Subgroups — C₂×C₅×#2526 #11957519

Order 1280.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2526	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#394	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#386	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
40	C₅×#400	C₂²	1	8	yes	complemented
41	C₅×#397	C₂²	1	8	yes	complemented
42	C₅×#396	C₂²	1	8	yes	complemented
43	C₅×#394	C₂²	1	8	yes	—
44	C₅×#390	C₂²	1	8	yes	—
45	C₅×#389	C₂²	1	8	yes	complemented
46	C₅×#388	C₂²	1	8	yes	complemented
47	C₅×#388	C₂²	1	8	yes	complemented
48	C₅×#388	C₂²	1	8	yes	complemented
49	C₅×#388	C₂²	1	8	yes	complemented
50	C₅×#387	C₂²	1	8	yes	complemented
51	C₅×#386	C₂²	1	8	yes	—
52	C₅×#381	C₂²	1	8	yes	complemented
53	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
54	C₅×#376	C₂²	1	8	yes	complemented
55	C₂×C₅×#95	C₂²	1	1	yes	characteristic
56	C₂×C₅×#95	C₂²	1	1	yes	characteristic
57	C₂×C₅×#95	C₂²	1	1	yes	characteristic
58	C₂×C₅×#95	C₂²	1	1	yes	characteristic
59	C₂×C₅×#95	C₂²	1	1	yes	characteristic
60	C₂×C₅×#95	C₂²	1	1	yes	characteristic
61	C₂×C₅×#95	C₂²	1	1	yes	characteristic
62	C₂×C₅×#95	C₂²	1	1	yes	characteristic
63	C₂×C₅×#95	C₂²	1	1	yes	characteristic
64	C₂×C₅×#95	C₂²	1	1	yes	characteristic
65	C₂×C₅×#95	C₂²	1	1	yes	characteristic
66	C₂×C₅×#95	C₂²	1	1	yes	characteristic
67	C₂×#2526	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁵×C₅	C₂³	1	1	yes	characteristic
69	C₂⁵×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₄	—	2	4	no	—
71	C₂²×C₅×D₄	—	2	4	no	—
72	C₂²×C₅×D₄	—	4	2	no	—
73	C₂²×C₅×D₄	C₂³	1	4	yes	—
74	C₂³×C₄×C₅	—	2	4	no	—
75	C₂³×C₄×C₅	—	2	4	no	—
76	C₂³×C₄×C₅	—	4	2	no	—
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	4	yes	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	—	2	4	no	—
92	C₂×C₅×C₄⋊C₄	—	2	4	no	—
93	C₂×C₅×C₄⋊C₄	—	4	2	no	—
94	C₂×C₅×C₄⋊C₄	—	4	2	no	—
95	C₂×C₅×C₄⋊C₄	—	4	2	no	—
96	C₂×C₅×C₄⋊C₄	—	4	2	no	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
110	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
111	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
113	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
114	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₄²×C₅	—	2	4	no	—
126	C₂×C₄²×C₅	—	2	4	no	—
127	C₂×C₄²×C₅	—	2	4	no	—
128	C₂×C₄²×C₅	—	4	2	no	—
129	C₂×C₄²×C₅	C₂³	1	4	yes	—
130	C₂×C₄²×C₅	C₂³	1	4	yes	—
131	C₂×C₄²×C₅	C₂³	1	4	yes	—
132	C₂×C₄²×C₅	C₂³	1	4	yes	—
133	C₅×#95	C₂³	1	4	yes	—
134	C₅×#95	C₂³	1	4	yes	—
135	C₅×#95	C₂³	1	4	yes	—
136	C₅×#95	C₂³	1	4	yes	—
137	C₅×#95	C₂³	1	4	yes	—
138	C₅×#95	C₂³	1	4	yes	—
139	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	4	yes	—
