Subgroups — C₅×#8104 #11930824

Order 1280.

914 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#407	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#407	C₂	1	1	yes	maximal, characteristic
3	C₅×#2280	C₂	1	1	yes	maximal, characteristic
4	C₅×#1305	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₅×M₁₆	—	2	1	no	—
7	C₂²×C₅×M₁₆	C₄	1	2	yes	complemented
8	C₂×C₅×#117	—	2	1	no	—
9	C₅×#407	—	2	1	no	—
10	C₅×#407	—	2	1	no	—
11	C₅×#407	—	2	1	no	—
12	C₅×#407	—	2	1	no	—
13	C₅×#407	C₄	1	2	yes	complemented
14	C₅×#407	C₄	1	2	yes	complemented
15	C₅×#407	C₂²	1	2	yes	—
16	C₅×#407	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	complemented
21	C₅×#381	—	2	1	no	—
22	C₅×#380	—	2	1	no	—
23	C₅×#380	C₂²	1	2	yes	—
24	C₅×#379	C₄	1	2	yes	—
25	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
26	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
27	#8104	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	—	4	4	no	—
30	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×M₁₆	—	2	2	no	—
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	—	4	4	no	—
48	C₂×C₅×M₁₆	—	4	4	no	—
49	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₅×#117	—	4	4	no	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₅	—	2	2	no	—
58	C₅×C₂²⋊C₈	—	2	2	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₅×C₂²⋊C₈	—	2	2	no	—
61	C₅×C₂²⋊C₈	—	2	2	no	—
62	C₅×C₂²⋊C₈	—	2	2	no	—
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₅×C₂²⋊C₈	—	2	2	no	—
65	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₅×#95	—	2	2	no	—
67	C₅×#95	—	2	2	no	—
68	C₂×#407	C₂×C₅	1	1	yes	characteristic
69	C₂×#407	C₂×C₅	1	1	yes	characteristic
70	#2280	C₂×C₅	1	1	yes	characteristic
71	#1305	C₂×C₅	1	4	yes	complemented
72	C₂⁴×C₅	—	4	2	no	—
73	C₂⁴×C₅	—	4	2	no	—
74	C₂⁴×C₅	—	4	2	no	—
75	C₂⁴×C₅	C₄²	1	1	yes	characteristic
76	C₂⁴×C₅	C₄²	1	1	yes	characteristic
77	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	4	no	—
83	C₂²×C₄×C₅	—	2	4	no	—
84	C₂²×C₄×C₅	—	2	4	no	—
85	C₂²×C₄×C₅	—	2	4	no	—
86	C₂²×C₄×C₅	—	4	2	no	—
87	C₂²×C₄×C₅	—	4	2	no	—
88	C₂²×C₄×C₅	—	4	2	no	—
89	C₂²×C₄×C₅	—	4	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	—	4	2	no	—
93	C₂²×C₄×C₅	—	4	2	no	—
94	C₂²×C₄×C₅	—	4	2	no	—
95	C₂²×C₄×C₅	—	4	2	no	—
96	C₂²×C₄×C₅	—	4	2	no	—
97	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
125	C₅×M₁₆	—	4	4	no	—
126	C₅×M₁₆	—	4	4	no	—
127	C₅×M₁₆	—	4	4	no	—
128	C₅×M₁₆	—	4	4	no	—
129	C₂×C₅×C₈	—	2	4	no	—
130	C₂×C₅×C₈	—	2	4	no	—
131	C₂×C₅×C₈	—	4	4	no	—
132	C₂×C₅×C₈	—	4	4	no	—
133	C₅×C₄⋊C₄	—	4	4	no	—
134	C₅×C₂²⋊C₄	—	4	4	no	—
135	C₅×C₂²⋊C₄	—	4	4	no	—
136	C₅×C₂²⋊C₄	—	4	4	no	—
137	C₄²×C₅	—	4	4	no	—
138	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂²×M₁₆	—	2	1	no	—
140	C₂²×M₁₆	C₄×C₅	1	2	yes	complemented
141	C₂×#117	—	2	1	no	—
142	#407	—	2	1	no	—
143	#407	—	2	1	no	—
144	#407	—	2	1	no	—
145	#407	—	2	1	no	—
146	#407	C₄×C₅	1	2	yes	complemented
147	#407	C₄×C₅	1	2	yes	complemented
148	#407	C₂²×C₅	1	2	yes	—
149	#407	C₂²×C₅	1	2	yes	—
150	C₂×C₂²⋊C₈	—	2	1	no	—
151	C₂×C₂²⋊C₈	—	2	1	no	—
152	C₂×C₂²⋊C₈	—	2	1	no	—
153	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	complemented
154	#381	—	2	1	no	—
155	#380	—	2	1	no	—
156	#380	C₂²×C₅	1	2	yes	—
157	#379	C₄×C₅	1	2	yes	—
158	C₄×C₂²⋊C₄	—	2	1	no	—
159	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
160	C₂³×C₅	—	2	2	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	2	2	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	—	4	1	no	—
172	C₂³×C₅	—	4	1	no	—
173	C₂³×C₅	—	4	1	no	—
174	C₂³×C₅	—	4	1	no	—
175	C₂³×C₅	—	4	1	no	—
176	C₂³×C₅	—	4	1	no	—
177	C₂³×C₅	—	4	1	no	—
178	C₂³×C₅	—	4	1	no	—
179	C₂³×C₅	—	4	1	no	—
180	C₂³×C₅	—	4	1	no	—
181	C₂³×C₅	—	4	16	no	—
182	C₂³×C₅	#95	1	1	yes	characteristic
183	C₂³×C₅	#95	1	1	yes	characteristic
184	C₂³×C₅	#95	1	1	yes	characteristic
185	C₂³×C₅	#95	1	1	yes	characteristic
186	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
187	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	4	no	—
217	C₂×C₄×C₅	—	4	4	no	—
218	C₂×C₄×C₅	—	4	4	no	—
219	C₂×C₄×C₅	#95	1	1	yes	characteristic
220	C₂×C₄×C₅	#95	1	1	yes	characteristic
221	C₂×C₄×C₅	#95	1	1	yes	characteristic
222	C₂×C₄×C₅	#95	1	1	yes	characteristic
223	C₂×C₄×C₅	#99	1	4	yes	—
224	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₅×C₈	—	4	4	no	—
229	C₅×C₈	—	4	4	no	—
230	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
