Subgroups — C₅×#20422 #11943142

Order 1280.

1458 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₅×#2873	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	C₂×C₅×#341	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	C₅×#568	—	2	4	no	—
12	C₅×#568	C₄	1	8	yes	complemented
13	C₂×C₅×#131	—	2	2	no	—
14	C₂×C₅×#131	C₂²	1	4	yes	—
15	C₂²×C₅×M₁₆	—	2	2	no	—
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₅×#421	C₄	1	8	yes	complemented
23	C₂×C₅×#104	C₂²	1	4	yes	—
24	C₅×#416	C₄	1	4	yes	complemented
25	C₅×#416	C₂²	1	2	yes	—
26	C₅×#416	C₂²	1	2	yes	—
27	C₂×C₅×#103	C₄	1	2	yes	complemented
28	C₂×C₅×#102	C₄	1	2	yes	complemented
29	C₅×#405	—	2	4	no	—
30	C₅×#405	—	2	2	no	—
31	C₅×#405	C₂²	1	4	yes	complemented
32	C₄×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×#97	C₂²	1	2	yes	complemented
34	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
35	C₅×#341	C₂²	1	2	yes	complemented
36	C₅×#341	C₂²	1	2	yes	complemented
37	C₅×#339	C₂²	1	4	yes	complemented
38	#20422	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	2	no	—
41	C₂×C₅×#41	—	2	1	no	—
42	C₂×C₅×#41	—	2	2	no	—
43	C₂×C₅×#41	C₂×C₄	1	4	yes	—
44	C₂×C₅×#41	C₂×C₄	1	4	yes	—
45	C₂×C₅×#41	C₂×C₄	1	2	yes	—
46	C₂×C₅×#41	C₂³	1	2	yes	—
47	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₅×D₄	—	2	1	no	—
49	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	—	2	1	no	—
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₅×#131	—	2	16	no	—
53	C₅×#131	—	2	8	no	—
54	C₅×#131	C₂×C₄	1	16	yes	complemented
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	16	no	—
60	C₂×C₅×M₁₆	—	2	4	no	—
61	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
62	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
63	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
64	C₂×C₅×M₁₆	D₄	1	2	yes	—
65	C₂×C₅×M₁₆	D₄	1	2	yes	—
66	C₂×C₅×M₁₆	D₄	1	4	yes	—
67	C₂×C₅×M₁₆	C₂³	1	2	yes	—
68	C₂×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₅×C₈	—	2	2	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₂²×C₅×C₈	—	2	2	no	—
73	C₂²×C₅×C₈	—	2	4	no	—
74	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
75	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	2	yes	—
79	C₅×#117	—	2	2	no	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	C₂×C₄	1	2	yes	—
83	C₅×#117	C₂×C₄	1	4	yes	—
84	C₅×#117	C₂³	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₅	—	2	1	no	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₅×#104	C₂×C₄	1	16	yes	complemented
92	C₅×#103	C₂×C₄	1	4	yes	—
93	C₅×#103	C₂×C₄	1	4	yes	—
94	C₅×#102	C₂×C₄	1	4	yes	—
95	C₅×#102	C₂×C₄	1	4	yes	—
96	C₅×#97	—	2	4	no	—
97	C₅×#97	—	2	4	no	—
98	C₄×C₅×C₈	—	2	4	no	—
99	C₄×C₅×C₈	—	2	4	no	—
100	C₂×#568	C₂×C₅	1	1	yes	characteristic
101	C₂×#421	C₂×C₅	1	1	yes	characteristic
102	C₂×#416	C₂×C₅	1	1	yes	characteristic
103	#2873	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
105	#1765	C₂×C₅	1	4	yes	complemented
106	#1764	C₂×C₅	1	4	yes	complemented
107	C₂×#341	C₂×C₅	1	1	yes	characteristic, complemented
108	#1733	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂⁴×C₅	—	2	1	no	—
110	C₂⁴×C₅	#41	1	1	yes	characteristic
111	C₅×#41	—	2	4	no	—
112	C₅×#41	—	2	4	no	—
113	C₅×#41	—	2	4	no	—
114	C₅×#41	—	2	4	no	—
115	C₅×#41	—	2	4	no	—
116	C₅×#41	—	2	2	no	—
117	C₅×#41	—	2	2	no	—
118	C₅×#41	C₄²	1	8	yes	—
119	C₅×#41	C₂²×C₄	1	4	yes	—
120	C₅×#41	C₂²×C₄	1	4	yes	—
121	C₂×C₅×Q₈	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	C₄²	1	4	yes	—
124	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
125	C₂×C₅×D₄	—	2	4	no	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	C₄²	1	4	yes	—
132	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	4	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	#41	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	2	yes	—
149	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₅×M₁₆	—	2	4	no	—
151	C₅×M₁₆	—	2	4	no	—
152	C₅×M₁₆	—	2	2	no	—
153	C₅×M₁₆	—	2	2	no	—
154	C₅×M₁₆	—	2	16	no	—
155	C₅×M₁₆	C₂²⋊C₄	1	8	yes	—
156	C₅×M₁₆	C₂²⋊C₄	1	8	yes	—
157	C₅×M₁₆	C₂²×C₄	1	4	yes	—
158	C₅×M₁₆	C₂²×C₄	1	4	yes	—
159	C₂×C₅×C₈	—	2	4	no	—
160	C₂×C₅×C₈	—	2	4	no	—
161	C₂×C₅×C₈	—	2	4	no	—
162	C₂×C₅×C₈	—	2	4	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	16	no	—
170	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
173	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
174	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
