Finite Group Databasebeta

← #14292018

Subgroups — #14292018

Order 1920.

332 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65123C211yesmaximal, characteristic
2#11747062C211yesmaximal, characteristic
3#11746929C211yesmaximal, characteristic, complemented
4#11746886C211yesmaximal, characteristic
5#11746307C211yesmaximal, characteristic, complemented
6C5×#4482C211yesmaximal, characteristic, complemented
7#11745864C211yesmaximal, characteristic, complemented
8#10599237—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×C8×D5—21no—
12C3×C4×D20C2211yescharacteristic
13C2×#6657—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×#3952—21no—
18C3×C4×#168C2211yescharacteristic
19#90989—21no—
20#90974—21no—
21#90973—21no—
22#90973—21no—
23#90964—21no—
24#70854—51nomaximal, Hall
25#65376—31no—
26#65370—31no—
27#65130—31no—
28#65123D311yescharacteristic
29C5×#332—31no—
30#64706—31no—
31#64700—31no—
32C2×Dic30—21no—
33C2×C5×Dic6—21no—
34C2×C3×D20D411yescharacteristic
35C2×C3×C4×D5—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168—21no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8—21no—
44C3×#685—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C2×C3×#168D411yescharacteristic
47C2×C3×#168D411yescharacteristic
48C3×C8×D5—42no—
49#6657—42no—
50C3×C8×D4—51no—
51#5019—51no—
52#5007—51no—
53#4681—51no—
54#4486—51no—
55#4482D511yescharacteristic, complemented
56#4457—51no—
57C5×C4⋊Q8—31no—
58C2×#677—61no—
59C2×C8×D5—21no—
60C4×D20C2×D311yescharacteristic
61#4015—31no—
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64#3967—61no—
65#3967—61no—
66#3952—21no—
67#3948—61no—
68#3941—61no—
69#3939—61no—
70C4⋊#168—31no—
71C4×#168C2×D311yescharacteristic
72#1679—151noSylow
73C22×C3×D5—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—41no—
78Dic30—41no—
79Dic30—41no—
80C2×C5×Dic3—41no—
81C5×Dic6—41no—
82C5×Dic6—41no—
83C2×C3×Dic5—21no—
84C3×D20—21no—
85C3×D20SD1612yes—
86C3×C4×D5—41no—
87C3×C4×D5—41no—
88C3×C5×C8—41no—
89C3⋊#168—41no—
90C3×#168—21no—
91C3×#168—21no—
92C5×C3⋊C8—41no—
93C22×C3×C8—101no—
94C3×C4×D4—51no—
95C2×#214—101no—
96#869—51no—
97#869C2×D511yescharacteristic
98C3×C4⋊C8C2×D511yescharacteristic
99C3×C22⋊C8—101no—
100C3×C4×C8—51no—
101#832—101no—
102#816—101no—
103#816—101no—
104#810—101no—
105#807—101no—
106C4⋊(C3⋊C8)—51no—
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108C2×C5×Q8—61no—
109C2×D20D1211yescharacteristic
110C2×C4×D5—21no—
111C2×Dic10—61no—
112C2×C5×C8—21no—
113C2×C5×C8—61no—
114C5×C4⋊C4—61no—
115C5×C4⋊C4—61no—
116C42×C5C22×D311yescharacteristic
117#685—21no—
118C4⋊Dic5—61no—
119C4⋊Dic5—61no—
120C4⋊Dic5D1211yescharacteristic
121C2×#168—61no—
122C2×#168#6711yescharacteristic
123C2×#168#6711yescharacteristic
124#677—122no—
125C8×D5—42no—
126#487—151no—
127#474—151no—
128#461—151no—
129C8×D4—51no—
130#334—151no—
131#332—31no—
132#332—151no—
133C22×C3×C5#12111yescharacteristic
134C2×C3×D5—22no—
135C2×C3×D5—41no—
136C2×C3×D5—41no—
137C3×C4×C5—21no—
138C3×C4×C5C2×SD1611yescharacteristic
139C3×C4×C5#13511yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
142Dic15—81no—
143C3×Dic5—41no—
144C5×Dic3—81no—
145C2×C3×D4—51no—
146C22×C3×C4—101no—
147C2×Dic6—21no—
148C2×Dic6—101no—
149C2×C3×C8—21no—
150C2×C3×C8—51no—
151C2×C3×C8—51no—
152C2×C3×C8—202no—
153C3×C4⋊C4—51no—
154C3×C22⋊C4—101no—
155C3×C42C22×D511yescharacteristic
156#214—202no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3—101no—
160C4⋊Dic3—101no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—101no—
163C22×D5—21no—
164C5×Q8—121no—
165C5×Q8—121no—
166C2×C4×C5—121no—
