Subgroups — C₅×#25227 #11947947

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#469	C₂	1	1	yes	maximal, characteristic
3	C₅×#2504	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1851	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#121	C₂²	1	1	yes	characteristic
19	C₂×C₅×#121	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×#480	—	2	4	no	—
24	C₅×#469	—	2	4	no	—
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#397	—	2	1	no	—
38	C₅×#397	—	2	1	no	—
39	C₅×#390	—	2	1	no	—
40	C₅×#390	C₂²	1	1	yes	characteristic
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#388	—	2	1	no	—
45	C₅×#386	—	2	1	no	—
46	C₅×#386	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#382	C₂²	1	1	yes	characteristic
49	C₅×#382	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₅×C₂²⋊C₄	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×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#25227	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×D₄	—	2	1	no	—
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×D₈	—	2	2	no	—
70	C₂×C₅×D₈	—	2	2	no	—
71	C₂×C₅×D₈	—	4	1	no	—
72	C₂×C₅×M₁₆	—	2	2	no	—
73	C₂×C₅×M₁₆	—	2	2	no	—
74	C₂×C₅×M₁₆	—	4	1	no	—
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₅×#121	—	2	2	no	—
80	C₅×#121	—	2	2	no	—
81	C₅×#121	—	2	2	no	—
82	C₅×#121	D₄	1	4	yes	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	4	1	no	—
85	C₅×#117	—	2	2	no	—
86	C₅×#117	—	4	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	2	no	—
88	C₂×C₅×C₄⋊C₄	—	2	2	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₅×#107	—	2	2	no	—
114	C₅×#107	—	2	2	no	—
115	C₅×#106	—	2	2	no	—
116	C₅×C₄⋊C₈	—	2	2	no	—
117	C₅×C₄⋊C₈	—	4	1	no	—
118	C₅×#102	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	4	1	no	—
124	C₅×C₂²⋊C₈	—	2	2	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	D₄	1	1	yes	characteristic
132	C₅×#95	D₄	1	1	yes	characteristic
133	C₂×#480	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#469	C₂×C₅	1	1	yes	characteristic
135	#2504	C₂×C₅	1	1	yes	characteristic, complemented
136	#2363	C₂×C₅	1	1	yes	characteristic, complemented
137	#2085	C₂×C₅	1	1	yes	characteristic, complemented
138	#2073	C₂×C₅	1	1	yes	characteristic, complemented
139	#2067	C₂×C₅	1	1	yes	characteristic, complemented
140	#2054	C₂×C₅	1	1	yes	characteristic, complemented
141	#1949	C₂×C₅	1	1	yes	characteristic, complemented
142	#1925	C₂×C₅	1	1	yes	characteristic, complemented
143	#1879	C₂×C₅	1	1	yes	characteristic, complemented
144	#1875	C₂×C₅	1	1	yes	characteristic, complemented
145	#1851	C₂×C₅	1	1	yes	characteristic, complemented
146	#1804	C₂×C₅	1	1	yes	characteristic, complemented
147	#1736	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	—	2	1	no	—
149	C₂⁴×C₅	—	2	1	no	—
150	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	4	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	4	2	no	—
164	C₂×C₅×D₄	—	4	2	no	—
165	C₂×C₅×D₄	—	4	2	no	—
166	C₂×C₅×D₄	—	8	1	no	—
167	C₂×C₅×D₄	—	8	1	no	—
168	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	8	1	no	—
183	C₂²×C₄×C₅	—	8	1	no	—
184	C₂²×C₄×C₅	—	8	1	no	—
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₅	#41	1	2	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₅×D₈	—	4	4	no	—
194	C₅×M₁₆	—	4	4	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	#41	1	2	yes	—
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	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	4	2	no	—
218	C₅×C₄⋊C₄	—	8	1	no	—
219	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
220	C₅×C₄⋊C₄	#41	1	2	yes	—
221	C₅×C₂²⋊C₄	—	2	4	no	—
222	C₅×C₂²⋊C₄	—	4	1	no	—
223	C₅×C₂²⋊C₄	—	4	1	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	C₅×C₂²⋊C₄	—	8	1	no	—
232	C₅×C₂²⋊C₄	—	8	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	—	2	1	no	—
237	C₄²×C₅	—	4	2	no	—
238	C₄²×C₅	—	8	1	no	—
239	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₂×#121	C₂²×C₅	1	1	yes	characteristic
