Subgroups — C₅×#35266 #11957986

Order 1280.

2018 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	C₅×#2860	C₂	1	4	yes	maximal, complemented
2	C₅×#2644	C₂	1	4	yes	maximal, complemented
3	C₅×#2513	C₂	1	4	yes	maximal, complemented
4	C₅×#2512	C₂	1	4	yes	maximal, complemented
5	C₅×#2480	C₂	1	8	yes	maximal, complemented
6	C₅×#2317	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2316	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2309	C₂	1	1	yes	maximal, characteristic
9	C₅×#2309	C₂	1	1	yes	maximal, characteristic
10	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic
12	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×#126	C₂²	1	8	yes	complemented
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#397	C₂²	1	8	yes	complemented
23	C₅×#397	C₂²	1	8	yes	complemented
24	C₅×#397	C₂²	1	8	yes	complemented
25	C₅×#396	C₂²	1	8	yes	complemented
26	C₅×#390	C₂²	1	2	yes	—
27	C₅×#390	C₂²	1	4	yes	—
28	C₅×#390	C₂²	1	4	yes	—
29	C₅×#390	C₂²	1	2	yes	—
30	C₅×#390	C₂²	1	2	yes	—
31	C₅×#390	C₂²	1	2	yes	—
32	C₅×#390	C₂²	1	4	yes	—
33	C₅×#390	C₂²	1	4	yes	—
34	C₅×#389	C₂²	1	4	yes	complemented
35	C₅×#389	C₂²	1	2	yes	complemented
36	C₅×#389	C₂²	1	2	yes	complemented
37	C₅×#389	C₂²	1	4	yes	complemented
38	C₅×#389	C₂²	1	4	yes	complemented
39	C₅×#388	C₂²	1	8	yes	complemented
40	C₅×#388	C₂²	1	8	yes	complemented
41	C₅×#388	C₂²	1	8	yes	complemented
42	C₅×#385	C₂²	1	4	yes	—
43	C₅×#385	C₂²	1	4	yes	—
44	C₅×#384	C₂²	1	2	yes	complemented
45	C₅×#382	C₂²	1	2	yes	complemented
46	C₅×#380	C₂²	1	4	yes	—
47	C₅×#379	C₂²	1	4	yes	—
48	C₅×#379	C₂²	1	4	yes	—
49	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
50	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
51	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
52	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₅×#376	C₂²	1	2	yes	complemented
54	C₄³×C₅	C₂²	1	2	yes	complemented
55	#35266	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₅	C₂³	1	2	yes	—
57	C₂²×C₅×D₄	—	2	4	no	—
58	C₂²×C₅×D₄	—	2	4	no	—
59	C₂²×C₅×D₄	—	2	4	no	—
60	C₂²×C₅×D₄	C₂³	1	2	yes	—
61	C₂²×C₅×D₄	C₂³	1	2	yes	—
62	C₂³×C₄×C₅	C₂³	1	2	yes	—
63	C₂³×C₄×C₅	C₂³	1	2	yes	—
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₅×#126	—	4	16	no	—
66	C₅×#117	—	2	4	no	—
67	C₅×#117	—	2	4	no	—
68	C₅×#117	—	2	4	no	—
69	C₅×#117	—	2	4	no	—
70	C₂×C₅×C₄⋊C₄	—	2	4	no	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
82	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
83	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₄²×C₅	—	2	4	no	—
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	2	yes	—
96	C₂×C₄²×C₅	C₂³	1	2	yes	—
97	C₂×C₄²×C₅	C₂³	1	4	yes	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	2	yes	—
100	C₂×C₄²×C₅	C₂³	1	2	yes	—
101	C₂×C₄²×C₅	C₂³	1	2	yes	—
102	C₂×C₄²×C₅	C₂³	1	4	yes	—
103	C₅×#95	C₂³	1	4	yes	—
104	C₅×#95	C₂³	1	4	yes	—
105	C₅×#95	C₂³	1	4	yes	—
106	C₅×#95	C₂³	1	4	yes	—
107	C₅×#95	C₂³	1	8	yes	—
108	C₅×#95	C₂³	1	8	yes	—
109	#2860	C₂×C₅	1	4	yes	complemented
110	#2644	C₂×C₅	1	4	yes	complemented
111	#2513	C₂×C₅	1	4	yes	complemented
112	#2512	C₂×C₅	1	4	yes	complemented
113	#2480	C₂×C₅	1	8	yes	complemented
114	#2317	C₂×C₅	1	1	yes	characteristic, complemented
115	#2316	C₂×C₅	1	1	yes	characteristic, complemented
