Subgroups — C₅×#60625 #11983345

Order 1280.

2066 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3500	C₂	1	1	yes	maximal, characteristic
3	C₅×#3141	C₂	1	3	yes	maximal, complemented
4	C₅×#3140	C₂	1	3	yes	maximal, complemented
5	C₅×#3137	C₂	1	6	yes	maximal, complemented
6	C₅×#3136	C₂	1	6	yes	maximal, complemented
7	C₅×#3135	C₂	1	3	yes	maximal, complemented
8	C₂×C₅×#489	C₂	1	3	yes	maximal, complemented
9	C₅×#2898	C₂	1	2	yes	maximal, complemented
10	C₅×#2897	C₂	1	2	yes	maximal, complemented
11	C₅×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	2	yes	—
15	C₅×Q₈²	—	2	1	no	—
16	C₅×#557	—	2	1	no	—
17	C₅×#554	—	2	3	no	—
18	C₅×D₄×Q₈	—	2	3	no	—
19	C₅×#548	—	2	1	no	—
20	C₅×#548	—	2	1	no	—
21	C₅×#546	—	2	3	no	—
22	C₅×#546	—	2	3	no	—
23	C₅×#544	C₂²	1	6	yes	complemented
24	C₅×#536	C₂²	1	3	yes	—
25	C₅×#535	C₂²	1	3	yes	—
26	C₅×#533	C₂²	1	3	yes	complemented
27	C₅×#532	C₂²	1	3	yes	—
28	C₂×C₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
29	C₂×C₅×#124	C₂²	1	3	yes	—
30	C₅×#520	C₂²	1	2	yes	—
31	C₄×C₅×#41	C₂²	1	1	yes	characteristic
32	C₅×#491	C₂²	1	6	yes	complemented
33	C₅×#490	C₂²	1	6	yes	complemented
34	C₅×#489	C₂²	1	3	yes	complemented
35	C₅×#489	C₂²	1	12	yes	complemented
36	C₅×#489	C₂²	1	6	yes	complemented
37	C₅×#489	C₂²	1	1	yes	characteristic, complemented
38	C₅×#489	C₂²	1	3	yes	complemented
39	C₅×#489	C₂²	1	3	yes	complemented
40	C₅×#488	C₂²	1	12	yes	complemented
41	C₅×#487	C₂²	1	6	yes	complemented
42	C₅×#486	C₂²	1	6	yes	complemented
43	C₅×#419	C₂²	1	6	yes	complemented
44	C₅×#418	C₂²	1	6	yes	—
45	C₅×#417	C₂²	1	6	yes	—
46	C₅×#417	C₂²	1	6	yes	complemented
47	C₅×#416	C₂²	1	6	yes	—
48	C₅×#416	C₂²	1	6	yes	complemented
49	C₂×C₅×#103	C₂²	1	6	yes	complemented
50	C₂×C₅×#102	C₂²	1	6	yes	—
51	C₅×#405	C₂²	1	6	yes	complemented
52	C₄×C₅×M₁₆	C₂²	1	3	yes	complemented
53	C₂×C₅×#97	C₂²	1	3	yes	complemented
54	#60625	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₅×2₋¹⁺⁴	—	2	8	no	—
56	C₅×H(5,𝔽₂)	—	2	8	no	—
57	C₂×C₅×#41	—	2	1	no	—
58	C₂×C₅×#41	—	2	3	no	—
59	C₂×C₅×#41	C₂³	1	3	yes	—
60	C₂×C₅×#41	C₂³	1	3	yes	—
61	C₂×C₅×#41	C₂³	1	1	yes	characteristic
62	C₂²×C₅×Q₈	—	2	1	no	—
63	C₂²×C₅×Q₈	—	2	3	no	—
64	C₂²×C₅×Q₈	C₂³	1	3	yes	—
65	C₂²×C₅×D₄	—	2	3	no	—
66	C₂²×C₅×D₄	C₂³	1	3	yes	—
67	C₅×#131	—	2	8	no	—
68	C₂×C₅×M₁₆	C₂³	1	6	yes	—
69	C₂²×C₅×C₈	C₂³	1	6	yes	—
70	C₅×C₄⋊Q₈	—	2	6	no	—
71	C₅×C₄⋊Q₈	—	2	3	no	—
72	C₅×C₄⋊Q₈	—	2	3	no	—
73	C₅×C₄⋊Q₈	C₂³	1	3	yes	—
