Subgroups — C₅×#21159 #11943879

Order 1280.

1058 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2296	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#389	C₂	1	1	yes	maximal, characteristic
6	C₅×#1944	C₂	1	2	yes	maximal, complemented
7	C₅×#1943	C₂	1	2	yes	maximal, complemented
8	C₅×#1942	C₂	1	2	yes	maximal, complemented
9	C₅×#1941	C₂	1	2	yes	maximal, complemented
10	C₅×#1736	C₂	1	1	yes	maximal, characteristic
11	C₅×#1736	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₅×#428	—	2	4	no	—
21	C₅×#428	C₄	1	8	yes	complemented
22	C₂×C₅×#107	C₂²	1	2	yes	—
23	C₂×C₅×#107	C₂²	1	2	yes	—
24	C₂×C₅×#106	C₂²	1	2	yes	—
25	C₂×C₅×#106	C₂²	1	2	yes	—
26	C₄×C₅×M₁₆	—	2	4	no	—
27	C₂×C₅×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
29	C₅×#389	—	2	1	no	—
30	C₅×#389	—	2	1	no	—
31	C₅×#389	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#389	C₂²	1	1	yes	characteristic
34	C₅×#389	C₂²	1	1	yes	characteristic
35	C₅×#389	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#385	—	2	1	no	—
38	C₅×#385	—	2	1	no	—
39	C₄×C₅×C₄⋊C₄	—	2	1	no	—
40	C₄×C₅×C₄⋊C₄	—	2	1	no	—
41	C₂×C₅×#95	—	2	1	no	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	2	yes	—
44	C₅×#340	C₂²	1	2	yes	—
45	C₅×#340	C₂²	1	2	yes	—
46	#21159	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
55	C₂×C₅×M₁₆	D₄	1	4	yes	—
56	C₂×C₅×M₁₆	Q₈	1	4	yes	—
57	C₂×C₅×M₁₆	Q₈	1	4	yes	—
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₂²×C₅×C₈	C₂³	1	2	yes	—
60	C₅×#117	—	2	2	no	—
61	C₅×#117	—	2	2	no	—
62	C₅×#117	—	2	2	no	—
63	C₅×#117	C₂×C₄	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	4	4	no	—
76	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	2	no	—
87	C₂×C₄²×C₅	—	2	2	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₅×#107	—	2	4	no	—
94	C₅×#107	C₂×C₄	1	8	yes	complemented
95	C₅×#106	—	2	4	no	—
96	C₅×#106	C₂×C₄	1	8	yes	complemented
97	C₅×#97	—	2	4	no	—
98	C₄×C₅×C₈	—	2	4	no	—
99	C₅×#95	—	2	2	no	—
100	C₅×#95	—	2	2	no	—
101	C₅×#95	—	2	1	no	—
102	C₅×#95	—	2	1	no	—
103	C₅×#95	—	2	1	no	—
104	C₅×#95	—	2	1	no	—
105	C₂×#428	C₂×C₅	1	1	yes	characteristic
106	C₂×#428	C₂×C₅	1	1	yes	characteristic
107	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
108	#2296	C₂×C₅	1	1	yes	characteristic
109	C₂×#389	C₂×C₅	1	1	yes	characteristic
110	#1944	C₂×C₅	1	2	yes	complemented
111	#1943	C₂×C₅	1	2	yes	complemented
112	#1942	C₂×C₅	1	2	yes	complemented
113	#1941	C₂×C₅	1	2	yes	complemented
114	#1736	C₂×C₅	1	1	yes	characteristic
115	#1736	C₂×C₅	1	1	yes	characteristic
116	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	—	2	4	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	—	4	1	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
131	C₂²×C₄×C₅	—	4	2	no	—
132	C₂²×C₄×C₅	—	4	2	no	—
133	C₂²×C₄×C₅	—	4	2	no	—
134	C₂²×C₄×C₅	—	4	2	no	—
135	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₅	#41	1	2	yes	—
145	C₂²×C₄×C₅	#41	1	2	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₅×M₁₆	—	2	8	no	—
148	C₅×M₁₆	C₄⋊C₄	1	16	yes	complemented
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
153	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
154	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	4	2	no	—
166	C₅×C₄⋊C₄	—	4	2	no	—
167	C₅×C₄⋊C₄	—	4	4	no	—
168	C₅×C₄⋊C₄	—	4	2	no	—
169	C₅×C₄⋊C₄	—	4	2	no	—
170	C₅×C₄⋊C₄	—	4	4	no	—
171	C₅×C₄⋊C₄	—	4	2	no	—
172	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
173	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
174	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	4	2	no	—
