Finite Group Databasebeta

← D3×#65711 #14320425

Subgroups — D3×#65711 #14320425

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
3D3×D5×C4⋊C4C211yesmaximal, characteristic
4#11752370C211yesmaximal, characteristic, complemented
5C3×#65711C211yesmaximal, characteristic, complemented
6D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
7D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
8D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
9D3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
10#11751845C211yesmaximal, characteristic, complemented
11#11751840C211yesmaximal, characteristic, complemented
12#11751839C211yesmaximal, characteristic, complemented
13#11751835C211yesmaximal, characteristic, complemented
14#11751747C211yesmaximal, characteristic, complemented
15#11751745C211yesmaximal, characteristic, complemented
16C2×#65711—31nomaximal, Hall
17C22×D3×AGL(1,𝔽5)C2211yescharacteristic
18C22×D3×AGL(1,𝔽5)C2211yescharacteristic
19C22×D3×AGL(1,𝔽5)C2211yescharacteristic
20C22×D3×AGL(1,𝔽5)C2211yescharacteristic
21C2×C4×D3×D5C2211yescharacteristic
22C2×C4×D3×D5C2211yescharacteristic
23C2×C4×D3×D5C2211yescharacteristic
24C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
25C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
26C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×C3×C4×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
32D3×C4⋊AGL(1,𝔽5)—24no—
33C4×D3×AGL(1,𝔽5)—24no—
34C4⋊C4×D15C411yescharacteristic, complemented
35C5×D3×C4⋊C4C411yescharacteristic, complemented
36C3×D5×C4⋊C4C2211yescharacteristic
37#91437C411yescharacteristic, complemented
38D3×C4⋊Dic5C411yescharacteristic, complemented
39D5×C4⋊Dic3C2211yescharacteristic
40#91404C411yescharacteristic, complemented
41#91404C411yescharacteristic, complemented
42D3×#683C411yescharacteristic, complemented
43D3×#683C411yescharacteristic, complemented
44D5×Dic3⋊C4C2211yescharacteristic
45D5×Dic3⋊C4C2211yescharacteristic
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(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
61(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
62D3×#387—51nomaximal, Hall
63C22×C4⋊AGL(1,𝔽5)—31no—
64C22×C4×AGL(1,𝔽5)—31no—
65C2×D5×C4⋊C4—31no—
66C2×(C2×AGL(1,𝔽5))⋊C4—31no—
67C2×(C2×AGL(1,𝔽5))⋊C4—31no—
68C2×(C2×AGL(1,𝔽5))⋊C4—31no—
69C2×(C2×AGL(1,𝔽5))⋊C4—31no—
70#65711—31no—
71#65711—31no—
72#65711—31no—
73#65711—31no—
74#65711—31no—
75#65711—31no—
76#65711—31no—
77#65711D311yescharacteristic, direct product factor
78C22×D3×D5C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C22×C3×AGL(1,𝔽5)C2311yescharacteristic
86C22×C3×AGL(1,𝔽5)C2311yescharacteristic
87C2×D3×AGL(1,𝔽5)—22no—
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)—22no—
93C2×D3×AGL(1,𝔽5)—22no—
94C2×D3×AGL(1,𝔽5)—22no—
95C2×D3×AGL(1,𝔽5)—22no—
96C2×D3×AGL(1,𝔽5)—22no—
97C2×D3×AGL(1,𝔽5)D414yes—
98C2×D3×AGL(1,𝔽5)Q814yes—
99C2×C4×D15C2×C411yescharacteristic
