Finite Group Databasebeta

← #14284617

Subgroups — #14284617

Order 1920.

512 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 114 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
1#11752671C211yesmaximal, characteristic
2#11752337C211yesmaximal, characteristic, complemented
3C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
4#11746509C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10604408—31nomaximal, Hall
7C2×#6771—21no—
8C2×C3×D5⋊C8—21no—
9C4×D60C411yescharacteristic
10C4×C5×D12C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91468C2211yescharacteristic
13#91451C2211yescharacteristic
14#91450C411yescharacteristic
15#91449C411yescharacteristic
16#91448—21no—
17C4×#1203—21no—
18#91350—21no—
19#91233C2212yes—
20#91232—21no—
21C4×C3⋊#170—21no—
22C3×#4004C2212yes—
23C3×C4⋊#170—21no—
24#70431—51nomaximal, Hall
25#65882—31no—
26D5⋊(C4⋊C8)D311yescharacteristic, complemented
27#65678—31no—
28#64925—32no—
29#64873—32no—
30C2×D60C2×C411yescharacteristic
31C2×C4×D15—21no—
32C2×C5×D12C2×C411yescharacteristic
33C2×C4×C5×D3—21no—
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1202—21no—
41C2×#1201—21no—
42#6771—42no—
43#6771—42no—
44C2×C3⋊#170—22no—
45C2×C3×#170—22no—
46C3×D5⋊C8—42no—
47C3×C42×C5C2×C411yescharacteristic
48#6714—21no—
49C4⋊Dic15C2×C411yescharacteristic
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5C2311yescharacteristic
55#6668—21no—
56#6667—21no—
57(C2×D3)⋊Dic5—21no—
58#5477—51no—
59C2×C3×C4⋊C8—51no—
60#4925—51no—
61#4485—52no—
62#4482—52no—
63C2×#709—61no—
64C2×D5⋊C8—21no—
65C4×C5×D4—31no—
66#4086—31no—
67#4084—31no—
68C4×C22⋊D5—61no—
69#4041—31no—
70#4034—31no—
71#4031—61no—
72#4030—61no—
73C4×D20—31no—
74C42×D5C2×D311yescharacteristic
75#4004—32no—
76#4004C2×D312yes—
77#4003—61no—
78C4⋊#170—21no—
79C4×#170—61no—
80#1540—151noSylow
81C22×D15—21no—
82C22×C5×D3—21no—
83C22×C3×D5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×Dic15—21no—
88D60—41no—
89C4×D15—42no—
90C2×C5×Dic3—21no—
91C5×D12—41no—
92C4×C5×D3—42no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C3×C4×D5—22no—
97C3×C4×D5—41no—
98C3×C4×D5D812yes—
99C3×C4×D5SD1612yes—
100#1204—41no—
101#1204—41no—
102#1203—41no—
103#1203—41no—
104#1203—42no—
105#1202—42no—
106#1201—42no—
107C3⋊#170—42no—
108C3×#170—42no—
109C2×#235—101no—
110C22×C3×C8—101no—
111C2×C3×C42—51no—
112#930—51no—
113#930—51no—
114#930—101no—
115#875—101no—
116#874—51no—
117C4×D12—51no—
118C4×D12—101no—
119C4×D12AGL(1,𝔽5)11yescharacteristic
120#869—51no—
121C3×C4⋊C8—52no—
122C3×C4⋊C8—101no—
123#830—101no—
124C4⋊(C3⋊C8)—52no—
125C4×C3⋊C8—101no—
126C2×C5×D4—31no—
127C22×C4×C5—61no—
128C2×C22⋊D5—61no—
129C2×C22⋊D5—61no—
130C2×C22⋊D5—61no—
131#709—122no—
132#709—122no—
133C2×D20—31no—
134C2×D20—61no—
135C2×C4×D5—61no—
136C2×C4×D5C4×D311yescharacteristic
137C2×C4×D5D1211yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×Dic10—61no—
140C2×#170—22no—
141C2×#170—62no—
142D5⋊C8—42no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C42×C5C4×D311yescharacteristic
146C22⋊Dic5—61no—
147#685—61no—
148#685—61no—
149C4⋊Dic5—31no—
150#683—61no—
151C4×Dic5D1211yescharacteristic
152C4×Dic5#6711yescharacteristic
153C4×Dic5C22×D311yescharacteristic
154#532—151no—
155#431—151no—
156C2×C4⋊C8—51no—
157#332—152no—
158#331—152no—
159C22×C3×C5C2×C22⋊C411yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C3×D5—21no—
167C2×C3×D5—21no—
168C2×C3×D5#10212yes—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5#10212yes—
172Dic15—41no—
173C3×Dic5—21no—
174C3×Dic5C2×D811yescharacteristic
175C3×Dic5C2×SD1611yescharacteristic
176C3×Dic5#13512yes—
177C5×Dic3—41no—
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4—51no—
181C2×#67—101no—
182C2×#67—101no—
183#235—202no—
184#235—202no—
185C2×D12—51no—
186C2×D12—101no—
187C2×D12—101no—
188C2×D12C2×AGL(1,𝔽5)11yescharacteristic
189C2×C4×D3—21no—
190C2×C4×D3—101no—
191C2×Dic6—101no—
192C2×C3×C8—102no—
193C2×C3×C8—202no—
194C3×C42—51no—
195C3×C42—51no—
196C3×C42—51no—
197C3×C42C2×AGL(1,𝔽5)11yescharacteristic
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—51no—
203C4⋊Dic3—101no—
204C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
205C2×C3⋊C8—102no—
206C23×C5—61no—
207C22×D5—61no—
208C22×D5(C2×D3)⋊C411yescharacteristic
209C5×D4—121no—
210C2×C4×C5—61no—
211C2×C4×C5—122no—
212C2×C4×C5(C2×D3)⋊C411yescharacteristic
213C2×C4×C5(C2×D3)⋊C411yescharacteristic
214C2×C4×C5C2×C4×D311yescharacteristic
215C22⋊D5—122no—
216C22⋊D5—122no—
217C22⋊D5—121no—
