Subgroups — C₅×#19919 #11942639

Order 1280.

586 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3340	C₂	1	1	yes	maximal, characteristic
4	C₅×#3329	C₂	1	1	yes	maximal, characteristic
5	C₅×#1707	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1703	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1634	C₂	1	1	yes	maximal, characteristic
13	C₅×#1633	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×Q₈²	C₂²	1	1	yes	characteristic
17	C₅×#556	C₂²	1	1	yes	characteristic
18	C₅×#555	C₂²	1	1	yes	characteristic
19	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#500	C₂²	1	1	yes	characteristic
21	C₅×#498	—	2	1	no	—
22	C₅×#498	C₂²	1	1	yes	characteristic
23	C₅×#498	C₂²	1	1	yes	characteristic
24	C₅×#494	C₂²	1	1	yes	characteristic
25	C₅×#489	—	2	1	no	—
26	C₅×#487	C₂²	1	1	yes	characteristic
27	C₅×#487	C₂²	1	1	yes	characteristic
28	C₅×#485	—	2	1	no	—
29	C₅×#485	—	2	1	no	—
30	C₅×#482	—	2	1	no	—
31	C₅×#477	C₂²	1	1	yes	characteristic
32	C₅×#477	C₂²	1	1	yes	characteristic
33	C₅×#476	—	2	1	no	—
34	C₅×#476	C₂²	1	1	yes	characteristic
35	C₅×#476	C₂²	1	1	yes	characteristic
36	C₅×#475	—	2	1	no	—
37	C₅×#475	—	2	1	no	—
38	C₅×#475	C₂²	1	1	yes	characteristic
39	C₅×#474	C₂²	1	1	yes	characteristic
40	C₅×#468	—	2	1	no	—
41	C₅×#465	—	2	1	no	—
42	C₅×#464	—	2	1	no	—
43	C₅×#462	C₂²	1	1	yes	characteristic
44	C₅×#461	C₂²	1	1	yes	characteristic
45	C₅×#448	—	2	1	no	—
46	C₅×#446	C₂²	1	1	yes	characteristic
47	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
48	C₅×#441	—	2	1	no	—
49	C₄×C₅×SD₁₆	—	2	1	no	—
50	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
52	C₅×#436	C₂²	1	1	yes	characteristic
53	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
54	C₅×#427	—	2	1	no	—
55	C₅×#419	—	2	1	no	—
56	C₅×#334	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#333	C₂²	1	1	yes	characteristic
59	C₅×#333	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#19919	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	—	4	1	no	—
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
73	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂²×C₅×C₈	—	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	—	4	1	no	—
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×#126	—	4	1	no	—
85	C₅×#124	—	2	1	no	—
86	C₅×#124	—	4	1	no	—
87	C₅×C₂²⋊Q₈	—	2	1	no	—
88	C₅×C₂²⋊Q₈	—	2	1	no	—
89	C₅×C₂²⋊Q₈	—	4	1	no	—
90	C₅×#121	—	2	1	no	—
91	C₅×#121	—	2	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	C₂³	1	1	yes	characteristic
96	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×D₄	—	2	1	no	—
98	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
100	C₅×#117	—	2	1	no	—
101	C₅×#117	—	2	1	no	—
102	C₅×#117	—	2	1	no	—
103	C₅×#107	—	2	1	no	—
104	C₅×#107	—	2	1	no	—
105	C₅×#107	—	2	1	no	—
106	C₅×#107	—	4	1	no	—
107	C₅×#106	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×#106	—	2	1	no	—
112	C₅×#106	—	2	1	no	—
113	C₅×#106	—	2	1	no	—
114	C₅×#106	D₄	1	1	yes	characteristic
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	—	2	1	no	—
117	C₅×C₄⋊C₈	—	2	1	no	—
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
132	C₅×#103	D₄	1	1	yes	characteristic
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×#102	—	2	1	no	—
136	C₅×#102	D₄	1	1	yes	characteristic
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	—	2	1	no	—
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×#97	—	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	Q₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
146	#3369	C₂×C₅	1	1	yes	characteristic, complemented
147	#3340	C₂×C₅	1	1	yes	characteristic
148	#3329	C₂×C₅	1	1	yes	characteristic
149	#1707	C₂×C₅	1	1	yes	characteristic, complemented
150	#1704	C₂×C₅	1	1	yes	characteristic, complemented
151	#1703	C₂×C₅	1	1	yes	characteristic, complemented
152	#1672	C₂×C₅	1	1	yes	characteristic, complemented
153	#1671	C₂×C₅	1	1	yes	characteristic, complemented
