Finite Group Databasebeta

← #14282057

Subgroups — #14282057

Order 1920.

436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 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#11754174C211yesmaximal, characteristic
2#11752407C211yesmaximal, characteristic
3C3×C4×#704C211yesmaximal, characteristic
4#11746495C212yesmaximal, complemented
5#11746493C212yesmaximal, complemented
6#10604512—31nomaximal, Hall
7C2×C3×#704—21no—
8#91813C411yescharacteristic
9C5×#924C411yescharacteristic
10C2×C3×C4×Dic5C2211yescharacteristic
11#91574—21no—
12#91528—21no—
13#91468C411yescharacteristic
14#91378—21no—
15#91376C411yescharacteristic
16#91333C2211yescharacteristic
17Dic5×Dic6C2211yescharacteristic
18#91323—21no—
19#91241—21no—
20C4⋊(C3⋊#170)C2212yes—
21C4×C3⋊#170—21no—
22C3×#4002—21no—
23C3×C4×#170C2212yes—
24#69856—51nomaximal, Hall
25#65956—31no—
26C4×#704D311yescharacteristic
27#65748—31no—
28Q8⋊#170—32no—
29#64872—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×Dic30C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C22×C3×Dic5D411yescharacteristic
34C22×C3×Dic5D411yescharacteristic
35C2×#1204—21no—
36C2×C3⋊#170—22no—
37C3×#704—24no—
38C2×C3×#170—22no—
39#6719—21no—
40C4⋊Dic15C2×C411yescharacteristic
41#6712—21no—
42C5×#217—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×Dic3⋊C4—21no—
45C3×C4×Dic5C2×C411yescharacteristic
46C3×C4×Dic5D411yescharacteristic
47C3×C4×Dic5D411yescharacteristic
48C3×C4×Dic5C2311yescharacteristic
49Dic3⋊Dic5—21no—
50#6669—21no—
51#6668—21no—
52#6668—21no—
53#6668—21no—
54Dic3×Dic5—21no—
55Dic3×Dic5—21no—
56#5470—51no—
57C3×C4×M16—51no—
58#4925—51no—
59#4456—52no—
60#4456—52no—
61C2×#704—21no—
62C5×C22⋊Q8—31no—
63Q8×Dic5—31no—
64#4090—31no—
65#4070—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4035—61no—
68#4034—31no—
69#4033—31no—
70#4033—61no—
71#4024—61no—
72#4023—61no—
73C22⋊#170—61no—
74#4002—21no—
75C4⋊#170—32no—
76C4×#170—61no—
77C4×#170C2×D312yes—
78#1485—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×Dic15—21no—
84C2×Dic15—21no—
85Dic30—22no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C5×Dic6—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95#1204—42no—
96C3⋊#170—42no—
97C3×#170—24no—
98C2×C3×M16—101no—
99C2×C3×C42—51no—
100#926—101no—
101#924—51no—
102#924—101no—
103#924AGL(1,𝔽5)11yescharacteristic
104#870—101no—
105#869—51no—
106#869—51no—
107C4×Dic6—51no—
108C4×Dic6—51no—
109C4×Dic6—101no—
110C3×#97—101no—
111C3×C4×C8—52no—
112#830—101no—
113C4⋊(C3⋊C8)—52no—
114C4×C3⋊C8—101no—
115C2×C5×Q8—31no—
116C22×C4×C5C4×D311yescharacteristic
117C22×Dic5D1211yescharacteristic
118C22×Dic5#6711yescharacteristic
119C2×Dic10—31no—
120C2×Dic10—61no—
121#704—24no—
122C2×#170—22no—
123C2×#170—62no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—61no—
126C5×C22⋊C4—61no—
127C22⋊Dic5—61no—
128C4⋊Dic5—31no—
129C4⋊Dic5—61no—
130#683—61no—
131#683—61no—
132#683—61no—
133#683—61no—
134#683—61no—
135C4×Dic5—61no—
136C4×Dic5—61no—
137C4×Dic5C4×D311yescharacteristic
138C4×Dic5D1211yescharacteristic
139C4×Dic5#6711yescharacteristic
140C4×Dic5C22×D311yescharacteristic
141#533—151no—
142#431—151no—
143C4×M16—51no—
144Q8⋊C8—152no—
145Q8⋊C8—152no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C3×C4×C5—21no—
151C3×C4×C5#13112yes—
152Dic15—41no—
153Dic15—41no—
154C3×Dic5—21no—
155C3×Dic5—21no—
156C3×Dic5#10412yes—
157C3×Dic5#13712yes—
158C5×Dic3—41no—
159C5×Dic3—41no—
160C22×C3×C4—51no—
161C22×C3×C4—51no—
162C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
163C2×Dic6—51no—
164C2×Dic6—101no—
165C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
166C3×M16—104no—
167C2×C3×C8—102no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172#217—21no—
