Subgroups — C₅×#29451 #11952171

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2860	C₂	1	1	yes	maximal, characteristic
2	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2086	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2067	C₂	1	1	yes	maximal, characteristic
5	C₅×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2055	C₂	1	1	yes	maximal, characteristic
7	C₅×#1973	C₂	1	1	yes	maximal, characteristic
8	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1936	C₂	1	1	yes	maximal, characteristic
10	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1926	C₂	1	1	yes	maximal, characteristic
12	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1880	C₂	1	1	yes	maximal, characteristic
14	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₅×#126	—	2	1	no	—
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#107	C₂²	1	1	yes	characteristic
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
21	C₂×C₅×#106	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×#103	C₂²	1	1	yes	characteristic
25	C₂×C₅×#103	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₅×#391	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#390	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#389	C₂²	1	1	yes	characteristic
42	C₅×#388	—	2	1	no	—
43	C₅×#388	—	2	1	no	—
44	C₅×#388	—	2	1	no	—
45	C₅×#387	—	2	1	no	—
46	C₅×#387	—	2	1	no	—
47	C₄×C₅×C₄⋊C₄	—	2	1	no	—
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×#376	—	2	1	no	—
50	C₄³×C₅	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29451	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×SD₁₆	—	2	2	no	—
63	C₂×C₅×SD₁₆	—	2	2	no	—
64	C₂×C₅×SD₁₆	—	4	1	no	—
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×#126	—	4	4	no	—
70	C₄×C₅×Q₈	—	2	2	no	—
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₅	—	2	1	no	—
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₅×#107	—	2	2	no	—
100	C₅×#107	—	2	2	no	—
101	C₅×#106	—	4	1	no	—
102	C₅×C₄⋊C₈	—	2	2	no	—
103	C₅×C₄⋊C₈	—	2	2	no	—
104	C₅×#103	—	2	2	no	—
105	C₅×#103	—	2	2	no	—
106	C₅×#103	—	4	1	no	—
107	C₅×#102	—	2	2	no	—
108	C₅×#102	—	2	2	no	—
109	C₅×#102	—	4	1	no	—
110	C₅×#97	—	4	1	no	—
111	C₅×#97	—	4	1	no	—
112	C₅×#95	—	2	1	no	—
113	C₅×#95	—	2	1	no	—
114	C₅×#95	—	2	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	#2860	C₂×C₅	1	1	yes	characteristic
123	#2295	C₂×C₅	1	1	yes	characteristic, complemented
124	#2086	C₂×C₅	1	1	yes	characteristic, complemented
125	#2067	C₂×C₅	1	1	yes	characteristic
126	#2066	C₂×C₅	1	1	yes	characteristic, complemented
127	#2055	C₂×C₅	1	1	yes	characteristic
128	#1973	C₂×C₅	1	1	yes	characteristic
129	#1943	C₂×C₅	1	1	yes	characteristic, complemented
130	#1936	C₂×C₅	1	1	yes	characteristic
131	#1935	C₂×C₅	1	1	yes	characteristic, complemented
132	#1926	C₂×C₅	1	1	yes	characteristic
133	#1921	C₂×C₅	1	1	yes	characteristic, complemented
134	#1880	C₂×C₅	1	1	yes	characteristic
135	#1863	C₂×C₅	1	1	yes	characteristic, complemented
136	#1767	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂⁴×C₅	—	2	1	no	—
138	C₂×C₅×Q₈	—	2	1	no	—
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	—	2	1	no	—
141	C₂×C₅×Q₈	—	2	1	no	—
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	#41	1	2	yes	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×SD₁₆	—	4	4	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	#41	1	2	yes	—
176	C₂×C₅×C₈	#41	1	2	yes	—
