Subgroups — C₅×#22468 #11945188

Order 1280.

1316 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2898	C₂	1	2	yes	maximal, complemented
5	C₅×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1908	C₂	1	2	yes	maximal, complemented
8	C₅×#1882	C₂	1	2	yes	maximal, complemented
9	C₅×#1816	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1793	C₂	1	2	yes	maximal, complemented
11	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₅×#578	—	2	4	no	—
14	C₅×#578	C₄	1	8	yes	complemented
15	C₂×C₅×#137	—	2	2	no	—
16	C₂×C₅×#137	C₂²	1	2	yes	—
17	C₂×C₅×#135	—	2	1	no	—
18	C₂×C₅×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Q₁₆	—	2	1	no	—
20	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₅×#131	C₂²	1	2	yes	—
22	C₂×C₅×#131	C₂²	1	1	yes	characteristic
23	C₅×#520	C₂²	1	2	yes	—
24	C₅×#443	—	2	4	no	—
25	C₅×#440	—	2	2	no	—
26	C₄×C₅×Q₁₆	—	2	1	no	—
27	C₄×C₅×D₈	—	2	1	no	—
28	C₂×C₅×#108	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	C₂²	1	1	yes	characteristic
31	C₂×C₅×#104	C₂²	1	2	yes	—
32	C₅×#419	—	2	2	no	—
33	C₅×#419	C₂²	1	2	yes	—
34	C₅×#417	—	2	2	no	—
35	C₅×#417	C₂²	1	2	yes	—
36	C₅×#417	C₂²	1	2	yes	—
37	C₅×#416	—	2	2	no	—
38	C₅×#416	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	—	2	2	no	—
40	C₂×C₅×#103	C₂²	1	2	yes	—
41	C₂×C₅×#101	C₂²	1	2	yes	—
42	C₅×#405	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	2	yes	—
45	C₅×#343	C₂²	1	2	yes	—
46	C₅×#341	C₂²	1	1	yes	characteristic
47	C₅×#339	C₂²	1	1	yes	characteristic
48	#22468	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₅×2₋¹⁺⁴	—	2	4	no	—
50	C₅×2₋¹⁺⁴	—	2	4	no	—
51	C₅×2₋¹⁺⁴	—	4	2	no	—
52	C₅×2₋¹⁺⁴	C₂×C₄	1	8	yes	complemented
53	C₂×C₅×#41	—	2	2	no	—
54	C₂×C₅×#41	—	2	2	no	—
55	C₂×C₅×#41	—	4	2	no	—
56	C₂×C₅×#41	C₂³	1	2	yes	—
57	C₂×C₅×#41	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Q₈	—	2	2	no	—
59	C₂²×C₅×Q₈	—	2	2	no	—
60	C₂²×C₅×Q₈	C₂³	1	2	yes	—
61	C₅×#137	—	2	4	no	—
62	C₅×#137	—	2	16	no	—
63	C₅×#137	C₂×C₄	1	8	yes	complemented
64	C₅×#135	—	2	8	no	—
65	C₅×#135	C₂×C₄	1	4	yes	—
66	C₅×#135	D₄	1	4	yes	—
67	C₂×C₅×Q₁₆	—	2	2	no	—
68	C₂×C₅×Q₁₆	—	2	8	no	—
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	—	2	1	no	—
71	C₂×C₅×Q₁₆	—	2	2	no	—
72	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
73	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
74	C₂×C₅×SD₁₆	—	2	2	no	—
75	C₂×C₅×SD₁₆	D₄	1	2	yes	—
76	C₂×C₅×D₈	D₄	1	1	yes	characteristic
77	C₅×#131	—	2	2	no	—
78	C₅×#131	—	2	4	no	—
79	C₅×#131	—	4	2	no	—
80	C₅×#131	C₂×C₄	1	4	yes	complemented
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	—	2	2	no	—
83	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₅×M₁₆	C₂³	1	2	yes	—
85	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₂²×C₅×C₈	—	2	2	no	—
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	4	2	no	—
93	C₅×#117	—	2	2	no	—
94	C₅×#117	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	—	2	2	no	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×#108	—	2	2	no	—
99	C₅×#107	—	2	1	no	—
100	C₅×#107	—	2	1	no	—
101	C₅×#104	—	2	4	no	—
102	C₅×#104	—	2	2	no	—
103	C₅×#103	—	2	2	no	—
104	C₅×#103	—	2	2	no	—
105	C₅×#103	—	2	2	no	—
106	C₅×#103	—	2	2	no	—
107	C₅×#103	—	2	2	no	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	D₄	1	1	yes	characteristic
110	C₅×#103	D₄	1	1	yes	characteristic
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	D₄	1	1	yes	characteristic
114	C₅×#102	D₄	1	1	yes	characteristic
115	C₅×#101	—	4	2	no	—
116	C₅×#97	—	2	1	no	—
117	C₄×C₅×C₈	—	2	2	no	—
118	C₄×C₅×C₈	—	2	1	no	—
119	C₅×#95	—	4	2	no	—
120	C₂×#578	C₂×C₅	1	1	yes	characteristic
121	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
122	#2951	C₂×C₅	1	1	yes	characteristic, complemented
123	#2898	C₂×C₅	1	2	yes	complemented
124	#1979	C₂×C₅	1	1	yes	characteristic, complemented
125	#1969	C₂×C₅	1	1	yes	characteristic, complemented
