Finite Group Databasebeta

← #14292812

Subgroups — #14292812

Order 1920.

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

normal subgroups only

This group has 304 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
1#11751179C211yesmaximal, characteristic
2C3×#65379C211yesmaximal, characteristic
3#11747095C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic
6#11745865C211yesmaximal, characteristic
7#11745860C211yesmaximal, characteristic
8#10599268—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C2×C3×#689—21no—
12C3×C4×Dic10C2211yescharacteristic
13C2×#6662—21no—
14#91091—21no—
15#91091—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3967—21no—
20C3×C4⋊#168C2211yescharacteristic
21#90982—21no—
22#90974—21no—
23#90952—21no—
24#71057—51nomaximal, Hall
25#65379D311yescharacteristic
26#65367—31no—
27#65138—31no—
28#65120—31no—
29C5×#332—31no—
30#64706—31no—
31#64700—31no—
32C2×C3×C5×Q8—21no—
33C2×Dic30—21no—
34C2×C3×Dic10D411yescharacteristic
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C2×C5×C3⋊C8—21no—
43C2×C5×C3⋊C8—21no—
44C3×#689—42no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48C2×C3×#168—21no—
49#6662—42no—
50C3×#462—51no—
51#5078—51no—
52#5031—51no—
53#5024—51no—
54#4547D511yescharacteristic
55#4482—51no—
56#4480—51no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#689—21no—
59C2×Dic20—61no—
60#4015—31no—
61C4×Dic10C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8—31no—
64#3967—21no—
65#3948—61no—
66#3947—61no—
67#3946—61no—
68#3939—61no—
69#3939—61no—
70C4⋊#168C2×D311yescharacteristic
71C4×#168—31no—
72#1694—151noSylow
73C3×C5×Q8—41no—
74C3×C5×Q8—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—41no—
80Dic30—41no—
81Dic30—41no—
82C2×C3×Dic5—21no—
83C2×C3×Dic5—21no—
84C3×Dic10—21no—
85C3×Dic10—21no—
86C3⋊#168—21no—
87C3⋊#168Q1612yescomplemented
88C3×#168—41no—
89C5×C3⋊C8—41no—
90C5×C3⋊C8—41no—
91C2×C3×Q16—101no—
92C3×C4⋊Q8C2×D511yescharacteristic
93C3×C4×Q8—51no—
94C2×#216—101no—
95#869—51no—
96C3×C4⋊C8—51no—
97C3×#103—101no—
98#810—101no—
99#807—101no—
100#807—101no—
101C4⋊(C3⋊C8)—101no—
102C4⋊(C3⋊C8)C2×D511yescharacteristic
103C4⋊(C3⋊C8)C2×D511yescharacteristic
104#803—101no—
105C4×C3⋊C8—51no—
106C2×C5×Q8—21no—
107C2×Dic10—61no—
108C2×Dic10#6711yescharacteristic
109C2×C5×C8—61no—
110C2×C5×C8—61no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C42×C5C22×D311yescharacteristic
114#689—42no—
115C4⋊Dic5—61no—
116C4⋊Dic5—61no—
117C4⋊Dic5#6711yescharacteristic
118#683—21no—
119C4×Dic5—21no—
120C2×#168—21no—
121C2×#168—31no—
122C2×#168—31no—
123Dic20—122no—
124#500—151no—
125#462—51no—
126#462—151no—
127#446—151no—
128#334—151no—
129#332—31no—
130#332—151no—
131C22×C3×C5#12111yescharacteristic
132C3×C4×C5—21no—
133C3×C4×C5—81no—
134C3×C4×C5C2×Q1611yescharacteristic
135C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C3×C4×C5#13711yescharacteristic
138Dic15—81no—
139C3×Dic5—41no—
140C3×Dic5—41no—
141C2×C3×Q8—21no—
142C2×C3×Q8—51no—
143C2×Dic6—101no—
144C3×Q16—202no—
145C2×C3×C8—101no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—51no—
149C3×C4⋊C4—101no—
150C3×C42—101no—
151C3×C42C22×D511yescharacteristic
152#216—202no—
153C4⋊Dic3—101no—
154C4⋊Dic3—101no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—51no—
