Finite Group Databasebeta

← #14284668

Subgroups — #14284668

Order 1920.

424 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 106 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#11752484C211yesmaximal, characteristic
2#11750934C211yesmaximal, characteristic
3#11747000C211yesmaximal, characteristic
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64702C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10599274—31nomaximal, Hall
9C42×D15C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12#91390—21no—
13#91384—21no—
14#91383C412yes—
15#91347—21no—
16#91344C412yes—
17#91331—21no—
18C2×#6648—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#68418—51nomaximal, Hall
27#66062—31no—
28#65122—31no—
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64706—31no—
33#64702D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6C2×C412yes—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4×Dic15C2×C411yescharacteristic
42C4×Dic15D411yescharacteristic
43C4×Dic15D411yescharacteristic
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C412yes—
50C2×C3×#168—21no—
51Dic3⋊Dic5—22no—
52#6668—22no—
53#6667—22no—
54Dic3×Dic5—22no—
55#6648—42no—
56#5728—51no—
57#4833—51no—
58D3×C4⋊C8—51no—
59C3×#332—51no—
60#4547—51no—
61#4481—51no—
62#4481D511yescharacteristic, complemented
63C5×C4⋊Q8—31no—
64#4092—32no—
65Q8×Dic5—32no—
66C2×C8×D5—61no—
67#4043—61no—
68#4038—61no—
69#4036—61no—
70#4033—61no—
71C42×D5—31no—
72#4015C2×D311yescharacteristic
73C5×C4⋊C8—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75#3952—61no—
76#3946—61no—
77C8×Dic5—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80#1542—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—21no—
89C4×D15—21no—
90C4×D15—41no—
91C4×D15SD1612yes—
92C4×D15Q1612yes—
93C2×C5×Dic3—22no—
94C5×Dic6—42no—
95C2×C3×Dic5—22no—
96C3×Dic10—41no—
97C3×Dic10—41no—
98C3×C5×C8—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103#946—101no—
104Q8×Dic3—101no—
105C2×D3×C8—101no—
106#897—52no—
107#892—101no—
108#890—101no—
109#887—52no—
110C42×D3—51no—
111#869C2×D511yescharacteristic
112C3×C4⋊C8—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114(C2×D3)⋊C8—101no—
115Dic3⋊C8—101no—
116C8×Dic3—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—32no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×Dic10—21no—
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130C4⋊Dic5—21no—
131C4⋊Dic5—62no—
132C4⋊Dic5C4×D312yes—
133#683—62no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—62no—
138C2×#168—21no—
139C2×#168—61no—
140C8×D5—122no—
141#533—151no—
142#431—151no—
143C2×C4⋊C8—151no—
144#333—31no—
145#333—151no—
146#332—51no—
147#332—151no—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C2×D15—21no—
150C2×D15—21no—
151C2×D15#10312yes—
152C3×C4×C5—21no—
153C3×C4×C5C2×SD1611yescharacteristic
154C3×C4×C5C2×Q1611yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157Dic15—21no—
158Dic15—21no—
159Dic15#10312yes—
160C3×Dic5—42no—
161C5×Dic3—42no—
162C2×C3×Q8—101no—
163C2×C4×D3—51no—
164C2×C4×D3—51no—
165C2×C4×D3—51no—
166C2×Dic6C4×D512yes—
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—101no—
171C3×C42C22×D511yescharacteristic
172(C2×D3)⋊C4—102no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—102no—
176Dic3⋊C4—102no—
177C4×Dic3—51no—
178C4×Dic3—51no—
179C4×Dic3—51no—
180C4×Dic3—102no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183D3×C8—202no—
184C22×D5—31no—
185C5×Q8—122no—
186C2×C4×C5—62no—
187C2×C4×C5C2×C4×D311yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×Dic5—22no—
