Subgroups — C₅×#23031 #11945751

Order 1280.

1038 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1925	C₂	1	2	yes	maximal, complemented
8	C₅×#1875	C₂	1	2	yes	maximal, complemented
9	C₅×#1862	C₂	1	2	yes	maximal, complemented
10	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#121	C₂²	1	2	yes	—
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂×C₅×#117	C₂²	1	2	yes	—
17	C₅×#466	C₄	1	8	yes	complemented
18	C₅×#442	—	2	4	no	—
19	C₅×#427	—	2	4	no	—
20	C₂×C₅×#107	C₂²	1	2	yes	—
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₅×#390	—	2	2	no	—
31	C₅×#390	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#388	—	2	2	no	—
34	C₅×#386	—	2	2	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
37	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	#23031	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×D₄	—	2	2	no	—
44	C₂²×C₅×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₅	—	2	2	no	—
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×D₈	—	2	2	no	—
48	C₂×C₅×D₈	—	2	2	no	—
49	C₂×C₅×D₈	C₂×C₄	1	4	yes	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#121	—	2	4	no	—
58	C₅×#121	C₂×C₄	1	8	yes	complemented
59	C₄×C₅×D₄	—	2	4	no	—
60	C₄×C₅×D₄	—	4	2	no	—
61	C₅×#117	—	2	4	no	—
62	C₅×#117	—	4	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	4	no	—
78	C₅×#107	C₂×C₄	1	4	yes	complemented
79	C₅×#106	—	2	2	no	—
80	C₅×#106	D₄	1	4	yes	complemented
81	C₅×#102	—	2	4	no	—
82	C₅×#102	—	4	2	no	—
83	C₅×#102	C₂×C₄	1	8	yes	complemented
84	C₅×C₂²⋊C₈	—	2	2	no	—
85	C₅×#97	—	2	2	no	—
86	C₅×#97	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	D₄	1	2	yes	—
90	C₂×#466	C₂×C₅	1	1	yes	characteristic
91	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
93	#2363	C₂×C₅	1	2	yes	complemented
94	#1972	C₂×C₅	1	1	yes	characteristic, complemented
95	#1943	C₂×C₅	1	1	yes	characteristic, complemented
96	#1925	C₂×C₅	1	2	yes	complemented
97	#1875	C₂×C₅	1	2	yes	complemented
98	#1862	C₂×C₅	1	2	yes	complemented
99	#1776	C₂×C₅	1	1	yes	characteristic, complemented
100	#1752	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	—	2	2	no	—
102	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₅×D₄	—	2	8	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	8	2	no	—
110	C₂×C₅×D₄	—	8	2	no	—
111	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	4	4	no	—
120	C₂²×C₄×C₅	—	4	4	no	—
121	C₂²×C₄×C₅	—	8	2	no	—
122	C₂²×C₄×C₅	C₂²×C₄	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	#41	1	2	yes	—
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₅×D₈	—	2	8	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	8	no	—
132	C₂×C₅×C₈	—	2	1	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	—	2	1	no	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅×C₈	#41	1	2	yes	—
142	C₅×C₄⋊C₄	—	2	2	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	—	8	2	no	—
147	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
148	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
149	C₅×C₂²⋊C₄	—	2	8	no	—
150	C₅×C₂²⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	4	4	no	—
152	C₅×C₂²⋊C₄	—	4	4	no	—
153	C₅×C₂²⋊C₄	—	4	4	no	—
154	C₅×C₂²⋊C₄	—	8	2	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	4	4	no	—
160	C₄²×C₅	—	8	2	no	—
161	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
162	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×#121	C₂²×C₅	1	2	yes	—
164	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
165	C₂×#117	C₂²×C₅	1	2	yes	—
166	#466	C₄×C₅	1	8	yes	complemented
167	#442	—	2	4	no	—
168	#427	—	2	4	no	—
169	C₂×#107	C₂²×C₅	1	2	yes	—
170	C₂×#107	C₂²×C₅	1	1	yes	characteristic
171	C₂×#106	C₂²×C₅	1	1	yes	characteristic
172	C₂×#106	C₂²×C₅	1	1	yes	characteristic
173	C₂×#102	C₂²×C₅	1	2	yes	—
174	C₂×#102	C₂²×C₅	1	2	yes	—
175	C₂×#102	C₂²×C₅	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×#97	C₂²×C₅	1	1	yes	characteristic
178	C₂×#97	C₂²×C₅	1	1	yes	characteristic
179	#390	—	2	2	no	—
180	#390	C₂²×C₅	1	2	yes	—
181	#389	C₂²×C₅	1	2	yes	—
182	#388	—	2	2	no	—
183	#386	—	2	2	no	—
184	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
185	C₄×C₂²⋊C₄	—	2	2	no	—
186	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	#340	C₂²×C₅	1	2	yes	—
188	#340	C₂²×C₅	1	2	yes	—
189	#336	C₂²×C₅	1	1	yes	characteristic
190	#336	C₂²×C₅	1	1	yes	characteristic
191	C₂³×C₅	—	2	1	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	4	2	no	—
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	4	2	no	—
199	C₂³×C₅	—	4	2	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	C₄×D₄	1	2	yes	—
203	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₅×D₄	—	2	4	no	—
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	8	8	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	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	4	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	8	8	no	—
231	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	4	1	no	—
241	C₅×C₈	C₄×D₄	1	4	yes	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	C₂³×C₅	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×D₈	C₂×C₄×C₅	1	4	yes	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
252	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	#121	—	2	4	no	—
257	#121	C₂×C₄×C₅	1	8	yes	complemented
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	4	2	no	—
260	#117	—	2	4	no	—
261	#117	—	4	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	#107	C₂×C₄×C₅	1	4	yes	complemented
278	#106	—	2	2	no	—
279	#106	C₅×D₄	1	4	yes	complemented
280	#102	—	2	4	no	—
281	#102	—	4	2	no	—
282	#102	C₂×C₄×C₅	1	8	yes	complemented
283	C₂²⋊C₈	—	2	2	no	—
284	#97	—	2	2	no	—
285	#97	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	C₅×D₄	1	2	yes	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	4	4	no	—
295	C₂²×C₅	—	4	4	no	—
296	C₂²×C₅	—	4	4	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	—	8	2	no	—
300	C₂²×C₅	—	8	2	no	—
301	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₅	D₄²	1	1	yes	characteristic
303	C₂²×C₅	#547	1	1	yes	characteristic
304	C₂²×C₅	#575	1	2	yes	—
305	C₂²×C₅	#576	1	2	yes	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	4	4	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	4	4	no	—
311	C₄×C₅	—	8	2	no	—
312	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
313	C₄×C₅	#520	1	1	yes	characteristic
314	C₄×C₅	#548	1	1	yes	characteristic
315	C₄×C₅	#553	1	1	yes	characteristic
316	C₂⁴	—	2	2	no	—
317	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂×D₄	—	8	2	no	—
326	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
338	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
339	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₅×#41	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
343	D₈	—	2	8	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₈	C₅×#41	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
363	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	8	2	no	—
376	C₂×C₅	—	4	2	no	—
377	C₂×C₅	—	8	4	no	—
378	C₂×C₅	#2361	1	1	yes	characteristic
379	C₂×C₅	#2943	1	1	yes	characteristic
380	C₂×C₅	#2948	1	1	yes	characteristic
381	C₂×C₅	#3268	1	2	yes	—
382	C₂×C₅	#3347	1	2	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₄×C₅×D₄	1	2	yes	—
395	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	8	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	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	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
428	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	1	no	—
433	C₈	C₄×C₅×D₄	1	4	yes	—
434	C₅	#23031	1	1	yes	characteristic, direct product factor, Sylow
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
448	C₂²	C₅×D₄²	1	1	yes	characteristic
449	C₂²	C₅×#547	1	1	yes	characteristic
450	C₂²	C₅×#575	1	2	yes	—
451	C₂²	C₅×#576	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
459	C₄	C₅×#520	1	1	yes	characteristic
460	C₄	C₅×#548	1	1	yes	characteristic
461	C₄	C₅×#553	1	1	yes	characteristic
462	C₂	—	4	2	no	—
463	C₂	—	8	4	no	—
464	C₂	C₅×#2361	1	1	yes	characteristic
465	C₂	C₅×#2943	1	1	yes	characteristic
466	C₂	C₅×#2948	1	1	yes	characteristic
467	C₂	C₅×#3268	1	2	yes	—
468	C₂	C₅×#3347	1	2	yes	—

