Subgroups — C₅×#34273 #11956993

Order 1280.

3578 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×#534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#518	C₂	1	2	yes	maximal, complemented
3	C₅×#2359	C₂	1	8	yes	maximal, complemented
4	C₅×#2358	C₂	1	8	yes	maximal, complemented
5	C₅×#2325	C₂	1	4	yes	maximal, complemented
6	C₅×#2315	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#121	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₅×D₄	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₅×#534	C₄	1	16	yes	complemented
13	C₂×C₅×#123	C₂²	1	4	yes	—
14	C₂×C₅×#121	C₂²	1	4	yes	—
15	C₂×C₅×#120	C₂²	1	4	yes	—
16	C₅×#518	—	2	16	no	—
17	C₂×C₄×C₅×D₄	C₂²	1	8	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
19	C₂×C₄×C₅×D₄	C₂²	1	4	yes	complemented
20	C₂×C₅×#117	C₂²	1	4	yes	complemented
21	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
27	C₅×#390	C₂²	1	4	yes	complemented
28	C₅×#389	C₂²	1	4	yes	complemented
29	C₅×#388	C₂²	1	8	yes	complemented
30	C₅×#388	C₂²	1	8	yes	complemented
31	C₅×#387	C₂²	1	8	yes	complemented
32	C₅×#386	C₂²	1	8	yes	—
33	C₅×#386	C₂²	1	4	yes	complemented
34	C₅×#386	C₂²	1	4	yes	complemented
35	C₅×#386	C₂²	1	8	yes	complemented
36	C₅×#385	C₂²	1	8	yes	complemented
37	C₅×#385	C₂²	1	8	yes	complemented
38	C₅×#380	C₂²	1	4	yes	complemented
39	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
40	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
42	C₂×C₅×#95	C₂²	1	2	yes	complemented
43	C₂×C₅×#95	C₂²	1	4	yes	complemented
44	#34273	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁵×C₅	C₂³	1	2	yes	—
46	C₂⁵×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×D₄	—	2	8	no	—
48	C₂²×C₅×D₄	—	2	8	no	—
49	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
50	C₂²×C₅×D₄	C₂³	1	4	yes	—
51	C₂²×C₅×D₄	C₂³	1	4	yes	—
52	C₂²×C₅×D₄	C₂³	1	4	yes	—
53	C₂³×C₄×C₅	—	2	4	no	—
54	C₂³×C₄×C₅	—	4	4	no	—
55	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₅	C₂³	1	4	yes	—
57	C₂³×C₄×C₅	C₂³	1	2	yes	—
58	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂³	1	4	yes	—
60	C₂³×C₄×C₅	C₂³	1	8	yes	—
61	C₂³×C₄×C₅	C₂³	1	2	yes	—
62	C₂³×C₄×C₅	C₂³	1	2	yes	—
63	C₅×#123	C₂×C₄	1	32	yes	complemented
64	C₅×#121	C₂×C₄	1	32	yes	complemented
65	C₅×#120	C₂×C₄	1	32	yes	complemented
66	C₄×C₅×D₄	—	2	32	no	—
67	C₄×C₅×D₄	—	2	32	no	—
68	C₄×C₅×D₄	—	4	8	no	—
69	C₅×#117	—	2	16	no	—
70	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
75	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
76	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
77	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
78	C₂×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
79	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₄²×C₅	—	4	4	no	—
88	C₂×C₄²×C₅	C₂³	1	4	yes	—
89	C₂×C₄²×C₅	C₂³	1	8	yes	—
90	C₂×C₄²×C₅	C₂³	1	4	yes	—
91	C₅×#95	C₂³	1	8	yes	—
92	C₅×#95	C₂³	1	8	yes	—
93	C₅×#95	C₂³	1	8	yes	—
94	C₅×#95	C₂³	1	8	yes	—
95	C₂×#534	C₂×C₅	1	1	yes	characteristic
96	C₂×#518	C₂×C₅	1	2	yes	complemented
97	#2359	C₂×C₅	1	8	yes	complemented
98	#2358	C₂×C₅	1	8	yes	complemented
99	#2325	C₂×C₅	1	4	yes	complemented
100	#2315	C₂×C₅	1	1	yes	characteristic, complemented
101	C₄×#121	C₂×C₅	1	4	yes	complemented
102	C₂×#386	C₂×C₅	1	2	yes	complemented
103	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	4	no	—
105	C₂⁴×C₅	—	2	4	no	—
106	C₂⁴×C₅	—	4	2	no	—
