Subgroups — C₅×#17762 #11940482

Order 1280.

1028 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3508	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1560	C₂	1	2	yes	maximal, complemented
5	C₅×#1557	C₂	1	2	yes	maximal, complemented
6	C₅×#1551	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1547	C₂	1	2	yes	maximal, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#559	—	2	1	no	—
14	C₅×#559	C₄	1	2	yes	—
15	C₅×#550	—	2	1	no	—
16	C₅×#550	C₄	1	2	yes	—
17	C₅×#546	—	2	2	no	—
18	C₅×#546	C₄	1	4	yes	—
19	C₅×#540	—	2	2	no	—
20	C₅×#535	—	2	1	no	—
21	C₅×#533	C₂²	1	1	yes	characteristic
22	C₅×#532	C₂²	1	2	yes	—
23	C₅×#532	C₂²	1	2	yes	—
24	C₂×C₅×#127	C₂²	1	1	yes	characteristic
25	C₅×#518	—	2	1	no	—
26	C₄×C₅×#41	C₂²	1	1	yes	characteristic
27	C₅×#446	—	2	1	no	—
28	C₅×#436	—	2	1	no	—
29	C₅×#435	—	2	2	no	—
30	C₅×#432	C₂²	1	2	yes	complemented
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#424	—	2	1	no	—
33	C₅×#424	—	2	2	no	—
34	C₅×#423	C₂²	1	1	yes	characteristic
35	C₅×#423	C₂²	1	2	yes	complemented
36	C₅×#423	C₂²	1	2	yes	complemented
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₅×#333	C₂²	1	1	yes	characteristic, complemented
41	C₅×#333	C₂²	1	1	yes	characteristic, complemented
42	C₅×#333	C₂²	1	2	yes	complemented
43	C₅×#332	C₂²	1	1	yes	characteristic, complemented
44	C₅×#332	C₂²	1	1	yes	characteristic, complemented
45	C₅×#332	C₂²	1	2	yes	complemented
46	C₅×#331	C₂²	1	2	yes	—
47	C₅×#331	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	C₅×#331	C₂²	1	2	yes	—
50	#17762	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	—	2	2	no	—
52	C₂×C₅×#41	C₂×C₄	1	4	yes	—
53	C₂×C₅×#41	D₄	1	1	yes	characteristic
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	2	1	no	—
56	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
57	C₅×#131	—	4	4	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂×C₅×M₁₆	—	2	2	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₅×#127	—	2	2	no	—
67	C₅×#127	—	2	1	no	—
68	C₅×#127	—	2	1	no	—
69	C₅×#127	C₂×C₄	1	2	yes	—
70	C₅×#127	C₂³	1	2	yes	—
71	C₅×#125	—	2	1	no	—
72	C₅×#124	—	2	2	no	—
73	C₅×#124	—	2	2	no	—
74	C₅×#124	C₂×C₄	1	4	yes	—
75	C₅×#123	—	2	4	no	—
76	C₅×#123	—	2	4	no	—
77	C₅×C₂²⋊Q₈	—	2	1	no	—
78	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
79	C₅×#121	—	2	2	no	—
80	C₅×#121	—	2	2	no	—
81	C₅×#121	—	2	2	no	—
82	C₅×#121	—	2	4	no	—
83	C₅×#121	—	2	4	no	—
84	C₅×#121	C₂×C₄	1	4	yes	—
85	C₅×#120	—	2	4	no	—
86	C₄×C₅×Q₈	—	2	1	no	—
87	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
88	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	2	2	no	—
95	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
96	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
97	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×D₄	D₄	1	2	yes	—
99	C₄×C₅×D₄	D₄	1	1	yes	characteristic
100	C₅×#117	—	2	1	no	—
101	C₅×#117	D₄	1	1	yes	characteristic
102	C₅×#117	D₄	1	2	yes	—
103	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	2	yes	—
106	C₅×C₄⋊C₈	—	2	1	no	—
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	—	2	1	no	—
110	C₅×C₄⋊C₈	—	2	2	no	—
111	C₅×C₄⋊C₈	—	2	2	no	—
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂³	1	2	yes	—
115	C₅×C₄⋊C₈	C₂³	1	2	yes	—
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₂²⋊C₈	—	2	1	no	—
119	C₅×C₂²⋊C₈	—	2	2	no	—
120	C₅×#97	—	2	2	no	—
121	C₄×C₅×C₈	—	2	1	no	—
122	#3508	C₂×C₅	1	1	yes	characteristic
123	#2989	C₂×C₅	1	1	yes	characteristic, complemented
124	#2906	C₂×C₅	1	1	yes	characteristic, complemented
125	#1560	C₂×C₅	1	2	yes	complemented
126	#1557	C₂×C₅	1	2	yes	complemented
127	#1551	C₂×C₅	1	2	yes	complemented