167C2×C4×C5C2×D1211yescharacteristic
168C2×C4×C5#23511yescharacteristic
169C2×C4×C5C2×#6711yescharacteristic
170C2×Dic5—21no—
171C2×Dic5—121no—
172D20—21no—
173D20#20412yes—
174C4×D5—41no—
175C4×D5—41no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—41no—
179C5×C8—121no—
180#168—21no—
181#168—21no—
182#168—121no—
183C2×SD16—301no—
184C22×C8—101no—
185C4⋊Q8—31no—
186C4⋊Q8—151no—
187C4×D4—51no—
188#107—301no—
189C4⋊C8—31no—
190C4⋊C8—151no—
191C4⋊C8D3×D511yescharacteristic
192#103—301no—
193#103—301no—
194#103—301no—
195#102—301no—
196C22⋊C8—101no—
197C4×C8—51no—
198C2×C3×C5#46311yescharacteristic
199C2×C3×C5#46511yescharacteristic
200C2×C3×C5#47311yescharacteristic
201C3×D5—42no—
202C23×C3—101no—
203C3×D4—52no—
204C3×D4—101no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4#70911yescharacteristic
209C2×C3×C4D4×D511yescharacteristic
210C2×C3×C4D4×D511yescharacteristic
211C2×Dic3—41no—
212C2×Dic3—201no—
213Dic6—41no—
214Dic6—41no—
215Dic6—201no—
216Dic6—201no—
217C3×C8—41no—
218C3×C8—101no—
219C3×C8—101no—
220C3⋊C8—41no—
221C3⋊C8—201no—
222C22×C5#93011yescharacteristic
223C2×D5—22no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—21no—
227C4×C5—241no—
228C4×C5C2×#20411yescharacteristic
229C4×C5#90411yescharacteristic
230C4×C5#93211yescharacteristic
231C4×C5#95011yescharacteristic
232Dic5—41no—
233Dic5—241no—
234C2×Q8—61no—
235C2×Q8—301no—
236C2×D4—51no—
237C22×C4—101no—
238SD16—602no—
239C2×C8—21no—
240C2×C8—51no—
241C2×C8—51no—
242C2×C8—61no—
243C2×C8—202no—
244C2×C8—301no—
245C4⋊C4—51no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—301no—
249C4⋊C4—301no—
250C22⋊C4—101no—
251C42C2×D3×D511yescharacteristic
252C3×C5#167911yescharacteristic, complemented, Hall
253C22×C3—102no—
254C22×C3—201no—
255C22×C3—201no—
256C22×C3#403011yescharacteristic
257C3×C4—21no—
258C3×C4—201no—
259C3×C4#405711yescharacteristic
260C3×C4D5×SD1611yescharacteristic
261C3×C4#406211yescharacteristic
262C3×C4#406511yescharacteristic
263Dic3—81no—
264Dic3—401no—
265C2×C5#501611yescharacteristic
266C2×C5#511411yescharacteristic
267C2×C5#514311yescharacteristic
268D5—42no—
269C23—101no—
270Q8—121no—
271Q8—121no—
272Q8—601no—
273Q8—601no—
274D4—52no—
275D4—101no—
276C2×C4—101no—
277C2×C4—121no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—601no—
281C2×C4#677111yescharacteristic
282C2×C4D5×D1211yescharacteristic
283C2×C4D5×#6711yescharacteristic
284C8—41no—
285C8—101no—
286C8—101no—
287C8—121no—
288C8—601no—
289C2×C3—202no—
290C2×C3#6504411yescharacteristic
291C2×C3#6507611yescharacteristic
292C2×C3#6509611yescharacteristic
293C5#7085411yescharacteristic, complemented, Sylow
294C22—102no—
295C22—201no—
296C22—201no—
297C22#9144811yescharacteristic
298C4—21no—
299C4—201no—
300C4—241no—
301C4—1201no—
302C4D5×#20411yescharacteristic
303C4#9127111yescharacteristic
304C4#9148911yescharacteristic
305C4#9151411yescharacteristic
306C3#1059923711yescharacteristic, complemented, Sylow
307C2—202no—
308C2#1174736811yescharacteristic
309C2#1174793811yescharacteristic
310C2#1174821711yescharacteristic
subgroupG/H
centerC22#91448
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1679
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
3. #11746929C2semidirect
5. #11746307C2semidirect
6. C5×#4482C2semidirect
7. #11745864C2semidirect
55. #4482D5semidirect
252. C3×C5#1679semidirect
293. C5#70854semidirect
306. C3#10599237semidirect

Maximal subgroups

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

subgroupindex
C3×#651232
#117470622
#117469292
#117468862
#117463072
C5×#44822
#117458642
#105992373
#708545