100C2×C4×D15C2×C411yescharacteristic
101C2×C4×D15C2×C411yescharacteristic
102C2×C4×C5×D3C2×C411yescharacteristic
103C2×C4×C5×D3C2×C411yescharacteristic
104C2×C4×C5×D3C2×C411yescharacteristic
105C2×C3×C4×D5C2311yescharacteristic
106C2×C3×C4×D5C2311yescharacteristic
107C2×C3×C4×D5C2311yescharacteristic
108C2×#1200C2×C411yescharacteristic
109C2×#1200C2×C411yescharacteristic
110C2×#1200C2×C411yescharacteristic
111C2×D3×Dic5C2×C411yescharacteristic
112C2×D3×Dic5C2×C411yescharacteristic
113C2×D3×Dic5C2×C411yescharacteristic
114C2×D5×Dic3C2311yescharacteristic
115C2×D5×Dic3C2311yescharacteristic
116C2×D5×Dic3C2311yescharacteristic
117C4×D3×D5—22no—
118C4×D3×D5—22no—
119C4×D3×D5—22no—
120C4×D3×D5—22no—
121C4×D3×D5—22no—
122C4×D3×D5—22no—
123C4⋊ΓL(1,𝔽16)—22no—
124C4×ΓL(1,𝔽16)—22no—
125C3×C4⋊AGL(1,𝔽5)—22no—
126C3×C4×AGL(1,𝔽5)—22no—
127Dic3⋊AGL(1,𝔽5)—22no—
128Dic3⋊AGL(1,𝔽5)—22no—
129Dic3×AGL(1,𝔽5)—22no—
130Dic3×AGL(1,𝔽5)—22no—
131C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
132C4⋊Dic15C2×C411yescharacteristic, complemented
133#6712C2×C411yescharacteristic, complemented
134#6712C2×C411yescharacteristic, complemented
135C5×C4⋊Dic3C2×C411yescharacteristic, complemented
136C5×Dic3⋊C4C2×C411yescharacteristic, complemented
137C5×Dic3⋊C4C2×C411yescharacteristic, complemented
138C3×C4⋊Dic5C2×C411yescharacteristic, complemented
139C3×#683C2×C411yescharacteristic, complemented
140C3×#683C2×C411yescharacteristic, complemented
141Dic3⋊Dic5C2×C411yescharacteristic, complemented
142Dic3⋊Dic5C2×C411yescharacteristic, complemented
143#6669C2×C411yescharacteristic, complemented
144#6669C2×C411yescharacteristic, complemented
145#6668C2×C411yescharacteristic, complemented
146#6668C2×C411yescharacteristic, complemented
147C2×D3×C4⋊C4—51no—
148C2×D3×C4⋊C4—51no—
149C2×C42×D3—51no—
150C3×#387—51no—
151#4980—51no—
152#4978—51no—
153#4933—51no—
154D3×#95—51no—
155D3×#95—51no—
156D3×#95—51no—
157D3×#95—51no—
158#4655—51no—
159#4654—51no—
160#4653—51no—
161#4652—51no—
162C23×AGL(1,𝔽5)—31no—
163C23×AGL(1,𝔽5)—31no—
164C23×AGL(1,𝔽5)—31no—
165C23×AGL(1,𝔽5)—31no—
166C22×C4×D5—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C2×C4⋊AGL(1,𝔽5)—31no—
170C2×C4⋊AGL(1,𝔽5)—31no—
171C2×C4⋊AGL(1,𝔽5)—31no—
172C2×C4⋊AGL(1,𝔽5)—64no—
173C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
174C2×C4×AGL(1,𝔽5)—31no—
175C2×C4×AGL(1,𝔽5)—31no—
176C2×C4×AGL(1,𝔽5)—31no—
177C2×C4×AGL(1,𝔽5)—64no—
178C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
179C2×C5×C4⋊C4—31no—
180C2×C4⋊Dic5—31no—
181C2×#683—31no—
182C2×#683—31no—
183D5×C4⋊C4—31no—
184D5×C4⋊C4—31no—
185D5×C4⋊C4—31no—
186D5×C4⋊C4—31no—
187D5×C4⋊C4—31no—
188D5×C4⋊C4—31no—
189D5×C4⋊C4—31no—
190D5×C4⋊C4C2×D311yescharacteristic
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))⋊C4—31no—
196(C2×AGL(1,𝔽5))⋊C4—31no—
197(C2×AGL(1,𝔽5))⋊C4—31no—
198(C2×AGL(1,𝔽5))⋊C4—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))⋊C4C2×D311yescharacteristic
