Finite Group Databasebeta

← #14285005

Subgroups — #14285005

Order 1920.

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

normal subgroups only

This group has 432 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#11756487C211yesmaximal, characteristic
2#11747015C211yesmaximal, characteristic
3#11747000C211yesmaximal, characteristic
4C5×#4547C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745863C211yesmaximal, characteristic, complemented
8#10599216—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—21no—
11Q8×Dic15—21no—
12#91786C412yes—
13#91781—21no—
14#91779—21no—
15#91776C412yes—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C2×#6651—21no—
19C2×#6648—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90983—21no—
25#90983—21no—
26#68423—51nomaximal, Hall
27#66062—31no—
28#65126—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767D311yescharacteristic, complemented
32#64701—31no—
33#64701—31no—
34C2×C3×C5×Q8—21no—
35C2×C4×D15C2×C411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×Dic30C2×C412yes—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4C2×C412yes—
41C3×C42×C5C2311yescharacteristic
42#6714—22no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—22no—
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#6648—42no—
57#5728—51no—
58#4837—51no—
59D3×C4⋊C8—51no—
60C3×#332—51no—
61#4547D511yescharacteristic, complemented
62#4481—51no—
63#4481—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4092—61no—
66Q8×Dic5—61no—
67C2×#676—61no—
68C2×C8×D5—61no—
69#4043—32no—
70#4038—61no—
71#4036—61no—
72#4033—32no—
73C42×D5—31no—
74#4015—31no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3946—61no—
78#3946—61no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81#1550—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C2×Dic15C22⋊C411yescharacteristic
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—41no—
96C4×D15SD1612yes—
97C4×D15Q1612yes—
98Dic30—42no—
99C3×#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#946—101no—
105Q8×Dic3—101no—
106C2×ΓL(1,𝔽25)—101no—
107C2×D3×C8—101no—
108#897—52no—
109#892—101no—
110#890—101no—
111#887—52no—
112C42×D3—51no—
113#869—51no—
114C3×C4⋊C8—51no—
115C3×C4⋊C8—51no—
116Dic3⋊C8—101no—
117Dic3⋊C8—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—21no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×Dic10—32no—
125C2×C5×C8—61no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C4×D312yes—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—62no—
132C4⋊Dic5—61no—
133C4⋊Dic5—61no—
134#683—62no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—21no—
141#676—122no—
142C8×D5—122no—
143#533—151no—
144#423—151no—
145C2×C4⋊C8—151no—
146#333—151no—
147#333—151no—
148#332—31no—
149#332—51no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×D15—21no—
152C2×D15—21no—
153C2×D15#10312yes—
154C3×C4×C5—21no—
155C3×C4×C5—42no—
156C3×C4×C5C2×SD1611yescharacteristic
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—21no—
161Dic15—21no—
162Dic15—42no—
163Dic15#10312yes—
164C2×C3×Q8—21no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×C4×D3—51no—
168C2×Dic6—52no—
169C2×C3×C8—101no—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4C4×D512yes—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—102no—
175C4⋊Dic3—102no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178Dic3⋊C4—102no—
179C4×Dic3—51no—
180C4×Dic3—51no—
181C4×Dic3—51no—
182C4×Dic3—102no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185ΓL(1,𝔽25)—202no—
186D3×C8—202no—
187C22×D5—31no—
188C5×Q8—41no—
189C5×Q8—41no—
190C2×C4×C5—22no—
191C2×C4×C5C2×C4×D311yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×Dic5—31no—
