Subgroups — C₅×#24918 #11947638

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2423	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2077	C₂	1	1	yes	maximal, characteristic
7	C₅×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2035	C₂	1	1	yes	maximal, characteristic
9	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1924	C₂	1	1	yes	maximal, characteristic
11	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₅×#451	—	2	4	no	—
24	C₅×#441	—	2	4	no	—
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#106	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	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×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#103	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×#97	C₂²	1	1	yes	characteristic
39	C₅×#399	—	2	1	no	—
40	C₅×#398	—	2	1	no	—
41	C₅×#391	—	2	1	no	—
42	C₅×#391	—	2	1	no	—
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#388	—	2	1	no	—
48	C₅×#387	—	2	1	no	—
49	C₅×#384	C₂²	1	1	yes	characteristic
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	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	#24918	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	—	2	2	no	—
63	C₂²×C₅×Q₈	—	2	2	no	—
64	C₂²×C₅×Q₈	—	2	1	no	—
65	C₂²×C₅×Q₈	—	2	2	no	—
66	C₂²×C₅×Q₈	—	2	2	no	—
67	C₂²×C₅×Q₈	—	4	1	no	—
68	C₂²×C₅×Q₈	—	4	1	no	—
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅	—	2	1	no	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₅×Q₁₆	—	2	2	no	—
75	C₂×C₅×Q₁₆	—	2	2	no	—
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	—	2	2	no	—
78	C₂×C₅×Q₁₆	—	4	1	no	—
79	C₂×C₅×Q₁₆	D₄	1	4	yes	—
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₅×C₂²⋊Q₈	—	2	2	no	—
85	C₅×C₂²⋊Q₈	—	4	1	no	—
86	C₄×C₅×Q₈	—	2	2	no	—
87	C₄×C₅×Q₈	—	2	2	no	—
88	C₄×C₅×Q₈	—	2	2	no	—
89	C₄×C₅×Q₈	—	4	1	no	—
90	C₄×C₅×Q₈	—	4	1	no	—
91	C₄×C₅×Q₈	—	4	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#106	—	2	2	no	—
115	C₅×#106	—	4	1	no	—
116	C₅×C₄⋊C₈	—	4	1	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	2	2	no	—
119	C₅×#103	—	2	2	no	—
120	C₅×#103	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#103	—	2	2	no	—
123	C₅×#103	—	4	1	no	—
124	C₅×#103	—	4	1	no	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	—	4	1	no	—
127	C₅×#97	—	2	2	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	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#451	C₂×C₅	1	1	yes	characteristic
140	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
141	#2423	C₂×C₅	1	1	yes	characteristic
142	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
143	#2096	C₂×C₅	1	1	yes	characteristic, complemented
144	#2077	C₂×C₅	1	1	yes	characteristic
145	#2056	C₂×C₅	1	1	yes	characteristic, complemented
146	#2035	C₂×C₅	1	1	yes	characteristic
147	#1935	C₂×C₅	1	1	yes	characteristic, complemented
148	#1924	C₂×C₅	1	1	yes	characteristic
149	#1878	C₂×C₅	1	1	yes	characteristic, complemented
150	#1878	C₂×C₅	1	1	yes	characteristic, complemented
151	#1865	C₂×C₅	1	1	yes	characteristic, complemented
152	#1803	C₂×C₅	1	1	yes	characteristic, complemented
153	#1787	C₂×C₅	1	1	yes	characteristic
154	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	4	2	no	—
170	C₂×C₅×Q₈	—	4	2	no	—
171	C₂×C₅×Q₈	—	4	4	no	—
172	C₂×C₅×Q₈	—	4	4	no	—
173	C₂×C₅×Q₈	—	4	4	no	—
174	C₂×C₅×Q₈	—	4	4	no	—
175	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
176	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
177	C₂×C₅×Q₈	#41	1	2	yes	—
178	C₂×C₅×Q₈	#41	1	2	yes	—
179	C₂×C₅×Q₈	#41	1	2	yes	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	4	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₅×Q₁₆	—	2	8	no	—
204	C₅×Q₁₆	—	4	4	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	4	2	no	—
228	C₅×C₄⋊C₄	—	4	2	no	—
229	C₅×C₄⋊C₄	—	4	2	no	—
230	C₅×C₄⋊C₄	—	4	2	no	—
231	C₅×C₄⋊C₄	—	4	2	no	—
232	C₅×C₄⋊C₄	—	8	1	no	—
233	C₅×C₄⋊C₄	—	8	1	no	—
234	C₅×C₂²⋊C₄	—	2	2	no	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	4	2	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₅×C₂²⋊C₄	—	8	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	4	2	no	—