204(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
205(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
206(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
207C2×#387—151noSylow
208C22×D15C22×C411yescharacteristic
209C22×C5×D3C22×C411yescharacteristic
210C22×C3×D5C2411yescharacteristic
211C2×D3×D5C2×D412yes—
212C2×D3×D5C2×Q812yes—
213C2×D3×D5#4112yes—
214C2×D3×D5#4112yes—
215C2×D3×D5#4112yes—
216C2×D3×D5#4112yes—
217C2×ΓL(1,𝔽16)—21no—
218C2×ΓL(1,𝔽16)—21no—
219C2×ΓL(1,𝔽16)—21no—
220C2×ΓL(1,𝔽16)—21no—
221C2×ΓL(1,𝔽16)—21no—
222C2×ΓL(1,𝔽16)—21no—
223C2×ΓL(1,𝔽16)—21no—
224C2×ΓL(1,𝔽16)—21no—
225C2×ΓL(1,𝔽16)—21no—
226C2×ΓL(1,𝔽16)—21no—
227C2×ΓL(1,𝔽16)C2×D412yes—
228C2×ΓL(1,𝔽16)C2×Q812yes—
229C2×C3×AGL(1,𝔽5)—21no—
230C2×C3×AGL(1,𝔽5)—21no—
231C2×C3×AGL(1,𝔽5)—21no—
232C2×C3×AGL(1,𝔽5)—21no—
233C2×C3×AGL(1,𝔽5)—21no—
234C2×C3×AGL(1,𝔽5)—21no—
235C2×C3×AGL(1,𝔽5)—21no—
236C2×C3×AGL(1,𝔽5)—21no—
237C2×C3×AGL(1,𝔽5)—21no—
238C2×C3×AGL(1,𝔽5)—21no—
239C2×C3×AGL(1,𝔽5)C2×D412yes—
240C2×C3×AGL(1,𝔽5)C2×Q812yes—
241D3×AGL(1,𝔽5)—28no—
242D3×AGL(1,𝔽5)—28no—
243D3×AGL(1,𝔽5)—44no—
244D3×AGL(1,𝔽5)—44no—
245C2×C3×C4×C5C22×C411yescharacteristic
246C2×C3×C4×C5C22×C411yescharacteristic
247C2×C3×C4×C5C22×C411yescharacteristic
248C2×Dic15C22×C411yescharacteristic
249C2×Dic15C22×C411yescharacteristic
250C2×Dic15C22×C411yescharacteristic
251C4×D15—22no—
252C4×D15—22no—
253C4×D15—22no—
254C2×C5×Dic3C22×C411yescharacteristic
255C2×C5×Dic3C22×C411yescharacteristic
256C2×C5×Dic3C22×C411yescharacteristic
257C4×C5×D3—22no—
258C4×C5×D3—22no—
259C4×C5×D3—22no—
260C2×C3×Dic5C22×C411yescharacteristic
261C2×C3×Dic5C22×C411yescharacteristic
262C2×C3×Dic5C22×C411yescharacteristic
263C3×C4×D5—21no—
264C3×C4×D5—21no—
265C3×C4×D5—21no—
266C3×C4×D5—21no—
267C3×C4×D5—21no—
268C3×C4×D5—21no—
269#1200—22no—
270#1200—22no—
271#1200—22no—
272D3×Dic5—22no—
273D3×Dic5—22no—
274D3×Dic5—22no—
275D5×Dic3—21no—
276D5×Dic3—21no—
277D5×Dic3—21no—
278D5×Dic3—21no—
279D5×Dic3—21no—
280D5×Dic3—21no—
281C22×C4×D3—51no—
282C22×C4×D3—51no—
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×C4×D3—51no—
287C22×C4×D3—51no—
288C2×C3×C4⋊C4—51no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C42—51no—
291C2×C4⋊Dic3—51no—
292C2×C4⋊Dic3—51no—
293C2×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4—51no—
296C2×Dic3⋊C4—51no—
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300D3×C4⋊C4—51no—
301D3×C4⋊C4—51no—
302D3×C4⋊C4—51no—
303D3×C4⋊C4—51no—
304D3×C4⋊C4—51no—
305D3×C4⋊C4—51no—
306D3×C4⋊C4—51no—
307D3×C4⋊C4—104no—
308D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
309C42×D3—104no—
310C3×#95—51no—
311C3×#95—51no—
312C3×#95—51no—
313C3×#95—51no—
314C3⋊#95—51no—
315C3⋊#95—51no—
316C3⋊#95—51no—
317C3⋊#95—51no—
318C3⋊#95—51no—
319C3⋊#95—51no—
320C3⋊#95—51no—
321C3⋊#95—51no—
322C3⋊#95—51no—
323C3⋊#95—51no—
324C3⋊#95—51no—
325C3⋊#95—51no—
326C23×D5—31no—