107	C₂⁴×C₅	—	4	2	no	—
108	C₂⁴×C₅	—	4	4	no	—
109	C₂⁴×C₅	—	4	4	no	—
110	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
111	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
112	C₂⁴×C₅	C₂×D₄	1	4	yes	—
113	C₂⁴×C₅	#41	1	4	yes	—
114	C₂⁴×C₅	C₂⁴	1	4	yes	—
115	C₂⁴×C₅	C₂⁴	1	2	yes	—
116	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₅×D₄	—	2	64	no	—
118	C₂×C₅×D₄	—	2	8	no	—
119	C₂×C₅×D₄	—	2	8	no	—
120	C₂×C₅×D₄	—	2	8	no	—
121	C₂×C₅×D₄	—	2	8	no	—
122	C₂×C₅×D₄	—	4	4	no	—
123	C₂×C₅×D₄	—	4	4	no	—
124	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
125	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
126	C₂×C₅×D₄	C₂²×C₄	1	16	yes	complemented
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	4	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	8	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	8	no	—
134	C₂²×C₄×C₅	—	2	8	no	—
135	C₂²×C₄×C₅	—	2	16	no	—
136	C₂²×C₄×C₅	—	4	2	no	—
137	C₂²×C₄×C₅	—	4	2	no	—
138	C₂²×C₄×C₅	—	4	4	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	—	4	2	no	—
141	C₂²×C₄×C₅	—	4	2	no	—
142	C₂²×C₄×C₅	—	4	4	no	—
143	C₂²×C₄×C₅	—	4	8	no	—
144	C₂²×C₄×C₅	—	4	8	no	—
145	C₂²×C₄×C₅	—	4	4	no	—
146	C₂²×C₄×C₅	—	4	16	no	—
147	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
149	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
156	C₅×C₄⋊C₄	—	2	16	no	—
157	C₅×C₄⋊C₄	—	4	4	no	—
158	C₅×C₄⋊C₄	—	4	4	no	—
159	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
160	C₅×C₂²⋊C₄	—	2	8	no	—
161	C₅×C₂²⋊C₄	—	2	8	no	—
162	C₅×C₂²⋊C₄	—	2	16	no	—
163	C₅×C₂²⋊C₄	—	2	16	no	—
164	C₅×C₂²⋊C₄	—	4	8	no	—
165	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
166	C₅×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
167	C₅×C₂²⋊C₄	C₂×D₄	1	16	yes	—
168	C₄²×C₅	—	2	16	no	—
169	C₄²×C₅	—	2	8	no	—
170	C₄²×C₅	—	4	4	no	—
171	C₂³×D₄	C₂²×C₅	1	2	yes	—
172	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
173	#534	C₄×C₅	1	16	yes	complemented
174	C₂×#123	C₂²×C₅	1	4	yes	—
175	C₂×#121	C₂²×C₅	1	4	yes	—
176	C₂×#120	C₂²×C₅	1	4	yes	—
177	#518	—	2	16	no	—
178	C₂×C₄×D₄	C₂²×C₅	1	8	yes	—
179	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
180	C₂×C₄×D₄	C₂²×C₅	1	4	yes	complemented
181	C₂×#117	C₂²×C₅	1	4	yes	complemented
182	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
186	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
187	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
188	#390	C₂²×C₅	1	4	yes	complemented
189	#389	C₂²×C₅	1	4	yes	complemented
190	#388	C₂²×C₅	1	8	yes	complemented
191	#388	C₂²×C₅	1	8	yes	complemented
192	#387	C₂²×C₅	1	8	yes	complemented
193	#386	C₂²×C₅	1	8	yes	—
194	#386	C₂²×C₅	1	4	yes	complemented
195	#386	C₂²×C₅	1	8	yes	complemented
196	#386	C₂²×C₅	1	4	yes	complemented
197	#385	C₂²×C₅	1	8	yes	complemented
198	#385	C₂²×C₅	1	8	yes	complemented
199	#380	C₂²×C₅	1	4	yes	complemented
200	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
201	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
202	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
203	C₂×#95	C₂²×C₅	1	2	yes	complemented
204	C₂×#95	C₂²×C₅	1	4	yes	complemented
205	C₂³×C₅	—	2	2	no	—
206	C₂³×C₅	—	2	4	no	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	—	2	4	no	—
209	C₂³×C₅	—	2	4	no	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	—	2	8	no	—
212	C₂³×C₅	—	2	8	no	—
213	C₂³×C₅	—	2	16	no	—
214	C₂³×C₅	—	4	4	no	—
