Subgroups — C₅×#29524 #11952244

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2644	C₂	1	1	yes	maximal, characteristic
2	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2092	C₂	1	1	yes	maximal, characteristic
5	C₅×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2023	C₂	1	1	yes	maximal, characteristic
7	C₅×#1944	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1936	C₂	1	1	yes	maximal, characteristic
10	C₅×#1934	C₂	1	1	yes	maximal, characteristic
11	C₅×#1926	C₂	1	1	yes	maximal, characteristic
12	C₅×#1926	C₂	1	1	yes	maximal, characteristic
13	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#107	C₂²	1	1	yes	characteristic
18	C₂×C₅×#106	C₂²	1	1	yes	characteristic
19	C₂×C₅×#106	C₂²	1	1	yes	characteristic
20	C₂×C₅×#106	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	1	yes	characteristic
22	C₂×C₅×#102	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#397	—	2	1	no	—
28	C₅×#397	—	2	1	no	—
29	C₅×#397	—	2	1	no	—
30	C₅×#396	—	2	1	no	—
31	C₅×#391	—	2	1	no	—
32	C₅×#391	—	2	1	no	—
33	C₅×#390	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	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×#387	—	2	1	no	—
42	C₅×#387	—	2	1	no	—
43	C₅×#382	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₅×#376	C₂²	1	1	yes	characteristic
47	C₅×#340	C₂²	1	1	yes	characteristic
48	C₅×#340	C₂²	1	1	yes	characteristic
49	C₅×#340	C₂²	1	1	yes	characteristic
50	C₅×#340	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×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29524	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	—	2	1	no	—
61	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊Q₈	—	2	2	no	—
67	C₅×C₄⋊Q₈	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₅×#107	—	2	2	no	—
93	C₅×#106	—	2	2	no	—
94	C₅×#106	—	2	2	no	—
95	C₅×#106	—	2	2	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#97	—	2	2	no	—
101	C₄×C₅×C₈	—	2	2	no	—
102	C₅×#95	—	2	1	no	—
103	C₅×#95	—	2	1	no	—
104	C₅×#95	—	2	1	no	—
105	C₅×#95	—	2	1	no	—
106	C₅×#95	—	2	1	no	—
107	C₅×#95	—	2	1	no	—
108	C₅×#95	—	2	1	no	—
109	C₅×#95	—	2	1	no	—
110	C₅×#95	—	2	1	no	—
111	C₅×#95	D₄	1	1	yes	characteristic
112	C₅×#95	D₄	1	1	yes	characteristic
113	C₅×#95	D₄	1	1	yes	characteristic
114	C₅×#95	D₄	1	1	yes	characteristic
115	#2644	C₂×C₅	1	1	yes	characteristic
116	#2331	C₂×C₅	1	1	yes	characteristic, complemented
117	#2101	C₂×C₅	1	1	yes	characteristic, complemented
118	#2092	C₂×C₅	1	1	yes	characteristic
119	#2058	C₂×C₅	1	1	yes	characteristic, complemented
120	#2023	C₂×C₅	1	1	yes	characteristic
121	#1944	C₂×C₅	1	1	yes	characteristic, complemented
122	#1941	C₂×C₅	1	1	yes	characteristic, complemented
123	#1936	C₂×C₅	1	1	yes	characteristic
124	#1934	C₂×C₅	1	1	yes	characteristic
125	#1926	C₂×C₅	1	1	yes	characteristic
126	#1926	C₂×C₅	1	1	yes	characteristic
127	#1920	C₂×C₅	1	1	yes	characteristic, complemented
128	#1918	C₂×C₅	1	1	yes	characteristic, complemented
129	#1746	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂⁴×C₅	—	2	1	no	—
131	C₂×C₅×Q₈	—	2	4	no	—
132	C₂×C₅×Q₈	—	8	1	no	—
133	C₂×C₅×Q₈	—	8	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	#41	1	2	yes	—
165	C₂×C₅×C₈	#41	1	2	yes	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	8	1	no	—
180	C₅×C₄⋊C₄	—	8	1	no	—
181	C₅×C₄⋊C₄	—	8	1	no	—
182	C₅×C₄⋊C₄	—	8	1	no	—
183	C₅×C₄⋊C₄	—	8	1	no	—
184	C₅×C₄⋊C₄	#41	1	2	yes	—
185	C₅×C₄⋊C₄	#41	1	2	yes	—
186	C₅×C₂²⋊C₄	—	8	1	no	—
187	C₅×C₂²⋊C₄	—	8	1	no	—
