Subgroups — C₅×#8033 #11930753

Order 1280.

722 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#382	C₂	1	1	yes	maximal, characteristic
4	C₅×#1295	C₂	1	4	yes	maximal, complemented
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
7	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₅×#432	—	2	2	no	—
9	C₅×#432	C₄	1	4	yes	complemented
10	C₂×C₅×C₄⋊C₈	—	2	1	no	—
11	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
12	C₄×C₅×M₁₆	—	2	2	no	—
13	C₄×C₅×M₁₆	C₄	1	4	yes	complemented
14	C₂×C₅×#97	C₂²	1	2	yes	—
15	C₂×C₅×#97	C₂²	1	2	yes	—
16	C₂×C₄×C₅×C₈	—	2	1	no	—
17	C₅×#382	—	2	1	no	—
18	C₅×#382	—	2	1	no	—
19	C₅×#382	C₄	1	2	yes	—
20	C₅×#382	C₂²	1	2	yes	—
21	C₂×C₅×#95	—	2	1	no	—
22	C₂×C₅×#95	—	2	1	no	—
23	#8033	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₅	—	2	2	no	—
25	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂×C₅×M₁₆	—	2	8	no	—
29	C₂×C₅×M₁₆	—	2	4	no	—
30	C₂²×C₅×C₈	—	2	2	no	—
31	C₂²×C₅×C₈	—	2	2	no	—
32	C₂×C₅×C₄⋊C₄	—	2	2	no	—
33	C₂×C₅×C₄⋊C₄	—	4	4	no	—
34	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	D₄	1	2	yes	—
41	C₂×C₄²×C₅	Q₈	1	2	yes	—
42	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₅×C₄⋊C₈	—	2	4	no	—
44	C₅×C₂²⋊C₈	—	2	4	no	—
45	C₅×#97	—	2	2	no	—
46	C₅×#97	—	2	2	no	—
47	C₅×#97	C₂×C₄	1	4	yes	complemented
48	C₅×#97	C₂×C₄	1	4	yes	complemented
49	C₄×C₅×C₈	—	2	4	no	—
50	C₅×#95	—	2	2	no	—
51	C₅×#95	—	2	2	no	—
52	C₅×#95	—	2	2	no	—
53	C₅×#95	—	2	2	no	—
54	C₂×#432	C₂×C₅	1	1	yes	characteristic
55	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
56	C₂×#382	C₂×C₅	1	1	yes	characteristic
57	#1295	C₂×C₅	1	4	yes	complemented
58	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₅	—	2	4	no	—
60	C₂²×C₄×C₅	—	2	2	no	—
61	C₂²×C₄×C₅	—	2	2	no	—
62	C₂²×C₄×C₅	—	2	4	no	—
63	C₂²×C₄×C₅	—	4	2	no	—
64	C₂²×C₄×C₅	—	4	4	no	—
65	C₂²×C₄×C₅	—	4	4	no	—
66	C₂²×C₄×C₅	—	4	4	no	—
67	C₂²×C₄×C₅	C₄²	1	2	yes	—
68	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₅×M₁₆	—	2	16	no	—
80	C₂×C₅×C₈	—	2	8	no	—
81	C₂×C₅×C₈	—	2	4	no	—
82	C₂×C₅×C₈	—	2	4	no	—
83	C₂×C₅×C₈	—	4	4	no	—
84	C₅×C₄⋊C₄	—	4	4	no	—
85	C₅×C₄⋊C₄	—	4	4	no	—
86	C₄²×C₅	C₄²	1	2	yes	—
87	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
88	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
89	C₄²×C₅	C₄⋊C₄	1	2	yes	—
90	C₄²×C₅	C₄⋊C₄	1	2	yes	—
91	C₄²×C₅	C₄⋊C₄	1	2	yes	—
92	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₂²×M₁₆	—	2	1	no	—
97	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
98	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
99	#432	—	2	2	no	—
100	#432	C₄×C₅	1	4	yes	complemented
101	C₂×C₄⋊C₈	—	2	1	no	—
102	C₂×C₂²⋊C₈	—	2	1	no	—
103	C₄×M₁₆	—	2	2	no	—
104	C₄×M₁₆	C₄×C₅	1	4	yes	complemented
105	C₂×#97	C₂²×C₅	1	2	yes	—
106	C₂×#97	C₂²×C₅	1	2	yes	—
107	C₂×C₄×C₈	—	2	1	no	—
108	#382	—	2	1	no	—
109	#382	—	2	1	no	—
110	#382	C₄×C₅	1	2	yes	—
