Finite Group Databasebeta

← #14289063

Subgroups — #14289063

Order 1920.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752718C211yesmaximal, characteristic, complemented
2#11751177C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic, complemented
5#11745863C211yesmaximal, characteristic, complemented
6#11745836C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601810—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—22no—
11#91758C2211yescharacteristic
12C2×C5×#213—21no—
13C4×C5×D12C2211yescharacteristic
14C2×C3×#686—21no—
15C3×C4×D20C2211yescharacteristic
16#91462—22no—
17#91456—21no—
18#91449—21no—
19#91358—21no—
20#91338—21no—
21C4×C3⋊#168C2211yescharacteristic
22C5×#832—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71017—51nomaximal, Hall
27#65897—31no—
28C5×#459—31no—
29#65365—31no—
30#65361D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D412yes—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1201—22no—
43C3×C42×C5C2311yescharacteristic
44#6716—44no—
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C2×C3⋊#168—21no—
48C5×#213—42no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×#686—42no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56(C2×D3)⋊Dic5—22no—
57#6665—22no—
58Dic3×Dic5—22no—
59#5563—51no—
60C3×#459—51no—
61#5076—51no—
62#5072D511yescharacteristic, complemented
63D4⋊(C3⋊C8)—51no—
64#4483—51no—
65#4481—51no—
66C2×C5×D8—61no—
67C5×#127C2×D311yescharacteristic
68C4×C5×D4—31no—
69#4084—61no—
70C2×#687—62no—
71C2×#686—21no—
72#4076—61no—
73#4072—61no—
74#4038—61no—
75#4031—62no—
76C4×D20C2×D311yescharacteristic
77#4015—31no—
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—21no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1624—151noSylow
84C23×C3×C5—41no—
85C22×C5×D3—21no—
86C22×C3×D5—21no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—22no—
96Dic30—42no—
97C2×C5×Dic3—21no—
98C5×D12—21no—
99C5×D12—21no—
100C4×C5×D3—41no—
101C4×C5×D3—41no—
102C2×C3×Dic5—21no—
103C3×D20—21no—
104C3×D20—21no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107#1201—82no—
108C3⋊#168—22no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C2×C3×D8—101no—
112C3×#127C2×D511yescharacteristic
113C3×C4×D4—51no—
114#938—101no—
115C2×#214—102no—
116C2×#213—21no—
117#930—101no—
118#926—101no—
119#892—101no—
120#885—102no—
121C4×D12C2×D511yescharacteristic
122#869—51no—
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—21no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8—51no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—31no—
132C22×C4×C5—61no—
133C2×C22⋊D5—62no—
134C2×D20#6711yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10—32no—
137C5×D8—122no—
138C2×C5×C8—61no—
139C5×C4⋊C4—31no—
140C5×C22⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142C22⋊Dic5—62no—
143#687—124no—
144#686—42no—
145#685—21no—
146#685—62no—
147C4⋊Dic5—61no—
148C4⋊Dic5—61no—
149C4⋊Dic5#6711yescharacteristic
150C4×Dic5—62no—
151C2×#168—21no—
152C2×#168—61no—
153#555—151no—
154#492—151no—
155#459—31no—
156#459—51no—
157#333—151no—
158D4⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—81no—
161C22×C3×C5—81no—
162C22×C3×C5—81no—
163C22×C3×C5#12011yescharacteristic
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5—41no—
170C3×C4×C5—21no—
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175Dic15—42no—
176C3×Dic5—41no—
177C5×Dic3—41no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—51no—
182C22×C3×C4—101no—
183C2×#67—102no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6—52no—
187C3×D8—202no—
188C2×C3×C8—101no—
189C3×C4⋊C4—51no—
190C3×C22⋊C4—101no—
191C3×C42C22×D511yescharacteristic
192#217—102no—
193#214—204no—
194#213—42no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—102no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C4⋊Dic3C22⋊D511yescharacteristic
200C4×Dic3—102no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—101no—
203C23×C5—41no—
204C23×C5—61no—
205C22×D5—21no—
206C5×D4—42no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—61no—
