Subgroups — C₅×#29555 #11952275

Order 1280.

856 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2858	C₂	1	1	yes	maximal, characteristic
2	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2041	C₂	1	1	yes	maximal, characteristic
5	C₅×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2014	C₂	1	1	yes	maximal, characteristic
7	C₅×#1968	C₂	1	2	yes	maximal, complemented
8	C₅×#1934	C₂	1	2	yes	maximal, complemented
9	C₅×#1926	C₂	1	2	yes	maximal, complemented
10	C₅×#1880	C₂	1	2	yes	maximal, complemented
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×#127	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	—	2	1	no	—
16	C₂×C₅×#124	—	2	1	no	—
17	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₅×#391	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	1	yes	characteristic
26	C₅×#390	—	2	1	no	—
27	C₅×#390	—	2	1	no	—
28	C₅×#390	C₂²	1	2	yes	—
29	C₅×#390	C₂²	1	2	yes	—
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#389	C₂²	1	1	yes	characteristic
32	C₅×#387	—	2	1	no	—
33	C₅×#387	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#376	—	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	#29555	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	—	2	1	no	—
48	C₂²×C₅×D₄	C₂³	1	2	yes	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	—	4	2	no	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₅×C₄⋊Q₈	—	4	2	no	—
55	C₅×#127	—	4	2	no	—
56	C₅×#124	—	4	4	no	—
57	C₅×#124	—	4	4	no	—
58	C₄×C₅×Q₈	—	2	2	no	—
59	C₄×C₅×Q₈	—	2	2	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	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
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	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#106	—	4	2	no	—
82	C₅×#103	—	4	2	no	—
83	C₅×#102	—	2	4	no	—
84	C₅×#102	—	2	4	no	—
85	C₅×#102	—	4	2	no	—
86	C₄×C₅×C₈	—	2	4	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	1	no	—
94	#2858	C₂×C₅	1	1	yes	characteristic
95	#2295	C₂×C₅	1	1	yes	characteristic, complemented
96	#2058	C₂×C₅	1	1	yes	characteristic, complemented
97	#2041	C₂×C₅	1	1	yes	characteristic
98	#2024	C₂×C₅	1	1	yes	characteristic, complemented
99	#2014	C₂×C₅	1	1	yes	characteristic
100	#1968	C₂×C₅	1	2	yes	complemented
101	#1934	C₂×C₅	1	2	yes	complemented
102	#1926	C₂×C₅	1	2	yes	complemented
103	#1880	C₂×C₅	1	2	yes	complemented
104	#1744	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	4	2	no	—
110	C₂×C₅×Q₈	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	#41	1	2	yes	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	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	—	4	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	—	4	2	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₅×SD₁₆	—	4	8	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	#41	1	4	yes	—
144	C₅×C₄⋊C₄	—	2	4	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	—	4	2	no	—
153	C₅×C₄⋊C₄	#41	1	2	yes	—
154	C₅×C₂²⋊C₄	—	4	4	no	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₅×C₂²⋊C₄	—	4	4	no	—
157	C₅×C₂²⋊C₄	—	4	4	no	—
158	C₄²×C₅	—	2	4	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	4	1	no	—
166	C₄²×C₅	—	4	2	no	—
167	C₄²×C₅	SD₁₆	1	4	yes	complemented
168	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
169	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₂×#127	C₂²×C₅	1	1	yes	characteristic
171	C₂×#124	—	2	1	no	—
172	C₂×#124	—	2	1	no	—
173	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₂×#106	C₂²×C₅	1	2	yes	—
175	C₂×#103	C₂²×C₅	1	2	yes	—
176	C₂×#102	C₂²×C₅	1	2	yes	—
177	C₂×#102	C₂²×C₅	1	2	yes	—
178	C₂×#102	C₂²×C₅	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
180	#391	C₂²×C₅	1	1	yes	characteristic
181	#391	C₂²×C₅	1	1	yes	characteristic
182	#390	—	2	1	no	—
183	#390	—	2	1	no	—
184	#390	C₂²×C₅	1	2	yes	—
185	#390	C₂²×C₅	1	2	yes	—
186	#389	C₂²×C₅	1	1	yes	characteristic
187	#389	C₂²×C₅	1	1	yes	characteristic
188	#387	—	2	1	no	—
189	#387	—	2	1	no	—
190	C₄×C₄⋊C₄	—	2	1	no	—
191	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	#376	—	2	1	no	—
193	C₄³	C₂²×C₅	1	1	yes	characteristic
194	#340	C₂²×C₅	1	2	yes	—
195	#340	C₂²×C₅	1	2	yes	—
196	#336	C₂²×C₅	1	1	yes	characteristic
197	#336	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	1	yes	characteristic
199	C₂³×C₅	—	4	2	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	4	2	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₅×Q₈	—	2	4	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	8	4	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	8	4	no	—
215	C₅×D₄	—	8	4	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	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	4	1	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	—	4	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
