Finite Group Databasebeta

← #14292788

Subgroups — #14292788

Order 1920.

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

normal subgroups only

This group has 332 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×#65130C211yesmaximal, characteristic
2#11747059C211yesmaximal, characteristic
3#11747013C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic, complemented
5#11746301C211yesmaximal, characteristic, complemented
6C5×#4482C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599244—31nomaximal, Hall
9C5×#869C2211yescharacteristic
10C2×C3×#677—21no—
11C3×C4×D20C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6655—21no—
14C2×#6649—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊#168)C2211yescharacteristic
17C4×C3⋊#168C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3948—21no—
20#90989—21no—
21#90989—21no—
22#90972—21no—
23#90955—21no—
24#71041—51nomaximal, Hall
25#65372—31no—
26#65367—31no—
27#65130D311yescharacteristic
28#65127—31no—
29C5×#332—31no—
30#64706—31no—
31#64700—31no—
32C2×C5×Dic6—21no—
33C2×C3×D20D411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38C2×C3⋊#168—21no—
39C2×C3⋊#168D411yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8—21no—
44C3×#685—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×#677—42no—
49#6655—42no—
50#6649—42no—
51C3×#461—51no—
52#5078—51no—
53#5019—51no—
54#5012—51no—
55#4547—51no—
56#4482D511yescharacteristic, complemented
57#4480—51no—
58C5×C4⋊Q8—31no—
59C2×#688—61no—
60C2×#677—21no—
61C2×#676—61no—
62C4×D20C2×D311yescharacteristic
63#4015C2×D311yescharacteristic
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66#3967—61no—
67#3952—61no—
68#3948—21no—
69#3939—61no—
70#3939—61no—
71C4⋊#168—31no—
72C4×#168—31no—
73#1693—151noSylow
74C22×C3×D5—21no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×C5×Dic3—41no—
79C5×Dic6—41no—
80C5×Dic6—41no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5—41no—
83C3×D20—21no—
84C3×D20—21no—
85C3×C4×D5—41no—
86C3×C4×D5—41no—
87C3×Dic10—41no—
88C3×Dic10—41no—
89C3×C5×C8—41no—
90C3⋊#168—21no—
91C3⋊#168—41no—
92C3⋊#168SD1612yescomplemented
93C5×C3⋊C8—41no—
94C2×C3×SD16—101no—
95C3×C4⋊Q8—51no—
96C3×C4×D4—51no—
97C2×#214—101no—
98C2×#208—101no—
99#869C2×D511yescharacteristic
100C3×C4⋊C8C2×D511yescharacteristic
101C3×#103—101no—
102#830—101no—
103#810—101no—
104#807—101no—
105#807—101no—
106C4⋊(C3⋊C8)—51no—
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108C4×C3⋊C8—51no—
109C2×C5×Q8—61no—
110C2×D20#6711yescharacteristic
111C2×C4×D5—21no—
112C2×Dic10—21no—
113C2×C5×C8—21no—
114C2×C5×C8—61no—
115C5×C4⋊C4—61no—
116C5×C4⋊C4—61no—
117C42×C5C22×D311yescharacteristic
118#688—122no—
119#685—21no—
120C4⋊Dic5—21no—
121C4⋊Dic5—21no—
122C4⋊Dic5#6711yescharacteristic
123C2×#168—31no—
124C2×#168—31no—
125C2×#168—61no—
126#677—42no—
127#676—122no—
128#500—151no—
129#461—51no—
130#461—151no—
131#436—151no—
132#334—151no—
133#332—31no—
134#332—151no—
135C22×C3×C5#12111yescharacteristic
136C2×C3×D5—41no—
137C2×C3×D5—41no—
138C2×C3×D5—41no—
139C3×C4×C5—21no—
140C3×C4×C5C2×SD1611yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×C4×C5#13711yescharacteristic
144C3×Dic5—41no—
145C3×Dic5—81no—
146C5×Dic3—81no—
147C2×C3×Q8—101no—
148C2×C3×D4—51no—
149C22×C3×C4—101no—
150C2×Dic6—21no—
151C3×SD16—202no—
152C2×C3×C8—21no—
153C3×C4⋊C4—51no—
154C3×C4⋊C4—101no—
155C3×C4⋊C4—101no—
156C3×C22⋊C4—101no—
157C3×C42C22×D511yescharacteristic
158#214—202no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161#208—202no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—51no—
164C2×C3⋊C8—51no—
165C2×C3⋊C8—101no—
166C22×D5—21no—
167C5×Q8—121no—