154	#1650	C₂×C₅	1	1	yes	characteristic, complemented
155	#1649	C₂×C₅	1	1	yes	characteristic, complemented
156	#1634	C₂×C₅	1	1	yes	characteristic
157	#1633	C₂×C₅	1	1	yes	characteristic, complemented
158	#1590	C₂×C₅	1	1	yes	characteristic, complemented
159	C₈×SD₁₆	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	1	no	—
166	C₂×C₅×Q₈	—	4	2	no	—
167	C₂×C₅×Q₈	—	8	1	no	—
168	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×D₄	—	4	1	no	—
171	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
172	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	4	1	no	—
176	C₅×Q₁₆	—	4	2	no	—
177	C₅×Q₁₆	—	8	2	no	—
178	C₅×SD₁₆	—	2	2	no	—
179	C₅×SD₁₆	—	2	2	no	—
180	C₅×SD₁₆	—	8	1	no	—
181	C₅×M₁₆	—	8	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	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	4	2	no	—
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	4	1	no	—
216	C₅×C₂²⋊C₄	—	4	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	Q₈²	C₂²×C₅	1	1	yes	characteristic
224	#556	C₂²×C₅	1	1	yes	characteristic
225	#555	C₂²×C₅	1	1	yes	characteristic
226	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	#500	C₂²×C₅	1	1	yes	characteristic
228	#498	—	2	1	no	—
229	#498	C₂²×C₅	1	1	yes	characteristic
230	#498	C₂²×C₅	1	1	yes	characteristic
231	#494	C₂²×C₅	1	1	yes	characteristic
232	#489	—	2	1	no	—
233	#487	C₂²×C₅	1	1	yes	characteristic
234	#487	C₂²×C₅	1	1	yes	characteristic
235	#485	—	2	1	no	—
236	#485	—	2	1	no	—
237	#482	—	2	1	no	—
238	#477	C₂²×C₅	1	1	yes	characteristic
239	#477	C₂²×C₅	1	1	yes	characteristic
240	#476	—	2	1	no	—
241	#476	C₂²×C₅	1	1	yes	characteristic
242	#476	C₂²×C₅	1	1	yes	characteristic
243	#475	—	2	1	no	—
244	#475	—	2	1	no	—
245	#475	C₂²×C₅	1	1	yes	characteristic
246	#474	C₂²×C₅	1	1	yes	characteristic
247	#468	—	2	1	no	—
248	#465	—	2	1	no	—
249	#464	—	2	1	no	—
250	#462	C₂²×C₅	1	1	yes	characteristic
251	#461	C₂²×C₅	1	1	yes	characteristic
252	#448	—	2	1	no	—
253	#446	C₂²×C₅	1	1	yes	characteristic
254	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
255	#441	—	2	1	no	—
256	C₄×SD₁₆	—	2	1	no	—
257	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
258	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
259	#436	C₂²×C₅	1	1	yes	characteristic
260	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
261	#427	—	2	1	no	—
262	#419	—	2	1	no	—
263	#334	C₂²×C₅	1	1	yes	characteristic
264	#334	C₂²×C₅	1	1	yes	characteristic
265	#333	C₂²×C₅	1	1	yes	characteristic
266	#333	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	D₄⋊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	C₂³×C₅	—	2	1	no	—
276	C₅×Q₈	—	2	1	no	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	8	2	no	—
284	C₅×Q₈	—	8	1	no	—
285	C₅×Q₈	—	8	1	no	—
286	C₅×Q₈	—	16	1	no	—
287	C₅×Q₈	#135	1	2	yes	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	16	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	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	8	2	no	—
308	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
311	C₅×C₈	—	2	2	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	4	1	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	#137	1	2	yes	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂×Q₁₆	—	2	1	no	—
322	C₂×Q₁₆	—	4	1	no	—
323	C₂×SD₁₆	—	2	1	no	—
324	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
325	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
326	C₂×M₁₆	—	2	1	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	—	4	1	no	—
332	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
336	#126	—	4	1	no	—
337	#124	—	2	1	no	—
338	#124	—	4	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	4	1	no	—
342	#121	—	2	1	no	—
343	#121	—	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×D₄	—	2	1	no	—
350	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
351	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	—	2	1	no	—
