Subgroups — C₅×#29554 #11952274

Order 1280.

808 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2293	C₂	1	1	yes	maximal, characteristic
3	C₅×#2058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2043	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2023	C₂	1	1	yes	maximal, characteristic
6	C₅×#2013	C₂	1	1	yes	maximal, characteristic
7	C₅×#1968	C₂	1	2	yes	maximal
8	C₅×#1933	C₂	1	2	yes	maximal, complemented
9	C₅×#1927	C₂	1	2	yes	maximal, complemented
10	C₅×#1877	C₂	1	2	yes	maximal
11	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	—	2	1	no	—
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#103	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₅×#391	—	2	1	no	—
24	C₅×#391	—	2	1	no	—
25	C₅×#391	C₂²	1	2	yes	—
26	C₅×#391	C₂²	1	2	yes	—
27	C₅×#390	C₂²	1	1	yes	characteristic
28	C₅×#390	C₂²	1	1	yes	characteristic
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#388	—	2	1	no	—
32	C₅×#388	—	2	1	no	—
33	C₅×#382	—	2	1	no	—
34	C₅×#382	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
37	C₄³×C₅	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	C₅×#336	C₂²	1	2	yes	—
43	#29554	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	C₂×C₅×SD₁₆	—	2	4	no	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	—	4	2	no	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₅×C₄⋊Q₈	—	4	2	no	—
54	C₅×C₄⋊Q₈	—	4	2	no	—
55	C₄×C₅×D₄	—	2	2	no	—
56	C₄×C₅×D₄	—	2	2	no	—
57	C₅×#117	—	4	4	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	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	1	no	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#106	—	4	2	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	4	2	no	—
84	C₅×#102	—	4	2	no	—
85	C₄×C₅×C₈	—	2	4	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	2	no	—
93	#2862	C₂×C₅	1	1	yes	characteristic, complemented
94	#2293	C₂×C₅	1	1	yes	characteristic
95	#2058	C₂×C₅	1	1	yes	characteristic, complemented
96	#2043	C₂×C₅	1	1	yes	characteristic, complemented
97	#2023	C₂×C₅	1	1	yes	characteristic
98	#2013	C₂×C₅	1	1	yes	characteristic
99	#1968	C₂×C₅	1	2	yes	—
100	#1933	C₂×C₅	1	2	yes	complemented
101	#1927	C₂×C₅	1	2	yes	complemented
102	#1877	C₂×C₅	1	2	yes	—
103	#1744	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	2	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	—	4	2	no	—
112	C₂×C₅×Q₈	—	4	2	no	—
113	C₂×C₅×Q₈	—	4	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	#41	1	2	yes	—
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₅×SD₁₆	—	4	8	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	#41	1	4	yes	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
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	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	#41	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	4	no	—
152	C₅×C₂²⋊C₄	—	4	2	no	—
153	C₅×C₂²⋊C₄	—	4	2	no	—
154	C₅×C₂²⋊C₄	—	4	2	no	—
155	C₅×C₂²⋊C₄	—	4	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	4	1	no	—
163	C₄²×C₅	—	4	2	no	—
164	C₄²×C₅	SD₁₆	1	4	yes	complemented
165	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×#117	—	2	1	no	—
170	C₂×#106	C₂²×C₅	1	2	yes	—
171	C₂×#103	C₂²×C₅	1	2	yes	—
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	2	yes	—
174	C₂×#102	C₂²×C₅	1	2	yes	—
175	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
176	#391	—	2	1	no	—
177	#391	—	2	1	no	—
178	#391	C₂²×C₅	1	2	yes	—
179	#391	C₂²×C₅	1	2	yes	—
180	#390	C₂²×C₅	1	1	yes	characteristic
181	#390	C₂²×C₅	1	1	yes	characteristic
182	#389	C₂²×C₅	1	1	yes	characteristic
183	#389	C₂²×C₅	1	1	yes	characteristic
184	#388	—	2	1	no	—
185	#388	—	2	1	no	—
186	#382	—	2	1	no	—
187	#382	—	2	1	no	—
188	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₄×C₂²⋊C₄	—	2	1	no	—
190	C₄³	C₂²×C₅	1	1	yes	characteristic
191	#340	C₂²×C₅	1	2	yes	—
192	#340	C₂²×C₅	1	2	yes	—
193	#336	C₂²×C₅	1	1	yes	characteristic
194	#336	C₂²×C₅	1	2	yes	—
195	#336	C₂²×C₅	1	1	yes	characteristic
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	4	no	—
210	C₅×D₄	—	4	2	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	4	8	no	—
226	C₂×C₄×C₅	—	4	1	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	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
241	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
242	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
243	C₂×C₄×C₅	#135	1	2	yes	—
244	C₂×C₄×C₅	#137	1	2	yes	—
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×#41	1	2	yes	—
