic3—51no—
411C22×Dic3—51no—
412C2×Dic6—51no—
413C2×Dic6—51no—
414C2×Dic6—51no—
415C2×Dic6—102no—
416C2×Dic6—102no—
417C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
418C3×C4⋊C4—51no—
419C3×C4⋊C4—51no—
420C3×C4⋊C4—51no—
421C3×C4⋊C4—102no—
422C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
423C3×C42—102no—
424C4⋊Dic3—102no—
425Dic3⋊C4—51no—
426Dic3⋊C4—51no—
427Dic3⋊C4—51no—
428Dic3⋊C4—51no—
429Dic3⋊C4—51no—
430Dic3⋊C4—51no—
431Dic3⋊C4—102no—
432Dic3⋊C4—102no—
433Dic3⋊C4—102no—
434Dic3⋊C4—102no—
435Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
436Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
437C4×Dic3—54no—
438C4×Dic3—51no—
439C4×Dic3—51no—
440C4×Dic3—51no—
441C4×Dic3—51no—
442C4×Dic3—51no—
443C4×Dic3—51no—
444C4×Dic3—51no—
445C4×Dic3—51no—
446C4×Dic3—51no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—102no—
450C4×Dic3—102no—
451C4×Dic3—102no—
452C4×Dic3—102no—
453C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
454C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
455C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
456C22×D5C23×D311yescharacteristic
457C2×AGL(1,𝔽5)—21no—
458C2×AGL(1,𝔽5)—21no—
459C2×AGL(1,𝔽5)—21no—
460C2×AGL(1,𝔽5)—21no—
461C2×AGL(1,𝔽5)—21no—
462C2×AGL(1,𝔽5)—21no—
463C2×AGL(1,𝔽5)—21no—
464C2×AGL(1,𝔽5)—21no—
465C2×AGL(1,𝔽5)—21no—
466C2×AGL(1,𝔽5)—21no—
467C2×AGL(1,𝔽5)—32no—
468C2×AGL(1,𝔽5)—32no—
469C2×AGL(1,𝔽5)—61no—
470C2×AGL(1,𝔽5)—61no—
471C2×AGL(1,𝔽5)—61no—
472C2×AGL(1,𝔽5)—61no—
473C2×AGL(1,𝔽5)—61no—
474C2×AGL(1,𝔽5)—61no—
475C2×AGL(1,𝔽5)—61no—
476C2×AGL(1,𝔽5)—61no—
477C2×AGL(1,𝔽5)—61no—
478C2×AGL(1,𝔽5)—61no—
479C2×AGL(1,𝔽5)#23712yes—
480C2×AGL(1,𝔽5)D3×Q812yes—
481C5×Q8—62no—
482C2×C4×C5—31no—
483C2×C4×C5—31no—
484C2×C4×C5—31no—
485C2×C4×C5—31no—
486C2×C4×C5C2×C4×D311yescharacteristic
487C2×C4×C5C2×C4×D311yescharacteristic
488C2×C4×C5C2×C4×D311yescharacteristic
489C2×Dic5—31no—
490C2×Dic5—31no—
491C2×Dic5—31no—
492C2×Dic5—31no—
493C2×Dic5C2×C4×D311yescharacteristic
494C2×Dic5C2×C4×D311yescharacteristic
495C2×Dic5C2×C4×D311yescharacteristic
496C4×D5—21no—
497C4×D5—21no—
498C4×D5—21no—
499C4×D5—21no—
500C4×D5—21no—
501C4×D5—21no—
502C4×D5—32no—
503C4×D5—32no—
504C4×D5—32no—
505C4×D5—32no—
506C4×D5—61no—
507C4×D5—61no—
508C4×D5—61no—
509C4×D5—61no—
510Dic10—62no—
511Dic10—62no—
512Dic10—62no—
513C22×Q8—151no—
514C4×Q8—31no—
515C4×Q8—151no—
516C4×Q8—151no—
517C4×Q8—151no—
518C4×Q8—151no—
519C4×Q8—151no—
520C4×Q8—151no—
521C4×Q8—151no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C42—51no—
532C2×C42—151no—
533C2×C42—151no—
534C2×C42—151no—
535C2×C42—151no—
536C2×C42—151no—
537C2×C42—151no—
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C42—151no—
542#95—51no—
543#95—51no—
544#95—51no—
545#95—51no—
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552#95—151no—
553#95—151no—
554#95—151no—
555#95—151no—
