Subgroups — C₅×#25241 #11947961

Order 1280.

850 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic
3	C₅×#2485	C₂	1	1	yes	maximal, characteristic
4	C₅×#2417	C₂	1	1	yes	maximal, characteristic
5	C₅×#2086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1892	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₅×#485	—	2	4	no	—
24	C₅×#435	—	2	4	no	—
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#103	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₅×#398	—	2	1	no	—
38	C₅×#397	—	2	1	no	—
39	C₅×#396	—	2	1	no	—
40	C₅×#394	—	2	1	no	—
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#389	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#388	—	2	1	no	—
46	C₅×#387	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#380	—	2	1	no	—
49	C₅×#380	C₂²	1	1	yes	characteristic
50	C₅×#380	C₂²	1	1	yes	characteristic
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#340	C₂²	1	1	yes	characteristic
61	#25241	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×M₁₆	—	2	2	no	—
68	C₂×C₅×M₁₆	—	2	2	no	—
69	C₂×C₅×M₁₆	—	4	1	no	—
70	C₂²×C₅×C₈	—	2	2	no	—
71	C₂²×C₅×C₈	—	2	2	no	—
72	C₂²×C₅×C₈	—	4	1	no	—
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×C₂²⋊Q₈	—	2	2	no	—
78	C₅×C₂²⋊Q₈	—	2	2	no	—
79	C₅×C₂²⋊Q₈	—	2	2	no	—
80	C₅×C₂²⋊Q₈	—	4	1	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₅×#117	—	2	2	no	—
84	C₅×#117	—	2	2	no	—
85	C₂×C₅×C₄⋊C₄	—	2	2	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	4	1	no	—
93	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#107	—	2	2	no	—
113	C₅×#107	—	2	2	no	—
114	C₅×#107	—	4	1	no	—
115	C₅×#106	—	2	2	no	—
116	C₅×C₄⋊C₈	—	2	2	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	2	2	no	—
120	C₅×#103	—	4	1	no	—
121	C₅×C₂²⋊C₈	—	2	2	no	—
122	C₅×C₂²⋊C₈	D₄	1	4	yes	—
123	C₅×#97	—	2	2	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₂×#485	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#435	C₂×C₅	1	1	yes	characteristic
135	#2485	C₂×C₅	1	1	yes	characteristic
136	#2417	C₂×C₅	1	1	yes	characteristic
137	#2086	C₂×C₅	1	1	yes	characteristic, complemented
138	#2077	C₂×C₅	1	1	yes	characteristic, complemented
139	#2068	C₂×C₅	1	1	yes	characteristic, complemented
140	#2036	C₂×C₅	1	1	yes	characteristic, complemented
141	#1943	C₂×C₅	1	1	yes	characteristic, complemented
142	#1935	C₂×C₅	1	1	yes	characteristic, complemented
143	#1894	C₂×C₅	1	1	yes	characteristic, complemented
144	#1892	C₂×C₅	1	1	yes	characteristic, complemented
145	#1852	C₂×C₅	1	1	yes	characteristic, complemented
146	#1808	C₂×C₅	1	1	yes	characteristic, complemented
147	#1736	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	4	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	4	2	no	—
178	C₂²×C₄×C₅	—	4	2	no	—
179	C₂²×C₄×C₅	—	8	1	no	—
180	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₅	#41	1	2	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₅×M₁₆	—	4	4	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	4	4	no	—
198	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
199	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
200	C₂×C₅×C₈	#41	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	4	2	no	—
216	C₅×C₄⋊C₄	—	4	2	no	—
217	C₅×C₄⋊C₄	—	4	2	no	—
218	C₅×C₄⋊C₄	—	4	2	no	—
219	C₅×C₄⋊C₄	—	8	1	no	—
220	C₅×C₄⋊C₄	—	8	1	no	—
221	C₅×C₄⋊C₄	#41	1	2	yes	—
222	C₅×C₂²⋊C₄	—	2	2	no	—
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₅×C₂²⋊C₄	—	4	2	no	—
225	C₅×C₂²⋊C₄	—	4	2	no	—
226	C₅×C₂²⋊C₄	—	4	2	no	—
227	C₅×C₂²⋊C₄	—	4	2	no	—
