Subgroups — C₅×#19171 #11941891

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3152	C₂	1	1	yes	maximal, characteristic
2	C₅×#3103	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1690	C₂	1	2	yes	maximal, complemented
6	C₅×#1686	C₂	1	2	yes	maximal, complemented
7	C₅×#1670	C₂	1	2	yes	maximal, complemented
8	C₅×#1666	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1547	C₂	1	1	yes	maximal, characteristic
11	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	1	no	—
13	C₂×C₅×#137	—	2	1	no	—
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₅×#497	—	2	2	no	—
18	C₅×#494	C₂²	1	2	yes	—
19	C₅×#492	C₂²	1	2	yes	—
20	C₅×#481	—	2	1	no	—
21	C₅×#475	—	2	1	no	—
22	C₅×#475	—	2	1	no	—
23	C₅×#475	C₂²	1	2	yes	—
24	C₅×#475	C₂²	1	2	yes	—
25	C₅×#475	C₂²	1	1	yes	characteristic
26	C₅×#475	C₂²	1	1	yes	characteristic
27	C₅×#460	C₂²	1	1	yes	characteristic
28	C₅×#460	C₂²	1	1	yes	characteristic
29	C₅×#448	—	2	1	no	—
30	C₅×#446	—	2	2	no	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×C₈×Q₈	C₂²	1	2	yes	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₄×C₅×SD₁₆	—	2	1	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₂×C₅×#106	—	2	1	no	—
37	C₅×#423	—	2	1	no	—
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	—	2	1	no	—
41	C₄×C₅×M₁₆	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#334	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19171	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
53	C₅×#137	—	4	4	no	—
54	C₅×#137	—	4	4	no	—
55	C₂×C₅×Q₁₆	—	2	2	no	—
56	C₂×C₅×Q₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×SD₁₆	—	2	1	no	—
59	C₂×C₅×SD₁₆	—	2	2	no	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
63	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₅×C₄⋊Q₈	—	2	1	no	—
66	C₅×C₄⋊Q₈	—	2	1	no	—
67	C₅×C₄⋊Q₈	—	2	1	no	—
68	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₅×#127	C₂³	1	1	yes	characteristic
71	C₅×#124	—	2	1	no	—
72	C₅×#121	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₄×C₅×Q₈	—	2	1	no	—
75	C₄×C₅×Q₈	—	2	1	no	—
76	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
77	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
78	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#106	—	2	2	no	—
89	C₅×#106	—	2	2	no	—
90	C₅×#106	—	2	1	no	—
91	C₅×#106	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	2	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	—	2	1	no	—
95	C₅×C₄⋊C₈	—	2	1	no	—
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×C₄⋊C₈	C₂³	1	2	yes	—
98	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×#103	—	2	2	no	—
101	C₅×#103	—	2	2	no	—
102	C₅×#103	—	2	1	no	—
103	C₅×#103	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×#102	—	2	1	no	—
106	C₅×C₂²⋊C₈	—	2	1	no	—
107	C₅×#97	—	2	2	no	—
108	C₅×#97	D₄	1	2	yes	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	#3152	C₂×C₅	1	1	yes	characteristic
113	#3103	C₂×C₅	1	1	yes	characteristic
114	C₂×#475	C₂×C₅	1	1	yes	characteristic, complemented
115	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
116	#1690	C₂×C₅	1	2	yes	complemented
117	#1686	C₂×C₅	1	2	yes	complemented
118	#1670	C₂×C₅	1	2	yes	complemented
119	#1666	C₂×C₅	1	2	yes	complemented
120	#1565	C₂×C₅	1	1	yes	characteristic, complemented
121	#1547	C₂×C₅	1	1	yes	characteristic
122	#1546	C₂×C₅	1	1	yes	characteristic, complemented
123	C₅×#41	—	4	2	no	—
124	C₅×#41	—	4	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	4	1	no	—
130	C₂×C₅×Q₈	—	4	1	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	—	4	2	no	—