327C22×AGL(1,𝔽5)—31no—
328C22×AGL(1,𝔽5)—31no—
329C22×AGL(1,𝔽5)—34no—
330C22×AGL(1,𝔽5)—34no—
331C22×AGL(1,𝔽5)—31no—
332C22×AGL(1,𝔽5)—31no—
333C22×AGL(1,𝔽5)—62no—
334C22×AGL(1,𝔽5)—62no—
335C22×AGL(1,𝔽5)—62no—
336C22×AGL(1,𝔽5)—62no—
337C22×AGL(1,𝔽5)—62no—
338C22×AGL(1,𝔽5)—62no—
339C22×AGL(1,𝔽5)—62no—
340C22×AGL(1,𝔽5)—62no—
341C22×AGL(1,𝔽5)—62no—
342C22×AGL(1,𝔽5)—62no—
343C22×AGL(1,𝔽5)C22×D311yescharacteristic
344C22×AGL(1,𝔽5)C22×D311yescharacteristic
345C22×AGL(1,𝔽5)C22×D311yescharacteristic
346C22×AGL(1,𝔽5)C22×D311yescharacteristic
347C22×C4×C5—31no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—31no—
353C2×C4×D5—31no—
354C2×C4×D5—31no—
355C2×C4×D5—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—62no—
363C2×C4×D5—62no—
364C2×C4×D5—62no—
365C2×C4×D5—62no—
366C2×C4×D5—62no—
367C2×C4×D5—62no—
368C2×C4×D5C22×D311yescharacteristic
369C2×C4×D5C22×D311yescharacteristic
370C2×C4×D5C22×D311yescharacteristic
371C4⋊AGL(1,𝔽5)—22no—
372C4⋊AGL(1,𝔽5)—62no—
373C4⋊AGL(1,𝔽5)—62no—
374C4⋊AGL(1,𝔽5)—62no—
375C4×AGL(1,𝔽5)—22no—
376C4×AGL(1,𝔽5)—62no—
377C4×AGL(1,𝔽5)—62no—
378C4×AGL(1,𝔽5)—62no—
379C5×C4⋊C4—31no—
380C5×C4⋊C4—31no—
381C5×C4⋊C4—31no—
382C5×C4⋊C4C4×D311yescharacteristic, complemented
383C4⋊Dic5—31no—
384C4⋊Dic5—31no—
385C4⋊Dic5—31no—
386C4⋊Dic5C4×D311yescharacteristic, complemented
387#683—31no—
388#683—31no—
389#683—31no—
390#683—31no—
391#683—31no—
392#683—31no—
393#683C4×D311yescharacteristic, complemented
394#683C4×D311yescharacteristic, complemented
395C22×C4⋊C4—151no—
396C22×C4⋊C4—151no—
397C22×C42—151no—
398#387—51no—
399#387—151no—
400#387—151no—
401#387—151no—
402#387—151no—
403#387—151no—
404#387—151no—
405#387—151no—
406C2×#95—151no—
407C2×#95—151no—
408C2×#95—151no—
409C2×#95—151no—
410C22×C3×C5C23×C411yescharacteristic
411C2×D15#11712yes—
412C2×D15C4×D412yes—
413C2×D15C4×Q812yes—
414C2×C5×D3#11712yes—
415C2×C5×D3C4×D412yes—
416C2×C5×D3C4×Q812yes—
417C2×C3×D5C22×D411yescharacteristic
418C2×C3×D5C22×Q811yescharacteristic
419C2×C3×D5C2×#4111yescharacteristic
420C2×C3×D5C2×#4111yescharacteristic
421C2×C3×D5C2×#4111yescharacteristic
422C2×C3×D5C2×#4111yescharacteristic
423D3×D5C22⋊Q814yes—
424D3×D5#12314yes—
425D3×D5#12514yes—
426D3×D5#12614yes—
427ΓL(1,𝔽16)—22no—
428ΓL(1,𝔽16)—22no—
429ΓL(1,𝔽16)—41no—
430ΓL(1,𝔽16)—41no—
431C3×AGL(1,𝔽5)—22no—
432C3×AGL(1,𝔽5)—22no—
433C3×AGL(1,𝔽5)—41no—
434C3×AGL(1,𝔽5)—41no—
435C3×C4×C5—21no—
436C3×C4×C5—21no—
437C3×C4×C5—21no—
438Dic15—21no—
439Dic15—21no—
440Dic15—21no—
441C3×Dic5—21no—
442C3×Dic5—21no—
443C3×Dic5—21no—
444C5×Dic3—21no—
445C5×Dic3—21no—
446C5×Dic3—21no—
447C23×D3—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×Dic3—51no—
456C22×Dic3—51no—
457C22×Dic3—51no—
458C22×Dic3—51no—
459C22×Dic3—51no—
460C22×Dic3—51no—
461C22×Dic3—51no—
462C2×C4×D3—54no—
463C2×C4×D3—54no—
464C2×C4×D3—51no—
465C2×C4×D3—51no—
466C2×C4×D3—51no—
467C2×C4×D3—51no—
468C2×C4×D3—51no—
469C2×C4×D3—51no—