245	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
246	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
247	C₂×C₄×C₅	#135	1	2	yes	—
248	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	2	yes	—
251	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
253	C₅×C₈	—	2	4	no	—
254	C₅×C₈	—	4	2	no	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂³×C₅	1	2	yes	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂×SD₁₆	—	4	2	no	—
263	C₂²×C₈	C₂³×C₅	1	2	yes	—
264	C₂²×C₈	C₂³×C₅	1	2	yes	—
265	C₄⋊Q₈	—	4	2	no	—
266	#127	—	4	2	no	—
267	#124	—	4	4	no	—
268	#124	—	4	4	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
286	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
287	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
288	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#106	—	4	2	no	—
293	#103	—	4	2	no	—
294	#102	—	2	4	no	—
295	#102	—	2	4	no	—
296	#102	—	4	2	no	—
297	C₄×C₈	—	2	4	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	C₂²×C₅	—	8	2	no	—
306	C₂²×C₅	—	8	2	no	—
307	C₂²×C₅	—	8	2	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	—	8	2	no	—
310	C₂²×C₅	—	8	2	no	—
311	C₂²×C₅	—	8	2	no	—
312	C₂²×C₅	#525	1	1	yes	characteristic
313	C₂²×C₅	#532	1	1	yes	characteristic
314	C₂²×C₅	#535	1	1	yes	characteristic
315	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
316	C₂²×C₅	C₂×#135	1	1	yes	characteristic
317	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²×C₅	#575	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	2	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	4	1	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	8	1	no	—
328	C₄×C₅	—	8	2	no	—
329	C₄×C₅	—	8	1	no	—
330	C₄×C₅	#551	1	2	yes	—
331	C₄×C₅	#555	1	2	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	C₅×#41	1	2	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
364	SD₁₆	—	4	8	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	C₅×#41	1	4	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	C₅×#41	1	2	yes	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	1	no	—
393	C₄²	—	4	2	no	—
394	C₄²	C₅×SD₁₆	1	4	yes	complemented
395	C₂×C₅	—	16	2	no	—
396	C₂×C₅	#2610	1	1	yes	characteristic
397	C₂×C₅	#3103	1	1	yes	characteristic
398	C₂×C₅	#3106	1	1	yes	characteristic
399	C₂×C₅	#3167	1	1	yes	characteristic
400	C₂×C₅	#3180	1	1	yes	characteristic
401	C₂×C₅	#3208	1	1	yes	characteristic
402	C₂×C₅	#3211	1	1	yes	characteristic
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	8	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	4	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
449	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
450	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
451	C₂×C₄	C₅×#135	1	2	yes	—
452	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
453	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₅×#41	1	2	yes	—
455	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
456	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₅	#29555	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	C₅×#525	1	1	yes	characteristic
468	C₂²	C₅×#532	1	1	yes	characteristic
469	C₂²	C₅×#535	1	1	yes	characteristic
470	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₅×#135	1	1	yes	characteristic
472	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂²	C₅×#575	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	1	no	—
485	C₄	C₅×#551	1	2	yes	—
486	C₄	C₅×#555	1	2	yes	—
487	C₂	—	16	2	no	—
488	C₂	C₅×#2610	1	1	yes	characteristic
489	C₂	C₅×#3103	1	1	yes	characteristic
490	C₂	C₅×#3106	1	1	yes	characteristic
491	C₂	C₅×#3167	1	1	yes	characteristic
492	C₂	C₅×#3180	1	1	yes	characteristic
493	C₂	C₅×#3208	1	1	yes	characteristic
494	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	C₂×C₅×#127	C₂²
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
2. C₅×#2295	C₂	semidirect
3. C₅×#2058	C₂	semidirect
5. C₅×#2024	C₂	semidirect
7. C₅×#1968	C₂	semidirect
8. C₅×#1934	C₂	semidirect
9. C₅×#1926	C₂	semidirect
10. C₅×#1880	C₂	semidirect
11. C₅×#1744	C₂	semidirect
43. #29555	C₅	direct (N × H)
95. #2295	C₂×C₅	semidirect
96. #2058	C₂×C₅	semidirect
98. #2024	C₂×C₅	semidirect
100. #1968	C₂×C₅	semidirect
101. #1934	C₂×C₅	semidirect
102. #1926	C₂×C₅	semidirect
103. #1880	C₂×C₅	semidirect
104. #1744	C₂×C₅	semidirect
167. C₄²×C₅	SD₁₆	semidirect
394. C₄²	C₅×SD₁₆	semidirect
459. C₅	#29555	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×#2858	2
C₅×#2295	2
C₅×#2058	2
C₅×#2041	2
C₅×#2024	2
C₅×#2014	2
C₅×#1968	2
C₅×#1934	2
C₅×#1926	2
C₅×#1880	2
C₅×#1744	2
#29555	5

Subgroups — C5×#29555 #11952275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29555 #11952275