Finite Group Databasebeta

← #14284907

Subgroups — #14284907

Order 1920.

480 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 108 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#11750934C211yesmaximal, characteristic
3#11747015C211yesmaximal, characteristic
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64701C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599276—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—
18C2×#6651—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21C8×Dic15—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68483—51nomaximal, Hall
27D5×C4⋊Q8—31no—
28#65126—31no—
29#65122—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—
56#6651—42no—
57D3×C4⋊Q8—51no—
58#4837—51no—
59#4833—51no—
60C3×#333—51no—
61#4546—51no—
62#4481—51no—
63#4481D511yescharacteristic, complemented
64C2×Q8×D5—32no—
65C5×C4⋊Q8—31no—
66#4090—32no—
67C2×#676—61no—
68D5×C4⋊C4—61no—
69D5×C4⋊C4—61no—
70#4034—61no—
71#4034—61no—
72C42×D5—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3952—61no—
77#3946—61no—
78C8×Dic5—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1548—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15C22⋊C411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C4×D15—21no—
90C4×D15—21no—
91C4×D15—22no—
92C4×D15SD1612yes—
93C4×D15Q1612yes—
94C2×C5×Dic3—22no—
95C5×Dic6—42no—
96C2×C3×Dic5—22no—
97C3×Dic10—42no—
98#1204—44no—
99#1200—44no—
100C3×C5×C8—41no—
101C3⋊#168—41no—
102C3×#168—41no—
103C5×C3⋊C8—41no—
104C2×D3×Q8—52no—
105C3×C4⋊Q8—51no—
106#944—52no—
107C2×ΓL(1,𝔽25)—101no—
108D3×C4⋊C4—101no—
109D3×C4⋊C4—101no—
110#888—101no—
111#888—101no—
112C42×D3—51no—
113#869C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116(C2×D3)⋊C8—101no—
117Dic3⋊C8—101no—
118C8×Dic3—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C2×C5×Q8—32no—
122Q8×D5—124no—
123C2×C4×D5—31no—
124C2×C4×D5—31no—
125C2×C4×D5—31no—
126C2×C4×D5—62no—
127C2×Dic10—62no—
128C2×Dic10C4×D312yes—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136#683—62no—
137#683—62no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C2×#168—21no—
142C2×#168—61no—
143#676—122no—
144C2×C4⋊Q8—151no—
145#431—151no—
146#423—151no—
147#333—31no—
148#333—51no—
149#333—151no—
150#333—151no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×D15—21no—
153C2×D15—21no—
154C2×D15#10312yes—
155C3×C4×C5—21no—
156C3×C4×C5C2×SD1611yescharacteristic
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—21no—
161Dic15#10012yes—
162Dic15#10312yes—
163C3×Dic5—42no—
164C5×Dic3—42no—
165C2×C3×Q8—52no—
166D3×Q8—204no—
167C2×C4×D3—51no—
168C2×C4×D3—51no—
169C2×C4×D3—51no—
170C2×C4×D3—102no—
171C2×Dic6—102no—
172C2×Dic6C4×D512yes—
173C2×C3×C8—21no—
174C2×C3×C8—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C42C22×D511yescharacteristic
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180Dic3⋊C4—102no—
181Dic3⋊C4—102no—
182C4×Dic3—51no—
183C4×Dic3—51no—
184C4×Dic3—51no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187ΓL(1,𝔽25)—202no—
188C22×D5—31no—
189C5×Q8—122no—
190C2×C4×C5—62no—
191C2×C4×C5C2×C4×D311yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—31no—
196C2×Dic5—31no—
197C2×Dic5—31no—
198C4×D5—32no—
199C4×D5—32no—
200C4×D5—62no—
201C4×D5—61no—
202C4×D5—61no—
203C4×D5—124no—
204Dic10—42no—
205Dic10—124no—
206C5×C8—41no—
207C5×C8—121no—
208#168—41no—