177	C₄²×C₅	—	2	4	no	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	—	4	2	no	—
185	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
187	C₂×#117	C₂²×C₅	1	1	yes	characteristic
188	C₂×#117	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	—	2	1	no	—
190	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
193	#428	—	2	4	no	—
194	#428	C₄×C₅	1	8	yes	complemented
195	C₂×#107	C₂²×C₅	1	2	yes	—
196	C₂×#107	C₂²×C₅	1	2	yes	—
197	C₂×#106	C₂²×C₅	1	2	yes	—
198	C₂×#106	C₂²×C₅	1	2	yes	—
199	C₄×M₁₆	—	2	4	no	—
200	C₂×#97	C₂²×C₅	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
202	#389	—	2	1	no	—
203	#389	—	2	1	no	—
204	#389	C₂²×C₅	1	1	yes	characteristic
205	#389	C₂²×C₅	1	2	yes	—
206	#389	C₂²×C₅	1	1	yes	characteristic
207	#389	C₂²×C₅	1	1	yes	characteristic
208	#389	C₂²×C₅	1	2	yes	—
209	#389	C₂²×C₅	1	1	yes	characteristic
210	#385	—	2	1	no	—
211	#385	—	2	1	no	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₂×#95	—	2	1	no	—
215	#340	C₂²×C₅	1	2	yes	—
216	#340	C₂²×C₅	1	2	yes	—
217	#340	C₂²×C₅	1	2	yes	—
218	#340	C₂²×C₅	1	2	yes	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	C₄×D₄	1	2	yes	—
224	C₂³×C₅	#121	1	2	yes	—
225	C₂³×C₅	C₄⋊Q₈	1	2	yes	—
226	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	—	4	4	no	—
242	C₂×C₄×C₅	—	4	8	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	8	4	no	—
259	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
260	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
261	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
262	C₂×C₄×C₅	#121	1	2	yes	—
263	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
264	C₂×C₄×C₅	#125	1	4	yes	—
265	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
266	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
267	C₂×C₄×C₅	#137	1	2	yes	—
268	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
274	C₅×C₈	—	2	4	no	—
275	C₅×C₈	C₂×C₄⋊C₄	1	8	yes	complemented
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
279	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
284	C₂×M₁₆	C₅×D₄	1	4	yes	—
285	C₂×M₁₆	C₅×Q₈	1	4	yes	—
286	C₂×M₁₆	C₅×Q₈	1	4	yes	—
287	C₂²×C₈	C₂³×C₅	1	2	yes	—
288	C₂²×C₈	C₂³×C₅	1	2	yes	—
289	#117	—	2	2	no	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	C₂×C₄×C₅	1	4	yes	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	4	4	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
319	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
322	#107	—	2	4	no	—
323	#107	C₂×C₄×C₅	1	8	yes	complemented
324	#106	—	2	4	no	—
325	#106	C₂×C₄×C₅	1	8	yes	complemented
326	#97	—	2	4	no	—
327	C₄×C₈	—	2	4	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	#389	1	4	yes	—
341	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
342	C₂²×C₅	C₂×#121	1	1	yes	characteristic
343	C₂²×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
344	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₂²×C₅	C₂×#137	1	1	yes	characteristic
346	C₂²×C₅	#575	1	1	yes	characteristic
347	C₂²×C₅	#575	1	1	yes	characteristic
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	4	4	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	4	1	no	—
354	C₄×C₅	—	4	1	no	—
355	C₄×C₅	—	8	1	no	—
356	C₄×C₅	—	8	2	no	—
357	C₄×C₅	—	8	1	no	—
358	C₄×C₅	#389	1	4	yes	—
359	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
360	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
361	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
362	C₄×C₅	C₂×#125	1	1	yes	characteristic
363	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
383	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
