Finite Group Databasebeta

← #14292829

Subgroups — #14292829

Order 1920.

304 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750932C211yesmaximal, characteristic
2#11747105C211yesmaximal, characteristic
3#11747104C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic
5C5×#4486C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic
7#11745865C211yesmaximal, characteristic
8#10599268—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6663—21no—
13C2×#6662—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15#91099—21no—
16#91098—21no—
17C4×C3⋊#168C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊#168C2211yescharacteristic
20#90989—21no—
21#90989—21no—
22#90973—21no—
23#90971—21no—
24#68475—51nomaximal, Hall
25#65379—31no—
26#65367—31no—
27#65138—31no—
28#65120—31no—
29C5×#332—31no—
30#64706D311yescharacteristic
31#64700—31no—
32C2×Dic30D411yescharacteristic
33C2×C5×Dic6—21no—
34C2×C3×Dic10—21no—
35C2×C3×C5×C8—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15D411yescharacteristic
38#6712—21no—
39C4×Dic15—21no—
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3—21no—
44C2×C5×C3⋊C8—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168—21no—
48#6663—42no—
49#6662—42no—
50#5090—51no—
51#5078—51no—
52#4849—51no—
53#4831—51no—
54C3×#332—51no—
55#4486D511yescharacteristic
56#4480—51no—
57C5×C4⋊Q8—31no—
58C2×#689—61no—
59C2×Dic20—61no—
60#4015C2×D311yescharacteristic
61C4×Dic10—31no—
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64#3967—61no—
65#3948—61no—
66#3947—61no—
67#3946—61no—
68#3939—61no—
69#3939—61no—
70C4⋊#168C2×D311yescharacteristic
71C4×#168—31no—
72#1694—151noSylow
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—21no—
77C2×Dic15—21no—
78Dic30—21no—
79Dic30—21no—
80C2×C5×Dic3—41no—
81C5×Dic6—41no—
82C5×Dic6—41no—
83C2×C3×Dic5—41no—
84C3×Dic10—41no—
85C3×Dic10—41no—
86C3×C5×C8—41no—
87C3⋊#168—21no—
88C3⋊#168Q1612yescomplemented
89C3×#168—41no—
90C5×C3⋊C8—41no—
91C3×C4⋊Q8—51no—
92C2×#216—101no—
93C2×Dic12—101no—
94#869C2×D511yescharacteristic
95C4×Dic6—51no—
96C3×C4⋊C8—51no—
97C3×C4⋊C8C2×D511yescharacteristic
98#835—101no—
99#816—101no—
100#815—101no—
101Dic3⋊C8—101no—
102#807—101no—
103#807—101no—
104C4⋊(C3⋊C8)C2×D511yescharacteristic
105C4×C3⋊C8—51no—
106C2×C5×Q8—61no—
107C2×Dic10—21no—
108C2×Dic10—31no—
109C2×C5×C8—21no—
110C2×C5×C8—61no—
111C5×C4⋊C4—61no—
112C5×C4⋊C4—61no—
113C42×C5C22×D311yescharacteristic
114#689—122no—
115C4⋊Dic5—21no—
116C4⋊Dic5—21no—
117C4⋊Dic5—31no—
118#683—61no—
119C4×Dic5—61no—
120C2×#168—21no—
121C2×#168—31no—
122C2×#168—31no—
123Dic20—122no—
124#500—151no—
125#462—151no—
126#462—151no—
127#446—151no—
128#334—151no—
129#332—31no—
130#332—51no—
131C22×C3×C5#12111yescharacteristic
132C3×C4×C5—21no—
133C3×C4×C5C2×Q1611yescharacteristic
134C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
135C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C3×C4×C5#13711yescharacteristic
137Dic15—41no—
138Dic15—41no—
139C3×Dic5—81no—
140C5×Dic3—81no—
141C2×C3×Q8—101no—
142C2×Dic6—21no—
143C2×Dic6—51no—
144C2×C3×C8—21no—
145C2×C3×C8—101no—
146C3×C4⋊C4—101no—
147C3×C4⋊C4—101no—
148C3×C42C22×D511yescharacteristic
149#216—202no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—51no—
153Dic3⋊C4—101no—