195C2×Dic5—31no—
196C2×Dic5—31no—
197C2×Dic5—62no—
198C4×D5—32no—
199C4×D5—32no—
200C4×D5—61no—
201C4×D5—61no—
202C4×D5—121no—
203Dic10—122no—
204C5×C8—121no—
205C5×C8—121no—
206#168—41no—
207#168—41no—
208C2×M16—301no—
209C22×C8—301no—
210C4⋊Q8—151no—
211C4⋊Q8D3×D511yescharacteristic
212#125—301no—
213C22⋊Q8—152no—
214C22⋊Q8—301no—
215C4×Q8—152no—
216C4×Q8—301no—
217#117—301no—
218C2×C42—151no—
219C4⋊C8—31no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222C4⋊C8—51no—
223C4⋊C8—301no—
224C4⋊C8—301no—
225C2×C3×C5#41311yescharacteristic
226C2×C3×C5C2×#10311yescharacteristic
227C2×C3×C5#41711yescharacteristic
228D15—22no—
229C22×D3—51no—
230C3×Q8—41no—
231C3×Q8—41no—
232C2×C3×C4—22no—
233C2×C3×C4C2×C4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—51no—
239C2×Dic3—102no—
240C4×D3—52no—
241C4×D3—52no—
242C4×D3—101no—
243C4×D3—101no—
244C4×D3—201no—
245Dic6—202no—
246C3×C8—201no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C22×C5D3×C22⋊C411yescharacteristic
251C2×D5—32no—
252C2×D5—61no—
253C2×D5—61no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5#91111yescharacteristic
257C4×C5D3×SD1611yescharacteristic
258C4×C5#91511yescharacteristic
259C4×C5D3×Q1611yescharacteristic
260Dic5—32no—
261Dic5—61no—
262Dic5—61no—
263Dic5—122no—
264C2×Q8—21no—
265C2×Q8—152no—
266C22×C4—151no—
267C22×C4—151no—
268C22×C4—151no—
269M16—602no—
270C2×C8—61no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—101no—
274C2×C8—602no—
275C4⋊C4—21no—
276C4⋊C4—302no—
277C4⋊C4—302no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4#120012yes—
281C22⋊C4—302no—
282C42—151no—
283C42—151no—
284C42—151no—
285C42—302no—
286C42C2×D3×D511yescharacteristic
287C3×C5#155011yescharacteristic, complemented, Hall
288C22×C3D5×C22⋊C411yescharacteristic
289C2×D3—52no—
290C2×D3—101no—
291C2×D3—101no—
292C3×C4—21no—
293C3×C4—42no—
294C3×C4#405711yescharacteristic
295C3×C4D5×SD1611yescharacteristic
296C3×C4#406111yescharacteristic
297C3×C4D5×Q1611yescharacteristic
298Dic3—52no—
299Dic3—101no—
300Dic3—101no—
301Dic3—202no—
302C2×C5#475111yescharacteristic
303C2×C5#477111yescharacteristic
304C2×C5D3×#10311yescharacteristic
305D5—62no—
306C23—151no—
307Q8—41no—
308Q8—41no—
309Q8—602no—
310C2×C4—22no—
311C2×C4—151no—
312C2×C4—152no—
313C2×C4—152no—
314C2×C4—151no—
315C2×C4—151no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—302no—
319C2×C4—601no—
320C2×C4C2×#120011yescharacteristic
321C2×C4#679011yescharacteristic
322C2×C4#679011yescharacteristic
323C8—121no—
324C8—121no—
325C8—201no—
326C8—201no—
327C2×C3#6504011yescharacteristic
328C2×C3#6506011yescharacteristic
329C2×C3D5×#10311yescharacteristic
330D3—102no—
331C5#6842311yescharacteristic, complemented, Sylow
332C22—152no—
333C22—301no—
334C22—301no—
335C22#9156111yescharacteristic
336C4—21no—
337C4—42no—
338C4—152no—
339C4—301no—
340C4—301no—
341C4—602no—
342C4#9148211yescharacteristic
343C4#9148811yescharacteristic
344C4#9150511yescharacteristic
345C4#9151111yescharacteristic
346C3#1059921611yescharacteristic, complemented, Sylow
347C2—302no—
348C2#1174895911yescharacteristic
349C2#1174920311yescharacteristic
350C2#1174937411yescharacteristic
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#1550
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×#4547C2semidirect
5. C3×#64767C2semidirect
6. #11745863C2semidirect
7. #11745863C2semidirect
31. #64767D3semidirect
61. #4547D5semidirect
287. C3×C5#1550semidirect
331. C5#68423semidirect
346. C3#10599216semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117470152
#117470002
C5×#45472
C3×#647672
#117458632
#105992163
#684235