390	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
391	C₂²×C₄	C₅×#41	1	2	yes	—
392	C₂²×C₄	C₅×#41	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
394	M₁₆	—	2	8	no	—
395	M₁₆	C₅×C₄⋊C₄	1	16	yes	complemented
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
399	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
400	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
401	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
420	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
421	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	4	2	no	—
432	C₂×C₅	—	2	4	no	—
433	C₂×C₅	C₂×#389	1	1	yes	characteristic
434	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂×C₅	C₄×#137	1	1	yes	characteristic
436	C₂×C₅	#3055	1	1	yes	characteristic
437	C₂×C₅	#3056	1	1	yes	characteristic
438	C₂×C₅	#3165	1	1	yes	characteristic
439	C₂×C₅	#3166	1	1	yes	characteristic
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	C₄×C₅×D₄	1	2	yes	—
445	C₂³	C₅×#121	1	2	yes	—
446	C₂³	C₅×C₄⋊Q₈	1	2	yes	—
447	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
481	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
482	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
483	C₂×C₄	C₅×#121	1	2	yes	—
484	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
485	C₂×C₄	C₅×#125	1	4	yes	—
486	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
487	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
488	C₂×C₄	C₅×#137	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
493	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
495	C₈	—	2	4	no	—
496	C₈	C₂×C₅×C₄⋊C₄	1	8	yes	complemented
497	C₅	#21159	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	C₅×#389	1	4	yes	—
505	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
506	C₂²	C₂×C₅×#121	1	1	yes	characteristic
507	C₂²	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
508	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
509	C₂²	C₂×C₅×#137	1	1	yes	characteristic
510	C₂²	C₅×#575	1	1	yes	characteristic
511	C₂²	C₅×#575	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	1	no	—
522	C₄	C₅×#389	1	4	yes	—
523	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
524	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
525	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
526	C₄	C₂×C₅×#125	1	1	yes	characteristic
527	C₂	—	2	4	no	—
528	C₂	C₂×C₅×#389	1	1	yes	characteristic
529	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₂	C₄×C₅×#137	1	1	yes	characteristic
531	C₂	C₅×#3055	1	1	yes	characteristic
532	C₂	C₅×#3056	1	1	yes	characteristic
533	C₂	C₅×#3165	1	1	yes	characteristic
534	C₂	C₅×#3166	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
6. C₅×#1944	C₂	semidirect
7. C₅×#1943	C₂	semidirect
8. C₅×#1942	C₂	semidirect
9. C₅×#1941	C₂	semidirect
21. C₅×#428	C₄	semidirect
46. #21159	C₅	direct (N × H)
94. C₅×#107	C₂×C₄	semidirect
96. C₅×#106	C₂×C₄	semidirect
110. #1944	C₂×C₅	semidirect
111. #1943	C₂×C₅	semidirect
112. #1942	C₂×C₅	semidirect
113. #1941	C₂×C₅	semidirect
148. C₅×M₁₆	C₄⋊C₄	semidirect
194. #428	C₄×C₅	semidirect
275. C₅×C₈	C₂×C₄⋊C₄	semidirect
323. #107	C₂×C₄×C₅	semidirect
325. #106	C₂×C₄×C₅	semidirect
395. M₁₆	C₅×C₄⋊C₄	semidirect
496. C₈	C₂×C₅×C₄⋊C₄	semidirect
497. C₅	#21159	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×#428	2
C₂×C₄×C₅×M₁₆	2
C₅×#2296	2
C₂×C₅×#389	2
C₅×#1944	2
C₅×#1943	2
C₅×#1942	2
C₅×#1941	2
C₅×#1736	2
#21159	5

Subgroups — C5×#21159 #11943879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21159 #11943879