188	C₅×C₂²⋊C₄	—	8	1	no	—
189	C₅×C₂²⋊C₄	—	8	1	no	—
190	C₅×C₂²⋊C₄	—	8	1	no	—
191	C₅×C₂²⋊C₄	—	8	1	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	8	1	no	—
199	C₄²×C₅	—	8	1	no	—
200	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×#107	C₂²×C₅	1	1	yes	characteristic
202	C₂×#106	C₂²×C₅	1	1	yes	characteristic
203	C₂×#106	C₂²×C₅	1	1	yes	characteristic
204	C₂×#106	C₂²×C₅	1	1	yes	characteristic
205	C₂×#102	C₂²×C₅	1	1	yes	characteristic
206	C₂×#102	C₂²×C₅	1	1	yes	characteristic
207	C₂×#102	C₂²×C₅	1	1	yes	characteristic
208	C₂×#102	C₂²×C₅	1	1	yes	characteristic
209	C₂×#97	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
211	#397	—	2	1	no	—
212	#397	—	2	1	no	—
213	#397	—	2	1	no	—
214	#396	—	2	1	no	—
215	#391	—	2	1	no	—
216	#391	—	2	1	no	—
217	#390	C₂²×C₅	1	1	yes	characteristic
218	#390	C₂²×C₅	1	1	yes	characteristic
219	#390	C₂²×C₅	1	1	yes	characteristic
220	#389	C₂²×C₅	1	1	yes	characteristic
221	#389	C₂²×C₅	1	1	yes	characteristic
222	#389	C₂²×C₅	1	1	yes	characteristic
223	#389	C₂²×C₅	1	1	yes	characteristic
224	#389	C₂²×C₅	1	1	yes	characteristic
225	#387	—	2	1	no	—
226	#387	—	2	1	no	—
227	#382	C₂²×C₅	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	#376	C₂²×C₅	1	1	yes	characteristic
231	#340	C₂²×C₅	1	1	yes	characteristic
232	#340	C₂²×C₅	1	1	yes	characteristic
233	#340	C₂²×C₅	1	1	yes	characteristic
234	#340	C₂²×C₅	1	1	yes	characteristic
235	#340	C₂²×C₅	1	1	yes	characteristic
236	#340	C₂²×C₅	1	1	yes	characteristic
237	#340	C₂²×C₅	1	1	yes	characteristic
238	#340	C₂²×C₅	1	1	yes	characteristic
239	#336	C₂²×C₅	1	1	yes	characteristic
240	#336	C₂²×C₅	1	1	yes	characteristic
241	#336	C₂²×C₅	1	1	yes	characteristic
242	#336	C₂²×C₅	1	1	yes	characteristic
243	C₂³×C₅	—	4	1	no	—
244	C₂³×C₅	—	4	1	no	—
245	C₂³×C₅	—	4	1	no	—
246	C₂³×C₅	—	4	1	no	—
247	C₂³×C₅	—	4	1	no	—
248	C₂³×C₅	—	4	1	no	—
249	C₂³×C₅	—	4	1	no	—
250	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₅×Q₈	—	8	4	no	—
252	C₅×D₄	—	4	1	no	—
253	C₅×D₄	—	4	1	no	—
254	C₅×D₄	—	4	1	no	—
255	C₅×D₄	—	4	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	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	—	4	1	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	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	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
300	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
301	C₅×C₈	—	2	2	no	—
302	C₅×C₈	—	2	2	no	—
303	C₅×C₈	—	4	1	no	—
304	C₅×C₈	—	4	1	no	—
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
337	#107	—	2	2	no	—
338	#106	—	2	2	no	—
339	#106	—	2	2	no	—
340	#106	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#97	—	2	2	no	—
346	C₄×C₈	—	2	2	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	C₅×D₄	1	1	yes	characteristic
357	#95	C₅×D₄	1	1	yes	characteristic
358	#95	C₅×D₄	1	1	yes	characteristic
359	#95	C₅×D₄	1	1	yes	characteristic
360	C₂²×C₅	—	8	1	no	—
361	C₂²×C₅	—	8	1	no	—
362	C₂²×C₅	—	8	1	no	—
363	C₂²×C₅	—	8	1	no	—
364	C₂²×C₅	—	8	1	no	—
365	C₂²×C₅	—	8	1	no	—
366	C₂²×C₅	—	8	1	no	—
367	C₂²×C₅	#525	1	1	yes	characteristic
368	C₂²×C₅	#532	1	1	yes	characteristic
369	C₂²×C₅	#536	1	1	yes	characteristic
370	C₂²×C₅	#576	1	1	yes	characteristic
371	C₂²×C₅	#577	1	1	yes	characteristic
372	C₂²×C₅	#577	1	1	yes	characteristic
373	C₂²×C₅	#577	1	1	yes	characteristic
374	C₄×C₅	—	4	1	no	—
375	C₄×C₅	—	4	2	no	—
376	C₄×C₅	—	4	2	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	—	4	1	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	8	1	no	—