242	C₂×#121	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×#117	C₂²×C₅	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	#480	—	2	4	no	—
247	#469	—	2	4	no	—
248	C₂×#107	C₂²×C₅	1	1	yes	characteristic
249	C₂×#107	C₂²×C₅	1	1	yes	characteristic
250	C₂×#106	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×#102	C₂²×C₅	1	1	yes	characteristic
254	C₂×#102	C₂²×C₅	1	1	yes	characteristic
255	C₂×#102	C₂²×C₅	1	1	yes	characteristic
256	C₂×#102	C₂²×C₅	1	1	yes	characteristic
257	C₂×#102	C₂²×C₅	1	1	yes	characteristic
258	C₂×#102	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	#397	—	2	1	no	—
261	#397	—	2	1	no	—
262	#390	—	2	1	no	—
263	#390	C₂²×C₅	1	1	yes	characteristic
264	#390	C₂²×C₅	1	1	yes	characteristic
265	#390	C₂²×C₅	1	1	yes	characteristic
266	#389	C₂²×C₅	1	1	yes	characteristic
267	#388	—	2	1	no	—
268	#386	—	2	1	no	—
269	#386	—	2	1	no	—
270	#386	—	2	1	no	—
271	#382	C₂²×C₅	1	1	yes	characteristic
272	#382	C₂²×C₅	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	—	2	1	no	—
275	C₄×C₂²⋊C₄	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	#340	C₂²×C₅	1	1	yes	characteristic
280	#340	C₂²×C₅	1	1	yes	characteristic
281	#340	C₂²×C₅	1	1	yes	characteristic
282	#336	C₂²×C₅	1	1	yes	characteristic
283	#336	C₂²×C₅	1	1	yes	characteristic
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	2	no	—
291	C₂³×C₅	—	4	1	no	—
292	C₂³×C₅	—	4	1	no	—
293	C₂³×C₅	—	4	1	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	4	1	no	—
296	C₂³×C₅	—	4	1	no	—
297	C₂³×C₅	—	4	1	no	—
298	C₂³×C₅	—	4	1	no	—
299	C₂³×C₅	—	4	1	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	4	1	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	#121	1	2	yes	—
305	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	1	no	—
313	C₅×D₄	—	4	1	no	—
314	C₅×D₄	—	8	4	no	—
315	C₅×D₄	—	8	4	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	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	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	8	4	no	—
353	C₂×C₄×C₅	—	8	4	no	—
354	C₂×C₄×C₅	#121	1	2	yes	—
355	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
361	C₅×C₈	—	2	2	no	—
362	C₅×C₈	—	4	1	no	—
363	C₅×C₈	—	4	1	no	—
364	C₅×C₈	—	4	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂×D₈	—	2	2	no	—
373	C₂×D₈	—	2	2	no	—
374	C₂×D₈	—	4	1	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	4	1	no	—
378	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	C₅×D₄	1	4	yes	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	4	1	no	—
388	#117	—	2	2	no	—
389	#117	—	4	1	no	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	2	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
416	#107	—	2	2	no	—
417	#107	—	2	2	no	—
418	#106	—	2	2	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	4	1	no	—
421	#102	—	2	2	no	—
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	4	1	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	C₅×D₄	1	1	yes	characteristic
435	#95	C₅×D₄	1	1	yes	characteristic
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	8	1	no	—
447	C₂²×C₅	—	8	1	no	—
448	C₂²×C₅	—	8	1	no	—
449	C₂²×C₅	—	8	1	no	—
450	C₂²×C₅	—	8	1	no	—
451	C₂²×C₅	—	8	1	no	—
452	C₂²×C₅	—	8	1	no	—
453	C₂²×C₅	—	8	1	no	—
454	C₂²×C₅	—	8	1	no	—
455	C₂²×C₅	—	8	1	no	—
456	C₂²×C₅	—	8	1	no	—
457	C₂²×C₅	C₂×#121	1	1	yes	characteristic
458	C₂²×C₅	#546	1	1	yes	characteristic
459	C₂²×C₅	#547	1	1	yes	characteristic
460	C₂²×C₅	#575	1	1	yes	characteristic
461	C₂²×C₅	#575	1	1	yes	characteristic
462	C₂²×C₅	#576	1	1	yes	characteristic
463	C₂²×C₅	#576	1	1	yes	characteristic
464	C₄×C₅	—	2	2	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	—	4	1	no	—
467	C₄×C₅	—	4	2	no	—
468	C₄×C₅	—	4	1	no	—
469	C₄×C₅	—	4	1	no	—
470	C₄×C₅	—	4	2	no	—
471	C₄×C₅	—	8	1	no	—
472	C₄×C₅	—	8	1	no	—
473	C₄×C₅	—	8	1	no	—
474	C₄×C₅	—	8	1	no	—
475	C₄×C₅	#529	1	1	yes	characteristic
476	C₄×C₅	#539	1	1	yes	characteristic
477	C₄×C₅	#546	1	1	yes	characteristic
478	C₄×C₅	#547	1	1	yes	characteristic
