Subgroups — C₅×#22995 #11945715

Order 1280.

1170 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₈	C₂	1	2	yes	maximal, complemented
3	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1957	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1934	C₂	1	2	yes	maximal, complemented
8	C₅×#1879	C₂	1	2	yes	maximal, complemented
9	C₅×#1862	C₂	1	2	yes	maximal, complemented
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×D₈	C₂²	1	2	yes	—
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
19	C₅×#459	C₄	1	8	yes	complemented
20	C₄×C₅×D₈	—	2	8	no	—
21	C₂×C₅×#107	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	2	yes	—
25	C₂×C₅×#102	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₅×#390	—	2	1	no	—
31	C₅×#390	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#386	—	2	2	no	—
34	C₅×#385	—	2	2	no	—
35	C₅×#384	C₂²	1	1	yes	characteristic
36	C₅×#380	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#22995	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	—	2	2	no	—
50	C₂³×C₄×C₅	—	2	2	no	—
51	C₂×C₅×D₈	—	2	4	no	—
52	C₂×C₅×D₈	—	2	4	no	—
53	C₂×C₅×D₈	C₂×C₄	1	8	yes	complemented
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	C₅×#127	—	2	2	no	—
58	C₅×#127	C₂×C₄	1	4	yes	complemented
59	C₄×C₅×D₄	—	2	4	no	—
60	C₄×C₅×D₄	—	2	4	no	—
61	C₄×C₅×D₄	—	2	2	no	—
62	C₄×C₅×D₄	—	4	2	no	—
63	C₄×C₅×D₄	—	4	2	no	—
64	C₄×C₅×D₄	—	4	4	no	—
65	C₄×C₅×D₄	C₂×C₄	1	4	yes	complemented
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	4	4	no	—
70	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₂×C₄²×C₅	C₂³	1	2	yes	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#107	—	2	4	no	—
85	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	4	no	—
88	C₅×#102	—	4	2	no	—
89	C₅×#102	C₂×C₄	1	8	yes	complemented
90	C₅×#102	D₄	1	4	yes	complemented
91	C₄×C₅×C₈	—	2	4	no	—
92	C₄×C₅×C₈	—	2	2	no	—
93	C₅×#95	—	2	1	no	—
94	C₅×#95	—	2	2	no	—
95	C₅×#95	D₄	1	2	yes	—
96	C₂×#459	C₂×C₅	1	1	yes	characteristic
97	C₂×C₄×D₈	C₂×C₅	1	2	yes	complemented
98	#2366	C₂×C₅	1	1	yes	characteristic, complemented
99	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
100	#1957	C₂×C₅	1	1	yes	characteristic, complemented
101	#1947	C₂×C₅	1	1	yes	characteristic, complemented
102	#1934	C₂×C₅	1	2	yes	complemented
103	#1879	C₂×C₅	1	2	yes	complemented
104	#1862	C₂×C₅	1	2	yes	complemented
105	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
106	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂⁴×C₅	—	2	1	no	—
108	C₂⁴×C₅	—	2	2	no	—
109	C₂×C₅×D₄	—	2	4	no	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	4	2	no	—
120	C₂×C₅×D₄	—	4	2	no	—
121	C₂×C₅×D₄	—	8	1	no	—
122	C₂×C₅×D₄	—	8	1	no	—
123	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
124	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
125	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
126	C₂×C₅×D₄	#41	1	2	yes	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	4	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	4	4	no	—
133	C₂²×C₄×C₅	—	4	4	no	—
134	C₂²×C₄×C₅	—	4	2	no	—
135	C₂²×C₄×C₅	—	4	2	no	—
136	C₂²×C₄×C₅	—	4	4	no	—
137	C₂²×C₄×C₅	—	4	4	no	—
138	C₂²×C₄×C₅	—	8	2	no	—
139	C₂²×C₄×C₅	—	8	2	no	—
140	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×D₈	—	2	16	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	4	4	no	—
163	C₅×C₄⋊C₄	—	4	2	no	—
164	C₅×C₄⋊C₄	—	8	1	no	—
165	C₅×C₄⋊C₄	D₈	1	4	yes	complemented
166	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
167	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₅×C₂²⋊C₄	—	2	4	no	—
169	C₅×C₂²⋊C₄	—	4	4	no	—
170	C₅×C₂²⋊C₄	—	4	4	no	—
171	C₅×C₂²⋊C₄	—	4	4	no	—
172	C₅×C₂²⋊C₄	—	8	2	no	—
173	C₄²×C₅	—	2	2	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	4	2	no	—
176	C₄²×C₅	C₂²×C₄	1	2	yes	—
177	C₄²×C₅	#41	1	2	yes	—
178	C₂²×D₈	C₂²×C₅	1	2	yes	—
179	C₂×#127	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×D₄	—	2	1	no	—
181	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
182	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
183	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	—	2	1	no	—
185	#459	C₄×C₅	1	8	yes	complemented
186	C₄×D₈	—	2	8	no	—
187	C₂×#107	C₂²×C₅	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×#102	C₂²×C₅	1	1	yes	characteristic