126	#1908	C₂×C₅	1	2	yes	complemented
127	#1882	C₂×C₅	1	2	yes	complemented
128	#1816	C₂×C₅	1	1	yes	characteristic, complemented
129	#1793	C₂×C₅	1	2	yes	complemented
130	#1764	C₂×C₅	1	1	yes	characteristic, complemented
131	C₅×#41	—	2	1	no	—
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₅×#41	—	2	1	no	—
135	C₅×#41	—	2	8	no	—
136	C₅×#41	—	2	8	no	—
137	C₅×#41	—	4	8	no	—
138	C₅×#41	—	4	4	no	—
139	C₅×#41	—	4	4	no	—
140	C₅×#41	—	4	8	no	—
141	C₅×#41	C₂²×C₄	1	4	yes	—
142	C₅×#41	C₂²×C₄	1	2	yes	—
143	C₅×#41	C₂×D₄	1	4	yes	—
144	C₅×#41	#41	1	2	yes	—
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	2	8	no	—
147	C₂×C₅×Q₈	—	2	8	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	—	4	2	no	—
153	C₂×C₅×Q₈	—	4	4	no	—
154	C₂×C₅×Q₈	—	4	4	no	—
155	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
156	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
157	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	4	2	no	—
161	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
162	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	2	no	—
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	4	2	no	—
169	C₂²×C₄×C₅	—	4	2	no	—
170	C₂²×C₄×C₅	—	4	2	no	—
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₅×Q₁₆	—	2	8	no	—
173	C₅×Q₁₆	—	2	4	no	—
174	C₅×Q₁₆	—	2	4	no	—
175	C₅×Q₁₆	C₂²⋊C₄	1	4	yes	—
176	C₅×SD₁₆	—	2	8	no	—
177	C₅×SD₁₆	C₂²⋊C₄	1	8	yes	—
178	C₅×D₈	C₂²⋊C₄	1	4	yes	—
179	C₅×M₁₆	—	2	1	no	—
180	C₅×M₁₆	—	2	4	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	—	2	1	no	—
183	C₅×M₁₆	—	2	2	no	—
184	C₅×M₁₆	—	2	1	no	—
185	C₅×M₁₆	—	4	4	no	—
186	C₅×M₁₆	C₂²×C₄	1	2	yes	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	4	no	—
191	C₂×C₅×C₈	—	2	2	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	4	4	no	—
194	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	4	2	no	—
203	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	4	2	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	4	2	no	—
211	C₂×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
212	#578	—	2	4	no	—
213	#578	C₄×C₅	1	8	yes	complemented
214	C₂×#137	—	2	2	no	—
215	C₂×#137	C₂²×C₅	1	2	yes	—
216	C₂×#135	—	2	1	no	—
217	C₂×#135	C₂²×C₅	1	1	yes	characteristic
218	C₂²×Q₁₆	—	2	1	no	—
219	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂×#131	C₂²×C₅	1	2	yes	—
221	C₂×#131	C₂²×C₅	1	1	yes	characteristic
222	#520	C₂²×C₅	1	2	yes	—
223	#443	—	2	4	no	—
224	#440	—	2	2	no	—
225	C₄×Q₁₆	—	2	1	no	—
226	C₄×D₈	—	2	1	no	—
227	C₂×#108	C₂²×C₅	1	1	yes	characteristic
228	C₂×#107	C₂²×C₅	1	1	yes	characteristic
229	C₂×#104	C₂²×C₅	1	1	yes	characteristic
230	C₂×#104	C₂²×C₅	1	2	yes	—
231	#419	—	2	2	no	—
232	#419	C₂²×C₅	1	2	yes	—
233	#417	—	2	2	no	—
234	#417	C₂²×C₅	1	2	yes	—
235	#417	C₂²×C₅	1	2	yes	—
236	#416	—	2	2	no	—
237	#416	C₂²×C₅	1	1	yes	characteristic
238	C₂×#103	—	2	2	no	—
239	C₂×#103	C₂²×C₅	1	2	yes	—
240	C₂×#101	C₂²×C₅	1	2	yes	—
241	#405	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
243	#391	C₂²×C₅	1	2	yes	—
244	#343	C₂²×C₅	1	2	yes	—
245	#341	C₂²×C₅	1	1	yes	characteristic
246	#339	C₂²×C₅	1	1	yes	characteristic
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	2	1	no	—
249	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₅×Q₈	—	2	1	no	—
251	C₅×Q₈	—	2	2	no	—
252	C₅×Q₈	—	2	4	no	—
253	C₅×Q₈	—	2	4	no	—
254	C₅×Q₈	—	4	8	no	—
255	C₅×Q₈	—	4	2	no	—
256	C₅×Q₈	—	4	2	no	—
257	C₅×Q₈	C₂×C₂²⋊C₄	1	4	yes	—
258	C₅×Q₈	C₄×D₄	1	2	yes	—
259	C₅×D₄	—	2	2	no	—
260	C₅×D₄	—	2	4	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	2	4	no	—
263	C₅×D₄	—	2	1	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	4	8	no	—
266	C₅×D₄	C₂×C₂²⋊C₄	1	4	yes	—
267	C₅×D₄	C₄×D₄	1	2	yes	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	4	no	—
272	C₂×C₄×C₅	—	2	4	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	4	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	4	8	no	—
