Subgroups — C₅×#7719 #11930439

Order 1280.

528 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2858	C₂	1	1	yes	maximal, characteristic
2	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1270	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₅×#127	C₄	1	1	yes	characteristic
7	C₂×C₅×#124	—	2	1	no	—
8	C₂×C₅×#124	—	2	1	no	—
9	C₂×C₅×C₄⋊C₈	—	2	1	no	—
10	C₅×#390	—	2	1	no	—
11	C₅×#390	—	2	1	no	—
12	C₅×#390	C₄	1	2	yes	—
13	C₅×#390	C₂²	1	2	yes	—
14	C₄³×C₅	C₂²	1	1	yes	characteristic
15	C₅×#336	—	2	1	no	—
16	C₅×#336	—	2	1	no	—
17	C₅×#336	—	2	1	no	—
18	C₅×#336	C₂²	1	2	yes	—
19	C₅×#336	C₂²	1	2	yes	—
20	#7719	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₅×Q₈	—	2	1	no	—
22	C₂²×C₅×D₄	—	2	1	no	—
23	C₂²×C₅×D₄	—	2	1	no	—
24	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
25	C₂²×C₅×C₈	—	2	2	no	—
26	C₂²×C₅×C₈	—	2	2	no	—
27	C₅×C₄⋊Q₈	—	4	2	no	—
28	C₅×#127	—	4	2	no	—
29	C₅×#124	—	4	4	no	—
30	C₅×#124	—	4	2	no	—
31	C₅×#124	—	4	2	no	—
32	C₂×C₅×C₄⋊C₄	—	2	1	no	—
33	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
34	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
35	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
36	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
37	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
38	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
45	C₅×C₄⋊C₈	—	4	2	no	—
46	#2858	C₂×C₅	1	1	yes	characteristic
47	#1839	C₂×C₅	1	1	yes	characteristic, complemented
48	#1831	C₂×C₅	1	1	yes	characteristic, complemented
49	#1270	C₂×C₅	1	4	yes	complemented
50	C₂⁴×C₅	—	2	2	no	—
51	C₂×C₅×Q₈	—	4	2	no	—
52	C₂×C₅×Q₈	—	4	2	no	—
53	C₂×C₅×Q₈	—	4	2	no	—
54	C₂×C₅×D₄	—	2	4	no	—
55	C₂×C₅×D₄	—	4	2	no	—
56	C₂×C₅×D₄	—	4	2	no	—
57	C₂×C₅×D₄	—	4	2	no	—
58	C₂×C₅×D₄	—	4	2	no	—
59	C₂×C₅×D₄	—	4	2	no	—
60	C₂×C₅×D₄	—	4	2	no	—
61	C₂×C₅×D₄	—	4	2	no	—
62	C₂×C₅×D₄	—	4	2	no	—
63	C₂²×C₄×C₅	—	2	2	no	—
64	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
71	C₂×C₅×C₈	—	4	2	no	—
72	C₂×C₅×C₈	—	4	2	no	—
73	C₂×C₅×C₈	—	4	2	no	—
74	C₂×C₅×C₈	—	4	2	no	—
75	C₂×C₅×C₈	—	4	2	no	—
76	C₂×C₅×C₈	—	4	2	no	—
77	C₅×C₄⋊C₄	—	4	2	no	—
78	C₅×C₄⋊C₄	—	4	2	no	—
79	C₅×C₂²⋊C₄	—	4	4	no	—
80	C₅×C₂²⋊C₄	—	4	4	no	—
81	C₅×C₂²⋊C₄	—	4	2	no	—
82	C₅×C₂²⋊C₄	—	4	2	no	—
83	C₅×C₂²⋊C₄	—	4	4	no	—
84	C₄²×C₅	—	2	2	no	—
85	C₄²×C₅	—	2	2	no	—
86	C₄²×C₅	—	2	2	no	—
87	C₄²×C₅	—	4	1	no	—
88	C₄²×C₅	—	4	1	no	—
89	C₄²×C₅	—	4	1	no	—
90	C₄²×C₅	D₈	1	2	yes	—
91	C₄²×C₅	SD₁₆	1	2	yes	—
92	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
93	C₂×#127	C₄×C₅	1	1	yes	characteristic
94	C₂×#124	—	2	1	no	—
95	C₂×#124	—	2	1	no	—
96	C₂×C₄⋊C₈	—	2	1	no	—
97	#390	—	2	1	no	—
98	#390	—	2	1	no	—
99	#390	C₄×C₅	1	2	yes	—
100	#390	C₂²×C₅	1	2	yes	—
101	C₄³	C₂²×C₅	1	1	yes	characteristic
102	#336	—	2	1	no	—
103	#336	—	2	1	no	—
104	#336	—	2	1	no	—
105	#336	C₂²×C₅	1	2	yes	—
106	#336	C₂²×C₅	1	2	yes	—
107	C₂³×C₅	—	4	2	no	—
108	C₂³×C₅	—	4	2	no	—
