Finite Group Databasebeta

← D15⋊#11925892 #49137506

Subgroups — D15⋊#11925892 #49137506

Order 36300.

672 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#10597243C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925892C211yesmaximal, characteristic, complemented
3C3×C5⋊#11925892C211yesmaximal, characteristic, complemented
4D5×#11925892—31nomaximal, Hall
5C3×C5×#10597243C2211yescharacteristic, complemented, Hall
6D15⋊(C11⋊D11)C511yesmaximal, characteristic, complemented
7D3×#11925892—51nomaximal
8D5×#10597243—31no—
9C5⋊#11925892D311yescharacteristic, complemented
10C5×#11925892—31no—
11C112×D15C2×C511yescharacteristic, complemented
12C5×C3⋊(C11⋊D11)C2×C511yescharacteristic, complemented
13C3×C5⋊(C11⋊D11)C2×C511yescharacteristic, complemented
14D3×#10597243—51no—
15C3⋊#11925892—21no—
16C3⋊#11925892—21no—
17C3⋊#11925892D511yescharacteristic, complemented
18C3×#11925892—51no—
19D15⋊AGL(1,𝔽11)—111nomaximal
20D15⋊AGL(1,𝔽11)—111nomaximal
21D15⋊AGL(1,𝔽11)—111nomaximal
22D15⋊AGL(1,𝔽11)—111nomaximal
23D15⋊AGL(1,𝔽11)—112nomaximal
24D15⋊AGL(1,𝔽11)—115nomaximal
25D15⋊AGL(1,𝔽11)—111nomaximal
26C5×#10597243C2×D311yescharacteristic, complemented, Hall
27D5×C11⋊D11—31no—
28C2×#11925892—151no—
29C3×C5×C112C22×C511yescharacteristic, complemented
30C3×#10597243—21no—
31C3×#10597243—21no—
32C3×#10597243C2×D511yescharacteristic, complemented
33D15×C11⋊C5—111no—
34D15×C11⋊C5—221no—
35D15×C11⋊C5—221no—
36D15×C11⋊C5—221no—
37D15×C11⋊C5—222no—
38D15×C11⋊C5—225no—
39D15×C11⋊C5—221no—
40C5×C3⋊AGL(1,𝔽11)—111no—
41C5×C3⋊AGL(1,𝔽11)—111no—
42C5×C3⋊AGL(1,𝔽11)—111no—
43C5×C3⋊AGL(1,𝔽11)—111no—
44C5×C3⋊AGL(1,𝔽11)—111no—
45C5×C3⋊AGL(1,𝔽11)—112no—
46C5×C3⋊AGL(1,𝔽11)—115no—
47C3×C5⋊AGL(1,𝔽11)—111no—
48C3×C5⋊AGL(1,𝔽11)—111no—
49C3×C5⋊AGL(1,𝔽11)—111no—
50C3×C5⋊AGL(1,𝔽11)—111no—
51C3×C5⋊AGL(1,𝔽11)—111no—
52C3×C5⋊AGL(1,𝔽11)—112no—
53C3×C5⋊AGL(1,𝔽11)—115no—
54D3×C11⋊D11—51noHall
55C5⋊(C11⋊D11)C5×D311yescharacteristic, complemented
56D5×C112—31no—
57C5×C11⋊D11—31no—
58C2×#10597243—151no—
59#11925892—31no—
60#11925892—51no—
61#11925892—61no—
62#11925892—61no—
63D5×AGL(1,𝔽11)—331no—
64D5×AGL(1,𝔽11)—331no—
65D5×AGL(1,𝔽11)—332no—
66D5×AGL(1,𝔽11)—331no—
67D5×AGL(1,𝔽11)—335no—
68D5×AGL(1,𝔽11)—331no—
69D5×AGL(1,𝔽11)—331no—
70C3×C5×C11⋊C5—111no—
71C3×C5×C11⋊C5—221no—
72C3×C5×C11⋊C5—221no—
73C3×C5×C11⋊C5—221no—
74C3×C5×C11⋊C5—221no—
75C3×C5×C11⋊C5—222no—
76C3×C5×C11⋊C5—225no—
77C3⋊(C11⋊D11)C5×D511yescharacteristic, complemented
78D3×C112—51no—
79C3×C11⋊D11—51no—
80D15⋊D11—111no—
81D15⋊D11—111no—
82D15⋊D11—111no—
83D15⋊D11—112no—
84D15⋊D11—115no—