74	C₅×C₄⋊Q₈	C₂³	1	6	yes	—
75	C₅×C₄⋊Q₈	C₂³	1	3	yes	—
76	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₅×#127	C₂³	1	3	yes	—
78	C₅×#125	—	2	6	no	—
79	C₅×#125	C₂³	1	6	yes	—
80	C₅×#124	—	2	3	no	—
81	C₅×#124	—	2	3	no	—
82	C₅×#124	C₂³	1	6	yes	—
83	C₅×#124	C₂³	1	3	yes	—
84	C₅×#124	C₂³	1	1	yes	characteristic
85	C₅×#123	—	2	6	no	—
86	C₅×C₂²⋊Q₈	—	2	3	no	—
87	C₅×C₂²⋊Q₈	—	2	3	no	—
88	C₅×C₂²⋊Q₈	—	2	3	no	—
89	C₅×C₂²⋊Q₈	—	2	3	no	—
90	C₅×C₂²⋊Q₈	—	2	12	no	—
91	C₅×#121	—	2	3	no	—
92	C₅×#121	—	2	3	no	—
93	C₅×#121	—	2	3	no	—
94	C₅×#121	—	2	3	no	—
95	C₅×#120	—	2	6	no	—
96	C₄×C₅×Q₈	—	2	2	no	—
97	C₄×C₅×Q₈	—	2	3	no	—
98	C₄×C₅×Q₈	—	2	3	no	—
99	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
100	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
101	C₄×C₅×D₄	—	2	6	no	—
102	C₄×C₅×D₄	—	2	3	no	—
103	C₄×C₅×D₄	—	2	3	no	—
104	C₄×C₅×D₄	D₄	1	3	yes	—
105	C₄×C₅×D₄	D₄	1	3	yes	—
106	C₅×#117	C₂³	1	6	yes	—
107	C₅×#117	C₂³	1	3	yes	—
108	C₂×C₅×C₄⋊C₄	—	2	3	no	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
110	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	3	no	—
112	C₂×C₄²×C₅	C₂³	1	3	yes	—
113	C₅×#103	C₂³	1	6	yes	—
114	C₅×#103	C₂³	1	12	yes	—
115	C₅×#103	C₂³	1	2	yes	—
116	C₅×#103	C₂³	1	6	yes	—
117	C₅×#103	C₂³	1	6	yes	—
118	C₅×#102	C₂³	1	6	yes	—
119	C₅×#102	C₂³	1	12	yes	—
120	C₅×#102	C₂³	1	6	yes	—
121	C₅×#102	C₂³	1	2	yes	—
122	C₅×#102	C₂³	1	6	yes	—
123	C₅×#97	C₂³	1	1	yes	characteristic
124	C₅×#97	C₂³	1	3	yes	—
125	C₅×#97	C₂³	1	6	yes	—
126	C₄×C₅×C₈	C₂³	1	6	yes	—
127	#3503	C₂×C₅	1	1	yes	characteristic, complemented
128	#3500	C₂×C₅	1	1	yes	characteristic
129	#3141	C₂×C₅	1	3	yes	complemented
130	#3140	C₂×C₅	1	3	yes	complemented
131	#3137	C₂×C₅	1	6	yes	complemented
132	#3136	C₂×C₅	1	6	yes	complemented
133	#3135	C₂×C₅	1	3	yes	complemented
134	C₂×#489	C₂×C₅	1	3	yes	complemented
135	#2898	C₂×C₅	1	2	yes	complemented
136	#2897	C₂×C₅	1	2	yes	complemented
137	#2875	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	—	2	3	no	—
139	C₅×#41	—	2	12	no	—
140	C₅×#41	—	2	12	no	—
141	C₅×#41	—	4	4	no	—
142	C₅×#41	—	4	12	no	—
143	C₅×#41	#41	1	8	yes	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	3	no	—
146	C₂×C₅×Q₈	—	2	3	no	—
147	C₂×C₅×Q₈	—	2	6	no	—
148	C₂×C₅×Q₈	—	2	12	no	—
149	C₂×C₅×Q₈	—	4	4	no	—
150	C₂×C₅×Q₈	—	8	6	no	—
151	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×Q₈	C₂⁴	1	3	yes	—
153	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