479	C₂⁴	—	2	1	no	—
480	C₂⁴	—	2	1	no	—
481	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	8	1	no	—
498	C₂×D₄	—	8	1	no	—
499	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	—	8	1	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
522	C₂²×C₄	C₅×#41	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
524	D₈	—	4	4	no	—
525	M₁₆	—	4	4	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	C₅×#41	1	2	yes	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	8	1	no	—
550	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
551	C₄⋊C₄	C₅×#41	1	2	yes	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₂²⋊C₄	—	8	1	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₂²⋊C₄	—	8	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	4	2	no	—
569	C₄²	—	8	1	no	—
570	C₂×C₅	—	4	2	no	—
571	C₂×C₅	—	8	2	no	—
572	C₂×C₅	—	16	1	no	—
573	C₂×C₅	#2425	1	1	yes	characteristic
574	C₂×C₅	#3040	1	1	yes	characteristic
575	C₂×C₅	#3041	1	1	yes	characteristic
576	C₂×C₅	#3309	1	1	yes	characteristic
577	C₂×C₅	#3322	1	1	yes	characteristic
578	C₂×C₅	#3347	1	1	yes	characteristic
579	C₂×C₅	#3355	1	1	yes	characteristic
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	C₅×#121	1	2	yes	—
601	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	D₄	—	8	4	no	—
611	D₄	—	8	4	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	8	4	no	—
649	C₂×C₄	—	8	4	no	—
650	C₂×C₄	C₅×#121	1	2	yes	—
651	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
653	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
654	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
655	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
657	C₈	—	2	2	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₅	#25227	1	1	yes	characteristic, direct product factor, Sylow
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	C₂×C₅×#121	1	1	yes	characteristic
684	C₂²	C₅×#546	1	1	yes	characteristic
685	C₂²	C₅×#547	1	1	yes	characteristic
686	C₂²	C₅×#575	1	1	yes	characteristic
687	C₂²	C₅×#575	1	1	yes	characteristic
688	C₂²	C₅×#576	1	1	yes	characteristic
689	C₂²	C₅×#576	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	8	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₅×#529	1	1	yes	characteristic
702	C₄	C₅×#539	1	1	yes	characteristic
703	C₄	C₅×#546	1	1	yes	characteristic
704	C₄	C₅×#547	1	1	yes	characteristic
705	C₂	—	4	2	no	—
706	C₂	—	8	2	no	—
707	C₂	—	16	1	no	—
708	C₂	C₅×#2425	1	1	yes	characteristic
709	C₂	C₅×#3040	1	1	yes	characteristic
710	C₂	C₅×#3041	1	1	yes	characteristic
711	C₂	C₅×#3309	1	1	yes	characteristic
712	C₂	C₅×#3322	1	1	yes	characteristic
713	C₂	C₅×#3347	1	1	yes	characteristic
714	C₂	C₅×#3355	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#469	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#480	C₂	semidirect
3. C₅×#2504	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2085	C₂	semidirect
6. C₅×#2073	C₂	semidirect
7. C₅×#2067	C₂	semidirect
8. C₅×#2054	C₂	semidirect
9. C₅×#1949	C₂	semidirect
10. C₅×#1925	C₂	semidirect
11. C₅×#1879	C₂	semidirect
12. C₅×#1875	C₂	semidirect
13. C₅×#1851	C₂	semidirect
14. C₅×#1804	C₂	semidirect
15. C₅×#1736	C₂	semidirect
61. #25227	C₅	direct (N × H)
133. C₂×#480	C₂×C₅	semidirect
135. #2504	C₂×C₅	semidirect
136. #2363	C₂×C₅	semidirect
137. #2085	C₂×C₅	semidirect
138. #2073	C₂×C₅	semidirect
139. #2067	C₂×C₅	semidirect
140. #2054	C₂×C₅	semidirect
141. #1949	C₂×C₅	semidirect
142. #1925	C₂×C₅	semidirect
143. #1879	C₂×C₅	semidirect
144. #1875	C₂×C₅	semidirect
145. #1851	C₂×C₅	semidirect
146. #1804	C₂×C₅	semidirect
147. #1736	C₂×C₅	semidirect
661. C₅	#25227	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×#480	2
C₂×C₅×#469	2
C₅×#2504	2
C₅×#2363	2
C₅×#2085	2
C₅×#2073	2
C₅×#2067	2
C₅×#2054	2
C₅×#1949	2
C₅×#1925	2
C₅×#1879	2
C₅×#1875	2
C₅×#1851	2
C₅×#1804	2
C₅×#1736	2
#25227	5

Subgroups — C5×#25227 #11947947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25227 #11947947