158C2×C3⋊C8—51no—
159C5×Q8—41no—
160C5×Q8—41no—
161C2×C4×C5—41no—
162C2×C4×C5D3×D411yescharacteristic
163C2×C4×C5#23711yescharacteristic
164C2×C4×C5C2×#6711yescharacteristic
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5—121no—
168Dic10—21no—
169Dic10—21no—
170Dic10—121no—
171Dic10—121no—
172C5×C8—121no—
173C5×C8—121no—
174#168—32no—
175#168—41no—
176#168—61no—
177C2×Q16—101no—
178C2×Q16—301no—
179C4⋊Q8—151no—
180C4⋊Q8D3×D511yescharacteristic
181C4×Q8—51no—
182#107—301no—
183#107—301no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—51no—
187C4⋊C8—301no—
188#103—101no—
189#103—301no—
190#97—301no—
191C4×C8—151no—
192C2×C3×C5#46211yescharacteristic
193C2×C3×C5#46911yescharacteristic
194C2×C3×C5#47311yescharacteristic
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—101no—
198C3×Q8—101no—
199C2×C3×C4—41no—
200C2×C3×C4—101no—
201C2×C3×C4—101no—
202C2×C3×C4#70911yescharacteristic
203C2×C3×C4D4×D511yescharacteristic
204C2×C3×C4D4×D511yescharacteristic
205C2×Dic3—201no—
206Dic6—201no—
207Dic6—201no—
208C3×C8—201no—
209C3⋊C8—41no—
210C3⋊C8—41no—
211C3⋊C8—52no—
212C3⋊C8—101no—
213C22×C5#93911yescharacteristic
214C4×C5—21no—
215C4×C5—81no—
216C4×C5D3×Q1611yescharacteristic
217C4×C5#91811yescharacteristic
218C4×C5#93211yescharacteristic
219C4×C5#94911yescharacteristic
220Dic5—41no—
221Dic5—41no—
222Dic5—241no—
223C2×Q8—21no—
224C2×Q8—51no—
225C2×Q8—301no—
226Q16—202no—
227Q16—602no—
228C2×C8—61no—
229C2×C8—61no—
230C2×C8—101no—
231C2×C8—151no—
232C2×C8—151no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—51no—
236C4⋊C4—101no—
237C4⋊C4—301no—
238C4⋊C4—301no—
239C42—101no—
240C42C2×D3×D511yescharacteristic
241C3×C5#169411yescharacteristic, complemented, Hall
242C22×C3#403011yescharacteristic
243C3×C4—21no—
244C3×C4—81no—
245C3×C4—201no—
246C3×C4—201no—
247C3×C4#405711yescharacteristic
248C3×C4#406011yescharacteristic
249C3×C4#406111yescharacteristic
250C3×C4D5×Q1611yescharacteristic
251Dic3—401no—
252C2×C5#503911yescharacteristic
253C2×C5#518211yescharacteristic
254C2×C5#520411yescharacteristic
255Q8—41no—
256Q8—41no—
257Q8—101no—
258Q8—101no—
259Q8—601no—
260Q8—601no—
261C2×C4—41no—
262C2×C4—101no—
263C2×C4—101no—
264C2×C4—601no—
265C2×C4#677911yescharacteristic
266C2×C4D5×#6711yescharacteristic
267C2×C4#679011yescharacteristic
268C8—121no—
269C8—121no—
270C8—152no—
271C8—201no—
272C8—301no—
273C2×C3#6504411yescharacteristic
274C2×C3#6507111yescharacteristic
275C2×C3#6508211yescharacteristic
276C5#7105711yescharacteristic, complemented, Sylow
277C22#9155011yescharacteristic
278C4—21no—
279C4—81no—
280C4—201no—
281C4—201no—
282C4—1201no—
283C4#9147811yescharacteristic
284C4#9149111yescharacteristic
285C4#9151111yescharacteristic
286C4#9152411yescharacteristic
287C3#1059926811yescharacteristic, complemented, Sylow
288C2#1174902711yescharacteristic
289C2#1174925411yescharacteristic
290C2#1174937811yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1694
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
87. C3⋊#168Q16semidirect
241. C3×C5#1694semidirect
276. C5#71057semidirect
287. C3#10599268semidirect

Maximal subgroups

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

subgroupindex
#117511792
C3×#653792
#117470952
#117468622
C5×#45472
#117458652
#117458602
#105992683
#710575