Subgroups — C₅×#19619 #11942339

Order 1280.

820 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3167	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#3131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1721	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1720	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1719	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1717	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1717	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1715	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1714	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	—	2	2	no	—
17	C₅×#533	C₂²	1	1	yes	characteristic
18	C₅×#532	C₂²	1	1	yes	characteristic
19	C₅×#532	C₂²	1	1	yes	characteristic
20	C₅×#532	C₂²	1	1	yes	characteristic
21	C₅×#500	C₂²	1	1	yes	characteristic
22	C₅×#500	C₂²	1	1	yes	characteristic
23	C₅×#498	C₂²	1	1	yes	characteristic
24	C₅×#498	C₂²	1	1	yes	characteristic
25	C₅×#495	—	2	2	no	—
26	C₅×#494	C₂²	1	1	yes	characteristic
27	C₅×#493	C₂²	1	1	yes	characteristic
28	C₅×#493	C₂²	1	1	yes	characteristic
29	C₅×#493	C₂²	1	1	yes	characteristic
30	C₅×#492	C₂²	1	1	yes	characteristic
31	C₅×#492	C₂²	1	1	yes	characteristic
32	C₅×#492	C₂²	1	1	yes	characteristic
33	C₅×#492	C₂²	1	1	yes	characteristic
34	C₅×#488	—	2	2	no	—
35	C₅×#487	C₂²	1	1	yes	characteristic
36	C₅×#487	C₂²	1	1	yes	characteristic
37	C₅×#487	C₂²	1	1	yes	characteristic
38	C₅×#487	C₂²	1	1	yes	characteristic
39	C₅×#486	C₂²	1	1	yes	characteristic
40	C₅×#486	C₂²	1	1	yes	characteristic
41	C₅×#486	C₂²	1	1	yes	characteristic
42	C₅×#486	C₂²	1	1	yes	characteristic
43	C₅×#486	C₂²	1	1	yes	characteristic
44	C₅×#486	C₂²	1	1	yes	characteristic
45	C₅×#486	C₂²	1	1	yes	characteristic
46	C₅×#486	C₂²	1	1	yes	characteristic
47	C₅×#466	—	2	2	no	—
48	C₅×#466	—	2	2	no	—
49	C₅×#465	—	2	2	no	—
50	C₅×#465	—	2	2	no	—
51	C₄×C₅×SD₁₆	—	2	2	no	—
52	C₄×C₅×SD₁₆	—	2	2	no	—
53	C₄×C₅×D₈	—	2	2	no	—
54	C₄×C₅×D₈	—	2	2	no	—
55	C₅×#416	—	2	2	no	—
56	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
59	C₅×#322	C₂²	1	1	yes	characteristic
60	C₅×#322	C₂²	1	1	yes	characteristic
61	C₅×#322	C₂²	1	1	yes	characteristic
62	C₅×#322	C₂²	1	1	yes	characteristic
63	#19619	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₅×#41	—	2	1	no	—
65	C₂×C₅×#41	—	2	1	no	—
66	C₂×C₅×#41	—	2	1	no	—
67	C₅×#135	—	4	8	no	—
68	C₂×C₅×Q₁₆	—	2	2	no	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×D₈	—	2	2	no	—
74	C₂×C₅×D₈	—	2	2	no	—
75	C₂×C₅×D₈	—	2	2	no	—
76	C₂²×C₅×C₈	D₄	1	2	yes	—
77	C₂²×C₅×C₈	D₄	1	2	yes	—
78	C₂²×C₅×C₈	D₄	1	2	yes	—
79	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×#127	C₂³	1	1	yes	characteristic
85	C₅×#127	C₂³	1	1	yes	characteristic
86	C₅×#127	C₂³	1	1	yes	characteristic
87	C₅×#125	—	2	1	no	—
88	C₅×#124	—	2	1	no	—
89	C₅×#124	—	2	1	no	—
90	C₅×#124	—	2	1	no	—
91	C₅×C₂²⋊Q₈	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×#121	—	2	1	no	—
94	C₅×#121	—	2	1	no	—
95	C₅×#121	—	2	1	no	—
96	C₅×#121	—	2	1	no	—
97	C₅×#121	—	2	1	no	—
98	C₅×#121	—	2	1	no	—
99	C₄×C₅×Q₈	—	2	1	no	—
100	C₄×C₅×Q₈	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	—	2	1	no	—
106	C₄×C₅×D₄	—	2	1	no	—
107	C₅×#117	—	2	1	no	—
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#107	—	2	2	no	—
110	C₅×#107	—	2	2	no	—
111	C₅×#106	—	2	2	no	—
112	C₅×#106	—	2	2	no	—
113	C₅×#103	—	2	2	no	—
114	C₅×#103	—	2	2	no	—
115	C₅×#103	—	2	2	no	—
116	C₅×#103	—	2	2	no	—
117	C₅×#102	—	2	2	no	—
