Subgroups — C₅×#25273 #11947993

Order 1280.

814 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×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#476	C₂	1	1	yes	maximal, characteristic
3	C₅×#2547	C₂	1	1	yes	maximal, characteristic
4	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2066	C₂	1	2	yes	maximal, complemented
6	C₅×#2042	C₂	1	2	yes	maximal
7	C₅×#1983	C₂	1	2	yes	maximal
8	C₅×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1927	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#124	C₂²	1	2	yes	—
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#487	—	2	4	no	—
17	C₅×#476	—	2	4	no	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#102	C₂²	1	1	yes	characteristic
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₅×#397	—	2	2	no	—
30	C₅×#391	—	2	2	no	—
31	C₅×#391	C₂²	1	2	yes	—
32	C₅×#389	—	2	1	no	—
33	C₅×#389	C₂²	1	2	yes	—
34	C₅×#380	—	2	1	no	—
35	C₅×#380	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#25273	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×C₄⋊Q₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	D₄	1	4	yes	—
55	C₅×#124	—	2	4	no	—
56	C₅×#124	—	4	2	no	—
57	C₄×C₅×D₄	—	2	2	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	C₂³	1	2	yes	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#106	—	2	4	no	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	4	2	no	—
79	C₅×#103	—	2	4	no	—
80	C₅×#103	—	2	4	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	4	2	no	—
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	2	4	no	—
85	C₅×#102	—	2	2	no	—
86	C₄×C₅×C₈	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	D₄	1	2	yes	—
93	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#476	C₂×C₅	1	1	yes	characteristic
95	#2547	C₂×C₅	1	1	yes	characteristic
96	#2369	C₂×C₅	1	1	yes	characteristic, complemented
97	#2066	C₂×C₅	1	2	yes	complemented
98	#2042	C₂×C₅	1	2	yes	—
99	#1983	C₂×C₅	1	2	yes	—
100	#1981	C₂×C₅	1	1	yes	characteristic, complemented
101	#1939	C₂×C₅	1	1	yes	characteristic, complemented
102	#1927	C₂×C₅	1	2	yes	complemented
103	C₄×#102	C₂×C₅	1	1	yes	characteristic
104	C₂⁴×C₅	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	4	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	8	1	no	—
113	C₂×C₅×Q₈	—	8	1	no	—
114	C₂×C₅×D₄	—	2	1	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	#41	1	2	yes	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	—	4	2	no	—
127	C₂²×C₄×C₅	—	4	2	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
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	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	—	4	2	no	—
153	C₅×C₄⋊C₄	—	8	2	no	—
154	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
155	C₅×C₄⋊C₄	#41	1	2	yes	—
156	C₅×C₂²⋊C₄	—	4	4	no	—
157	C₅×C₂²⋊C₄	—	4	4	no	—
158	C₅×C₂²⋊C₄	—	4	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	4	2	no	—
162	C₄²×C₅	—	8	2	no	—
163	C₄²×C₅	C₂×D₄	1	2	yes	—
164	C₄²×C₅	#41	1	2	yes	—
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×#124	C₂²×C₅	1	2	yes	—
168	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
169	#487	—	2	4	no	—
170	#476	—	2	4	no	—
171	C₂×#106	C₂²×C₅	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#103	C₂²×C₅	1	2	yes	—
176	C₂×#103	C₂²×C₅	1	2	yes	—
177	C₂×#103	C₂²×C₅	1	2	yes	—
178	C₂×#102	C₂²×C₅	1	1	yes	characteristic
179	C₂×#102	C₂²×C₅	1	2	yes	—
180	C₂×#102	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	#397	—	2	2	no	—
183	#391	—	2	2	no	—
184	#391	C₂²×C₅	1	2	yes	—
185	#389	—	2	1	no	—
186	#389	C₂²×C₅	1	2	yes	—
187	#380	—	2	1	no	—
188	#380	—	2	1	no	—
189	C₄×C₄⋊C₄	—	2	1	no	—
190	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
191	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	#340	C₂²×C₅	1	1	yes	characteristic
194	#340	C₂²×C₅	1	1	yes	characteristic
195	#336	C₂²×C₅	1	2	yes	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	—	4	1	no	—
202	C₂³×C₅	—	4	1	no	—
203	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₅×Q₈	—	4	2	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	8	4	no	—
209	C₅×D₄	—	2	2	no	—
210	C₅×D₄	—	2	2	no	—
211	C₅×D₄	—	4	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	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	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	2	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	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	8	4	no	—
237	C₂×C₄×C₅	#121	1	2	yes	—
238	C₂×C₄×C₅	#121	1	2	yes	—
239	C₂×C₄×C₅	#135	1	2	yes	—