144	C₅×#95	C₂³	1	4	yes	—
145	#2526	C₂×C₅	1	16	yes	direct product factor
146	C₂×#400	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#397	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#396	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#394	C₂×C₅	1	1	yes	characteristic
150	C₂×#390	C₂×C₅	1	1	yes	characteristic
151	C₂×#389	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#388	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#388	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#388	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#388	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#387	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#386	C₂×C₅	1	1	yes	characteristic
158	C₂×#381	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#376	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	2	2	no	—
162	C₂⁴×C₅	—	2	2	no	—
163	C₂⁴×C₅	—	2	2	no	—
164	C₂⁴×C₅	—	2	2	no	—
165	C₂⁴×C₅	—	2	2	no	—
166	C₂⁴×C₅	—	2	2	no	—
167	C₂⁴×C₅	—	2	2	no	—
168	C₂⁴×C₅	—	2	2	no	—
169	C₂⁴×C₅	—	2	2	no	—
170	C₂⁴×C₅	—	2	2	no	—
171	C₂⁴×C₅	—	2	2	no	—
172	C₂⁴×C₅	—	2	2	no	—
173	C₂⁴×C₅	—	2	2	no	—
174	C₂⁴×C₅	#41	1	4	yes	—
175	C₂⁴×C₅	C₂⁴	1	2	yes	—
176	C₂⁴×C₅	C₂⁴	1	2	yes	—
177	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
178	C₂×C₅×D₄	—	2	8	no	—
179	C₂×C₅×D₄	—	2	8	no	—
180	C₂×C₅×D₄	—	4	4	no	—
181	C₂×C₅×D₄	—	4	16	no	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	2	2	no	—
184	C₂²×C₄×C₅	—	2	2	no	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	—	2	2	no	—
188	C₂²×C₄×C₅	—	2	2	no	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	—	2	2	no	—
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	—	2	8	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	—	2	2	no	—
208	C₂²×C₄×C₅	—	2	2	no	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	2	2	no	—
211	C₂²×C₄×C₅	—	2	2	no	—
212	C₂²×C₄×C₅	—	2	2	no	—
213	C₂²×C₄×C₅	—	2	2	no	—
214	C₂²×C₄×C₅	—	2	2	no	—
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	2	no	—
217	C₂²×C₄×C₅	—	2	2	no	—
218	C₂²×C₄×C₅	—	2	8	no	—
219	C₂²×C₄×C₅	—	4	4	no	—
220	C₂²×C₄×C₅	—	4	16	no	—
221	C₂²×C₄×C₅	#41	1	4	yes	—
222	C₂²×C₄×C₅	#41	1	4	yes	—
223	C₂²×C₄×C₅	#41	1	4	yes	—
224	C₂²×C₄×C₅	#41	1	4	yes	—
225	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₅×C₄⋊C₄	—	2	8	no	—
239	C₅×C₄⋊C₄	—	2	8	no	—
240	C₅×C₄⋊C₄	—	4	4	no	—
241	C₅×C₄⋊C₄	—	4	4	no	—
242	C₅×C₄⋊C₄	—	4	4	no	—
243	C₅×C₄⋊C₄	—	4	4	no	—
244	C₅×C₂²⋊C₄	—	2	8	no	—
245	C₅×C₂²⋊C₄	—	2	8	no	—
246	C₅×C₂²⋊C₄	—	2	8	no	—
247	C₅×C₂²⋊C₄	—	2	8	no	—
248	C₅×C₂²⋊C₄	—	2	8	no	—
249	C₅×C₂²⋊C₄	—	2	8	no	—
250	C₅×C₂²⋊C₄	—	4	4	no	—
251	C₅×C₂²⋊C₄	—	4	4	no	—
