Finite Group Databasebeta

← #14285347

Subgroups — #14285347

Order 1920.

456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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#11752562C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic
3#11746867C211yesmaximal, characteristic
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64701C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599280—31nomaximal, Hall
9C2×D15⋊Q8C412yes—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91470—21no—
14#91470—21no—
15#91437—21no—
16#91437—21no—
17#91385C412yes—
18C3×C5×C4⋊C8C2211yescharacteristic
19#91104—21no—
20#91099—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90957—21no—
25#90954—21no—
26#68487—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65124—31no—
29#65124—31no—
30C5×#333—31no—
31#64766—31no—
32#64701—31no—
33#64701D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6C2×C412yes—
38C2×C3×Dic10C2×C412yes—
39C2×#1204—22no—
40C2×#1200—22no—
41D15⋊Q8—44no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4×Dic15C2×C411yescharacteristic
45C4×Dic15D411yescharacteristic
46C4×Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C2×C3×#168—21no—
54#6669—22no—
55#6669—22no—
56D3×C4⋊Q8—51no—
57#4835—51no—
58#4835—51no—
59C3×#333—51no—
60#4546—51no—
61#4481—51no—
62#4481D511yescharacteristic, complemented
63C2×Q8×D5—32no—
64C5×C4⋊Q8—31no—
65#4090—32no—
66D5×C4⋊C4—61no—
67D5×C4⋊C4—61no—
68#4034—61no—
69#4034—61no—
70C42×D5—31no—
71#4015C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C5×C4⋊C8C2×D311yescharacteristic
74#3952—61no—
75#3952—61no—
76#3947—61no—
77#3947—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1558—151noSylow
81C22×D15C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15C22⋊C411yescharacteristic
86C2×Dic15C22⋊C411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C4×D15—22no—
89C4×D15—21no—
90C4×D15—21no—
91C4×D15—21no—
92C4×D15—21no—
93C2×C5×Dic3—22no—
94C5×Dic6—42no—
95C2×C3×Dic5—22no—
96C3×Dic10—42no—
97#1204—44no—
98#1200—44no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C2×D3×Q8—52no—
104C3×C4⋊Q8—51no—
105#944—52no—
106D3×C4⋊C4—101no—
107D3×C4⋊C4—101no—
108#888—101no—
109#888—101no—
110C42×D3—51no—
111#869C2×D511yescharacteristic
112C3×C4⋊C8—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114(C2×D3)⋊C8—101no—
115(C2×D3)⋊C8—101no—
116#815—101no—
117#815—101no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—32no—
121Q8×D5—124no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×C4×D5—62no—
126C2×Dic10—62no—
127C2×Dic10C4×D312yes—
128C2×C5×C8—21no—
129C2×C5×C8—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C42×C5C22×D311yescharacteristic
133C4⋊Dic5—21no—
134C4⋊Dic5—21no—
135#683—62no—
136#683—62no—
137C4×Dic5—31no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C2×#168—21no—
141C2×#168—61no—
142C2×C4⋊Q8—151no—
143#432—151no—
144#432—151no—
145#333—31no—
146#333—51no—
147#333—151no—
148#333—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15#10012yes—
153C3×C4×C5—21no—
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—21no—
159Dic15—21no—
160Dic15—21no—
161C3×Dic5—42no—
162C5×Dic3—42no—
163C2×C3×Q8—52no—
164D3×Q8—204no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×C4×D3—51no—
168C2×C4×D3—102no—
169C2×Dic6—102no—
170C2×Dic6C4×D512yes—
171C2×C3×C8—21no—
172C2×C3×C8—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C42C22×D511yescharacteristic
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178Dic3⋊C4—102no—
179Dic3⋊C4—102no—
180C4×Dic3—51no—
181C4×Dic3—51no—
182C4×Dic3—51no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—101no—
185C22×D5—31no—
186C5×Q8—122no—
187C2×C4×C5—62no—