190	C₂×#102	C₂²×C₅	1	2	yes	—
191	C₂×#102	C₂²×C₅	1	2	yes	—
192	C₂×#102	C₂²×C₅	1	2	yes	—
193	C₂×#102	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
196	#390	—	2	1	no	—
197	#390	C₂²×C₅	1	2	yes	—
198	#389	C₂²×C₅	1	2	yes	—
199	#386	—	2	2	no	—
200	#385	—	2	2	no	—
201	#384	C₂²×C₅	1	1	yes	characteristic
202	#380	—	2	1	no	—
203	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	#340	C₂²×C₅	1	1	yes	characteristic
206	#340	C₂²×C₅	1	2	yes	—
207	#340	C₂²×C₅	1	1	yes	characteristic
208	#336	C₂²×C₅	1	2	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	4	no	—
213	C₂³×C₅	—	4	1	no	—
214	C₂³×C₅	—	4	1	no	—
215	C₂³×C₅	—	4	1	no	—
216	C₂³×C₅	—	4	1	no	—
217	C₂³×C₅	—	4	2	no	—
218	C₂³×C₅	—	4	2	no	—
219	C₂³×C₅	—	4	2	no	—
220	C₂³×C₅	—	4	2	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₅×D₄	—	2	4	no	—
225	C₅×D₄	—	2	2	no	—
226	C₅×D₄	—	2	4	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	4	2	no	—
230	C₅×D₄	—	4	2	no	—
231	C₅×D₄	—	4	8	no	—
232	C₅×D₄	—	8	4	no	—
233	C₅×D₄	C₄×D₄	1	4	yes	complemented
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	1	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	2	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	8	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	8	8	no	—
255	C₂×C₄×C₅	—	8	8	no	—
256	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₂×D₈	1	4	yes	—
259	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
260	C₂×C₄×C₅	#135	1	2	yes	—
261	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
267	C₅×C₈	—	2	4	no	—
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	4	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	C₂³×C₅	1	2	yes	—
273	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂×D₈	—	2	4	no	—
278	C₂×D₈	—	2	4	no	—
279	C₂×D₈	C₂×C₄×C₅	1	8	yes	complemented
280	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₅	1	2	yes	—
282	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
283	#127	—	2	2	no	—
284	#127	C₂×C₄×C₅	1	4	yes	complemented
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	4	2	no	—
289	C₄×D₄	—	4	2	no	—
290	C₄×D₄	—	4	4	no	—
291	C₄×D₄	C₂×C₄×C₅	1	4	yes	complemented
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	4	4	no	—
296	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₅	1	2	yes	—
309	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
310	#107	—	2	4	no	—
311	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
312	#102	—	2	2	no	—
313	#102	—	2	4	no	—
314	#102	—	4	2	no	—
315	#102	C₂×C₄×C₅	1	8	yes	complemented
316	#102	C₅×D₄	1	4	yes	complemented
317	C₄×C₈	—	2	4	no	—
318	C₄×C₈	—	2	2	no	—
319	#95	—	2	1	no	—
320	#95	—	2	2	no	—
321	#95	C₅×D₄	1	2	yes	—
322	C₂²×C₅	—	2	4	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	4	2	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	4	no	—
330	C₂²×C₅	—	4	4	no	—
331	C₂²×C₅	—	4	4	no	—
332	C₂²×C₅	—	8	2	no	—
333	C₂²×C₅	—	8	2	no	—
334	C₂²×C₅	—	8	2	no	—
335	C₂²×C₅	—	8	2	no	—
336	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
337	C₂²×C₅	D₄²	1	1	yes	characteristic
338	C₂²×C₅	#548	1	1	yes	characteristic
339	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
340	C₂²×C₅	C₂×#135	1	1	yes	characteristic
341	C₂²×C₅	#576	1	1	yes	characteristic
342	C₂²×C₅	#577	1	1	yes	characteristic
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	4	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	8	1	no	—
349	C₄×C₅	—	8	2	no	—
350	C₄×C₅	C₄×D₈	1	4	yes	complemented
351	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₄×C₅	#520	1	1	yes	characteristic
353	C₄×C₅	#547	1	1	yes	characteristic
354	C₄×C₅	#553	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂⁴	—	2	2	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	8	1	no	—
370	C₂×D₄	—	8	1	no	—
371	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
372	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
373	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
374	C₂×D₄	C₅×#41	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
389	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
391	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
393	D₈	—	2	16	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
