Subgroups — C₅×#19164 #11941884

Order 1280.

706 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3165	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3101	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic
4	C₅×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅×#1693	C₂	1	2	yes	maximal, complemented
6	C₅×#1691	C₂	1	2	yes	maximal, complemented
7	C₅×#1673	C₂	1	2	yes	maximal, complemented
8	C₅×#1671	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	—	2	1	no	—
13	C₂²×C₅×M₁₆	—	2	1	no	—
14	C₅×#533	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×#501	—	2	2	no	—
18	C₅×#500	C₂²	1	2	yes	complemented
19	C₅×#498	C₂²	1	2	yes	complemented
20	C₅×#483	—	2	1	no	—
21	C₅×#476	C₂²	1	1	yes	characteristic
22	C₅×#476	C₂²	1	1	yes	characteristic
23	C₅×#461	—	2	1	no	—
24	C₅×#461	—	2	1	no	—
25	C₅×#461	C₂²	1	2	yes	—
26	C₅×#461	C₂²	1	2	yes	—
27	C₅×#461	C₂²	1	1	yes	characteristic
28	C₅×#461	C₂²	1	1	yes	characteristic
29	C₅×#450	—	2	1	no	—
30	C₄×C₅×SD₁₆	—	2	1	no	—
31	C₄×C₅×SD₁₆	—	2	1	no	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#435	—	2	2	no	—
34	C₅×C₈×D₄	C₂²	1	2	yes	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#428	—	2	1	no	—
37	C₅×#428	—	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	C₅×#407	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#333	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#332	C₂²	1	2	yes	complemented
49	#19164	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₅×Q₈	—	2	1	no	—
51	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	4	4	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂×C₅×M₁₆	—	4	4	no	—
61	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
62	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	2	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₅×#125	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₄×C₅×Q₈	—	2	1	no	—
75	C₄×C₅×Q₈	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	D₄	1	1	yes	characteristic
80	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₅×#117	—	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×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#107	—	2	2	no	—
89	C₅×#107	—	2	2	no	—
90	C₅×#106	—	2	2	no	—
91	C₅×#106	—	2	2	no	—
92	C₅×#106	—	2	1	no	—
93	C₅×#106	—	2	1	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	1	yes	characteristic
98	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂³	1	2	yes	—
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×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	—	2	2	no	—
109	C₅×#97	D₄	1	2	yes	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	#3165	C₂×C₅	1	1	yes	characteristic, complemented
113	#3101	C₂×C₅	1	1	yes	characteristic
114	C₂×#461	C₂×C₅	1	1	yes	characteristic
115	D₄×M₁₆	C₂×C₅	1	1	yes	characteristic
116	#1693	C₂×C₅	1	2	yes	complemented
117	#1691	C₂×C₅	1	2	yes	complemented
118	#1673	C₂×C₅	1	2	yes	complemented
119	#1671	C₂×C₅	1	2	yes	complemented
120	#1565	C₂×C₅	1	1	yes	characteristic, complemented
121	#1550	C₂×C₅	1	1	yes	characteristic, complemented
122	#1549	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂⁴×C₅	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	4	2	no	—
128	C₂×C₅×Q₈	—	4	2	no	—
129	C₂×C₅×Q₈	—	4	1	no	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	4	1	no	—
133	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	4	2	no	—
141	C₂²×C₄×C₅	—	4	2	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×SD₁₆	—	4	2	no	—
147	C₅×SD₁₆	—	4	4	no	—
148	C₅×SD₁₆	—	4	2	no	—
149	C₅×SD₁₆	—	4	4	no	—
150	C₅×M₁₆	—	2	2	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₅×M₁₆	—	4	4	no	—
153	C₅×M₁₆	SD₁₆	1	4	yes	complemented
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	4	2	no	—