556C2×C3×C5C2×#11711yescharacteristic
557C2×C3×C5C2×C4×Q811yescharacteristic
558C2×C3×C5C4×#4111yescharacteristic
559C3×D5#52911yescharacteristic
560C3×D5#52911yescharacteristic
561C3×D5#53311yescharacteristic
562C3×D5#53311yescharacteristic
563C23×C3—51no—
564C2×C3×C4—52no—
565C2×C3×C4—52no—
566C2×C3×C4—51no—
567C2×C3×C4—51no—
568C2×C3×C4—51no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
586C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
587C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
588C2×Dic3—51no—
589C2×Dic3—51no—
590C2×Dic3—52no—
591C2×Dic3—52no—
592C2×Dic3—52no—
593C2×Dic3—52no—
594C2×Dic3—52no—
595C2×Dic3—52no—
596C2×Dic3—51no—
597C2×Dic3—51no—
598C2×Dic3—101no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—101no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3—101no—
605C2×Dic3—101no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
613C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
614C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
615C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
616Dic6—22no—
617Dic6—102no—
618Dic6—102no—
619Dic6—102no—
620C22×C5C22×C4×D311yescharacteristic
621C2×D5C2×#23711yescharacteristic
622C2×D5C2×D3×Q811yescharacteristic
623C2×D5D3×#4111yescharacteristic
624C2×D5D3×#4111yescharacteristic
625C2×D5D3×#4111yescharacteristic
626C2×D5D3×#4111yescharacteristic
627AGL(1,𝔽5)—22no—
628AGL(1,𝔽5)—22no—
629AGL(1,𝔽5)—41no—
630AGL(1,𝔽5)—41no—
631AGL(1,𝔽5)—62no—
632AGL(1,𝔽5)—62no—
633AGL(1,𝔽5)—121no—
634AGL(1,𝔽5)—121no—
635C4×C5—21no—
636C4×C5—21no—
637C4×C5—21no—
638C4×C5—32no—
639C4×C5—32no—
640C4×C5—61no—
641C4×C5—61no—
642Dic5—21no—
643Dic5—21no—
644Dic5—21no—
645Dic5—32no—
646Dic5—32no—
647Dic5—61no—
648Dic5—61no—
649C2×Q8—31no—
650C2×Q8—151no—
651C2×Q8—151no—
652C2×Q8—151no—
653C2×Q8—302no—
654C2×Q8—302no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—151no—
669C22×C4—151no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—51no—
673C4⋊C4—51no—
674C4⋊C4—51no—
675C4⋊C4—102no—
676C4⋊C4—151no—
677C4⋊C4—151no—
678C4⋊C4—151no—
679C4⋊C4—151no—
680C4⋊C4—151no—
681C4⋊C4—151no—
682C4⋊C4—302no—
683C4⋊C4—302no—
684C4⋊C4—302no—
685C4⋊C4—302no—
686C4⋊C4—302no—
687C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
688C42—31no—
689C42—31no—
690C42—31no—
691C42—102no—
692C42—151no—
693C42—151no—
694C42—151no—
695C42—151no—
696C42—151no—
697C42—151no—
698C42—154no—
699C42—151no—
700C42—151no—
701C42—151no—
702C42—302no—
703C42—302no—
704C42—302no—
705C42—302no—
706C42—302no—
707C42—302no—
708C3×C5#229511yescharacteristic, complemented, Hall
709C22×C3—51no—
710C22×C3—51no—
711C22×C3—51no—
712C22×C3—51no—
713C22×C3—51no—
714C22×C3—51no—
715C22×C3C23×AGL(1,𝔽5)11yescharacteristic
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—102no—
720C3×C4—102no—
721C3×C4—101no—
722C3×C4—101no—
723C3×C4—101no—
724C3×C4—201no—
