Subgroups — C₅×#7983 #11930703

Order 1280.

1026 conjugacy classes of subgroups.

The subgroup lattice has 544 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	C₅×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#380	C₂	1	1	yes	maximal, characteristic
4	C₅×#1289	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₅×M₁₆	C₄	1	2	yes	complemented
7	C₂×C₅×#117	—	2	1	no	—
8	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂²×C₅×C₂²⋊C₄	—	2	1	no	—
10	C₅×#407	—	2	1	no	—
11	C₅×#407	—	2	1	no	—
12	C₅×#407	—	2	1	no	—
13	C₅×#407	—	2	1	no	—
14	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	complemented
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₅×#381	C₄	1	2	yes	complemented
17	C₅×#380	—	2	1	no	—
18	C₅×#380	—	2	1	no	—
19	C₅×#380	—	2	1	no	—
20	C₅×#380	C₄	1	2	yes	complemented
21	C₅×#380	C₂²	1	2	yes	—
22	C₅×#380	C₂²	1	2	yes	—
23	C₅×#379	—	2	1	no	—
24	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
25	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	complemented
26	C₂×C₅×#95	C₄	1	2	yes	complemented
27	#7983	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂⁵×C₅	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	—	2	2	no	—
30	C₂³×C₄×C₅	—	4	4	no	—
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	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	—	4	4	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₅×#117	—	4	4	no	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	—	2	2	no	—
53	C₂×C₅×C₄⋊C₄	—	4	4	no	—
54	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
60	C₂×C₄²×C₅	—	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×#95	—	2	2	no	—
66	C₅×#95	—	2	2	no	—
67	C₅×#95	C₂×C₄	1	4	yes	—
68	C₅×#95	C₂×C₄	1	4	yes	complemented
69	C₂×#407	C₂×C₅	1	1	yes	characteristic
70	#2280	C₂×C₅	1	1	yes	characteristic
71	C₂×#380	C₂×C₅	1	1	yes	characteristic
72	#1289	C₂×C₅	1	4	yes	complemented
73	C₂⁴×C₅	—	2	2	no	—
74	C₂⁴×C₅	—	2	2	no	—
75	C₂⁴×C₅	—	4	2	no	—
76	C₂⁴×C₅	—	4	2	no	—
77	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	—	2	4	no	—
85	C₂²×C₄×C₅	—	2	4	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	—	2	4	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	—	4	2	no	—
98	C₂²×C₄×C₅	—	4	2	no	—
99	C₂²×C₄×C₅	—	4	2	no	—
100	C₂²×C₄×C₅	—	4	4	no	—
101	C₂²×C₄×C₅	—	4	4	no	—
102	C₂²×C₄×C₅	—	4	4	no	—
103	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
131	C₅×M₁₆	—	4	4	no	—
132	C₅×M₁₆	—	4	4	no	—
133	C₂×C₅×C₈	—	2	4	no	—
134	C₂×C₅×C₈	—	4	4	no	—
135	C₅×C₄⋊C₄	—	4	4	no	—
136	C₅×C₄⋊C₄	—	4	4	no	—
137	C₅×C₄⋊C₄	—	4	4	no	—
138	C₅×C₂²⋊C₄	—	4	4	no	—
139	C₅×C₂²⋊C₄	—	4	4	no	—
140	C₅×C₂²⋊C₄	—	4	4	no	—
141	C₅×C₂²⋊C₄	—	4	2	no	—
142	C₅×C₂²⋊C₄	—	4	4	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₄²×C₅	—	4	4	no	—
145	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂²×M₁₆	C₄×C₅	1	2	yes	complemented
147	C₂×#117	—	2	1	no	—
148	C₂²×C₄⋊C₄	—	2	1	no	—
149	C₂²×C₂²⋊C₄	—	2	1	no	—
150	#407	—	2	1	no	—
151	#407	—	2	1	no	—
152	#407	—	2	1	no	—
153	#407	—	2	1	no	—
154	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	complemented
155	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
156	#381	C₄×C₅	1	2	yes	complemented
157	#380	—	2	1	no	—
158	#380	—	2	1	no	—
159	#380	—	2	1	no	—
160	#380	C₄×C₅	1	2	yes	complemented
161	#380	C₂²×C₅	1	2	yes	—
162	#380	C₂²×C₅	1	2	yes	—
163	#379	—	2	1	no	—
164	C₄×C₂²⋊C₄	—	2	1	no	—
165	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	complemented
166	C₂×#95	C₄×C₅	1	2	yes	complemented
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	2	1	no	—
170	C₂³×C₅	—	2	1	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	—	4	8	no	—
190	C₂³×C₅	—	4	8	no	—
191	C₂³×C₅	#95	1	1	yes	characteristic
192	C₂³×C₅	#95	1	1	yes	characteristic
193	C₂³×C₅	#95	1	1	yes	characteristic
194	C₂³×C₅	#95	1	1	yes	characteristic
195	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
199	C₂³×C₅	#137	1	2	yes	—
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	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	4	no	—
228	C₂×C₄×C₅	—	4	4	no	—
229	C₂×C₄×C₅	—	4	4	no	—
230	C₂×C₄×C₅	—	4	4	no	—
231	C₂×C₄×C₅	—	4	4	no	—
232	C₂×C₄×C₅	—	4	4	no	—
233	C₂×C₄×C₅	—	8	8	no	—
234	C₂×C₄×C₅	#95	1	1	yes	characteristic
235	C₂×C₄×C₅	#95	1	1	yes	characteristic
236	C₂×C₄×C₅	#95	1	1	yes	characteristic
237	C₂×C₄×C₅	#95	1	1	yes	characteristic
238	C₂×C₄×C₅	#99	1	4	yes	—
239	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₅×C₈	—	4	4	no	—
244	C₂⁵	C₅×D₄	1	1	yes	characteristic
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	4	4	no	—
247	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
253	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
254	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
255	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
256	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
257	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
258	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