116	#2309	C₂×C₅	1	1	yes	characteristic
117	#2309	C₂×C₅	1	1	yes	characteristic
118	#2296	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#390	C₂×C₅	1	1	yes	characteristic
120	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂⁴×C₅	—	2	4	no	—
122	C₂⁴×C₅	—	2	4	no	—
123	C₂⁴×C₅	—	2	4	no	—
124	C₂⁴×C₅	—	4	4	no	—
125	C₂⁴×C₅	—	4	4	no	—
126	C₂⁴×C₅	C₂⁴	1	4	yes	—
127	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	—	2	4	no	—
130	C₂×C₅×D₄	—	2	4	no	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	4	16	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	4	no	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	4	2	no	—
139	C₂²×C₄×C₅	—	4	4	no	—
140	C₂²×C₄×C₅	#41	1	4	yes	—
141	C₂²×C₄×C₅	#41	1	4	yes	—
142	C₂²×C₄×C₅	#41	1	4	yes	—
143	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	8	no	—
161	C₅×C₄⋊C₄	—	4	4	no	—
162	C₅×C₄⋊C₄	—	4	8	no	—
163	C₅×C₄⋊C₄	—	4	8	no	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₅×C₂²⋊C₄	—	2	16	no	—
169	C₅×C₂²⋊C₄	—	4	8	no	—
170	C₅×C₂²⋊C₄	—	4	8	no	—
171	C₅×C₂²⋊C₄	—	4	8	no	—
172	C₅×C₂²⋊C₄	—	4	8	no	—
173	C₅×C₂²⋊C₄	—	4	8	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	2	4	no	—
178	C₄²×C₅	—	2	4	no	—
179	C₄²×C₅	—	2	4	no	—
180	C₄²×C₅	—	2	4	no	—
181	C₄²×C₅	—	2	8	no	—
182	C₄²×C₅	—	4	4	no	—
183	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×#126	C₂²×C₅	1	8	yes	complemented
185	C₂×#117	C₂²×C₅	1	1	yes	characteristic
186	C₂×#117	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	C₂²×C₅	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
191	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
192	#397	C₂²×C₅	1	8	yes	complemented
193	#397	C₂²×C₅	1	8	yes	complemented
194	#397	C₂²×C₅	1	8	yes	complemented
195	#396	C₂²×C₅	1	8	yes	complemented
196	#390	C₂²×C₅	1	4	yes	—
197	#390	C₂²×C₅	1	4	yes	—
198	#390	C₂²×C₅	1	2	yes	—
199	#390	C₂²×C₅	1	4	yes	—
200	#390	C₂²×C₅	1	2	yes	—
201	#390	C₂²×C₅	1	2	yes	—
202	#390	C₂²×C₅	1	2	yes	—
203	#390	C₂²×C₅	1	4	yes	—
204	#389	C₂²×C₅	1	4	yes	complemented
205	#389	C₂²×C₅	1	4	yes	complemented
206	#389	C₂²×C₅	1	4	yes	complemented
207	#389	C₂²×C₅	1	2	yes	complemented
208	#389	C₂²×C₅	1	2	yes	complemented
209	#388	C₂²×C₅	1	8	yes	complemented
210	#388	C₂²×C₅	1	8	yes	complemented
211	#388	C₂²×C₅	1	8	yes	complemented
212	#385	C₂²×C₅	1	4	yes	—
213	#385	C₂²×C₅	1	4	yes	—
214	#384	C₂²×C₅	1	2	yes	complemented
215	#382	C₂²×C₅	1	2	yes	complemented
216	#380	C₂²×C₅	1	4	yes	—
217	#379	C₂²×C₅	1	4	yes	—
218	#379	C₂²×C₅	1	4	yes	—
219	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
220	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
221	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
222	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
223	#376	C₂²×C₅	1	2	yes	complemented
224	C₄³	C₂²×C₅	1	2	yes	complemented
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	2	4	no	—
228	C₂³×C₅	—	2	4	no	—
229	C₂³×C₅	—	2	4	no	—
230	C₂³×C₅	—	2	8	no	—
231	C₂³×C₅	—	2	8	no	—
232	C₂³×C₅	—	4	16	no	—
233	C₂³×C₅	—	4	8	no	—
234	C₂³×C₅	—	8	8	no	—
235	C₂³×C₅	—	8	4	no	—
236	C₂³×C₅	—	8	4	no	—
237	C₂³×C₅	C₂×#41	1	2	yes	—
238	C₂³×C₅	C₂×#41	1	2	yes	—
239	C₂³×C₅	C₂×#41	1	2	yes	—
240	C₂³×C₅	C₂⁵	1	1	yes	characteristic
241	C₅×D₄	—	4	8	no	—
