Subgroups — C₅×#21160 #11943880

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#2317	C₂	1	1	yes	maximal, characteristic
5	C₅×#2316	C₂	1	1	yes	maximal, characteristic
6	C₅×#1944	C₂	1	2	yes	maximal, complemented
7	C₅×#1943	C₂	1	2	yes	maximal, complemented
8	C₅×#1942	C₂	1	2	yes	maximal, complemented
9	C₅×#1941	C₂	1	2	yes	maximal, complemented
10	C₅×#1735	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₅×#428	—	2	4	no	—
20	C₅×#428	C₄	1	8	yes	complemented
21	C₂×C₅×#107	C₂²	1	2	yes	—
22	C₂×C₅×#107	C₂²	1	2	yes	—
23	C₂×C₅×#106	C₂²	1	2	yes	—
24	C₂×C₅×#106	C₂²	1	2	yes	—
25	C₅×#405	—	2	4	no	—
26	C₂×C₅×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
28	C₅×#389	—	2	1	no	—
29	C₅×#389	—	2	1	no	—
30	C₅×#389	C₂²	1	2	yes	—
31	C₅×#389	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#389	C₂²	1	2	yes	—
34	C₅×#385	—	2	2	no	—
35	C₅×#384	—	2	1	no	—
36	C₅×#382	—	2	1	no	—
37	C₅×#380	—	2	2	no	—
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	1	yes	characteristic
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	1	yes	characteristic
44	#21160	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
49	C₂×C₅×M₁₆	D₄	1	4	yes	—
50	C₂×C₅×M₁₆	Q₈	1	4	yes	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	Q₈	1	4	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₅×#117	—	2	2	no	—
58	C₅×#117	—	2	2	no	—
59	C₅×#117	—	2	2	no	—
60	C₅×#117	—	2	2	no	—
61	C₅×#117	—	2	2	no	—
62	C₅×#117	C₂×C₄	1	4	yes	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	—	2	2	no	—
71	C₂×C₅×C₄⋊C₄	—	2	2	no	—
72	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₅	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	1	no	—
86	C₂×C₄²×C₅	C₂³	1	2	yes	—
87	C₅×#107	—	2	4	no	—
88	C₅×#107	C₂×C₄	1	8	yes	complemented
89	C₅×#106	—	2	4	no	—
90	C₅×#106	C₂×C₄	1	8	yes	complemented
91	C₅×#97	—	2	4	no	—
92	C₄×C₅×C₈	—	2	4	no	—
93	C₅×#95	—	2	2	no	—
94	C₅×#95	—	2	2	no	—
95	C₅×#95	—	2	2	no	—
96	C₅×#95	—	2	2	no	—
97	C₂×#428	C₂×C₅	1	1	yes	characteristic
98	C₂×#428	C₂×C₅	1	1	yes	characteristic
99	C₂×#405	C₂×C₅	1	1	yes	characteristic
100	#2317	C₂×C₅	1	1	yes	characteristic
101	#2316	C₂×C₅	1	1	yes	characteristic
102	#1944	C₂×C₅	1	2	yes	complemented
103	#1943	C₂×C₅	1	2	yes	complemented
104	#1942	C₂×C₅	1	2	yes	complemented
105	#1941	C₂×C₅	1	2	yes	complemented
106	#1735	C₂×C₅	1	1	yes	characteristic
107	C₂×#340	C₂×C₅	1	1	yes	characteristic
108	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	4	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	—	8	1	no	—
118	C₂²×C₄×C₅	—	8	1	no	—
119	C₂²×C₄×C₅	—	8	1	no	—
120	C₂²×C₄×C₅	—	8	1	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₅	#41	1	2	yes	—
129	C₂²×C₄×C₅	#41	1	2	yes	—
130	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₅×M₁₆	C₄⋊C₄	1	16	yes	complemented
132	C₂×C₅×C₈	—	2	8	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
139	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
140	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
141	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
142	C₅×C₄⋊C₄	—	2	4	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	—	8	2	no	—
156	C₅×C₄⋊C₄	—	8	2	no	—
157	C₅×C₄⋊C₄	—	8	2	no	—
158	C₅×C₄⋊C₄	—	8	2	no	—
159	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
160	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
161	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₅×C₂²⋊C₄	—	4	2	no	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	2	2	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	4	2	no	—
