Subgroups — C₅×#19920 #11942640

Order 1280.

572 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×#3374	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3364	C₂	1	1	yes	maximal, characteristic
3	C₅×#3359	C₂	1	1	yes	maximal, characteristic
4	C₅×#3328	C₂	1	1	yes	maximal, characteristic
5	C₅×#1710	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1700	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1699	C₂	1	1	yes	maximal, characteristic
8	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1650	C₂	1	1	yes	maximal, characteristic
11	C₅×#1649	C₂	1	1	yes	maximal, characteristic
12	C₅×#1648	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1648	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic
15	C₅×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#557	C₂²	1	1	yes	characteristic
17	C₅×#557	C₂²	1	1	yes	characteristic
18	C₅×#556	C₂²	1	1	yes	characteristic
19	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#500	C₂²	1	1	yes	characteristic
21	C₅×#500	C₂²	1	1	yes	characteristic
22	C₅×#491	—	2	1	no	—
23	C₅×#488	—	2	1	no	—
24	C₅×#487	—	2	1	no	—
25	C₅×#487	C₂²	1	1	yes	characteristic
26	C₅×#487	C₂²	1	1	yes	characteristic
27	C₅×#487	C₂²	1	1	yes	characteristic
28	C₅×#487	C₂²	1	1	yes	characteristic
29	C₅×#485	—	2	1	no	—
30	C₅×#479	—	2	1	no	—
31	C₅×#479	—	2	1	no	—
32	C₅×#475	—	2	1	no	—
33	C₅×#475	C₂²	1	1	yes	characteristic
34	C₅×#475	C₂²	1	1	yes	characteristic
35	C₅×#475	C₂²	1	1	yes	characteristic
36	C₅×#474	C₂²	1	1	yes	characteristic
37	C₅×#470	—	2	1	no	—
38	C₅×#464	—	2	1	no	—
39	C₅×#462	—	2	1	no	—
40	C₅×#462	C₂²	1	1	yes	characteristic
41	C₅×#462	C₂²	1	1	yes	characteristic
42	C₅×#462	C₂²	1	1	yes	characteristic
43	C₅×#461	—	2	1	no	—
44	C₅×#461	C₂²	1	1	yes	characteristic
45	C₅×#451	—	2	1	no	—
46	C₅×#446	C₂²	1	1	yes	characteristic
47	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
48	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
49	C₅×#441	—	2	1	no	—
50	C₄×C₅×Q₁₆	—	2	1	no	—
51	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₅×SD₁₆	—	2	1	no	—
53	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
54	C₅×#436	C₂²	1	1	yes	characteristic
55	C₅×#419	—	2	1	no	—
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#332	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#19920	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	—	2	1	no	—
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	—	2	1	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₅×C₄⋊Q₈	—	2	1	no	—
77	C₅×C₄⋊Q₈	—	2	1	no	—
78	C₅×C₄⋊Q₈	—	2	1	no	—
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×#126	—	4	1	no	—
84	C₅×#125	—	2	1	no	—
85	C₅×#125	—	2	1	no	—
86	C₅×#125	—	4	1	no	—
87	C₅×#125	—	4	1	no	—
88	C₅×#124	—	2	1	no	—
89	C₅×C₂²⋊Q₈	—	2	1	no	—
90	C₅×C₂²⋊Q₈	—	2	1	no	—
91	C₅×C₂²⋊Q₈	—	4	1	no	—
92	C₄×C₅×Q₈	—	2	1	no	—
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
102	C₅×#117	—	2	1	no	—
103	C₅×#107	—	2	1	no	—
104	C₅×#107	—	4	1	no	—
105	C₅×#107	—	4	1	no	—
106	C₅×#107	D₄	1	1	yes	characteristic
107	C₅×#106	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	D₄	1	1	yes	characteristic
111	C₅×C₄⋊C₈	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	—	2	1	no	—
114	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×#103	—	2	1	no	—
119	C₅×#103	—	2	1	no	—
120	C₅×#103	—	2	1	no	—
121	C₅×#103	—	2	1	no	—
122	C₅×#103	—	2	1	no	—
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	2	1	no	—
129	C₅×#103	—	2	1	no	—
130	C₅×#103	—	2	1	no	—
131	C₅×#103	—	2	1	no	—
132	C₅×#103	—	2	1	no	—
133	C₅×#103	D₄	1	1	yes	characteristic
134	C₅×#103	D₄	1	1	yes	characteristic
135	C₅×#103	D₄	1	1	yes	characteristic
136	C₅×#102	—	2	1	no	—
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	—	2	1	no	—
139	C₅×#97	—	2	1	no	—
140	C₄×C₅×C₈	—	2	1	no	—
141	C₄×C₅×C₈	—	2	1	no	—
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3374	C₂×C₅	1	1	yes	characteristic, complemented
146	#3364	C₂×C₅	1	1	yes	characteristic