252	C₅×C₂²⋊C₄	—	4	4	no	—
253	C₅×C₂²⋊C₄	—	4	4	no	—
254	C₅×C₂²⋊C₄	—	4	4	no	—
255	C₄²×C₅	—	2	8	no	—
256	C₄²×C₅	—	2	8	no	—
257	C₄²×C₅	—	2	8	no	—
258	C₄²×C₅	—	4	4	no	—
259	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
280	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
282	#400	C₂²×C₅	1	8	yes	complemented
283	#397	C₂²×C₅	1	8	yes	complemented
284	#396	C₂²×C₅	1	8	yes	complemented
285	#394	C₂²×C₅	1	8	yes	—
286	#390	C₂²×C₅	1	8	yes	—
287	#389	C₂²×C₅	1	8	yes	complemented
288	#388	C₂²×C₅	1	8	yes	complemented
289	#388	C₂²×C₅	1	8	yes	complemented
290	#388	C₂²×C₅	1	8	yes	complemented
291	#388	C₂²×C₅	1	8	yes	complemented
292	#387	C₂²×C₅	1	8	yes	complemented
293	#386	C₂²×C₅	1	8	yes	—
294	#381	C₂²×C₅	1	8	yes	complemented
295	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
296	#376	C₂²×C₅	1	8	yes	complemented
297	C₂×#95	C₂²×C₅	1	1	yes	characteristic
298	C₂×#95	C₂²×C₅	1	1	yes	characteristic
299	C₂×#95	C₂²×C₅	1	1	yes	characteristic
300	C₂×#95	C₂²×C₅	1	1	yes	characteristic
301	C₂×#95	C₂²×C₅	1	1	yes	characteristic
302	C₂×#95	C₂²×C₅	1	1	yes	characteristic
303	C₂×#95	C₂²×C₅	1	1	yes	characteristic
304	C₂×#95	C₂²×C₅	1	1	yes	characteristic
305	C₂×#95	C₂²×C₅	1	1	yes	characteristic
306	C₂×#95	C₂²×C₅	1	1	yes	characteristic
307	C₂×#95	C₂²×C₅	1	1	yes	characteristic
308	C₂×#95	C₂²×C₅	1	1	yes	characteristic
309	C₂³×C₅	—	2	8	no	—
310	C₂³×C₅	—	2	8	no	—
311	C₂³×C₅	—	2	8	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	2	2	no	—
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	2	2	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	2	2	no	—
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	—	2	2	no	—
321	C₂³×C₅	—	2	2	no	—
322	C₂³×C₅	—	2	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	2	2	no	—
325	C₂³×C₅	—	4	4	no	—
326	C₂³×C₅	—	4	4	no	—
327	C₂³×C₅	—	4	4	no	—
328	C₂³×C₅	—	4	4	no	—
329	C₂³×C₅	—	4	4	no	—
330	C₂³×C₅	—	4	4	no	—
331	C₂³×C₅	—	4	4	no	—
332	C₂³×C₅	—	4	4	no	—
333	C₂³×C₅	—	4	4	no	—
334	C₂³×C₅	—	4	4	no	—
335	C₂³×C₅	—	4	4	no	—
336	C₂³×C₅	C₂×#41	1	4	yes	—
337	C₂³×C₅	C₂×#41	1	2	yes	—
338	C₂³×C₅	C₂×#41	1	2	yes	—
339	C₂³×C₅	C₂×#41	1	2	yes	—
340	C₂³×C₅	C₂×#41	1	2	yes	—
341	C₂³×C₅	C₂×#41	1	2	yes	—
342	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
343	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
344	C₂³×C₅	C₂⁵	1	1	yes	characteristic
345	C₅×D₄	—	4	16	no	—
346	C₂×C₄×C₅	—	2	8	no	—
347	C₂×C₄×C₅	—	2	8	no	—
348	C₂×C₄×C₅	—	2	8	no	—
349	C₂×C₄×C₅	—	2	8	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	2	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	2	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	4	16	no	—
