Finite Group Databasebeta

← #14289556

Subgroups — #14289556

Order 1920.

412 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752473C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic
3C5×#5092C211yesmaximal, characteristic
4C3×#65380C211yesmaximal, characteristic
5#11745862C211yesmaximal, characteristic
6#11745844C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic
8#10602100—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C2×C5×#216—22no—
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91470—21no—
15#91468—21no—
16#91333—21no—
17#91331—21no—
18#91329—22no—
19#91094—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71161—51nomaximal, Hall
27#66056—31no—
28C5×#494—31no—
29#65380—31no—
30#65380D311yescharacteristic
31#64766—31no—
32#64676—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D412yes—
37C2×C3×Dic10D411yescharacteristic
38C2×#1204—22no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×#216—44no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54#6669—22no—
55#6668—22no—
56Dic3×Dic5—22no—
57Q8×Dic6—51no—
58C3×#477—51no—
59#5092D511yescharacteristic
60#5091—51no—
61#4535—51no—
62#4484—51no—
63#4481—51no—
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4090—62no—
68#4034—61no—
69#4034—61no—
70#4033—61no—
71#4033—61no—
72C4×Dic10—31no—
73C4×Dic10C2×D311yescharacteristic
74C4×C5×C8—31no—
75#3942—21no—
76#3942—61no—
77#3939—21no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1633—151noSylow
82C3×C5×Q8—42no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89Dic30—21no—
90Dic30Q1612yescomplemented
91C2×C5×Dic3—22no—
92C5×Dic6—42no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×Dic10—21no—
96C3×Dic10Q1612yescomplemented
97#1204—82no—
98C3⋊#168—41no—
99C3×#168—41no—
100C5×C3⋊C8—22no—
101C3×C4⋊Q8C2×D511yescharacteristic
102C3×C4×Q8—51no—
103Q8×Dic3—101no—
104C2×#216—22no—
105#888—101no—
106#888—102no—
107#869—101no—
108#869C2×D511yescharacteristic
109C4×Dic6—51no—
110C4×Dic6—101no—
111C3×#107—101no—
112C3×C4⋊C8—51no—
113C3×#103—101no—
114#810—101no—
115#807—101no—
116C4⋊(C3⋊C8)—51no—
117C4×C3⋊C8C2×D511yescharacteristic
118C2×C5×Q8—21no—
119C2×C5×Q8—32no—
120C2×Dic10—31no—
121C2×Dic10—62no—
122C2×Dic10#6711yescharacteristic
123C5×Q16—124no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130C4⋊Dic5—31no—
131C4⋊Dic5#6711yescharacteristic
132#683—21no—
133#683—62no—
134#683—62no—
135#683—61no—
136C4×Dic5—21no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—21no—
140C2×#168—61no—
141Q82—151no—
142#494—31no—
143#477—51no—
144#477—151no—
145#333—151no—
146Q8⋊C8—151no—
147Q8⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C3×C4×C5—21no—
150C3×C4×C5—81no—
151C3×C4×C5C2×Q1611yescharacteristic
152C3×C4×C5C2×Q1611yescharacteristic
153C3×C4×C5#13711yescharacteristic
154C3×C4×C5#13711yescharacteristic
155Dic15—22no—
156Dic15—41no—
157C3×Dic5—22no—
158C3×Dic5—41no—
159C5×Dic3—42no—
160C2×C3×Q8—21no—
161C2×C3×Q8—51no—
162C2×Dic6—51no—
163C2×Dic6—102no—
164C2×Dic6C22⋊D512yes—
165C2×C3×C8—101no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—101no—
170C3×C42—101no—
171C3×C42C22×D511yescharacteristic
172#216—44no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—51no—
176C4⋊Dic3—102no—
177Dic3⋊C4—102no—
178Dic3⋊C4—101no—
179C4×Dic3—102no—
180C4×Dic3—101no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183C5×Q8—42no—
184C5×Q8—122no—
185C2×C4×C5—41no—