133	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	4	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	4	1	no	—
142	C₂²×C₄×C₅	—	4	1	no	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	#41	1	1	yes	characteristic
146	C₅×Q₁₆	—	4	4	no	—
147	C₅×Q₁₆	—	4	4	no	—
148	C₅×SD₁₆	—	4	4	no	—
149	C₅×SD₁₆	—	4	2	no	—
150	C₅×SD₁₆	—	4	2	no	—
151	C₅×SD₁₆	—	4	4	no	—
152	C₅×M₁₆	—	2	2	no	—
153	C₅×M₁₆	—	4	2	no	—
154	C₅×M₁₆	SD₁₆	1	4	yes	complemented
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	4	2	no	—
160	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	4	1	no	—
172	C₅×C₄⋊C₄	—	4	1	no	—
173	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	—	4	1	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₅	#41	1	1	yes	characteristic
184	C₄²×C₅	C₂⁴	1	1	yes	characteristic
185	C₂×#137	—	2	1	no	—
186	C₂×#137	—	2	1	no	—
187	#532	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
190	#497	—	2	2	no	—
191	#494	C₂²×C₅	1	2	yes	—
192	#492	C₂²×C₅	1	2	yes	—
193	#481	—	2	1	no	—
194	#475	—	2	1	no	—
195	#475	—	2	1	no	—
196	#475	C₂²×C₅	1	2	yes	—
197	#475	C₂²×C₅	1	2	yes	—
198	#475	C₂²×C₅	1	1	yes	characteristic
199	#475	C₂²×C₅	1	1	yes	characteristic
200	#460	C₂²×C₅	1	1	yes	characteristic
201	#460	C₂²×C₅	1	1	yes	characteristic
202	#448	—	2	1	no	—
203	#446	—	2	2	no	—
204	#446	C₂²×C₅	1	2	yes	—
205	C₈×Q₈	C₂²×C₅	1	2	yes	—
206	C₄×SD₁₆	—	2	1	no	—
207	C₄×SD₁₆	—	2	1	no	—
208	#431	C₂²×C₅	1	1	yes	characteristic
209	C₂×#106	—	2	1	no	—
210	#423	—	2	1	no	—
211	#423	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	C₂×#103	—	2	1	no	—
214	C₄×M₁₆	—	2	1	no	—
215	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
216	#335	C₂²×C₅	1	2	yes	—
217	#334	C₂²×C₅	1	2	yes	—
218	#332	C₂²×C₅	1	2	yes	—
219	#332	C₂²×C₅	1	2	yes	—
220	#332	C₂²×C₅	1	2	yes	—
221	#331	C₂²×C₅	1	2	yes	—
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	#121	1	1	yes	characteristic
224	C₅×Q₈	—	2	1	no	—
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	—	2	1	no	—
227	C₅×Q₈	—	4	2	no	—
228	C₅×Q₈	—	4	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×Q₈	—	4	2	no	—
231	C₅×Q₈	—	4	1	no	—
232	C₅×Q₈	—	8	2	no	—
233	C₅×Q₈	#137	1	2	yes	complemented
234	C₅×D₄	—	4	1	no	—
235	C₅×D₄	—	4	1	no	—
236	C₅×D₄	—	4	1	no	—
237	C₅×D₄	—	4	1	no	—
238	C₅×D₄	—	8	1	no	—
239	C₅×D₄	—	8	2	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	8	1	no	—
251	C₂×C₄×C₅	—	8	2	no	—
252	C₂×C₄×C₅	—	8	2	no	—
253	C₂×C₄×C₅	#121	1	1	yes	characteristic
254	C₂×C₄×C₅	#121	1	1	yes	characteristic
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
257	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	2	no	—
263	C₅×C₈	—	4	1	no	—
264	C₅×C₈	—	4	2	no	—
265	C₅×C₈	—	4	1	no	—
266	C₅×C₈	C₂×SD₁₆	1	4	yes	—
267	C₂×#41	—	2	1	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
270	#137	—	4	4	no	—
271	#137	—	4	4	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	1	no	—
275	C₂×SD₁₆	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
280	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
287	#127	C₂³×C₅	1	1	yes	characteristic
288	#124	—	2	1	no	—
289	#121	—	2	1	no	—
290	#121	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
294	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
295	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
305	#106	—	2	2	no	—
306	#106	—	2	2	no	—
307	#106	—	2	1	no	—
308	#106	—	2	1	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂³×C₅	1	2	yes	—
314	C₄⋊C₈	C₂³×C₅	1	2	yes	—
315	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	1	no	—
320	#103	—	2	1	no	—
321	#102	—	2	1	no	—
322	#102	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	#97	—	2	2	no	—