154	C₂×C₅×D₄	—	2	3	no	—
155	C₂×C₅×D₄	—	2	3	no	—
156	C₂×C₅×D₄	—	2	3	no	—
157	C₂×C₅×D₄	—	2	3	no	—
158	C₂×C₅×D₄	—	2	3	no	—
159	C₂×C₅×D₄	—	2	12	no	—
160	C₂×C₅×D₄	—	4	12	no	—
161	C₂×C₅×D₄	C₂×D₄	1	3	yes	—
162	C₂×C₅×D₄	C₂⁴	1	3	yes	—
163	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₅	—	2	3	no	—
165	C₂²×C₄×C₅	—	2	6	no	—
166	C₂²×C₄×C₅	—	2	3	no	—
167	C₂²×C₄×C₅	—	2	3	no	—
168	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
169	C₂²×C₄×C₅	C₂×D₄	1	3	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
171	C₅×M₁₆	—	2	12	no	—
172	C₂×C₅×C₈	—	2	12	no	—
173	C₂×C₅×C₈	C₂⁴	1	2	yes	—
174	C₂×C₅×C₈	C₂⁴	1	6	yes	—
175	C₅×C₄⋊C₄	—	2	3	no	—
176	C₅×C₄⋊C₄	—	2	6	no	—
177	C₅×C₄⋊C₄	—	2	6	no	—
178	C₅×C₄⋊C₄	—	2	3	no	—
179	C₅×C₄⋊C₄	—	2	3	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	6	no	—
182	C₅×C₄⋊C₄	—	2	6	no	—
183	C₅×C₄⋊C₄	C₂×D₄	1	3	yes	—
184	C₅×C₄⋊C₄	C₂×D₄	1	3	yes	—
185	C₅×C₄⋊C₄	C₂⁴	1	6	yes	—
186	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
187	C₅×C₂²⋊C₄	—	2	6	no	—
188	C₅×C₂²⋊C₄	—	2	3	no	—
189	C₅×C₂²⋊C₄	—	2	3	no	—
190	C₅×C₂²⋊C₄	—	2	6	no	—
191	C₅×C₂²⋊C₄	—	2	6	no	—
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₅×C₂²⋊C₄	C₂×D₄	1	6	yes	—
195	C₄²×C₅	—	2	6	no	—
196	C₄²×C₅	C₂×D₄	1	3	yes	—
197	C₄²×C₅	C₂×D₄	1	3	yes	—
198	C₄²×C₅	C₂⁴	1	1	yes	characteristic
199	C₄²×C₅	C₂⁴	1	3	yes	—
200	C₂×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic
201	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
202	C₂×#131	C₂²×C₅	1	2	yes	—
203	Q₈²	—	2	1	no	—
204	#557	—	2	1	no	—
205	#554	—	2	3	no	—
206	D₄×Q₈	—	2	3	no	—
207	#548	—	2	1	no	—
208	#548	—	2	1	no	—
209	#546	—	2	3	no	—
210	#546	—	2	3	no	—
211	#544	C₂²×C₅	1	6	yes	complemented
212	#536	C₂²×C₅	1	3	yes	—
213	#535	C₂²×C₅	1	3	yes	—
214	#533	C₂²×C₅	1	3	yes	complemented
215	#532	C₂²×C₅	1	3	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₅	1	3	yes	complemented
217	C₂×#124	C₂²×C₅	1	3	yes	—
218	#520	C₂²×C₅	1	2	yes	—
219	C₄×#41	C₂²×C₅	1	1	yes	characteristic
220	#491	C₂²×C₅	1	6	yes	complemented
221	#490	C₂²×C₅	1	6	yes	complemented
222	#489	C₂²×C₅	1	3	yes	complemented
223	#489	C₂²×C₅	1	12	yes	complemented
224	#489	C₂²×C₅	1	6	yes	complemented
225	#489	C₂²×C₅	1	1	yes	characteristic, complemented
226	#489	C₂²×C₅	1	3	yes	complemented
227	#489	C₂²×C₅	1	3	yes	complemented
228	#488	C₂²×C₅	1	12	yes	complemented
229	#487	C₂²×C₅	1	6	yes	complemented
230	#486	C₂²×C₅	1	6	yes	complemented