128	#1550	C₂×C₅	1	1	yes	characteristic, complemented
129	#1547	C₂×C₅	1	2	yes	complemented
130	#1545	C₂×C₅	1	1	yes	characteristic, complemented
131	#1542	C₂×C₅	1	1	yes	characteristic, complemented
132	C₂×#331	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂⁴×C₅	—	2	2	no	—
134	C₅×#41	—	2	2	no	—
135	C₅×#41	—	2	2	no	—
136	C₅×#41	—	8	2	no	—
137	C₅×#41	—	8	2	no	—
138	C₅×#41	—	8	4	no	—
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅×D₄	—	2	4	no	—
143	C₂×C₅×D₄	—	2	4	no	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	4	2	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	—	8	1	no	—
152	C₂×C₅×D₄	—	8	1	no	—
153	C₂×C₅×D₄	—	8	2	no	—
154	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
155	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	2	4	no	—
159	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₅×M₁₆	—	4	4	no	—
166	C₅×M₁₆	—	4	2	no	—
167	C₅×M₁₆	—	8	2	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	2	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	4	4	no	—
175	C₂×C₅×C₈	—	4	2	no	—
176	C₂×C₅×C₈	—	8	1	no	—
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	—	2	2	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	C₂²⋊C₄	1	1	yes	characteristic
183	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
184	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
185	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
186	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
187	C₅×C₂²⋊C₄	—	2	2	no	—
188	C₅×C₂²⋊C₄	—	2	4	no	—
189	C₅×C₂²⋊C₄	—	2	4	no	—
190	C₅×C₂²⋊C₄	—	2	4	no	—
191	C₅×C₂²⋊C₄	—	2	4	no	—
192	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
193	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
194	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
195	C₄²×C₅	—	2	2	no	—
196	C₄²×C₅	C₂²×C₄	1	2	yes	—
197	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₅	C₂×D₄	1	2	yes	—
199	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₅	C₂×D₄	1	2	yes	—
201	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₅	C₂⁴	1	1	yes	characteristic
203	C₂×#131	—	2	1	no	—
204	#559	—	2	1	no	—
205	#559	C₄×C₅	1	2	yes	—
206	#550	—	2	1	no	—
207	#550	C₄×C₅	1	2	yes	—
208	#546	—	2	2	no	—
209	#546	C₄×C₅	1	4	yes	—
210	#540	—	2	2	no	—
211	#535	—	2	1	no	—
212	#533	C₂²×C₅	1	1	yes	characteristic
213	#532	C₂²×C₅	1	2	yes	—
214	#532	C₂²×C₅	1	2	yes	—
215	C₂×#127	C₂²×C₅	1	1	yes	characteristic
216	#518	—	2	1	no	—
217	C₄×#41	C₂²×C₅	1	1	yes	characteristic
218	#446	—	2	1	no	—
219	#436	—	2	1	no	—
220	#435	—	2	2	no	—
221	#432	C₂²×C₅	1	2	yes	complemented
222	#431	C₂²×C₅	1	1	yes	characteristic
223	#424	—	2	2	no	—
224	#424	—	2	1	no	—
225	#423	C₂²×C₅	1	1	yes	characteristic
226	#423	C₂²×C₅	1	2	yes	complemented
227	#423	C₂²×C₅	1	2	yes	complemented
228	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
231	#333	C₂²×C₅	1	1	yes	characteristic, complemented
232	#333	C₂²×C₅	1	1	yes	characteristic, complemented
233	#333	C₂²×C₅	1	2	yes	complemented
234	#332	C₂²×C₅	1	1	yes	characteristic, complemented
235	#332	C₂²×C₅	1	1	yes	characteristic, complemented
236	#332	C₂²×C₅	1	2	yes	complemented
237	#331	C₂²×C₅	1	2	yes	—
238	#331	C₂²×C₅	1	2	yes	—
239	#331	C₂²×C₅	1	2	yes	—
240	#331	C₂²×C₅	1	2	yes	—
241	C₂³×C₅	—	2	4	no	—
242	C₂³×C₅	—	4	4	no	—
243	C₂³×C₅	—	8	2	no	—
244	C₂³×C₅	—	8	2	no	—
245	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₅×Q₈	—	2	2	no	—
248	C₅×Q₈	—	4	2	no	—
249	C₅×Q₈	—	4	1	no	—
250	C₅×Q₈	—	4	1	no	—
251	C₅×D₄	—	2	4	no	—
252	C₅×D₄	—	2	2	no	—
253	C₅×D₄	—	4	4	no	—
254	C₅×D₄	—	4	2	no	—
255	C₅×D₄	—	4	2	no	—
256	C₅×D₄	—	4	2	no	—
257	C₅×D₄	—	4	2	no	—
258	C₅×D₄	—	4	4	no	—
259	C₅×D₄	—	8	2	no	—