85D15⋊D11—111no—
86D15⋊D11—111no—
87D3×AGL(1,𝔽11)—551no—
88D3×AGL(1,𝔽11)—551no—
89D3×AGL(1,𝔽11)—551no—
90D3×AGL(1,𝔽11)—552no—
91D3×AGL(1,𝔽11)—555no—
92D3×AGL(1,𝔽11)—551no—
93D3×AGL(1,𝔽11)—551no—
94C5×C112C2×C5×D311yescharacteristic, complemented
95#10597243—21no—
96#10597243—21no—
97#10597243D3×D511yescharacteristic, complemented
98C5⋊AGL(1,𝔽11)—111no—
99C5⋊AGL(1,𝔽11)—111no—
100C5⋊AGL(1,𝔽11)—111no—
101C5⋊AGL(1,𝔽11)—111no—
102C5⋊AGL(1,𝔽11)—112no—
103C5⋊AGL(1,𝔽11)—111no—
104C5⋊AGL(1,𝔽11)—115no—
105D5×C11⋊C5—331no—
106D5×C11⋊C5—661no—
107D5×C11⋊C5—662no—
108D5×C11⋊C5—661no—
109D5×C11⋊C5—665no—
110D5×C11⋊C5—661no—
111D5×C11⋊C5—661no—
112C5×AGL(1,𝔽11)—331no—
113C5×AGL(1,𝔽11)—331no—
114C5×AGL(1,𝔽11)—331no—
115C5×AGL(1,𝔽11)—331no—
116C5×AGL(1,𝔽11)—332no—
117C5×AGL(1,𝔽11)—331no—
118C5×AGL(1,𝔽11)—335no—
119C2×C11⋊D11—151noHall
120C3×C112C2×C5×D511yescharacteristic, complemented, Hall
121C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
122C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
123C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
124C11×D15AGL(1,𝔽11)12yescomplemented
125C11×D15AGL(1,𝔽11)15yescomplemented
126C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
127C11×D15AGL(1,𝔽11)11yescharacteristic, complemented
128C5×D33—111no—
129C5×D33—111no—
130C5×D33—111no—
131C5×D33—111no—
132C5×D33—111no—
133C5×D33—112no—
134C5×D33—115no—
135C3×D55—111no—
136C3×D55—111no—
137C3×D55—111no—
138C3×D55—111no—
139C3×D55—111no—
140C3×D55—112no—
141C3×D55—115no—
142C3⋊AGL(1,𝔽11)—111no—
143C3⋊AGL(1,𝔽11)—111no—
144C3⋊AGL(1,𝔽11)—111no—
145C3⋊AGL(1,𝔽11)—111no—
146C3⋊AGL(1,𝔽11)—111no—
147C3⋊AGL(1,𝔽11)—112no—
148C3⋊AGL(1,𝔽11)—115no—
149C3⋊AGL(1,𝔽11)—221no—
150C3⋊AGL(1,𝔽11)—221no—
151C3⋊AGL(1,𝔽11)—222no—
152C3⋊AGL(1,𝔽11)—221no—
153C3⋊AGL(1,𝔽11)—221no—
154C3⋊AGL(1,𝔽11)—221no—
155C3⋊AGL(1,𝔽11)—221no—
156C3⋊AGL(1,𝔽11)—221no—
157C3⋊AGL(1,𝔽11)—221no—
158C3⋊AGL(1,𝔽11)—225no—
159C3⋊AGL(1,𝔽11)—221no—
160C3⋊AGL(1,𝔽11)—221no—
161C3⋊AGL(1,𝔽11)—222no—
162C3⋊AGL(1,𝔽11)—225no—
163D3×C11⋊C5—551no—
164D3×C11⋊C5—1101no—
165D3×C11⋊C5—1101no—
166D3×C11⋊C5—1102no—
167D3×C11⋊C5—1105no—
168D3×C11⋊C5—1101no—
169D3×C11⋊C5—1101no—
170C3×AGL(1,𝔽11)—551no—
171C3×AGL(1,𝔽11)—551no—
172C3×AGL(1,𝔽11)—551no—
173C3×AGL(1,𝔽11)—551no—
174C3×AGL(1,𝔽11)—551no—
175C3×AGL(1,𝔽11)—552no—
176C3×AGL(1,𝔽11)—555no—
177C5×D3×D5—1211noHall
178C5×C11⋊C5—111no—
179C5×C11⋊C5—221no—
180C5×C11⋊C5—221no—
181C5×C11⋊C5—221no—
182C5×C11⋊C5—222no—
183C5×C11⋊C5—221no—
184C5×C11⋊C5—225no—
185C2×C112—151no—
186C11⋊D11—31no—
187C11⋊D11—51no—
188D5×D11—331no—