228	C₅×C₂²⋊C₄	—	8	1	no	—
229	C₅×C₂²⋊C₄	—	8	1	no	—
230	C₅×C₂²⋊C₄	—	8	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	4	2	no	—
234	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×#117	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	#485	—	2	4	no	—
242	#435	—	2	4	no	—
243	C₂×#107	C₂²×C₅	1	1	yes	characteristic
244	C₂×#107	C₂²×C₅	1	1	yes	characteristic
245	C₂×#107	C₂²×C₅	1	1	yes	characteristic
246	C₂×#106	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅	1	1	yes	characteristic
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#103	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
254	C₂×#97	C₂²×C₅	1	1	yes	characteristic
255	#398	—	2	1	no	—
256	#397	—	2	1	no	—
257	#396	—	2	1	no	—
258	#394	—	2	1	no	—
259	#391	C₂²×C₅	1	1	yes	characteristic
260	#389	C₂²×C₅	1	1	yes	characteristic
261	#389	C₂²×C₅	1	1	yes	characteristic
262	#389	C₂²×C₅	1	1	yes	characteristic
263	#388	—	2	1	no	—
264	#387	—	2	1	no	—
265	#386	—	2	1	no	—
266	#380	—	2	1	no	—
267	#380	C₂²×C₅	1	1	yes	characteristic
268	#380	C₂²×C₅	1	1	yes	characteristic
269	#380	C₂²×C₅	1	1	yes	characteristic
270	#380	C₂²×C₅	1	1	yes	characteristic
271	#340	C₂²×C₅	1	1	yes	characteristic
272	#340	C₂²×C₅	1	1	yes	characteristic
273	#340	C₂²×C₅	1	1	yes	characteristic
274	#340	C₂²×C₅	1	1	yes	characteristic
275	#340	C₂²×C₅	1	1	yes	characteristic
276	#340	C₂²×C₅	1	1	yes	characteristic
277	#340	C₂²×C₅	1	1	yes	characteristic
278	#340	C₂²×C₅	1	1	yes	characteristic
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	#121	1	2	yes	—
292	C₂³×C₅	#137	1	2	yes	—
293	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
294	C₅×Q₈	—	4	1	no	—
295	C₅×Q₈	—	4	1	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×D₄	—	4	4	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	8	4	no	—
343	C₂×C₄×C₅	#121	1	2	yes	—
344	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
350	C₅×C₈	—	2	2	no	—
351	C₅×C₈	—	2	2	no	—
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	—	4	1	no	—
354	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	4	1	no	—
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	—	2	2	no	—
364	C₂²×C₈	—	4	1	no	—
365	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	4	1	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	#117	—	2	2	no	—
376	#117	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	4	1	no	—
385	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
404	#107	—	2	2	no	—
405	#107	—	2	2	no	—
406	#107	—	4	1	no	—
407	#106	—	2	2	no	—
408	C₄⋊C₈	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	#103	—	4	1	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	C₅×D₄	1	4	yes	—
415	#97	—	2	2	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	4	1	no	—
437	C₂²×C₅	—	4	1	no	—
438	C₂²×C₅	—	4	1	no	—
439	C₂²×C₅	C₂×#121	1	1	yes	characteristic
440	C₂²×C₅	#546	1	1	yes	characteristic
441	C₂²×C₅	#547	1	1	yes	characteristic
442	C₂²×C₅	C₂×#137	1	1	yes	characteristic
443	C₂²×C₅	#575	1	1	yes	characteristic
444	C₂²×C₅	#576	1	1	yes	characteristic
445	C₂²×C₅	#578	1	1	yes	characteristic
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	—	8	1	no	—
453	C₄×C₅	—	8	1	no	—
454	C₄×C₅	—	8	1	no	—
455	C₄×C₅	—	8	1	no	—
456	C₄×C₅	—	8	1	no	—
457	C₄×C₅	—	8	1	no	—
458	C₄×C₅	#529	1	1	yes	characteristic
459	C₄×C₅	#539	1	1	yes	characteristic
460	C₄×C₅	#546	1	1	yes	characteristic
461	C₄×C₅	#547	1	1	yes	characteristic
462	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