386	C₂×C₄×C₅	—	4	4	no	—
387	C₂×C₄×C₅	—	4	4	no	—
388	C₂×C₄×C₅	—	4	4	no	—
389	C₂×C₄×C₅	—	4	4	no	—
390	C₂×C₄×C₅	—	4	4	no	—
391	C₂×C₄×C₅	—	4	4	no	—
392	C₂×C₄×C₅	—	4	4	no	—
393	C₂×C₄×C₅	—	4	4	no	—
394	C₂×C₄×C₅	—	4	4	no	—
395	C₂×C₄×C₅	C₂×#41	1	4	yes	—
396	C₂×C₄×C₅	C₂×#41	1	4	yes	—
397	C₂×C₄×C₅	C₂×#41	1	4	yes	—
398	C₂×C₄×C₅	C₂×#41	1	4	yes	—
399	C₂⁵	C₂³×C₅	1	1	yes	characteristic
400	C₂⁵	C₂³×C₅	1	1	yes	characteristic
401	C₂²×D₄	—	2	4	no	—
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	—	4	2	no	—
404	C₂²×D₄	C₂³×C₅	1	4	yes	—
405	C₂³×C₄	—	2	4	no	—
406	C₂³×C₄	—	2	4	no	—
407	C₂³×C₄	—	4	2	no	—
408	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₅	1	4	yes	—
418	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	—	2	4	no	—
424	C₂×C₄⋊C₄	—	4	2	no	—
425	C₂×C₄⋊C₄	—	4	2	no	—
426	C₂×C₄⋊C₄	—	4	2	no	—
427	C₂×C₄⋊C₄	—	4	2	no	—
428	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
434	C₂×C₂²⋊C₄	—	2	4	no	—
435	C₂×C₂²⋊C₄	—	2	4	no	—
436	C₂×C₂²⋊C₄	—	2	4	no	—
437	C₂×C₂²⋊C₄	—	2	4	no	—
438	C₂×C₂²⋊C₄	—	2	4	no	—
439	C₂×C₂²⋊C₄	—	2	4	no	—
440	C₂×C₂²⋊C₄	—	4	2	no	—
441	C₂×C₂²⋊C₄	—	4	2	no	—
442	C₂×C₂²⋊C₄	—	4	2	no	—
443	C₂×C₂²⋊C₄	—	4	2	no	—
444	C₂×C₂²⋊C₄	—	4	2	no	—
445	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
456	C₂×C₄²	—	2	4	no	—
457	C₂×C₄²	—	2	4	no	—
458	C₂×C₄²	—	2	4	no	—
459	C₂×C₄²	—	4	2	no	—
460	C₂×C₄²	C₂³×C₅	1	4	yes	—
461	C₂×C₄²	C₂³×C₅	1	4	yes	—
462	C₂×C₄²	C₂³×C₅	1	4	yes	—
463	C₂×C₄²	C₂³×C₅	1	4	yes	—
464	#95	C₂³×C₅	1	4	yes	—
465	#95	C₂³×C₅	1	4	yes	—
466	#95	C₂³×C₅	1	4	yes	—
467	#95	C₂³×C₅	1	4	yes	—
468	#95	C₂³×C₅	1	4	yes	—
469	#95	C₂³×C₅	1	4	yes	—
470	#95	C₂³×C₅	1	4	yes	—
471	#95	C₂³×C₅	1	4	yes	—
472	#95	C₂³×C₅	1	4	yes	—
473	#95	C₂³×C₅	1	4	yes	—
474	#95	C₂³×C₅	1	4	yes	—
475	#95	C₂³×C₅	1	4	yes	—
476	C₂²×C₅	—	2	4	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	2	4	no	—
479	C₂²×C₅	—	4	2	no	—
480	C₂²×C₅	—	4	2	no	—
481	C₂²×C₅	—	4	2	no	—
482	C₂²×C₅	—	4	2	no	—
483	C₂²×C₅	—	4	16	no	—
484	C₂²×C₅	—	4	2	no	—
485	C₂²×C₅	—	4	2	no	—
486	C₂²×C₅	—	4	2	no	—
487	C₂²×C₅	—	4	2	no	—
488	C₂²×C₅	—	4	2	no	—
489	C₂²×C₅	—	4	2	no	—
490	C₂²×C₅	—	4	2	no	—
491	C₂²×C₅	—	8	8	no	—
492	C₂²×C₅	#529	1	4	yes	—
493	C₂²×C₅	#529	1	4	yes	—
494	C₂²×C₅	#540	1	4	yes	—
495	C₂²×C₅	#551	1	4	yes	—
496	C₂²×C₅	#551	1	4	yes	—
497	C₂²×C₅	#553	1	4	yes	—
498	C₂²×C₅	#555	1	4	yes	—
499	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
501	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
502	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
503	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