189D5×D11—331no—
190D5×D11—332no—
191D5×D11—331no—
192D5×D11—335no—
193D5×D11—331no—
194D5×D11—331no—
195C2×AGL(1,𝔽11)—1651no—
196C2×AGL(1,𝔽11)—1651no—
197C2×AGL(1,𝔽11)—1651no—
198C2×AGL(1,𝔽11)—1652no—
199C2×AGL(1,𝔽11)—1655no—
200C2×AGL(1,𝔽11)—1651no—
201C2×AGL(1,𝔽11)—1651no—
202C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
203C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
204C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
205C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
206C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
207C3×C5×C11C2×AGL(1,𝔽11)12yescomplemented
208C3×C5×C11C2×AGL(1,𝔽11)15yescomplemented
209C3×C11⋊C5—111no—
210C3×C11⋊C5—221no—
211C3×C11⋊C5—221no—
212C3×C11⋊C5—221no—
213C3×C11⋊C5—221no—
214C3×C11⋊C5—221no—
215C3×C11⋊C5—222no—
216C3×C11⋊C5—225no—
217C3×C11⋊C5—221no—
218C3×C11⋊C5—442no—
219C3×C11⋊C5—441no—
220C3×C11⋊C5—441no—
221C3×C11⋊C5—441no—
222C3×C11⋊C5—441no—
223C3×C11⋊C5—441no—
224C3×C11⋊C5—445no—
225C3×C11⋊C5—441no—
226C3×C11⋊C5—441no—
227C3×C11⋊C5—441no—
228C3×C11⋊C5—442no—
229C3×C11⋊C5—445no—
230C5×D15—2421no—
231C52×D3—1211no—
232C3×C5×D5—1211no—
233D3×D11—551no—
234D3×D11—551no—
235D3×D11—552no—
236D3×D11—551no—
237D3×D11—555no—
238D3×D11—551no—
239D3×D11—551no—
240C112C5×D3×D511yescharacteristic, complemented, Sylow
241D55—111no—
242D55—111no—
243D55—111no—
244D55—111no—
245D55—112no—
246D55—111no—
247D55—115no—
248C5×D11—331no—
249C5×D11—331no—
250C5×D11—331no—
251C5×D11—331no—
252C5×D11—332no—
253C5×D11—331no—
254C5×D11—335no—
255D5×C11—31no—
256D5×C11—31no—
257D5×C11—32no—
258D5×C11—31no—
259D5×C11—35no—
260D5×C11—31no—
261D5×C11—31no—
262C2×C11⋊C5—3301no—
263C2×C11⋊C5—3301no—
264C2×C11⋊C5—3301no—
265C2×C11⋊C5—3302no—
266C2×C11⋊C5—3305no—
267C2×C11⋊C5—1651no—
268C2×C11⋊C5—1651no—
269AGL(1,𝔽11)—331no—
270AGL(1,𝔽11)—331no—
271AGL(1,𝔽11)—331no—
272AGL(1,𝔽11)—331no—
273AGL(1,𝔽11)—331no—
274AGL(1,𝔽11)—332no—
275AGL(1,𝔽11)—335no—
276AGL(1,𝔽11)—551no—
277AGL(1,𝔽11)—551no—
278AGL(1,𝔽11)—551no—
279AGL(1,𝔽11)—551no—
280AGL(1,𝔽11)—551no—
281AGL(1,𝔽11)—552no—
282AGL(1,𝔽11)—555no—
283AGL(1,𝔽11)—661no—
284AGL(1,𝔽11)—662no—
285AGL(1,𝔽11)—661no—
286AGL(1,𝔽11)—661no—
287AGL(1,𝔽11)—661no—
288AGL(1,𝔽11)—661no—
289AGL(1,𝔽11)—661no—
290AGL(1,𝔽11)—665no—
291AGL(1,𝔽11)—661no—
292AGL(1,𝔽11)—661no—
293AGL(1,𝔽11)—661no—
294AGL(1,𝔽11)—662no—
295AGL(1,𝔽11)—661no—
296AGL(1,𝔽11)—665no—
297C2×C5×D5—3631noHall
298C3×C52—2421noHall
299D33—111no—
300D33—111no—
301D33—111no—
302D33—111no—
303D33—112no—
304D33—111no—
305D33—115no—
306C3×D11—551no—
307C3×D11—551no—