231	#419	C₂²×C₅	1	6	yes	complemented
232	#418	C₂²×C₅	1	6	yes	—
233	#417	C₂²×C₅	1	6	yes	—
234	#417	C₂²×C₅	1	6	yes	complemented
235	#416	C₂²×C₅	1	6	yes	—
236	#416	C₂²×C₅	1	6	yes	complemented
237	C₂×#103	C₂²×C₅	1	6	yes	complemented
238	C₂×#102	C₂²×C₅	1	6	yes	—
239	#405	C₂²×C₅	1	6	yes	complemented
240	C₄×M₁₆	C₂²×C₅	1	3	yes	complemented
241	C₂×#97	C₂²×C₅	1	3	yes	complemented
242	C₂³×C₅	—	2	3	no	—
243	C₂³×C₅	—	2	1	no	—
244	C₂³×C₅	—	4	6	no	—
245	C₂³×C₅	—	8	3	no	—
246	C₂³×C₅	—	8	3	no	—
247	C₂³×C₅	C₂²×D₄	1	3	yes	—
248	C₅×Q₈	—	2	6	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₅×Q₈	—	4	6	no	—
252	C₅×Q₈	—	4	6	no	—
253	C₅×Q₈	—	8	6	no	—
254	C₅×Q₈	#124	1	4	yes	—
255	C₅×D₄	—	2	6	no	—
256	C₅×D₄	—	2	2	no	—
257	C₅×D₄	—	4	6	no	—
258	C₅×D₄	—	4	6	no	—
259	C₅×D₄	—	4	6	no	—
260	C₅×D₄	—	8	3	no	—
261	C₅×D₄	—	8	3	no	—
262	C₅×D₄	#124	1	12	yes	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	6	no	—
265	C₂×C₄×C₅	—	2	3	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	4	3	no	—
268	C₂×C₄×C₅	—	4	3	no	—
269	C₂×C₄×C₅	—	4	6	no	—
270	C₂×C₄×C₅	—	4	6	no	—
271	C₂×C₄×C₅	—	4	6	no	—
272	C₂×C₄×C₅	—	8	6	no	—
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
276	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
277	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
278	C₂×C₄×C₅	C₂×#41	1	12	yes	—
279	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	2	6	no	—
282	2₋¹⁺⁴	—	2	8	no	—
283	H(5,𝔽₂)	—	2	8	no	—
284	C₂×#41	—	2	1	no	—
285	C₂×#41	—	2	3	no	—
286	C₂×#41	C₂³×C₅	1	3	yes	—
287	C₂×#41	C₂³×C₅	1	3	yes	—
288	C₂×#41	C₂³×C₅	1	1	yes	characteristic
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	—	2	3	no	—
291	C₂²×Q₈	C₂³×C₅	1	3	yes	—
292	C₂²×D₄	—	2	3	no	—
293	C₂²×D₄	C₂³×C₅	1	3	yes	—
294	#131	—	2	8	no	—
295	C₂×M₁₆	C₂³×C₅	1	6	yes	—
296	C₂²×C₈	C₂³×C₅	1	6	yes	—
297	C₄⋊Q₈	—	2	6	no	—
298	C₄⋊Q₈	—	2	3	no	—
299	C₄⋊Q₈	—	2	3	no	—
300	C₄⋊Q₈	C₂³×C₅	1	3	yes	—
301	C₄⋊Q₈	C₂³×C₅	1	3	yes	—
302	C₄⋊Q₈	C₂³×C₅	1	6	yes	—
303	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
304	#127	C₂³×C₅	1	3	yes	—
305	#125	—	2	6	no	—
306	#125	C₂³×C₅	1	6	yes	—
307	#124	—	2	3	no	—
308	#124	—	2	3	no	—
309	#124	C₂³×C₅	1	3	yes	—
310	#124	C₂³×C₅	1	6	yes	—
311	#124	C₂³×C₅	1	1	yes	characteristic
312	#123	—	2	6	no	—
313	C₂²⋊Q₈	—	2	3	no	—
314	C₂²⋊Q₈	—	2	3	no	—
315	C₂²⋊Q₈	—	2	3	no	—
316	C₂²⋊Q₈	—	2	3	no	—
317	C₂²⋊Q₈	—	2	12	no	—
318	#121	—	2	3	no	—
319	#121	—	2	3	no	—
320	#121	—	2	3	no	—