279	C₂×C₄×C₅	—	4	8	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	2	no	—
284	C₂×C₄×C₅	—	4	2	no	—
285	C₂×C₄×C₅	—	8	2	no	—
286	C₂×C₄×C₅	—	16	2	no	—
287	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂²×D₄	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	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
293	C₅×C₈	—	2	2	no	—
294	C₅×C₈	—	2	1	no	—
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	4	2	no	—
297	C₅×C₈	—	4	1	no	—
298	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
299	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
300	2₋¹⁺⁴	—	2	4	no	—
301	2₋¹⁺⁴	—	2	4	no	—
302	2₋¹⁺⁴	—	4	2	no	—
303	2₋¹⁺⁴	C₂×C₄×C₅	1	8	yes	complemented
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	4	2	no	—
307	C₂×#41	C₂³×C₅	1	2	yes	—
308	C₂×#41	C₂³×C₅	1	1	yes	characteristic
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	C₂³×C₅	1	2	yes	—
312	#137	—	2	4	no	—
313	#137	—	2	16	no	—
314	#137	C₂×C₄×C₅	1	8	yes	complemented
315	#135	—	2	8	no	—
316	#135	C₂×C₄×C₅	1	4	yes	—
317	#135	C₅×D₄	1	4	yes	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×Q₁₆	—	2	8	no	—
320	C₂×Q₁₆	—	2	1	no	—
321	C₂×Q₁₆	—	2	1	no	—
322	C₂×Q₁₆	—	2	2	no	—
323	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
324	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×SD₁₆	C₅×D₄	1	2	yes	—
327	C₂×D₈	C₅×D₄	1	1	yes	characteristic
328	#131	—	2	2	no	—
329	#131	—	2	4	no	—
330	#131	—	4	2	no	—
331	#131	C₂×C₄×C₅	1	4	yes	complemented
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	C₂³×C₅	1	2	yes	—
335	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
336	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₄×Q₈	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	4	2	no	—
344	#117	—	2	2	no	—
345	#117	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
348	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
349	#108	—	2	2	no	—
350	#107	—	2	1	no	—
351	#107	—	2	1	no	—
352	#104	—	2	4	no	—
353	#104	—	2	2	no	—
354	#103	—	2	2	no	—
355	#103	—	2	2	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	C₅×D₄	1	1	yes	characteristic
361	#103	C₅×D₄	1	1	yes	characteristic
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	C₅×D₄	1	1	yes	characteristic
365	#102	C₅×D₄	1	1	yes	characteristic
366	#101	—	4	2	no	—
367	#97	—	2	1	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	1	no	—
370	#95	—	4	2	no	—
371	C₂²×C₅	—	2	1	no	—
372	C₂²×C₅	—	2	1	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	#518	1	1	yes	characteristic
380	C₂²×C₅	D₄²	1	1	yes	characteristic
381	C₂²×C₅	#546	1	1	yes	characteristic
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	2	4	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	—	4	4	no	—
386	C₄×C₅	—	4	1	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	8	2	no	—
389	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
390	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
391	C₄×C₅	D₄²	1	1	yes	characteristic
392	C₄×C₅	#546	1	1	yes	characteristic
393	#41	—	2	1	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	1	no	—
397	#41	—	2	8	no	—
398	#41	—	2	8	no	—
399	#41	—	4	8	no	—
400	#41	—	4	4	no	—
401	#41	—	4	4	no	—
402	#41	—	4	8	no	—
403	#41	C₂²×C₄×C₅	1	4	yes	—
404	#41	C₂²×C₄×C₅	1	2	yes	—
405	#41	C₂×C₅×D₄	1	4	yes	—
406	#41	C₅×#41	1	2	yes	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	8	no	—
409	C₂×Q₈	—	2	8	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	4	2	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
418	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
419	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
424	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
434	Q₁₆	—	2	8	no	—
435	Q₁₆	—	2	4	no	—
436	Q₁₆	—	2	4	no	—
437	Q₁₆	C₅×C₂²⋊C₄	1	4	yes	—
438	SD₁₆	—	2	8	no	—
439	SD₁₆	C₅×C₂²⋊C₄	1	8	yes	—
440	D₈	C₅×C₂²⋊C₄	1	4	yes	—
