Subgroups — C₅×#17750 #11940470

Order 1280.

1276 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1560	C₂	1	4	yes	maximal, complemented
5	C₅×#1551	C₂	1	4	yes	maximal, complemented
6	C₅×#1548	C₂	1	2	yes	maximal, complemented
7	C₅×#1545	C₂	1	2	yes	maximal, complemented
8	C₂²×C₅×#41	C₄	1	2	yes	—
9	C₂²×C₅×M₁₆	—	2	1	no	—
10	C₅×#532	—	2	1	no	—
11	C₅×#532	—	2	1	no	—
12	C₅×#532	—	2	1	no	—
13	C₅×#532	—	2	1	no	—
14	C₅×#532	C₄	1	2	yes	—
15	C₅×#532	C₄	1	2	yes	—
16	C₅×#532	C₂²	1	2	yes	—
17	C₅×#532	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#127	C₂²	1	1	yes	characteristic
20	C₂×C₅×#124	C₄	1	2	yes	—
21	C₂×C₅×#121	—	2	1	no	—
22	C₂×C₅×#121	—	2	1	no	—
23	C₂×C₄×C₅×D₄	—	2	1	no	—
24	C₂×C₄×C₅×D₄	—	2	1	no	—
25	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₅×#432	—	2	1	no	—
27	C₅×#432	C₂²	1	2	yes	complemented
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#423	—	2	1	no	—
31	C₅×#423	—	2	1	no	—
32	C₅×#423	C₂²	1	2	yes	—
33	C₅×#423	C₂²	1	2	yes	complemented
34	C₅×#423	C₂²	1	2	yes	complemented
35	C₂×C₅×C₄⋊C₈	—	2	1	no	—
36	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₅×#407	—	2	1	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₅×#333	C₂²	1	8	yes	complemented
40	C₅×#331	C₂²	1	8	yes	complemented
41	#17750	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	—	2	2	no	—
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	4	8	no	—
45	C₂×C₅×#41	C₂×C₄	1	4	yes	—
46	C₂×C₅×#41	C₂×C₄	1	4	yes	—
47	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
48	C₂²×C₅×D₄	—	2	2	no	—
49	C₂²×C₅×D₄	—	2	1	no	—
50	C₂²×C₅×D₄	—	2	1	no	—
51	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₅	—	2	2	no	—
53	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	4	4	no	—
60	C₂²×C₅×C₈	—	2	2	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₅×#127	—	2	1	no	—
66	C₅×#127	—	2	1	no	—
67	C₅×#127	C₂×C₄	1	2	yes	—
68	C₅×#127	C₂³	1	2	yes	—
69	C₅×#124	—	2	2	no	—
70	C₅×#124	—	2	2	no	—
71	C₅×#124	C₂×C₄	1	4	yes	—
72	C₅×#124	C₂×C₄	1	4	yes	—
73	C₅×#121	—	2	2	no	—
74	C₅×#121	—	2	2	no	—
75	C₅×#121	—	2	2	no	—
76	C₅×#121	—	2	2	no	—
77	C₅×#121	—	2	2	no	—
78	C₅×#121	—	2	2	no	—
79	C₅×#121	—	2	2	no	—
80	C₅×#121	—	2	2	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×C₄⋊C₈	—	2	2	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	2	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	C₂³	1	4	yes	—
110	C₅×C₄⋊C₈	C₂³	1	4	yes	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×C₂²⋊C₈	—	2	2	no	—
113	C₅×#97	—	2	2	no	—
114	C₄×C₅×C₈	—	2	2	no	—
115	C₂×#532	C₂×C₅	1	1	yes	characteristic
116	#2920	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×#423	C₂×C₅	1	1	yes	characteristic, complemented
118	#1560	C₂×C₅	1	4	yes	complemented
119	#1551	C₂×C₅	1	4	yes	complemented
120	#1548	C₂×C₅	1	2	yes	complemented
121	#1545	C₂×C₅	1	2	yes	complemented
122	C₂⁴×C₅	—	2	2	no	—
123	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₅×#41	—	4	8	no	—
125	C₅×#41	—	4	8	no	—
126	C₅×#41	—	4	8	no	—
127	C₅×#41	—	4	8	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	4	4	no	—
130	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	4	4	no	—
139	C₂×C₅×D₄	—	4	4	no	—
140	C₂×C₅×D₄	—	4	8	no	—
141	C₂×C₅×D₄	—	4	2	no	—
142	C₂×C₅×D₄	—	4	2	no	—
143	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	2	4	no	—
150	C₂²×C₄×C₅	—	4	2	no	—
151	C₂²×C₄×C₅	—	4	8	no	—
152	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₅×M₁₆	—	4	4	no	—
171	C₅×M₁₆	—	4	4	no	—
172	C₅×M₁₆	—	4	4	no	—
173	C₂×C₅×C₈	—	2	4	no	—
174	C₂×C₅×C₈	—	2	4	no	—
175	C₂×C₅×C₈	—	4	4	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	4	no	—
181	C₅×C₂²⋊C₄	—	2	4	no	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
186	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
187	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
188	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
189	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
190	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₅	C₂⁴	1	1	yes	characteristic
