Subgroups — C₅×#20420 #11943140

Order 1280.

1474 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
3	C₅×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1765	C₂	1	4	yes	maximal, complemented
7	C₅×#1764	C₂	1	4	yes	maximal, complemented
8	C₅×#1738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1733	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×C₅×#131	—	2	4	no	—
12	C₂×C₅×#131	—	2	1	no	—
13	C₂×C₅×#131	—	2	1	no	—
14	C₂×C₅×#131	C₄	1	8	yes	complemented
15	C₂×C₅×#131	C₂²	1	2	yes	—
16	C₂×C₅×#131	C₂²	1	2	yes	—
17	C₂²×C₅×M₁₆	—	2	1	no	—
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂³×C₅×C₈	—	2	1	no	—
22	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂×C₅×#117	C₂²	1	1	yes	characteristic
25	C₅×#421	C₄	1	8	yes	complemented
26	C₂×C₅×#104	C₂²	1	4	yes	—
27	C₅×#419	C₄	1	2	yes	complemented
28	C₅×#418	C₄	1	2	yes	complemented
29	C₅×#417	C₄	1	4	yes	complemented
30	C₅×#416	C₂²	1	4	yes	—
31	C₅×#405	—	2	1	no	—
32	C₅×#405	—	2	4	no	—
33	C₅×#405	—	2	1	no	—
34	C₅×#405	C₂²	1	2	yes	complemented
35	C₅×#405	C₂²	1	2	yes	complemented
36	C₂×C₅×#97	—	2	1	no	—
37	C₂×C₅×#97	C₂²	1	2	yes	complemented
38	C₂×C₄×C₅×C₈	—	2	1	no	—
39	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
40	C₅×#341	C₂²	1	4	yes	complemented
41	C₅×#339	C₂²	1	4	yes	complemented
42	#20420	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	2	1	no	—
46	C₂×C₅×#41	—	2	2	no	—
47	C₂×C₅×#41	C₂×C₄	1	4	yes	—
48	C₂×C₅×#41	C₂×C₄	1	4	yes	—
49	C₂×C₅×#41	C₂×C₄	1	2	yes	—
50	C₂×C₅×#41	C₂³	1	2	yes	—
51	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×D₄	—	2	1	no	—
53	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅	—	2	1	no	—
55	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₅×#131	—	2	8	no	—
57	C₅×#131	—	2	8	no	—
58	C₅×#131	—	2	4	no	—
59	C₅×#131	—	2	4	no	—
60	C₅×#131	C₂×C₄	1	8	yes	complemented
61	C₅×#131	C₂×C₄	1	8	yes	complemented
62	C₂×C₅×M₁₆	—	2	1	no	—
63	C₂×C₅×M₁₆	—	2	2	no	—
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	—	2	2	no	—
67	C₂×C₅×M₁₆	—	2	2	no	—
68	C₂×C₅×M₁₆	—	2	8	no	—
69	C₂×C₅×M₁₆	—	2	2	no	—
70	C₂×C₅×M₁₆	—	2	2	no	—
71	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
72	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
73	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
74	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
75	C₂×C₅×M₁₆	C₂³	1	2	yes	—
76	C₂×C₅×M₁₆	C₂³	1	2	yes	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	8	no	—
80	C₂²×C₅×C₈	—	2	2	no	—
81	C₂²×C₅×C₈	—	2	2	no	—
82	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
83	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
84	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
85	C₂²×C₅×C₈	D₄	1	4	yes	—
86	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
87	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂³	1	2	yes	—
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₅×#117	—	2	1	no	—
92	C₅×#117	—	2	2	no	—
93	C₅×#117	—	2	1	no	—
94	C₅×#117	C₂×C₄	1	2	yes	—
95	C₅×#117	C₂×C₄	1	4	yes	—
96	C₅×#117	C₂³	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂³	1	2	yes	—
103	C₅×#104	C₂×C₄	1	16	yes	complemented
104	C₅×#103	C₂×C₄	1	8	yes	—
105	C₅×#102	C₂×C₄	1	8	yes	—
106	C₅×#97	—	2	2	no	—
107	C₅×#97	—	2	2	no	—
108	C₅×#97	—	2	4	no	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₄×C₅×C₈	—	2	4	no	—
111	C₄×C₅×C₈	—	2	2	no	—
112	C₂²×#131	C₂×C₅	1	1	yes	characteristic
113	C₂×#421	C₂×C₅	1	1	yes	characteristic
114	#2896	C₂×C₅	1	1	yes	characteristic
115	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
117	#1765	C₂×C₅	1	4	yes	complemented
118	#1764	C₂×C₅	1	4	yes	complemented
119	#1738	C₂×C₅	1	1	yes	characteristic, complemented
120	#1733	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂⁴×C₅	—	2	1	no	—
122	C₂⁴×C₅	#41	1	1	yes	characteristic
123	C₅×#41	—	2	4	no	—
124	C₅×#41	—	2	4	no	—
125	C₅×#41	—	2	4	no	—
126	C₅×#41	—	2	4	no	—
127	C₅×#41	—	2	4	no	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	C₄²	1	8	yes	—
131	C₅×#41	C₂²×C₄	1	4	yes	—
132	C₅×#41	C₂²×C₄	1	4	yes	—
133	C₂×C₅×Q₈	—	2	1	no	—
134	C₂×C₅×Q₈	—	2	2	no	—