111	#382	C₂²×C₅	1	2	yes	—
112	C₂×#95	—	2	1	no	—
113	C₂×#95	—	2	1	no	—
114	C₂³×C₅	—	2	1	no	—
115	C₂³×C₅	—	2	1	no	—
116	C₂³×C₅	—	2	2	no	—
117	C₂³×C₅	#95	1	2	yes	—
118	C₂³×C₅	#104	1	4	yes	—
119	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₅	—	2	4	no	—
121	C₂×C₄×C₅	—	2	4	no	—
122	C₂×C₄×C₅	—	2	1	no	—
123	C₂×C₄×C₅	—	2	1	no	—
124	C₂×C₄×C₅	—	2	2	no	—
125	C₂×C₄×C₅	—	2	2	no	—
126	C₂×C₄×C₅	—	2	2	no	—
127	C₂×C₄×C₅	—	2	2	no	—
128	C₂×C₄×C₅	—	2	4	no	—
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	4	2	no	—
131	C₂×C₄×C₅	—	4	2	no	—
132	C₂×C₄×C₅	—	4	4	no	—
133	C₂×C₄×C₅	—	4	4	no	—
134	C₂×C₄×C₅	—	4	4	no	—
135	C₂×C₄×C₅	—	8	8	no	—
136	C₂×C₄×C₅	#95	1	2	yes	—
137	C₂×C₄×C₅	#95	1	2	yes	—
138	C₂×C₄×C₅	#95	1	2	yes	—
139	C₂×C₄×C₅	#100	1	2	yes	—
140	C₂×C₄×C₅	#101	1	2	yes	—
141	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₅×C₈	—	2	8	no	—
148	C₅×C₈	—	4	4	no	—
149	C₂³×C₄	—	2	2	no	—
150	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
151	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
152	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
153	C₂×M₁₆	—	2	8	no	—
154	C₂×M₁₆	—	2	4	no	—
155	C₂²×C₈	—	2	2	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	4	4	no	—
159	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
160	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
161	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
162	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
163	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
164	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
165	C₂×C₄²	C₅×D₄	1	2	yes	—
166	C₂×C₄²	C₅×Q₈	1	2	yes	—
167	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
168	C₄⋊C₈	—	2	4	no	—
169	C₂²⋊C₈	—	2	4	no	—
170	#97	—	2	2	no	—
171	#97	—	2	2	no	—
172	#97	C₂×C₄×C₅	1	4	yes	complemented
173	#97	C₂×C₄×C₅	1	4	yes	complemented
174	C₄×C₈	—	2	4	no	—
175	#95	—	2	2	no	—
176	#95	—	2	2	no	—
177	#95	—	2	2	no	—
178	#95	—	2	2	no	—
179	C₂²×C₅	—	2	2	no	—
180	C₂²×C₅	—	2	2	no	—
181	C₂²×C₅	—	2	4	no	—
182	C₂²×C₅	—	2	4	no	—
183	C₂²×C₅	#339	1	4	yes	—
184	C₂²×C₅	C₂×#95	1	1	yes	characteristic
185	C₂²×C₅	C₂×#100	1	1	yes	characteristic
186	C₂²×C₅	C₂×#101	1	1	yes	characteristic
187	C₂²×C₅	C₂×#104	1	2	yes	—
188	C₂²×C₅	#421	1	2	yes	—
189	C₄×C₅	—	2	1	no	—
190	C₄×C₅	—	2	2	no	—
191	C₄×C₅	—	2	1	no	—
192	C₄×C₅	—	2	1	no	—
193	C₄×C₅	—	2	2	no	—
194	C₄×C₅	—	2	1	no	—
195	C₄×C₅	—	2	1	no	—
196	C₄×C₅	—	2	1	no	—
197	C₄×C₅	—	8	4	no	—
198	C₄×C₅	#343	1	4	yes	—
199	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄	—	2	4	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	2	4	no	—
204	C₂²×C₄	—	4	2	no	—
205	C₂²×C₄	—	4	4	no	—
206	C₂²×C₄	—	4	4	no	—
207	C₂²×C₄	—	4	4	no	—
208	C₂²×C₄	C₄²×C₅	1	2	yes	—
209	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
210	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