186C2×C4×C5—62no—
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5C2×#6711yescharacteristic
190C2×Dic5—21no—
191C2×Dic5—21no—
192C2×Dic5—61no—
193C2×Dic5—61no—
194Dic10—21no—
195Dic10—32no—
196Dic10—61no—
197Dic10—242no—
198Dic10#21612yescomplemented
199C5×C8—62no—
200#168—41no—
201#168—121no—
202C2×Q16—62no—
203C4⋊Q8—31no—
204C4⋊Q8—301no—
205C4⋊Q8—301no—
206C4⋊Q8—302no—
207C4⋊Q8D3×D511yescharacteristic
208C4×Q8—51no—
209C4×Q8—151no—
210C4×Q8—301no—
211C4×Q8—301no—
212#107—101no—
213#107—301no—
214C4⋊C8—51no—
215C4⋊C8—151no—
216#103—101no—
217#103—301no—
218C4×C8—31no—
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—42no—
223C3×Q8—52no—
224C3×Q8—101no—
225C2×C3×C4—41no—
226C2×C3×C4—101no—
227C2×C3×C4—101no—
228C2×C3×C4D4×D511yescharacteristic
229C2×C3×C4D4×D511yescharacteristic
230C2×C3×C4C2×C22⋊D511yescharacteristic
231C2×Dic3—22no—
232C2×Dic3—101no—
233C2×Dic3—101no—
234Dic6—42no—
235Dic6—52no—
236Dic6—101no—
237Dic6—402no—
238C3×C8—201no—
239C3⋊C8—22no—
240C3⋊C8—201no—
241C22×C5#93711yescharacteristic
242C4×C5—21no—
243C4×C5—81no—
244C4×C5—122no—
245C4×C5D3×Q1611yescharacteristic
246C4×C5#91811yescharacteristic
247C4×C5C2×#21611yescharacteristic
248C4×C5#95111yescharacteristic
249Dic5—22no—
250Dic5—41no—
251Dic5—62no—
252Dic5—121no—
253C2×Q8—21no—
254C2×Q8—32no—
255C2×Q8—51no—
256C2×Q8—151no—
257C2×Q8—302no—
258Q16—124no—
259C2×C8—61no—
260C2×C8—101no—
261C2×C8—301no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—51no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—101no—
268C4⋊C4—151no—
269C4⋊C4—302no—
270C4⋊C4—302no—
271C4⋊C4—301no—
272C42—101no—
273C42—302no—
274C42—301no—
275C42C2×D3×D511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#408311yescharacteristic
278C3×C4—21no—
279C3×C4—81no—
280C3×C4—102no—
281C3×C4—201no—
282C3×C4D5×Q1611yescharacteristic
283C3×C4D5×Q1611yescharacteristic
284C3×C4#406411yescharacteristic
285C3×C4#406411yescharacteristic
286Dic3—42no—
287Dic3—102no—
288Dic3—201no—
289C2×C5#505011yescharacteristic
290C2×C5#518611yescharacteristic
291C2×C5#519811yescharacteristic
292Q8—42no—
293Q8—52no—
294Q8—101no—
295Q8—122no—
296Q8—152no—
297Q8—301no—
298Q8—1202no—
299C2×C4—41no—
300C2×C4—62no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—301no—
304C2×C4—301no—
305C2×C4D5×#6711yescharacteristic
306C2×C4D3×C22⋊D511yescharacteristic
307C2×C4#679011yescharacteristic
308C8—62no—
309C8—201no—
310C8—601no—
311C2×C3#6536611yescharacteristic
312C2×C3#6547511yescharacteristic
313C2×C3#6547511yescharacteristic
314C5#7116111yescharacteristic, complemented, Sylow
315C22#9157711yescharacteristic
316C4—21no—
317C4—81no—
318C4—102no—
319C4—122no—
320C4—201no—
321C4—302no—
322C4—601no—
323C4D5×#21611yescharacteristic
324C4#9150811yescharacteristic
325C4#9151111yescharacteristic
326C4#9151211yescharacteristic
327C3#1060210011yescharacteristic, complemented, Sylow
328C2#1174916511yescharacteristic
329C2#1174940011yescharacteristic
330C2#1174940211yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1633
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
90. Dic30Q16semidirect
96. C3×Dic10Q16semidirect
198. Dic10#216semidirect
276. C3×C5#1633semidirect
314. C5#71161semidirect
327. C3#10602100semidirect

Maximal subgroups

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

subgroupindex
#117524732
#117511922
C5×#50922
C3×#653802
#117458622
#117458442
#117458412
#106021003
#711615