200	C₂²×#41	C₄×C₅	1	2	yes	—
201	C₂²×M₁₆	—	2	1	no	—
202	#532	—	2	1	no	—
203	#532	—	2	1	no	—
204	#532	—	2	1	no	—
205	#532	—	2	1	no	—
206	#532	C₄×C₅	1	2	yes	—
207	#532	C₄×C₅	1	2	yes	—
208	#532	C₂²×C₅	1	2	yes	—
209	#532	C₂²×C₅	1	2	yes	—
210	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
211	C₂×#127	C₂²×C₅	1	1	yes	characteristic
212	C₂×#124	C₄×C₅	1	2	yes	—
213	C₂×#121	—	2	1	no	—
214	C₂×#121	—	2	1	no	—
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
218	#432	—	2	1	no	—
219	#432	C₂²×C₅	1	2	yes	complemented
220	#431	—	2	1	no	—
221	#431	C₂²×C₅	1	2	yes	—
222	#423	—	2	1	no	—
223	#423	—	2	1	no	—
224	#423	C₂²×C₅	1	2	yes	—
225	#423	C₂²×C₅	1	2	yes	complemented
226	#423	C₂²×C₅	1	2	yes	complemented
227	C₂×C₄⋊C₈	—	2	1	no	—
228	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
229	#407	—	2	1	no	—
230	C₄×M₁₆	—	2	1	no	—
231	#333	C₂²×C₅	1	8	yes	complemented
232	#331	C₂²×C₅	1	8	yes	complemented
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	4	1	no	—
237	C₂³×C₅	—	4	4	no	—
238	C₂³×C₅	—	4	4	no	—
239	C₂³×C₅	—	4	4	no	—
240	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₅×Q₈	—	4	4	no	—
244	C₅×Q₈	—	4	4	no	—
245	C₅×D₄	—	4	4	no	—
246	C₅×D₄	—	4	4	no	—
247	C₅×D₄	—	4	8	no	—
248	C₅×D₄	—	4	8	no	—
249	C₅×D₄	—	4	2	no	—
250	C₅×D₄	—	4	2	no	—
251	C₅×D₄	—	4	4	no	—
252	C₅×D₄	—	4	4	no	—
253	C₅×D₄	—	4	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	4	1	no	—
271	C₂×C₄×C₅	—	4	1	no	—
272	C₂×C₄×C₅	—	4	1	no	—
273	C₂×C₄×C₅	—	4	8	no	—
274	C₂×C₄×C₅	—	4	4	no	—
275	C₂×C₄×C₅	—	4	8	no	—
276	C₂×C₄×C₅	#100	1	4	yes	—
277	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
287	C₂×C₄×C₅	#137	1	2	yes	—
288	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₅×C₈	—	4	4	no	—
292	C₅×C₈	—	4	4	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	4	8	no	—
296	C₂×#41	C₂×C₄×C₅	1	4	yes	—
297	C₂×#41	C₂×C₄×C₅	1	4	yes	—
298	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
305	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
306	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	4	4	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
316	#127	—	2	1	no	—
317	#127	—	2	1	no	—
318	#127	C₂×C₄×C₅	1	2	yes	—
319	#127	C₂³×C₅	1	2	yes	—
320	#124	—	2	2	no	—
321	#124	—	2	2	no	—
322	#124	C₂×C₄×C₅	1	4	yes	—
323	#124	C₂×C₄×C₅	1	4	yes	—
324	#121	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	#121	—	2	2	no	—
329	#121	—	2	2	no	—
330	#121	—	2	2	no	—
331	#121	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
345	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
346	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
347	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
348	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
349	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
350	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
351	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
352	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	C₂³×C₅	1	4	yes	—
361	C₄⋊C₈	C₂³×C₅	1	4	yes	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	#97	—	2	2	no	—
365	C₄×C₈	—	2	2	no	—
366	C₂²×C₅	—	2	1	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	1	no	—
370	C₂²×C₅	—	2	1	no	—
371	C₂²×C₅	—	2	1	no	—
372	C₂²×C₅	—	2	1	no	—
373	C₂²×C₅	—	4	4	no	—
374	C₂²×C₅	—	4	4	no	—
375	C₂²×C₅	—	4	4	no	—
376	C₂²×C₅	—	4	4	no	—
377	C₂²×C₅	—	8	8	no	—
378	C₂²×C₅	C₂×#100	1	2	yes	—
379	C₂²×C₅	#417	1	2	yes	—
380	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
381	C₄×C₅	—	2	1	no	—
382	C₄×C₅	—	2	1	no	—
383	C₄×C₅	—	2	1	no	—
384	C₄×C₅	—	2	1	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	4	4	no	—
389	C₄×C₅	C₂×#100	1	2	yes	—
390	C₄×C₅	C₂×#100	1	2	yes	—
391	C₄×C₅	#417	1	2	yes	—
392	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄×C₅	C₂×#137	1	1	yes	characteristic
394	C₄×C₅	#575	1	2	yes	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
397	#41	—	4	8	no	—
398	#41	—	4	8	no	—
399	#41	—	4	8	no	—