147	#3359	C₂×C₅	1	1	yes	characteristic
148	#3328	C₂×C₅	1	1	yes	characteristic
149	#1710	C₂×C₅	1	1	yes	characteristic, complemented
150	#1700	C₂×C₅	1	1	yes	characteristic, complemented
151	#1699	C₂×C₅	1	1	yes	characteristic
152	#1680	C₂×C₅	1	1	yes	characteristic, complemented
153	#1680	C₂×C₅	1	1	yes	characteristic, complemented
154	#1650	C₂×C₅	1	1	yes	characteristic
155	#1649	C₂×C₅	1	1	yes	characteristic
156	#1648	C₂×C₅	1	1	yes	characteristic, complemented
157	#1648	C₂×C₅	1	1	yes	characteristic, complemented
158	#1590	C₂×C₅	1	1	yes	characteristic
159	C₈×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×Q₈	—	4	2	no	—
166	C₂×C₅×Q₈	—	8	1	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	4	1	no	—
173	C₅×Q₁₆	—	2	2	no	—
174	C₅×Q₁₆	—	4	2	no	—
175	C₅×Q₁₆	—	4	2	no	—
176	C₅×Q₁₆	—	8	1	no	—
177	C₅×SD₁₆	—	4	1	no	—
178	C₅×SD₁₆	—	4	2	no	—
179	C₅×M₁₆	—	8	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
201	C₅×C₄⋊C₄	—	4	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	—	4	1	no	—
208	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	4	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	4	1	no	—
220	C₄²×C₅	—	4	1	no	—
221	C₄²×C₅	—	4	1	no	—
222	C₄²×C₅	C₂⁴	1	1	yes	characteristic
223	#557	C₂²×C₅	1	1	yes	characteristic
224	#557	C₂²×C₅	1	1	yes	characteristic
225	#556	C₂²×C₅	1	1	yes	characteristic
226	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	#500	C₂²×C₅	1	1	yes	characteristic
228	#500	C₂²×C₅	1	1	yes	characteristic
229	#491	—	2	1	no	—
230	#488	—	2	1	no	—
231	#487	—	2	1	no	—
232	#487	C₂²×C₅	1	1	yes	characteristic
233	#487	C₂²×C₅	1	1	yes	characteristic
234	#487	C₂²×C₅	1	1	yes	characteristic
235	#487	C₂²×C₅	1	1	yes	characteristic
236	#485	—	2	1	no	—
237	#479	—	2	1	no	—
238	#479	—	2	1	no	—
239	#475	—	2	1	no	—
240	#475	C₂²×C₅	1	1	yes	characteristic
241	#475	C₂²×C₅	1	1	yes	characteristic
242	#475	C₂²×C₅	1	1	yes	characteristic
243	#474	C₂²×C₅	1	1	yes	characteristic
244	#470	—	2	1	no	—
245	#464	—	2	1	no	—
246	#462	—	2	1	no	—
247	#462	C₂²×C₅	1	1	yes	characteristic
248	#462	C₂²×C₅	1	1	yes	characteristic
249	#462	C₂²×C₅	1	1	yes	characteristic
250	#461	—	2	1	no	—
251	#461	C₂²×C₅	1	1	yes	characteristic
252	#451	—	2	1	no	—
253	#446	C₂²×C₅	1	1	yes	characteristic
254	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
255	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
256	#441	—	2	1	no	—
257	C₄×Q₁₆	—	2	1	no	—
258	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₄×SD₁₆	—	2	1	no	—
260	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
261	#436	C₂²×C₅	1	1	yes	characteristic
262	#419	—	2	1	no	—
263	#335	C₂²×C₅	1	1	yes	characteristic
264	#334	C₂²×C₅	1	1	yes	characteristic
265	#332	C₂²×C₅	1	1	yes	characteristic
266	#332	C₂²×C₅	1	1	yes	characteristic
267	#332	C₂²×C₅	1	1	yes	characteristic
268	#332	C₂²×C₅	1	1	yes	characteristic
269	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₈²	C₂²×C₅	1	1	yes	characteristic
274	C₂³×C₅	—	2	1	no	—
275	C₅×Q₈	—	2	1	no	—
276	C₅×Q₈	—	2	1	no	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	2	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	4	1	no	—
284	C₅×Q₈	—	4	1	no	—
285	C₅×Q₈	—	4	1	no	—
286	C₅×Q₈	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	8	2	no	—
289	C₅×Q₈	#135	1	2	yes	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	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	—	8	2	no	—
306	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
309	C₅×C₈	—	2	2	no	—
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	4	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₂²×Q₈	—	2	1	no	—
319	C₂×Q₁₆	—	2	1	no	—
320	C₂×Q₁₆	—	2	1	no	—
321	C₂×Q₁₆	—	2	1	no	—
322	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
323	C₂×SD₁₆	—	2	1	no	—
324	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
325	C₂×M₁₆	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
330	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
333	#126	—	4	1	no	—
334	#125	—	2	1	no	—