135	C₂×C₅×Q₈	C₄²	1	4	yes	—
136	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×D₄	—	2	4	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	—	2	2	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₄²	1	4	yes	—
144	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	2	yes	—
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₅	#41	1	1	yes	characteristic
160	C₂²×C₄×C₅	#41	1	2	yes	—
161	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₅×M₁₆	—	2	4	no	—
163	C₅×M₁₆	—	2	4	no	—
164	C₅×M₁₆	—	2	4	no	—
165	C₅×M₁₆	—	2	4	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	2	2	no	—
168	C₅×M₁₆	—	2	8	no	—
169	C₅×M₁₆	—	2	8	no	—
170	C₅×M₁₆	C₂²×C₄	1	4	yes	—
171	C₅×M₁₆	C₂²×C₄	1	4	yes	—
172	C₂×C₅×C₈	—	2	4	no	—
173	C₂×C₅×C₈	—	2	4	no	—
174	C₂×C₅×C₈	—	2	2	no	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	2	8	no	—
179	C₂×C₅×C₈	—	2	8	no	—
180	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
181	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
182	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
183	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
184	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
185	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
186	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
191	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	4	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	C₂²×C₄	1	4	yes	—
203	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
204	C₂×#131	—	2	4	no	—
205	C₂×#131	—	2	1	no	—
206	C₂×#131	—	2	1	no	—
207	C₂×#131	C₄×C₅	1	8	yes	complemented
208	C₂×#131	C₂²×C₅	1	2	yes	—
209	C₂×#131	C₂²×C₅	1	2	yes	—
210	C₂²×M₁₆	—	2	1	no	—
211	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
214	C₂³×C₈	—	2	1	no	—
215	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×#117	C₂²×C₅	1	1	yes	characteristic
217	C₂×#117	C₂²×C₅	1	1	yes	characteristic
218	#421	C₄×C₅	1	8	yes	complemented
219	C₂×#104	C₂²×C₅	1	4	yes	—
220	#419	C₄×C₅	1	2	yes	complemented
221	#418	C₄×C₅	1	2	yes	complemented
222	#417	C₄×C₅	1	4	yes	complemented
223	#416	C₂²×C₅	1	4	yes	—
224	#405	—	2	1	no	—
225	#405	—	2	1	no	—
226	#405	—	2	4	no	—
227	#405	C₂²×C₅	1	2	yes	complemented
228	#405	C₂²×C₅	1	2	yes	complemented
229	C₂×#97	—	2	1	no	—
230	C₂×#97	C₂²×C₅	1	2	yes	complemented
231	C₂×C₄×C₈	—	2	1	no	—
232	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
233	#341	C₂²×C₅	1	4	yes	complemented
234	#339	C₂²×C₅	1	4	yes	complemented
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	4	2	no	—
238	C₂³×C₅	—	4	4	no	—
239	C₂³×C₅	#117	1	2	yes	—
240	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
241	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
242	C₂³×C₅	C₄×D₄	1	2	yes	—
243	C₂³×C₅	C₂×#41	1	1	yes	characteristic
244	C₅×Q₈	—	2	2	no	—
245	C₅×Q₈	—	2	4	no	—
246	C₅×Q₈	C₂×C₄²	1	4	yes	—
247	C₅×D₄	—	2	4	no	—
248	C₅×D₄	—	2	4	no	—
249	C₅×D₄	—	2	8	no	—
250	C₅×D₄	—	2	2	no	—
251	C₅×D₄	—	2	4	no	—
252	C₅×D₄	C₂×C₄²	1	4	yes	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	2	8	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	4	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	—	4	4	no	—
262	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
263	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
264	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
265	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₅	#117	1	2	yes	—
267	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
269	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
280	C₅×C₈	—	2	4	no	—
281	C₅×C₈	—	2	4	no	—
282	C₅×C₈	—	2	4	no	—
283	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
284	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
285	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
286	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	C₂×C₄×C₅	1	4	yes	—
292	C₂×#41	C₂×C₄×C₅	1	4	yes	—
293	C₂×#41	C₂×C₄×C₅	1	2	yes	—
294	C₂×#41	C₂³×C₅	1	2	yes	—
295	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
300	#131	—	2	8	no	—
301	#131	—	2	8	no	—
302	#131	—	2	4	no	—
303	#131	—	2	4	no	—