169	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
170	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×#117	C₂²×C₅	1	1	yes	characteristic
172	C₂×#117	C₂²×C₅	1	1	yes	characteristic
173	C₂×#117	C₂²×C₅	1	1	yes	characteristic
174	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	#428	—	2	4	no	—
177	#428	C₄×C₅	1	8	yes	complemented
178	C₂×#107	C₂²×C₅	1	2	yes	—
179	C₂×#107	C₂²×C₅	1	2	yes	—
180	C₂×#106	C₂²×C₅	1	2	yes	—
181	C₂×#106	C₂²×C₅	1	2	yes	—
182	#405	—	2	4	no	—
183	C₂×#97	C₂²×C₅	1	2	yes	—
184	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
185	#389	—	2	1	no	—
186	#389	—	2	1	no	—
187	#389	C₂²×C₅	1	2	yes	—
188	#389	C₂²×C₅	1	2	yes	—
189	#389	C₂²×C₅	1	2	yes	—
190	#389	C₂²×C₅	1	2	yes	—
191	#385	—	2	2	no	—
192	#384	—	2	1	no	—
193	#382	—	2	1	no	—
194	#380	—	2	2	no	—
195	#340	C₂²×C₅	1	1	yes	characteristic
196	#340	C₂²×C₅	1	2	yes	—
197	#340	C₂²×C₅	1	1	yes	characteristic
198	#340	C₂²×C₅	1	1	yes	characteristic
199	#340	C₂²×C₅	1	2	yes	—
200	#340	C₂²×C₅	1	1	yes	characteristic
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	C₄×D₄	1	2	yes	—
206	C₂³×C₅	#121	1	2	yes	—
207	C₂³×C₅	C₄⋊Q₈	1	2	yes	—
208	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	8	4	no	—
234	C₂×C₄×C₅	—	8	4	no	—
235	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
236	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
238	C₂×C₄×C₅	#121	1	2	yes	—
239	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
240	C₂×C₄×C₅	#125	1	4	yes	—
241	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
242	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₅×C₈	—	2	2	no	—
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	C₂×C₄⋊C₄	1	8	yes	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	—	2	1	no	—
253	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
255	C₂×M₁₆	C₅×D₄	1	4	yes	—
256	C₂×M₁₆	C₅×Q₈	1	4	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	C₅×Q₈	1	4	yes	—
260	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₅	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
279	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₅	1	2	yes	—
293	#107	—	2	4	no	—
294	#107	C₂×C₄×C₅	1	8	yes	complemented
295	#106	—	2	4	no	—
296	#106	C₂×C₄×C₅	1	8	yes	complemented
297	#97	—	2	4	no	—
298	C₄×C₈	—	2	4	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	#389	1	4	yes	—
310	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂²×C₅	C₂×#121	1	1	yes	characteristic
312	C₂²×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
313	C₂²×C₅	#576	1	1	yes	characteristic
314	C₂²×C₅	#577	1	1	yes	characteristic
315	C₂²×C₅	#577	1	1	yes	characteristic
316	C₂²×C₅	#578	1	1	yes	characteristic
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	4	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	8	1	no	—
323	C₄×C₅	—	8	2	no	—
324	C₄×C₅	—	8	1	no	—
325	C₄×C₅	#389	1	4	yes	—
326	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
327	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
328	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
329	C₄×C₅	C₂×#125	1	1	yes	characteristic
330	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	8	1	no	—
340	C₂²×C₄	—	8	1	no	—
341	C₂²×C₄	—	8	1	no	—
342	C₂²×C₄	—	8	1	no	—
343	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
344	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
345	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
346	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
347	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
349	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