383	C₄×C₅	—	8	1	no	—
384	C₄×C₅	—	8	1	no	—
385	C₄×C₅	—	8	1	no	—
386	C₄×C₅	—	8	1	no	—
387	C₄×C₅	#552	1	1	yes	characteristic
388	C₄×C₅	#552	1	1	yes	characteristic
389	C₄×C₅	#556	1	1	yes	characteristic
390	C₄×C₅	#556	1	1	yes	characteristic
391	C₂⁴	—	2	1	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	8	1	no	—
394	C₂×Q₈	—	8	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	C₅×#41	1	2	yes	—
426	C₂×C₈	C₅×#41	1	2	yes	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	8	1	no	—
441	C₄⋊C₄	—	8	1	no	—
442	C₄⋊C₄	—	8	1	no	—
443	C₄⋊C₄	—	8	1	no	—
444	C₄⋊C₄	—	8	1	no	—
445	C₄⋊C₄	C₅×#41	1	2	yes	—
446	C₄⋊C₄	C₅×#41	1	2	yes	—
447	C₂²⋊C₄	—	8	1	no	—
448	C₂²⋊C₄	—	8	1	no	—
449	C₂²⋊C₄	—	8	1	no	—
450	C₂²⋊C₄	—	8	1	no	—
451	C₂²⋊C₄	—	8	1	no	—
452	C₂²⋊C₄	—	8	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	8	1	no	—
460	C₄²	—	8	1	no	—
461	C₂×C₅	—	16	1	no	—
462	C₂×C₅	#2604	1	1	yes	characteristic
463	C₂×C₅	#3118	1	1	yes	characteristic
464	C₂×C₅	#3126	1	1	yes	characteristic
465	C₂×C₅	#3173	1	1	yes	characteristic
466	C₂×C₅	#3179	1	1	yes	characteristic
467	C₂×C₅	#3241	1	1	yes	characteristic
468	C₂×C₅	#3244	1	1	yes	characteristic
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
477	Q₈	—	8	4	no	—
478	D₄	—	4	1	no	—
479	D₄	—	4	1	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
522	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
523	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
524	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
525	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
526	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	2	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₅	#29524	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	C₅×#525	1	1	yes	characteristic
540	C₂²	C₅×#532	1	1	yes	characteristic
541	C₂²	C₅×#536	1	1	yes	characteristic
542	C₂²	C₅×#576	1	1	yes	characteristic
543	C₂²	C₅×#577	1	1	yes	characteristic
544	C₂²	C₅×#577	1	1	yes	characteristic
545	C₂²	C₅×#577	1	1	yes	characteristic
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	C₅×#552	1	1	yes	characteristic
560	C₄	C₅×#552	1	1	yes	characteristic
561	C₄	C₅×#556	1	1	yes	characteristic
562	C₄	C₅×#556	1	1	yes	characteristic
563	C₂	—	16	1	no	—
564	C₂	C₅×#2604	1	1	yes	characteristic
565	C₂	C₅×#3118	1	1	yes	characteristic
566	C₂	C₅×#3126	1	1	yes	characteristic
567	C₂	C₅×#3173	1	1	yes	characteristic
568	C₂	C₅×#3179	1	1	yes	characteristic
569	C₂	C₅×#3241	1	1	yes	characteristic
570	C₂	C₅×#3244	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 ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2331	C₂	semidirect
3. C₅×#2101	C₂	semidirect
5. C₅×#2058	C₂	semidirect
7. C₅×#1944	C₂	semidirect
8. C₅×#1941	C₂	semidirect
13. C₅×#1920	C₂	semidirect
14. C₅×#1918	C₂	semidirect
15. C₅×#1746	C₂	semidirect
59. #29524	C₅	direct (N × H)
116. #2331	C₂×C₅	semidirect
117. #2101	C₂×C₅	semidirect
119. #2058	C₂×C₅	semidirect
121. #1944	C₂×C₅	semidirect
122. #1941	C₂×C₅	semidirect
127. #1920	C₂×C₅	semidirect
128. #1918	C₂×C₅	semidirect
129. #1746	C₂×C₅	semidirect
531. C₅	#29524	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×#2644	2
C₅×#2331	2
C₅×#2101	2
C₅×#2092	2
C₅×#2058	2
C₅×#2023	2
C₅×#1944	2
C₅×#1941	2
C₅×#1936	2
C₅×#1934	2
C₅×#1926	2
C₅×#1920	2
C₅×#1918	2
C₅×#1746	2
#29524	5

Subgroups — C5×#29524 #11952244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29524 #11952244