231	C₂³×C₄	—	4	4	no	—
232	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
238	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
239	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
240	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
241	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
242	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
243	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
244	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	4	4	no	—
250	C₂×M₁₆	—	4	4	no	—
251	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	#117	—	4	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
259	C₂×C₄²	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	2	2	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	4	4	no	—
289	C₂²×C₅	—	4	4	no	—
290	C₂²×C₅	—	4	4	no	—
291	C₂²×C₅	—	4	4	no	—
292	C₂²×C₅	—	4	4	no	—
293	C₂²×C₅	—	4	4	no	—
294	C₂²×C₅	—	4	4	no	—
295	C₂²×C₅	#342	1	2	yes	—
296	C₂²×C₅	#344	1	2	yes	—
297	C₂²×C₅	C₂×#95	1	1	yes	characteristic
298	C₂²×C₅	#413	1	2	yes	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	8	4	no	—
306	C₄×C₅	#342	1	2	yes	—
307	C₄×C₅	C₂×#99	1	2	yes	—
308	C₂⁴	—	4	2	no	—
309	C₂⁴	—	4	2	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	C₄²×C₅	1	1	yes	characteristic
312	C₂⁴	C₄²×C₅	1	1	yes	characteristic
313	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
314	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
316	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
317	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
335	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
337	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
338	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
344	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
345	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
346	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
347	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
348	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
361	M₁₆	—	4	4	no	—
362	M₁₆	—	4	4	no	—
363	M₁₆	—	4	4	no	—
364	M₁₆	—	4	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	—	4	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₄²	—	4	4	no	—
374	C₂×C₅	—	2	2	no	—
375	C₂×C₅	—	2	2	no	—
376	C₂×C₅	—	2	2	no	—
377	C₂×C₅	—	4	1	no	—
378	C₂×C₅	—	4	1	no	—
379	C₂×C₅	—	4	1	no	—
380	C₂×C₅	—	4	1	no	—
381	C₂×C₅	C₂×#342	1	1	yes	characteristic
382	C₂×C₅	#1742	1	1	yes	characteristic
383	C₂×C₅	C₂×#344	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	16	no	—
406	C₂³	C₅×#95	1	1	yes	characteristic
407	C₂³	C₅×#95	1	1	yes	characteristic
408	C₂³	C₅×#95	1	1	yes	characteristic
409	C₂³	C₅×#95	1	1	yes	characteristic
410	C₂³	C₂×C₄²×C₅	1	1	yes	characteristic
411	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	C₅×#95	1	1	yes	characteristic
444	C₂×C₄	C₅×#95	1	1	yes	characteristic
445	C₂×C₄	C₅×#95	1	1	yes	characteristic
446	C₂×C₄	C₅×#95	1	1	yes	characteristic
447	C₂×C₄	C₅×#99	1	4	yes	—
448	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
452	C₈	—	4	4	no	—
453	C₈	—	4	4	no	—
454	C₅	#8104	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	C₅×#342	1	2	yes	—
481	C₂²	C₅×#344	1	2	yes	—
482	C₂²	C₂×C₅×#95	1	1	yes	characteristic
483	C₂²	C₅×#413	1	2	yes	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	8	4	no	—
491	C₄	C₅×#342	1	2	yes	—
492	C₄	C₂×C₅×#99	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	2	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	—	4	1	no	—
499	C₂	—	4	1	no	—
500	C₂	C₂×C₅×#342	1	1	yes	characteristic
501	C₂	C₅×#1742	1	1	yes	characteristic
502	C₂	C₂×C₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#95
commutator	C₂³	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁵×C₅	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂⁴×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1305	C₂	semidirect
7. C₂²×C₅×M₁₆	C₄	semidirect
13. C₅×#407	C₄	semidirect
14. C₅×#407	C₄	semidirect
20. C₂×C₅×C₂²⋊C₈	C₄	semidirect
27. #8104	C₅	direct (N × H)
71. #1305	C₂×C₅	semidirect
140. C₂²×M₁₆	C₄×C₅	semidirect
146. #407	C₄×C₅	semidirect
147. #407	C₄×C₅	semidirect
153. C₂×C₂²⋊C₈	C₄×C₅	semidirect
454. C₅	#8104	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×#407	2
C₅×#2280	2
C₅×#1305	2
#8104	5

Subgroups — C5×#8104 #11930824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8104 #11930824