Finite Group Databasebeta

← #14284735

Subgroups — #14284735

Order 1920.

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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#11752673C211yesmaximal, characteristic
2#11752337C211yesmaximal, characteristic, complemented
3C3×#65678C211yesmaximal, characteristic, complemented
4#11746511C212yesmaximal, complemented
5#11746508C212yesmaximal, complemented
6#10604556—31nomaximal, Hall
7C2×#6773C411yescharacteristic
8C2×#6772C411yescharacteristic
9#91764C411yescharacteristic
10C5×#875C411yescharacteristic
11C3×C42×D5C2211yescharacteristic
12#91451C2211yescharacteristic
13#91448—21no—
14#91448—21no—
15#91405—21no—
16#91405—21no—
17#91376C2211yescharacteristic
18#91233C2212yes—
19#91232—21no—
20C4×C3⋊#170—21no—
21C3×#4004C2212yes—
22C3×#4003—21no—
23C3×C4×#170—21no—
24#70773—51nomaximal, Hall
25#66002—31no—
26#65678—31no—
27#65678D311yescharacteristic, complemented
28#64931—32no—
29#64925—32no—
30C2×D60C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×D12C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×C4×D5D411yescharacteristic
36C2×C3×C4×D5D411yescharacteristic
37C2×#1203—21no—
38C2×#1203—21no—
39C2×#1202—21no—
40C2×#1201—21no—
41C2×#1200—21no—
42C2×D3×Dic5—21no—
43#6773—42no—
44#6772—42no—
45C2×C3⋊#170—22no—
46C2×C3×#170—22no—
47C3×C42×C5C2×C411yescharacteristic
48#6714—21no—
49#6714—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C3×C4×Dic5D411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5C2311yescharacteristic
55#6668—21no—
56#6668—21no—
57#5477—51no—
58C3×#431—51no—
59#4925—51no—
60#4485—52no—
61#4481—52no—
62C2×#713—31no—
63C2×#711—31no—
64C5×#124—31no—
65#4090—31no—
66#4086—31no—
67#4030—61no—
68#4030—61no—
69#4027—61no—
70#4027—61no—
71#4021—31no—
72C42×D5C2×D311yescharacteristic
73#4004—32no—
74#4004C2×D312yes—
75#4003—21no—
76#4003—61no—
77C4×#170—21no—
78C4×#170—61no—
79#1543—151noSylow
80C22×D15—21no—
81C22×C5×D3—21no—
82C22×C3×D5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×Dic15—21no—
87D60—41no—
88Dic30—41no—
89C2×C5×Dic3—21no—
90C5×D12—41no—
91C5×Dic6—41no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C3×C4×D5—22no—
96C3×C4×D5—22no—
97C3×C4×D5—22no—
98#1203—42no—
99#1203—42no—
100#1202—42no—
101#1201—42no—
102#1200—42no—
103D3×Dic5—42no—
104C3⋊#170—42no—
105C3×#170—42no—
106C2×#235—51no—
107C2×#235—51no—
108C2×C3×C42—51no—
109#930—101no—
110#930—101no—
111#875—51no—
112#875AGL(1,𝔽5)11yescharacteristic
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—
123C2×C5×Q8—31no—
124C2×C5×D4—31no—
125C2×C22⋊D5—61no—
126C2×C22⋊D5—61no—
127C2×C22⋊D5—61no—
128C22×Dic5—61no—
129#713—122no—
130#711—122no—
131C2×D20—31no—
132C2×D20—61no—
133C2×C4×D5—61no—
134C2×C4×D5C4×D311yescharacteristic
135C2×C4×D5D1211yescharacteristic
136C2×C4×D5#6711yescharacteristic
137C2×Dic10—31no—
138C2×#170—22no—
139C2×#170—62no—
140C5×C22⋊C4—61no—
141C5×C22⋊C4—61no—
142C42×C5C4×D311yescharacteristic
143#685—61no—
144#685—61no—
145#683—61no—
146#683—61no—
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×C5C2×C22⋊C411yescharacteristic
156C2×D15—41no—
157C2×D15—41no—
158C2×D15—41no—
159C2×C5×D3—41no—
160C2×C5×D3—41no—
161C2×C5×D3—41no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—41no—
169C3×Dic5#10012yes—
170C3×Dic5#13512yes—
171C3×Dic5#13512yes—
172C5×Dic3—41no—
173C22×C3×C4—51no—
174C22×C3×C4—51no—
175C22×C3×C4—51no—
176C2×#67—101no—
177C2×#67—101no—
178#235—202no—
179#235—202no—
180C2×D12—51no—
181C2×D12—101no—
182C2×D12—101no—
183C2×D12C2×AGL(1,𝔽5)11yescharacteristic
184C2×C4×D3—101no—
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×C42C2×AGL(1,𝔽5)11yescharacteristic
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—101no—
196(C2×D3)⋊C4—101no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C2×C3⋊C8—102no—
200C23×C5—61no—
201C22×D5—61no—
202C22×D5(C2×D3)⋊C411yescharacteristic
203C5×Q8—121no—
204C5×D4—121no—
205C2×C4×C5—61no—
206C2×C4×C5(C2×D3)⋊C411yescharacteristic
207C2×C4×C5(C2×D3)⋊C411yescharacteristic