159	C₂×C₅×C₈	—	4	4	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	2	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	—	4	1	no	—
170	C₅×C₄⋊C₄	—	4	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	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₅×C₂²⋊C₄	—	2	1	no	—
179	C₅×C₂²⋊C₄	—	4	1	no	—
180	C₄²×C₅	—	4	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	C₂²×SD₁₆	—	2	1	no	—
186	C₂²×M₁₆	—	2	1	no	—
187	#533	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
190	#501	—	2	2	no	—
191	#500	C₂²×C₅	1	2	yes	complemented
192	#498	C₂²×C₅	1	2	yes	complemented
193	#483	—	2	1	no	—
194	#476	C₂²×C₅	1	1	yes	characteristic
195	#476	C₂²×C₅	1	1	yes	characteristic
196	#461	—	2	1	no	—
197	#461	—	2	1	no	—
198	#461	C₂²×C₅	1	1	yes	characteristic
199	#461	C₂²×C₅	1	1	yes	characteristic
200	#461	C₂²×C₅	1	2	yes	—
201	#461	C₂²×C₅	1	2	yes	—
202	#450	—	2	1	no	—
203	C₄×SD₁₆	—	2	1	no	—
204	C₄×SD₁₆	—	2	1	no	—
205	#436	C₂²×C₅	1	2	yes	—
206	#435	—	2	2	no	—
207	C₈×D₄	C₂²×C₅	1	2	yes	—
208	#431	C₂²×C₅	1	1	yes	characteristic
209	#428	—	2	1	no	—
210	#428	—	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	#407	—	2	1	no	—
215	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
216	#335	C₂²×C₅	1	2	yes	complemented
217	#334	C₂²×C₅	1	2	yes	complemented
218	#333	C₂²×C₅	1	2	yes	complemented
219	#332	C₂²×C₅	1	2	yes	complemented
220	#332	C₂²×C₅	1	2	yes	complemented
221	#332	C₂²×C₅	1	2	yes	complemented
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	—	2	1	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	—	4	2	no	—
226	C₂³×C₅	—	8	1	no	—
227	C₂³×C₅	#121	1	1	yes	characteristic
228	C₅×Q₈	—	4	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×Q₈	—	4	1	no	—
231	C₅×Q₈	—	4	2	no	—
232	C₅×Q₈	—	8	1	no	—
233	C₅×Q₈	—	8	2	no	—
234	C₅×D₄	—	2	1	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	—	2	1	no	—
237	C₅×D₄	—	4	2	no	—
238	C₅×D₄	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
244	C₂×C₄×C₅	—	4	2	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	8	2	no	—
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	#121	1	1	yes	characteristic
257	C₂×C₄×C₅	#121	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
259	C₂×C₄×C₅	#137	1	2	yes	—
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	4	2	no	—
265	C₅×C₈	—	4	2	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	4	1	no	—
268	C₅×C₈	C₂×SD₁₆	1	4	yes	complemented
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
271	C₂³×C₄	—	2	1	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	1	no	—
275	C₂×SD₁₆	—	2	1	no	—
276	C₂×SD₁₆	—	4	4	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	4	4	no	—
280	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
281	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
289	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
290	#125	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	C₅×D₄	1	1	yes	characteristic
298	C₄×D₄	C₅×D₄	1	1	yes	characteristic
299	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
300	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	—	2	1	no	—
312	#106	—	2	1	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	C₂³×C₅	1	2	yes	—
316	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
318	C₄⋊C₈	C₂³×C₅	1	2	yes	—
319	#103	—	2	2	no	—
320	#103	—	2	2	no	—
321	#103	—	2	1	no	—
322	#103	—	2	1	no	—
323	#102	—	2	1	no	—
324	#102	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	#97	C₅×D₄	1	2	yes	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	C₂³×C₅	1	2	yes	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	8	4	no	—
340	C₂²×C₅	#461	1	2	yes	—
341	C₂²×C₅	C₂×#121	1	1	yes	characteristic