321	#121	—	2	3	no	—
322	#120	—	2	6	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	3	no	—
325	C₄×Q₈	—	2	3	no	—
326	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
327	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
328	C₄×D₄	—	2	6	no	—
329	C₄×D₄	—	2	3	no	—
330	C₄×D₄	—	2	3	no	—
331	C₄×D₄	C₅×D₄	1	3	yes	—
332	C₄×D₄	C₅×D₄	1	3	yes	—
333	#117	C₂³×C₅	1	6	yes	—
334	#117	C₂³×C₅	1	3	yes	—
335	C₂×C₄⋊C₄	—	2	3	no	—
336	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
337	C₂×C₂²⋊C₄	—	2	3	no	—
338	C₂×C₂²⋊C₄	—	2	3	no	—
339	C₂×C₄²	C₂³×C₅	1	3	yes	—
340	#103	C₂³×C₅	1	6	yes	—
341	#103	C₂³×C₅	1	12	yes	—
342	#103	C₂³×C₅	1	2	yes	—
343	#103	C₂³×C₅	1	6	yes	—
344	#103	C₂³×C₅	1	6	yes	—
345	#102	C₂³×C₅	1	6	yes	—
346	#102	C₂³×C₅	1	12	yes	—
347	#102	C₂³×C₅	1	6	yes	—
348	#102	C₂³×C₅	1	2	yes	—
349	#102	C₂³×C₅	1	6	yes	—
350	#97	C₂³×C₅	1	1	yes	characteristic
351	#97	C₂³×C₅	1	3	yes	—
352	#97	C₂³×C₅	1	6	yes	—
353	C₄×C₈	C₂³×C₅	1	6	yes	—
354	C₂²×C₅	—	2	3	no	—
355	C₂²×C₅	—	2	3	no	—
356	C₂²×C₅	—	4	1	no	—
357	C₂²×C₅	—	4	3	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	3	no	—
360	C₂²×C₅	—	4	1	no	—
361	C₂²×C₅	—	4	3	no	—
362	C₂²×C₅	—	16	6	no	—
363	C₂²×C₅	C₂×#124	1	6	yes	—
364	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	3	no	—
367	C₄×C₅	—	2	1	no	—
368	C₄×C₅	—	2	3	no	—
369	C₄×C₅	—	4	6	no	—
370	C₄×C₅	—	4	2	no	—
371	C₄×C₅	—	4	1	no	—
372	C₄×C₅	—	4	3	no	—
373	C₄×C₅	C₂×#124	1	6	yes	—
374	C₄×C₅	C₂²×#41	1	2	yes	—
375	C₂⁴	—	2	3	no	—
376	#41	—	2	12	no	—
377	#41	—	2	12	no	—
378	#41	—	4	4	no	—
379	#41	—	4	12	no	—
380	#41	C₅×#41	1	8	yes	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	3	no	—
383	C₂×Q₈	—	2	3	no	—
384	C₂×Q₈	—	2	6	no	—
385	C₂×Q₈	—	2	12	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	—	8	6	no	—
388	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×Q₈	C₂⁴×C₅	1	3	yes	—
390	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
391	C₂×D₄	—	2	3	no	—
392	C₂×D₄	—	2	3	no	—
393	C₂×D₄	—	2	3	no	—
394	C₂×D₄	—	2	3	no	—
395	C₂×D₄	—	2	3	no	—
396	C₂×D₄	—	2	12	no	—
397	C₂×D₄	—	4	12	no	—
398	C₂×D₄	C₂×C₅×D₄	1	3	yes	—
399	C₂×D₄	C₂⁴×C₅	1	3	yes	—
400	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
401	C₂²×C₄	—	2	3	no	—
402	C₂²×C₄	—	2	6	no	—
403	C₂²×C₄	—	2	3	no	—
404	C₂²×C₄	—	2	3	no	—
405	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
406	C₂²×C₄	C₂×C₅×D₄	1	3	yes	—
407	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