168C5×Q8—121no—
169C2×C4×C5—121no—
170C2×C4×C5D3×D411yescharacteristic
171C2×C4×C5#23711yescharacteristic
172C2×C4×C5C2×#6711yescharacteristic
173C2×Dic5—21no—
174C2×Dic5—41no—
175D20—21no—
176D20—21no—
177C4×D5—41no—
178C4×D5—41no—
179Dic10—41no—
180Dic10—41no—
181C5×C8—41no—
182C5×C8—121no—
183#168—32no—
184#168—61no—
185#168—121no—
186C2×SD16—101no—
187C2×SD16—301no—
188C2×M16—301no—
189C4⋊Q8—31no—
190C4⋊Q8—51no—
191C4×D4—51no—
192#107—301no—
193#107—301no—
194C4⋊C8—31no—
195C4⋊C8—151no—
196C4⋊C8D3×D511yescharacteristic
197#103—101no—
198#103—301no—
199C22⋊C8—301no—
200C4×C8—151no—
201C2×C3×C5#46111yescharacteristic
202C2×C3×C5#46911yescharacteristic
203C2×C3×C5#47311yescharacteristic
204C3×D5—81no—
205C23×C3—101no—
206C3×Q8—201no—
207C3×Q8—201no—
208C3×D4—101no—
209C3×D4—101no—
210C2×C3×C4—101no—
211C2×C3×C4—201no—
212C2×C3×C4—201no—
213C2×C3×C4—201no—
214C2×C3×C4#70911yescharacteristic
215C2×C3×C4D4×D511yescharacteristic
216C2×C3×C4D4×D511yescharacteristic
217C2×Dic3—41no—
218Dic6—41no—
219Dic6—41no—
220C3×C8—41no—
221C3⋊C8—41no—
222C3⋊C8—52no—
223C3⋊C8—101no—
224C3⋊C8—201no—
225C22×C5#93911yescharacteristic
226C2×D5—41no—
227C2×D5—41no—
228C2×D5—41no—
229C4×C5—21no—
230C4×C5—241no—
231C4×C5D3×SD1611yescharacteristic
232C4×C5#91511yescharacteristic
233C4×C5#93211yescharacteristic
234C4×C5#94911yescharacteristic
235Dic5—41no—
236Dic5—81no—
237C2×Q8—61no—
238C2×Q8—101no—
239C2×D4—51no—
240C22×C4—101no—
241SD16—202no—
242SD16—602no—
243M16—602no—
244C2×C8—21no—
245C2×C8—61no—
246C2×C8—151no—
247C2×C8—151no—
248C2×C8—301no—
249C4⋊C4—51no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—101no—
253C4⋊C4—101no—
254C22⋊C4—101no—
255C42C2×D3×D511yescharacteristic
256C3×C5#169311yescharacteristic, complemented, Hall
257C22×C3—201no—
258C22×C3—201no—
259C22×C3—201no—
260C22×C3#403011yescharacteristic
261C3×C4—21no—
262C3×C4—201no—
263C3×C4—401no—
264C3×C4#405711yescharacteristic
265C3×C4D5×SD1611yescharacteristic
266C3×C4#406011yescharacteristic
267C3×C4#406411yescharacteristic
268Dic3—81no—
269C2×C5#503911yescharacteristic
270C2×C5#516211yescharacteristic
271C2×C5#520411yescharacteristic
272D5—81no—
273C23—101no—
274Q8—121no—
275Q8—121no—
276Q8—201no—
277Q8—201no—
278D4—101no—
279D4—101no—
280C2×C4—101no—
281C2×C4—121no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4#676511yescharacteristic
286C2×C4#677711yescharacteristic
287C2×C4D5×#6711yescharacteristic
288C8—41no—
289C8—121no—
290C8—152no—
291C8—301no—
292C8—601no—
293C2×C3—401no—
294C2×C3#6504411yescharacteristic
295C2×C3#6507111yescharacteristic
296C2×C3#6510711yescharacteristic
297C5#7104111yescharacteristic, complemented, Sylow
298C22—201no—
299C22—201no—
300C22—201no—
301C22#9140811yescharacteristic
302C4—21no—
303C4—201no—
304C4—241no—
305C4—401no—
306C4#9125511yescharacteristic
307C4#9127811yescharacteristic
308C4#9148911yescharacteristic
309C4#9150211yescharacteristic
310C3#1059924411yescharacteristic, complemented, Sylow
311C2—401no—
312C2#1174731211yescharacteristic
313C2#1174774911yescharacteristic
314C2#1174818011yescharacteristic
subgroupG/H
centerC22#91408
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1693
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
4. #11746962C2semidirect
5. #11746301C2semidirect
6. C5×#4482C2semidirect
7. #11745855C2semidirect
56. #4482D5semidirect
92. C3⋊#168SD16semidirect
256. C3×C5#1693semidirect
297. C5#71041semidirect
310. C3#10599244semidirect

Maximal subgroups

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

subgroupindex
C3×#651302
#117470592
#117470132
#117469622
#117463012
C5×#44822
#117458552
#105992443
#710415