	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×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#442	C₂	semidirect
3. C₂×C₅×#427	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#1972	C₂	semidirect
6. C₅×#1943	C₂	semidirect
7. C₅×#1925	C₂	semidirect
8. C₅×#1875	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×#1776	C₂	semidirect
11. C₅×#1752	C₂	semidirect
17. C₅×#466	C₄	semidirect
42. #23031	C₅	direct (N × H)
52. C₂²×C₅×C₈	C₂×C₄	semidirect
58. C₅×#121	C₂×C₄	semidirect
78. C₅×#107	C₂×C₄	semidirect
80. C₅×#106	D₄	semidirect
83. C₅×#102	C₂×C₄	semidirect
91. C₂×#442	C₂×C₅	semidirect
92. C₂×#427	C₂×C₅	semidirect
93. #2363	C₂×C₅	semidirect
94. #1972	C₂×C₅	semidirect
95. #1943	C₂×C₅	semidirect
96. #1925	C₂×C₅	semidirect
97. #1875	C₂×C₅	semidirect
98. #1862	C₂×C₅	semidirect
99. #1776	C₂×C₅	semidirect
100. #1752	C₂×C₅	semidirect
166. #466	C₄×C₅	semidirect
251. C₂²×C₈	C₂×C₄×C₅	semidirect
257. #121	C₂×C₄×C₅	semidirect
277. #107	C₂×C₄×C₅	semidirect
279. #106	C₅×D₄	semidirect
282. #102	C₂×C₄×C₅	semidirect
434. C₅	#23031	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×#466	2
C₂×C₅×#442	2
C₂×C₅×#427	2
C₅×#2363	2
C₅×#1972	2
C₅×#1943	2
C₅×#1925	2
C₅×#1875	2
C₅×#1862	2
C₅×#1776	2
C₅×#1752	2
#23031	5

Subgroups — C5×#23031 #11945751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23031 #11945751