177	C₅×C₄⋊C₄	—	2	4	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	4	2	no	—
190	C₅×C₄⋊C₄	—	4	2	no	—
191	C₅×C₄⋊C₄	—	4	2	no	—
192	C₅×C₄⋊C₄	—	4	2	no	—
193	C₅×C₄⋊C₄	—	4	2	no	—
194	C₅×C₄⋊C₄	#41	1	2	yes	—
195	C₅×C₂²⋊C₄	—	4	2	no	—
196	C₅×C₂²⋊C₄	—	4	2	no	—
197	C₅×C₂²⋊C₄	—	4	2	no	—
198	C₅×C₂²⋊C₄	—	4	2	no	—
199	C₅×C₂²⋊C₄	—	4	2	no	—
200	C₅×C₂²⋊C₄	—	4	2	no	—
201	C₄²×C₅	—	2	4	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	4	1	no	—
211	C₄²×C₅	—	4	1	no	—
212	C₄²×C₅	—	4	2	no	—
213	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
214	C₂×#126	—	2	1	no	—
215	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×#107	C₂²×C₅	1	1	yes	characteristic
217	C₂×#107	C₂²×C₅	1	1	yes	characteristic
218	C₂×#106	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×#103	C₂²×C₅	1	1	yes	characteristic
222	C₂×#103	C₂²×C₅	1	1	yes	characteristic
223	C₂×#103	C₂²×C₅	1	1	yes	characteristic
224	C₂×#102	C₂²×C₅	1	1	yes	characteristic
225	C₂×#102	C₂²×C₅	1	1	yes	characteristic
226	C₂×#102	C₂²×C₅	1	1	yes	characteristic
227	C₂×#97	C₂²×C₅	1	1	yes	characteristic
228	C₂×#97	C₂²×C₅	1	1	yes	characteristic
229	#391	C₂²×C₅	1	1	yes	characteristic
230	#391	C₂²×C₅	1	1	yes	characteristic
231	#390	C₂²×C₅	1	1	yes	characteristic
232	#390	C₂²×C₅	1	1	yes	characteristic
233	#390	C₂²×C₅	1	1	yes	characteristic
234	#389	C₂²×C₅	1	1	yes	characteristic
235	#389	C₂²×C₅	1	1	yes	characteristic
236	#389	C₂²×C₅	1	1	yes	characteristic
237	#389	C₂²×C₅	1	1	yes	characteristic
238	#389	C₂²×C₅	1	1	yes	characteristic
239	#388	—	2	1	no	—
240	#388	—	2	1	no	—
241	#388	—	2	1	no	—
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	C₄×C₄⋊C₄	—	2	1	no	—
245	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	#376	—	2	1	no	—
247	C₄³	C₂²×C₅	1	1	yes	characteristic
248	#340	C₂²×C₅	1	1	yes	characteristic
249	#340	C₂²×C₅	1	1	yes	characteristic
250	#340	C₂²×C₅	1	1	yes	characteristic
251	#340	C₂²×C₅	1	1	yes	characteristic
252	#340	C₂²×C₅	1	1	yes	characteristic
253	#340	C₂²×C₅	1	1	yes	characteristic
254	#336	C₂²×C₅	1	1	yes	characteristic
255	#336	C₂²×C₅	1	1	yes	characteristic
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	—	4	1	no	—
259	C₂³×C₅	—	4	1	no	—
260	C₂³×C₅	—	4	1	no	—
261	C₂³×C₅	—	4	1	no	—
262	C₂³×C₅	—	4	1	no	—
263	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	4	1	no	—
267	C₅×Q₈	—	4	1	no	—
268	C₅×D₄	—	4	1	no	—
269	C₅×D₄	—	4	1	no	—
270	C₅×D₄	—	4	1	no	—
271	C₅×D₄	—	4	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
310	C₂×C₄×C₅	#137	1	2	yes	—
311	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
317	C₅×C₈	—	2	2	no	—
318	C₅×C₈	—	2	2	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	—	4	1	no	—
326	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
330	#126	—	4	4	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
354	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
355	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
356	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
360	#107	—	2	2	no	—
361	#107	—	2	2	no	—
362	#106	—	4	1	no	—
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	#103	—	4	1	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	4	1	no	—
371	#97	—	4	1	no	—
372	#97	—	4	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	C₂²×C₅	—	8	1	no	—
384	C₂²×C₅	—	8	1	no	—
385	C₂²×C₅	—	8	1	no	—
386	C₂²×C₅	—	8	1	no	—
387	C₂²×C₅	—	8	1	no	—
388	C₂²×C₅	—	8	1	no	—
389	C₂²×C₅	—	8	1	no	—
390	C₂²×C₅	#525	1	1	yes	characteristic
391	C₂²×C₅	#532	1	1	yes	characteristic