308C3×D11—551no—
309C3×D11—551no—
310C3×D11—552no—
311C3×D11—551no—
312C3×D11—555no—
313D3×C11—51no—
314D3×C11—51no—
315D3×C11—52no—
316D3×C11—51no—
317D3×C11—55no—
318D3×C11—51no—
319D3×C11—51no—
320C2×C5×D3—6051no—
321D3×D5—1211no—
322C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
323C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
324C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
325C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
326C5×C11D3×AGL(1,𝔽11)12yescomplemented
327C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
328C5×C11D3×AGL(1,𝔽11)15yescomplemented
329C11⋊C5—111no—
330C11⋊C5—111no—
331C11⋊C5—221no—
332C11⋊C5—222no—
333C11⋊C5—221no—
334C11⋊C5—221no—
335C11⋊C5—221no—
336C11⋊C5—222no—
337C11⋊C5—225no—
338C11⋊C5—441no—
339C11⋊C5—441no—
340C11⋊C5—441no—
341C11⋊C5—441no—
342C11⋊C5—441no—
343C11⋊C5—445no—
344C11⋊C5—441no—
345C11⋊C5—441no—
346C11⋊C5—441no—
347C11⋊C5—442no—
348C11⋊C5—441no—
349C11⋊C5—445no—
350C2×C52—3631no—
351C5×D5—1211no—
352C5×D5—7261no—
353C2×D11—1651no—
354C2×D11—1652no—
355C2×D11—1651no—
356C2×D11—1651no—
357C2×D11—1655no—
358C2×D11—1651no—
359C2×D11—1651no—
360C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
361C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
362C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
363C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
364C3×C11D5×AGL(1,𝔽11)12yescomplemented
365C3×C11D5×AGL(1,𝔽11)11yescharacteristic, complemented
366C3×C11D5×AGL(1,𝔽11)15yescomplemented
367C2×C3×C5—6051no—
368D15#1192589211yescharacteristic, complemented
369C3×D5—1211no—
370C5×D3—1211no—
371C5×D3—1211no—
372C5×D3—12101no—
373C5×D3—2421no—
374C5×D3—2421no—
375C52—2421noSylow
376C2×C11—151no—
377C2×C11—152no—
378C2×C11—151no—
379C2×C11—151no—
380C2×C11—155no—
381C2×C11—151no—
382C2×C11—151no—
383D11—331no—
384D11—331no—
385D11—331no—
386D11—332no—
387D11—331no—
388D11—331no—
389D11—335no—
390D11—551no—
391D11—551no—
392D11—551no—
393D11—552no—
394D11—551no—
395D11—551no—
396D11—555no—
397C22×C5—18151no—
398C2×D5—3631no—
399C3×C5—4841no—
400C3×C5—4841no—
401C3×C5—2421no—
402C3×C5C2×#1192589211yescharacteristic, complemented
403C2×D3—6051noHall
404C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
405C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
406C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
407C11D15⋊AGL(1,𝔽11)12yescomplemented
408C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
409C11D15⋊AGL(1,𝔽11)11yescharacteristic, complemented
410C11D15⋊AGL(1,𝔽11)15yescomplemented
411C2×C5—36301no—