109	C₂³×C₅	—	4	2	no	—
110	C₂³×C₅	—	4	2	no	—
111	C₂³×C₅	—	4	2	no	—
112	C₂³×C₅	—	4	2	no	—
113	C₂³×C₅	—	4	2	no	—
114	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₅×Q₈	—	8	4	no	—
116	C₅×D₄	—	8	4	no	—
117	C₅×D₄	—	8	4	no	—
118	C₅×D₄	—	8	4	no	—
119	C₂×C₄×C₅	—	2	1	no	—
120	C₂×C₄×C₅	—	2	1	no	—
121	C₂×C₄×C₅	—	2	1	no	—
122	C₂×C₄×C₅	—	2	1	no	—
123	C₂×C₄×C₅	—	2	1	no	—
124	C₂×C₄×C₅	—	2	1	no	—
125	C₂×C₄×C₅	—	2	1	no	—
126	C₂×C₄×C₅	—	2	1	no	—
127	C₂×C₄×C₅	—	2	1	no	—
128	C₂×C₄×C₅	—	2	1	no	—
129	C₂×C₄×C₅	—	2	1	no	—
130	C₂×C₄×C₅	—	2	1	no	—
131	C₂×C₄×C₅	—	2	1	no	—
132	C₂×C₄×C₅	—	2	1	no	—
133	C₂×C₄×C₅	—	2	1	no	—
134	C₂×C₄×C₅	—	4	2	no	—
135	C₂×C₄×C₅	—	4	2	no	—
136	C₂×C₄×C₅	—	4	2	no	—
137	C₂×C₄×C₅	#100	1	2	yes	—
138	C₂×C₄×C₅	#102	1	2	yes	—
139	C₂×C₄×C₅	#102	1	2	yes	—
140	C₂×C₄×C₅	#131	1	2	yes	—
141	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
143	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
144	C₅×C₈	—	8	2	no	—
145	C₅×C₈	—	8	2	no	—
146	C₂²×Q₈	—	2	1	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	—	2	1	no	—
149	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	—	2	2	no	—
152	C₄⋊Q₈	—	4	2	no	—
153	#127	—	4	2	no	—
154	#124	—	4	4	no	—
155	#124	—	4	2	no	—
156	#124	—	4	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
159	C₂×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₂²⋊C₄	—	2	2	no	—
161	C₂×C₂²⋊C₄	—	2	2	no	—
162	C₂×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
164	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
165	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
166	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
167	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
168	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
169	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
170	C₄⋊C₈	—	4	2	no	—
171	C₂²×C₅	—	8	2	no	—
172	C₂²×C₅	—	8	2	no	—
173	C₂²×C₅	—	8	2	no	—
174	C₂²×C₅	—	8	2	no	—
175	C₂²×C₅	—	8	2	no	—
176	C₂²×C₅	—	8	2	no	—
177	C₂²×C₅	—	8	2	no	—
178	C₂²×C₅	#408	1	1	yes	characteristic
179	C₂²×C₅	#410	1	1	yes	characteristic
180	C₂²×C₅	C₂×#100	1	1	yes	characteristic
181	C₂²×C₅	C₂×#102	1	1	yes	characteristic
182	C₂²×C₅	#418	1	1	yes	characteristic
183	C₂²×C₅	#421	1	1	yes	characteristic
184	C₂²×C₅	#421	1	1	yes	characteristic
185	C₄×C₅	—	2	2	no	—
186	C₄×C₅	—	2	2	no	—
187	C₄×C₅	—	2	2	no	—
188	C₄×C₅	—	2	2	no	—
189	C₄×C₅	—	2	1	no	—
190	C₄×C₅	—	2	1	no	—
191	C₄×C₅	—	2	2	no	—
192	C₄×C₅	—	4	1	no	—
193	C₄×C₅	—	8	2	no	—
194	C₂⁴	—	2	2	no	—
195	C₂×Q₈	—	4	2	no	—
196	C₂×Q₈	—	4	2	no	—
197	C₂×Q₈	—	4	2	no	—
198	C₂×D₄	—	2	4	no	—
199	C₂×D₄	—	4	2	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂×D₄	—	4	2	no	—
202	C₂×D₄	—	4	2	no	—
203	C₂×D₄	—	4	2	no	—
204	C₂×D₄	—	4	2	no	—
205	C₂×D₄	—	4	2	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
213	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