392	C₂²×C₅	#537	1	1	yes	characteristic
393	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂²×C₅	C₂×#137	1	1	yes	characteristic
395	C₂²×C₅	#575	1	1	yes	characteristic
396	C₂²×C₅	#575	1	1	yes	characteristic
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	8	1	no	—
406	C₄×C₅	—	8	1	no	—
407	C₄×C₅	—	8	1	no	—
408	C₄×C₅	—	8	1	no	—
409	C₄×C₅	—	8	1	no	—
410	C₄×C₅	#551	1	1	yes	characteristic
411	C₄×C₅	#552	1	1	yes	characteristic
412	C₄×C₅	#553	1	1	yes	characteristic
413	C₄×C₅	#556	1	1	yes	characteristic
414	C₂⁴	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₅×#41	1	2	yes	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
441	SD₁₆	—	4	4	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	C₅×#41	1	2	yes	—
453	C₂×C₈	C₅×#41	1	2	yes	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	C₅×#41	1	2	yes	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	—	4	2	no	—
490	C₂×C₅	—	16	1	no	—
491	C₂×C₅	#2601	1	1	yes	characteristic
492	C₂×C₅	#3115	1	1	yes	characteristic
493	C₂×C₅	#3117	1	1	yes	characteristic
494	C₂×C₅	#3172	1	1	yes	characteristic
495	C₂×C₅	#3180	1	1	yes	characteristic
496	C₂×C₅	#3254	1	1	yes	characteristic
497	C₂×C₅	#3256	1	1	yes	characteristic
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
552	C₂×C₄	C₅×#137	1	2	yes	—
553	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
554	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
555	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
556	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
557	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
559	C₈	—	2	2	no	—
560	C₈	—	2	2	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₅	#29451	1	1	yes	characteristic, direct product factor, Sylow
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	C₅×#525	1	1	yes	characteristic
572	C₂²	C₅×#532	1	1	yes	characteristic
573	C₂²	C₅×#537	1	1	yes	characteristic
574	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
575	C₂²	C₂×C₅×#137	1	1	yes	characteristic
576	C₂²	C₅×#575	1	1	yes	characteristic
577	C₂²	C₅×#575	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	C₅×#551	1	1	yes	characteristic
592	C₄	C₅×#552	1	1	yes	characteristic
593	C₄	C₅×#553	1	1	yes	characteristic
594	C₄	C₅×#556	1	1	yes	characteristic
595	C₂	—	16	1	no	—
596	C₂	C₅×#2601	1	1	yes	characteristic
597	C₂	C₅×#3115	1	1	yes	characteristic
598	C₂	C₅×#3117	1	1	yes	characteristic
599	C₂	C₅×#3172	1	1	yes	characteristic
600	C₂	C₅×#3180	1	1	yes	characteristic
601	C₂	C₅×#3254	1	1	yes	characteristic
602	C₂	C₅×#3256	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
2. C₅×#2295	C₂	semidirect
3. C₅×#2086	C₂	semidirect
5. C₅×#2066	C₂	semidirect
8. C₅×#1943	C₂	semidirect
10. C₅×#1935	C₂	semidirect
12. C₅×#1921	C₂	semidirect
14. C₅×#1863	C₂	semidirect
15. C₅×#1767	C₂	semidirect
59. #29451	C₅	direct (N × H)
123. #2295	C₂×C₅	semidirect
124. #2086	C₂×C₅	semidirect
126. #2066	C₂×C₅	semidirect
129. #1943	C₂×C₅	semidirect
131. #1935	C₂×C₅	semidirect
133. #1921	C₂×C₅	semidirect
135. #1863	C₂×C₅	semidirect
136. #1767	C₂×C₅	semidirect
563. C₅	#29451	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×#2860	2
C₅×#2295	2
C₅×#2086	2
C₅×#2067	2
C₅×#2066	2
C₅×#2055	2
C₅×#1973	2
C₅×#1943	2
C₅×#1936	2
C₅×#1935	2
C₅×#1926	2
C₅×#1921	2
C₅×#1880	2
C₅×#1863	2
C₅×#1767	2
#29451	5

Subgroups — C5×#29451 #11952171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29451 #11952171