Finite Group Databasebeta

← #14292545

Subgroups — #14292545

Order 1920.

368 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#65137C211yesmaximal, characteristic, complemented
2#11747060C211yesmaximal, characteristic, complemented
3#11747039C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic, complemented
5#11746301C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599206—31nomaximal, Hall
9C5×#874C2211yescharacteristic
10C2×C3×#677—21no—
11C3×#4020C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13C2×#6656—21no—
14C2×#6652—21no—
15C2×#6652—21no—
16C3×C5×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊#168)C2211yescharacteristic
18C4×C3⋊#168C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×#3953—21no—
21#90982—21no—
22#90966—21no—
23#90952—21no—
24#71025—51nomaximal, Hall
25#65364—31no—
26#65362—31no—
27#65137D311yescharacteristic, complemented
28#65120—31no—
29C5×#331—31no—
30#64705—31no—
31#64700—31no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C2×C3⋊#168—21no—
42C2×C3⋊#168D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44C2×C5×C3⋊C8—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C3×#677—42no—
49#6656—42no—
50#6652—42no—
51#6652—42no—
52C3×#460—51no—
53#5073—51no—
54#5027—51no—
55#5024—51no—
56#4544—51no—
57#4485D511yescharacteristic, complemented
58#4480—51no—
59C5×#127—31no—
60C2×#687—61no—
61C2×#686—61no—
62C2×#686—61no—
63C2×#677—21no—
64#4020C2×D311yescharacteristic
65C4×Dic10C2×D311yescharacteristic
66C5×C4⋊C8—31no—
67C5×C4⋊C8C2×D311yescharacteristic
68#3964—61no—
69#3953—21no—
70#3947—61no—
71#3946—61no—
72C4⋊#168—31no—
73C4×#168—31no—
74#1688—151noSylow
75C22×C5×D3—41no—
76C22×C3×D5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C5×D12—41no—
81C5×D12—41no—
82C5×D12—41no—
83C5×D12—41no—
84C5×D12—81no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C3×D20—41no—
88C3×D20—41no—
89C3×D20—41no—
90C3×D20—41no—
91C3×D20—81no—
92C3×Dic10—21no—
93C3×Dic10—21no—
94C3×C5×C8—41no—
95C3⋊#168—21no—
96C3⋊#168—41no—
97C3⋊#168SD1612yescomplemented
98C5×C3⋊C8—41no—
99C2×C3×SD16—101no—
100C3×#127—51no—
101C3×C4×Q8—51no—
102C2×#215—101no—
103C2×#213—101no—
104C2×#213—101no—
105#874C2×D511yescharacteristic
106C3×C4⋊C8C2×D511yescharacteristic
107C3×#102—101no—
108#809—101no—
109C4⋊(C3⋊C8)—51no—
110C4⋊(C3⋊C8)—101no—
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112#803—101no—
113C4×C3⋊C8—51no—
114C2×C5×D4—61no—
115C2×C5×D4—61no—
116C2×C5×D4—61no—
117C2×D20—21no—
118C2×D20—21no—
119C2×D20—21no—
120C2×Dic10#6711yescharacteristic
121C2×C5×C8—21no—
122C2×C5×C8—61no—
123C42×C5C22×D311yescharacteristic
124#687—122no—
125#686—122no—
126#686—122no—
127C4⋊Dic5#6711yescharacteristic
128#683—21no—
129C4×Dic5—21no—
130C2×#168—31no—
131C2×#168—31no—
132C2×#168—61no—
133#677—42no—
134#493—151no—
135#460—51no—
136#460—151no—
137#446—151no—
138#334—151no—
139#331—31no—
140#331—151no—
141C22×C3×C5#12111yescharacteristic
142C2×C5×D3—81no—
143C2×C5×D3—81no—
144C2×C5×D3—81no—
145C2×C3×D5—81no—
146C2×C3×D5—81no—
147C2×C3×D5—81no—
148C3×C4×C5—21no—
149C3×C4×C5C2×SD1611yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×Dic5—41no—
154C3×Dic5—41no—
155C2×C3×Q8—51no—
156C2×C3×D4—101no—
157C2×C3×D4—101no—
158C2×C3×D4—101no—
159C2×D12—21no—
160C2×D12—21no—
161C2×D12—21no—
162C3×SD16—202no—
163C2×C3×C8—21no—
164C3×C4⋊C4—51no—
165C3×C4⋊C4—101no—
166C3×C42—101no—
167C3×C42C22×D511yescharacteristic
168#215—202no—
169#213—202no—
170#213—202no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—51no—
173C2×C3⋊C8—51no—
174C2×C3⋊C8—101no—
175C23×C5—121no—
176C22×D5—41no—
177C5×D4—121no—
178C5×D4—121no—
179C5×D4—121no—
180C5×D4—121no—
181C5×D4—241no—
182C2×C4×C5D3×D411yescharacteristic
183C2×C4×C5#23711yescharacteristic
184C2×C4×C5C2×#6711yescharacteristic
185C2×Dic5—21no—
186C2×Dic5—21no—
187D20—41no—
