Subgroups — C₅×#22509 #11945229

Order 1280.

1064 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1985	C₂	1	2	yes	maximal, complemented
5	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1984	C₂	1	2	yes	maximal, complemented
7	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1798	C₂	1	2	yes	maximal
9	C₅×#1797	C₂	1	1	yes	maximal, characteristic
10	C₅×#1750	C₂	1	2	yes	maximal
11	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	—	2	4	no	—
13	C₅×#533	—	2	4	no	—
14	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₅×#125	C₄	1	2	yes	—
17	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	2	yes	—
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#446	—	2	4	no	—
26	C₅×C₈×Q₈	—	2	4	no	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×#97	C₂²	1	2	yes	—
35	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	1	yes	characteristic
45	#22509	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
48	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₅×C₄⋊Q₈	—	2	4	no	—
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₅×#125	—	2	8	no	—
61	C₅×C₂²⋊Q₈	—	2	4	no	—
62	C₅×C₂²⋊Q₈	—	2	4	no	—
63	C₅×C₂²⋊Q₈	—	2	8	no	—
64	C₄×C₅×Q₈	—	2	4	no	—
65	C₄×C₅×Q₈	—	2	4	no	—
66	C₄×C₅×Q₈	—	2	2	no	—
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×Q₈	D₄	1	4	yes	—
69	C₄×C₅×Q₈	D₄	1	4	yes	—
70	C₅×#117	—	2	4	no	—
71	C₅×#117	—	2	4	no	—
72	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₅	—	2	2	no	—
84	C₂×C₄²×C₅	—	2	2	no	—
85	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	2	yes	—
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	—	2	2	no	—
92	C₅×C₄⋊C₈	—	2	4	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	—	2	4	no	—
95	C₅×C₂²⋊C₈	—	2	4	no	—
96	C₅×C₂²⋊C₈	—	2	2	no	—
97	C₅×C₂²⋊C₈	Q₈	1	4	yes	complemented
98	C₅×#97	—	2	4	no	—
99	C₄×C₅×C₈	—	2	2	no	—
100	C₄×C₅×C₈	—	2	4	no	—
101	C₄×C₅×C₈	—	2	2	no	—
102	C₂×#533	C₂×C₅	1	1	yes	characteristic
103	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
105	#1985	C₂×C₅	1	2	yes	complemented
106	#1984	C₂×C₅	1	1	yes	characteristic, complemented
107	#1984	C₂×C₅	1	1	yes	characteristic, complemented
108	#1984	C₂×C₅	1	2	yes	complemented
109	#1798	C₂×C₅	1	2	yes	—
110	#1797	C₂×C₅	1	1	yes	characteristic
111	#1750	C₂×C₅	1	2	yes	—
112	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
113	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	—	4	2	no	—
122	C₂×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	4	1	no	—
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₅	#41	1	2	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
162	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
171	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₅×C₂²⋊C₄	—	2	4	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	C₂×D₄	1	2	yes	—
181	C₄²×C₅	C₂×D₄	1	2	yes	—
182	C₄²×C₅	C₂×D₄	1	4	yes	—
183	C₄²×C₅	C₂×D₄	1	4	yes	—
184	#533	—	2	4	no	—
185	#533	—	2	4	no	—
186	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
188	C₂×#125	C₄×C₅	1	2	yes	—
189	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
190	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
191	C₂×C₂²⋊Q₈	C₄×C₅	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×#117	C₂²×C₅	1	2	yes	—
196	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
197	#446	—	2	4	no	—
198	C₈×Q₈	—	2	4	no	—
199	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×#97	C₂²×C₅	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
210	#336	C₂²×C₅	1	2	yes	—
211	#336	C₂²×C₅	1	2	yes	—
212	#336	C₂²×C₅	1	2	yes	—
213	#336	C₂²×C₅	1	1	yes	characteristic
214	#336	C₂²×C₅	1	2	yes	—
215	#336	C₂²×C₅	1	2	yes	—
216	#336	C₂²×C₅	1	1	yes	characteristic
217	C₂³×C₅	—	2	1	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	C₄×Q₈	1	2	yes	—
224	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
225	C₅×Q₈	—	2	8	no	—
226	C₅×Q₈	—	4	8	no	—
227	C₅×Q₈	—	4	4	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
255	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
256	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
258	C₂×C₄×C₅	#131	1	2	yes	—
259	C₂×C₄×C₅	#131	1	2	yes	—
260	C₂×C₄×C₅	#131	1	2	yes	—
261	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
267	C₅×C₈	—	2	2	no	—
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	2	no	—
273	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
275	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₅	1	2	yes	—
280	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₅	1	2	yes	—
283	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	4	no	—
286	C₄⋊Q₈	—	2	4	no	—
287	#125	—	2	8	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	C₅×D₄	1	4	yes	—