244	C₄²×C₅	—	4	2	no	—
245	C₄²×C₅	—	4	2	no	—
246	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
247	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
248	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
253	#451	—	2	4	no	—
254	#441	—	2	4	no	—
255	C₂×#106	C₂²×C₅	1	1	yes	characteristic
256	C₂×#106	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
258	C₂×#103	C₂²×C₅	1	1	yes	characteristic
259	C₂×#103	C₂²×C₅	1	1	yes	characteristic
260	C₂×#103	C₂²×C₅	1	1	yes	characteristic
261	C₂×#103	C₂²×C₅	1	1	yes	characteristic
262	C₂×#103	C₂²×C₅	1	1	yes	characteristic
263	C₂×#103	C₂²×C₅	1	1	yes	characteristic
264	C₂×#103	C₂²×C₅	1	1	yes	characteristic
265	C₂×#103	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×#97	C₂²×C₅	1	1	yes	characteristic
269	#399	—	2	1	no	—
270	#398	—	2	1	no	—
271	#391	—	2	1	no	—
272	#391	—	2	1	no	—
273	#391	C₂²×C₅	1	1	yes	characteristic
274	#391	C₂²×C₅	1	1	yes	characteristic
275	#391	C₂²×C₅	1	1	yes	characteristic
276	#389	C₂²×C₅	1	1	yes	characteristic
277	#388	—	2	1	no	—
278	#387	—	2	1	no	—
279	#384	C₂²×C₅	1	1	yes	characteristic
280	#380	—	2	1	no	—
281	#380	C₂²×C₅	1	1	yes	characteristic
282	#380	C₂²×C₅	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	—	2	1	no	—
284	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	#340	C₂²×C₅	1	1	yes	characteristic
286	#340	C₂²×C₅	1	1	yes	characteristic
287	#340	C₂²×C₅	1	1	yes	characteristic
288	#340	C₂²×C₅	1	1	yes	characteristic
289	#336	C₂²×C₅	1	1	yes	characteristic
290	#336	C₂²×C₅	1	1	yes	characteristic
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	#137	1	2	yes	—
298	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
299	C₅×Q₈	—	2	2	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	2	2	no	—
306	C₅×Q₈	—	4	8	no	—
307	C₅×Q₈	—	4	1	no	—
308	C₅×Q₈	—	4	1	no	—
309	C₅×Q₈	—	4	1	no	—
310	C₅×Q₈	—	4	1	no	—
311	C₅×Q₈	#123	1	4	yes	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	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	—	4	8	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	—	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	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	#137	1	2	yes	—
356	C₂×C₄×C₅	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
362	C₅×C₈	—	2	2	no	—
363	C₅×C₈	—	4	1	no	—
364	C₅×C₈	—	4	1	no	—
365	C₅×C₈	—	4	1	no	—
366	C₂²×Q₈	—	2	2	no	—
367	C₂²×Q₈	—	2	2	no	—
368	C₂²×Q₈	—	2	1	no	—
369	C₂²×Q₈	—	2	2	no	—
370	C₂²×Q₈	—	2	2	no	—
371	C₂²×Q₈	—	4	1	no	—
372	C₂²×Q₈	—	4	1	no	—
373	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂×Q₁₆	—	2	2	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	2	no	—
381	C₂×Q₁₆	—	2	2	no	—
382	C₂×Q₁₆	—	4	1	no	—
383	C₂×Q₁₆	C₅×D₄	1	4	yes	—
384	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	4	1	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	4	1	no	—
394	C₄×Q₈	—	4	1	no	—
395	C₄×Q₈	—	4	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	#106	—	2	2	no	—
419	#106	—	4	1	no	—
420	C₄⋊C₈	—	4	1	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	4	1	no	—
428	#103	—	4	1	no	—
429	C₂²⋊C₈	—	2	2	no	—
430	C₂²⋊C₈	—	4	1	no	—
431	#97	—	2	2	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	C₅×D₄	1	1	yes	characteristic
442	#95	C₅×D₄	1	1	yes	characteristic
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	2	2	no	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	4	1	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	—	4	1	no	—
449	C₂²×C₅	—	4	1	no	—
450	C₂²×C₅	#525	1	1	yes	characteristic
451	C₂²×C₅	D₄²	1	1	yes	characteristic
452	C₂²×C₅	#546	1	1	yes	characteristic
453	C₂²×C₅	C₂×#137	1	1	yes	characteristic
454	C₂²×C₅	C₂×#137	1	1	yes	characteristic
455	C₂²×C₅	#577	1	1	yes	characteristic
456	C₂²×C₅	#578	1	1	yes	characteristic
457	C₄×C₅	—	2	4	no	—
458	C₄×C₅	—	2	2	no	—
459	C₄×C₅	—	4	1	no	—
460	C₄×C₅	—	4	2	no	—
461	C₄×C₅	—	4	2	no	—
462	C₄×C₅	—	4	1	no	—