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	4	1	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	8	2	no	—
348	C₄×C₅	—	8	1	no	—
349	C₄×C₅	—	8	1	no	—
350	C₄×C₅	#461	1	2	yes	—
351	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
352	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₄×C₅	C₂×#137	1	1	yes	characteristic
354	C₄×C₅	#575	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₅×#41	1	1	yes	characteristic
378	SD₁₆	—	4	4	no	—
379	SD₁₆	—	4	2	no	—
380	SD₁₆	—	4	4	no	—
381	SD₁₆	—	4	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	4	2	no	—
384	M₁₆	—	4	4	no	—
385	M₁₆	C₅×SD₁₆	1	4	yes	complemented
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
393	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₄²	—	4	1	no	—
413	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
414	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
415	C₄²	C₅×#41	1	1	yes	characteristic
416	C₄²	C₂⁴×C₅	1	1	yes	characteristic
417	C₂×C₅	—	2	2	no	—
418	C₂×C₅	—	4	2	no	—
419	C₂×C₅	—	8	1	no	—
420	C₂×C₅	C₂×#461	1	1	yes	characteristic
421	C₂×C₅	#3055	1	1	yes	characteristic
422	C₂×C₅	#3069	1	1	yes	characteristic
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	8	1	no	—
428	C₂³	C₅×#121	1	1	yes	characteristic
429	Q₈	—	4	2	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	8	1	no	—
434	Q₈	—	8	2	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	2	1	no	—
438	D₄	—	4	2	no	—
439	D₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	C₅×#121	1	1	yes	characteristic
457	C₂×C₄	C₅×#121	1	1	yes	characteristic
458	C₂×C₄	C₅×#121	1	1	yes	characteristic
459	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
460	C₂×C₄	C₅×#137	1	2	yes	—
461	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
464	C₈	—	2	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	C₂×C₅×SD₁₆	1	4	yes	complemented
470	C₅	#19164	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	8	4	no	—
480	C₂²	C₅×#461	1	2	yes	—
481	C₂²	C₂×C₅×#121	1	1	yes	characteristic
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₄	C₅×#461	1	2	yes	—
491	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
492	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
493	C₄	C₂×C₅×#137	1	1	yes	characteristic
494	C₄	C₅×#575	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	C₂×C₅×#461	1	1	yes	characteristic
499	C₂	C₅×#3055	1	1	yes	characteristic
500	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	D₄
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
1. C₅×#3165	C₂	semidirect
5. C₅×#1693	C₂	semidirect
6. C₅×#1691	C₂	semidirect
7. C₅×#1673	C₂	semidirect
8. C₅×#1671	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₅×#1549	C₂	semidirect
18. C₅×#500	C₂²	semidirect
19. C₅×#498	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#332	C₂²	semidirect
49. #19164	C₅	direct (N × H)
112. #3165	C₂×C₅	semidirect
116. #1693	C₂×C₅	semidirect
117. #1691	C₂×C₅	semidirect
118. #1673	C₂×C₅	semidirect
119. #1671	C₂×C₅	semidirect
120. #1565	C₂×C₅	semidirect
121. #1550	C₂×C₅	semidirect
122. #1549	C₂×C₅	semidirect
153. C₅×M₁₆	SD₁₆	semidirect
191. #500	C₂²×C₅	semidirect
192. #498	C₂²×C₅	semidirect
216. #335	C₂²×C₅	semidirect
217. #334	C₂²×C₅	semidirect
218. #333	C₂²×C₅	semidirect
219. #332	C₂²×C₅	semidirect
220. #332	C₂²×C₅	semidirect
221. #332	C₂²×C₅	semidirect
268. C₅×C₈	C₂×SD₁₆	semidirect
385. M₁₆	C₅×SD₁₆	semidirect
469. C₈	C₂×C₅×SD₁₆	semidirect
470. C₅	#19164	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×#3165	2
C₅×#3101	2
C₂×C₅×#461	2
C₅×D₄×M₁₆	2
C₅×#1693	2
C₅×#1691	2
C₅×#1673	2
C₅×#1671	2
C₅×#1565	2
C₅×#1550	2
C₅×#1549	2
#19164	5

Subgroups — C5×#19164 #11941884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19164 #11941884