470C2×C4×D3—51no—
471C2×C4×D3—51no—
472C2×C4×D3—51no—
473C2×C4×D3—102no—
474C2×C4×D3—102no—
475C2×C4×D3—102no—
476C2×C4×D3—102no—
477C2×C4×D3—102no—
478C2×C4×D3—102no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—102no—
486C2×C4×D3—102no—
487C2×C4×D3—102no—
488C2×C4×D3—102no—
489C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
490C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
491C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
492C3×C4⋊C4—51no—
493C3×C4⋊C4—51no—
494C3×C4⋊C4—51no—
495C3×C4⋊C4—102no—
496C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
497C3×C42—102no—
498C4⋊Dic3—51no—
499C4⋊Dic3—51no—
500C4⋊Dic3—51no—
501C4⋊Dic3—102no—
502C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
503Dic3⋊C4—51no—
504Dic3⋊C4—51no—
505Dic3⋊C4—51no—
506Dic3⋊C4—51no—
507Dic3⋊C4—51no—
508Dic3⋊C4—51no—
509Dic3⋊C4—102no—
510Dic3⋊C4—102no—
511Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
512Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
513C4×Dic3—102no—
514C4×Dic3—102no—
515C4×Dic3—102no—
516C23×C5—31no—
517C22×D5—31no—
518C22×D5—32no—
519C22×D5—32no—
520C22×D5—32no—
521C22×D5—32no—
522C22×D5—32no—
523C22×D5—32no—
524C22×D5C23×D311yescharacteristic
525C2×AGL(1,𝔽5)—21no—
526C2×AGL(1,𝔽5)—21no—
527C2×AGL(1,𝔽5)—21no—
528C2×AGL(1,𝔽5)—21no—
529C2×AGL(1,𝔽5)—21no—
530C2×AGL(1,𝔽5)—21no—
531C2×AGL(1,𝔽5)—21no—
532C2×AGL(1,𝔽5)—21no—
533C2×AGL(1,𝔽5)—21no—
534C2×AGL(1,𝔽5)—21no—
535C2×AGL(1,𝔽5)—32no—
536C2×AGL(1,𝔽5)—32no—
537C2×AGL(1,𝔽5)—68no—
538C2×AGL(1,𝔽5)—68no—
539C2×AGL(1,𝔽5)—61no—
540C2×AGL(1,𝔽5)—61no—
541C2×AGL(1,𝔽5)—61no—
542C2×AGL(1,𝔽5)—61no—
543C2×AGL(1,𝔽5)—61no—
544C2×AGL(1,𝔽5)—61no—
545C2×AGL(1,𝔽5)—61no—
546C2×AGL(1,𝔽5)—61no—
547C2×AGL(1,𝔽5)—61no—
548C2×AGL(1,𝔽5)—61no—
549C2×AGL(1,𝔽5)—124no—
550C2×AGL(1,𝔽5)—124no—
551C2×AGL(1,𝔽5)D3×D412yes—
552C2×AGL(1,𝔽5)D3×Q812yes—
553C2×C4×C5—31no—
554C2×C4×C5—31no—
555C2×C4×C5—31no—
556C2×C4×C5—62no—
557C2×C4×C5—62no—
558C2×C4×C5—62no—
559C2×C4×C5C2×C4×D311yescharacteristic
560C2×C4×C5C2×C4×D311yescharacteristic
561C2×C4×C5C2×C4×D311yescharacteristic
562C2×Dic5—31no—
563C2×Dic5—31no—
564C2×Dic5—31no—
565C2×Dic5—62no—
566C2×Dic5—62no—
567C2×Dic5—62no—
568C2×Dic5C2×C4×D311yescharacteristic
569C2×Dic5C2×C4×D311yescharacteristic
570C2×Dic5C2×C4×D311yescharacteristic
571C4×D5—21no—
572C4×D5—21no—
573C4×D5—21no—
574C4×D5—21no—
575C4×D5—21no—
576C4×D5—21no—
577C4×D5—62no—
578C4×D5—62no—
579C4×D5—62no—
580C4×D5—62no—
581C4×D5—62no—
582C4×D5—62no—
583C4×D5—61no—
584C4×D5—61no—
585C4×D5—61no—
586C4×D5—61no—
587C4×D5—61no—
588C4×D5—61no—
589C23×C4—151no—
590C23×C4—151no—
591C23×C4—151no—
592C23×C4—151no—
593C23×C4—151no—
594C23×C4—151no—
595C23×C4—151no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—51no—
598C2×C4⋊C4—51no—
599C2×C4⋊C4—151no—
600C2×C4⋊C4—151no—
601C2×C4⋊C4—151no—
602C2×C4⋊C4—151no—
603C2×C4⋊C4—151no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C4⋊C4—304no—