412C2×C5—6051no—
413C2×C5—3631no—
414C2×C5—3631no—
415C2×C5—7261no—
416C2×C5—7261no—
417D5—31no—
418D5—1211no—
419C2×C3—6051no—
420D3—51no—
421D3—1211no—
422C5—4841no—
423C5—4841no—
424C5—2421no—
425C5D3×#1192589211yescharacteristic, complemented
426C22—18151noSylow
427C3D5×#1192589211yescharacteristic, complemented, Sylow
428C2—151no—
429C2—6051no—
430C2—3631no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. D15×#10597243C2semidirect
2. C5×C3⋊#11925892C2semidirect
3. C3×C5⋊#11925892C2semidirect
5. C3×C5×#10597243C22semidirect
6. D15⋊(C11⋊D11)C5semidirect
9. C5⋊#11925892D3semidirect
11. C112×D15C2×C5semidirect
12. C5×C3⋊(C11⋊D11)C2×C5semidirect
13. C3×C5⋊(C11⋊D11)C2×C5semidirect
17. C3⋊#11925892D5semidirect
26. C5×#10597243C2×D3semidirect
29. C3×C5×C112C22×C5semidirect
32. C3×#10597243C2×D5semidirect
55. C5⋊(C11⋊D11)C5×D3semidirect
77. C3⋊(C11⋊D11)C5×D5semidirect
94. C5×C112C2×C5×D3semidirect
97. #10597243D3×D5semidirect
120. C3×C112C2×C5×D5semidirect
121. C11×D15AGL(1,𝔽11)semidirect
122. C11×D15AGL(1,𝔽11)semidirect
123. C11×D15AGL(1,𝔽11)semidirect
124. C11×D15AGL(1,𝔽11)semidirect
125. C11×D15AGL(1,𝔽11)semidirect
126. C11×D15AGL(1,𝔽11)semidirect
127. C11×D15AGL(1,𝔽11)semidirect
202. C3×C5×C11C2×AGL(1,𝔽11)semidirect
203. C3×C5×C11C2×AGL(1,𝔽11)semidirect
204. C3×C5×C11C2×AGL(1,𝔽11)semidirect
205. C3×C5×C11C2×AGL(1,𝔽11)semidirect
206. C3×C5×C11C2×AGL(1,𝔽11)semidirect
207. C3×C5×C11C2×AGL(1,𝔽11)semidirect
208. C3×C5×C11C2×AGL(1,𝔽11)semidirect
240. C112C5×D3×D5semidirect
322. C5×C11D3×AGL(1,𝔽11)semidirect
323. C5×C11D3×AGL(1,𝔽11)semidirect
324. C5×C11D3×AGL(1,𝔽11)semidirect
325. C5×C11D3×AGL(1,𝔽11)semidirect
326. C5×C11D3×AGL(1,𝔽11)semidirect
327. C5×C11D3×AGL(1,𝔽11)semidirect
328. C5×C11D3×AGL(1,𝔽11)semidirect
360. C3×C11D5×AGL(1,𝔽11)semidirect
361. C3×C11D5×AGL(1,𝔽11)semidirect
362. C3×C11D5×AGL(1,𝔽11)semidirect
363. C3×C11D5×AGL(1,𝔽11)semidirect
364. C3×C11D5×AGL(1,𝔽11)semidirect
365. C3×C11D5×AGL(1,𝔽11)semidirect
366. C3×C11D5×AGL(1,𝔽11)semidirect
368. D15#11925892semidirect
402. C3×C5C2×#11925892semidirect
404. C11D15⋊AGL(1,𝔽11)semidirect
405. C11D15⋊AGL(1,𝔽11)semidirect
406. C11D15⋊AGL(1,𝔽11)semidirect
407. C11D15⋊AGL(1,𝔽11)semidirect
408. C11D15⋊AGL(1,𝔽11)semidirect
409. C11D15⋊AGL(1,𝔽11)semidirect
410. C11D15⋊AGL(1,𝔽11)semidirect
425. C5D3×#11925892semidirect
427. C3D5×#11925892semidirect

Maximal subgroups

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

subgroupindex
D15×#105972432
C5×C3⋊#119258922
C3×C5⋊#119258922
D5×#119258923
D15⋊(C11⋊D11)5
D3×#119258925
D15⋊AGL(1,𝔽11)11