Finite Group Databasebeta

← #14284732

Subgroups — #14284732

Order 1920.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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#11754572C211yesmaximal, characteristic
2#11752413C211yesmaximal, characteristic, complemented
3C3×#65754C211yesmaximal, characteristic, complemented
4#11746511C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10605004—31nomaximal, Hall
7C2×#6817C411yescharacteristic
8C2×C5×#235C411yescharacteristic
9C2×C3×C4×Dic5C2211yescharacteristic
10#91566—21no—
11#91566—21no—
12#91451C2211yescharacteristic
13C4×#1203—21no—
14C4×#1203—21no—
15#91376C2211yescharacteristic
16#91375C411yescharacteristic
17#91373C411yescharacteristic
18#91241—21no—
19#91233C2212yes—
20C4×C3⋊#170—21no—
21C3×C22⋊#170—21no—
22C3×#4004C2212yes—
23C3×C4×#170—21no—
24#70773—51nomaximal, Hall
25#66166—31no—
26#65754—31no—
27#65754D311yescharacteristic, complemented
28#64931—32no—
29#64925—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32#6817—42no—
33C2×D60C2×C411yescharacteristic
34C2×C4×D15—21no—
35C2×Dic30C2×C411yescharacteristic
36C2×C5×#67—21no—
37C5×#235—42no—
38C2×C5×D12C2×C411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×#1203—21no—
44C2×#1203—21no—
45C2×C3⋊#170—22no—
46C2×C3×#170—22no—
47C3×C4×Dic5C2×C411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5C2311yescharacteristic
51#6668—21no—
52#6668—21no—
53#6667—21no—
54#6667—21no—
55(C2×D3)⋊Dic5—21no—
56(C2×D3)⋊Dic5—21no—
57#5477—51no—
58C3×#431—51no—
59#4925—51no—
60#4485—52no—
61#4481—52no—
62C2×C5×#41—31no—
63C2×#709—31no—
64#4093—31no—
65#4090—31no—
66#4086—31no—
67#4085—61no—
68#4085—61no—
69#4082—31no—
70C4×C22⋊D5—61no—
71C4×C22⋊D5—61no—
72C2×C4×Dic5C2×D311yescharacteristic
73C22⋊#170—21no—
74C22⋊#170—61no—
75#4004—32no—
76#4004C2×D312yes—
77C4×#170—21no—
78C4×#170—61no—
79#1543—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C22×D15—21no—
82C22×C5×D3—21no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86#1220—42no—
87C2×Dic15—21no—
88D60—41no—
89C4×D15—42no—
90Dic30—41no—
91C5×#67—42no—
92C2×C5×Dic3—21no—
93C5×D12—41no—
94C4×C5×D3—42no—
95C5×Dic6—41no—
96C2×C3×Dic5—22no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5C22⋊C411yescharacteristic
99C2×C3×Dic5C22⋊C411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101C2×C3×Dic5C2×D411yescharacteristic
102#1203—42no—
103#1203—42no—
104C3⋊#170—42no—
105C3×#170—42no—
106C2×#235—51no—
107C2×#235AGL(1,𝔽5)11yescharacteristic
108C2×C3×C42—51no—
109#930—101no—
110#930—101no—
111#875—51no—
112#875—51no—
113#874—51no—
114C4×D12—101no—
115C4×D12—101no—
116#869—51no—
117C3×C4⋊C8—52no—
118C3×C22⋊C8—101no—
119C3×C4×C8—101no—
120#830—101no—
121C4⋊(C3⋊C8)—52no—
122C4×C3⋊C8—101no—
123C5×#41—122no—
124C2×C5×Q8—31no—
125C2×C5×D4—31no—
126C2×C5×D4—61no—
127C22×C4×C5—61no—
128C22×C4×C5C4×D311yescharacteristic
129C2×C22⋊D5—61no—
130C2×C22⋊D5—61no—
131C2×C22⋊D5—61no—
132C22×Dic5D1211yescharacteristic
133C22×Dic5#6711yescharacteristic
134#709—122no—
135C2×D20—31no—
136C2×C4×D5—61no—
137C2×Dic10—31no—
138C2×#170—22no—
139C2×#170—62no—
140C22⋊Dic5—61no—
141C22⋊Dic5—61no—
142#685—61no—
143#685—61no—
144#683—61no—
145#683—61no—
146C4×Dic5C4×D311yescharacteristic
147C4×Dic5D1211yescharacteristic
148C4×Dic5#6711yescharacteristic
149C4×Dic5C22×D311yescharacteristic
150#532—151no—
151#431—51no—
152#431—151no—
153#333—152no—
154#331—152no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×D15—41no—
160C2×D15—41no—
161C2×D15—41no—
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C3×C4×C5—21no—
166C3×C4×C5#10012yes—
167Dic15—41no—
168C3×Dic5—21no—
169C3×Dic5—21no—
170C3×Dic5#13512yes—
171C3×Dic5#13512yes—
172C5×Dic3—41no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
176C2×#67—21no—
177C2×#67—101no—
178#235—42no—
179#235—202no—
180C2×D12—51no—
181C2×D12—101no—
182C2×D12—101no—
183C2×D12C2×AGL(1,𝔽5)11yescharacteristic
184C2×C4×D3—21no—
185C2×C4×D3—101no—
186C2×Dic6—51no—
187C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
188C2×C3×C8—102no—
189C3×C42—51no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42—51no—
193(C2×D3)⋊C4—101no—
194(C2×D3)⋊C4—101no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C2×C3⋊C8—102no—
200C23×C5—61no—
201C23×C5(C2×D3)⋊C411yescharacteristic
202C22×D5—61no—