154C4×Dic3—101no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—51no—
157C2×C3⋊C8—51no—
158Dic12—202no—
159C5×Q8—121no—
160C5×Q8—121no—
161C2×C4×C5—121no—
162C2×C4×C5#23511yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5D3×D411yescharacteristic
165C2×Dic5—41no—
166C2×Dic5—61no—
167C2×Dic5—61no—
168Dic10—41no—
169Dic10—41no—
170Dic10—61no—
171Dic10—61no—
172C5×C8—41no—
173C5×C8—121no—
174#168—32no—
175#168—41no—
176#168—61no—
177C2×Q16—301no—
178C2×Q16—301no—
179C4⋊Q8—31no—
180C4⋊Q8—51no—
181C4×Q8—151no—
182#107—301no—
183#107—301no—
184C4⋊C8—31no—
185C4⋊C8—51no—
186C4⋊C8—301no—
187C4⋊C8D3×D511yescharacteristic
188#103—301no—
189#103—301no—
190#97—301no—
191C4×C8—151no—
192C2×C3×C5#46211yescharacteristic
193C2×C3×C5#46911yescharacteristic
194C2×C3×C5#47311yescharacteristic
195C3×Q8—201no—
196C3×Q8—201no—
197C2×C3×C4—201no—
198C2×C3×C4#70911yescharacteristic
199C2×C3×C4D4×D511yescharacteristic
200C2×C3×C4D4×D511yescharacteristic
201C2×Dic3—41no—
202C2×Dic3—101no—
203C2×Dic3—101no—
204Dic6—41no—
205Dic6—41no—
206Dic6—101no—
207Dic6—101no—
208C3×C8—41no—
209C3×C8—201no—
210C3⋊C8—41no—
211C3⋊C8—52no—
212C3⋊C8—101no—
213C22×C5#88411yescharacteristic
214C4×C5—21no—
215C4×C5—241no—
216C4×C5#91111yescharacteristic
217C4×C5#91411yescharacteristic
218C4×C5#91511yescharacteristic
219C4×C5D3×Q1611yescharacteristic
220Dic5—81no—
221Dic5—121no—
222Dic5—121no—
223C2×Q8—61no—
224C2×Q8—101no—
225C2×Q8—151no—
226Q16—602no—
227Q16—602no—
228C2×C8—21no—
229C2×C8—61no—
230C2×C8—101no—
231C2×C8—151no—
232C2×C8—151no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—101no—
236C4⋊C4—101no—
237C4⋊C4—151no—
238C4⋊C4—301no—
239C42—301no—
240C42C2×D3×D511yescharacteristic
241C3×C5#169411yescharacteristic, complemented, Hall
242C22×C3#403011yescharacteristic
243C3×C4—21no—
244C3×C4—401no—
245C3×C4#405711yescharacteristic
246C3×C4#406011yescharacteristic
247C3×C4#406111yescharacteristic
248C3×C4D5×Q1611yescharacteristic
249Dic3—81no—
250Dic3—201no—
251Dic3—201no—
252C2×C5#475511yescharacteristic
253C2×C5#478211yescharacteristic
254C2×C5#479511yescharacteristic
255Q8—121no—
256Q8—121no—
257Q8—201no—
258Q8—201no—
259Q8—301no—
260Q8—301no—
261C2×C4—121no—
262C2×C4—201no—
263C2×C4—301no—
264C2×C4—301no—
265C2×C4#677111yescharacteristic
266C2×C4#677711yescharacteristic
267C2×C4#679011yescharacteristic
268C8—41no—
269C8—121no—
270C8—152no—
271C8—201no—
272C8—301no—
273C2×C3#6504411yescharacteristic
274C2×C3#6507111yescharacteristic
275C2×C3#6508211yescharacteristic
276C5#6847511yescharacteristic, complemented, Sylow
277C22#9146111yescharacteristic
278C4—21no—
279C4—241no—
280C4—401no—
281C4—601no—
282C4—601no—
283C4#9125711yescharacteristic
284C4#9125811yescharacteristic
285C4#9148811yescharacteristic
286C4#9151111yescharacteristic
287C3#1059926811yescharacteristic, complemented, Sylow
288C2#1174742711yescharacteristic
289C2#1174792511yescharacteristic
290C2#1174820111yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1694
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
88. C3⋊#168Q16semidirect
241. C3×C5#1694semidirect
276. C5#68475semidirect
287. C3#10599268semidirect

Maximal subgroups

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

subgroupindex
#117509322
#117471052
#117471042
#117469622
C5×#44862
C3×#647062
#117458652
#105992683
#684755