215	C₂³×C₅	—	4	8	no	—
216	C₂³×C₅	—	4	8	no	—
217	C₂³×C₅	—	4	4	no	—
218	C₂³×C₅	—	4	16	no	—
219	C₂³×C₅	—	8	4	no	—
220	C₂³×C₅	—	8	4	no	—
221	C₂³×C₅	—	8	8	no	—
222	C₂³×C₅	C₄×D₄	1	16	yes	complemented
223	C₂³×C₅	C₂³×C₄	1	8	yes	—
224	C₂³×C₅	C₂³×C₄	1	4	yes	—
225	C₂³×C₅	C₂³×C₄	1	2	yes	—
226	C₂³×C₅	C₂²×D₄	1	2	yes	—
227	C₂³×C₅	C₂²×D₄	1	4	yes	—
228	C₂³×C₅	C₂×#41	1	4	yes	—
229	C₂³×C₅	C₂×#41	1	2	yes	—
230	C₂³×C₅	C₂⁵	1	1	yes	characteristic
231	C₅×D₄	—	2	32	no	—
232	C₅×D₄	—	2	32	no	—
233	C₅×D₄	—	4	16	no	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	16	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	4	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	8	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	8	no	—
249	C₂×C₄×C₅	—	4	8	no	—
250	C₂×C₄×C₅	—	4	8	no	—
251	C₂×C₄×C₅	—	4	16	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	—	8	16	no	—
254	C₂×C₄×C₅	—	8	8	no	—
255	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
256	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
257	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
258	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
259	C₂⁵	C₂³×C₅	1	2	yes	—
260	C₂⁵	C₂³×C₅	1	1	yes	characteristic
261	C₂²×D₄	—	2	8	no	—
262	C₂²×D₄	—	2	8	no	—
263	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
264	C₂²×D₄	C₂³×C₅	1	4	yes	—
265	C₂²×D₄	C₂³×C₅	1	4	yes	—
266	C₂²×D₄	C₂³×C₅	1	4	yes	—
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	4	4	no	—
269	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₅	1	4	yes	—
271	C₂³×C₄	C₂³×C₅	1	2	yes	—
272	C₂³×C₄	C₂³×C₅	1	4	yes	—
273	C₂³×C₄	C₂³×C₅	1	8	yes	—
274	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₅	1	2	yes	—
276	C₂³×C₄	C₂³×C₅	1	2	yes	—
277	#123	C₂×C₄×C₅	1	32	yes	complemented
278	#121	C₂×C₄×C₅	1	32	yes	complemented
279	#120	C₂×C₄×C₅	1	32	yes	complemented
280	C₄×D₄	—	2	32	no	—
281	C₄×D₄	—	2	32	no	—
282	C₄×D₄	—	4	8	no	—
283	#117	—	2	16	no	—
284	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
287	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	16	no	—
290	C₂×C₂²⋊C₄	—	4	8	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
292	C₂×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
293	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
300	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
301	C₂×C₄²	—	4	4	no	—
302	C₂×C₄²	C₂³×C₅	1	8	yes	—
303	C₂×C₄²	C₂³×C₅	1	4	yes	—
304	C₂×C₄²	C₂³×C₅	1	4	yes	—
305	#95	C₂³×C₅	1	8	yes	—
306	#95	C₂³×C₅	1	8	yes	—
307	#95	C₂³×C₅	1	8	yes	—
308	#95	C₂³×C₅	1	8	yes	—
309	C₂²×C₅	—	2	4	no	—
310	C₂²×C₅	—	2	8	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	4	no	—
313	C₂²×C₅	—	2	4	no	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	2	8	no	—
317	C₂²×C₅	—	2	8	no	—
318	C₂²×C₅	—	2	16	no	—
319	C₂²×C₅	—	4	16	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	8	no	—
323	C₂²×C₅	—	8	16	no	—
324	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
325	C₂²×C₅	C₂×C₄×D₄	1	4	yes	—
326	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
327	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
328	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂²×C₅	#585	1	2	yes	—
331	C₄×C₅	—	2	8	no	—
332	C₄×C₅	—	2	8	no	—
333	C₄×C₅	—	2	4	no	—
334	C₄×C₅	—	2	8	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	—	4	8	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	4	2	no	—