408	M₁₆	—	2	12	no	—
409	C₂×C₈	—	2	12	no	—
410	C₂×C₈	C₂⁴×C₅	1	6	yes	—
411	C₂×C₈	C₂⁴×C₅	1	2	yes	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	6	no	—
414	C₄⋊C₄	—	2	6	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	6	no	—
419	C₄⋊C₄	—	2	6	no	—
420	C₄⋊C₄	C₂×C₅×D₄	1	3	yes	—
421	C₄⋊C₄	C₂×C₅×D₄	1	3	yes	—
422	C₄⋊C₄	C₂⁴×C₅	1	6	yes	—
423	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
424	C₂²⋊C₄	—	2	6	no	—
425	C₂²⋊C₄	—	2	3	no	—
426	C₂²⋊C₄	—	2	3	no	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	C₂×C₅×D₄	1	6	yes	—
432	C₄²	—	2	6	no	—
433	C₄²	C₂×C₅×D₄	1	3	yes	—
434	C₄²	C₂×C₅×D₄	1	3	yes	—
435	C₄²	C₂⁴×C₅	1	3	yes	—
436	C₄²	C₂⁴×C₅	1	1	yes	characteristic
437	C₂×C₅	—	2	6	no	—
438	C₂×C₅	—	8	1	no	—
439	C₂×C₅	—	8	3	no	—
440	C₂×C₅	C₂²×#124	1	1	yes	characteristic
441	C₂×C₅	#3585	1	1	yes	characteristic
442	C₂×C₅	#3586	1	1	yes	characteristic
443	C₂³	—	2	3	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	4	6	no	—
446	C₂³	—	8	3	no	—
447	C₂³	—	8	3	no	—
448	C₂³	C₂²×C₅×D₄	1	3	yes	—
449	Q₈	—	2	6	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	4	6	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	6	no	—
454	Q₈	—	8	6	no	—
455	Q₈	C₅×#124	1	4	yes	—
456	D₄	—	2	6	no	—
457	D₄	—	2	2	no	—
458	D₄	—	4	6	no	—
459	D₄	—	4	6	no	—
460	D₄	—	4	6	no	—
461	D₄	—	8	3	no	—
462	D₄	—	8	3	no	—
463	D₄	C₅×#124	1	12	yes	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	6	no	—
466	C₂×C₄	—	2	3	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	4	3	no	—
469	C₂×C₄	—	4	3	no	—
470	C₂×C₄	—	4	6	no	—
471	C₂×C₄	—	4	6	no	—
472	C₂×C₄	—	4	6	no	—
473	C₂×C₄	—	8	6	no	—
474	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
477	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
478	C₂×C₄	C₂²×C₅×D₄	1	3	yes	—
479	C₂×C₄	C₂×C₅×#41	1	12	yes	—
480	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	2	6	no	—
483	C₅	#60625	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²	—	2	3	no	—
485	C₂²	—	2	3	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	3	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	3	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	3	no	—
492	C₂²	—	16	6	no	—
493	C₂²	C₂×C₅×#124	1	6	yes	—
494	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	3	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	3	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	3	no	—
501	C₄	—	4	6	no	—
502	C₄	—	4	2	no	—
503	C₄	C₂×C₅×#124	1	6	yes	—