304	#131	C₂×C₄×C₅	1	8	yes	complemented
305	#131	C₂×C₄×C₅	1	8	yes	complemented
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	8	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
316	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
317	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
318	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
319	C₂×M₁₆	C₂³×C₅	1	2	yes	—
320	C₂×M₁₆	C₂³×C₅	1	2	yes	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	8	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
327	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
328	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
329	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
330	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
331	C₂²×C₈	C₅×D₄	1	4	yes	—
332	C₂²×C₈	C₂³×C₅	1	2	yes	—
333	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
335	#117	—	2	1	no	—
336	#117	—	2	2	no	—
337	#117	—	2	1	no	—
338	#117	C₂×C₄×C₅	1	2	yes	—
339	#117	C₂×C₄×C₅	1	4	yes	—
340	#117	C₂³×C₅	1	2	yes	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₄²	—	2	1	no	—
346	C₂×C₄²	C₂³×C₅	1	2	yes	—
347	#104	C₂×C₄×C₅	1	16	yes	complemented
348	#103	C₂×C₄×C₅	1	8	yes	—
349	#102	C₂×C₄×C₅	1	8	yes	—
350	#97	—	2	2	no	—
351	#97	—	2	2	no	—
352	#97	—	2	4	no	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	—	2	4	no	—
356	C₂²×C₅	—	2	2	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	2	2	no	—
359	C₂²×C₅	—	2	4	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	8	no	—
363	C₂²×C₅	—	4	4	no	—
364	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
365	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
366	C₂²×C₅	C₂×#117	1	1	yes	characteristic
367	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
368	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₄×C₅	—	2	4	no	—
370	C₄×C₅	—	4	4	no	—
371	C₄×C₅	—	4	4	no	—
372	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
373	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
374	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
375	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
376	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
377	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
378	C₂⁴	—	2	1	no	—
379	C₂⁴	C₅×#41	1	1	yes	characteristic
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	4	no	—
384	#41	—	2	4	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	C₄²×C₅	1	8	yes	—
388	#41	C₂²×C₄×C₅	1	4	yes	—
389	#41	C₂²×C₄×C₅	1	4	yes	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	C₄²×C₅	1	4	yes	—
393	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	C₄²×C₅	1	4	yes	—
401	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
410	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
413	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
416	C₂²×C₄	C₅×#41	1	1	yes	characteristic
417	C₂²×C₄	C₅×#41	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	M₁₆	—	2	4	no	—
420	M₁₆	—	2	4	no	—
421	M₁₆	—	2	4	no	—
422	M₁₆	—	2	4	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	8	no	—
426	M₁₆	—	2	8	no	—
427	M₁₆	C₂²×C₄×C₅	1	4	yes	—
428	M₁₆	C₂²×C₄×C₅	1	4	yes	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	—	2	4	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	8	no	—
436	C₂×C₈	—	2	8	no	—
437	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
438	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
439	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
440	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
441	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
442	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
443	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
444	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
447	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	C₂²×C₄×C₅	1	4	yes	—
460	C₂×C₅	—	2	1	no	—
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	2	2	no	—
464	C₂×C₅	—	4	4	no	—
465	C₂×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₅	#2955	1	2	yes	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	4	no	—