242	C₅×D₄	—	4	8	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	4	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	8	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	4	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	4	8	no	—
264	C₂×C₄×C₅	—	8	4	no	—
265	C₂×C₄×C₅	#126	1	16	yes	complemented
266	C₂×C₄×C₅	C₂×#41	1	2	yes	—
267	C₂×C₄×C₅	C₂×#41	1	2	yes	—
268	C₂×C₄×C₅	C₂×#41	1	2	yes	—
269	C₂×C₄×C₅	C₂×#41	1	2	yes	—
270	C₂×C₄×C₅	C₂×#41	1	2	yes	—
271	C₂×C₄×C₅	C₂×#41	1	2	yes	—
272	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
273	C₂⁵	C₂³×C₅	1	2	yes	—
274	C₂²×D₄	—	2	4	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	C₂³×C₅	1	2	yes	—
278	C₂²×D₄	C₂³×C₅	1	2	yes	—
279	C₂³×C₄	C₂³×C₅	1	2	yes	—
280	C₂³×C₄	C₂³×C₅	1	2	yes	—
281	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
282	#126	—	4	16	no	—
283	#117	—	2	4	no	—
284	#117	—	2	4	no	—
285	#117	—	2	4	no	—
286	#117	—	2	4	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
296	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
298	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
299	C₂×C₂²⋊C₄	—	4	8	no	—
300	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
310	C₂×C₄²	—	2	4	no	—
311	C₂×C₄²	C₂³×C₅	1	2	yes	—
312	C₂×C₄²	C₂³×C₅	1	2	yes	—
313	C₂×C₄²	C₂³×C₅	1	2	yes	—
314	C₂×C₄²	C₂³×C₅	1	2	yes	—
315	C₂×C₄²	C₂³×C₅	1	4	yes	—
316	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₅	1	2	yes	—
319	C₂×C₄²	C₂³×C₅	1	4	yes	—
320	#95	C₂³×C₅	1	4	yes	—
321	#95	C₂³×C₅	1	4	yes	—
322	#95	C₂³×C₅	1	4	yes	—
323	#95	C₂³×C₅	1	4	yes	—
324	#95	C₂³×C₅	1	8	yes	—
325	#95	C₂³×C₅	1	8	yes	—
326	C₂²×C₅	—	2	4	no	—
327	C₂²×C₅	—	2	4	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	4	4	no	—
331	C₂²×C₅	—	4	8	no	—
332	C₂²×C₅	—	4	8	no	—
333	C₂²×C₅	—	4	4	no	—
334	C₂²×C₅	—	4	4	no	—
335	C₂²×C₅	—	8	16	no	—
336	C₂²×C₅	C₂×#126	1	4	yes	—
337	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
338	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₅	#585	1	2	yes	—
342	C₄×C₅	—	2	4	no	—
343	C₄×C₅	—	4	4	no	—
344	C₄×C₅	—	4	4	no	—
345	C₄×C₅	—	4	4	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	4	4	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	C₂×#126	1	4	yes	—
351	C₄×C₅	C₂×#126	1	4	yes	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	4	4	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	C₂⁴×C₅	1	4	yes	—
358	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	4	16	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	C₅×#41	1	4	yes	—
372	C₂²×C₄	C₅×#41	1	4	yes	—
373	C₂²×C₄	C₅×#41	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	4	8	no	—
393	C₄⋊C₄	—	4	8	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	16	no	—
400	C₂²⋊C₄	—	4	8	no	—
401	C₂²⋊C₄	—	4	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₂²⋊C₄	—	4	8	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	4	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	8	no	—
413	C₄²	—	4	4	no	—
414	C₂×C₅	—	2	4	no	—
415	C₂×C₅	—	8	4	no	—
416	C₂×C₅	C₂²×#126	1	1	yes	characteristic
417	C₂×C₅	#3460	1	2	yes	—
418	C₂×C₅	#3494	1	2	yes	—
419	C₂×C₅	#3508	1	1	yes	characteristic
420	C₂×C₅	#3510	1	1	yes	characteristic
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	4	16	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	8	8	no	—
431	C₂³	—	8	4	no	—
432	C₂³	—	8	4	no	—