213	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
215	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
216	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
217	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
220	M₁₆	—	2	16	no	—
221	C₂×C₈	—	2	8	no	—
222	C₂×C₈	—	2	4	no	—
223	C₂×C₈	—	2	4	no	—
224	C₂×C₈	—	4	4	no	—
225	C₄⋊C₄	—	4	4	no	—
226	C₄⋊C₄	—	4	4	no	—
227	C₄²	C₄²×C₅	1	2	yes	—
228	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
229	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
230	C₄²	C₅×C₄⋊C₄	1	2	yes	—
231	C₄²	C₅×C₄⋊C₄	1	2	yes	—
232	C₄²	C₅×C₄⋊C₄	1	2	yes	—
233	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
234	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
235	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
236	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
237	C₂×C₅	—	2	4	no	—
238	C₂×C₅	#1527	1	2	yes	—
239	C₂×C₅	#1528	1	2	yes	—
240	C₂×C₅	C₂×#339	1	1	yes	characteristic
241	C₂×C₅	#1733	1	1	yes	characteristic
242	C₂×C₅	C₂×#343	1	1	yes	characteristic
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	—	2	2	no	—
246	C₂³	C₅×#95	1	2	yes	—
247	C₂³	C₅×#104	1	4	yes	—
248	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	4	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	8	8	no	—
265	C₂×C₄	C₅×#95	1	2	yes	—
266	C₂×C₄	C₅×#95	1	2	yes	—
267	C₂×C₄	C₅×#95	1	2	yes	—
268	C₂×C₄	C₅×#100	1	2	yes	—
269	C₂×C₄	C₅×#101	1	2	yes	—
270	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
271	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
274	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₈	—	2	8	no	—
277	C₈	—	4	4	no	—
278	C₅	#8033	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	C₅×#339	1	4	yes	—
284	C₂²	C₂×C₅×#95	1	1	yes	characteristic
285	C₂²	C₂×C₅×#100	1	1	yes	characteristic
286	C₂²	C₂×C₅×#101	1	1	yes	characteristic
287	C₂²	C₂×C₅×#104	1	2	yes	—
288	C₂²	C₅×#421	1	2	yes	—
289	C₄	—	2	1	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	1	no	—
293	C₄	—	2	1	no	—
294	C₄	—	2	2	no	—
295	C₄	—	2	1	no	—
296	C₄	—	2	1	no	—
297	C₄	—	8	4	no	—
298	C₄	C₅×#343	1	4	yes	—
299	C₂	—	2	4	no	—
300	C₂	C₅×#1527	1	2	yes	—
301	C₂	C₅×#1528	1	2	yes	—
302	C₂	C₂×C₅×#339	1	1	yes	characteristic
303	C₂	C₅×#1733	1	1	yes	characteristic
304	C₂	C₂×C₅×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1295	C₂	semidirect
9. C₅×#432	C₄	semidirect
13. C₄×C₅×M₁₆	C₄	semidirect
23. #8033	C₅	direct (N × H)
47. C₅×#97	C₂×C₄	semidirect
48. C₅×#97	C₂×C₄	semidirect
57. #1295	C₂×C₅	semidirect
100. #432	C₄×C₅	semidirect
104. C₄×M₁₆	C₄×C₅	semidirect
172. #97	C₂×C₄×C₅	semidirect
173. #97	C₂×C₄×C₅	semidirect
278. C₅	#8033	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#432	2
C₂×C₄×C₅×M₁₆	2
C₂×C₅×#382	2
C₅×#1295	2
#8033	5

Subgroups — C5×#8033 #11930753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8033 #11930753