240	C₂×C₄×C₅	#137	1	2	yes	—
241	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	1	no	—
249	C₅×C₈	—	4	2	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	C₂³×C₅	1	2	yes	—
252	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₅	1	2	yes	—
256	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	C₅×D₄	1	4	yes	—
261	#124	—	2	4	no	—
262	#124	—	4	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂³×C₅	1	2	yes	—
281	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
282	#106	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	4	2	no	—
285	#103	—	2	4	no	—
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#103	—	4	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	4	no	—
291	#102	—	2	2	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	C₅×D₄	1	2	yes	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	8	1	no	—
303	C₂²×C₅	—	8	1	no	—
304	C₂²×C₅	—	8	1	no	—
305	C₂²×C₅	—	8	1	no	—
306	C₂²×C₅	C₂×#121	1	1	yes	characteristic
307	C₂²×C₅	#546	1	1	yes	characteristic
308	C₂²×C₅	#548	1	1	yes	characteristic
309	C₂²×C₅	C₂×#135	1	1	yes	characteristic
310	C₂²×C₅	C₂×#137	1	1	yes	characteristic
311	C₂²×C₅	#577	1	1	yes	characteristic
312	C₂²×C₅	#577	1	1	yes	characteristic
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	4	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	8	2	no	—
319	C₄×C₅	—	8	1	no	—
320	C₄×C₅	—	8	1	no	—
321	C₄×C₅	#464	1	4	yes	—
322	C₄×C₅	#529	1	1	yes	characteristic
323	C₄×C₅	#542	1	1	yes	characteristic
324	C₄×C₅	#548	1	1	yes	characteristic
325	C₄×C₅	#550	1	1	yes	characteristic
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₅×#41	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
351	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
352	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
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	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
377	C₄⋊C₄	C₅×#41	1	2	yes	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	8	2	no	—
385	C₄²	C₂×C₅×D₄	1	2	yes	—
386	C₄²	C₅×#41	1	2	yes	—
387	C₂×C₅	—	8	2	no	—
388	C₂×C₅	#2426	1	1	yes	characteristic
389	C₂×C₅	C₂×#464	1	1	yes	characteristic
390	C₂×C₅	#3042	1	1	yes	characteristic
391	C₂×C₅	#3303	1	1	yes	characteristic
392	C₂×C₅	#3331	1	1	yes	characteristic
393	C₂×C₅	#3360	1	1	yes	characteristic
394	C₂×C₅	#3369	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	8	4	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	8	4	no	—
436	C₂×C₄	C₅×#121	1	2	yes	—
437	C₂×C₄	C₅×#121	1	2	yes	—
438	C₂×C₄	C₅×#135	1	2	yes	—
439	C₂×C₄	C₅×#137	1	2	yes	—
440	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
441	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
442	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
443	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
444	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	2	no	—
449	C₅	#25273	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	C₂×C₅×#121	1	1	yes	characteristic
458	C₂²	C₅×#546	1	1	yes	characteristic
459	C₂²	C₅×#548	1	1	yes	characteristic
460	C₂²	C₂×C₅×#135	1	1	yes	characteristic
461	C₂²	C₂×C₅×#137	1	1	yes	characteristic
462	C₂²	C₅×#577	1	1	yes	characteristic
463	C₂²	C₅×#577	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	C₅×#464	1	4	yes	—
473	C₄	C₅×#529	1	1	yes	characteristic
474	C₄	C₅×#542	1	1	yes	characteristic
475	C₄	C₅×#548	1	1	yes	characteristic
476	C₄	C₅×#550	1	1	yes	characteristic
477	C₂	—	8	2	no	—
478	C₂	C₅×#2426	1	1	yes	characteristic
479	C₂	C₂×C₅×#464	1	1	yes	characteristic
480	C₂	C₅×#3042	1	1	yes	characteristic
481	C₂	C₅×#3303	1	1	yes	characteristic
482	C₂	C₅×#3331	1	1	yes	characteristic
483	C₂	C₅×#3360	1	1	yes	characteristic
484	C₂	C₅×#3369	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×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
1. C₂×C₅×#487	C₂	semidirect
4. C₅×#2369	C₂	semidirect
5. C₅×#2066	C₂	semidirect
8. C₅×#1981	C₂	semidirect
9. C₅×#1939	C₂	semidirect
10. C₅×#1927	C₂	semidirect
43. #25273	C₅	direct (N × H)
93. C₂×#487	C₂×C₅	semidirect
96. #2369	C₂×C₅	semidirect
97. #2066	C₂×C₅	semidirect
100. #1981	C₂×C₅	semidirect
101. #1939	C₂×C₅	semidirect
102. #1927	C₂×C₅	semidirect
449. C₅	#25273	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×#487	2
C₂×C₅×#476	2
C₅×#2547	2
C₅×#2369	2
C₅×#2066	2
C₅×#2042	2
C₅×#1983	2
C₅×#1981	2
C₅×#1939	2
C₅×#1927	2
C₄×C₅×#102	2
#25273	5

Subgroups — C5×#25273 #11947993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25273 #11947993