350	C₂²×C₄	C₅×#41	1	2	yes	—
351	C₂²×C₄	C₅×#41	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
353	M₁₆	C₅×C₄⋊C₄	1	16	yes	complemented
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
360	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
361	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
362	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
363	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₄⋊C₄	—	8	2	no	—
379	C₄⋊C₄	—	8	2	no	—
380	C₄⋊C₄	—	8	2	no	—
381	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
382	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
383	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	4	2	no	—
391	C₂×C₅	—	2	4	no	—
392	C₂×C₅	C₂×#389	1	1	yes	characteristic
393	C₂×C₅	#2946	1	1	yes	characteristic
394	C₂×C₅	#2947	1	1	yes	characteristic
395	C₂×C₅	#3062	1	1	yes	characteristic
396	C₂×C₅	#3063	1	1	yes	characteristic
397	C₂×C₅	#3163	1	1	yes	characteristic
398	C₂×C₅	#3164	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	C₄×C₅×D₄	1	2	yes	—
404	C₂³	C₅×#121	1	2	yes	—
405	C₂³	C₅×C₄⋊Q₈	1	2	yes	—
406	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
434	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
435	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
436	C₂×C₄	C₅×#121	1	2	yes	—
437	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
438	C₂×C₄	C₅×#125	1	4	yes	—
439	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
440	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
444	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
445	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	C₈	—	2	2	no	—
447	C₈	—	2	2	no	—
448	C₈	C₂×C₅×C₄⋊C₄	1	8	yes	—
449	C₅	#21160	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	C₅×#389	1	4	yes	—
457	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
458	C₂²	C₂×C₅×#121	1	1	yes	characteristic
459	C₂²	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
460	C₂²	C₅×#576	1	1	yes	characteristic
461	C₂²	C₅×#577	1	1	yes	characteristic
462	C₂²	C₅×#577	1	1	yes	characteristic
463	C₂²	C₅×#578	1	1	yes	characteristic
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	C₅×#389	1	4	yes	—
473	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
474	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
475	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
476	C₄	C₂×C₅×#125	1	1	yes	characteristic
477	C₂	—	2	4	no	—
478	C₂	C₂×C₅×#389	1	1	yes	characteristic
479	C₂	C₅×#2946	1	1	yes	characteristic
480	C₂	C₅×#2947	1	1	yes	characteristic
481	C₂	C₅×#3062	1	1	yes	characteristic
482	C₂	C₅×#3063	1	1	yes	characteristic
483	C₂	C₅×#3163	1	1	yes	characteristic
484	C₂	C₅×#3164	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1944	C₂	semidirect
7. C₅×#1943	C₂	semidirect
8. C₅×#1942	C₂	semidirect
9. C₅×#1941	C₂	semidirect
20. C₅×#428	C₄	semidirect
44. #21160	C₅	direct (N × H)
88. C₅×#107	C₂×C₄	semidirect
90. C₅×#106	C₂×C₄	semidirect
102. #1944	C₂×C₅	semidirect
103. #1943	C₂×C₅	semidirect
104. #1942	C₂×C₅	semidirect
105. #1941	C₂×C₅	semidirect
131. C₅×M₁₆	C₄⋊C₄	semidirect
177. #428	C₄×C₅	semidirect
294. #107	C₂×C₄×C₅	semidirect
296. #106	C₂×C₄×C₅	semidirect
353. M₁₆	C₅×C₄⋊C₄	semidirect
449. C₅	#21160	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×#428	2
C₂×C₅×#405	2
C₅×#2317	2
C₅×#2316	2
C₅×#1944	2
C₅×#1943	2
C₅×#1942	2
C₅×#1941	2
C₅×#1735	2
C₂×C₅×#340	2
#21160	5

Subgroups — C5×#21160 #11943880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21160 #11943880