260	C₅×D₄	—	8	2	no	—
261	C₅×D₄	—	8	4	no	—
262	C₅×D₄	—	8	4	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	4	1	no	—
272	C₂×C₄×C₅	—	4	2	no	—
273	C₂×C₄×C₅	—	8	4	no	—
274	C₂×C₄×C₅	—	8	4	no	—
275	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
282	C₂×C₄×C₅	#137	1	2	yes	—
283	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₅×C₈	—	4	1	no	—
287	C₅×C₈	—	4	2	no	—
288	C₅×C₈	—	4	1	no	—
289	C₅×C₈	—	4	2	no	—
290	C₅×C₈	—	4	1	no	—
291	C₅×C₈	—	4	1	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	C₂×C₄×C₅	1	4	yes	—
294	C₂×#41	C₅×D₄	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
298	#131	—	4	4	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
306	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
307	#127	—	2	2	no	—
308	#127	—	2	1	no	—
309	#127	—	2	1	no	—
310	#127	C₂×C₄×C₅	1	2	yes	—
311	#127	C₂³×C₅	1	2	yes	—
312	#125	—	2	1	no	—
313	#124	—	2	2	no	—
314	#124	—	2	2	no	—
315	#124	C₂×C₄×C₅	1	4	yes	—
316	#123	—	2	4	no	—
317	#123	—	2	4	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
320	#121	—	2	2	no	—
321	#121	—	2	2	no	—
322	#121	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	—	2	4	no	—
325	#121	C₂×C₄×C₅	1	4	yes	—
326	#120	—	2	4	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
329	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
330	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
337	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
338	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₄×D₄	C₅×D₄	1	2	yes	—
340	C₄×D₄	C₅×D₄	1	1	yes	characteristic
341	#117	—	2	1	no	—
342	#117	C₅×D₄	1	1	yes	characteristic
343	#117	C₅×D₄	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₅	1	2	yes	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	—	2	1	no	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	2	no	—
353	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
354	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
355	C₄⋊C₈	C₂³×C₅	1	2	yes	—
356	C₄⋊C₈	C₂³×C₅	1	2	yes	—
357	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
358	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	#97	—	2	2	no	—
362	C₄×C₈	—	2	1	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	4	4	no	—
369	C₂²×C₅	—	4	4	no	—
370	C₂²×C₅	—	4	4	no	—
371	C₂²×C₅	—	16	4	no	—
372	C₂²×C₅	#417	1	2	yes	—
373	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
374	C₄×C₅	—	2	1	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	1	no	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	#417	1	2	yes	—
383	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₄×C₅	C₂×#137	1	1	yes	characteristic
385	C₄×C₅	#576	1	1	yes	characteristic
386	C₄×C₅	#577	1	1	yes	characteristic
387	C₂⁴	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	8	2	no	—
391	#41	—	8	2	no	—
392	#41	—	8	4	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	8	1	no	—
406	C₂×D₄	—	8	1	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
409	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
414	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
416	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
418	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	M₁₆	—	4	4	no	—
420	M₁₆	—	4	2	no	—
421	M₁₆	—	8	2	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	—	4	2	no	—
430	C₂×C₈	—	8	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
437	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
438	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
439	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
440	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
447	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