340	C₂⁴	—	4	2	no	—
341	C₂⁴	—	4	4	no	—
342	C₂⁴	—	4	4	no	—
343	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
344	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
345	C₂⁴	C₂×C₅×D₄	1	4	yes	—
346	C₂⁴	C₅×#41	1	4	yes	—
347	C₂⁴	C₂⁴×C₅	1	4	yes	—
348	C₂⁴	C₂⁴×C₅	1	2	yes	—
349	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
350	C₂×D₄	—	2	64	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
358	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
359	C₂×D₄	C₂²×C₄×C₅	1	16	yes	complemented
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	16	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	8	no	—
377	C₂²×C₄	—	4	8	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	16	no	—
380	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
381	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
382	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
383	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
385	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
389	C₄⋊C₄	—	2	16	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	complemented
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	16	no	—
396	C₂²⋊C₄	—	2	16	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
399	C₂²⋊C₄	C₂²×C₄×C₅	1	32	yes	complemented
400	C₂²⋊C₄	C₂×C₅×D₄	1	16	yes	—
401	C₄²	—	2	16	no	—
402	C₄²	—	2	8	no	—
403	C₄²	—	4	4	no	—
404	C₂×C₅	—	2	8	no	—
405	C₂×C₅	—	2	4	no	—
406	C₂×C₅	—	4	8	no	—
407	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
408	C₂×C₅	C₄×H(5,𝔽₂)	1	2	yes	—
409	C₂×C₅	#3490	1	1	yes	characteristic
410	C₂×C₅	#3491	1	1	yes	characteristic
411	C₂×C₅	#3496	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	8	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	16	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	16	no	—
426	C₂³	—	8	4	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	8	8	no	—
429	C₂³	C₄×C₅×D₄	1	16	yes	complemented
430	C₂³	C₂³×C₄×C₅	1	8	yes	—
431	C₂³	C₂³×C₄×C₅	1	4	yes	—
432	C₂³	C₂³×C₄×C₅	1	2	yes	—
433	C₂³	C₂²×C₅×D₄	1	2	yes	—
434	C₂³	C₂²×C₅×D₄	1	4	yes	—
435	C₂³	C₂×C₅×#41	1	4	yes	—
436	C₂³	C₂×C₅×#41	1	2	yes	—
437	C₂³	C₂⁵×C₅	1	1	yes	characteristic
438	D₄	—	2	32	no	—
439	D₄	—	2	32	no	—
440	D₄	—	4	16	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	16	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	16	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	8	16	no	—
461	C₂×C₄	—	8	8	no	—
462	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
463	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
464	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
465	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
466	C₅	#34273	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	4	no	—
468	C₂²	—	2	8	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	16	no	—
477	C₂²	—	4	16	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	8	16	no	—
482	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
483	C₂²	C₂×C₄×C₅×D₄	1	4	yes	—
484	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
485	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
486	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
487	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
488	C₂²	C₅×#585	1	2	yes	—
489	C₄	—	2	8	no	—
490	C₄	—	2	8	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	8	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	8	no	—