208C2×C4×C5C2×C4×D311yescharacteristic
209C22⋊D5—122no—
210C22⋊D5—122no—
211C22⋊D5—122no—
212C2×Dic5—61no—
213C2×Dic5—122no—
214C2×Dic5(C2×D3)⋊C411yescharacteristic
215C2×Dic5C2×D1211yescharacteristic
216C2×Dic5C2×#6711yescharacteristic
217D20—121no—
218D20—122no—
219C4×D5—22no—
220C4×D5—22no—
221C4×D5—22no—
222C4×D5—122no—
223Dic10—121no—
224#170—42no—
225#170—122no—
226C2×#41—151no—
227C2×#41—151no—
228C4⋊Q8—151no—
229#127—151no—
230#124—31no—
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×C5C2×#10011yescharacteristic
244C2×C3×C5#41611yescharacteristic
245C2×C3×C5#41611yescharacteristic
246D15—81no—
247C3×D5—41no—
248C5×D3—81no—
249C23×C3—51no—
250C22×D3—21no—
251C22×D3—101no—
252C2×C3×C4—51no—
253C2×C3×C4—51no—
254C2×C3×C4—51no—
255C2×C3×C4—102no—
256C2×C3×C4—102no—
257C2×C3×C4—102no—
258C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
259C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
260C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
261#67—202no—
262#67—202no—
263C2×Dic3—21no—
264C2×Dic3—101no—
265D12—41no—
266D12—201no—
267D12—202no—
268D12—202no—
269C4×D3—202no—
270C4×D3—202no—
271Dic6—41no—
272Dic6—201no—
273C3×C8—202no—
274C3⋊C8—202no—
275C22×C5—121no—
276C22×C5—121no—
277C22×C5—121no—
278C22×C5C2×(C2×D3)⋊C411yescharacteristic
279C2×D5—21no—
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—121no—
283C2×D5—121no—
284C2×D5—121no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—121no—
289Dic5—121no—
290Dic5#82312yes—
291Dic5#90412yes—
292Dic5#95012yes—
293#41—602no—
294#41—602no—
295C2×Q8—31no—
296C2×Q8—151no—
297C2×D4—31no—
298C2×D4—151no—
299C2×D4—301no—
300C2×D4—301no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—51no—
304C22×C4—51no—
305C22×C4—51no—
306C22×C4—301no—
307C22×C4—301no—
308C2×C8—102no—
309C2×C8—302no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C22⋊C4—301no—
315C22⋊C4—301no—
316C42—51no—
317C42—51no—
318C42—51no—
319C42D3×AGL(1,𝔽5)11yescharacteristic
320C3×C5#154311yescharacteristic, complemented, Hall
321C22×C3—101no—
322C22×C3—101no—
323C22×C3—101no—
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—21no—
333C3×C4—21no—
334C3×C4—52no—
335C3×C4—52no—
336C3×C4—52no—
337Dic3—41no—
338Dic3—201no—
339C2×C5—241no—
340C2×C5#500211yescharacteristic
341C2×C5#511311yescharacteristic
342C2×C5C2×#82311yescharacteristic
343D5—41no—
344D5—241no—
345C23—51no—
346C23—61no—
347C23—301no—
348Q8—121no—
349Q8—601no—
350D4—121no—
351D4—601no—
352D4—602no—
353D4—602no—
354D4—602no—
355D4—602no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—61no—
360C2×C4—102no—
361C2×C4—102no—
362C2×C4—102no—
363C2×C4—301no—
364C2×C4—602no—
365C2×C4—602no—
366C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
367C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
368C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
369C8—202no—
370C8—602no—
371C2×C3—201no—
372C2×C3D5⋊#10011yescharacteristic
373C2×C3#6579411yescharacteristic
374C2×C3#6579411yescharacteristic
375D3—81no—
376D3—401no—
377C5#7077311yescharacteristic, complemented, Sylow
378C22—101no—
379C22—101no—
380C22—101no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22—601no—
385C22—601no—
386C22—601no—
387C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—52no—
392C4—52no—
393C4—52no—
394C4—121no—
395C4—601no—
396C3#1060455611yescharacteristic, complemented, Sylow
397C2—201no—
398C2—241no—
399C2—1201no—
400C2#1175170311yescharacteristic
401C2#1175170411yescharacteristic
402C2D5⋊#82311yescharacteristic
subgroupG/H
centerC22C2×(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#11752673C2
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752337C2semidirect
3. C3×#65678C2semidirect
4. #11746511C2semidirect
5. #11746508C2semidirect
27. #65678D3semidirect
320. C3×C5#1543semidirect
377. C5#70773semidirect
396. C3#10604556semidirect

Maximal subgroups

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

subgroupindex
#117526732
#117523372
C3×#656782
#117465112
#117465082
#106045563
#707735