296	C₄×Q₈	C₅×D₄	1	4	yes	—
297	#117	—	2	4	no	—
298	#117	—	2	4	no	—
299	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
303	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
304	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₅	1	2	yes	—
315	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₅	1	2	yes	—
317	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	4	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	4	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	C₅×Q₈	1	4	yes	complemented
325	#97	—	2	4	no	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	4	no	—
328	C₄×C₈	—	2	2	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	1	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
337	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
338	C₂²×C₅	#519	1	1	yes	characteristic
339	C₂²×C₅	C₂×#131	1	1	yes	characteristic
340	C₂²×C₅	C₂×#131	1	1	yes	characteristic
341	C₂²×C₅	C₂×#131	1	1	yes	characteristic
342	C₂²×C₅	#568	1	1	yes	characteristic
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	4	no	—
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	4	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	#408	1	4	yes	—
352	C₄×C₅	#548	1	1	yes	characteristic
353	C₄×C₅	#548	1	1	yes	characteristic
354	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
355	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
356	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	C₅×C₂²⋊C₄	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
381	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
382	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
386	C₂²×C₄	C₅×#41	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
405	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
414	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	C₂×C₅×D₄	1	2	yes	—
424	C₄²	C₂×C₅×D₄	1	2	yes	—
425	C₄²	C₂×C₅×D₄	1	4	yes	—
426	C₄²	C₂×C₅×D₄	1	4	yes	—
427	C₂×C₅	—	4	2	no	—
428	C₂×C₅	Q₈×C₂²⋊C₄	1	1	yes	characteristic
429	C₂×C₅	C₂×#408	1	1	yes	characteristic
430	C₂×C₅	#2880	1	1	yes	characteristic
431	C₂×C₅	#2960	1	1	yes	characteristic
432	C₂×C₅	#2962	1	1	yes	characteristic
433	C₂×C₅	#2985	1	1	yes	characteristic
434	C₂×C₅	#2986	1	1	yes	characteristic
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	C₄×C₅×Q₈	1	2	yes	—
442	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
443	Q₈	—	2	8	no	—
444	Q₈	—	4	8	no	—
445	Q₈	—	4	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
472	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
473	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
474	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
475	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
476	C₂×C₄	C₅×#131	1	2	yes	—
477	C₂×C₄	C₅×#131	1	2	yes	—
478	C₂×C₄	C₅×#131	1	2	yes	—
479	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
482	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
483	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₈	—	4	1	no	—
488	C₈	—	4	2	no	—
489	C₈	—	4	1	no	—
490	C₈	—	4	2	no	—
491	C₅	#22509	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
500	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
501	C₂²	C₅×#519	1	1	yes	characteristic
502	C₂²	C₂×C₅×#131	1	1	yes	characteristic
503	C₂²	C₂×C₅×#131	1	1	yes	characteristic
504	C₂²	C₂×C₅×#131	1	1	yes	characteristic
505	C₂²	C₅×#568	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	C₅×#408	1	4	yes	—
515	C₄	C₅×#548	1	1	yes	characteristic
516	C₄	C₅×#548	1	1	yes	characteristic
517	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
518	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	C₅×Q₈×C₂²⋊C₄	1	1	yes	characteristic
521	C₂	C₂×C₅×#408	1	1	yes	characteristic
522	C₂	C₅×#2880	1	1	yes	characteristic
523	C₂	C₅×#2960	1	1	yes	characteristic
524	C₂	C₅×#2962	1	1	yes	characteristic
525	C₂	C₅×#2985	1	1	yes	characteristic
526	C₂	C₅×#2986	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#446	C₂	semidirect
3. C₂×C₅×C₈×Q₈	C₂	semidirect
4. C₅×#1985	C₂	semidirect
5. C₅×#1984	C₂	semidirect
6. C₅×#1984	C₂	semidirect
7. C₅×#1984	C₂	semidirect
45. #22509	C₅	direct (N × H)
97. C₅×C₂²⋊C₈	Q₈	semidirect
103. C₂×#446	C₂×C₅	semidirect
104. C₂×C₈×Q₈	C₂×C₅	semidirect
105. #1985	C₂×C₅	semidirect
106. #1984	C₂×C₅	semidirect
107. #1984	C₂×C₅	semidirect
108. #1984	C₂×C₅	semidirect
324. C₂²⋊C₈	C₅×Q₈	semidirect
491. C₅	#22509	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×#533	2
C₂×C₅×#446	2
C₂×C₅×C₈×Q₈	2
C₅×#1985	2
C₅×#1984	2
C₅×#1798	2
C₅×#1797	2
C₅×#1750	2
C₄×C₅×C₂²⋊C₈	2
#22509	5

Subgroups — C5×#22509 #11945229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22509 #11945229