335	#125	—	2	1	no	—
336	#125	—	4	1	no	—
337	#125	—	4	1	no	—
338	#124	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	4	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
348	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
349	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#107	—	2	1	no	—
354	#107	—	4	1	no	—
355	#107	—	4	1	no	—
356	#107	C₅×D₄	1	1	yes	characteristic
357	#106	—	2	1	no	—
358	#106	—	2	1	no	—
359	#106	—	2	1	no	—
360	#106	C₅×D₄	1	1	yes	characteristic
361	C₄⋊C₈	—	2	1	no	—
362	C₄⋊C₈	—	2	1	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
365	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
366	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
368	#103	—	2	1	no	—
369	#103	—	2	1	no	—
370	#103	—	2	1	no	—
371	#103	—	2	1	no	—
372	#103	—	2	1	no	—
373	#103	—	2	1	no	—
374	#103	—	2	1	no	—
375	#103	—	2	1	no	—
376	#103	—	2	1	no	—
377	#103	—	2	1	no	—
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#103	—	2	1	no	—
382	#103	—	2	1	no	—
383	#103	C₅×D₄	1	1	yes	characteristic
384	#103	C₅×D₄	1	1	yes	characteristic
385	#103	C₅×D₄	1	1	yes	characteristic
386	#102	—	2	1	no	—
387	#102	C₅×D₄	1	1	yes	characteristic
388	C₂²⋊C₈	—	2	1	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	D₄²	1	1	yes	characteristic
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	8	1	no	—
408	C₄×C₅	—	8	1	no	—
409	C₄×C₅	—	8	1	no	—
410	C₄×C₅	—	8	1	no	—
411	C₄×C₅	C₂×#135	1	1	yes	characteristic
412	C₄×C₅	#575	1	1	yes	characteristic
413	C₄×C₅	#577	1	1	yes	characteristic
414	C₄×C₅	#578	1	1	yes	characteristic
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	—	4	1	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	—	8	1	no	—
422	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	Q₁₆	—	2	2	no	—
429	Q₁₆	—	4	2	no	—
430	Q₁₆	—	4	2	no	—
431	Q₁₆	—	8	1	no	—
432	SD₁₆	—	4	1	no	—
433	SD₁₆	—	4	2	no	—
434	M₁₆	—	8	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
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	—	2	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	—	4	1	no	—
477	C₄²	C₂⁴×C₅	1	1	yes	characteristic
478	C₂×C₅	—	8	1	no	—
479	C₂×C₅	#3277	1	1	yes	characteristic
480	C₂×C₅	#3282	1	1	yes	characteristic
481	C₂×C₅	#3293	1	1	yes	characteristic
482	C₂³	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	8	2	no	—
497	Q₈	C₅×#135	1	2	yes	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	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	—	8	2	no	—
514	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
516	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₅	#19920	1	1	yes	characteristic, direct product factor, Sylow
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	C₅×D₄²	1	1	yes	characteristic
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	C₂×C₅×#135	1	1	yes	characteristic
544	C₄	C₅×#575	1	1	yes	characteristic
545	C₄	C₅×#577	1	1	yes	characteristic
546	C₄	C₅×#578	1	1	yes	characteristic
547	C₂	—	8	1	no	—
548	C₂	C₅×#3277	1	1	yes	characteristic
549	C₂	C₅×#3282	1	1	yes	characteristic
550	C₂	C₅×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×D₄	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3374	C₂	semidirect
5. C₅×#1710	C₂	semidirect
6. C₅×#1700	C₂	semidirect
8. C₅×#1680	C₂	semidirect
9. C₅×#1680	C₂	semidirect
12. C₅×#1648	C₂	semidirect
13. C₅×#1648	C₂	semidirect
15. C₅×C₈×Q₁₆	C₂	semidirect
67. #19920	C₅	direct (N × H)
145. #3374	C₂×C₅	semidirect
149. #1710	C₂×C₅	semidirect
150. #1700	C₂×C₅	semidirect
152. #1680	C₂×C₅	semidirect
153. #1680	C₂×C₅	semidirect
156. #1648	C₂×C₅	semidirect
157. #1648	C₂×C₅	semidirect
159. C₈×Q₁₆	C₂×C₅	semidirect
526. C₅	#19920	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×#3374	2
C₅×#3364	2
C₅×#3359	2
C₅×#3328	2
C₅×#1710	2
C₅×#1700	2
C₅×#1699	2
C₅×#1680	2
C₅×#1650	2
C₅×#1649	2
C₅×#1648	2
C₅×#1590	2
C₅×C₈×Q₁₆	2
#19920	5

Subgroups — C5×#19920 #11942640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19920 #11942640