613C2×C42—51no—
614C2×C42—151no—
615C2×C42—151no—
616C2×C42—151no—
617C2×C42—304no—
618#95—51no—
619#95—51no—
620#95—51no—
621#95—51no—
622#95—151no—
623#95—151no—
624#95—151no—
625#95—151no—
626#95—151no—
627#95—151no—
628#95—151no—
629#95—151no—
630#95—151no—
631#95—151no—
632#95—151no—
633#95—151no—
634C2×C3×C5C2×#11711yescharacteristic
635C2×C3×C5C2×C4×D411yescharacteristic
636C2×C3×C5C2×C4×Q811yescharacteristic
637D15#38714yescomplemented
638C3×D5C2×C22⋊Q811yescharacteristic
639C3×D5C2×#12311yescharacteristic
640C3×D5C2×#12511yescharacteristic
641C3×D5C2×#12611yescharacteristic
642C5×D3#38714yescomplemented
643C23×C3—51no—
644C22×D3—51no—
645C22×D3—52no—
646C22×D3—52no—
647C22×D3—52no—
648C22×D3—52no—
649C22×D3—52no—
650C22×D3—52no—
651C22×D3C22×AGL(1,𝔽5)11yescharacteristic
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—51no—
655C2×C3×C4—51no—
656C2×C3×C4—51no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—101no—
662C2×C3×C4—101no—
663C2×C3×C4—101no—
664C2×C3×C4—101no—
665C2×C3×C4—101no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
674C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
675C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
676C2×Dic3—52no—
677C2×Dic3—52no—
678C2×Dic3—51no—
679C2×Dic3—51no—
680C2×Dic3—51no—
681C2×Dic3—101no—
682C2×Dic3—101no—
683C2×Dic3—101no—
684C2×Dic3—101no—
685C2×Dic3—101no—
686C2×Dic3—101no—
687C2×Dic3—101no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3—101no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
698C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
699C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
700C4×D3—22no—
701C4×D3—22no—
702C4×D3—22no—
703C4×D3—102no—
704C4×D3—102no—
705C4×D3—102no—
706C4×D3—102no—
707C4×D3—102no—
708C4×D3—102no—
709C4×D3—108no—
710C4×D3—108no—
711C4×D3—102no—
712C4×D3—102no—
713C4×D3—102no—
714C4×D3—204no—
715C4×D3—204no—
716C22×C5—32no—
717C22×C5—32no—
718C22×C5—32no—
719C22×C5C22×C4×D311yescharacteristic
720C2×D5—32no—
721C2×D5—32no—
722C2×D5—32no—
723C2×D5—34no—
724C2×D5—34no—
725C2×D5—34no—
726C2×D5—34no—
727C2×D5C2×D3×D411yescharacteristic
728C2×D5C2×D3×Q811yescharacteristic
729C2×D5D3×#4111yescharacteristic
730C2×D5D3×#4111yescharacteristic
731C2×D5D3×#4111yescharacteristic
732C2×D5D3×#4111yescharacteristic
733AGL(1,𝔽5)—22no—
734AGL(1,𝔽5)—22no—
735AGL(1,𝔽5)—41no—
736AGL(1,𝔽5)—41no—
737AGL(1,𝔽5)—62no—
738AGL(1,𝔽5)—62no—
739AGL(1,𝔽5)—121no—
740AGL(1,𝔽5)—121no—
741C4×C5—21no—
742C4×C5—21no—
743C4×C5—21no—
744C4×C5—61no—
745C4×C5—61no—
746C4×C5—61no—
747Dic5—21no—
748Dic5—21no—
749Dic5—21no—
750Dic5—61no—
751Dic5—61no—
752Dic5—61no—
753C24—151no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—51no—
758C22×C4—51no—
759C22×C4—51no—
760C22×C4—51no—
761C22×C4—51no—
762C22×C4—51no—
763C22×C4—51no—
764C22×C4—151no—
765C22×C4—151no—
766C22×C4—151no—
767C22×C4—151no—
768C22×C4—151no—
769C22×C4—151no—