218C22⋊D5—121no—
219C2×Dic5—61no—
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C2×Dic5C2×D1211yescharacteristic
222C2×Dic5C2×#6711yescharacteristic
223D20—121no—
224D20—122no—
225C4×D5—22no—
226C4×D5—41no—
227C4×D5—122no—
228C4×D5#21312yes—
229C4×D5#21512yes—
230Dic10—121no—
231Dic10—121no—
232#170—42no—
233#170—122no—
234C2×#41—301no—
235C22×C8—101no—
236C4⋊Q8—151no—
237#127—151no—
238#124—301no—
239#121—151no—
240#121—151no—
241#121—301no—
242C4×D4—31no—
243C4×D4—151no—
244C4×D4—301no—
245C2×C42—51no—
246C4⋊C8—52no—
247C4⋊C8—101no—
248C4⋊C8—152no—
249C22⋊C8—301no—
250C4×C8—301no—
251C2×C3×C5#41311yescharacteristic
252C2×C3×C5C2×#10211yescharacteristic
253C2×C3×C5#41611yescharacteristic
254D15—81no—
255C3×D5—22no—
256C5×D3—81no—
257C23×C3—51no—
258C22×D3—21no—
259C22×D3—101no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—52no—
263C2×C3×C4—52no—
264C2×C3×C4—51no—
265C2×C3×C4—102no—
266C2×C3×C4—201no—
267C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
268C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
269C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
270#67—202no—
271#67—202no—
272C2×Dic3—21no—
273C2×Dic3—101no—
274D12—41no—
275D12—201no—
276D12—202no—
277D12—201no—
278D12—201no—
279C4×D3—42no—
280C4×D3—202no—
281Dic6—201no—
282Dic6—201no—
283C3×C8—202no—
284C3⋊C8—202no—
285C22×C5—121no—
286C22×C5—121no—
287C22×C5—121no—
288C22×C5C2×(C2×D3)⋊C411yescharacteristic
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—121no—
292C2×D5—121no—
293C2×D5—121no—
294C2×D5#80912yes—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—121no—
298C4×C5#80912yes—
299Dic5—21no—
300Dic5—121no—
301Dic5#90412yes—
302Dic5C2×#21311yescharacteristic
303Dic5C2×#21511yescharacteristic
304#41—602no—
305#41—602no—
306C2×Q8—301no—
307C2×D4—31no—
308C2×D4—151no—
309C2×D4—301no—
310C2×D4—301no—
311C2×D4—301no—
312C2×D4—301no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—61no—
317C22×C4—301no—
318C2×C8—102no—
319C2×C8—202no—
320C2×C8—302no—
321C4⋊C4—31no—
322C4⋊C4—151no—
323C4⋊C4—301no—
324C22⋊C4—61no—
325C22⋊C4—301no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—51no—
329C42—51no—
330C42—51no—
331C42D3×AGL(1,𝔽5)11yescharacteristic
332C3×C5#154011yescharacteristic, complemented, Hall
333C22×C3—52no—
334C22×C3—101no—
335C22×C3—101no—
336C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—201no—
341C2×D3—201no—
342C2×D3—201no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—52no—
346C3×C4—51no—
347C3×C4—51no—
348C3×C4—101no—
349C3×C4#400712yes—
350Dic3—41no—
351Dic3—201no—
352C2×C5—241no—
353C2×C5C2×#80911yescharacteristic
354C2×C5#511311yescharacteristic
355C2×C5#513211yescharacteristic
356D5—22no—
357D5—241no—
358C23—51no—
359C23—61no—
360C23—301no—
361Q8—601no—
362Q8—601no—
363D4—121no—
364D4—601no—
365D4—601no—
366D4—601no—
367D4—602no—
368D4—602no—
369D4—602no—
370C2×C4—51no—
371C2×C4—51no—
372C2×C4—52no—
373C2×C4—52no—
374C2×C4—51no—
375C2×C4—61no—
376C2×C4—102no—
377C2×C4—122no—
378C2×C4—201no—
379C2×C4—301no—
380C2×C4—602no—
381C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
382C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
383C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
384C8—202no—
385C8—602no—
386C2×C3—102no—
387C2×C3#6576111yescharacteristic
388C2×C3C2×#400711yescharacteristic
389C2×C3#6579411yescharacteristic
390D3—81no—
391D3—401no—
392C5#7043111yescharacteristic, complemented, Sylow
393C22—52no—
394C22—101no—
395C22—101no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22—601no—
400C22—601no—
401C22—601no—
402C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
403C4—21no—
404C4—21no—
405C4—51no—
406C4—51no—
407C4—52no—
408C4—101no—
409C4—121no—
410C4—601no—
411C4#9115112yes—
412C3#1060440811yescharacteristic, complemented, Sylow
413C2—102no—
414C2—241no—
415C2—1201no—
416C2C2×#9115111yescharacteristic
417C2#1175170411yescharacteristic
418C2#1175181811yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11752671C2
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1540
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752337C2semidirect
3. C3×D5⋊(C4⋊C8)C2semidirect
4. #11746509C2semidirect
5. #11746508C2semidirect
26. D5⋊(C4⋊C8)D3semidirect
332. C3×C5#1540semidirect
392. C5#70431semidirect
412. C3#10604408semidirect

Maximal subgroups

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

subgroupindex
#117526712
#117523372
C3×D5⋊(C4⋊C8)2
#117465092
#117465082
#106044083
#704315