402	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	8	1	no	—
413	C₄⋊C₄	C₅×D₈	1	4	yes	complemented
414	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
415	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	8	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	2	no	—
424	C₄²	C₂²×C₄×C₅	1	2	yes	—
425	C₄²	C₅×#41	1	2	yes	—
426	C₂×C₅	—	4	4	no	—
427	C₂×C₅	—	8	4	no	—
428	C₂×C₅	#2361	1	1	yes	characteristic
429	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
430	C₂×C₅	#2946	1	1	yes	characteristic
431	C₂×C₅	D₄×D₈	1	1	yes	characteristic
432	C₂×C₅	#3284	1	1	yes	characteristic
433	C₂×C₅	#3358	1	1	yes	characteristic
434	C₂×C₅	#3361	1	1	yes	characteristic
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
450	D₄	—	2	4	no	—
451	D₄	—	2	2	no	—
452	D₄	—	2	4	no	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	4	8	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	4	no	—
459	D₄	C₄×C₅×D₄	1	4	yes	complemented
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	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	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
483	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
484	C₂×C₄	C₂×C₅×D₈	1	4	yes	—
485	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
486	C₂×C₄	C₅×#135	1	2	yes	—
487	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
488	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
491	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
493	C₈	—	2	4	no	—
494	C₈	—	2	2	no	—
495	C₈	—	4	1	no	—
496	C₅	#22995	1	1	yes	characteristic, direct product factor, Sylow
497	C₂²	—	2	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
512	C₂²	C₅×D₄²	1	1	yes	characteristic
513	C₂²	C₅×#548	1	1	yes	characteristic
514	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
515	C₂²	C₂×C₅×#135	1	1	yes	characteristic
516	C₂²	C₅×#576	1	1	yes	characteristic
517	C₂²	C₅×#577	1	1	yes	characteristic
518	C₄	—	2	4	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₄	—	8	1	no	—
525	C₄	C₄×C₅×D₈	1	4	yes	complemented
526	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
527	C₄	C₅×#520	1	1	yes	characteristic
528	C₄	C₅×#547	1	1	yes	characteristic
529	C₄	C₅×#553	1	1	yes	characteristic
530	C₂	—	4	4	no	—
531	C₂	—	8	4	no	—
532	C₂	C₅×#2361	1	1	yes	characteristic
533	C₂	C₂×C₄×C₅×D₈	1	1	yes	characteristic
534	C₂	C₅×#2946	1	1	yes	characteristic
535	C₂	C₅×D₄×D₈	1	1	yes	characteristic
536	C₂	C₅×#3284	1	1	yes	characteristic
537	C₂	C₅×#3358	1	1	yes	characteristic
538	C₂	C₅×#3361	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	C₂×C₅×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×D₈	C₂	semidirect
3. C₅×#2366	C₂	semidirect
4. C₅×D₄×C₄⋊C₄	C₂	semidirect
5. C₅×#1957	C₂	semidirect
6. C₅×#1947	C₂	semidirect
7. C₅×#1934	C₂	semidirect
8. C₅×#1879	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×C₈×C₄⋊C₄	C₂	semidirect
11. C₄×C₅×#102	C₂	semidirect
19. C₅×#459	C₄	semidirect
43. #22995	C₅	direct (N × H)
53. C₂×C₅×D₈	C₂×C₄	semidirect
58. C₅×#127	C₂×C₄	semidirect
65. C₄×C₅×D₄	C₂×C₄	semidirect
85. C₅×C₄⋊C₈	C₂×C₄	semidirect
89. C₅×#102	C₂×C₄	semidirect
90. C₅×#102	D₄	semidirect
97. C₂×C₄×D₈	C₂×C₅	semidirect
98. #2366	C₂×C₅	semidirect
99. D₄×C₄⋊C₄	C₂×C₅	semidirect
100. #1957	C₂×C₅	semidirect
101. #1947	C₂×C₅	semidirect
102. #1934	C₂×C₅	semidirect
103. #1879	C₂×C₅	semidirect
104. #1862	C₂×C₅	semidirect
105. C₈×C₄⋊C₄	C₂×C₅	semidirect
106. C₄×#102	C₂×C₅	semidirect
165. C₅×C₄⋊C₄	D₈	semidirect
185. #459	C₄×C₅	semidirect
233. C₅×D₄	C₄×D₄	semidirect
279. C₂×D₈	C₂×C₄×C₅	semidirect
284. #127	C₂×C₄×C₅	semidirect
291. C₄×D₄	C₂×C₄×C₅	semidirect
311. C₄⋊C₈	C₂×C₄×C₅	semidirect
315. #102	C₂×C₄×C₅	semidirect
316. #102	C₅×D₄	semidirect
350. C₄×C₅	C₄×D₈	semidirect
413. C₄⋊C₄	C₅×D₈	semidirect
459. D₄	C₄×C₅×D₄	semidirect
496. C₅	#22995	direct (N × H)
525. C₄	C₄×C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#459	2
C₂×C₄×C₅×D₈	2
C₅×#2366	2
C₅×D₄×C₄⋊C₄	2
C₅×#1957	2
C₅×#1947	2
C₅×#1934	2
C₅×#1879	2
C₅×#1862	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#102	2
#22995	5

Subgroups — C5×#22995 #11945715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22995 #11945715