441	M₁₆	—	2	1	no	—
442	M₁₆	—	2	4	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	1	no	—
445	M₁₆	—	2	1	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	4	4	no	—
448	M₁₆	C₂²×C₄×C₅	1	2	yes	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	4	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	4	4	no	—
456	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
457	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
459	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
461	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	4	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	4	2	no	—
473	C₂×C₅	—	2	1	no	—
474	C₂×C₅	—	2	1	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	—	4	4	no	—
477	C₂×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×C₅	#3290	1	1	yes	characteristic
479	C₂×C₅	#3293	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	1	no	—
482	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
483	Q₈	—	2	1	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	4	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	4	8	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	C₂×C₅×C₂²⋊C₄	1	4	yes	—
491	Q₈	C₄×C₅×D₄	1	2	yes	—
492	D₄	—	2	2	no	—
493	D₄	—	2	4	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	1	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	8	no	—
499	D₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
500	D₄	C₄×C₅×D₄	1	2	yes	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	8	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	16	2	no	—
520	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
525	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	2	no	—
530	C₈	—	4	1	no	—
531	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
532	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
533	C₅	#22468	1	1	yes	characteristic, direct product factor, Sylow
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₅×#518	1	1	yes	characteristic
543	C₂²	C₅×D₄²	1	1	yes	characteristic
544	C₂²	C₅×#546	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	4	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	4	no	—
551	C₄	—	8	2	no	—
552	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
553	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
554	C₄	C₅×D₄²	1	1	yes	characteristic
555	C₄	C₅×#546	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	4	2	no	—
559	C₂	—	4	4	no	—
560	C₂	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic
561	C₂	C₅×#3290	1	1	yes	characteristic
562	C₂	C₅×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#578	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#443	C₂	semidirect
3. C₅×#2951	C₂	semidirect
4. C₅×#2898	C₂	semidirect
5. C₅×#1979	C₂	semidirect
6. C₅×#1969	C₂	semidirect
7. C₅×#1908	C₂	semidirect
8. C₅×#1882	C₂	semidirect
9. C₅×#1816	C₂	semidirect
10. C₅×#1793	C₂	semidirect
11. C₅×#1764	C₂	semidirect
14. C₅×#578	C₄	semidirect
48. #22468	C₅	direct (N × H)
52. C₅×2₋¹⁺⁴	C₂×C₄	semidirect
63. C₅×#137	C₂×C₄	semidirect
72. C₂×C₅×Q₁₆	C₂×C₄	semidirect
80. C₅×#131	C₂×C₄	semidirect
121. C₂×#443	C₂×C₅	semidirect
122. #2951	C₂×C₅	semidirect
123. #2898	C₂×C₅	semidirect
124. #1979	C₂×C₅	semidirect
125. #1969	C₂×C₅	semidirect
126. #1908	C₂×C₅	semidirect
127. #1882	C₂×C₅	semidirect
128. #1816	C₂×C₅	semidirect
129. #1793	C₂×C₅	semidirect
130. #1764	C₂×C₅	semidirect
213. #578	C₄×C₅	semidirect
303. 2₋¹⁺⁴	C₂×C₄×C₅	semidirect
314. #137	C₂×C₄×C₅	semidirect
323. C₂×Q₁₆	C₂×C₄×C₅	semidirect
331. #131	C₂×C₄×C₅	semidirect
533. C₅	#22468	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×#578	2
C₂×C₅×#443	2
C₅×#2951	2
C₅×#2898	2
C₅×#1979	2
C₅×#1969	2
C₅×#1908	2
C₅×#1882	2
C₅×#1816	2
C₅×#1793	2
C₅×#1764	2
#22468	5

Subgroups — C5×#22468 #11945188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22468 #11945188