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
249	C₅×C₈	—	2	4	no	—
250	C₅×C₈	—	4	2	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	C₂³×C₅	1	2	yes	—
253	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	4	2	no	—
258	C₂²×C₈	C₂³×C₅	1	2	yes	—
259	C₂²×C₈	C₂³×C₅	1	2	yes	—
260	C₄⋊Q₈	—	4	2	no	—
261	C₄⋊Q₈	—	4	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	#117	—	4	4	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	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
281	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
282	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
283	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
287	#106	—	4	2	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	#103	—	4	2	no	—
291	#102	—	4	2	no	—
292	C₄×C₈	—	2	4	no	—
293	#95	—	2	1	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	8	1	no	—
304	C₂²×C₅	—	8	1	no	—
305	C₂²×C₅	—	8	1	no	—
306	C₂²×C₅	—	8	1	no	—
307	C₂²×C₅	#525	1	1	yes	characteristic
308	C₂²×C₅	#532	1	1	yes	characteristic
309	C₂²×C₅	#535	1	1	yes	characteristic
310	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
311	C₂²×C₅	C₂×#135	1	1	yes	characteristic
312	C₂²×C₅	C₂×#137	1	1	yes	characteristic
313	C₂²×C₅	#575	1	1	yes	characteristic
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	2	no	—
317	C₄×C₅	—	2	2	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	—	8	2	no	—
322	C₄×C₅	—	8	1	no	—
323	C₄×C₅	—	8	1	no	—
324	C₄×C₅	—	8	2	no	—
325	C₄×C₅	#551	1	2	yes	—
326	C₄×C₅	#555	1	2	yes	—
327	C₂⁴	—	2	1	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	—	4	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₅×#41	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
356	SD₁₆	—	4	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	C₅×#41	1	4	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	C₅×#41	1	2	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₅×SD₁₆	1	4	yes	complemented
388	C₂×C₅	—	8	2	no	—
389	C₂×C₅	#2610	1	1	yes	characteristic
390	C₂×C₅	#3101	1	1	yes	characteristic
391	C₂×C₅	#3107	1	1	yes	characteristic
392	C₂×C₅	#3167	1	1	yes	characteristic
393	C₂×C₅	#3181	1	1	yes	characteristic
394	C₂×C₅	#3206	1	1	yes	characteristic
395	C₂×C₅	#3211	1	1	yes	characteristic
396	C₂³	—	2	2	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	—	4	1	no	—
403	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	8	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
441	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
442	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
443	C₂×C₄	C₅×#135	1	2	yes	—
444	C₂×C₄	C₅×#137	1	2	yes	—
445	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	C₂×C₄	C₂×C₅×#41	1	2	yes	—
447	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
448	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
449	C₈	—	2	4	no	—
450	C₈	—	4	2	no	—
451	C₅	#29554	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₅×#525	1	1	yes	characteristic
460	C₂²	C₅×#532	1	1	yes	characteristic
461	C₂²	C₅×#535	1	1	yes	characteristic
462	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
463	C₂²	C₂×C₅×#135	1	1	yes	characteristic
464	C₂²	C₂×C₅×#137	1	1	yes	characteristic
465	C₂²	C₅×#575	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	2	no	—
477	C₄	C₅×#551	1	2	yes	—
478	C₄	C₅×#555	1	2	yes	—
479	C₂	—	8	2	no	—
480	C₂	C₅×#2610	1	1	yes	characteristic
481	C₂	C₅×#3101	1	1	yes	characteristic
482	C₂	C₅×#3107	1	1	yes	characteristic
483	C₂	C₅×#3167	1	1	yes	characteristic
484	C₂	C₅×#3181	1	1	yes	characteristic
485	C₂	C₅×#3206	1	1	yes	characteristic
486	C₂	C₅×#3211	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 ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2862	C₂	semidirect
3. C₅×#2058	C₂	semidirect
4. C₅×#2043	C₂	semidirect
8. C₅×#1933	C₂	semidirect
9. C₅×#1927	C₂	semidirect
11. C₅×#1744	C₂	semidirect
43. #29554	C₅	direct (N × H)
93. #2862	C₂×C₅	semidirect
95. #2058	C₂×C₅	semidirect
96. #2043	C₂×C₅	semidirect
100. #1933	C₂×C₅	semidirect
101. #1927	C₂×C₅	semidirect
103. #1744	C₂×C₅	semidirect
164. C₄²×C₅	SD₁₆	semidirect
387. C₄²	C₅×SD₁₆	semidirect
451. C₅	#29554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2862	2
C₅×#2293	2
C₅×#2058	2
C₅×#2043	2
C₅×#2023	2
C₅×#2013	2
C₅×#1968	2
C₅×#1933	2
C₅×#1927	2
C₅×#1877	2
C₅×#1744	2
#29554	5

Subgroups — C5×#29554 #11952274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29554 #11952274