175	C₅×C₄⋊C₄	—	2	4	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	—	2	4	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	2	2	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	C₂²×C₄	1	4	yes	—
185	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
186	#568	—	2	4	no	—
187	#568	C₄×C₅	1	8	yes	complemented
188	C₂×#131	—	2	2	no	—
189	C₂×#131	C₂²×C₅	1	4	yes	—
190	C₂²×M₁₆	—	2	2	no	—
191	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
192	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×#117	C₂²×C₅	1	1	yes	characteristic
196	C₂×#117	C₂²×C₅	1	1	yes	characteristic
197	#421	C₄×C₅	1	8	yes	complemented
198	C₂×#104	C₂²×C₅	1	4	yes	—
199	#416	C₄×C₅	1	4	yes	complemented
200	#416	C₂²×C₅	1	2	yes	—
201	#416	C₂²×C₅	1	2	yes	—
202	C₂×#103	C₄×C₅	1	2	yes	complemented
203	C₂×#102	C₄×C₅	1	2	yes	complemented
204	#405	—	2	4	no	—
205	#405	—	2	2	no	—
206	#405	C₂²×C₅	1	4	yes	complemented
207	C₄×M₁₆	—	2	2	no	—
208	C₂×#97	C₂²×C₅	1	2	yes	complemented
209	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
210	#341	C₂²×C₅	1	2	yes	complemented
211	#341	C₂²×C₅	1	2	yes	complemented
212	#339	C₂²×C₅	1	4	yes	complemented
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	—	2	4	no	—
215	C₂³×C₅	—	4	2	no	—
216	C₂³×C₅	—	8	2	no	—
217	C₂³×C₅	#117	1	2	yes	—
218	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₅	C₄×D₄	1	2	yes	—
221	C₂³×C₅	C₂×#41	1	1	yes	characteristic
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	2	4	no	—
224	C₅×Q₈	C₂×C₄²	1	4	yes	—
225	C₅×D₄	—	2	4	no	—
226	C₅×D₄	—	2	4	no	—
227	C₅×D₄	—	2	8	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	2	4	no	—
230	C₅×D₄	C₂×C₄²	1	4	yes	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	8	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	4	4	no	—
239	C₂×C₄×C₅	—	8	2	no	—
240	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂×C₄×C₅	#117	1	2	yes	—
245	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₅×C₈	—	2	4	no	—
259	C₅×C₈	—	2	2	no	—
260	C₅×C₈	—	2	2	no	—
261	C₅×C₈	—	2	4	no	—
262	C₅×C₈	C₂×C₂²⋊C₄	1	8	yes	—
263	C₂×#41	—	2	1	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	1	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	C₂×C₄×C₅	1	4	yes	—
268	C₂×#41	C₂×C₄×C₅	1	4	yes	—
269	C₂×#41	C₂×C₄×C₅	1	2	yes	—
270	C₂×#41	C₂³×C₅	1	2	yes	—
271	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
276	#131	—	2	16	no	—
277	#131	—	2	8	no	—
278	#131	C₂×C₄×C₅	1	16	yes	complemented
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	16	no	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
286	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
287	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
288	C₂×M₁₆	C₅×D₄	1	2	yes	—
289	C₂×M₁₆	C₅×D₄	1	2	yes	—
290	C₂×M₁₆	C₅×D₄	1	4	yes	—
291	C₂×M₁₆	C₂³×C₅	1	2	yes	—
292	C₂×M₁₆	C₂³×C₅	1	2	yes	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	2	4	no	—
298	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
299	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
300	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₅	1	2	yes	—
303	#117	—	2	1	no	—
304	#117	—	2	2	no	—
305	#117	—	2	1	no	—
306	#117	C₂×C₄×C₅	1	2	yes	—
307	#117	C₂×C₄×C₅	1	4	yes	—
308	#117	C₂³×C₅	1	2	yes	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₅	1	2	yes	—
315	#104	C₂×C₄×C₅	1	16	yes	complemented
316	#103	C₂×C₄×C₅	1	4	yes	—
317	#103	C₂×C₄×C₅	1	4	yes	—
318	#102	C₂×C₄×C₅	1	4	yes	—
319	#102	C₂×C₄×C₅	1	4	yes	—
320	#97	—	2	4	no	—
321	#97	—	2	4	no	—
322	C₄×C₈	—	2	4	no	—
323	C₄×C₈	—	2	4	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	4	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	4	no	—
331	C₂²×C₅	—	8	4	no	—
332	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
333	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
334	C₂²×C₅	C₂×#117	1	1	yes	characteristic
335	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₅	—	2	4	no	—
338	C₄×C₅	—	4	4	no	—
339	C₄×C₅	—	4	4	no	—
340	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
341	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
342	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
343	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
344	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
345	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₅×#41	1	1	yes	characteristic
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	2	4	no	—
352	#41	—	2	4	no	—
353	#41	—	2	2	no	—
354	#41	—	2	2	no	—
355	#41	C₄²×C₅	1	8	yes	—
356	#41	C₂²×C₄×C₅	1	4	yes	—
357	#41	C₂²×C₄×C₅	1	4	yes	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₄²×C₅	1	4	yes	—
