Finite Group Databasebeta

← #14289557

Subgroups — #14289557

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#11752472C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic
3C5×#5091C211yesmaximal, characteristic
4C3×#65381C211yesmaximal, characteristic
5#11745861C211yesmaximal, characteristic
6#11745845C211yesmaximal, characteristic
7#11745843C211yesmaximal, characteristic
8#10601954—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C2×C3×#689—22no—
13C3×#4015C2211yescharacteristic
14#91470—21no—
15#91469—21no—
16#91344—21no—
17#91340—21no—
18#91327—22no—
19#91094—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#810—21no—
23C5×#807—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#71307—51nomaximal, Hall
27Q8×Dic10—31no—
28C5×#477—31no—
29#65381D311yescharacteristic
30#65380—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64701—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10D412yes—
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×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×#689—44no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6669—22no—
56Dic3×Dic5—22no—
57#5722—51no—
58C3×#494—51no—
59#5091—51no—
60#5091D511yescharacteristic
61#4546—51no—
62#4456—51no—
63#4456—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×Q8—31no—
66Q8×Dic5—61no—
67C2×#689—22no—
68#4034—61no—
69#4034—62no—
70#4015—61no—
71#4015C2×D311yescharacteristic
72C4×Dic10—31no—
73C4×Dic10—61no—
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3942—61no—
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—21no—
92C2×C5×Dic3—21no—
93C5×Dic6—21no—
94C5×Dic6Q1612yescomplemented
95C2×C3×Dic5—22no—
96C3×Dic10—42no—
97#1204—82no—
98C3⋊#168—41no—
99C3×#168—22no—
100C5×C3⋊C8—41no—
101C2×C3×Q16—102no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#944—102no—
105#888—101no—
106#888—101no—
107#887—101no—
108#887—101no—
109C4×Dic6—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×C4×C8—51no—
112#810—21no—
113#810—101no—
114#807—21no—
115#807—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C2×C5×Q8—21no—
119C2×C5×Q8—31no—
120C2×Dic10—31no—
121C2×Dic10—62no—
122C2×Dic10#6712yes—
123C2×C5×C8—61no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C42×C5—61no—
129C42×C5C22×D311yescharacteristic
130#689—44no—
131C4⋊Dic5—21no—
132C4⋊Dic5—21no—
133C4⋊Dic5—31no—
134C4⋊Dic5—62no—
135#683—62no—
136#683—61no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—21no—
140C2×#168—61no—
141Q82—151no—
142#494—51no—
143#477—31no—
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—42no—
158C5×Dic3—22no—
159C5×Dic3—41no—
160C2×C3×Q8—21no—
161C2×C3×Q8—52no—
162C2×Dic6—51no—
163C2×Dic6—102no—
164C2×Dic6C22⋊D511yescharacteristic
165C3×Q16—204no—
166C2×C3×C8—101no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C42C22×D511yescharacteristic
172C4⋊Dic3—51no—
173C4⋊Dic3C22⋊D511yescharacteristic
174Dic3⋊C4—21no—
175Dic3⋊C4—102no—
176Dic3⋊C4—102no—
177Dic3⋊C4—101no—
178C4×Dic3—21no—
179C4×Dic3—102no—
180C4×Dic3—101no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183C5×Q8—32no—
184C5×Q8—42no—
185C5×Q8—61no—
186C2×C4×C5—41no—
187C2×C4×C5—61no—
188C2×C4×C5—61no—
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—22no—
193C2×Dic5—61no—
194C2×Dic5—61no—
195Dic10—32no—
196Dic10—42no—
197Dic10—61no—
198Dic10—242no—
199C5×C8—121no—
200#168—22no—
201#168—121no—
202C2×Q16—102no—
203C4⋊Q8—51no—
204C4⋊Q8—301no—
205C4⋊Q8—301no—
206C4⋊Q8—302no—
207C4⋊Q8D3×D511yescharacteristic
208C4×Q8—31no—
209C4×Q8—151no—
210C4×Q8—301no—
211C4×Q8—301no—
212#107—61no—
213#107—301no—
214C4⋊C8—31no—
215C4⋊C8—151no—
216#103—61no—
217#103—301no—
218C4×C8—51no—
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—42no—
223C3×Q8—202no—
224C2×C3×C4—41no—
225C2×C3×C4—102no—
226C2×C3×C4D4×D511yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4C2×C22⋊D511yescharacteristic
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—101no—
232C2×Dic3—101no—
233Dic6—21no—
234Dic6—52no—
235Dic6—101no—
236Dic6—402no—
237Dic6#68912yescomplemented
238C3×C8—102no—
239C3⋊C8—41no—
240C3⋊C8—201no—
241C22×C5#93711yescharacteristic
242C4×C5—21no—
243C4×C5—62no—
244C4×C5—81no—
245C4×C5—121no—
246C4×C5D3×Q1611yescharacteristic
247C4×C5D3×Q1611yescharacteristic
248C4×C5#91811yescharacteristic
249C4×C5#91811yescharacteristic
250Dic5—42no—
251Dic5—62no—
252Dic5—121no—
253C2×Q8—21no—
254C2×Q8—31no—
255C2×Q8—52no—
256C2×Q8—151no—
257C2×Q8—302no—
258Q16—204no—
259C2×C8—61no—
260C2×C8—101no—
261C2×C8—301no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—31no—
265C4⋊C4—61no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C4⋊C4—151no—
269C4⋊C4—302no—
270C4⋊C4—302no—
271C4⋊C4—301no—
272C42—61no—
273C42—302no—
274C42—301no—
275C42C2×D3×D511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#408311yescharacteristic
278C3×C4—21no—
279C3×C4—81no—
280C3×C4—202no—
281C3×C4D5×Q1611yescharacteristic
282C3×C4#406411yescharacteristic
283C3×C4C2×#68911yescharacteristic
284C3×C4#409711yescharacteristic
285Dic3—22no—
286Dic3—41no—
287Dic3—102no—
288Dic3—201no—
289C2×C5#507711yescharacteristic
290C2×C5#518611yescharacteristic
291C2×C5#518611yescharacteristic
292Q8—32no—
293Q8—42no—
294Q8—61no—
295Q8—152no—
296Q8—202no—
297Q8—301no—
298Q8—1202no—
299C2×C4—41no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—102no—
303C2×C4—301no—
304C2×C4—301no—
305C2×C4D5×#6711yescharacteristic
306C2×C4D3×C22⋊D511yescharacteristic
307C2×C4#679011yescharacteristic
308C8—102no—
309C8—121no—
310C8—601no—
311C2×C3#6533911yescharacteristic
312C2×C3#6547511yescharacteristic
313C2×C3#6548711yescharacteristic
314C5#7130711yescharacteristic, complemented, Sylow
315C22#9157711yescharacteristic
316C4—21no—
317C4—62no—
318C4—81no—
319C4—121no—
320C4—202no—
321C4—302no—
322C4—601no—
323C4D3×#68911yescharacteristic
324C4#9151011yescharacteristic
325C4#9151111yescharacteristic
326C4#9151211yescharacteristic
327C3#1060195411yescharacteristic, complemented, Sylow
328C2#1174916311yescharacteristic
329C2#1174940111yescharacteristic
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
94. C5×Dic6Q16semidirect
237. Dic6#689semidirect
276. C3×C5#1633semidirect
314. C5#71307semidirect
327. C3#10601954semidirect

Maximal subgroups

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

subgroupindex
#117524722
#117511922
C5×#50912
C3×#653812
#117458612
#117458452
#117458432
#106019543
#713075