400	#41	—	4	8	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	8	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	8	no	—
425	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
427	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
429	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
431	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
433	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
443	M₁₆	—	4	4	no	—
444	M₁₆	—	4	4	no	—
445	M₁₆	—	4	4	no	—
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	—	4	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
458	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
459	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
462	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
463	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
464	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
467	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
468	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
469	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
470	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
471	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
472	C₄²	C₂⁴×C₅	1	1	yes	characteristic
473	C₂×C₅	—	2	2	no	—
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	4	1	no	—
476	C₂×C₅	—	8	4	no	—
477	C₂×C₅	C₂²×#100	1	1	yes	characteristic
478	C₂×C₅	C₂×#417	1	1	yes	characteristic
479	C₂×C₅	#2896	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
488	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
489	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
490	Q₈	—	4	4	no	—
491	Q₈	—	4	4	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	8	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	C₅×#100	1	4	yes	—
524	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
527	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
528	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
529	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
530	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
533	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
534	C₂×C₄	C₅×#137	1	2	yes	—
535	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
536	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
538	C₈	—	4	4	no	—
539	C₈	—	4	4	no	—
540	C₅	#17750	1	1	yes	characteristic, direct product factor, Sylow
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	8	8	no	—
553	C₂²	C₂×C₅×#100	1	2	yes	—
554	C₂²	C₅×#417	1	2	yes	—
555	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	4	no	—
564	C₄	C₂×C₅×#100	1	2	yes	—
565	C₄	C₂×C₅×#100	1	2	yes	—
566	C₄	C₅×#417	1	2	yes	—
567	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
568	C₄	C₂×C₅×#137	1	1	yes	characteristic
569	C₄	C₅×#575	1	2	yes	—
570	C₂	—	2	2	no	—
571	C₂	—	2	2	no	—
572	C₂	—	4	1	no	—
573	C₂	—	8	4	no	—
574	C₂	C₂²×C₅×#100	1	1	yes	characteristic
575	C₂	C₂×C₅×#417	1	1	yes	characteristic
576	C₂	C₅×#2896	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2920	C₂	semidirect
3. C₂×C₅×#423	C₂	semidirect
4. C₅×#1560	C₂	semidirect
5. C₅×#1551	C₂	semidirect
6. C₅×#1548	C₂	semidirect
7. C₅×#1545	C₂	semidirect
27. C₅×#432	C₂²	semidirect
33. C₅×#423	C₂²	semidirect
34. C₅×#423	C₂²	semidirect
36. C₂×C₅×C₄⋊C₈	C₂²	semidirect
39. C₅×#333	C₂²	semidirect
40. C₅×#331	C₂²	semidirect
41. #17750	C₅	direct (N × H)
116. #2920	C₂×C₅	semidirect
117. C₂×#423	C₂×C₅	semidirect
118. #1560	C₂×C₅	semidirect
119. #1551	C₂×C₅	semidirect
120. #1548	C₂×C₅	semidirect
121. #1545	C₂×C₅	semidirect
219. #432	C₂²×C₅	semidirect
225. #423	C₂²×C₅	semidirect
226. #423	C₂²×C₅	semidirect
228. C₂×C₄⋊C₈	C₂²×C₅	semidirect
231. #333	C₂²×C₅	semidirect
232. #331	C₂²×C₅	semidirect
540. C₅	#17750	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×#532	2
C₅×#2920	2
C₂×C₅×#423	2
C₅×#1560	2
C₅×#1551	2
C₅×#1548	2
C₅×#1545	2
#17750	5

Subgroups — C5×#17750 #11940470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17750 #11940470