471	C₂³	C₅×#117	1	2	yes	—
472	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
473	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
474	C₂³	C₄×C₅×D₄	1	2	yes	—
475	C₂³	C₂×C₅×#41	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	C₂×C₄²×C₅	1	4	yes	—
479	D₄	—	2	8	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	2	no	—
484	D₄	C₂×C₄²×C₅	1	4	yes	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
495	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
496	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
497	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
498	C₂×C₄	C₅×#117	1	2	yes	—
499	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
500	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
501	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
502	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
503	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
504	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
505	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
506	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
507	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
508	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
509	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
511	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
512	C₈	—	2	4	no	—
513	C₈	—	2	4	no	—
514	C₈	—	2	4	no	—
515	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
516	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
517	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
518	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
519	C₅	#20420	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	8	no	—
527	C₂²	—	4	4	no	—
528	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
529	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
530	C₂²	C₂×C₅×#117	1	1	yes	characteristic
531	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
532	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	4	no	—
536	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
537	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
538	C₄	C₂²×C₄²×C₅	1	1	yes	characteristic
539	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
540	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
541	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
542	C₂	—	2	1	no	—
543	C₂	—	2	2	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
548	C₂	C₅×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₅×C₈	C₂×D₄
commutator	C₄	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#405	C₂	semidirect
5. C₂×C₅×#405	C₂	semidirect
6. C₅×#1765	C₂	semidirect
7. C₅×#1764	C₂	semidirect
8. C₅×#1738	C₂	semidirect
9. C₅×#1733	C₂	semidirect
14. C₂×C₅×#131	C₄	semidirect
25. C₅×#421	C₄	semidirect
27. C₅×#419	C₄	semidirect
28. C₅×#418	C₄	semidirect
29. C₅×#417	C₄	semidirect
34. C₅×#405	C₂²	semidirect
35. C₅×#405	C₂²	semidirect
37. C₂×C₅×#97	C₂²	semidirect
39. C₂×C₄×C₅×C₈	C₂²	semidirect
40. C₅×#341	C₂²	semidirect
41. C₅×#339	C₂²	semidirect
42. #20420	C₅	direct (N × H)
60. C₅×#131	C₂×C₄	semidirect
61. C₅×#131	C₂×C₄	semidirect
103. C₅×#104	C₂×C₄	semidirect
115. C₂×#405	C₂×C₅	semidirect
116. C₂×#405	C₂×C₅	semidirect
117. #1765	C₂×C₅	semidirect
118. #1764	C₂×C₅	semidirect
119. #1738	C₂×C₅	semidirect
120. #1733	C₂×C₅	semidirect
207. C₂×#131	C₄×C₅	semidirect
218. #421	C₄×C₅	semidirect
220. #419	C₄×C₅	semidirect
221. #418	C₄×C₅	semidirect
222. #417	C₄×C₅	semidirect
227. #405	C₂²×C₅	semidirect
228. #405	C₂²×C₅	semidirect
230. C₂×#97	C₂²×C₅	semidirect
232. C₂×C₄×C₈	C₂²×C₅	semidirect
233. #341	C₂²×C₅	semidirect
234. #339	C₂²×C₅	semidirect
304. #131	C₂×C₄×C₅	semidirect
305. #131	C₂×C₄×C₅	semidirect
347. #104	C₂×C₄×C₅	semidirect
519. C₅	#20420	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×#131	2
C₂×C₅×#421	2
C₅×#2896	2
C₂×C₅×#405	2
C₅×#1765	2
C₅×#1764	2
C₅×#1738	2
C₅×#1733	2
#20420	5

Subgroups — C5×#20420 #11943140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20420 #11943140