499	C₂²×C₄	C₅×#41	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
501	M₁₆	—	4	4	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	4	4	no	—
512	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
513	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
514	C₂×C₈	C₅×#41	1	2	yes	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	—	8	1	no	—
535	C₄⋊C₄	C₅×#41	1	2	yes	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	8	1	no	—
543	C₂²⋊C₄	—	8	1	no	—
544	C₂²⋊C₄	—	8	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	4	2	no	—
548	C₂×C₅	—	4	2	no	—
549	C₂×C₅	—	4	2	no	—
550	C₂×C₅	#2425	1	1	yes	characteristic
551	C₂×C₅	#3056	1	1	yes	characteristic
552	C₂×C₅	#3061	1	1	yes	characteristic
553	C₂×C₅	#3312	1	1	yes	characteristic
554	C₂×C₅	#3319	1	1	yes	characteristic
555	C₂×C₅	#3346	1	1	yes	characteristic
556	C₂×C₅	#3349	1	1	yes	characteristic
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	C₅×#121	1	2	yes	—
570	C₂³	C₅×#137	1	2	yes	—
571	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	D₄	—	4	4	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	8	4	no	—
621	C₂×C₄	C₅×#121	1	2	yes	—
622	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
623	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
624	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
625	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
626	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
628	C₈	—	2	2	no	—
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₈	—	4	1	no	—
632	C₅	#25241	1	1	yes	characteristic, direct product factor, Sylow
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	C₂×C₅×#121	1	1	yes	characteristic
648	C₂²	C₅×#546	1	1	yes	characteristic
649	C₂²	C₅×#547	1	1	yes	characteristic
650	C₂²	C₂×C₅×#137	1	1	yes	characteristic
651	C₂²	C₅×#575	1	1	yes	characteristic
652	C₂²	C₅×#576	1	1	yes	characteristic
653	C₂²	C₅×#578	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	C₅×#529	1	1	yes	characteristic
667	C₄	C₅×#539	1	1	yes	characteristic
668	C₄	C₅×#546	1	1	yes	characteristic
669	C₄	C₅×#547	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	4	2	no	—
672	C₂	C₅×#2425	1	1	yes	characteristic
673	C₂	C₅×#3056	1	1	yes	characteristic
674	C₂	C₅×#3061	1	1	yes	characteristic
675	C₂	C₅×#3312	1	1	yes	characteristic
676	C₂	C₅×#3319	1	1	yes	characteristic
677	C₂	C₅×#3346	1	1	yes	characteristic
678	C₂	C₅×#3349	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#485	C₂	semidirect
5. C₅×#2086	C₂	semidirect
6. C₅×#2077	C₂	semidirect
7. C₅×#2068	C₂	semidirect
8. C₅×#2036	C₂	semidirect
9. C₅×#1943	C₂	semidirect
10. C₅×#1935	C₂	semidirect
11. C₅×#1894	C₂	semidirect
12. C₅×#1892	C₂	semidirect
13. C₅×#1852	C₂	semidirect
14. C₅×#1808	C₂	semidirect
15. C₅×#1736	C₂	semidirect
61. #25241	C₅	direct (N × H)
133. C₂×#485	C₂×C₅	semidirect
137. #2086	C₂×C₅	semidirect
138. #2077	C₂×C₅	semidirect
139. #2068	C₂×C₅	semidirect
140. #2036	C₂×C₅	semidirect
141. #1943	C₂×C₅	semidirect
142. #1935	C₂×C₅	semidirect
143. #1894	C₂×C₅	semidirect
144. #1892	C₂×C₅	semidirect
145. #1852	C₂×C₅	semidirect
146. #1808	C₂×C₅	semidirect
147. #1736	C₂×C₅	semidirect
632. C₅	#25241	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×#485	2
C₂×C₅×#435	2
C₅×#2485	2
C₅×#2417	2
C₅×#2086	2
C₅×#2077	2
C₅×#2068	2
C₅×#2036	2
C₅×#1943	2
C₅×#1935	2
C₅×#1894	2
C₅×#1892	2
C₅×#1852	2
C₅×#1808	2
C₅×#1736	2
#25241	5

Subgroups — C5×#25241 #11947961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25241 #11947961