212C5×D4—61no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C22⋊D5—242no—
220C2×Dic5—21no—
221C2×Dic5—62no—
222D20—21no—
223D20—21no—
224C4×D5—41no—
225C4×D5—41no—
226Dic10—122no—
227C5×C8—121no—
228#168—41no—
229#168—62no—
230C2×SD16—302no—
231C2×D8—61no—
232C2×D8—101no—
233C4⋊Q8—151no—
234#127D3×D511yescharacteristic
235#124—302no—
236#121—301no—
237#121—301no—
238C4×D4—31no—
239C4×D4—51no—
240#117—301no—
241#117—301no—
242C4⋊C8—31no—
243C4⋊C8—51no—
244#102—61no—
245#102—101no—
246C4×C8—151no—
247C2×C3×C5—161no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251C3×D5—81no—
252C5×D3—81no—
253C23×C3—41no—
254C23×C3—101no—
255C22×D3—21no—
256C3×D4—42no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—101no—
262C3×D4—101no—
263C2×C3×C4—101no—
264C2×C3×C4—201no—
265C2×C3×C4—201no—
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268C2×C3×C4C2×C22⋊D511yescharacteristic
269#67—402no—
270C2×Dic3—21no—
271C2×Dic3—102no—
272D12—21no—
273D12—21no—
274C4×D3—41no—
275C4×D3—41no—
276Dic6—202no—
277C3×C8—201no—
278C3⋊C8—41no—
279C3⋊C8—102no—
280C22×C5—81no—
281C22×C5—81no—
282C22×C5—81no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5#93711yescharacteristic
287C2×D5—41no—
288C2×D5—41no—
289C2×D5—41no—
290C4×C5—21no—
291C4×C5—121no—
292C4×C5#91111yescharacteristic
293C4×C5#91211yescharacteristic
294C4×C5#93211yescharacteristic
295C4×C5#95011yescharacteristic
296Dic5—41no—
297Dic5—122no—
298C2×Q8—152no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—31no—
303C2×D4—51no—
304C2×D4—302no—
305C22×C4—61no—
306C22×C4—101no—
307SD16—604no—
308D8—122no—
309D8—202no—
310C2×C8—61no—
311C2×C8—101no—
312C2×C8—301no—
313C4⋊C4—31no—
314C4⋊C4—51no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C22⋊C4—61no—
318C22⋊C4—101no—
319C22⋊C4—302no—
320C22⋊C4—302no—
321C42—302no—
322C42C2×D3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3—201no—
328C22×C3—201no—
329C22×C3—201no—
330C22×C3#408311yescharacteristic
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C3×C4—21no—
335C3×C4—201no—
336C3×C4#405711yescharacteristic
337C3×C4#405811yescharacteristic
338C3×C4#407811yescharacteristic
339C3×C4#409611yescharacteristic
340Dic3—41no—
341Dic3—202no—
342C2×C5—161no—
343C2×C5—241no—
344C2×C5#503711yescharacteristic
345C2×C5#515811yescharacteristic
346C2×C5#519811yescharacteristic
347D5—81no—
348C23—41no—
349C23—61no—
350C23—101no—
351Q8—602no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—61no—
358D4—61no—
359D4—101no—
360D4—101no—
361D4—1202no—
362C2×C4—61no—
363C2×C4—101no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—201no—
367C2×C4—201no—
368C2×C4—302no—
369C2×C4D5×#6711yescharacteristic
370C2×C4D3×C22⋊D511yescharacteristic
371C2×C4#679011yescharacteristic
372C8—121no—
373C8—201no—
374C8—302no—
375C2×C3—161no—
376C2×C3—401no—
377C2×C3#6532611yescharacteristic
378C2×C3#6544711yescharacteristic
379C2×C3#6548711yescharacteristic
380D3—81no—
381C5#7101711yescharacteristic, complemented, Sylow
382C22—81no—
383C22—81no—
384C22—81no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22—201no—
389C22—201no—
390C22—201no—
391C22#9157711yescharacteristic
392C4—21no—
393C4—121no—
394C4—201no—
395C4—602no—
396C4#9148911yescharacteristic
397C4#9149011yescharacteristic
398C4#9149311yescharacteristic
399C4#9149411yescharacteristic
400C3#1060181011yescharacteristic, complemented, Sylow
401C2—161no—
402C2—241no—
403C2—401no—
404C2#1174915711yescharacteristic
405C2#1174915911yescharacteristic
406C2#1174916411yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752718C2semidirect
2. #11751177C2semidirect
3. C5×#5072C2semidirect
4. C3×#65361C2semidirect
5. #11745863C2semidirect
6. #11745836C2semidirect
7. #11745834C2semidirect
30. #65361D3semidirect
62. #5072D5semidirect
323. C3×C5#1624semidirect
381. C5#71017semidirect
400. C3#10601810semidirect

Maximal subgroups

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

subgroupindex
#117527182
#117511772
C5×#50722
C3×#653612
#117458632
#117458362
#117458342
#106018103
#710175