118	C₅×#102	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₄×C₅×C₈	D₄	1	2	yes	—
126	C₄×C₅×C₈	D₄	1	2	yes	—
127	C₄×C₅×C₈	D₄	1	2	yes	—
128	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
129	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
130	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
132	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
133	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
134	#3169	C₂×C₅	1	1	yes	characteristic, complemented
135	#3169	C₂×C₅	1	1	yes	characteristic, complemented
136	#3167	C₂×C₅	1	1	yes	characteristic, complemented
137	#3167	C₂×C₅	1	1	yes	characteristic, complemented
138	#3147	C₂×C₅	1	1	yes	characteristic, complemented
139	#3131	C₂×C₅	1	1	yes	characteristic, complemented
140	#1723	C₂×C₅	1	1	yes	characteristic, complemented
141	#1721	C₂×C₅	1	1	yes	characteristic, complemented
142	#1720	C₂×C₅	1	1	yes	characteristic, complemented
143	#1719	C₂×C₅	1	1	yes	characteristic, complemented
144	#1717	C₂×C₅	1	1	yes	characteristic, complemented
145	#1717	C₂×C₅	1	1	yes	characteristic, complemented
146	#1715	C₂×C₅	1	1	yes	characteristic, complemented
147	#1714	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#322	C₂×C₅	1	1	yes	characteristic, complemented
149	C₅×#41	—	4	4	no	—
150	C₅×#41	—	4	4	no	—
151	C₅×#41	—	4	4	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	4	1	no	—
167	C₂×C₅×D₄	—	4	1	no	—
168	C₂×C₅×D₄	—	4	1	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	—	4	1	no	—
171	C₂²×C₄×C₅	—	4	1	no	—
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₅×Q₁₆	—	4	4	no	—
176	C₅×SD₁₆	—	4	4	no	—
177	C₅×SD₁₆	—	4	4	no	—
178	C₅×SD₁₆	—	4	4	no	—
179	C₅×SD₁₆	—	4	4	no	—
180	C₅×D₈	—	4	4	no	—
181	C₅×D₈	—	4	4	no	—
182	C₅×D₈	—	4	4	no	—
183	C₂×C₅×C₈	—	2	4	no	—
184	C₂×C₅×C₈	—	2	4	no	—
185	C₂×C₅×C₈	—	4	2	no	—
186	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
187	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
188	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
189	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
190	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
191	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₂²⋊C₄	—	4	1	no	—
205	C₅×C₂²⋊C₄	—	4	1	no	—
206	C₅×C₂²⋊C₄	—	4	1	no	—
207	C₅×C₂²⋊C₄	—	4	1	no	—
208	C₅×C₂²⋊C₄	—	4	1	no	—
209	C₅×C₂²⋊C₄	—	4	1	no	—
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₄²×C₅	—	4	1	no	—
212	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₅	C₂⁴	1	1	yes	characteristic
216	C₂×#135	—	2	2	no	—
217	#533	C₂²×C₅	1	1	yes	characteristic
218	#532	C₂²×C₅	1	1	yes	characteristic
219	#532	C₂²×C₅	1	1	yes	characteristic
220	#532	C₂²×C₅	1	1	yes	characteristic
221	#500	C₂²×C₅	1	1	yes	characteristic
222	#500	C₂²×C₅	1	1	yes	characteristic
223	#498	C₂²×C₅	1	1	yes	characteristic
224	#498	C₂²×C₅	1	1	yes	characteristic
225	#495	—	2	2	no	—
226	#494	C₂²×C₅	1	1	yes	characteristic
227	#493	C₂²×C₅	1	1	yes	characteristic
228	#493	C₂²×C₅	1	1	yes	characteristic
229	#493	C₂²×C₅	1	1	yes	characteristic
230	#492	C₂²×C₅	1	1	yes	characteristic
231	#492	C₂²×C₅	1	1	yes	characteristic
232	#492	C₂²×C₅	1	1	yes	characteristic
233	#492	C₂²×C₅	1	1	yes	characteristic
234	#488	—	2	2	no	—
235	#487	C₂²×C₅	1	1	yes	characteristic
236	#487	C₂²×C₅	1	1	yes	characteristic
237	#487	C₂²×C₅	1	1	yes	characteristic
238	#487	C₂²×C₅	1	1	yes	characteristic
239	#486	C₂²×C₅	1	1	yes	characteristic
240	#486	C₂²×C₅	1	1	yes	characteristic
241	#486	C₂²×C₅	1	1	yes	characteristic
242	#486	C₂²×C₅	1	1	yes	characteristic