259	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	4	4	no	—
264	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
265	#117	—	4	4	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	4	4	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	4	4	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	C₂×C₄×C₅	1	4	yes	—
284	#95	C₂×C₄×C₅	1	4	yes	complemented
285	C₂²×C₅	—	2	4	no	—
286	C₂²×C₅	—	2	4	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	1	no	—
298	C₂²×C₅	—	2	1	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	4	no	—
306	C₂²×C₅	—	4	4	no	—
307	C₂²×C₅	—	4	4	no	—
308	C₂²×C₅	—	4	4	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	H(3,ℤ/4)	1	2	yes	—
312	C₂²×C₅	#342	1	2	yes	—
313	C₂²×C₅	C₂×#95	1	1	yes	characteristic
314	C₂²×C₅	#417	1	2	yes	—
315	C₂²×C₅	#418	1	1	yes	characteristic
316	C₂²×C₅	#419	1	1	yes	characteristic
317	C₂²×C₅	#428	1	2	yes	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	8	4	no	—
325	C₄×C₅	—	8	4	no	—
326	C₄×C₅	#342	1	2	yes	—
327	C₄×C₅	C₂×#99	1	2	yes	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	—	2	2	no	—
330	C₂⁴	—	4	2	no	—
331	C₂⁴	—	4	2	no	—
332	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
333	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
335	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
337	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
338	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
360	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
373	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
374	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
375	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
376	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
377	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
378	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
379	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
386	M₁₆	—	4	4	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₄²	—	4	4	no	—
400	C₂×C₅	—	2	1	no	—
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	2	2	no	—
403	C₂×C₅	—	2	2	no	—
404	C₂×C₅	—	2	1	no	—
405	C₂×C₅	—	2	2	no	—
406	C₂×C₅	—	4	1	no	—
407	C₂×C₅	—	4	1	no	—
408	C₂×C₅	C₂×H(3,ℤ/4)	1	1	yes	characteristic
409	C₂×C₅	#1736	1	1	yes	characteristic
410	C₂×C₅	C₂×#342	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	8	no	—
435	C₂³	C₅×#95	1	1	yes	characteristic
436	C₂³	C₅×#95	1	1	yes	characteristic
437	C₂³	C₅×#95	1	1	yes	characteristic
438	C₂³	C₅×#95	1	1	yes	characteristic
439	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
440	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
441	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
442	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
443	C₂³	C₅×#137	1	2	yes	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	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	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	8	no	—
478	C₂×C₄	C₅×#95	1	1	yes	characteristic
479	C₂×C₄	C₅×#95	1	1	yes	characteristic
480	C₂×C₄	C₅×#95	1	1	yes	characteristic
481	C₂×C₄	C₅×#95	1	1	yes	characteristic
482	C₂×C₄	C₅×#99	1	4	yes	—
483	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
487	C₈	—	4	4	no	—
488	C₅	#7983	1	1	yes	characteristic, direct product factor, Sylow
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	2	no	—
515	C₂²	C₅×H(3,ℤ/4)	1	2	yes	—
516	C₂²	C₅×#342	1	2	yes	—
517	C₂²	C₂×C₅×#95	1	1	yes	characteristic
518	C₂²	C₅×#417	1	2	yes	—
519	C₂²	C₅×#418	1	1	yes	characteristic
520	C₂²	C₅×#419	1	1	yes	characteristic
521	C₂²	C₅×#428	1	2	yes	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	8	4	no	—
529	C₄	—	8	4	no	—
530	C₄	C₅×#342	1	2	yes	—
531	C₄	C₂×C₅×#99	1	2	yes	—
532	C₂	—	2	1	no	—
533	C₂	—	2	2	no	—
534	C₂	—	2	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	2	1	no	—
537	C₂	—	2	2	no	—
538	C₂	—	4	1	no	—
539	C₂	—	4	1	no	—
540	C₂	C₂×C₅×H(3,ℤ/4)	1	1	yes	characteristic
541	C₂	C₅×#1736	1	1	yes	characteristic
542	C₂	C₂×C₅×#342	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
prime radical	C₂⁵×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂⁴×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1289	C₂	semidirect
6. C₂²×C₅×M₁₆	C₄	semidirect
14. C₂×C₅×C₂²⋊C₈	C₄	semidirect
16. C₅×#381	C₄	semidirect
20. C₅×#380	C₄	semidirect
25. C₄×C₅×C₂²⋊C₄	C₄	semidirect
26. C₂×C₅×#95	C₄	semidirect
27. #7983	C₅	direct (N × H)
48. C₂²×C₅×C₈	C₂×C₄	semidirect
68. C₅×#95	C₂×C₄	semidirect
72. #1289	C₂×C₅	semidirect
146. C₂²×M₁₆	C₄×C₅	semidirect
154. C₂×C₂²⋊C₈	C₄×C₅	semidirect
156. #381	C₄×C₅	semidirect
160. #380	C₄×C₅	semidirect
165. C₄×C₂²⋊C₄	C₄×C₅	semidirect
166. C₂×#95	C₄×C₅	semidirect
264. C₂²×C₈	C₂×C₄×C₅	semidirect
284. #95	C₂×C₄×C₅	semidirect
488. C₅	#7983	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
C₂×C₅×#380	2
C₅×#1289	2
#7983	5

Subgroups — C5×#7983 #11930703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7983 #11930703