Finite Group Databasebeta

← #14285385

Subgroups — #14285385

Order 1920.

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

normal subgroups only

This group has 404 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#11756487C211yesmaximal, characteristic
2#11747015C211yesmaximal, characteristic
3#11746867C211yesmaximal, characteristic
4C5×#4546C211yesmaximal, characteristic, complemented
5C3×#64766C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599281—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835C412yes—
11Q8×Dic15C412yes—
12#91786—21no—
13#91781—21no—
14#91779—21no—
15#91776—21no—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C2×#6651—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90983—21no—
24#90957—21no—
25#90954—21no—
26#68488—51nomaximal, Hall
27#66062—31no—
28#65126—31no—
29#65124—31no—
30C5×#333—31no—
31#64766D311yescharacteristic, complemented
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8C2×C412yes—
35C2×C4×D15C2×C411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×Dic30—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6714—22no—
43C4⋊Dic15—21no—
44C4⋊Dic15—22no—
45C4⋊Dic15C2×C412yes—
46#6712—22no—
47C4×Dic15—22no—
48C4×Dic15C2×C411yescharacteristic
49C4×Dic15D411yescharacteristic
50C4×Dic15D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55#6651—42no—
56#5728—51no—
57#4837—51no—
58#4835—51no—
59C3×#333—51no—
60#4546D511yescharacteristic, complemented
61#4486—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64#4092—32no—
65Q8×Dic5—32no—
66C2×#676—61no—
67#4043—61no—
68#4038—61no—
69#4036—61no—
70#4033—61no—
71C42×D5—31no—
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3947—61no—
77#3946—61no—
78C4⋊#168C2×D311yescharacteristic
79C4⋊#168C2×D311yescharacteristic
80#1559—151noSylow
81C22×D15C22⋊C411yescharacteristic
82C3×C5×Q8—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—41no—
96Dic30—41no—
97Dic30—41no—
98C3×#168—41no—
99C3×#168—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103#946—52no—
104Q8×Dic3—52no—
105C2×ΓL(1,𝔽25)—101no—
106#897—101no—
107#892—101no—
108#890—101no—
109#887—101no—
110C42×D3—51no—
111#869—51no—
112C3×C4⋊C8—51no—
113C3×C4⋊C8—51no—
114(C2×D3)⋊C8—101no—
115#815—101no—
116Dic3⋊C8—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8C4×D312yes—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130C4⋊Dic5—32no—
131C4⋊Dic5—62no—
132C4⋊Dic5—61no—
133#683—62no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—62no—
138C2×#168—21no—
139C2×#168—21no—
140#676—122no—
141#533—151no—
142#432—151no—
143#423—151no—
144#333—31no—
145#333—51no—
146#332—151no—
147#332—151no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×D15—21no—
150C2×D15—21no—
151C2×D15—21no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—21no—
159Dic15—21no—
160Dic15—21no—
161Dic15—42no—
162C2×C3×Q8C4×D512yes—
163C2×C4×D3—51no—
164C2×C4×D3—51no—
165C2×C4×D3—51no—
166C2×Dic6—101no—
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—102no—
173C4⋊Dic3—52no—
174C4⋊Dic3—102no—
175C4⋊Dic3—101no—
176Dic3⋊C4—102no—
177C4×Dic3—51no—
178C4×Dic3—51no—
179C4×Dic3—51no—
180C4×Dic3—102no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183ΓL(1,𝔽25)—202no—
184C22×D5—31no—
185C5×Q8—42no—
186C2×C4×C5—22no—
187C2×C4×C5C2×C4×D311yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×Dic5—31no—
191C2×Dic5—31no—
192C2×Dic5—31no—
193C2×Dic5—62no—
194C4×D5—61no—
195C4×D5—61no—
196C4×D5—61no—
197C4×D5—61no—
198C4×D5—121no—
199Dic10—121no—
200Dic10—121no—