504	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₄×C₅	—	2	4	no	—
507	C₄×C₅	—	2	4	no	—
508	C₄×C₅	—	2	4	no	—
509	C₄×C₅	—	2	4	no	—
510	C₄×C₅	—	4	2	no	—
511	C₄×C₅	—	4	2	no	—
512	C₄×C₅	—	4	2	no	—
513	C₄×C₅	—	4	2	no	—
514	C₄×C₅	—	4	2	no	—
515	C₄×C₅	—	4	2	no	—
516	C₄×C₅	—	4	2	no	—
517	C₄×C₅	—	4	2	no	—
518	C₄×C₅	—	4	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	2	no	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	C₅×#41	1	4	yes	—
533	C₂⁴	C₂⁴×C₅	1	2	yes	—
534	C₂⁴	C₂⁴×C₅	1	2	yes	—
535	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	16	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	8	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	16	no	—
579	C₂²×C₄	C₅×#41	1	4	yes	—
580	C₂²×C₄	C₅×#41	1	4	yes	—
581	C₂²×C₄	C₅×#41	1	4	yes	—
582	C₂²×C₄	C₅×#41	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	4	4	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	4	4	no	—
610	C₂²⋊C₄	—	4	4	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₄²	—	2	8	no	—
614	C₄²	—	2	8	no	—
615	C₄²	—	2	8	no	—
616	C₄²	—	4	4	no	—
617	C₂×C₅	—	4	4	no	—
618	C₂×C₅	—	8	2	no	—
619	C₂×C₅	#2526	1	8	yes	direct product factor
620	C₂×C₅	C₂×#529	1	1	yes	characteristic
621	C₂×C₅	C₂×#529	1	1	yes	characteristic
622	C₂×C₅	C₂×#540	1	1	yes	characteristic
623	C₂×C₅	C₂×#551	1	1	yes	characteristic
624	C₂×C₅	C₂×#551	1	1	yes	characteristic
625	C₂×C₅	C₂×#553	1	1	yes	characteristic
626	C₂×C₅	C₂×#555	1	1	yes	characteristic
627	C₂³	—	2	8	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	8	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	C₂×C₅×#41	1	4	yes	—
655	C₂³	C₂×C₅×#41	1	2	yes	—
656	C₂³	C₂×C₅×#41	1	2	yes	—
657	C₂³	C₂×C₅×#41	1	2	yes	—
658	C₂³	C₂×C₅×#41	1	2	yes	—
659	C₂³	C₂×C₅×#41	1	2	yes	—
660	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
661	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
662	C₂³	C₂⁵×C₅	1	1	yes	characteristic
663	D₄	—	4	16	no	—
664	C₂×C₄	—	2	8	no	—
665	C₂×C₄	—	2	8	no	—
666	C₂×C₄	—	2	8	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	16	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	C₂×C₅×#41	1	4	yes	—
714	C₂×C₄	C₂×C₅×#41	1	4	yes	—
715	C₂×C₄	C₂×C₅×#41	1	4	yes	—
716	C₂×C₄	C₂×C₅×#41	1	4	yes	—
717	C₅	C₂×#2526	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	4	16	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	8	no	—
734	C₂²	C₅×#529	1	4	yes	—
735	C₂²	C₅×#529	1	4	yes	—
736	C₂²	C₅×#540	1	4	yes	—
737	C₂²	C₅×#551	1	4	yes	—
738	C₂²	C₅×#551	1	4	yes	—
739	C₂²	C₅×#553	1	4	yes	—
740	C₂²	C₅×#555	1	4	yes	—
741	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
742	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