188C2×C4×C5C2×C4×D311yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×Dic5—22no—
192C2×Dic5—31no—
193C2×Dic5—31no—
194C2×Dic5—31no—
195C4×D5—62no—
196C4×D5—61no—
197C4×D5—61no—
198C4×D5—61no—
199C4×D5—61no—
200C4×D5—124no—
201Dic10—42no—
202Dic10—124no—
203C5×C8—41no—
204C5×C8—121no—
205#168—41no—
206#168—121no—
207C22×Q8—152no—
208C4⋊Q8—31no—
209C4⋊Q8—51no—
210C4⋊Q8—152no—
211C4⋊Q8—301no—
212C4⋊Q8—301no—
213C2×C4⋊C4—301no—
214C2×C4⋊C4—301no—
215C2×C42—151no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218C4⋊C8—151no—
219C4⋊C8D3×D511yescharacteristic
220C22⋊C8—301no—
221C22⋊C8—301no—
222#97—301no—
223#97—301no—
224C2×C3×C5C2×#10011yescharacteristic
225C2×C3×C5#41911yescharacteristic
226C2×C3×C5#41911yescharacteristic
227D15—22no—
228C22×D3—51no—
229C3×Q8—202no—
230C2×C3×C4—102no—
231C2×C3×C4C2×C4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×Dic3—22no—
235C2×Dic3—51no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C4×D3—102no—
239C4×D3—101no—
240C4×D3—101no—
241C4×D3—101no—
242C4×D3—101no—
243C4×D3—204no—
244Dic6—42no—
245Dic6—204no—
246C3×C8—41no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5D3×C22⋊C411yescharacteristic
251C2×D5—32no—
252C2×D5—61no—
253C2×D5—61no—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#91511yescharacteristic
257C4×C5#91511yescharacteristic
258C4×C5#91811yescharacteristic
259C4×C5#91811yescharacteristic
260Dic5—42no—
261Dic5—61no—
262Dic5—61no—
263Dic5—61no—
264C2×Q8—32no—
265C2×Q8—52no—
266C2×Q8—302no—
267C2×Q8—604no—
268C22×C4—151no—
269C22×C4—151no—
270C22×C4—151no—
271C22×C4—302no—
272C2×C8—21no—
273C2×C8—61no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C42—151no—
283C42—151no—
284C42—151no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155811yescharacteristic, complemented, Hall
287C22×C3D5×C22⋊C411yescharacteristic
288C2×D3—52no—
289C2×D3—101no—
290C2×D3—101no—
291C3×C4—21no—
292C3×C4—202no—
293C3×C4#406111yescharacteristic
294C3×C4#406111yescharacteristic
295C3×C4#406411yescharacteristic
296C3×C4#406411yescharacteristic
297Dic3—42no—
298Dic3—101no—
299Dic3—101no—
300Dic3—101no—
301C2×C5D3×#10011yescharacteristic
302C2×C5#480211yescharacteristic
303C2×C5#480211yescharacteristic
304D5—62no—
305C23—151no—
306Q8—122no—
307Q8—202no—
308Q8—604no—
309C2×C4—62no—
310C2×C4—102no—
311C2×C4—151no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—302no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—604no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4#677711yescharacteristic
322C2×C4#679011yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3D5×#10011yescharacteristic
328C2×C3#6509111yescharacteristic
329C2×C3#6509111yescharacteristic
330D3—102no—
331C5#6848711yescharacteristic, complemented, Sylow
332C22—152no—
333C22—301no—
334C22—301no—
335C22#9147311yescharacteristic
336C4—21no—
337C4—122no—
338C4—202no—
339C4—301no—
340C4—301no—
341C4—301no—
342C4#9127811yescharacteristic
343C4#9128011yescharacteristic
344C4#9148811yescharacteristic
345C4#9151211yescharacteristic
346C3#1059928011yescharacteristic, complemented, Sylow
347C2—302no—
348C2#1174749111yescharacteristic
349C2#1174764411yescharacteristic
350C2#1174822411yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1558
LCSG ▷ C2×C3×C4×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
4. C5×#4481C2semidirect
5. C3×#64701C2semidirect
6. #11745862C2semidirect
7. #11745861C2semidirect
33. #64701D3semidirect
62. #4481D5semidirect
286. C3×C5#1558semidirect
331. C5#68487semidirect
346. C3#10599280semidirect

Maximal subgroups

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

subgroupindex
#117525622
#117509362
#117468672
C5×#44812
C3×#647012
#117458622
#117458612
#105992803
#684875