173#217—101no—
174C4⋊Dic3—51no—
175C4⋊Dic3—101no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
179Dic3⋊C4—21no—
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183C4×Dic3—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—102no—
186C23×C5(C2×D3)⋊C411yescharacteristic
187C5×Q8—62no—
188C2×C4×C5—22no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5C2×C4×D311yescharacteristic
193C2×Dic5—22no—
194C2×Dic5—22no—
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5(C2×D3)⋊C411yescharacteristic
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5C2×D1211yescharacteristic
200C2×Dic5C2×#6711yescharacteristic
201Dic10—62no—
202Dic10—122no—
203#170—24no—
204#170—122no—
205C2×M16—101no—
206C4⋊Q8—151no—
207C4⋊Q8—151no—
208#125—301no—
209C22⋊Q8—31no—
210C22⋊Q8—151no—
211C22⋊Q8—301no—
212C4×Q8—151no—
213C4×Q8—151no—
214C4×Q8—301no—
215#117—301no—
216C2×C42—51no—
217C4⋊C8—152no—
218C22⋊C8—301no—
219#97—101no—
220C4×C8—52no—
221C4×C8—301no—
222C2×C3×C5—41no—
223C2×C3×C5#40811yescharacteristic
224C2×C3×C5#41911yescharacteristic
225C2×C3×C5C2×#10411yescharacteristic
226C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
227C2×C3×C4—22no—
228C2×C3×C4—51no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—102no—
233C2×C3×C4—102no—
234C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
235C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—101no—
239C2×Dic3—101no—
240Dic6—22no—
241Dic6—102no—
242Dic6—202no—
243C3×C8—104no—
244C3⋊C8—202no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5C2×(C2×D3)⋊C411yescharacteristic
249C4×C5—21no—
250C4×C5—121no—
251C4×C5—121no—
252C4×C5#90712yes—
253Dic5—21no—
254Dic5—21no—
255Dic5—121no—
256Dic5—121no—
257Dic5#80512yes—
258Dic5#90912yes—
259C2×Q8—31no—
260C2×Q8—151no—
261C2×Q8—301no—
262C22×C4—51no—
263C22×C4—51no—
264C22×C4D3×AGL(1,𝔽5)11yescharacteristic
265M16—104no—
266C2×C8—102no—
267C2×C8—302no—
268C4⋊C4—31no—
269C4⋊C4—61no—
270C4⋊C4—151no—
271C4⋊C4—301no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C22⋊C4—61no—
278C22⋊C4—301no—
279C42—51no—
280C42—51no—
281C42—51no—
282C42—51no—
283C42—301no—
284C42—301no—
285C3×C5#148511yescharacteristic, complemented, Hall
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
290C3×C4—21no—
291C3×C4—52no—
292C3×C4—52no—
293C3×C4—101no—
294C3×C4—101no—
295C3×C4#413112yes—
296Dic3—41no—
297Dic3—41no—
298Dic3—201no—
299Dic3—201no—
300C2×C5—41no—
301C2×C5C2×#80511yescharacteristic
302C2×C5#512011yescharacteristic
303C2×C5#512911yescharacteristic
304C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
305Q8—62no—
306Q8—302no—
307Q8—602no—
308C2×C4—22no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
320C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
321C8—104no—
322C8—602no—
323C2×C3—41no—
324C2×C3#6577511yescharacteristic
325C2×C3#6578211yescharacteristic
326C2×C3D5⋊#10411yescharacteristic
327C5#6985611yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—21no—
331C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
332C4—21no—
333C4—52no—
334C4—52no—
335C4—101no—
336C4—101no—
337C4—121no—
338C4—121no—
339C4—601no—
340C4—601no—
341C4#9192912yes—
342C3#1060451211yescharacteristic, complemented, Sylow
343C2—41no—
344C2#1175171211yescharacteristic
345C2D5⋊#80511yescharacteristic
346C2#1175200111yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11746495C2semidirect
5. #11746493C2semidirect
285. C3×C5#1485semidirect
327. C5#69856semidirect
342. C3#10604512semidirect

Maximal subgroups

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

subgroupindex
#117541742
#117524072
C3×C4×#7042
#117464952
#117464932
#106045123
#698565