191C2×Dic5—31no—
192C2×Dic5—31no—
193C2×Dic5—31no—
194C4×D5—32no—
195C4×D5—32no—
196C4×D5—61no—
197C4×D5—61no—
198C4×D5—121no—
199Dic10—41no—
200Dic10—41no—
201C5×C8—41no—
202C5×C8—121no—
203#168—41no—
204#168—121no—
205C22×C8—301no—
206C4⋊Q8—31no—
207C4⋊Q8—51no—
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—51no—
217C4⋊C8—151no—
218C4⋊C8—301no—
219C4⋊C8D3×D511yescharacteristic
220C22⋊C8—301no—
221C4×C8—301no—
222C2×C3×C5#41311yescharacteristic
223C2×C3×C5C2×#10311yescharacteristic
224C2×C3×C5#41611yescharacteristic
225D15—22no—
226C22×D3—51no—
227C3×Q8—201no—
228C3×Q8—201no—
229C2×C3×C4—102no—
230C2×C3×C4C2×C4×D511yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×Dic3—22no—
234C2×Dic3—51no—
235C2×Dic3—51no—
236C2×Dic3—51no—
237C4×D3—52no—
238C4×D3—52no—
239C4×D3—101no—
240C4×D3—101no—
241C4×D3—201no—
242Dic6—42no—
243C3×C8—41no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5D3×C22⋊C411yescharacteristic
248C2×D5—32no—
249C2×D5—61no—
250C2×D5—61no—
251C4×C5—21no—
252C4×C5—122no—
253C4×C5#91211yescharacteristic
254C4×C5D3×SD1611yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5D3×Q1611yescharacteristic
257Dic5—32no—
258Dic5—42no—
259Dic5—61no—
260Dic5—61no—
261C2×Q8—32no—
262C2×Q8—101no—
263C22×C4—151no—
264C22×C4—151no—
265C22×C4—151no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—101no—
269C2×C8—301no—
270C2×C8—602no—
271C4⋊C4—52no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—101no—
275C4⋊C4—302no—
276C4⋊C4—302no—
277C22⋊C4—302no—
278C42—151no—
279C42—151no—
280C42—151no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#154211yescharacteristic, complemented, Hall
284C22×C3D5×C22⋊C411yescharacteristic
285C2×D3—52no—
286C2×D3—101no—
287C2×D3—101no—
288C3×C4—21no—
289C3×C4—202no—
290C3×C4D5×SD1611yescharacteristic
291C3×C4#406211yescharacteristic
292C3×C4D5×Q1611yescharacteristic
293C3×C4#406511yescharacteristic
294Dic3—42no—
295Dic3—52no—
296Dic3—101no—
297Dic3—101no—
298C2×C5#475111yescharacteristic
299C2×C5#477211yescharacteristic
300C2×C5D3×#10311yescharacteristic
301D5—62no—
302C23—151no—
303Q8—122no—
304Q8—201no—
305Q8—201no—
306C2×C4—62no—
307C2×C4—102no—
308C2×C4—151no—
309C2×C4—152no—
310C2×C4—152no—
311C2×C4—151no—
312C2×C4—151no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—601no—
316C2×C4C4×D3×D511yescharacteristic
317C2×C4#677711yescharacteristic
318C2×C4#679011yescharacteristic
319C8—41no—
320C8—121no—
321C8—201no—
322C8—601no—
323C2×C3#6503411yescharacteristic
324C2×C3D5×#10311yescharacteristic
325C2×C3#6509311yescharacteristic
326D3—102no—
327C5#6841811yescharacteristic, complemented, Sylow
328C22—152no—
329C22—301no—
330C22—301no—
331C22#9147311yescharacteristic
332C4—21no—
333C4—122no—
334C4—152no—
335C4—202no—
336C4—301no—
337C4—301no—
338C4#9125511yescharacteristic
339C4#9126411yescharacteristic
340C4#9149711yescharacteristic
341C4#9152111yescharacteristic
342C3#1059927411yescharacteristic, complemented, Sylow
343C2—302no—
344C2#1174750611yescharacteristic
345C2#1174760911yescharacteristic
346C2#1174823911yescharacteristic
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#1542
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×#64702C2semidirect
6. #11745862C2semidirect
7. #11745855C2semidirect
33. #64702D3semidirect
62. #4481D5semidirect
283. C3×C5#1542semidirect
327. C5#68418semidirect
342. C3#10599274semidirect

Maximal subgroups

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

subgroupindex
#117524842
#117509342
#117470002
C5×#44812
C3×#647022
#117458622
#117458552
#105992743
#684185