243	#486	C₂²×C₅	1	1	yes	characteristic
244	#486	C₂²×C₅	1	1	yes	characteristic
245	#486	C₂²×C₅	1	1	yes	characteristic
246	#486	C₂²×C₅	1	1	yes	characteristic
247	#466	—	2	2	no	—
248	#466	—	2	2	no	—
249	#465	—	2	2	no	—
250	#465	—	2	2	no	—
251	C₄×SD₁₆	—	2	2	no	—
252	C₄×SD₁₆	—	2	2	no	—
253	C₄×D₈	—	2	2	no	—
254	C₄×D₈	—	2	2	no	—
255	#416	—	2	2	no	—
256	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
259	#322	C₂²×C₅	1	1	yes	characteristic
260	#322	C₂²×C₅	1	1	yes	characteristic
261	#322	C₂²×C₅	1	1	yes	characteristic
262	#322	C₂²×C₅	1	1	yes	characteristic
263	C₂³×C₅	—	4	1	no	—
264	C₂³×C₅	—	4	1	no	—
265	C₂³×C₅	—	4	1	no	—
266	C₂³×C₅	#127	1	1	yes	characteristic
267	C₅×Q₈	—	4	2	no	—
268	C₅×Q₈	—	4	2	no	—
269	C₅×Q₈	—	4	2	no	—
270	C₅×Q₈	—	4	2	no	—
271	C₅×Q₈	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₅×D₄	—	4	2	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	2	no	—
277	C₅×D₄	—	4	2	no	—
278	C₅×D₄	—	4	2	no	—
279	C₅×D₄	—	4	2	no	—
280	C₅×D₄	—	4	2	no	—
281	C₅×D₄	—	8	2	no	—
282	C₅×D₄	—	8	2	no	—
283	C₅×D₄	—	8	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	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	—	8	2	no	—
292	C₂×C₄×C₅	—	8	2	no	—
293	C₂×C₄×C₅	—	8	2	no	—
294	C₂×C₄×C₅	#127	1	1	yes	characteristic
295	C₂×C₄×C₅	#127	1	1	yes	characteristic
296	C₂×C₄×C₅	#127	1	1	yes	characteristic
297	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
298	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
301	C₅×C₈	—	2	2	no	—
302	C₅×C₈	—	2	2	no	—
303	C₅×C₈	—	2	2	no	—
304	C₅×C₈	—	2	2	no	—
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	#135	1	4	yes	complemented
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	1	no	—
309	C₂×#41	—	2	1	no	—
310	#135	—	4	8	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×D₈	—	2	2	no	—
317	C₂×D₈	—	2	2	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂²×C₈	C₅×D₄	1	2	yes	—
320	C₂²×C₈	C₅×D₄	1	2	yes	—
321	C₂²×C₈	C₅×D₄	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
326	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
327	#127	C₂³×C₅	1	1	yes	characteristic
328	#127	C₂³×C₅	1	1	yes	characteristic
329	#127	C₂³×C₅	1	1	yes	characteristic
330	#125	—	2	1	no	—
331	#124	—	2	1	no	—
332	#124	—	2	1	no	—
333	#124	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	1	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	—	2	1	no	—
350	#117	—	2	1	no	—
351	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
352	#107	—	2	2	no	—
353	#107	—	2	2	no	—
354	#106	—	2	2	no	—
355	#106	—	2	2	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#102	—	2	2	no	—
361	#102	—	2	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	2	no	—
368	C₄×C₈	C₅×D₄	1	2	yes	—
369	C₄×C₈	C₅×D₄	1	2	yes	—
370	C₄×C₈	C₅×D₄	1	2	yes	—
371	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
373	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
376	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₅	—	2	1	no	—
378	C₂²×C₅	—	2	1	no	—
379	C₂²×C₅	—	8	1	no	—
380	C₂²×C₅	—	8	1	no	—
381	C₂²×C₅	—	8	1	no	—
382	C₂²×C₅	—	8	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	#496	1	2	yes	—
389	C₂²×C₅	C₂×#127	1	1	yes	characteristic
390	C₄×C₅	—	2	1	no	—
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	8	1	no	—
393	C₄×C₅	—	8	1	no	—
394	C₄×C₅	—	8	1	no	—
395	C₄×C₅	—	8	1	no	—
396	C₄×C₅	—	8	1	no	—
397	C₄×C₅	#496	1	2	yes	—
398	C₄×C₅	C₂×#135	1	2	yes	—
399	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
400	C₄×C₅	#575	1	2	yes	—