188D20—41no—
189D20—41no—
190D20—41no—
191D20—81no—
192Dic10—21no—
193Dic10—21no—
194C5×C8—41no—
195C5×C8—121no—
196#168—32no—
197#168—61no—
198#168—121no—
199C2×SD16—101no—
200C2×SD16—301no—
201C2×D8—301no—
202C2×D8—301no—
203#127—31no—
204#127—51no—
205C4×Q8—51no—
206C4⋊C8—31no—
207C4⋊C8—151no—
208C4⋊C8—301no—
209C4⋊C8D3×D511yescharacteristic
210#102—101no—
211#102—301no—
212#97—301no—
213C4×C8—151no—
214C2×C3×C5#46011yescharacteristic
215C2×C3×C5#46911yescharacteristic
216C2×C3×C5#47211yescharacteristic
217C3×D5—161no—
218C5×D3—161no—
219C23×C3—201no—
220C22×D3—41no—
221C3×Q8—101no—
222C3×Q8—101no—
223C3×D4—201no—
224C3×D4—201no—
225C3×D4—201no—
226C3×D4—201no—
227C3×D4—401no—
228C2×C3×C4—101no—
229C2×C3×C4—101no—
230C2×C3×C4#70911yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233D12—41no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—81no—
238C3×C8—41no—
239C3⋊C8—41no—
240C3⋊C8—52no—
241C3⋊C8—101no—
242C3⋊C8—201no—
243C22×C5—241no—
244C22×C5—241no—
245C22×C5—241no—
246C22×C5#93911yescharacteristic
247C2×D5—81no—
248C2×D5—81no—
249C2×D5—81no—
250C4×C5—21no—
251C4×C5D3×SD1611yescharacteristic
252C4×C5#91411yescharacteristic
253C4×C5#93211yescharacteristic
254C4×C5#94911yescharacteristic
255Dic5—41no—
256Dic5—41no—
257C2×Q8—51no—
258C2×D4—61no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—101no—
262C2×D4—101no—
263C2×D4—101no—
264SD16—202no—
265SD16—602no—
266D8—602no—
267D8—602no—
268C2×C8—21no—
269C2×C8—61no—
270C2×C8—151no—
271C2×C8—151no—
272C2×C8—301no—
273C4⋊C4—51no—
274C4⋊C4—101no—
275C42—101no—
276C42C2×D3×D511yescharacteristic
277C3×C5#168811yescharacteristic, complemented, Hall
278C22×C3—401no—
279C22×C3—401no—
280C22×C3—401no—
281C22×C3#403011yescharacteristic
282C2×D3—81no—
283C2×D3—81no—
284C2×D3—81no—
285C3×C4—21no—
286C3×C4—201no—
287C3×C4—201no—
288C3×C4#405711yescharacteristic
289C3×C4#405711yescharacteristic
290C3×C4D5×SD1611yescharacteristic
291C3×C4#406011yescharacteristic
292C2×C5—481no—
293C2×C5#503911yescharacteristic
294C2×C5#516311yescharacteristic
295C2×C5#519911yescharacteristic
296D5—161no—
297C23—121no—
298C23—201no—
299Q8—101no—
300Q8—101no—
301D4—121no—
302D4—121no—
303D4—121no—
304D4—121no—
305D4—201no—
306D4—201no—
307D4—201no—
308D4—201no—
309D4—241no—
310D4—401no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4#676511yescharacteristic
314C2×C4#677711yescharacteristic
315C2×C4D5×#6711yescharacteristic
316C8—41no—
317C8—121no—
318C8—152no—
319C8—301no—
320C8—601no—
321C2×C3—801no—
322C2×C3#6503811yescharacteristic
323C2×C3#6505111yescharacteristic
324C2×C3#6507111yescharacteristic
325D3—161no—
326C5#7102511yescharacteristic, complemented, Sylow
327C22—241no—
328C22—241no—
329C22—241no—
330C22—401no—
331C22—401no—
332C22—401no—
333C22#9140811yescharacteristic
334C4—21no—
335C4—201no—
336C4—201no—
337C4#9125511yescharacteristic
338C4#9125711yescharacteristic
339C4#9148911yescharacteristic
340C4#9150211yescharacteristic
341C3#1059920611yescharacteristic, complemented, Sylow
342C2—481no—
343C2—801no—
344C2#1174731211yescharacteristic
345C2#1174799311yescharacteristic
346C2#1174818111yescharacteristic
subgroupG/H
centerC22#91408
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radical#11747039C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1688
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#65137C2semidirect
2. #11747060C2semidirect
4. #11746862C2semidirect
5. #11746301C2semidirect
6. C5×#4485C2semidirect
7. #11745852C2semidirect
27. #65137D3semidirect
57. #4485D5semidirect
97. C3⋊#168SD16semidirect
277. C3×C5#1688semidirect
326. C5#71025semidirect
341. C3#10599206semidirect

Maximal subgroups

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

subgroupindex
C3×#651372
#117470602
#117470392
#117468622
#117463012
C5×#44852
#117458522
#105992063
#710255