203C5×Q8—121no—
204C5×D4—121no—
205C5×D4—122no—
206C2×C4×C5—22no—
207C2×C4×C5—61no—
208C2×C4×C5—122no—
209C2×C4×C5(C2×D3)⋊C411yescharacteristic
210C2×C4×C5C2×C4×D311yescharacteristic
211C22⋊D5—122no—
212C22⋊D5—122no—
213C22⋊D5—122no—
214C2×Dic5—22no—
215C2×Dic5—22no—
216C2×Dic5—61no—
217C2×Dic5(C2×D3)⋊C411yescharacteristic
218C2×Dic5(C2×D3)⋊C411yescharacteristic
219C2×Dic5C2×D1211yescharacteristic
220C2×Dic5C2×#6711yescharacteristic
221D20—121no—
222C4×D5—122no—
223Dic10—121no—
224#170—42no—
225#170—122no—
226C2×#41—31no—
227C2×#41—151no—
228C4⋊Q8—151no—
229#127—151no—
230#124—151no—
231#124—151no—
232#121—301no—
233#121—301no—
234C4×D4—301no—
235C4×D4—301no—
236C2×C42—51no—
237C4⋊C8—52no—
238C4⋊C8—152no—
239C22⋊C8—101no—
240C22⋊C8—301no—
241C4×C8—101no—
242C4×C8—301no—
243C2×C3×C5—41no—
244C2×C3×C5C2×#10011yescharacteristic
245C2×C3×C5#41611yescharacteristic
246C2×C3×C5#41611yescharacteristic
247D15—81no—
248C5×D3—81no—
249C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
250C22×D3—21no—
251C22×D3—101no—
252C2×C3×C4—22no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—102no—
258C2×C3×C4—102no—
259C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
260C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
261#67—42no—
262#67—202no—
263C2×Dic3—21no—
264C2×Dic3—101no—
265D12—41no—
266D12—201no—
267D12—202no—
268D12—202no—
269C4×D3—42no—
270C4×D3—202no—
271Dic6—41no—
272Dic6—201no—
273C3×C8—202no—
274C3⋊C8—202no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5C2×(C2×D3)⋊C411yescharacteristic
282C2×D5—121no—
283C2×D5—121no—
284C2×D5—121no—
285C4×C5—21no—
286C4×C5—121no—
287C4×C5#82312yes—
288Dic5—21no—
289Dic5—21no—
290Dic5—121no—
291Dic5#90412yes—
292Dic5#95012yes—
293#41—122no—
294#41—602no—
295C2×Q8—31no—
296C2×Q8—151no—
297C2×D4—31no—
298C2×D4—61no—
299C2×D4—151no—
300C2×D4—301no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—51no—
304C22×C4—51no—
305C22×C4—61no—
306C22×C4—301no—
307C22×C4D3×AGL(1,𝔽5)11yescharacteristic
308C2×C8—102no—
309C2×C8—302no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C22⋊C4—301no—
313C22⋊C4—301no—
314C22⋊C4—301no—
315C22⋊C4—301no—
316C42—51no—
317C42—51no—
318C42—51no—
319C42—51no—
320C3×C5#154311yescharacteristic, complemented, Hall
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—201no—
329C2×D3—201no—
330C2×D3—201no—
331C3×C4—21no—
332C3×C4—52no—
333C3×C4—52no—
334C3×C4—101no—
335C3×C4—101no—
336C3×C4#401312yes—
337Dic3—41no—
338Dic3—201no—
339C2×C5—41no—
340C2×C5—241no—
341C2×C5#500211yescharacteristic
342C2×C5#511311yescharacteristic
343C2×C5C2×#82311yescharacteristic
344D5—241no—
345C23—61no—
346C23—301no—
347C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
348Q8—121no—
349Q8—601no—
350D4—121no—
351D4—122no—
352D4—601no—
353D4—602no—
354D4—602no—
355D4—602no—
356C2×C4—22no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—51no—
360C2×C4—51no—
361C2×C4—61no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—122no—
365C2×C4—301no—
366C2×C4—602no—
367C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
368C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
369C8—202no—
370C8—602no—
371C2×C3—41no—
372C2×C3#6579411yescharacteristic
373C2×C3#6579411yescharacteristic
374C2×C3C2×#401311yescharacteristic
375D3—81no—
376D3—401no—
377C5#7077311yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22—21no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22—601no—
385C22—601no—
386C22—601no—
387C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
388C4—21no—
389C4—52no—
390C4—52no—
391C4—101no—
392C4—101no—
393C4—121no—
394C4—601no—
395C4#9117412yes—
396C3#1060500411yescharacteristic, complemented, Sylow
397C2—41no—
398C2—241no—
399C2—1201no—
400C2#1175170311yescharacteristic
401C2#1175170411yescharacteristic
402C2C2×#9117411yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754572C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752413C2semidirect
3. C3×#65754C2semidirect
4. #11746511C2semidirect
5. #11746508C2semidirect
27. #65754D3semidirect
320. C3×C5#1543semidirect
377. C5#70773semidirect
396. C3#10605004semidirect

Maximal subgroups

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

subgroupindex
#117545722
#117524132
C3×#657542
#117465112
#117465082
#106050043
#707735