201C5×C8—121no—
202C5×C8—121no—
203#168—41no—
204#168—41no—
205C2×M16—301no—
206C4⋊Q8—151no—
207C4⋊Q8D3×D511yescharacteristic
208#125—301no—
209C22⋊Q8—152no—
210C22⋊Q8—301no—
211C4×Q8—152no—
212C4×Q8—301no—
213#117—301no—
214C2×C42—151no—
215C4⋊C8—31no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218C4⋊C8—51no—
219C4⋊C8—301no—
220C22⋊C8—301no—
221#97—301no—
222C2×C3×C5#41311yescharacteristic
223C2×C3×C5#41711yescharacteristic
224C2×C3×C5#41911yescharacteristic
225D15—41no—
226C22×D3—51no—
227C3×Q8—42no—
228C2×C3×C4—22no—
229C2×C3×C4C2×C4×D511yescharacteristic
230C2×C3×C4D4×D511yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×Dic3—51no—
233C2×Dic3—51no—
234C2×Dic3—51no—
235C2×Dic3—102no—
236C4×D3—101no—
237C4×D3—101no—
238C4×D3—101no—
239C4×D3—101no—
240C4×D3—201no—
241Dic6—201no—
242Dic6—201no—
243C3×C8—201no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C22×C5D3×C22⋊C411yescharacteristic
248C2×D5—61no—
249C2×D5—61no—
250C2×D5—61no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5#91411yescharacteristic
254C4×C5#91511yescharacteristic
255C4×C5#91811yescharacteristic
256C4×C5#91811yescharacteristic
257Dic5—61no—
258Dic5—61no—
259Dic5—61no—
260Dic5—122no—
261C2×Q8—301no—
262C2×Q8#120012yes—
263C22×C4—151no—
264C22×C4—151no—
265C22×C4—151no—
266M16—602no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—101no—
270C2×C8—101no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—152no—
274C4⋊C4—302no—
275C4⋊C4—302no—
276C4⋊C4—301no—
277C22⋊C4—302no—
278C42—151no—
279C42—151no—
280C42—151no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#155911yescharacteristic, complemented, Hall
284C22×C3D5×C22⋊C411yescharacteristic
285C2×D3—101no—
286C2×D3—101no—
287C2×D3—101no—
288C3×C4—21no—
289C3×C4—42no—
290C3×C4#406011yescharacteristic
291C3×C4#406111yescharacteristic
292C3×C4#406411yescharacteristic
293C3×C4#406411yescharacteristic
294Dic3—101no—
295Dic3—101no—
296Dic3—101no—
297Dic3—202no—
298C2×C5#474511yescharacteristic
299C2×C5#480211yescharacteristic
300C2×C5#480311yescharacteristic
301D5—121no—
302C23—151no—
303Q8—42no—
304Q8—601no—
305Q8—601no—
306C2×C4—22no—
307C2×C4—151no—
308C2×C4—151no—
309C2×C4—151no—
310C2×C4—301no—
311C2×C4—301no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4C2×#120011yescharacteristic
317C2×C4#679011yescharacteristic
318C2×C4#679011yescharacteristic
319C8—121no—
320C8—121no—
321C8—201no—
322C8—201no—
323C2×C3#6503411yescharacteristic
324C2×C3#6509111yescharacteristic
325C2×C3#6509211yescharacteristic
326D3—201no—
327C5#6848811yescharacteristic, complemented, Sylow
328C22—301no—
329C22—301no—
330C22—301no—
331C22#9156111yescharacteristic
332C4—21no—
333C4—42no—
334C4—301no—
335C4—301no—
336C4—301no—
337C4—602no—
338C4#9150611yescharacteristic
339C4#9151211yescharacteristic
340C4#9152211yescharacteristic
341C4#9152411yescharacteristic
342C3#1059928111yescharacteristic, complemented, Sylow
343C2—601no—
344C2#1174912811yescharacteristic
345C2#1174920511yescharacteristic
346C2#1174921811yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1559
LCSG ▷ C2×C3×C4×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
4. C5×#4546C2semidirect
5. C3×#64766C2semidirect
6. #11745860C2semidirect
7. #11745859C2semidirect
31. #64766D3semidirect
60. #4546D5semidirect
283. C3×C5#1559semidirect
327. C5#68488semidirect
342. C3#10599281semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117470152
#117468672
C5×#45462
C3×#647662
#117458602
#117458592
#105992813
#684885