770C22×C4—151no—
771C22×C4—151no—
772C22×C4—151no—
773C22×C4—154no—
774C22×C4—154no—
775C22×C4—151no—
776C22×C4—151no—
777C22×C4—151no—
778C22×C4—151no—
779C22×C4—151no—
780C22×C4—151no—
781C22×C4—151no—
782C22×C4—302no—
783C22×C4—302no—
784C22×C4—302no—
785C22×C4—302no—
786C22×C4—302no—
787C22×C4—302no—
788C22×C4—302no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C4⋊C4—31no—
799C4⋊C4—31no—
800C4⋊C4—31no—
801C4⋊C4—51no—
802C4⋊C4—51no—
803C4⋊C4—51no—
804C4⋊C4—102no—
805C4⋊C4—151no—
806C4⋊C4—151no—
807C4⋊C4—151no—
808C4⋊C4—151no—
809C4⋊C4—151no—
810C4⋊C4—151no—
811C4⋊C4—151no—
812C4⋊C4—151no—
813C4⋊C4—151no—
814C4⋊C4—302no—
815C4⋊C4—302no—
816C4⋊C4—302no—
817C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
818C42—102no—
819C42—302no—
820C42—302no—
821C42—302no—
822C3×C5C2×#38711yescharacteristic, complemented, Hall
823C22×C3—51no—
824C22×C3—51no—
825C22×C3—51no—
826C22×C3—51no—
827C22×C3—51no—
828C22×C3—51no—
829C22×C3C23×AGL(1,𝔽5)11yescharacteristic
830C2×D3—52no—
831C2×D3—52no—
832C2×D3—52no—
833C2×D3—54no—
834C2×D3—54no—
835C2×D3—54no—
836C2×D3—54no—
837C2×D3#413012yes—
838C2×D3D4×AGL(1,𝔽5)12yes—
839C2×D3Q8×AGL(1,𝔽5)12yes—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—102no—
844C3×C4—102no—
845C3×C4—101no—
846C3×C4—101no—
847C3×C4—101no—
848C3×C4—201no—
849C3×C4—201no—
850Dic3—21no—
851Dic3—21no—
852Dic3—21no—
853Dic3—102no—
854Dic3—102no—
855Dic3—101no—
856Dic3—101no—
857Dic3—101no—
858Dic3—201no—
859Dic3—201no—
860C2×C5—34no—
861C2×C5D3×#11711yescharacteristic
862C2×C5C4×D3×D411yescharacteristic
863C2×C5C4×D3×Q811yescharacteristic
864D5—34no—
865D5D3×C22⋊Q811yescharacteristic
866D5D3×#12311yescharacteristic
867D5D3×#12511yescharacteristic
868D5D3×#12611yescharacteristic
869C23—31no—
870C23—51no—
871C23—152no—
872C23—152no—
873C23—152no—
874C23—152no—
875C23—152no—
876C23—152no—
877C23—151no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—52no—
882C2×C4—52no—
883C2×C4—51no—
884C2×C4—51no—
885C2×C4—51no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—101no—
890C2×C4—101no—
891C2×C4—101no—
892C2×C4—101no—
893C2×C4—101no—
894C2×C4—101no—
895C2×C4—101no—
896C2×C4—101no—
897C2×C4—101no—
898C2×C4—101no—
899C2×C4—101no—
900C2×C4—101no—
901C2×C4—101no—
902C2×C4—101no—
903C2×C4—101no—
904C2×C4—101no—
905C2×C4—152no—
906C2×C4—152no—
907C2×C4—151no—
908C2×C4—151no—
909C2×C4—151no—
910C2×C4—302no—
911C2×C4—302no—
912C2×C4—302no—
913C2×C4—302no—
914C2×C4—302no—
915C2×C4—302no—
916C2×C4—301no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—302no—
923C2×C4—302no—
924C2×C4—302no—
925C2×C4—308no—
926C2×C4—308no—
927C2×C4—301no—
928C2×C4—301no—
929C2×C4—301no—
930C2×C4—301no—
931C2×C4—301no—
932C2×C4—301no—
933C2×C4—301no—
934C2×C4—301no—
935C2×C4—301no—
936C2×C4—301no—
937C2×C4—604no—
938C2×C4—604no—
939C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
940C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