355	#107	—	2	1	no	—
356	#107	—	2	1	no	—
357	#107	—	2	1	no	—
358	#107	—	4	1	no	—
359	#106	—	2	1	no	—
360	#106	—	2	1	no	—
361	#106	—	2	1	no	—
362	#106	—	2	1	no	—
363	#106	—	2	1	no	—
364	#106	—	2	1	no	—
365	#106	—	2	1	no	—
366	#106	C₅×D₄	1	1	yes	characteristic
367	#106	C₅×D₄	1	1	yes	characteristic
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
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	#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	#102	—	2	1	no	—
386	#102	—	2	1	no	—
387	#102	—	2	1	no	—
388	#102	C₅×D₄	1	1	yes	characteristic
389	#102	C₅×D₄	1	1	yes	characteristic
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	D₄²	1	1	yes	characteristic
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	8	1	no	—
412	C₄×C₅	—	8	1	no	—
413	C₄×C₅	—	8	1	no	—
414	C₄×C₅	—	8	1	no	—
415	C₄×C₅	C₂×#135	1	1	yes	characteristic
416	C₄×C₅	C₂×#137	1	1	yes	characteristic
417	C₄×C₅	#577	1	1	yes	characteristic
418	C₄×C₅	#578	1	1	yes	characteristic
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	4	1	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	2	no	—
426	C₂×Q₈	—	8	1	no	—
427	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	Q₁₆	—	4	2	no	—
436	Q₁₆	—	8	2	no	—
437	SD₁₆	—	2	2	no	—
438	SD₁₆	—	2	2	no	—
439	SD₁₆	—	8	1	no	—
440	M₁₆	—	8	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	4	2	no	—
447	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
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	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	C₂⁴×C₅	1	1	yes	characteristic
482	C₂×C₅	—	8	1	no	—
483	C₂×C₅	—	8	1	no	—
484	C₂×C₅	#3276	1	1	yes	characteristic
485	C₂×C₅	#3282	1	1	yes	characteristic
486	C₂×C₅	#3291	1	1	yes	characteristic
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	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	—	8	1	no	—
498	Q₈	—	8	1	no	—
499	Q₈	—	16	1	no	—
500	Q₈	C₅×#135	1	2	yes	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	16	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	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	—	8	2	no	—
521	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
523	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	C₅×#137	1	2	yes	—
533	C₅	#19919	1	1	yes	characteristic, direct product factor, Sylow
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	C₅×D₄²	1	1	yes	characteristic
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	C₂×C₅×#135	1	1	yes	characteristic
553	C₄	C₂×C₅×#137	1	1	yes	characteristic
554	C₄	C₅×#577	1	1	yes	characteristic
555	C₄	C₅×#578	1	1	yes	characteristic
556	C₂	—	8	1	no	—
557	C₂	—	8	1	no	—
558	C₂	C₅×#3276	1	1	yes	characteristic
559	C₂	C₅×#3282	1	1	yes	characteristic
560	C₂	C₅×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#555	C₂²
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×Q₈×SD₁₆	C₂	semidirect
2. C₅×#3369	C₂	semidirect
5. C₅×#1707	C₂	semidirect
6. C₅×#1704	C₂	semidirect
7. C₅×#1703	C₂	semidirect
8. C₅×#1672	C₂	semidirect
9. C₅×#1671	C₂	semidirect
10. C₅×#1650	C₂	semidirect
11. C₅×#1649	C₂	semidirect
13. C₅×#1633	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×SD₁₆	C₂	semidirect
67. #19919	C₅	direct (N × H)
145. Q₈×SD₁₆	C₂×C₅	semidirect
146. #3369	C₂×C₅	semidirect
149. #1707	C₂×C₅	semidirect
150. #1704	C₂×C₅	semidirect
151. #1703	C₂×C₅	semidirect
152. #1672	C₂×C₅	semidirect
153. #1671	C₂×C₅	semidirect
154. #1650	C₂×C₅	semidirect
155. #1649	C₂×C₅	semidirect
157. #1633	C₂×C₅	semidirect
158. #1590	C₂×C₅	semidirect
159. C₈×SD₁₆	C₂×C₅	semidirect
533. C₅	#19919	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×Q₈×SD₁₆	2
C₅×#3369	2
C₅×#3340	2
C₅×#3329	2
C₅×#1707	2
C₅×#1704	2
C₅×#1703	2
C₅×#1672	2
C₅×#1671	2
C₅×#1650	2
C₅×#1649	2
C₅×#1634	2
C₅×#1633	2
C₅×#1590	2
C₅×C₈×SD₁₆	2
#19919	5

Subgroups — C5×#19919 #11942639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19919 #11942639