433	C₂³	C₂×C₅×#41	1	2	yes	—
434	C₂³	C₂×C₅×#41	1	2	yes	—
435	C₂³	C₂×C₅×#41	1	2	yes	—
436	C₂³	C₂⁵×C₅	1	1	yes	characteristic
437	D₄	—	4	8	no	—
438	D₄	—	4	8	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	C₅×#126	1	16	yes	complemented
462	C₂×C₄	C₂×C₅×#41	1	2	yes	—
463	C₂×C₄	C₂×C₅×#41	1	2	yes	—
464	C₂×C₄	C₂×C₅×#41	1	2	yes	—
465	C₂×C₄	C₂×C₅×#41	1	2	yes	—
466	C₂×C₄	C₂×C₅×#41	1	2	yes	—
467	C₂×C₄	C₂×C₅×#41	1	2	yes	—
468	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
469	C₅	#35266	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	16	no	—
480	C₂²	C₂×C₅×#126	1	4	yes	—
481	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
482	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
483	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
484	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
485	C₂²	C₅×#585	1	2	yes	—
486	C₄	—	2	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	C₂×C₅×#126	1	4	yes	—
495	C₄	C₂×C₅×#126	1	4	yes	—
496	C₂	—	2	4	no	—
497	C₂	—	8	4	no	—
498	C₂	C₂²×C₅×#126	1	1	yes	characteristic
499	C₂	C₅×#3460	1	2	yes	—
500	C₂	C₅×#3494	1	2	yes	—
501	C₂	C₅×#3508	1	1	yes	characteristic
502	C₂	C₅×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2860	C₂	semidirect
2. C₅×#2644	C₂	semidirect
3. C₅×#2513	C₂	semidirect
4. C₅×#2512	C₂	semidirect
5. C₅×#2480	C₂	semidirect
6. C₅×#2317	C₂	semidirect
7. C₅×#2316	C₂	semidirect
10. C₅×#2296	C₂	semidirect
12. C₄×C₅×#117	C₂	semidirect
14. C₂×C₅×#126	C₂²	semidirect
22. C₅×#397	C₂²	semidirect
23. C₅×#397	C₂²	semidirect
24. C₅×#397	C₂²	semidirect
25. C₅×#396	C₂²	semidirect
34. C₅×#389	C₂²	semidirect
35. C₅×#389	C₂²	semidirect
36. C₅×#389	C₂²	semidirect
37. C₅×#389	C₂²	semidirect
38. C₅×#389	C₂²	semidirect
39. C₅×#388	C₂²	semidirect
40. C₅×#388	C₂²	semidirect
41. C₅×#388	C₂²	semidirect
44. C₅×#384	C₂²	semidirect
45. C₅×#382	C₂²	semidirect
49. C₄×C₅×C₄⋊C₄	C₂²	semidirect
50. C₄×C₅×C₄⋊C₄	C₂²	semidirect
51. C₄×C₅×C₄⋊C₄	C₂²	semidirect
53. C₅×#376	C₂²	semidirect
54. C₄³×C₅	C₂²	semidirect
55. #35266	C₅	direct (N × H)
109. #2860	C₂×C₅	semidirect
110. #2644	C₂×C₅	semidirect
111. #2513	C₂×C₅	semidirect
112. #2512	C₂×C₅	semidirect
113. #2480	C₂×C₅	semidirect
114. #2317	C₂×C₅	semidirect
115. #2316	C₂×C₅	semidirect
118. #2296	C₂×C₅	semidirect
120. C₄×#117	C₂×C₅	semidirect
184. C₂×#126	C₂²×C₅	semidirect
192. #397	C₂²×C₅	semidirect
193. #397	C₂²×C₅	semidirect
194. #397	C₂²×C₅	semidirect
195. #396	C₂²×C₅	semidirect
204. #389	C₂²×C₅	semidirect
205. #389	C₂²×C₅	semidirect
206. #389	C₂²×C₅	semidirect
207. #389	C₂²×C₅	semidirect
208. #389	C₂²×C₅	semidirect
209. #388	C₂²×C₅	semidirect
210. #388	C₂²×C₅	semidirect
211. #388	C₂²×C₅	semidirect
214. #384	C₂²×C₅	semidirect
215. #382	C₂²×C₅	semidirect
219. C₄×C₄⋊C₄	C₂²×C₅	semidirect
220. C₄×C₄⋊C₄	C₂²×C₅	semidirect
221. C₄×C₄⋊C₄	C₂²×C₅	semidirect
223. #376	C₂²×C₅	semidirect
224. C₄³	C₂²×C₅	semidirect
265. C₂×C₄×C₅	#126	semidirect
461. C₂×C₄	C₅×#126	semidirect
469. C₅	#35266	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×#2860	2
C₅×#2644	2
C₅×#2513	2
C₅×#2512	2
C₅×#2480	2
C₅×#2317	2
C₅×#2316	2
C₅×#2309	2
C₅×#2296	2
C₂×C₅×#390	2
C₄×C₅×#117	2
#35266	5

Subgroups — C5×#35266 #11957986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35266 #11957986