725C3×C4—201no—
726Dic3—21no—
727Dic3—21no—
728Dic3—52no—
729Dic3—52no—
730Dic3—102no—
731Dic3—102no—
732Dic3—101no—
733Dic3—101no—
734Dic3—201no—
735Dic3—201no—
736Dic3#413012yes—
737Dic3Q8×AGL(1,𝔽5)12yes—
738C2×C5D3×#11711yescharacteristic
739C2×C5C4×#23711yescharacteristic
740C2×C5C4×D3×Q811yescharacteristic
741D5#562211yescharacteristic
742D5#564911yescharacteristic
743D5#568811yescharacteristic
744D5#570611yescharacteristic
745C23—51no—
746Q8—62no—
747Q8—302no—
748Q8—302no—
749Q8—302no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—51no—
757C2×C4—51no—
758C2×C4—51no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—101no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—101no—
772C2×C4—101no—
773C2×C4—101no—
774C2×C4—101no—
775C2×C4—152no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—151no—
780C2×C4—151no—
781C2×C4—152no—
782C2×C4—152no—
783C2×C4—151no—
784C2×C4—151no—
785C2×C4—301no—
786C2×C4—301no—
787C2×C4—301no—
788C2×C4—301no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—301no—
792C2×C4—301no—
793C2×C4—301no—
794C2×C4—301no—
795C2×C4—301no—
796C2×C4—301no—
797C2×C4—301no—
798C2×C4—301no—
799C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
800C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
801C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
802C2×C3—51no—
803C2×C3—51no—
804C2×C3—51no—
805C2×C3—51no—
806C2×C3C2×#413011yescharacteristic
807C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
808C2×C3#41×AGL(1,𝔽5)11yescharacteristic
809C5#7493811yescharacteristic, complemented, Sylow
810C22—51no—
811C22—51no—
812C22—51no—
813C22—51no—
814C22—51no—
815C22—51no—
816C22C22×D3×AGL(1,𝔽5)11yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—32no—
821C4—32no—
822C4—61no—
823C4—61no—
824C4—102no—
825C4—102no—
826C4—101no—
827C4—101no—
828C4—101no—
829C4—152no—
830C4—152no—
831C4—201no—
832C4—201no—
833C4—302no—
834C4—302no—
835C4—301no—
836C4—301no—
837C4—601no—
838C4—601no—
839C3#1061720911yescharacteristic, complemented, Sylow
840C2—51no—
841C2—51no—
842C2—51no—
843C2—51no—
844C2D3×#413011yescharacteristic
845C2AGL(1,𝔽5)×#23711yescharacteristic
846C2D3×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#2295
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
32. #91776C4semidirect
33. C5×#887C4semidirect
40. #91344C4semidirect
41. #91340C4semidirect
42. #91325C4semidirect
43. #91325C4semidirect
44. #91324C4semidirect
45. #91324C4semidirect
110. Dic3×AGL(1,𝔽5)Q8semidirect
279. #887AGL(1,𝔽5)semidirect
708. C3×C5#2295semidirect
809. C5#74938semidirect
839. C3#10617209semidirect

Maximal subgroups

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

subgroupindex
D5×#8872
#117523702
C3×#657112
#117518442
Dic3×C4⋊AGL(1,𝔽5)2
#117518422
#117518372
#117518342
#117518322
C4×Dic3×AGL(1,𝔽5)2
#117517472
#117517452
#106172093
#749385