214	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
215	C₂×C₈	—	4	2	no	—
216	C₂×C₈	—	4	2	no	—
217	C₂×C₈	—	4	2	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	—	4	2	no	—
221	C₄⋊C₄	—	4	2	no	—
222	C₄⋊C₄	—	4	2	no	—
223	C₂²⋊C₄	—	4	4	no	—
224	C₂²⋊C₄	—	4	2	no	—
225	C₂²⋊C₄	—	4	2	no	—
226	C₂²⋊C₄	—	4	4	no	—
227	C₂²⋊C₄	—	4	4	no	—
228	C₄²	—	2	2	no	—
229	C₄²	—	2	2	no	—
230	C₄²	—	2	2	no	—
231	C₄²	—	4	1	no	—
232	C₄²	—	4	1	no	—
233	C₄²	—	4	1	no	—
234	C₄²	C₅×D₈	1	2	yes	—
235	C₄²	C₅×SD₁₆	1	2	yes	—
236	C₂×C₅	—	16	2	no	—
237	C₂×C₅	#1469	1	1	yes	characteristic
238	C₂×C₅	#1480	1	1	yes	characteristic
239	C₂×C₅	#1496	1	1	yes	characteristic
240	C₂×C₅	#1514	1	1	yes	characteristic
241	C₂×C₅	#1517	1	1	yes	characteristic
242	C₂×C₅	#1533	1	1	yes	characteristic
243	C₂×C₅	#1545	1	1	yes	characteristic
244	C₂³	—	4	2	no	—
245	C₂³	—	4	2	no	—
246	C₂³	—	4	2	no	—
247	C₂³	—	4	2	no	—
248	C₂³	—	4	2	no	—
249	C₂³	—	4	2	no	—
250	C₂³	—	4	2	no	—
251	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
252	Q₈	—	8	4	no	—
253	D₄	—	8	4	no	—
254	D₄	—	8	4	no	—
255	D₄	—	8	4	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	C₅×#100	1	2	yes	—
275	C₂×C₄	C₅×#102	1	2	yes	—
276	C₂×C₄	C₅×#102	1	2	yes	—
277	C₂×C₄	C₅×#131	1	2	yes	—
278	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
279	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
280	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
281	C₈	—	8	2	no	—
282	C₈	—	8	2	no	—
283	C₅	#7719	1	1	yes	characteristic, direct product factor, Sylow
284	C₂²	—	8	2	no	—
285	C₂²	—	8	2	no	—
286	C₂²	—	8	2	no	—
287	C₂²	—	8	2	no	—
288	C₂²	—	8	2	no	—
289	C₂²	—	8	2	no	—
290	C₂²	—	8	2	no	—
291	C₂²	C₅×#408	1	1	yes	characteristic
292	C₂²	C₅×#410	1	1	yes	characteristic
293	C₂²	C₂×C₅×#100	1	1	yes	characteristic
294	C₂²	C₂×C₅×#102	1	1	yes	characteristic
295	C₂²	C₅×#418	1	1	yes	characteristic
296	C₂²	C₅×#421	1	1	yes	characteristic
297	C₂²	C₅×#421	1	1	yes	characteristic
298	C₄	—	2	2	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	2	no	—
302	C₄	—	2	2	no	—
303	C₄	—	2	2	no	—
304	C₄	—	2	2	no	—
305	C₄	—	4	1	no	—
306	C₄	—	8	2	no	—
307	C₂	—	16	2	no	—
308	C₂	C₅×#1469	1	1	yes	characteristic
309	C₂	C₅×#1480	1	1	yes	characteristic
310	C₂	C₅×#1496	1	1	yes	characteristic
311	C₂	C₅×#1514	1	1	yes	characteristic
312	C₂	C₅×#1517	1	1	yes	characteristic
313	C₂	C₅×#1533	1	1	yes	characteristic
314	C₂	C₅×#1545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂×C₅×#127	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#1839	C₂	semidirect
3. C₅×#1831	C₂	semidirect
4. C₅×#1270	C₂	semidirect
20. #7719	C₅	direct (N × H)
47. #1839	C₂×C₅	semidirect
48. #1831	C₂×C₅	semidirect
49. #1270	C₂×C₅	semidirect
283. C₅	#7719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2858	2
C₅×#1839	2
C₅×#1831	2
C₅×#1270	2
#7719	5

Subgroups — C5×#7719 #11930439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7719 #11930439