743	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
744	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
745	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
746	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₅×#2526	1	8	yes	direct product factor
764	C₂	C₂×C₅×#529	1	1	yes	characteristic
765	C₂	C₂×C₅×#529	1	1	yes	characteristic
766	C₂	C₂×C₅×#540	1	1	yes	characteristic
767	C₂	C₂×C₅×#551	1	1	yes	characteristic
768	C₂	C₂×C₅×#551	1	1	yes	characteristic
769	C₂	C₂×C₅×#553	1	1	yes	characteristic
770	C₂	C₂×C₅×#555	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#2526	C₂	direct (N × H)
2. C₂×C₅×#400	C₂	semidirect
3. C₂×C₅×#397	C₂	semidirect
4. C₂×C₅×#396	C₂	semidirect
7. C₂×C₅×#389	C₂	semidirect
8. C₂×C₅×#388	C₂	semidirect
9. C₂×C₅×#388	C₂	semidirect
10. C₂×C₅×#388	C₂	semidirect
11. C₂×C₅×#388	C₂	semidirect
12. C₂×C₅×#387	C₂	semidirect
14. C₂×C₅×#381	C₂	semidirect
15. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₂×C₅×#376	C₂	semidirect
40. C₅×#400	C₂²	semidirect
41. C₅×#397	C₂²	semidirect
42. C₅×#396	C₂²	semidirect
45. C₅×#389	C₂²	semidirect
46. C₅×#388	C₂²	semidirect
47. C₅×#388	C₂²	semidirect
48. C₅×#388	C₂²	semidirect
49. C₅×#388	C₂²	semidirect
50. C₅×#387	C₂²	semidirect
52. C₅×#381	C₂²	semidirect
53. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
54. C₅×#376	C₂²	semidirect
67. C₂×#2526	C₅	direct (N × H)
145. #2526	C₂×C₅	direct (N × H)
146. C₂×#400	C₂×C₅	semidirect
147. C₂×#397	C₂×C₅	semidirect
148. C₂×#396	C₂×C₅	semidirect
151. C₂×#389	C₂×C₅	semidirect
152. C₂×#388	C₂×C₅	semidirect
153. C₂×#388	C₂×C₅	semidirect
154. C₂×#388	C₂×C₅	semidirect
155. C₂×#388	C₂×C₅	semidirect
156. C₂×#387	C₂×C₅	semidirect
158. C₂×#381	C₂×C₅	semidirect
159. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
160. C₂×#376	C₂×C₅	semidirect
282. #400	C₂²×C₅	semidirect
283. #397	C₂²×C₅	semidirect
284. #396	C₂²×C₅	semidirect
287. #389	C₂²×C₅	semidirect
288. #388	C₂²×C₅	semidirect
289. #388	C₂²×C₅	semidirect
290. #388	C₂²×C₅	semidirect
291. #388	C₂²×C₅	semidirect
292. #387	C₂²×C₅	semidirect
294. #381	C₂²×C₅	semidirect
295. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
296. #376	C₂²×C₅	semidirect
619. C₂×C₅	#2526	direct (N × H)
717. C₅	C₂×#2526	direct (N × H)
763. C₂	C₅×#2526	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×#2526	2
C₂×C₅×#400	2
C₂×C₅×#397	2
C₂×C₅×#396	2
C₂×C₅×#394	2
C₂×C₅×#390	2
C₂×C₅×#389	2
C₂×C₅×#388	2
C₂×C₅×#387	2
C₂×C₅×#386	2
C₂×C₅×#381	2
C₂×C₄×C₅×C₂²⋊C₄	2
C₂×C₅×#376	2
C₂×#2526	5

Subgroups — C2×C5×#2526 #11957519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2526 #11957519