504	C₄	C₂²×C₅×#41	1	2	yes	—
505	C₂	—	2	6	no	—
506	C₂	—	8	3	no	—
507	C₂	—	8	1	no	—
508	C₂	C₂²×C₅×#124	1	1	yes	characteristic
509	C₂	C₅×#3585	1	1	yes	characteristic
510	C₂	C₅×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₅×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3503	C₂	semidirect
3. C₅×#3141	C₂	semidirect
4. C₅×#3140	C₂	semidirect
5. C₅×#3137	C₂	semidirect
6. C₅×#3136	C₂	semidirect
7. C₅×#3135	C₂	semidirect
8. C₂×C₅×#489	C₂	semidirect
9. C₅×#2898	C₂	semidirect
10. C₅×#2897	C₂	semidirect
11. C₅×#2875	C₂	semidirect
23. C₅×#544	C₂²	semidirect
26. C₅×#533	C₂²	semidirect
28. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₅×#491	C₂²	semidirect
33. C₅×#490	C₂²	semidirect
34. C₅×#489	C₂²	semidirect
35. C₅×#489	C₂²	semidirect
36. C₅×#489	C₂²	semidirect
37. C₅×#489	C₂²	semidirect
38. C₅×#489	C₂²	semidirect
39. C₅×#489	C₂²	semidirect
40. C₅×#488	C₂²	semidirect
41. C₅×#487	C₂²	semidirect
42. C₅×#486	C₂²	semidirect
43. C₅×#419	C₂²	semidirect
46. C₅×#417	C₂²	semidirect
48. C₅×#416	C₂²	semidirect
49. C₂×C₅×#103	C₂²	semidirect
51. C₅×#405	C₂²	semidirect
52. C₄×C₅×M₁₆	C₂²	semidirect
53. C₂×C₅×#97	C₂²	semidirect
54. #60625	C₅	direct (N × H)
127. #3503	C₂×C₅	semidirect
129. #3141	C₂×C₅	semidirect
130. #3140	C₂×C₅	semidirect
131. #3137	C₂×C₅	semidirect
132. #3136	C₂×C₅	semidirect
133. #3135	C₂×C₅	semidirect
134. C₂×#489	C₂×C₅	semidirect
135. #2898	C₂×C₅	semidirect
136. #2897	C₂×C₅	semidirect
137. #2875	C₂×C₅	semidirect
211. #544	C₂²×C₅	semidirect
214. #533	C₂²×C₅	semidirect
216. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
220. #491	C₂²×C₅	semidirect
221. #490	C₂²×C₅	semidirect
222. #489	C₂²×C₅	semidirect
223. #489	C₂²×C₅	semidirect
224. #489	C₂²×C₅	semidirect
225. #489	C₂²×C₅	semidirect
226. #489	C₂²×C₅	semidirect
227. #489	C₂²×C₅	semidirect
228. #488	C₂²×C₅	semidirect
229. #487	C₂²×C₅	semidirect
230. #486	C₂²×C₅	semidirect
231. #419	C₂²×C₅	semidirect
234. #417	C₂²×C₅	semidirect
236. #416	C₂²×C₅	semidirect
237. C₂×#103	C₂²×C₅	semidirect
239. #405	C₂²×C₅	semidirect
240. C₄×M₁₆	C₂²×C₅	semidirect
241. C₂×#97	C₂²×C₅	semidirect
483. C₅	#60625	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×#3503	2
C₅×#3500	2
C₅×#3141	2
C₅×#3140	2
C₅×#3137	2
C₅×#3136	2
C₅×#3135	2
C₂×C₅×#489	2
C₅×#2898	2
C₅×#2897	2
C₅×#2875	2
#60625	5

Subgroups — C5×#60625 #11983345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60625 #11983345