495	C₂	—	2	8	no	—
496	C₂	—	2	4	no	—
497	C₂	—	4	8	no	—
498	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
499	C₂	C₄×C₅×H(5,𝔽₂)	1	2	yes	—
500	C₂	C₅×#3490	1	1	yes	characteristic
501	C₂	C₅×#3491	1	1	yes	characteristic
502	C₂	C₅×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#518	C₂	semidirect
3. C₅×#2359	C₂	semidirect
4. C₅×#2358	C₂	semidirect
5. C₅×#2325	C₂	semidirect
6. C₅×#2315	C₂	semidirect
7. C₄×C₅×#121	C₂	semidirect
8. C₂×C₅×#386	C₂	semidirect
9. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
12. C₅×#534	C₄	semidirect
18. C₂×C₄×C₅×D₄	C₂²	semidirect
19. C₂×C₄×C₅×D₄	C₂²	semidirect
20. C₂×C₅×#117	C₂²	semidirect
24. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₅	C₂²	semidirect
27. C₅×#390	C₂²	semidirect
28. C₅×#389	C₂²	semidirect
29. C₅×#388	C₂²	semidirect
30. C₅×#388	C₂²	semidirect
31. C₅×#387	C₂²	semidirect
33. C₅×#386	C₂²	semidirect
34. C₅×#386	C₂²	semidirect
35. C₅×#386	C₂²	semidirect
36. C₅×#385	C₂²	semidirect
37. C₅×#385	C₂²	semidirect
38. C₅×#380	C₂²	semidirect
39. C₄×C₅×C₄⋊C₄	C₂²	semidirect
40. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₅×#95	C₂²	semidirect
43. C₂×C₅×#95	C₂²	semidirect
44. #34273	C₅	direct (N × H)
49. C₂²×C₅×D₄	C₂×C₄	semidirect
63. C₅×#123	C₂×C₄	semidirect
64. C₅×#121	C₂×C₄	semidirect
65. C₅×#120	C₂×C₄	semidirect
77. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
78. C₂×C₅×C₂²⋊C₄	D₄	semidirect
96. C₂×#518	C₂×C₅	semidirect
97. #2359	C₂×C₅	semidirect
98. #2358	C₂×C₅	semidirect
99. #2325	C₂×C₅	semidirect
100. #2315	C₂×C₅	semidirect
101. C₄×#121	C₂×C₅	semidirect
102. C₂×#386	C₂×C₅	semidirect
103. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
126. C₂×C₅×D₄	C₂²×C₄	semidirect
159. C₅×C₄⋊C₄	C₂²×C₄	semidirect
166. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
173. #534	C₄×C₅	semidirect
179. C₂×C₄×D₄	C₂²×C₅	semidirect
180. C₂×C₄×D₄	C₂²×C₅	semidirect
181. C₂×#117	C₂²×C₅	semidirect
185. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
186. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
187. C₂²×C₄²	C₂²×C₅	semidirect
188. #390	C₂²×C₅	semidirect
189. #389	C₂²×C₅	semidirect
190. #388	C₂²×C₅	semidirect
191. #388	C₂²×C₅	semidirect
192. #387	C₂²×C₅	semidirect
194. #386	C₂²×C₅	semidirect
195. #386	C₂²×C₅	semidirect
196. #386	C₂²×C₅	semidirect
197. #385	C₂²×C₅	semidirect
198. #385	C₂²×C₅	semidirect
199. #380	C₂²×C₅	semidirect
200. C₄×C₄⋊C₄	C₂²×C₅	semidirect
201. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
202. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
203. C₂×#95	C₂²×C₅	semidirect
204. C₂×#95	C₂²×C₅	semidirect
222. C₂³×C₅	C₄×D₄	semidirect
263. C₂²×D₄	C₂×C₄×C₅	semidirect
277. #123	C₂×C₄×C₅	semidirect
278. #121	C₂×C₄×C₅	semidirect
279. #120	C₂×C₄×C₅	semidirect
291. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
292. C₂×C₂²⋊C₄	C₅×D₄	semidirect
359. C₂×D₄	C₂²×C₄×C₅	semidirect
392. C₄⋊C₄	C₂²×C₄×C₅	semidirect
399. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
429. C₂³	C₄×C₅×D₄	semidirect
466. C₅	#34273	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×#534	2
C₂×C₅×#518	2
C₅×#2359	2
C₅×#2358	2
C₅×#2325	2
C₅×#2315	2
C₄×C₅×#121	2
C₂×C₅×#386	2
C₂×C₄×C₅×C₂²⋊C₄	2
#34273	5

Subgroups — C5×#34273 #11956993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34273 #11956993