361	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	C₄²×C₅	1	4	yes	—
369	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
384	C₂²×C₄	C₅×#41	1	1	yes	characteristic
385	C₂²×C₄	C₅×#41	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	16	no	—
392	M₁₆	C₅×C₂²⋊C₄	1	8	yes	—
393	M₁₆	C₅×C₂²⋊C₄	1	8	yes	—
394	M₁₆	C₂²×C₄×C₅	1	4	yes	—
395	M₁₆	C₂²×C₄×C₅	1	4	yes	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	16	no	—
407	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
408	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
409	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
410	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
411	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	C₂²×C₄×C₅	1	4	yes	—
422	C₂×C₅	—	2	1	no	—
423	C₂×C₅	—	2	2	no	—
424	C₂×C₅	—	2	1	no	—
425	C₂×C₅	—	2	2	no	—
426	C₂×C₅	—	4	4	no	—
427	C₂×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₅	#2957	1	2	yes	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	8	2	no	—
433	C₂³	C₅×#117	1	2	yes	—
434	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
435	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
436	C₂³	C₄×C₅×D₄	1	2	yes	—
437	C₂³	C₂×C₅×#41	1	1	yes	characteristic
438	Q₈	—	2	4	no	—
439	Q₈	—	2	2	no	—
440	Q₈	C₂×C₄²×C₅	1	4	yes	—
441	D₄	—	2	8	no	—
442	D₄	—	2	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	2	no	—
446	D₄	C₂×C₄²×C₅	1	4	yes	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
457	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
458	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
459	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
460	C₂×C₄	C₅×#117	1	2	yes	—
461	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
463	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
465	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
466	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
467	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
468	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
469	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
474	C₈	—	2	4	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₈	C₂×C₅×C₂²⋊C₄	1	8	yes	—
479	C₅	#20422	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	8	4	no	—
488	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
489	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
490	C₂²	C₂×C₅×#117	1	1	yes	characteristic
491	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
492	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
497	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
498	C₄	C₂²×C₄²×C₅	1	1	yes	characteristic
499	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
500	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
501	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	1	no	—
506	C₂	—	4	4	no	—
507	C₂	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
508	C₂	C₅×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×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×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2873	C₂	semidirect
5. C₂×C₅×#405	C₂	semidirect
6. C₅×#1765	C₂	semidirect
7. C₅×#1764	C₂	semidirect
8. C₂×C₅×#341	C₂	semidirect
9. C₅×#1733	C₂	semidirect
12. C₅×#568	C₄	semidirect
22. C₅×#421	C₄	semidirect
24. C₅×#416	C₄	semidirect
27. C₂×C₅×#103	C₄	semidirect
28. C₂×C₅×#102	C₄	semidirect
31. C₅×#405	C₂²	semidirect
33. C₂×C₅×#97	C₂²	semidirect
34. C₂×C₄×C₅×C₈	C₂²	semidirect
35. C₅×#341	C₂²	semidirect
36. C₅×#341	C₂²	semidirect
37. C₅×#339	C₂²	semidirect
38. #20422	C₅	direct (N × H)
54. C₅×#131	C₂×C₄	semidirect
91. C₅×#104	C₂×C₄	semidirect
103. #2873	C₂×C₅	semidirect
104. C₂×#405	C₂×C₅	semidirect
105. #1765	C₂×C₅	semidirect
106. #1764	C₂×C₅	semidirect
107. C₂×#341	C₂×C₅	semidirect
108. #1733	C₂×C₅	semidirect
187. #568	C₄×C₅	semidirect
197. #421	C₄×C₅	semidirect
199. #416	C₄×C₅	semidirect
202. C₂×#103	C₄×C₅	semidirect
203. C₂×#102	C₄×C₅	semidirect
206. #405	C₂²×C₅	semidirect
208. C₂×#97	C₂²×C₅	semidirect
209. C₂×C₄×C₈	C₂²×C₅	semidirect
210. #341	C₂²×C₅	semidirect
211. #341	C₂²×C₅	semidirect
212. #339	C₂²×C₅	semidirect
278. #131	C₂×C₄×C₅	semidirect
315. #104	C₂×C₄×C₅	semidirect
479. C₅	#20422	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×#568	2
C₂×C₅×#421	2
C₂×C₅×#416	2
C₅×#2873	2
C₂×C₅×#405	2
C₅×#1765	2
C₅×#1764	2
C₂×C₅×#341	2
C₅×#1733	2
#20422	5

Subgroups — C5×#20422 #11943142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20422 #11943142