209#168—121no—
210C22×Q8—152no—
211C2×M16—301no—
212C4⋊Q8—31no—
213C4⋊Q8—51no—
214C4⋊Q8—152no—
215C4⋊Q8—301no—
216C4⋊Q8—301no—
217C2×C4⋊C4—301no—
218C2×C4⋊C4—301no—
219C2×C42—151no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222C4⋊C8—151no—
223C4⋊C8—301no—
224C4⋊C8D3×D511yescharacteristic
225C22⋊C8—301no—
226C4×C8—301no—
227C2×C3×C5C2×#10011yescharacteristic
228C2×C3×C5C2×#10311yescharacteristic
229C2×C3×C5#41911yescharacteristic
230D15—22no—
231C22×D3—51no—
232C3×Q8—202no—
233C2×C3×C4—102no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—51no—
239C2×Dic3—51no—
240C2×Dic3—51no—
241C4×D3—52no—
242C4×D3—52no—
243C4×D3—102no—
244C4×D3—101no—
245C4×D3—101no—
246C4×D3—204no—
247Dic6—42no—
248Dic6—204no—
249C3×C8—41no—
250C3×C8—201no—
251C3⋊C8—41no—
252C3⋊C8—201no—
253C22×C5D3×C22⋊C411yescharacteristic
254C2×D5—32no—
255C2×D5—61no—
256C2×D5—61no—
257C4×C5—21no—
258C4×C5—122no—
259C4×C5D3×SD1611yescharacteristic
260C4×C5#91511yescharacteristic
261C4×C5D3×Q1611yescharacteristic
262C4×C5#91811yescharacteristic
263Dic5—32no—
264Dic5—32no—
265Dic5—42no—
266Dic5—61no—
267C2×Q8—32no—
268C2×Q8—52no—
269C2×Q8—302no—
270C2×Q8—604no—
271C22×C4—151no—
272C22×C4—151no—
273C22×C4—151no—
274C22×C4—302no—
275M16—602no—
276C2×C8—21no—
277C2×C8—61no—
278C2×C8—101no—
279C2×C8—301no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—101no—
283C4⋊C4—101no—
284C4⋊C4—302no—
285C4⋊C4—302no—
286C42—151no—
287C42—151no—
288C42—151no—
289C42C2×D3×D511yescharacteristic
290C3×C5#154811yescharacteristic, complemented, Hall
291C22×C3D5×C22⋊C411yescharacteristic
292C2×D3—52no—
293C2×D3—101no—
294C2×D3—101no—
295C3×C4—21no—
296C3×C4—202no—
297C3×C4D5×SD1611yescharacteristic
298C3×C4#406111yescharacteristic
299C3×C4D5×Q1611yescharacteristic
300C3×C4#406411yescharacteristic
301Dic3—42no—
302Dic3—52no—
303Dic3—52no—
304Dic3—101no—
305C2×C5D3×#10011yescharacteristic
306C2×C5D3×#10311yescharacteristic
307C2×C5#480211yescharacteristic
308D5—62no—
309C23—151no—
310Q8—122no—
311Q8—202no—
312Q8—604no—
313C2×C4—62no—
314C2×C4—102no—
315C2×C4—151no—
316C2×C4—151no—
317C2×C4—152no—
318C2×C4—152no—
319C2×C4—151no—
320C2×C4—302no—
321C2×C4—301no—
322C2×C4—301no—
323C2×C4—604no—
324C2×C4C4×D3×D511yescharacteristic
325C2×C4#677711yescharacteristic
326C2×C4#679011yescharacteristic
327C8—41no—
328C8—121no—
329C8—201no—
330C8—601no—
331C2×C3D5×#10011yescharacteristic
332C2×C3D5×#10311yescharacteristic
333C2×C3#6509111yescharacteristic
334D3—102no—
335C5#6848311yescharacteristic, complemented, Sylow
336C22—152no—
337C22—301no—
338C22—301no—
339C22#9147311yescharacteristic
340C4—21no—
341C4—122no—
342C4—152no—
343C4—152no—
344C4—202no—
345C4—301no—
346C4#9125511yescharacteristic
347C4#9126411yescharacteristic
348C4#9148811yescharacteristic
349C4#9151211yescharacteristic
350C3#1059927611yescharacteristic, complemented, Sylow
351C2—302no—
352C2#1174749111yescharacteristic
353C2#1174760911yescharacteristic
354C2#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#1548
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
63. #4481D5semidirect
290. C3×C5#1548semidirect
335. C5#68483semidirect
350. C3#10599276semidirect

Maximal subgroups

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

subgroupindex
#117525622
#117509342
#117470152
C5×#44812
C3×#647012
#117458622
#117458612
#105992763
#684835