448	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂²×C₄×C₅	1	2	yes	—
451	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
452	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
453	C₄²	C₂×C₅×D₄	1	2	yes	—
454	C₄²	C₂×C₅×D₄	1	2	yes	—
455	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
456	C₄²	C₂⁴×C₅	1	1	yes	characteristic
457	C₂×C₅	—	2	2	no	—
458	C₂×C₅	—	4	2	no	—
459	C₂×C₅	—	8	4	no	—
460	C₂×C₅	#2888	1	1	yes	characteristic
461	C₂×C₅	C₂×#417	1	1	yes	characteristic
462	C₂×C₅	#2897	1	1	yes	characteristic
463	C₂³	—	2	4	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	8	2	no	—
466	C₂³	—	8	2	no	—
467	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
468	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
469	Q₈	—	2	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	4	1	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	4	no	—
484	D₄	—	8	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	4	no	—
496	C₂×C₄	—	8	4	no	—
497	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
498	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
499	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
500	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
501	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
502	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
504	C₂×C₄	C₅×#137	1	2	yes	—
505	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
508	C₈	—	4	1	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	1	no	—
511	C₈	—	4	2	no	—
512	C₈	—	4	1	no	—
513	C₈	—	4	1	no	—
514	C₅	#17762	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	16	4	no	—
524	C₂²	C₅×#417	1	2	yes	—
525	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	C₅×#417	1	2	yes	—
535	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
536	C₄	C₂×C₅×#137	1	1	yes	characteristic
537	C₄	C₅×#576	1	1	yes	characteristic
538	C₄	C₅×#577	1	1	yes	characteristic
539	C₂	—	2	2	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	4	no	—
542	C₂	C₅×#2888	1	1	yes	characteristic
543	C₂	C₂×C₅×#417	1	1	yes	characteristic
544	C₂	C₅×#2897	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₅×#2989	C₂	semidirect
3. C₅×#2906	C₂	semidirect
4. C₅×#1560	C₂	semidirect
5. C₅×#1557	C₂	semidirect
6. C₅×#1551	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1547	C₂	semidirect
9. C₅×#1545	C₂	semidirect
10. C₅×#1542	C₂	semidirect
11. C₂×C₅×#331	C₂	semidirect
30. C₅×#432	C₂²	semidirect
35. C₅×#423	C₂²	semidirect
36. C₅×#423	C₂²	semidirect
39. C₂×C₅×C₄⋊C₈	C₂²	semidirect
40. C₅×#333	C₂²	semidirect
41. C₅×#333	C₂²	semidirect
42. C₅×#333	C₂²	semidirect
43. C₅×#332	C₂²	semidirect
44. C₅×#332	C₂²	semidirect
45. C₅×#332	C₂²	semidirect
50. #17762	C₅	direct (N × H)
123. #2989	C₂×C₅	semidirect
124. #2906	C₂×C₅	semidirect
125. #1560	C₂×C₅	semidirect
126. #1557	C₂×C₅	semidirect
127. #1551	C₂×C₅	semidirect
128. #1550	C₂×C₅	semidirect
129. #1547	C₂×C₅	semidirect
130. #1545	C₂×C₅	semidirect
131. #1542	C₂×C₅	semidirect
132. C₂×#331	C₂×C₅	semidirect
221. #432	C₂²×C₅	semidirect
226. #423	C₂²×C₅	semidirect
227. #423	C₂²×C₅	semidirect
230. C₂×C₄⋊C₈	C₂²×C₅	semidirect
231. #333	C₂²×C₅	semidirect
232. #333	C₂²×C₅	semidirect
233. #333	C₂²×C₅	semidirect
234. #332	C₂²×C₅	semidirect
235. #332	C₂²×C₅	semidirect
236. #332	C₂²×C₅	semidirect
514. C₅	#17762	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×#3508	2
C₅×#2989	2
C₅×#2906	2
C₅×#1560	2
C₅×#1557	2
C₅×#1551	2
C₅×#1550	2
C₅×#1547	2
C₅×#1545	2
C₅×#1542	2
C₂×C₅×#331	2
#17762	5

Subgroups — C5×#17762 #11940482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17762 #11940482