325	#97	C₅×D₄	1	2	yes	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	C₂³×C₅	1	2	yes	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	8	1	no	—
332	C₂²×C₅	—	8	1	no	—
333	C₂²×C₅	—	8	1	no	—
334	C₂²×C₅	#460	1	2	yes	—
335	C₂²×C₅	C₂×#121	1	1	yes	characteristic
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	4	1	no	—
341	C₄×C₅	—	4	1	no	—
342	C₄×C₅	—	4	1	no	—
343	C₄×C₅	—	8	1	no	—
344	C₄×C₅	—	8	2	no	—
345	C₄×C₅	#460	1	2	yes	—
346	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
347	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₄×C₅	C₂×#137	1	1	yes	characteristic
349	C₄×C₅	#575	1	1	yes	characteristic
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	1	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₅×#41	1	1	yes	characteristic
373	Q₁₆	—	4	4	no	—
374	Q₁₆	—	4	4	no	—
375	SD₁₆	—	4	4	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	2	no	—
378	SD₁₆	—	4	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	4	2	no	—
381	M₁₆	C₅×SD₁₆	1	4	yes	complemented
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
388	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
409	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
410	C₄²	C₅×#41	1	1	yes	characteristic
411	C₄²	C₂⁴×C₅	1	1	yes	characteristic
412	C₂×C₅	—	2	2	no	—
413	C₂×C₅	—	16	1	no	—
414	C₂×C₅	C₂×#460	1	1	yes	characteristic
415	C₂×C₅	#3056	1	1	yes	characteristic
416	C₂×C₅	#3069	1	1	yes	characteristic
417	C₂³	—	4	1	no	—
418	C₂³	C₅×#121	1	1	yes	characteristic
419	Q₈	—	2	1	no	—
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	8	2	no	—
428	Q₈	C₅×#137	1	2	yes	complemented
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	8	1	no	—
434	D₄	—	8	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	C₅×#121	1	1	yes	characteristic
449	C₂×C₄	C₅×#121	1	1	yes	characteristic
450	C₂×C₄	C₅×#121	1	1	yes	characteristic
451	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
452	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
453	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	4	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	1	no	—
461	C₈	C₂×C₅×SD₁₆	1	4	yes	—
462	C₅	#19171	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	C₅×#460	1	2	yes	—
469	C₂²	C₂×C₅×#121	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	C₅×#460	1	2	yes	—
480	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
481	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
482	C₄	C₂×C₅×#137	1	1	yes	characteristic
483	C₄	C₅×#575	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	16	1	no	—
486	C₂	C₂×C₅×#460	1	1	yes	characteristic
487	C₂	C₅×#3056	1	1	yes	characteristic
488	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#475	C₂	semidirect
4. C₅×Q₈×M₁₆	C₂	semidirect
5. C₅×#1690	C₂	semidirect
6. C₅×#1686	C₂	semidirect
7. C₅×#1670	C₂	semidirect
8. C₅×#1666	C₂	semidirect
9. C₅×#1565	C₂	semidirect
11. C₅×#1546	C₂	semidirect
49. #19171	C₅	direct (N × H)
114. C₂×#475	C₂×C₅	semidirect
115. Q₈×M₁₆	C₂×C₅	semidirect
116. #1690	C₂×C₅	semidirect
117. #1686	C₂×C₅	semidirect
118. #1670	C₂×C₅	semidirect
119. #1666	C₂×C₅	semidirect
120. #1565	C₂×C₅	semidirect
122. #1546	C₂×C₅	semidirect
154. C₅×M₁₆	SD₁₆	semidirect
233. C₅×Q₈	#137	semidirect
381. M₁₆	C₅×SD₁₆	semidirect
428. Q₈	C₅×#137	semidirect
462. C₅	#19171	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×#3152	2
C₅×#3103	2
C₂×C₅×#475	2
C₅×Q₈×M₁₆	2
C₅×#1690	2
C₅×#1686	2
C₅×#1670	2
C₅×#1666	2
C₅×#1565	2
C₅×#1547	2
C₅×#1546	2
#19171	5

Subgroups — C5×#19171 #11941891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19171 #11941891