401	#41	—	4	4	no	—
402	#41	—	4	4	no	—
403	#41	—	4	4	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
427	Q₁₆	—	4	4	no	—
428	SD₁₆	—	4	4	no	—
429	SD₁₆	—	4	4	no	—
430	SD₁₆	—	4	4	no	—
431	SD₁₆	—	4	4	no	—
432	D₈	—	4	4	no	—
433	D₈	—	4	4	no	—
434	D₈	—	4	4	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	4	2	no	—
438	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
439	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
440	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
441	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
442	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
443	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	—	4	1	no	—
459	C₂²⋊C₄	—	4	1	no	—
460	C₂²⋊C₄	—	4	1	no	—
461	C₂²⋊C₄	—	4	1	no	—
462	C₂²⋊C₄	—	4	1	no	—
463	C₄²	—	4	1	no	—
464	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
465	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
466	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
467	C₄²	C₂⁴×C₅	1	1	yes	characteristic
468	C₂×C₅	—	2	2	no	—
469	C₂×C₅	—	16	1	no	—
470	C₂×C₅	—	16	1	no	—
471	C₂×C₅	—	16	1	no	—
472	C₂×C₅	#3147	1	1	yes	characteristic
473	C₂×C₅	C₂×#496	1	1	yes	characteristic
474	C₂×C₅	#3150	1	1	yes	characteristic
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	C₅×#127	1	1	yes	characteristic
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	C₅×#127	1	1	yes	characteristic
507	C₂×C₄	C₅×#127	1	1	yes	characteristic
508	C₂×C₄	C₅×#127	1	1	yes	characteristic
509	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
510	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
513	C₈	—	2	2	no	—
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	2	no	—
518	C₈	C₅×#135	1	4	yes	complemented
519	C₅	#19619	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	C₅×#496	1	2	yes	—
532	C₂²	C₂×C₅×#127	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	C₅×#496	1	2	yes	—
541	C₄	C₂×C₅×#135	1	2	yes	—
542	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
543	C₄	C₅×#575	1	2	yes	—
544	C₂	—	2	2	no	—
545	C₂	—	16	1	no	—
546	C₂	—	16	1	no	—
547	C₂	—	16	1	no	—
548	C₂	C₅×#3147	1	1	yes	characteristic
549	C₂	C₂×C₅×#496	1	1	yes	characteristic
550	C₂	C₅×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3169	C₂	semidirect
2. C₅×#3169	C₂	semidirect
3. C₅×#3167	C₂	semidirect
4. C₅×#3167	C₂	semidirect
5. C₅×#3147	C₂	semidirect
6. C₅×#3131	C₂	semidirect
7. C₅×#1723	C₂	semidirect
8. C₅×#1721	C₂	semidirect
9. C₅×#1720	C₂	semidirect
10. C₅×#1719	C₂	semidirect
11. C₅×#1717	C₂	semidirect
12. C₅×#1717	C₂	semidirect
13. C₅×#1715	C₂	semidirect
14. C₅×#1714	C₂	semidirect
15. C₂×C₅×#322	C₂	semidirect
63. #19619	C₅	direct (N × H)
134. #3169	C₂×C₅	semidirect
135. #3169	C₂×C₅	semidirect
136. #3167	C₂×C₅	semidirect
137. #3167	C₂×C₅	semidirect
138. #3147	C₂×C₅	semidirect
139. #3131	C₂×C₅	semidirect
140. #1723	C₂×C₅	semidirect
141. #1721	C₂×C₅	semidirect
142. #1720	C₂×C₅	semidirect
143. #1719	C₂×C₅	semidirect
144. #1717	C₂×C₅	semidirect
145. #1717	C₂×C₅	semidirect
146. #1715	C₂×C₅	semidirect
147. #1714	C₂×C₅	semidirect
148. C₂×#322	C₂×C₅	semidirect
306. C₅×C₈	#135	semidirect
518. C₈	C₅×#135	semidirect
519. C₅	#19619	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×#3169	2
C₅×#3167	2
C₅×#3147	2
C₅×#3131	2
C₅×#1723	2
C₅×#1721	2
C₅×#1720	2
C₅×#1719	2
C₅×#1717	2
C₅×#1715	2
C₅×#1714	2
C₂×C₅×#322	2
#19619	5

Subgroups — C5×#19619 #11942339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19619 #11942339