941C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
942C2×C3—51no—
943C2×C3—51no—
944C2×C3—51no—
945C2×C3—51no—
946C2×C3C2×#413011yescharacteristic
947C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
948C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
949D3—54no—
950D3#6571114yesdirect product factor
951C5D3×#38711yescharacteristic, complemented, Sylow
952C22—32no—
953C22—32no—
954C22—32no—
955C22—51no—
956C22—51no—
957C22—51no—
958C22—51no—
959C22—51no—
960C22—51no—
961C22—154no—
962C22—154no—
963C22—154no—
964C22—154no—
965C22—152no—
966C22—152no—
967C22—152no—
968C22C22×D3×AGL(1,𝔽5)11yescharacteristic
969C4—21no—
970C4—21no—
971C4—21no—
972C4—61no—
973C4—61no—
974C4—61no—
975C4—102no—
976C4—102no—
977C4—101no—
978C4—101no—
979C4—101no—
980C4—201no—
981C4—201no—
982C4—302no—
983C4—302no—
984C4—301no—
985C4—301no—
986C4—301no—
987C4—601no—
988C4—601no—
989C3C2×#6571111yescharacteristic, complemented, Sylow
990C2—34no—
991C2—51no—
992C2—51no—
993C2—51no—
994C2—51no—
995C2—154no—
996C2D3×#413011yescharacteristic
997C2D3×D4×AGL(1,𝔽5)11yescharacteristic
998C2D3×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×C5C2×#387
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11752370C2semidirect
5. C3×#65711C2semidirect
10. #11751845C2semidirect
11. #11751840C2semidirect
12. #11751839C2semidirect
13. #11751835C2semidirect
14. #11751747C2semidirect
15. #11751745C2semidirect
34. C4⋊C4×D15C4semidirect
35. C5×D3×C4⋊C4C4semidirect
37. #91437C4semidirect
38. D3×C4⋊Dic5C4semidirect
40. #91404C4semidirect
41. #91404C4semidirect
42. D3×#683C4semidirect
43. D3×#683C4semidirect
77. #65711D3direct (N × H)
131. C3×C5×C4⋊C4C2×C4semidirect
132. C4⋊Dic15C2×C4semidirect
133. #6712C2×C4semidirect
134. #6712C2×C4semidirect
135. C5×C4⋊Dic3C2×C4semidirect
136. C5×Dic3⋊C4C2×C4semidirect
137. C5×Dic3⋊C4C2×C4semidirect
138. C3×C4⋊Dic5C2×C4semidirect
139. C3×#683C2×C4semidirect
140. C3×#683C2×C4semidirect
141. Dic3⋊Dic5C2×C4semidirect
142. Dic3⋊Dic5C2×C4semidirect
143. #6669C2×C4semidirect
144. #6669C2×C4semidirect
145. #6668C2×C4semidirect
146. #6668C2×C4semidirect
308. D3×C4⋊C4AGL(1,𝔽5)semidirect
382. C5×C4⋊C4C4×D3semidirect
386. C4⋊Dic5C4×D3semidirect
393. #683C4×D3semidirect
394. #683C4×D3semidirect
496. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
502. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
511. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
512. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
637. D15#387semidirect
642. C5×D3#387semidirect
817. C4⋊C4D3×AGL(1,𝔽5)semidirect
822. C3×C5C2×#387semidirect
950. D3#65711direct (N × H)
951. C5D3×#387semidirect
989. C3C2×#65711semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊AGL(1,𝔽5)2
C2×C4×D3×AGL(1,𝔽5)2
D3×D5×C4⋊C42
#117523702
C3×#657112
D3×(C2×AGL(1,𝔽5))⋊C42
#117518452
#117518402
#117518392
#117518352
#117517472
#117517452
C2×#657113
D3×#3875