463	C₄×C₅	—	4	1	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	8	1	no	—
466	C₄×C₅	—	8	1	no	—
467	C₄×C₅	—	8	1	no	—
468	C₄×C₅	—	8	1	no	—
469	C₄×C₅	—	8	1	no	—
470	C₄×C₅	C₂×#123	1	1	yes	characteristic
471	C₄×C₅	#538	1	1	yes	characteristic
472	C₄×C₅	#546	1	1	yes	characteristic
473	C₄×C₅	#551	1	1	yes	characteristic
474	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	4	2	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	4	no	—
492	C₂×Q₈	—	4	4	no	—
493	C₂×Q₈	—	4	4	no	—
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
496	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
497	C₂×Q₈	C₅×#41	1	2	yes	—
498	C₂×Q₈	C₅×#41	1	2	yes	—
499	C₂×Q₈	C₅×#41	1	2	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	4	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	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
523	Q₁₆	—	2	8	no	—
524	Q₁₆	—	4	4	no	—
525	C₂×C₈	—	2	1	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	C₂×C₅×D₄	1	2	yes	—
537	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	8	1	no	—
553	C₄⋊C₄	—	8	1	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	4	2	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	2	no	—
566	C₂×C₅	—	4	2	no	—
567	C₂×C₅	#2418	1	1	yes	characteristic
568	C₂×C₅	#3113	1	1	yes	characteristic
569	C₂×C₅	#3121	1	1	yes	characteristic
570	C₂×C₅	#3270	1	1	yes	characteristic
571	C₂×C₅	#3278	1	1	yes	characteristic
572	C₂×C₅	#3312	1	1	yes	characteristic
573	C₂×C₅	#3316	1	1	yes	characteristic
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	C₅×#137	1	2	yes	—
581	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	4	8	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	C₅×#123	1	4	yes	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	4	8	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	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	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	C₅×#137	1	2	yes	—
639	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
640	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
641	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
643	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₅	#24918	1	1	yes	characteristic, direct product factor, Sylow
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	C₅×#525	1	1	yes	characteristic
658	C₂²	C₅×D₄²	1	1	yes	characteristic
659	C₂²	C₅×#546	1	1	yes	characteristic
660	C₂²	C₂×C₅×#137	1	1	yes	characteristic
661	C₂²	C₂×C₅×#137	1	1	yes	characteristic
662	C₂²	C₅×#577	1	1	yes	characteristic
663	C₂²	C₅×#578	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	—	8	1	no	—
677	C₄	C₂×C₅×#123	1	1	yes	characteristic
678	C₄	C₅×#538	1	1	yes	characteristic
679	C₄	C₅×#546	1	1	yes	characteristic
680	C₄	C₅×#551	1	1	yes	characteristic
681	C₂	—	4	2	no	—
682	C₂	C₅×#2418	1	1	yes	characteristic
683	C₂	C₅×#3113	1	1	yes	characteristic
684	C₂	C₅×#3121	1	1	yes	characteristic
685	C₂	C₅×#3270	1	1	yes	characteristic
686	C₂	C₅×#3278	1	1	yes	characteristic
687	C₂	C₅×#3312	1	1	yes	characteristic
688	C₂	C₅×#3316	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
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
2. C₂×C₅×#441	C₂	semidirect
5. C₅×#2096	C₂	semidirect
7. C₅×#2056	C₂	semidirect
9. C₅×#1935	C₂	semidirect
11. C₅×#1878	C₂	semidirect
12. C₅×#1878	C₂	semidirect
13. C₅×#1865	C₂	semidirect
14. C₅×#1803	C₂	semidirect
61. #24918	C₅	direct (N × H)
140. C₂×#441	C₂×C₅	semidirect
143. #2096	C₂×C₅	semidirect
145. #2056	C₂×C₅	semidirect
147. #1935	C₂×C₅	semidirect
149. #1878	C₂×C₅	semidirect
150. #1878	C₂×C₅	semidirect
151. #1865	C₂×C₅	semidirect
152. #1803	C₂×C₅	semidirect
649. C₅	#24918	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×#451	2
C₂×C₅×#441	2
C₅×#2423	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#2096	2
C₅×#2077	2
C₅×#2056	2
C₅×#2035	2
C₅×#1935	2
C₅×#1924	2
C₅×#1878	2
C₅×#1865	2
C₅×#1803	2
C₅×#1787	2
#24918	5

Subgroups — C5×#24918 #11947638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24918 #11947638